Propagation of axions in a strongly magnetized medium

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英语小作文介绍公牛的外形

The bull, a majestic creature that has long been a symbol of strength and resilience, is a sight to behold in its natural habitat. From its imposing stature to its distinctive features, the bulls physical appearance is nothing short of aweinspiring.First and foremost, the bulls size is truly impressive. Standing tall on sturdy legs, a mature bull can reach heights of up to six feet at the shoulder, with some breeds even exceeding this. Its muscular frame is a testament to its raw power, with welldefined muscles rippling under its thick, glossy coat of fur.The bulls head is perhaps its most striking feature. Its broad, squareshaped skull is adorned with a pair of large, expressive eyes that convey a sense of intelligence and alertness. The most prominent aspect of its head, however, is undoubtedly the formidable pair of horns that curve gracefully from its forehead. These horns, which can measure up to several feet in length, are not only a formidable weapon for defense but also a symbol of dominance and status within the herd.The bulls coat is another aspect of its appearance that deserves attention. Depending on the breed, the coat can range from a glossy black to a rich chestnut brown, with some bulls even sporting a unique white or piebald pattern. The coat is typically short and sleek, allowing the bull to move with agility and grace despite its size.One cannot overlook the bulls impressive set of hooves. These large, sturdy hooves are not only essential for supporting the bulls weight butalso serve as a means of communication with the ground. The bulls hooves are well adapted for various terrains, allowing it to navigate rocky hillsides and muddy fields with ease.The bulls tail is another distinctive feature, often described as a switch due to its whiplike appearance. This tail is not only used for balance but also serves as a means of communication with other members of the herd. A flick of the tail can signal a variety of emotions, from contentment to agitation.In terms of behavior, the bull is known for its calm and composed demeanor. Despite its imposing size and strength, the bull is generally peaceful and nonaggressive unless provoked. It is a social creature, often found in the company of other members of its herd, where it plays a crucial role in maintaining social order and protecting the group from potential threats.In conclusion, the bulls physical appearance is a testament to its strength, agility, and resilience. From its muscular frame and imposing horns to its glossy coat and sturdy hooves, the bull is a creature of remarkable beauty and power. Its calm demeanor and social nature further contribute to its status as a symbol of strength and resilience, making it a truly captivating sight to behold.。

A toroidal resolution for the bad reduction of some Shimura varieties

they can be performed over Z), Faltings ([F 1]) constructs a semi-stable resolution of the Siegel modular variety with level structures deﬁned by the Siegel parahoric. His methods also work for an analogous parahoric in the unitary case – in a recent preprint ([F 2]) which was a source of inspiration for the present work, Faltings resolves the unitary Shimura varieties whose deﬁning hermitian form has signature (2, n − 2) or (3, n − 3) and the Siegel modular variety of genus 3 – a semi-stable resolution of the Siegel modular variety of genus 3 with Iwahori levelstructures is also constructed in [G]. In the present work we prove the following one. THEOREM A. — Under the above assumptions for the groups G and Kp , SK (G, µ)Z(p) has a canonical log-smooth resolution. Remark: In fact the resolution SK (G, µ)Z(p) that we obtain satisﬁes a stronger condition (not appealing to logarithmic geometry: cf. 2.2.6) than log–smoothness over Z(p) . Using this stronger statement and ([KKMS], III. 4), one can see that SK (G, µ)Z(p) has a (non canonical) semi–stable resolution over an extension Z(p) [p1/ν ] of Z(p) . To prove theorem A, it will be suﬃcient to prove an analogous statement for the local model. Following Cha¨ ı, Norman, Rapoport and Zink ([CN], [R], [RZ]), SK (G, µ)Z(p) has a local model Mp ; this is a projective scheme over Z(p) such that for every point s in SK (G, µ)Z(p) , there exists a (non unique) point m in Mp such that s and m have isomorphic ´ etale neighbourhoods. This scheme is deﬁned in terms of linear algebra and so is easier to deal with than S (g, µ)Zp . The couple (G, µ) enters in its deﬁnition only through GQp (i.e. (GLn × Gm )Qp or Gsp2g,Qp ) and (in the unitary case) the signature (r, n − r ) of the hermitian form ; the parahoric Kp enters in its deﬁnition only through the partition of n or g deﬁning it (recall that in the symplectic case we assumed that Kp is contained in the Siegel parahoric). The local model Mp is endowed with an action of a certain aﬃne smooth Z(p) -groupscheme K associated to the combinatorial data deﬁning the parahoric Kp = K(Zp ) (see [dJ 2], [RZ]), and one has a diagram T © SK (G, µ)Z(p) d d Mp

