Symmetric boundary knot method
3 有限差分法基础
尺度的比值。上式变为： u j
1 un un j j
t
c
n un j u j 1
x
o
(FTBS 格式)
当 c 0 为迎风格式 （2）仍然采用线性插值，但取 A、C 两点进行插值
uD u A
uC u A x ct 2x cr n 1 1 n un u n u j 1 u n j j 1 u j 1 j 1 2 2 1 1 n n un u n j j 1 u j 1 un j 1 u j 1 2 c 0 t 2x
—Lax 格式
（3）仍然采用线性拟合，采用 B、C 点外插：
un un uC uB j 1 j n 1 n ct u n cr u n un uD uP uB ct u j u j j j 1 j x x
2
（4）若设未知量 u 在 P 的领域满足二次曲线分布，即： u x ao a1 x a2 x
uD uB
uC u A u u 2u 2 ct A C 2 B ct ，即： 2x 2x
4
1 un un j j
ct 1 ct ct uB u A 1 u A 2uB uC x 2 x x ct n 1 ct ct n n n u j un j 1 1 u j 1 2u j u j 1 x 2 x x cr n cr 2 n n u u j 1 j 1 2 u j 1 2u nj u nj 1 2
n un j u j 1
FTBS：
t
1 un un j j
正倒向随机微分方程组的数值解法_赵卫东
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B-spline+techniques
9 11 13 15 17 17 19 20 22 22
25 27 27 29 30 32 32 34 35
IX
X 3.10 3.11 3.12 3.13 Simple C r joints Degree elevation Convergence under degree elevation Problems
B´ ezier- and B-spline techniques
Hartmut Prautzsch Wolfgang Boehm Marco Paluszny March 26, 2002
2
To Paul de Faget de Casteljau
Preface
Computer-aided modeling techniques have been developed since the advent of NC milling machines in the late 40’s. Since the early 60’s B´ ezier and Bspline representations evolved as the major tool to handle curves and surfaces. These representations are geometrically intuitive and meaningful and they lead to constructive numerically robust algorithms. It is the purpose of this book to provide a solid and unified derivation of the various properties of B´ ezier and B-spline representations and to show the beauty of the underlying rich mathematical structure. The book focuses on the core concepts of Computer-aided Geometric Design (CAGD) with the intent to provide a clear and illustrative presentation of the basic principles as well as a treatment of advanced material, including multivariate splines, some subdivision techniques and constructions of arbitrarily smooth free-form surfaces. In order to keep the book focused, many further CAGD methods are excluded. In particular, rational B´ ezier and B-spline techniques are not addressed since a rigorous treatment within the appropriate context of projective geometry would have been beyond the scope of this book. The book grew out of several courses taught repeatedly at the graduate and intermediate under-graduate levels by the authors at the Rensselaer Polytechnic Institute, USA, the Universities of Braunschweig and Karlsruhe, Germany, and the Universidad Central de Venezuela. These courses were taught as part of the curricula in mathematics and computer sciences, and they were regularly attended also by students from electrical and mechanical engineering, geophysics and other sciences. For the careful proofreading of parts of the manuscript, we like to thank Stefan Bischoff, Bernhard Garz, Georg Umlauf, Claudia Bangert and Norbert Luscher. Especially, we thank Christoph Pennekamp and Natalie Spinner for preparing the LaTeX file and Bernd Hamann for his critical, thorough and final proofreading. Wolfenb¨ uttel, Caracas, Karlsruhe, Wolfgang Boehm Marco Paluszny Hartmut Prautzsch
数学家范德蒙生平
Alexandre-Théophile VandermondeBorn: 28 Feb 1735 in Paris, FranceDied: 1 Jan 1796 in Paris, FranceArticle by:J J O'Connor and E F RobertsonMarch 2001Edited by XiaJingbo, mail to: xjb@ Alexandre-Theophile Vandermonde's father was a medical doctor who was originally from Landrices but had spent 12 years in the Orient. He had set up a medical practice in Paris and was working there as a doctor when his son Alexandre-Théophile was born. He did not encourage his son to follow a medical profession but rather encouraged him to take up a career in music. Certainly he was not interested in mathematics when he was young. Alexandre-Théophile was awarded his bachelier on 7 September 1755 and his licencie on 7 September 1757.His first love was music and his instrument was the violin. He pursued a music career and he only turned to mathematics when he was 35 years old. It was Fontaine des Bertins whose enthusiasm for mathematics rubbed off on Vandermonde. Perhaps surprisingly he was elected to the Académie des Sciences in 1771 with little evidence of his mathematical genius other than his first paper which, although he was not a member at the time, was read to the Academy in November 1770. However, he did make quite a remarkable contribution to mathematics in this paper and three further papers which he presented to the Academy between 1771 and 1772. These four papers represent his total mathematical output and we will discuss their content below together with the views of a number of historians of mathematics on his contribution.Vandermonde's election to the Académie des Sciences did motivate him to work hard for the Academy and to publish other works on science and music. In 1777 he published the results of experiments he had carried out with Bézout and the chemist Lavoisier on low temperatures, in particular investigating the effects of a very severe frost which had occurred in 1776. Ten years later he published two papers on manufacturing steel, this time joint work with Monge and Bertholet. The aimof this research was to improve the steel used for bayonets but experimenting with different mixtures of iron and carbon. That he work closely with Monge reflected the fact that the two were very close friends, in fact he so close that he was known as femme de Monge.In 1778 Vandermonde presented the first of a two part work on the theory of music to the Académie des Sciences. The second part was presented two years later. This work Système d'harmonie applicable à l'état actuel de la musique did not propose a mathematical theory of music as one mighthave expected from someone who was an expert in both fields. On the contrary the aim of the work was to put forward the idea that musicians should ignore all theory of music and rely solely on their trained ears when judging music. As one might expect this proved a controversial work with musicians being sharply divided as to whether they agreed with Vandermonde or not. Despite the opposition of many musicians at first, the ideas put