齐墩果酸治疗APOE小鼠AS

Cardiovascular PharmacologyAntiatherogenic effects of oleanolic acid in apolipoprotein E knockout miceNiels Henrik Buus a ,b ,⁎,Nicolaj C.Hansson a ,Rosalia Rodriguez-Rodriguez a ,c ,Edgaras Stankevicius a ,Malene Rohr Andersen d ,Ulf Simonsen aaDepartment of Pharmacology,Institute of Biomedicine,Aarhus University,Aarhus,Denmark bDepartment of Renal Medicine,Aarhus University Hospital,Aarhus,Denmark cDepartment of Pharmacology,University of Sevilla,Spain dDepartment of Clinical Biochemistry,Copenhagen University Hospital,Gentofte,Denmarka b s t r a c ta r t i c l e i n f o Article history:Received 14June 2011Received in revised form 8September 2011Accepted 11September 2011Available online 21September 2011Keywords:AtherosclerosisApolipoprotein E knockout mouse Oleanolic acid Nitric oxideOleanolic acid (OA)is a plant triterpenoid steroid with potentially antiatherogenic properties.We investigated whether OA affected atherosclerosis development and vascular function in apolipoprotein E knockout (ApoE −/−)mice.ApoE −/−mice were fed a high cholesterol Western-type diet in combination with OA (100mg/kg/day),ﬂuvastatin (5mg/kg/day)or vehicle,with wild type (WT)mice serving as controls.After 8weeks of treatment atherosclerotic plaque areas in the aortic arch and plasma lipid concentrations were determined.Vasoconstriction and relaxation of the proximal part of aorta were investigated in vitro.Inducible nitric oxide synthase (iNOS)was visualized using immunoblotting.As opposed to WT and ﬂuvastatin-and vehicle-treated mice,OA-fed ApoE −/−mice gained no weight during the treatment period.Plasma concentrations of total-cholesterol and triglyceride were not signi ﬁcantly reduced by OA-or ﬂuvastatin treatment.Plaque area of vehicle-treated mice was 25%,but only 14%in OA-and 19%in ﬂuvastatin-treated mice.As compared to WT,vasoconstriction to phenylephrine was attenuated in ApoE −/−mice.The NOS inhibitor asymmetric dimethylarginine (ADMA)enhanced phenyleph-rine constriction,but signi ﬁcantly more so in vehicle-and ﬂuvastatin-treated than in OA-treated and WT mice.Relaxation to acetylcholine was only slightly attenuated in ApoE −/−mice and not affected by OA or ﬂuvastatin treatment.ADMA abolished acetylcholine relaxation almost completely.In ApoE −/−mice iNOS expression was reduced by OA treatment.In conclusion OA exerts potent antiatherogenic effects independent of plasma lipid levels and without major changes in eNOS-mediated acetylcholine relaxation.However,OA reduced iNOS expres-sion possibly altering vascular reactivity to phenylephrine.©2011Elsevier B.V.All rights reserved.1.IntroductionCardiovascular disease is a major contributor to morbidity and mortality and despite antihypertensive,antithrombotic and cholesterol lowering treatments,atherosclerosis remains prevalent and further in-terventions to delay disease progression are warranted.Both epidemio-logical and interventional studies have documented the consumption of a traditional Mediterranean diet,with olive oil as the principal source of fat,to be associated with a reduction of cardiovascular risk factors and incidence of coronary heart disease (de Lorgeril et al.,1994;Trichopoulou et al.,2003).These effects have mainly been ascribed to the high content of monounsaturated fatty acids combined with a low content of saturat-ed fatty acids in olive oil.Evidence suggests though,that the bene ﬁcial effects of olive oil cannot be fully explained by the favorable fatty acid composition (Perona et al.,2006).Hence,research has been performed to elucidate the cardiovascular effects of some minor constituents in olive oil,particularly phenols and tocopherols (El and Karakaya,2009).However,during the recent years also the triterpenoids,such as oleanolic acid (OA,Fig.1),have received increased attention.Triterpenoids are ubiquitous in the plant kingdom and possess a wide range of biological effects.Hepatoprotective and antitumoral activ-ities of OA have long been recognized (Liu,1995),but also evidence of potentially antiatherogenic effects is now emerging.Chronic adminis-tration of OA to Dahl salt-sensitive rats,demonstrated antihyperlipi-demic,antioxidant and antihypertensive effects (Somova et al.,2003a ).Furthermore,in vitro studies on isolated rat aortic segments showed en-dothelium-dependent,nitric oxide (NO)-mediated vasorelaxing proper-ties of OA,presumably due to enhanced phosphorylation of endothelial NO synthase (eNOS)(Rodriguez-Rodriguez et al.,2008).Cholesterol-lowering statins are traditionally considered to exert their effects through inhibition of cholesterol synthesis,but they may also enhance the bioavailability of NO through increased eNOS expression or antioxi-dant effects (Mason et al.,2004).Thus,the pleiotropic actions of statins correspond to some of the expected mechanisms,by which OA may also exert its antiatherogenic effects.The homozygous apolipoprotein E-de ﬁcient (ApoE −/−)mouse is a widely used animal model of atherosclerosis,due to the spontaneous de-velopment of severe hypercholesterolemia and atherosclerotic lesions,European Journal of Pharmacology 670(2011)519–526⁎Corresponding author at:Department of Renal Medicine,Aarhus University Hospital,Brendstrupgaardsvej,8200Aarhus N,Denmark.Tel.:+4589495566.E-mail address:nhbuus@dadlnet.dk (N.H.Buus).0014-2999/$–see front matter ©2011Elsevier B.V.All rights reserved.doi:10.1016/j.ejphar.2011.09.037Contents lists available at SciVerse ScienceDirectEuropean Journal of Pharmacologyj o u r n a l h o m e pa ge :w ww.e l s e v i e r.c o m/l o c a t e /e j p h a rwhich mimics many pathological features of the humane plaque (Zhang et al.,1992).In this model the minor constituents of olive oil,as for example triterpenoids,seem to have an antiatherosclerotic potential (Acín et al.,2007).However,the effect of isolated OA on de-velopment of atherosclerosis in ApoE −/−mice remains to be tested.In the present study,we therefore investigated whether long-term administration of OA affects the development of atherosclerotic lesions and vascular function in ApoE −/−mice.To obtain a reference to the OA treatment,the effect of ﬂuvastatin treatment was also investigated.2.Material and methods2.1.Mouse model of atherosclerosis and treatment protocolTen male C57BL/6wild type (WT)and 30male 12-week old ho-mozygous ApoE −/−mice on a C57BL/6background were obtained from Taconic (Ry,Denmark).The ApoE −/−mice were randomized into 3groups:1)treatment with OA orally (100mg/kg/day),2)treat-ment with ﬂuvastatin (5mg/kg/day)or 3)treatment with vehicle (dimethyl sulphoxide (DMSO)).The WT mice were also treated with vehicle orally.For 8weeks all mice were fed a Western type-diet containing 21%fat and 0.21%cholesterol (D12079B,Research Diets,News Brunswick,USA)to accelerate the spontaneous develop-ment of atherosclerotic lesions.The mice were housed two per cage in an air-conditioned room with a 12:12h light:dark cycle.The mixture of food and OA or ﬂuvas-tatin was freshly made every second day.One mg of OA or ﬂuvastatin was dissolved in DMSO (20μl)and bidistilled water (60μl).This solu-tion was then easily mixed with food which was manufactured as a powder.Vehicle-treated animals had the same amount of DMSO and bidistilled water added to the food.The consumption of food per cage was calculated by weighing and changing residual food every second day,while tap water was provided ad libitum.All experiments were performed with approval from the Danish Institutional Animal Care and Use Committee.2.2.Recovery of blood and tissue samplesAt age 20weeks the mice were anesthetized with iso ﬂurane (3–5%)following 12–14h of overnight fasting.Blood samples were obtained through cardiac puncture and immediately thereafter the mice were killed by cervical dislocation.Then the blood samples were centrifuged and plasma samples were stored at −70°C until further analysis.The aorta was carefully removed and dissected free from connective tissue in a Petri dish ﬁlled with a cold physiological salt solution (PSS).2.3.Analysis of atherosclerotic lesion areaThe aortic arch and descending aorta were thoroughly cleaned of adventitial fat and cut open longitudinally.To obtain a ﬂat prepara-tion the segments were pinned down in the Petri dish.For detection of atherosclerotic lesions,the segments were stained with Oil Red O solution for 60min and subsequently rinsed with isopropanol anddistilled water.For quanti ﬁcation of lesion area images of the stained preparation were taken through a dissection microscope with a stan-dard digital camera.The images were manually analyzed in a blinded manner using Image Pro (Media Cybernetics,Silver Spring,MD,USA)and the results were expressed as percentage of the total surface area covered by Oil Red O staining.2.4.Plasma lipid analysesPlasma total cholesterol and triglyceride levels were quanti ﬁed by enzymatic colorimetric assays (Roche Diagnostics,Hvidovre,Denmark)using the COBAS Integra 400analyzer.2.5.In vitro experiments of endothelium-mediated relaxationFrom each mouse one segment (approximately 2mm long)of the most proximal part of the descending aorta was mounted in an isomet-ric wire myograph (Danish Myotechnology,Aarhus,Denmark)for as-sessment of vasoreactivity.Two segments from randomlyselectedFig.1.Chemical structure of oleanolic acid(OA).Fig.2.(A)Body weights and (B)food consumption during the 8week treatment period.Body weights were signi ﬁcantly lower in ApoE −/−-oleanolic acid (OA)mice during weeks 2–8compared to the 3other groups (P b 0.05),while food consumption was signif-icantly lower in ApoE −/−-OA mice during weeks 6–8(P b 0.05).*P b 0.05ApoE −/−-OA vs.ApoE −/−-Vehicle,ApoE −/−-Fluvastatin or WT.n=7–10in each group.Table 1Plasma concentrations of total cholesterol and triglycerides in wild type (WT)and apo-lipoprotein E knockout (ApoE −/−)mice after 8weeks of treatment with oleanolic acid (OA),ﬂuvastatin or vehicle.WTApoE −/−OA ApoE −/−ﬂuvastatin ApoE −/−vehicle Total cholesterol (mM) 4.3±0.431.8±2.0a 27.4±3.0a 32.9±1.9a Triglycerides (mM)1.5±0.21.2±0.21.5±0.21.5±0.2Values are expressed as mean±S.E.M.n=7–10in each group.aP b 0.01vs.WT.520N.H.Buus et al./European Journal of Pharmacology 670(2011)519–526mice were studied in parallel.In brief the vessel segments were mounted on two 100μm thin steel wires for recordings of tension as previously described for other types of arteries (Simonsen et al.,1992).After an equilibration period of 30min,vessel diameter was adjusted to that resulting in the maximal active tension development.To check vessel vi-ability a standard start involving stimulation with PSS containing 60mM of potassium chloride (KPSS)and 1μM phenylephrine was performed.Only segments with a tension development of 1.5N/m were accepted for further studies.A cumulative concentration –response curve for phenylephrine was then obtained and the concentration resulting in a response of 60–70%of the maximal contraction was used for preconstriction of the vessel segment during the subsequent relaxation experiments.First a cumula-tive concentration –response curve for acetylcholine was performed.After thorough wash-out the vessel was incubated with the NO synthase inhibitor N G ,N G -dimethyl-L -arginine (ADMA 300μM)and after 30min the concentration –response curve for acetylcholine was repeated.Finally,a cumulative concentration –response curve for the NO donor S-nitroso-N-acetylpenicillamine (SNAP)was constructed.Acute effects of OA on vascular tone were tested in isolated aorta segments constricted with phenylephrine (1μM).2.6.ImmunostainingTo study the localization of inducible NOS (iNOS),glucose-related protein 78(GRP78),and 3-nitrotyrosine thoracic aorta segments were ﬁxed with cold (4°C)4%paraformaldehyde,pH 7.0,for 1h,and embed-ded in paraf ﬁn.Longitudinal sections 5μm thick were obtained and pro-cessed following the avidin –biotin –peroxidase method as previously described (Hernanz et al.,2004).Thus,the sections were incubated overnight with rabbit polyclonal anti-iNOS (1:1000,Transduction Laboratories,Lexington,UK),anti-GRP78(1:400,ABR Bioreagents,AH Diagnostic,Copenhagen,Denmark),or rabbit polyclonal antibody anti-3-nitrotyrosine (1:400)diluted in 1%bovine serum albumin.Then,the sections were reacted with a biotinylated antirabbit immuno-globulins followed by incubation with streptavidin which was conju-gated to horseradish peroxidase (LSAB 2kit for rat tissue,DAKO,Denmark),and the immunocomplex was visualized as a brown prod-uct after incubating with 0.05%3,3-diamino-benzidine and 0.0225%H 2O 2.Controls were obtained using arterial sections incubated with-out the corresponding primary antibody.2.7.ImmunoblottingFrom each animal one proximal abdominal segment was quick-frozen in liquid nitrogen and kept at −70°C until protein expression analysis.Western blots for iNOS and GRP78were performed as previ-ously described (Hernanz et al.,2004;Østergaard et al.,2009).Immu-noblotting for 3-nitrotyrosine was also intended,but required to large amounts of proteins.Panactin was used as a comparative control and did not change in the aorta samples from wild type versus vehicle,oleanolic acid,and ﬂuvastatin-treated ApoE −/−mice.2.8.Drugs and solutionsThe PSS used was of the following composition (mM):NaCl 119,KCl 4.7,KH 2PO 41.18,MgSO 41.17,NaHCO 325,CaCl 22.5,ethylen diamine tetraacetate (EDTA)0.027and glucose 5.5.KPSS was similar to PSS except that NaCl was substituted for KCl to yield a potassium concentra-tion of 60mM.Phenylephrine,acetylcholine,SNAP,ADMA,Red Oil O,and DMSO were purchased from Sigma-Aldrich (Brøndby,Denmark).OA was obtained from Extrasynthese (Genay,France),while ﬂuvastatin was obtained from the pharmacy at Aarhus University Hospital.Stock solutions of SNAP,OA,and ﬂuvastatin were prepared using DMSO as a solvent and further dilution was made in bidistilled water.Oil Red O was dissolved in 60%isopropanol and subsequently dextrin was added to reduce precipitation.All other drugs were diluted in bidistilled water.2.9.Calculations and statistical analysisAll results are expressed as means±S.E.M.,where n equals the num-ber of animals per group.The concentration –response curves and the data concerning changes in body weight and food consumptionduringFig.3.(A)Representative examples of atherosclerotic lesion formation in the ascending thoracic aorta,as evaluated by en face Oil Red O staining from WT mice,ApoE −/−-Vehicle,ApoE −/−-oleanolic acid (OA),and ApoE −/−-Fluvastatin-treated mice.Mean values of atherosclerotic lesion formation in the aortic arch (B)and descending thoracic aorta (C).*P b 0.05for ApoE −/−-Fluvastatin vs.ApoE −/−-Vehicle,**P b 0.01for ApoE −/−-OA vs.ApoE −/−-Vehicle,***P b 0.001for ApoE −/−-Vehicle vs.ApoE −/−-OA.n =7–10in each group.521N.H.Buus et al./European Journal of Pharmacology 670(2011)519–526the treatment period were compared by two-way ANOVA followed by Bonferroni post-test.Data on atherosclerotic lesion formation,plasma lipids and ratio between tension development to phenylephrine with and without ADMA were statistically evaluated by one-way ANOVA fol-lowed by Bonferroni post-test.A P -value of 0.05was considered statis-tically signi ﬁcant.All statistical calculations were performed using Graph Pad Prism (version 4.00,Graph Pad Software Inc.,San Diego,CA,USA).3.Results3.1.Body weight and food consumptionDuring the 8-week treatment period ApoE −/−-OA mice had con-stant food consumption and kept a stable body weight of about 30g,while ApoE −/−-Vehicle,ApoE −/−-Fluvastatin,and WT mice had signif-icantly increased daily food intake and increased body weight to about 40g (Fig.2A and B).3.2.Plasma lipidsApoE −/−mice had pronouncedly elevated plasma levels of choles-terol,which remained unaffected by OA and was only slightly reducedby ﬂuvastatin (Table 1).The levels of plasma triglyceride were similar in all 4groups of mice (Table 1).3.3.Atherosclerotic lesion areaAs expected WT mice expressed no signs of atherosclerotic lesions in neither the aortic arch nor in the descending aorta.In contrast ApoE −/−-Vehicle mice developed extensive lesions in the aortic arch,whereas formation in the descending aorta was less pronounced (Fig.3A).Atherosclerotic lesion formation in the aortic arch was sig-ni ﬁcantly reduced in OA-and ﬂuvastatin treated ApoE −/−mice (Fig.3B),but only signi ﬁcantly decreased in the thoracic aorta in the OA treated group (Fig.3C).3.4.Phenylephrine contractionThe contractile response to increased concentrations of phenyl-ephrine was signi ﬁcantly higher in aorta segments from WT and ApoE −/−-OA mice as compared to segments from ApoE −/−-Vehicle and ApoE −/−-Fluvastatin mice (Fig.4A).The phenylephrine dose resulting in 60–70%of the maximal contraction to the initialstimulationFig.4.The contractile responses of aortic segments to phenylephrine (PE)(A)and the ratio between the responses obtained to the PE concentration inducing 60–70%of maximal con-traction after and before incubation with asymmetric dimethylarginine (ADMA;0.3mM)(B).The contractile responses to PE were increased in WT and ApoE −/−-oleanolic acid (OA)mice as compared to ApoE −/−-Vehicle and ApoE −/−-Fluvastatin (*P b 0.05).**P b 0.01for ApoE −/−-OA vs.ApoE −/−-Vehicle.n=6–8in eachgroup.Fig.5.Average relaxations of aortic segments to acetylcholine (ACh)before (A)and after (B)incubation with asymmetric dimethylarginine (ADMA).ACh-induced vasore-laxation was signi ﬁcantly impaired in the three groups of ApoE −/−mice compared to WT mice (P b 0.05).Incubation with ADMA had similar effects in all groups,and nearly blocked the response to ACh.n =6–8in each group.522N.H.Buus et al./European Journal of Pharmacology 670(2011)519–526with KPSS and phenylephrine (10μM)was between 0.3and 3μM.After incubation with ADMA the same concentration of phenylephrine resulted in a signi ﬁcantly enhanced contractile response in all groups.The ampli ﬁcation of this response was however signi ﬁcantly smaller in OA-treated and WT mice as compared to ﬂuvastatin-and vehicle-treated ApoE −/−mice (Fig.4B).3.5.Responses to acetylcholine and SNAPIn phenylephrine-contracted aorta segments,acetylcholine induced concentration-dependent pared to WT all the ApoE −/−groups displayed a small,but signi ﬁcant,reduction in acetylcholine relax-ation (Fig.5A).After incubation with ADMA acetylcholine relaxation was nearly abolished in all 4groups of mice (Fig.5B).In contrast,there were no effects of OA on vascular tone in phenylephrine-constricted aorta seg-ments from ApoE −/−mice (Fig.6).However,the same solution of OA did induce relaxation in phenylephrine-constricted small mesenteric arteries from Wistar rats as previously described (Rodriguez-Rodriguez et al.,2008).Relaxation to SNAP was slightly more pronounced in OA-and ﬂuvastatin-treated mice,although at the highest concentration of SNAP no difference could be detected between any of the groups (Fig.7).3.6.Immunostaining and immunoblottingRepresentative examples of immunostaining with iNOS,GRP78and 3-nitrotyrosine are shown in Fig.8.iNOS was mainly expressed in the media of aorta (Fig.8A-D),and immunoblotting revealed a slightly,but not signi ﬁcantly,increased expression of iNOS in vehicle-treated ApoE −/−mice,whereas OA treatment reduced iNOS expression with no effect of ﬂuvastatin (Fig.9A).GRP78was expressed in all three layers of aorta (Fig.8E –H),but there were no differences in the expression of GRP78between any of the groups (Fig.9B).Immunoreaction to 3-nitrotyrosine was found in media and adventitia of ApoE −/−mice (Fig.8I-L),and scoring of the immunostainings con ﬁrmed that 3-nitrotyrosine was markedly upregulated in aortas from ApoE −/−mice treated with vehicle or ﬂuvastatin,whereas this was not the case in aortas from OA-treated animals (Fig.10).4.DiscussionThe main ﬁnding of the present study is that oral treatment with OA effectively reduces atherosclerosis development in the aortic arch and descending aorta of ApoE −/−mice.The mechanism behind this is ap-parently independent of plasma total cholesterol and triglyceride levels but seems associated with alterations in vascular contractile reactivity without directly in ﬂuencing eNOS-dependent acetylcholine-induced relaxation.Instead OA seems to reduce iNOS activity.4.1.Effects of OA on body weightApoE −/−mice fed a diet mixed with OA,had considerably lower food consumption and body weights after 2weeks of treatment.A possible explanation could be that OA has a repellent taste or smell to mice,although we did not discover such effects in an initial pilot study.Potential toxic effects of OA have to be considered,especially given the fact that this compound appear to exert a variety of biolog-ical effects.Data on toxicity of isolated OA in vivo is sparse,but the acute toxicity of OA is not likely to have any implication in this study,as the oral LD50value in mice has been reported to be greater than 2g/kg (Singh et al.,1992).The chronic toxicity of OA in mice has not yet been studied,but in rats treated daily with 60mg/kg i.p.for 6weeks,there were no reports of adverse effects on animal health (Somova et al.,2003b ).Interestingly,a recent study suggests that the effect of OA on body weight in mice could be related to improved glucose tolerance and reduced visceral fat deposition (de Melo et al.,2010).4.2.Antiatherogenic effects of OAThis is the ﬁrst report on OA treatment in atherosclerotic mice and our results demonstrate a pronounced effect on atherosclerosis de-velopment in aorta.The effect is completely independent on total cholesterol levels which remained very high despite OA treatment.Previous studies of OA treatment have mainly been carried out in rats (Somova et al.,2003a;Rodriguez-Rodriguez et al.,2007;Rodriguez-Rodriguez et al.,2009).However,despite feeding rats a high-fat diet there is only minimal development of atherosclerosis andinsteadFig.6.Representative relaxations in thoracic aortic segments constricted with phenyl-ephrine (PE)followed by addition of increasing concentrations of (A)acetylcholine (ACh)or (B)oleanolic acid (OA).In contrast to ACh,OA did not induce signi ﬁcant re-laxations.The traces are representative of 6experiments.Fig.7.Relaxation of aortic segments to S-nitroso-N-acetylpenicillamine (SNAP).ApoE −/−-oleanolic acid (OA)and ApoE −/−-Fluvastatin mice had a slightly increased relaxation to SNAP compared with ApoE −/−-Vehicle and WT mice (P b 0.05).The relaxations of ApoE −/−-OA mice were signi ﬁcantly enhanced compared to ApoE −/−-Fluvastatin mice (P b 0.05).n=6–8in each group.523N.H.Buus et al./European Journal of Pharmacology 670(2011)519–526focus have been on the antioxidant properties of olive oil and its various components (Fitóet al.,2007).The aortic wall of female ApoE −/−mice has a high level of activation of enzyme systems involved in the production of reactive oxygen spe-cies thought to contribute to plaque formation (Husain et al.,2010).Feeding of ApoE −/−mice with olive oil enriched in minor components,including triterpenoids,decreased induced lipid peroxidation and 8-isoprostaglandin F 2αplasma levels with less formation of atherosclerot-ic lesions (Acín et al.,2007;Rosenblat et al.,2008).In the present study expression of GRP78,which is a chaperone and can protect against cel-lular oxidative stress in the endoplasmic reticulum (Xu et al.,2004),was measured and found unaltered.However,another indicator of oxidative stress and peroxynitrite formation (Chew et al.,2009),3-nitrotyrosine,was markedly upregulated in aorta from ApoE −/−mice compared to aorta from control mice and as opposed to treatment with vehicle or ﬂuvastatin OA reduced immunoreaction to 3-nitrotyrosine to the level of WT mice.The precise antiatherogenic effects of OA are still unknown and sev-eral mechanisms can be of importance.Thus OA may protect against low density lipoprotein oxidation (Andrikopoulos et al.,2002)or re-duce pro-in ﬂammatory cytokine production (Marquez-Martin et al.,2006).Whether OA affects macrophage and foam cell apoptosis is not known,but a structural analog to OA,betulinic acid,is a potent antipro-liferative and proapoptotic agent (Yun et al.,2003).Another potential mechanism that may delay development of atherosclerosis could be a reduction in blood pressure level.ApoE knockout mice often develop a minor increase in blood pressure as compared to their WT controls (Husain et al.,2010).The effect of OA on blood pressure in ApoE knock-out mice has not been investigated,but in the Dahl salt-sensitive rat model of hypertension long term OA treatment to some extent prevents the increase in blood pressure (Somova et al.,2003b )while oral admin-istration to spontaneously hypertensive rats did not change blood pres-sure (Rodriguez-Rodriguez et al.,2007).Although we cannot exclude a potential effect of OA on blood pressure that may contribute to the ben-e ﬁcial effects on atherosclerosis,it seems an unlikely explanation.We found ﬂuvastatin to have an antiatherogenic effect despite almost unchanged levels of plasma lipids supporting the concept of “pleiotro-pic ”effects of statins (Davignon,2004)and the ﬁndings of other studies investigating the effect of statins in ApoE −/−mice (Johnson et al.,2005;Sparrow et al.,2001).It is notably though,that ﬂuvastatin in one study had no effect on atherosclerosis even though it decreased plasma choles-terol (Gervais et al.,2003).The discrepancy between this study and our ﬁnding may relate to the 10-fold smaller dose and shorter duration of treatment used in ourstudy.Fig.8.Immunostaining for (A –D)inducible nitric oxide synthase (iNOS);(E –H)glucose-related protein (GRP78);and (I –L)3-nitrotyrosine in thoracic aortic segments from vehicle-treated wild type (WT)mice,ApoE −/−mice which were treated with either vehicle,oleanolic acid (OA),or ﬂuvastatin.The brown precipitations indicate a positive immunoreac-tion.Immunoreaction for 3-nitrotyrosine was markedly increased in all ApoE −/−mice compared to WT with no differences between the different treatments of ApoE −/−mice.The pictures are representative for 8–10mice in each group.524N.H.Buus et al./European Journal of Pharmacology 670(2011)519–5264.3.Vascular function and OAThe effects of hypercholesterolemia and atherosclerosis on vascular contractile function are controversial,as both decreased and increased contractions have been reported.This difference may depend on the contracting agent used (Ibengwe and Suzuki,1986).We demonstrated a signi ﬁcantly decreased response to phenylephrine in aortic segments from ApoE −/−mice as compared to WT mice,a ﬁnding which has not previously been reported in this animal model.Moreover,inhibition of NO synthesis by ADMA had greater impact on phenylephrine-induced contractions in arteries from vehicle-treated ApoE −/−mice,indicating that the decreased contractility in atherosclerotic vessels might be due to a higher basal release of NO.However,as acetylcho-line-induced relaxation was only minimally changed in aorta from ApoE −/−mice,the results suggest alterations in non-eNOS derived NO production.This observation is supported by ﬁndings of induction of a non-eNOS NO synthase in atherosclerotic aortic segments from rab-bits (Verbeuren et al.,1993).Although not evident in the present study,upregulation of iNOS has previously been detected in atherosclerotic vessels of ApoE −/−mice (Detmers et al.,2000;Wilcox et al.,1997;Husain et al.,2010)and,could be partly responsible for the increased NO synthesis.OA treatment normalized both the contractile response to phenylephrine and the effect of ADMA on contractility,to the level of WT mice,suggesting that OA has an inhibitory effect on iNOS.In mu-rine macrophages treated with lipopolysaccharide to induce iNOS ex-pression,OA has in fact been shown to suppress NO release (Ha et al.,2006).Furthermore,OA can inhibit production of tumor necrosis fac-tor-αand interleukin-1βin murine macrophages,thus providing a pos-sible mechanistic linkage to iNOS inhibition (Ha et al.,2006).It can be speculated whether iNOS has a causative role in the path-ophysiology of atherosclerosis.This issue has been elucidated through the investigation of iNOS and ApoE double knockout mice.These mice,when fed a Western-type diet,were found to develop signi ﬁcantly less atherosclerosis compared to ApoE −/−control mice,and this impact of iNOS knockout was shown to be more pronounced in older animals with severe lesions (Detmers et al.,2000;Kuhlencordt et al.,2001).As these data indicate an important role of iNOS in atherosclerosis,the potential iNOS-suppressing effect of OA could account for the anti-atherogenic properties of this compound observed in the present study.In aortae from ﬂuvastatin-treated ApoE −/−mice,the response to phenylephrine,both with and without ADMA present,was not altered compared to aortae from vehicle-treated ApoE −/−mice,indi-cating that the mechanism behind the antiatherogenic effect of ﬂuvas-tatin was different from that of OA.4.4.Effects of OA on endothelial functionOne of the hallmarks of atherosclerosis is an impaired endothelial function,due to a decreased bioavailability of NO.Indeed,in ApoE −/−mice,impaired endothelium-dependent vasorelaxations in response to acetylcholine has been observed in segments of the atherosclerosis-prone,proximal descending aorta (Crauwels et al.,2003;d'Uscio et al.,2001).In the present study though,the endothelial dysfunction in the proximal aorta of ApoE −/−mice was not especially pronounced com-pared to the aforementioned studies.These discrepancies are likely to be due to the shorter period of Western diet feeding and the younger age of our mice.As opposed to previous observations obtained in rat aorta and resis-tance arteries (Rodriguez-Rodriguez et al.,2004;Rodriguez-Rodriguez et al.,2008),OA did not relax the isolated mouse aorta.In rat vessels this effect of OA involves phosphorylation and activation of eNOS (Rodriguez-Rodriguez et al.,2008).In the present study we did not per-form measurements of eNOS and thus cannot rule out an effect of OA on this enzyme.However,we could not demonstrate any functional conse-quence of such an effect.Moreover,in ApoE −/−mice the abundance of iNOS seems far to outweigh the amount of eNOS (Husain et al.,2010)rendering the iNOS a much more important contributor to the basal NO level in this animal model.Taken together our results suggest that OA treatment has no major effect on eNOS-responsible vasorelaxation but instead attenuates iNOS induction in the ApoE −/−model of atherosclerosis.In conclusion,our study demonstrates for the ﬁrst time that OA has bene ﬁcial effects,exceeding those of ﬂuvastatin,on development of atherosclerosis in ApoE −/−mice.The mechanism by which OA exerts its antiatherogenic effects is lipid-independent,and may be mediated by an inhibition of iNOS,rather than effects on the bioavailabilityofFig.9.(A)Expression of inducible nitric oxide synthase (iNOS)and (B)and glucose-regulated protein (GRP78)in aorta from wild-type mice (WT),and ApoE −/−mice treated with vehicle,oleanolic acid (OA),or ﬂuvastatin.n=5–6mice in each group.*P b 0.05OA-treated vs.vehicle-treated ApoE −/−mice.Fig.10.Immunoreaction scoring of 3-nitrotyrosine in wild type mice (WT)and ApoE −/−mice treated with vehicle,oleanolic acid (OA),or ﬂuvastatin.n =5–6mice in each group.*P b 0.05as compared to WT.525N.H.Buus et al./European Journal of Pharmacology 670(2011)519–526。

我要看关于僵尸的作文英语

Zombies,a popular figure in horror fiction,have captivated audiences with their relentless pursuit of human flesh.They are often depicted as reanimated corpses,devoid of consciousness and driven by a primal hunger for brains.Heres a detailed essay on the topic of zombies,exploring their origins,cultural significance,and impact on society. Title:The Undead Phenomenon:A Journey Through the World of ZombiesIntroductionThe concept of the undead has been a part of human mythology for centuries,but the modern zombie as we know it today has its roots in Haitian folklore and has evolved significantly through literature,film,and television.This essay delves into the fascinating world of zombies,examining their origins,the reasons behind their popularity,and the societal implications of their portrayal.Origins and FolkloreZombies trace their origins back to West African spiritual beliefs,which were then brought to Haiti through the slave trade.In Haitian Vodou,a zombie is a corpse reanimated by a sorcerer,often as a form of punishment or for labor.This early depiction was quite different from the aggressive,flesheating creatures we see today. Evolution in Popular CultureThe modern zombie archetype was popularized by George A.Romero in his1968film Night of the Living Dead.Romeros zombies were not the result of voodoo,but of a space probe returning from Venus,carrying a radiation that reanimated the dead.This film introduced the concept of zombies as mindless,cannibalistic creatures that could only be stopped by destroying their brains.Cultural SignificanceZombies have become a staple of horror and science fiction,reflecting societal fears and anxieties.They symbolize the loss of individuality and the fear of being consumed by the masses.The zombie apocalypse narrative often serves as a commentary on consumerism, overpopulation,and the fragility of human civilization.Impact on SocietyThe popularity of zombies has led to a cultural phenomenon,with zombie walks and zombie runs becoming popular events.These gatherings,where participants dress as zombies and walk through public spaces,have become a form of social commentary and community bonding.Media RepresentationIn literature,film,and television,zombies have been used to explore a variety of themes. From the classic survival horror of28Days Later to the satirical social commentary of Shaun of the Dead,zombies have been employed to tell stories that resonate with audiences on multiple levels.The Zombie ApocalypseThe concept of a zombie apocalypse has become a popular subgenre within horror.It often serves as a metaphor for realworld disasters,prompting discussions about preparedness,survival strategies,and the human capacity for resilience in the face of overwhelming odds.ConclusionZombies,as both a cultural phenomenon and a narrative device,have left an indelible mark on our collective imagination.They continue to evolve,reflecting and amplifying our deepest fears and societal concerns.As we explore the world of the undead,we are also examining the complexities of the human condition and our place in the world.This essay provides a comprehensive look at the zombie mythos,from its historical roots to its current status as a cultural icon.It highlights the versatility of the zombie as a narrative tool and its ability to engage audiences on a variety of levels,from pure entertainment to thoughtprovoking social commentary.。

Remarks on 1-motivic sheaves

a r X i v :0801.3153v1[mat h.A G]21J a n28REMARKS ON 1-MOTIVIC SHEA VES A.BERTAPELLE Abstract.We generalize the construction of the category of 1-motives with torsion t M 1in [4]as well as the construction of the category of 1-motivic sheaves Shv 1in [3]to perfect ﬁelds (without inverting the exponential charac-teristic).We extend a result in [3]showing that t M 1and Shv 1have equivalent bounded derived categories.Over a ﬁeld of characteristic zero,the previous constructions work also for Laumon 1-motives,i.e.,allowing additive factors and formal k -groups. 1.Introduction Let k be a ﬁeld of characteristic 0.In [3]the authors introduce the category of 1-motivic sheaves Shv 1and show that D b (Shv 1)and the bounded derived category of 1-motives with torsion D b (t M 1)are both equivalent to the thick subcategory of Voevodsky’s triangulated category of motives DM eﬀgm (k )generated by motives of smooth curves.When k is a perfect ﬁeld of positive characteristic p ,the classical deﬁnition of t M 1in [4]doesn’t work well,for example it does not provide an abelian category.One possibility is then to invert p as done in [3]getting a Z [1/p ]-linear abelian category of 1-motives with torsion.Also the deﬁnition of 1-motivic sheaves can be extended to the characteristic p context paying attention to invert p -multiplications and a comparison result for bounded derived categories that generalizes the one above still holds (cf.[3],3.9).As the authors explain,if one is interested in comparison results with Voevodsky’s category DM,one can not avoid to invert the exponential characteristic.In the following sections,we show that an integral deﬁnition of t M 1is possible over any perfect ﬁeld,i.e.,without inverting the exponential characteristic,if we allow ﬁnite connected k -group schemes in the component of degree −1of1-motives.We get then an abelian category t M ﬂ1that contains the category ofDeligne’s 1-motives as a full exact subcategory.Also the deﬁnition of 1-motivic sheaves works “integrally”over any perfect ﬁeld passing to the fppf topology.Both constructions are equivalent to the ones in [3]over a ﬁeld of characteristic 0.Furthermore we show that D b (Shv fppf 1)and D b (t Mﬂ1)are equivalent,i.e.,weget an integral version of [3],3.9.2,without passing through Voevodsky’s category DM.When working over a ﬁeld k of characteristic 0,it is natural to ask if the previ-ous deﬁnitions and proofs extend to Laumon 1-motives ,i.e.,to those 1-motives with additive factors in degree 0and formal k -groups in degree −1(cf.[11]).The abelian category of (generalized)1-motives with torsion t M a 1that extends12 A.BERTAPELLEthe category of Laumon’s1-motives has already been introduced in[2].The aim there,was to produce a new one-dimensional“sharp de Rham cohomology”of algebraic varieties following the construction of classical one-dimensional de Rham cohomology in[8].In this paper we deﬁne the category of generalized1-motivic sheaves Shv a1;this category contains Shv fppf1as an abelian subcategorybut also new objects such as the quotient of a smooth commutative k-group G by its formal completion at the originˆG(cf.3.2.3).We show then that D b(t M a1) is equivalent to D b(Shv a1).We hope that1-motivic sheaves can help to develop a theory of generalized1-motives overﬁelds of positive characteristic.2.The derived category of1-motivesNotations:Let k be any perfectﬁeld.We say that a k-group scheme is discrete if it isﬁnitely generated locally constant for the´e tale topology(cf.[3],1.1.1). Let CE be the category of commutative k-group schemes extension of a discrete group scheme by aﬁnite commutative connected group scheme.(Recall that such connected group schemes areﬂat and that the extension is automatically split.) Denote by M1the category of Deligne1-motives.2.1.The category of1-motives with torsion.2.1.1.Deﬁnition.An eﬀective1-motive with torsion is a complex M=[u:L→G]of k-group schemes where:L is an object in CE and G is semi-abelian.An eﬀective morphism M→M′is a map of complexes(f,g),with f:L→L′, g:G→G′morphisms of group schemes.M is said to be´e tale if L is´e tale.Denote by t M eﬀ,ﬂ1the category of eﬀective1-motives and by t M eﬀ,´e t1the fullsubcategory of´e tale ones.The category M1of Deligne’s1-motives is the full subcategory of t M eﬀ,´e t1consisting of those M with L torsion-free.2.1.2.Deﬁnition.LetΣbe the class of quasi-isomorphisms of eﬀective1-motives with torsion,i.e.,the class of eﬀective maps(f,g):M→M′where g is an isogeny,f is faithfullyﬂat and Ker(f)=Ker(g)is aﬁnite group scheme.Deﬁnethen the category of1-motives with torsion t Mﬂ1as the localization of t M eﬀ,ﬂ1atΣ.Similarly we get the category of´e tale1-motives with torsion t M´e t1.The category t M´e t1wasﬁrstly introduced in[4](for k of characteristic0and denoted as M1)and then in[3](over any perfectﬁeld and denoted as t M1).It was proved to be equivalent to the category of Mixed Hodge Structures of level ≤1for k=C(cf.[4],1.5).For k of characteristic0,one has thatt M1=t M´e t1=t Mﬂ1is an abelian category(cf.[4],[3]).Over aﬁeld of positive characteristic pt M1=t M´e t1is a full subcategory of our category t Mﬂ1that becomes abelian up to inverting p-multiplications(cf.[3],C.5.3).REMARKS ON1-MOTIVIC SHEAVES3 We will show below that t Mﬂ1is indeed an abelian category.Before proving this fact,observe that in the characteristic zero case,starting with an eﬀective1-motive M=[L→G]and an isogeny g:G′→G,by pull-back one always gets a q.i.(f,g):[L′→G′]→M.Overﬁelds of positive characteristic this is not always the case if L is forced to be a discrete group because there are isogenies with connected kernel.Hence one can generalize the construction of the category of1-motives with torsion in[4]either inverting p-multiplications as done in[3]or accepting to work with non-´e taleﬁnite group schemes as we do. To show that t Mﬂ1is an abelian category,we will follow the analogous proof for t M1[1/p]in[3],Appendix C.2.1.3.Lemma.Morphisms inΣare simpliﬁable on the left and on the right. Proof.(cf.[3],C.2.3.)Let(f,g)∈Σ.As f:L→L′,g:G→G′are epimor-phisms,they are simpliﬁable on the right.Suppose given a(f′,g′)with ff′=0, gg′=0.As g is an isogeny,say of degree n,the n multiplication on G factors through g and ng′=0.Hence g′=0;furthermore f′=0because f′,g′factor both through Ker(g)=Ker(f).2.1.4.Lemma.Σadmits the calculus of right fractions.Proof.(cf.[3],C.2.4.)Let(f′,g′):M′′→M′be a q.i.and(f,g):M→M′be an eﬀective map.Deﬁne˜G as the reduced subgroup of the identity component of G×G′G′′.It is a semi-abelian group scheme isogenous to G.Deﬁne then ˜M:=[˜L→˜G]via pull-back.This result,together with the previous Lemma,says thatΣis a left multiplicative system. Also[3],C.2.6in loc.cit.works the same.Moreover:2.1.5.Proposition.The categories t M eﬀ,ﬂ1,M1have allﬁnite limits and colim-its.The canonical functort M eﬀ,ﬂ1→t Mﬂ1is left exact and faithfulProof.(cf.[3],C.1.3.)For the deﬁnition of the kernel of an eﬀective morphism ϕ=(f,g)take Ker(ϕ)=[Ker0(f)→Ker0(g)]where Ker0(g)is the reduced subgroup of the identity component of the kernel(as group schemes)of g and Ker0(f)is the pull-back of Ker0(g)along Ker(f)→Ker(g).The cokernel ofϕis the cokernel as group schemes in each degree.For the last statement,see[3],C.5.1.2.1.6.Deﬁnition.An eﬀective morphism(f,g):M→M′is strict if g has smooth connected kernel,i.e.,the kernel of g is still semi-abelian.2.1.7.Proposition.Any eﬀective morphismϕ:M→M′factors asσ˜ϕ=ϕwith σa quasi-isomorphism and˜ϕstrict.Proof.The proof in[4],1.3,works the same.4 A.BERTAPELLE2.1.8.Example.Let n be a positive integer and consider the n-multiplication n:G m→G m.It factors as→G m→[µn→G m](0,n)G m(0,id)where theﬁrst map is a strict morphism and the second one is a quasi-isomorphism. Observe that the1-motive in the middle is not a1-motive with torsion in the sense of[4]if n is not invertible in k.We can generalize results[3],C.5.3and[4],1.3getting:2.1.9.Theorem.i)t Mﬂ1is an abelian category.ii)Given a short exact sequence of1-motives in t Mﬂ10→M′→M→M′′→0this can be represented(up to isomorphisms)by a sequence of eﬀective1-motives that is exact as sequence of complexes.iii)The natural functor M1→t Mﬂ1is fully faithful and makes M1an exact sub-category of t Mﬂ1.Proof.For i)one observes that results C.4.2,C.4.4,C.5.2in[3]still hold and hence the proofs in[3],C.5.3,[4],1.3,work the same.Also ii)follows immediately as corollary to i).For iii)one follows the proof in[3],C.7.1. We will see that all informations needed to understand the bounded derived category of t Mﬂ1are all encoded in M1and indeed in the following subcategory: 2.1.10.Deﬁnition.Denote by M⋆1the full subcategory of M1whose objects are [u:L→G]with Ker u=0.2.1.11.Remark.Observe that there are no non-trivial q.i.in M⋆1.Moreover, given two quasi-isomorphic1-motives with torsion M i=[u i:L i→G i],i=1,2, Ker(u1)is trivial if and only if Ker(u2)is trivial.In particular,M=[u:L→G] is quasi-isomorphic to a1-motive in M⋆1if and only if Ker(u)=0.2.1.12.Lemma.M⋆1is a full subcategory of t Mﬂ1closed by kernels,closed by extensions and generating.Moreover,given a monomorphism M→M′in t Mﬂ1 with M′in M⋆1then also M is in M⋆1.Proof.M⋆1is a full subcategory of M1and the latter is a full subcategory of t Mﬂ1. Given a morphismϕ:M→M′in M⋆1,this factors through a strict morphism ˜ϕ:M→˜M withσ:˜M→M′a q.i.(cf.2.1.7).As the kernel of˜ϕis the complex of kernels,it is an object of M⋆1.Similarly one proves the last assertion.Given a short exact sequence M•=0→M′→M→M′′→0in t Mﬂ1with M′,M′′in M⋆1,by Theorem2.1.9ii)and Remark2.1.11we get Ker(u)=0. Moreover M1is closed by extensions and M is(up to quasi-isomorphisms)a Deligne1-motive˜M.Hence M is q.i.to an object of M⋆1.To see that M⋆1is generating,we have to see that for any1-motive with torsion M=[u:L→G]there exists an epimorphismϕ:M′→M with M′in M⋆1.Observe that given a group scheme L in CE there always exists an abelianREMARKS ON1-MOTIVIC SHEAVES5 variety B and a monomorphism1a:L→B;deﬁne then˜M:=[˜u:L→B×G],˜u=(a,u),and˜ϕ=(id L,p G):˜M→M with p G the usual projection map.It is clear that Ker(˜u)=0and˜ϕis a strict epimorphism and hence it remains an epimorphism in t Mﬂ1(cf.[3],C.5.2).Deﬁne now,M′=[L fr→B×G/˜u(L tor)] with L fr,L tor respectively the free and torsion subgroup of L.The1-motive M′is q.i.to˜M and lies in M⋆1.2.2.The category of1-motivic sheaves.2.2.1.Deﬁnition.A sheaf F for the fppf topology over Spec(k)is1-motivic if there exists a morphism of sheaves b:G→F with G a semi-abelian scheme over k and Ker b,Coker b in CE.The map b is said to be normalized if Ker b is´e tale torsion-free.In particular,we have an exact sequence0→L→G b→F→E→0(2.2.2)with L and E in CE.Denote by Shv fppf1the category of1-motivic sheaves.For kof characteristic0,the category Shv fppf1is equivalent to the category Shv1deﬁnedin[3](cf.[3],3.3.2).We will explain in Section A.1the relation between Shv1in [3]and our Shv fppf1over general perfectﬁelds.Denote by Shv fppf0the full subcategory of Shv fppf1consisting of those F withG=0,i.e.,it is equivalent to CE.Proposition[3],3.2.3,generalizes immediately.2.2.3.Proposition.a)In Deﬁnition2.2.1we may choose b normalized.b)Given two1-motivic sheaves F,F′,normalized morphisms b:G→F, b′:G′→F′and a morphism of sheavesϕ:F′→F there exists a unique ho-momorphism of group schemesϕG:G′→G aboveϕ.c)Given a1-motivic sheaf F,a morphism b:G→F as above with b normalized is uniquely(up to isomorphisms)determined by F.d)Shv fppf1and Shv fppfare exact abelian sub-categories of the category of fppfsheaves over Spec(k).2.2.4.Deﬁnition.Denote by Shv⋆1the full subcategory of Shv fppf1consisting ofthose F such that there exists a b:G→F with b epimorphism i.e.,E=0. Observe that Hom(F,L)=0for F in Shv⋆1and L in CE.2.2.5.Lemma.For a1-motivic sheaf F there exist unique(up to isomorphisms) F⋆in Shv⋆1,E in Shv0and an exact sequence0→F⋆→F→E→0.Proof.Take simply E=Coker b for any b:G→F as in2.2.1. The”dual”of Lemma2.1.12holds:6 A.BERTAPELLE2.2.6.Lemma.Shv ⋆1is a full subcategory of Shv 1,closed by cokernels,closed by extensions and cogenerating.Moreover given an epimorphism F →F ′in Shv 1with F in Shv ⋆1then also F ′is an object of Shv ⋆1.Proof.The only non-trivial fact is that Shv ⋆1is cogenerating,i.e.,that for any1-motivic sheaf F there exists a F ′in Shv ⋆1and a monomorphism ϕ:F →F ′.By Proposition A.2.2,F is Coker(F 1→F 0)with F 1in CE and F 0extension of a group scheme in CE by a semi-abelian group scheme.It is suﬃcient to prove that F 0embeds in a semi-abelian group G ′and then take F ′=Coker(F 1→G ′).Moreover,we can treat separately the case E =Coker b ´e tale and connected.Suppose E ´e tale.Then the extension F 0of E by G splits over a suitable ﬁnite separable extension k ′of k .Let f :Spec(k ′)→Spec(k )so that f ∗F 0=F 0,k ′is isomorphic to G k ′×E k ′.We may assume that E is constant over k ′.Embed Ek ′into an abelian variety A k ′over k ′.Then we have a monomorphismE →f ∗A k ′,where f ∗Ak ′is still an abelian variety,the Weil restriction of A k ′.Moreover,G →f ∗f ∗G is a monomorphism.Hence we have a monomorphismF 0→f ∗f ∗F 0=(f ∗f ∗G )×f ∗Ak ′where the latter is semi-abelian.Suppose E ﬁnite connected of order n .Let n F 0denotes the kernel of the n -multiplication on F 0,and similar notation for n G .Then n F 0is extension of E byn G ,hence ﬁnite and F 0/n F0∼=G .Let then f :n F 0→B be an embedding intoan abelian variety B and let f ′:F 0→C be the push-out of F 0along f .As C is extension of G by B it is a semi-abelian group scheme and we are done.2.3.Equivalence on bounded derived categories.Consider the following picture:M 1d Shv fppf 1M ⋆1ιREMARKS ON1-MOTIVIC SHEAVES7 2.3.3.Lemma.Denote by N b(Shv⋆1)the full subcategory of K b(Shv⋆1)consisting of complexes that are acyclic as complexes of1-motivic sheaves.The natural functor)K b(Shv⋆1)/N b(Shv⋆1)→D b(Shv fppf1is an equivalence of categories.Proof.It follows from[10],13.2.2and Lemma2.2.6.2.3.4.Lemma.Denote by N b(M⋆1)the full subcategory of K b(M⋆1)consisting of complexes that are acyclic as complexes of1-motives with torsion.The natural functorK b(M⋆1)/N(M⋆1)→D b(t Mﬂ1)is an equivalence of categories.Proof.By Lemma2.1.12the”dual”conditions required in[10],13.2.2ii)are satisﬁed.One checks that the”dual”statement of[10],13.2.1holds the same and hence one can apply[10],10.2.7ii). Similar,with M1in place of M⋆1:2.3.5.Lemma.Denote by N b(M1)the full subcategory of K b(M1)consisting of complexes that are acyclic as complexes of1-motives with torsion.The natural functorD b(M1):=K b(M1)/N(M1)→D b(t Mﬂ1)is an equivalence of categories.It remains to check that the functor a preserves the exact structures.2.3.6.Lemma.Let M•be a complex in K b(M⋆1).Then M•∈N(M⋆1)if and only if a(M•)∈N(Shv⋆1).In particular a induces an equivalence of categoriesK b(t M⋆1)/N(t M⋆1)→K b(Shv⋆1)/N(Shv⋆1).Proof.For the only if part it is suﬃcient to check the case of an acyclic com-plex of objects of t Mﬂ1,M•=0→M0d0→M1d1→M2→0with Ker(u i)=0 (cf.Lemma2.1.12/proof);indeed any short exact sequence is represented up to q.i.by an acyclic complex of eﬀective1-motives(cf.Thm.2.1.9ii)and Re-mark2.1.11).The result follows then from the usual ker-coker sequence.For the if part,suppose to have a complex M•of objects in t Mﬂ1such that all Ker(u i)=0 and∂i:Coker d i→Ker d i+1are monomorphisms such that a(∂i)become isomor-phisms.We know that Ker d i+1is in M⋆1,because kernel of a morphism in M⋆1; hence also Coker d i is in M⋆1and a(∂i)=0implies that∂i is a q.i.in M⋆1,hence an isomorphism. All the Lemmas above provide immediately the main result of this section that generalizes[3],1.6.1,3.9.2:2.3.7.Theorem.We have canonical equivalences of categoriesD b(M1)∼=D b(t Mﬂ1)∼=D b(Shv fppf)1where D b(M1)was deﬁned in Lemma2.3.5.8 A.BERTAPELLE2.3.8.Remark.For X a smooth projective k-variety the sheaf Pic X/k is clearly 1-motivic being representable by a group scheme ofﬁnite type whose reduced identity component is an abelian variety.In[3],3.4.1the authors prove that the relative Picard functor is1-motivic for the´e tale topology as soon as X is smooth over k,i.e.with the notations in(A.1.1)π∗Pic X/k is a sheaf in Shv1. Unfortunately the proof in[3],3.4.1does not work in the fppf context and it is not clear at the present if a similar result holds.3.The derived category of Laumon’s1-motives. Notations:Let in this section k be aﬁeld of characteristic0.Denote by M a1 the category of Laumon1-motives(cf.[11],[2]).The category M1of Deligne 1-motives over k is a full subcategory of M a1.Denote by Ab/k the category of fppf sheaves on the category of aﬃne schemes over k,by For/k the category of formal k-groups and by Alg/k the category of(non necessarily connected) algebraic k-groups.Both For/k and the category of algebraic k-groups may be viewed as thick subcategories of Ab/k.Given a formal k-group L,L0denotes its maximal connected subgroup and L´e t:=L/L0.In the following we generalize to Laumon1-motives constructions and results of Section2.3.1.The category of generalized1-motives with torsion.3.1.1.Deﬁnition.A(generalized)eﬀective1-motive with torsion is a complex [L→G]of sheaves in Ab/k where:L is a formal k-group and G is a connected algebraic k-group.An eﬀective morphism is a map of complexes.Denote by t M eﬀ,a1the category of(generalized)eﬀective1-motives.Recall thatan eﬀective morphism(f,g):M→M′is a quasi-isomorphism if g is an isogeny and Ker(f)=Ker(g)is aﬁnite group scheme.3.1.2.Deﬁnition.The category of(generalized)1-motives with torsion t M a1is the localization of t M eﬀ,a1with respect to the multiplicative class of quasi-isomorphisms.The category t M a1was introduced in[2]showing that it is abelian and,when k=C,equivalent to the category of Formal Hodge Structures of level≤1;see also[1]for the“torsion free”case.This result generalizes equivalences in[4]and [8]for Deligne’s1-motives.3.1.3.Proposition.The canonical functor d:M a1→t M a1makes M a1an exact subcategory of t M a1in the sense of Quillen.Denote by M a⋆1the full subcategory of M a1whose objects are those[u:L→G] with Ker u=0.Observe that there are no non-trivial quasi-isomorphisms in M⋆1.3.1.4.Lemma.M a⋆1(resp.M a1)is a full subcategory of t M a1closed by kernels, closed by extensions and generating.Moreover,given a monomorphism M→M′in t M a1with M′in M a⋆1(resp.M a1)then also M is in M a⋆1(resp.M a1). Proof.Almost word by word as the proof of2.1.12.REMARKS ON1-MOTIVIC SHEAVES93.2.Generalized1-motivic sheaves.3.2.1.Deﬁnition.A sheaf F in Ab/k is1-motivic if there exists a morphism of sheaves b:G→F with G a smooth connected algebraic k-group,Ker(b),Coker(b) formal k-groups.The morphism b is said to be normalized if Ker(b)is torsion free.Hence a generalized1-motivic sheaf Fﬁts in a sequence0→L→F→G b→F→E→0(3.2.2)with L,E formal k-groups and G a smooth connected algebraic k-group. Denote by Shv a1the category of(generalized)1-motivic sheaves and by Shv a0 the subcategory equivalent to For/k,consisting of those F with G=0.3.2.3.Examples.•The category Shv fppf1is equivalent to the full subcategory ofShv a1consisting of those F with L,E discrete.One has to be careful because the ﬁrst category consists of sheaves for the fppf topology on the category of schemes over k while the second is a subcategory of Ab/k,i.e.,sheaves for the fppf topology on the category of aﬃne schemes over k.However,letπ:(Sch/k)fppf→(Aﬀ/k)fppf be the canonical morphism of sites.By[12],III,3.1π∗is exact and F∼=π∗π∗F.Moreover,proceeding as in A.1oneﬁnds thatπ∗X=X for commutative group schemes and thatπ∗is exact on1-motivic sheaves viewed as cokernels of morphisms of commutative group schemes.(cf.A.2,Appendix B).•Let M=[L→G]be a Deligne k-1-motive.It is shown in[5]that for M♮=[u:L→G♮]a universal G a-extension of M the sheaf Coker(u)is the sheaf of♮-extensions of M by G m.As G♮is a connected algebraic k-group but,in general not a semi-abelian group scheme,and L is a discrete group,Coker(u)is an example of generalized1-motivic sheaf that is not1-motivic in the sense of 2.2.1.•Let A,A′be dual abelian varieties over k andˆA′the completion of A′at the origin.The Laumon1-motive[ˆA′i→A′],for i the canonical embedding,is the Cartier dual of[0→A♮]where A♮is the universal G a-extension of A(cf.[11]). The sheaf of G m-extensions of A♮is isomorphic to Coker(i)and is a generalized 1-motivic sheaf.•More generally,given a smooth connected algebraic k-group G,letˆG be its formal completion at the origin.Then[ι:ˆG→G]is a generalized1-motive and Coker(ι)is a1-motivic sheaf.Proposition2.2.3generalizes easily.3.2.4.Proposition.a)In Deﬁnition3.2.1we may choose b normalized.b)Given two1-motivic sheaves F,F′,normalized morphisms b:G→F, b′:G′→F′and a mapϕ:F′→F in Ab/k,there exists a unique homomorphism of group schemesϕ0:G′→G aboveϕ.In particular Shv1is a full subcategory of Ab/k.c)Given a1-motivic sheaf F,a morphism b:G→F as above with b normalized is uniquely(up to isomorphisms)determined by F.d)Shv a1and Shv a0are exact abelian subcategories of Ab/k.10 A.BERTAPELLEProof.a)as in[3].b)as in[3]replacing Lemma3.1.5in loc.cit.by[2],Lemma A.4.5.For the uniqueness ofϕG one uses[2],Lemma A.4.4.c)follows from b). Point d)is proved with the same construction as in[3]. Denote by Shv a⋆1the full subcategory of Shv a1consisting of those objects with Coker(b)=0.3.2.5.Lemma.Shv a⋆1is a full subcategory of Shv a1,closed by cokernels,closed by extensions and cogenerating.Moreover given an epimorphism F→F′in Shv a1 with F in Shv a⋆1then also F′is an object of Shv a⋆1.Proof.(cf.2.2.6).Again the problem is to see that Shv a⋆1is cogenerating,i.e., that for any1-motivic sheaf F there exists a F′in Shv a⋆1and a monomorphism ϕ:F→F′.Consider the extension(3.2.2)and let F⋆=G/L.We can treat separately the connected and´e tale cases.If E is formal connected,from Propositions C.0.10and C.0.12it follows that F=F⋆×E.Let E→G s a be an embedding;then the induced map F→F⋆×G s a is a monomorphism.If E and L are both discrete,F comes from a sheaf in Shv fppf1and the resultfollows from2.2.6.If L is formal connected and E is´e tale,by C.0.11it holds F=H/L for H an extension of E by G.Proceeding as in the proof of2.2.6(´e tale case)we can embed H into a connected algebraic group over aﬁniteﬁeld extension of k.Hence by restriction of scalars,we get a monomorphism H→H′with H′connected algebraic k-group and F′is the cokernel of L→H′. As in the classical case any generalized1-motivic sheaf F can be viewed as extension of a formal k-group E by a1-motivic sheaf F⋆in Shv a⋆1.3.3.Equivalence on bounded derived categories.We have the following picture that generalizes2.3.1:M a1d Shv a1M a⋆1ιREMARKS ON1-MOTIVIC SHEAVES114.1-motives with cotorsion and Cartier dualityCartier duality on the category of1-motives does not extend to an anti-equivalence on the category1-motives with torsion:it is necessary to introduce a new category,the category of1-motives with cotorsion as done in[3],1.8,in order to get a reasonable duality result.We show in this section that duality results in loc.cit.extend both to the category t Mﬂ1and to t M a1.4.1.k perfect.Let notations be as in Section2.4.1.1.Deﬁnition.Let t M eﬀ,ﬂ1be the category of complexes M=[u:L→G]where L is a torsion free,discrete group scheme over k and G is a commutative group scheme extension of an abelian scheme A by a commutative k-group Q that is product of a group scheme of multiplicative type and aﬁnite group scheme N. M is said to be multiplicative if Q is of multiplicative type.The category of1-motives with cotorsion t Mﬂ1is the localization of t M eﬀ,ﬂ1at the class of quasi-isomorphisms.Similarly for the subcategory t M mult1of1-motives with cotorsionof multiplicative type.Observe that we may suppose that N in the above deﬁnition contains no group schemes of multiplicative type.Furthermore,a quasi-isomorphism(f,g):M→M′is such that f,g have trivial kernel and Coker(f)=Coker(g)isﬁnite´e tale. The category of1-motives with cotorsion in[3],denoted there by t M1,is with our notations,the full subcategory t M mult1of t Mﬂ1.4.1.2.Lemma.Cartier duality on M1extends to a contravariant additive functor()∗:t M eﬀ,ﬂ1→t M eﬀ,ﬂ1which sends quasi-isomorphisms to quasi-isomorphisms.Proof.(cf.[3],1.8.3.)The eﬀective1-motive with cotorsion M∗=[u′:L′→G′] associated to the1-motive with torsion M=[u:L→G]is deﬁned as follows: Let M A=[L→A]be the1-motive obtained via the composition of u with the projection G→A.Then•L′is the Cartier dual of the maximal torus in G;•G′is the commutative k-group that represents the fppf sheaf over kExt(T,G m)→Ext(L,G m)→Ext(A,G m)=A′→0where the exactness on the right is due to[12],III,4.17and the local triviality of G m-torsors.As L is product of its discrete part and aﬁnite connected part, G′satisﬁes the condition in Deﬁnition4.1.1.12 A.BERTAPELLEFor the assertion on quasi-isomorphisms one can use the same proof as in[3].4.1.4.Proposition.The functor()∗in Lemma4.1.2induces an anti-equivalence of abelian categories()∗:t Mﬂ1→t Mﬂ1.Moreover,Cartier duality is an exact functor on M1and hence it induces a triangulated self-duality on D b(M1).Proof.(cf.[3],1.8.4.)Observe that that the proof in loc.cit.part a),works also without inverting the the exponential characteristic,i.e.,it works for t M1=t M´e t1and t M1=t M mult1.More generally it works for our categories t Mﬂ1and t Mﬂ1.Also the other assertions can be proved with the same arguments. Hence we can generalize[3],1.8.6:4.1.5.Theorem.The natural functor t M1→t Mﬂ1is fully faithful and induces an equivalence of categoriesD b(M1)∼→D b(t Mﬂ1).Cartier duality exchanges t Mﬂ1and t Mﬂ1inside D b(M1).4.2.k of characteristic0.Let notations be as in Section3.We can introduce also generalized1-motives with cotorsion.4.2.1.Deﬁnition.Let t M eﬀ,a1be the category of complexes M=[u:L→G]where L is a formal k-group with torsion free´e tale part and G is a commutative group scheme extension of an abelian scheme A by an aﬃne k-group Q product of a vector group by a group of multiplicative type.The category of(generalized)1-motives with cotorsion t M a1is the localization of t M eﬀ,a1at the class of quasi-isomorphisms.Repeating the arguments of the previous subsection,we can prove that4.2.2.Proposition.i)Cartier duality on M a1induces an anti-equivalence of abelian categories()∗:t M a1→t M a1,that is exact.Moreover,Cartier duality is an exact functor on M a1and hence it induces a triangulated self-duality on D b(M a1).ii)The natural functor M a1→t M a1is fully faithful and induces an equivalence of categoriesD b(M a1)∼→D b(t M a1).Cartier duality exchanges t M a1and t M a1inside D b(M a1).One should be cautious with the construction of the Cartier dual of a gener-alized1-motive with(co-)torsion.However,as ExtREMARKS ON1-MOTIVIC SHEAVES13 Appendix A.More results on1-motivic sheaves.We collect in this section results used in the proof of the equivalence of bounded derived categories in Section2.Moreover we describe the relation between our deﬁnition of1-motivic sheaves and the one in[3].We provide also an alternative deﬁnition of1-motivic sheaf as cokernel of a morphism of group schemes F1→F0 where F1is an object in CE,i.e.,product of a discrete group by aﬁnite connected group scheme and F0is a commutative group scheme over k extension of an object of CE by a semi-abelian group scheme.Following this idea,one can construct acategory of presentations S1equivalent to Shv fppf1.Notations:Let notations be as in Section2and denote by p the exponen-tial characteristic of k.Denote furthermore by Sm/k the category of smooth separated k-schemes.parison of topologies.Let Shv′1be the full subcategory of Shv fppf1 whose objects are those F as in(2.2.2)with L,E discrete.It coincides withShv fppf1in characteristic0.Let Shv´e t1be the category of´e tale sheaves on(Sm/k)thatﬁt in a sequence as(2.2.2)with G semi-abelian,L,E discrete.The deﬁnition of the category of 1-motivic sheaves Shv1in[3],is with our notationsShv1:=Shv´e t1[1/p].Denote by Shv´e t,⋆1the full subcategory of Shv´e t1consisting of sheaves with E=0.Letπ:(Sch/k)fppf→(Sm/k)´e t be the usual morphism of sites.We have the following pictureShv⋆1Shv fppf1(A.1.1)whereπ∗restricted to Shv´e t1or Shv´e t,⋆1are exact equivalences of categories withquasi-inverseπ∗.We spend some words on these facts(see also[3],3.3.2)First of all observe that for X a smooth k-scheme it holdsπ∗X=X(proof as in[12], p.69).Moreover,π∗π∗X=X.Indeed,let U be a smooth k-scheme.Then Γ(U,π∗π∗X)=Γ(U,π∗X)by deﬁnition ofπ∗;we have just seen that the last group equalsΓ(U,X)and this does not change when working with the´e tale or theﬂat topology.Observe now that if we prove that R iπ∗π∗G=R iπ∗G=0(and similar for L)we get that also R iπ∗π∗(G/L)=R iπ∗(G/L)=0;henceπ∗and π∗π∗are exact on1-motivic sheaves andπ∗π∗F∼=F for any1-motivic sheaf F. Consider then a k-group scheme F;it holds R iπ∗F=0if and only if for all X smooth over k,H i(X´e t,F)=H i(X fppf,F).But this follows from[9],11.7.It remains to check thatπ∗is exact on1-motivic sheaves.Now the functorπ∗is right exact and thenπ∗L=L,π∗G=G imply that it sends0→L→G→F∗→0into an exact sequence.Moreover it is exact on Shv´e t,∗.Indeed given a。

叠加效应英语

叠加效应英语《The Power of the Superposition Effect》In the world of science and mathematics, the concept of the superposition effect holds great significance. It refers to the phenomenon where the combined effect of multiple factors is greater than the sum of their individual effects. This principle can be observed in various fields, from physics to economics, and has profound implications for our understanding of complex systems. In this article, we will explore the superposition effect in detail, its applications, and the importance of considering it in our daily lives.To understand the superposition effect, let’s consider a simple example. Imagine a group of people pushing a heavy object. Each person exerts a certain amount of force, and when these forces are combined, the object moves with a greater force than any individual could achieve alone. This is the essence of the superposition effect – the collective action of multiple elements results in a more significant outcome.In the field of physics, the superposition principle is widely used to describe the behavior of waves. When two or more waves interact, their amplitudes add up, creating a resultant wave with a unique pattern. This principle is crucial in understanding phenomena such as interference and diffraction, which have important applications in areas like optics and telecommunications.The superposition effect also plays a crucial role in economics. For instance, in a market, the combined actions of consumers and producers determine the overall supply and demand. When there is an increase in both consumer demand and producer supply, the market experiences a greater impact than if only one of these factors were to change. This understanding is essential for policymakers and businesses to make informed decisions and predict market trends.In the realm of human behavior, the superposition effect can be observed in various situations. For example, in a team environment, the combined skills and efforts of team members can lead to more significant achievements than if each member were to work independently. Similarly, in a social setting, the cumulative effect of individual actions can have a profound impact on the community as a whole.One of the key implications of the superposition effect is that it highlights the importance of considering multiple factors when analyzing a situation. By looking beyond individual elements and considering their interactions, we can gain a more comprehensive understanding of complex systems. This approach is particularly relevant in fields such as climate science, where the combined effects of various factors, such as greenhouse gas emissions and natural phenomena, determine the state of the climate.Furthermore, the superposition effect reminds us of the power of collective action. When individuals come together and work towards a common goal, their combined efforts can have a far-reaching impact. This is evident in social movements, where the collective voice of many can bring about significant change.The superposition effect is a powerful concept that has wide-ranging applications in various fields. It emphasizes the importance of considering the combined effects of multiple factors and the potential for collective action to create more significant outcomes. By understanding and applying this principle, we can better analyze complex systems, make informed decisions, and work towards achieving greater goals. So, the next time you encounter a situation where multiple factors are at play, remember the power of the superposition effect and its potential to shape our world.。

constipation

ConstipationConstipation is a common problem regardless of sex, age or race. It is deﬁned as infrequent, difﬁcult or incomplete bowel movements. Normal bowel movement frequency may range from three bowel movements per day to three bowel movements per week. Constipation is therefore deﬁned by most authorities as less than three bowel movements a week. However, constipation may have other deﬁning features. These include:•The passage of hard, pellet-like stools• A decrease in one’s typical bowel movement frequency (not necessarily less than three bowel movement’s a week)•The need to strain when having a bowel movement• A sense of incomplete evacuation of the rectum with a bowel movement•The need to use enemas, suppositories, oral laxatives or manual maneuvers such as digital stimulation or pelvic ﬂoor support to maintain regularity of bowel movementsWhat are the causes?There are many reasons for the development of constipation. These include dietary and lifestyle habits, medications and behavioral issues. For some constipation may be a symptom associated with a medical condition including a number of structural, metabolic, myopathic, neuropathic or functional disorders. For many there may be more than one underlying cause for their constipation.Common causes of constipation:•Inadequate ﬁber in the diet•Inadequate hydration (dehydration)•Lack of physical activity (especially in elderly)•Medications•Changes in life or routine such as pregnancy, aging, and travel•Ignoring the urge to have a bowel movement•Irritable bowel syndrome•Mechanical obstruction of the colon and/or rectum•Systemic diseases and other medical conditionsLack of adequate dietary ﬁberPeople who eat a high-ﬁber diet are less likely to become constipated. A diet low in ﬁber or a diet high in fats is commonly associated with constipation. Fiber—both soluble and insoluble—is the part of fruits, vegetables, and grains that the body cannot digest. Soluble ﬁber dissolves easily in water and takes on a soft, gel-like texture in the intestines. Insolubleﬁber passes through the intestines almost unchanged. The bulk and soft texture of ﬁber help prevent hard, dry stools that may be difﬁcult to pass.Americans eat an average of 5 to 14 grams of ﬁber daily [1], which is short of the 25 to 35 grams recommended by the American Dietetic Association. Both children and adults often eat too many reﬁned and processed foods from which the natural ﬁber has been removed.A low-ﬁber diet also plays a key role in constipation among older adults, who may lose interest in eating and choose foods that are quick to make or buy. These fast foods or prepared foods, both are typically low in ﬁber and high in fat. Also, difﬁculties with chewing or swallowing may cause older people to eat soft foods that are processed and consequently low inﬁber.[1] National Center for Health Statistics. Dietary Intake of Macronutrients, Micronutrients, and Other Dietary Constituents: United States, 1988–94. Vital and Health Statistics, Series 11, Number 245. July 2002.Adequate hydrationResearch has not yet demonstrated that a low ﬂuid intake causes constipation or that an increase in orally ingested ﬂuids alone effectively treats constipation. Nonetheless, many individuals report relief of their constipation with an increase intake of oral ﬂuids. Orally ingested liquids are believed to add ﬂuid to the colon and bulk to stools, making bowel movements softer and easier to pass. However caution must be exercised as beverages containing caffeine, such as coffee and soft drinks, are likely to worsen one’s symptoms by promoting dehydration. Alcohol is another beverage that causes dehydration and may worsen constipation in the long run. It is important to drink ﬂuids that hydrate the body, especially in the heat or when consuming large quantities of caffeine-containing or alcoholic beverages.Lack of physical activityA lack of physical activity can lead to constipation. For example, constipation often occurs after an accident or during an illness when one must stay in bed and cannot exercise. Lack of physical activity is thought to be one of the reasons constipation is more common in older people. Moreover, increased physical activity is more likely to stimulate bowel motility and improve the symptoms of constipation.MedicationsMany medications can cause constipation, including prescription and nonprescription drugs. The list below includes commonly prescribed drugs and common over-the-counter drugs that may promote constipation. Be aware that there are many other drugs not listed below that may cause constipation. If you notice the development of constipation with the use of a medication, this should be brought to the attention of your physician.Prescriptions drugs•Pain medications, particularly those containing opiates•Muscle relaxants•Antispasmodics•Antidepressants•Antiparkinson drugs•Blood pressure medications (beta blockers and calcium channel blockers)•Diuretics•Anticonvulsants•Antipsychotic drugs•AntihistaminesNonprescription drugs•Antacids that contain aluminum and calcium•Iron supplements•Antihistamines•Antidiarrheal agents•Calcium supplements•Nonsteroidal anti-inﬂammatory agentsChanges in life or routineDuring pregnancy, women may be constipated because of hormonal changes or because the uterus compresses the intestine. Aging may also affect bowel regularity possibly due to slowing metabolism, decreased intestinal motor activity or decreased muscle tone and strength. Finally, people may become constipated when traveling, because their normal diet and daily routine are disrupted.Ignoring the urge to have a bowel movementPeople who ignore the urge to have a bowel movement may eventually stop feeling the need to have one, which can lead to constipation. Some people delay having a bowel movement because they do not ﬁnd it convenient to use toilets outside the home. Others ignore the urge because of emotional stress or because they are simply too busy. Children may postpone having a bowel movement because of stressful toilet training or because they do not want to interrupt their play.Irritable bowel syndrome (IBS)IBS is a common chronic disorder causing alteration in one’s bowel habits as well as abdominal discomfort, although pain is usually relieved with bowel movement. Bowel habit alterations can include constipation, diarrhea, and a mixed pattern in which the bowels alternate between that of diarrhea and constipation. IBS is believed to occur due to disruption in the proper function of the bowels. This may include alterations in normal bowel motility, bowel secretion or bowel pain sensation. IBS is therefore referred to as a functional bowel disorder. There are speciﬁc therapies for IBS that may also help the associated symptom of constipation.Mechanical obstruction of the colon or rectumThere are a number of disorders that may compress, squeeze or narrow the intestines. This may result in a physical barrier to the easy passage of the stool through the bowels. Such conditions may present with constipation.Causes of mechanical obstruction•Colon cancer•Strictures of the colon, rectum or anus•Adhesions (scar tissue from prior surgery)•Diverticulosis•External compression of the colon•Rectocele•Megacolon (Hirschsprung’s disease)•Anal ﬁssure•Rectal outlet obstruction due to pelvic ﬂoor dyssynergia or anismus (abnormal muscle contraction and relaxation impairing the ability to expel stool from the rectum)Systemic diseases and conditionsA number of systemic diseases and conditions may also cause constipation. These include neurologic disorders, myopathies, metabolic and endocrine disorders. These disorders can slow the movement of stool through the colon, rectum, or anus.Conditions that can cause constipation:•Neurological disorders◦Multiple sclerosis◦Parkinson's disease◦Stroke (cerebral vascular disease)◦Spinal cord injury or tumor•Myopathies◦Amyloidosis◦Scleroderma•Metabolic and endocrine conditions◦Diabetes Mellitus◦Hypothyroidism (under active thyroid)◦Uremia (kidney failure)◦Hypercalcemia (high calcium level in blood◦Hypokalemia (low potassium level in blood)◦Hypomagnesemia (low magnesium level in blood)◦Heavy metal poisoning•Other conditions◦Depression◦History of physical or sexual abuseWhat to do about constipation?You should see your primary care provider if the above-mentioned lifestyle, dietary or behavioral changes do not relieve the constipation.You should see a physician right away if there are associated symptoms of blood in the stool, rectal bleeding, abdominal pain, painful bowel movements, unexplained weight loss, associated nausea or vomiting or constipation lasting more than three weeks.If you are 50 or older, you should have a routine colonoscopy. Your physician may pursue addtional testing such as lab work, radiographic studies of the bowels or manometric studies of the bowels or rectum.Remember, constipation is common, may have one or more causes and is treatable.Information provided by the Michigan Bowel Control Program, March, 14, 2008。

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a rXiv:h ep-ph/994356v116Apr1999Propagation of axions in a strongly magnetized medium ∗A.V.Borisov †and P.E.Sizin M.V.Lomonosov Moscow State University,119899Moscow,Russia The polarization operator of an axion in a degenerate gas of electrons occupying the ground-state Landau level in a superstrong magnetic ﬁeld H ≫H 0=m 2e c 3/e =4.41·1013G is investigated in a model with a tree-level axion-electron coupling.It is shown that a dynamic axion mass,which can fall within the allowed range of values (10−5eV m a 10−2eV),is generated under the conditions of strongly magnetized neutron stars.As a result,the dispersion relation for axions is appreciably diﬀerent from that in a vacuum.1.The a priori strong nonconservation of CP parity in the standard model can be elim-inated in a natural manner by introducing axions —pseudo-Goldstone bosons associated with the spontaneous breaking of the additional Peccei–Quinn global symmetry U (1)P Q .1,2According to the experimental data,3the energy scale v a for the U (1)P Q symmetry breaking is much greater than the electroweak scale —v a 1010GeV,and the constants of the pos-sible couplings of an axion to the standard particles (∼1/v a )are very small (the “invisible”axion:see Ref.4for a review of various axion models).Axion eﬀects can be appreciable under the astrophysical conditions of high matter den-sities,high temperatures,and strong magnetic ﬁelds (for example,in neutron stars 5).Axion production processes,which result in additional energy losses by stars,and the limits ob-tained by astrophysical methods on the parameters of axion models are examined in Ref.4.In so doing,the inﬂuence of electromagnetic ﬁelds was neglected.The investigation of axion processes in strong magnetic ﬁelds commenced comparativelyrecently.The Compton and Primakoﬀmechanisms of axion production on nonrelativistic electrons by thermal photons(γ+e→e+a)in the presence of a magneticﬁeld are studied in Ref.6.The extension to relativistic electrons in a constant external electromagneticﬁeld is given in Ref.7(Primakoﬀeﬀect)and Refs.8and9(Compton eﬀect),where7,9estimates were also obtained for the contributions of the indicated processes to the axion luminosity of a magnetized strongly degenerate relativistic electron gas under the conditions of the crust of a neutron star.A new axion production mechanism—synchrotron emission of axions (e→e+a)by relativistic electrons—was proposed in Ref.10and its contribution to the energy losses by a neutron star was calculated.In Refs.6–10it was assumed that the externalﬁeld intensity F≪H0=m20c3/e ≃4.41·1013G.In Ref.11,numerical methods were used to extend the results of Ref.10to superstrong magneticﬁelds H H0.It was found that the basic equation derived in Ref.10for the axion synchrotron luminosity for the semiclassical case of high electron energies(ε≫m e c2)andﬁelds H≪H0agrees with the numerical calculations up to H/H0 20.The axion synchrotron luminosity of neutron stars and white dwarfs was also investigated in Ref.11.In Refs.8–11a model with a derivative axion-electron coupling eae,described by the interaction Lagrangian4L ae=g aeψγµγ5ψ ∂µa,(1) was used.Here m e is the electron mass andγ5=−iγ0γ1γ2γ3;the system of units such that =c=1is used;the signature of the metric is(+−−−);andm eg ae=c eRefs.6and7.The synchrotron process e→ea in the absence of a tree-level axion–electron coupling was considered recently in Ref.12.This process is due to resonant conversion of a longitudinal plasmon(a photon in a medium),emitted by a relativistic electron in a magneticﬁeld,into an axion.Decay of an axion in a strong magneticﬁeld into a fermion pair(a→f¯f)13and two photons(a→γγ)14are also of interest for astrophysics and cosmology.In the present paper the model(1)is used to calculate the polarization operator of an axion moving in a strongly magnetized degenerate electron gas and the change in the dispersion relation of an axion in a medium is investigated using this operator.2.Taking account of the contribution of the electrons only(see Eq.(1))we obtain,using the real-time formalism of theﬁnite-temperature quantumﬁeld theory(see,for example, Ref.15),the following momentum representation for the one-loop polarization operator of an axion:Π(k,k′)=−iG2a d4x d4x′exp(ikx−ik′x′)Tr ˆkγ5G(x,x′)ˆk′γ5G(x′,x) .(3) Here k(k′)is theﬁnal(initial)4-momentum of an axion;G(x,x′)is the time-dependent single-particle Green’s function of an ideal electron-positron gas in a constant magnetic ﬁeld;15notations have also been introduced for the contractionˆa=γµaµof a4-vector aµwith the Diracγmatrices and for the dimensional coupling constantg aeG a=where m a is the free-axion mass(in the absence of aﬁeld and a medium),which is generated by the chiral anomaly of QCD:2m a∼Λ2QCD/v a.The renormalized valueΠR(k)(see below) gives the dispersion relationk2=m2a+ΠR(k).(7)3.We give the constant uniform magneticﬁeld H ˆz in terms of the4-potential Aµin the gaugeAµ=(0,0,xH,0).(8)Then the Green’s function G(x,x′)can be represented in the following form after summing over the spin quantum number and the sign of the energy in the general expression for G in the form of a series in quadratic combinations of the eigenfunctions of the Dirac operator15:G(x,x′)=[γµ(i∂µ+eAµ)+m e]K(x,x′);K(x,x′)=√(2π)3∞n=0∞ −∞dp0dp y dp z exp[−ip0(t−t′)+ip y(y−y′)+ip z(z−z′)]××u n(η)u n(η′)(R n+1Σ++R nΣ−),(9)R n= p20−p2z−2hn−m2e+i0 −1+2πiδ(p20−p2z−2hn−m2e)N F(p0).Here the electron charge−e<0,h=eH;n=0,1,2,...is the principal quantum number(the number of the Landau level);p y and p z are the eigenvalues of the operators of the canonical momenta—the constants of motion in the gauge(8);and u n(η)is a Hermite function of argumentη=√N F(p0)=θ(p0)[exp[β(p0−µ)]+1]−1+θ(−p0)[exp[β(−p0+µ)]+1]−1(10) is expressed in terms of the Fermi distribution function of electrons and positrons in a medium with temperature T=1/βand chemical potentialµ,andθ(±p0)is the Heaviside step function.4.It is diﬃcult to make a general analysis of the axion polarization operator for arbitrary values of the parameters H,T,andµ.In the present paper we conﬁne our attention to superstrong magneticﬁelds and comparatively low temperaturesH≫H0,T≪µ−m e,(11)and we require the chemical potential to satisfyµ2−m2e<2h.(12) It follows from Eqs.(11)and(12)that in this case the contribution of positrons in Eq.(10)can be neglected(it is suppressed by the factor exp[−β(µ−m e)])and the medium is a degenerate gas of electrons occupying the ground-state Landau level(n=0):N F(p0)=θ(p0)θ(µ−p0),p0=π 1/2∞−∞dp y2(η2+η′2)+ip y(y−y′) ×× d2pHere p=(p0,0,0,p z)andG(p)=(ˆp+m e) (p2−m2e+i0)−1+2πiδ(p2−m2e)N F(p0) (16) is the Fourier transform of the Green’s function in the two-dimensional space(0,3).For N F=0(no medium)the expression(15)is the well-known,eﬀectively two-dimensional, electron propagator used in the theory of electrodynamic processes in superstrong magnetic ﬁelds and,speciﬁcally,for investigation of the photon polarization operator.165.Let us substitute the expression(15)into Eq.(3)and integrate over t,t′,y,y′,z,and z′.This gives in the form of a product of delta functionsn=0,y,zδ(k′n−k n)δ(p′n+k n−p n)the laws of conservation of energy and of the corresponding projections of the momentum. The subsequent calculation of the Gaussian integrals over x,x′and the trivial integral over p y givesδ(k′x−k x).As a result,as should be the case,we obtain a diagonal representation of the polarization operator(5),whereΠ(k)=G2a2h [F(l)+M(l)],(17)F(l)=−i d2p(2π)2δ(p2−m2e)N F(p0) T(l,p)2Tr ˆkγ5(ˆp+m e)Σ−ˆkγ5 ˆp−ˆl+m e Σ− .(20) In Eq.(17)the function F corresponds to the purelyﬁeld contribution,and M describes the inﬂuence of the medium.We note that M does not contain a term∝N F(p0)N F(p0−l0), sinceδ(p2−m2e)δ (p−l)2−m2e θ(p0)θ(p0−l0)=0.Using the relations[Σ−,ˆp]=0,[Σ−,γ5]=0,γnΣ−=Σ+γn(n=1,2),Σ+Σ−=0the trace of Eq.(20)reduces to a two-dimensional form and can be easily calculated as T(l,p)=1F(l2)=−im2eτF(l2)=F(l2,m2)−F(l2,Λ2)with the regulator massΛ→∞.The renormalized polarization operatorΠR(τ)can be obtained¿from the dispersion relation with one subtraction(as well as it was done for the photon polarization operator in Ref.16)1π∞dt ImΠ(t)Im 21 0dv δ 1−(1−v 2)τ =−m 2eθ(τ−1) 1−1πm 2e H 2h1−ξ4ξ,(26)which is convenient for analytical continuation in l 2=4m 2e τ.For τ>1,a channel is open for axion decay into an electron-positron pair (a →e −e +)in a magnetic ﬁeld.Its rate w for a real axion is related with the imaginary part of the polarization operator on the mass shell by the well-known relationw =−1ωH 2hθ(τ−1) 1−12πl 2µ m e dεε2−m 2e ,and the two-dimensionalscalar products are lp =k 0ε−k z q and l ˜p =k 0ε+k z q .The imaginary part of the expression(28)is determined using Sokhotski˘ı’s formula1x−iπδ(x),(29) where P signiﬁes a principal value.From Eqs.(28)and(29)we obtain on the mass shellIm M=m2e2±k zτ 1/2.(30)Hereε±are the roots of the equations l2−2ωε±2k z q=0.¿From Eqs.(17),(24),and(30)weﬁnd the ratew M=1πτλdx 1τ−cosh2(x+ψ) .(32)Here the substitution of the variableε→x was used:ε=m e cosh x and q=m e sinh x,and the parametersλandψ,deﬁned ascoshλ=µω,(33)were introduced.The integral(32)can be expressed in terms of elementary functions.We shall conﬁne our attention below to the limiting cases that are of interest for astro-physical applications.6.For an axion on the mass shelll2=4m2eτ=ω2−k2z=m2a+k2⊥>0,(34) and the condition(14)gives k2⊥≪h,so that exp(−k2⊥/2h)≃1.We note that the imag-inary part of the polarization operator is formed by the contribution of real electrons and positrons,and the expression for it holds under the weaker condition k2⊥<2h.Therefore the exponential factor can be retained in Eq.(27).Forτ≪1(substantially below the threshold of the decay process a→e−e+),weﬁnd from Eqs.(25),(32),and(17)ΠR=Π(F)R +Π(M)=−αaH0τ(2−ν+−ν−).(35)Hereν±=tanh(λ±ψ)=νω±k zµ 21/2.We note thatΠR<0and if the axion moves in the direction of theﬁeld H(k⊥=0),then according to Eqs.(34)and(35)ΠR→0in the limit of a massless axion(m a→0).At high energies(τ≫(µ/m e)2≫1)we obtain for the polarization operator the asymp-totic representationΠR=αaH0 lnτ m eπeH ln k⊥2 ,(36)and it does not depend of the electron mass m e as it should be in this limit.Let us write the dispersion relation(7)in the formω2=k2⊥+k2z+m2a+ΠR(k).(37)It follows from Eqs.(35)–(37)that in a magnetized medium a radiative shift of the axion mass is generated—a dynamic mass,whose square,according to the deﬁnition in Ref.15, isδm2a=ReΠR.Forτ 1andµ/m e≫1we obtain the estimateδm a∼g ae m e H1013G 1/2eV.(38) For g ae∼10−13(Refs.4and10)and H 1017G(suchﬁelds18,19and even H∼1018−1020 G(Ref.20)can exist in the interior regions of neutron stars),Eq.(38)givesδm a 10−5 eV.The chemical potentialµof a degenerate gas of electrons occupying the ground-state Landau level(n=0)in a magneticﬁeld is related with the electron density n e by the well-known relationhp Fn e=µ2−m2e is the Fermi momentum.Writing Eq.(12)in the formH2 p Fλ−3e2π2 Hλe=1/m e is the electron Compton wavelength.For H=2·1017G Eqs.(40)and(41) give p F<50MeV and n e<1036cm−3.Next,let T∼1010K∼1MeV and k⊥ T.Then the conditions(11),(12),and(14)can be satisﬁed and the estimate(38)can be justiﬁed.In summary,under the conditions of strongly magnetized neutron stars a dynamic axion mass,which can fall within the existing limits on the axion mass3,4,12—10−5eV m a 10−2 eV—is generated.Thereforeδm a∼m a and the dispersion relation(37)diﬀers appreciably from the vacuum relation(k2=m2a).This must be taken into account,for example,when investigating the resonant conversion of a plasmon into an axion(γ→a)in a magneticﬁeld as a result of the crossing of the corresponding dispersion curves(as already noted above, this process inﬁelds H≪H0and in the absence of the direct coupling(1)was studied in Ref.12).We also note that the rate(27)of the decay a→e−e+in a magneticﬁeld has11a square-root threshold singularity(asτ→1+0).This singularity can be removed by taking into account accurately the dispersion law of an axion near threshold,and the decay rate is found to beﬁnite:13w∼m e(αa H/H0)2/3.A detailed analysis of the same threshold singularity(of cyclotron resonance)in a magneticﬁeld and its elimination for the photon decay process(γ→e−e+)was given earlier in Ref.21,where,speciﬁcally,it is underscored that the indicated singularity can be explained by the quantization of the phase space of charged particles in a magneticﬁeld.12N.V.Mikheev,G.Raﬀelt,and L.A.Vassilevskaya,Phys.Rev.D58,055008(1998);E-print archive hep-ph/9803486.13N.V.Mikheev and L.A.Vassilevskaya,Phys.Lett.B410,203(1997).14N.V.Mikheev and L.A.Vassilevskaya,Phys.Lett.B410,207(1997);L.A.Vassilevskaya,N. V.Mikheev,and A.Ya.Parkhomenko,Yad.Fiz.60,2224(1997)[Phys.At.Nuclei60,2041 (1997)].15A.V.Borisov,A.S.Vshivtsev,V.Ch.Zhukovski˘ı,and P.A.´Eminov,Usp.Fiz.Nauk167,241 (1997)[Physics–Uspekhi40,229(1997)].16V.V.Skobelev,Izv.Vyssh.Ucheb.Zaved.,Fiz.,No.10,142(1975);V.V.Skobelev,Doctoral Dissertation in Physicomathematical Sciences(MIIGAiK,Moscow,1982).17V.B.Berestetski˘ı,E.M.Lifshitz,and L.P.Pitaevski˘ı,Quantum Electrodynamics(Pergamon Press,New York,1982)[Russian original,Nauka,Moscow,1989,p.563].18I.M.Ternov and O.F.Dorofeev,Fiz.´Element.Chastits At.Yadra25,5(1994)[Phys.Part. Nuclei25,1(1994)].19M.Bocquet,S.Bonazzola,E.Gourgoulhon,and J.Novak,Astron.Astrophys.301,757(1995). 20D.Bandyopadhyay,S.Chakrabarty,and S.Pal,Phys.Rev.Lett.79,2176(1997).21A.E.Shabad,Tr.FIAN192,5(1988).Translated by M.E.Alferieﬀ13。