forward by Vandermonde gained favour over the years and by the beginning of the nineteenth century the Académie des Sciences had moved music from the mathematical area to the arts area. It is worth repeating that it is strange that a mathematician of the highest rank should have argued against music as a mathematical art, a position it had held since the days of ancient Greece.Positions which Vandermonde held include director of the Conservatoire des Arts et Métiers in 1782 and chief of the Bureau de l'Habillement des Armées in 1792. In the same year of 1792 he sat with Lagrange on a committee of the Académie des Sciences which had to examine the violon harmonique, a newly invented musical instrument. He was involved with the École Normale, which was founded in October 1794, and was on the team designing a course in political economy. His friend Monge was also involved with the École Normale as were Lagrange and Laplace. However the establishment only operated for six months after it opened in the Muséum d'Histoire Naturelle in January 1795 before being closed down.Like Monge, Vandermonde was a strong supporter of the Revolution which began with the storming of the Bastille on 14 July 1789. The politics of Revolution in France long before this event had been so exciting for Vandermonde that it diverted him from a possible longer mathematical and scientific career. However the truth of the matter is that he suffered from poor health all his life and, but for this, he might well have been able to be highly involved in politics yet continue with mathematical and scientific activities.Perhaps the name of Vandermonde is best known today for the Vandermonde determinant. While it is certainly true that he made a major contribution to the theory of determinants, yet nowhere in his four mathematical papers does this determinant appear. It is rather strange, therefore, that this determinant should be named after him and several authors have puzzled over the fact for some time. Lebesgue's conjecture in [3] (first published in 1940) that it resulted for someone misreading Vandermonde's notation, and therefore believing that this determinant was in his work, seems the most likely.Vandermonde's four mathematical papers, with their dates of publication by the Académie des Sciences, were Mémoire sur la résolution des équations (1771), Remarques sur des problèmes de situation (1771), Mémoire sur des irrationnelles de différens ordres avec une application au cercle (1772), and Mémoire sur l'élimination (1772).The first of these four papers presented a formula for the sum of the m th powers of the roots of an equation. It also presented a formula for the sum of the symmetric functions of the powers of such roots. Neither of these were new having appeared in Waring's work shortly before but, although he was aware of this Vandermonde claimed, rightly in my [EFR] opinion, that his approach was sufficiently different to make publication of these results for a second time worthwhile. The paper also shows that if n is a prime less than 10 the equation x n - 1 = 0 can be solved in radicals. Jones writes in [1]:- ... Vandermonde's real and unrecognised claim to fame was lodged in his first paper, in which he approached the general problem of the solubility of algebraic equations through a study of functions invariant under permutations of the roots of the equation.Kronecker claimed in 1888 that the study of modern algebra began with this first paper of Vandermonde. Cauchy states quite clearly that Vandermonde had priority over Lagrange for this remarkable idea which eventually led to the study of group theory.In his second paper Vandermonde considered the problem of the knight's tour on the chess board. This paper is an early example of the study of topological ideas. Vandermonde considers the intertwining of the curves generated by the moving knight and his work in this area marks the beginning of ideas which would be extended first by Gauss and then by Maxwell in the context of electrical circuits.In his third paper Vandermonde studied combinatorial ideas. He defined the symbol[p]n = p(p-1)(p-2)(p-3)...(p-n+1)and[p]-n = 1/(p+1)(p+2)(p+3)...(p+n).He gave an identity for the expansion of [x + y]n and also proved thatπ/2 = [1/2]1/2.[-1/2]-1/2It is interesting to note that at this time no notation existed for n! yet with his notation Vandermonde had defined something more general. Clearly[n]n = n!The final of Vandermonde's four papers studied the theory of determinants. Muir [4] claims that because of this paper Vandermonde was:-The only one fit to be viewed as the founder of the theory of determinants.The reason for this strong claim by Muir is that, although mathematicians such as Leibniz had studied determinants earlier than Vandermonde, all earlier work had simply used the determinant as a tool to solve linear equations. Vandermonde, however, thought of the determinant as a function and gaveproperties of the determinant function. He showed the effect of interchanging two rows and of interchanging two columns. From this he deduced that a determinant with two identical rows or two identical columns is zero. Finally he gave a remarkably clever notation for determinants which has not survived.References for Alexandre-TheophileVandermonde1.P S Jones, Biography in Dictionary of Scientific Biography (New York 1970-1990).Articles:2.H Lebesgue, L'oeuvre mathématique de Vandermonde, Thales, recueil des travaux del'Institut d'histoire des sciences IV (1937-39), 28-42.3.H Lebesgue, L'oeuvre mathématique de Vandermonde, Enseignement Math. (2) 1 (1956),203-223.4.T Muir, History of determinants V olume 3 (1920).5.J H Przytycki, History of the knot theory from Vandermonde to Jones, in XXIVth NationalCongress of the Mexican Mathematical Society (México City, 1992), 173-185.6.J J Tattersall, Who put the 'C' in A-T Vandermonde?, Historia Math.15 (4) (1988),361-367.7.J J Tattersall, Vandermonde's contributions to the early history of combinatorial theory,Eleventh British Combinatorial Conference, Ars Combin.25 (1988), C, 195-203.。
汽车车身曲线曲面造型的数学方法
第二章 微分几何基础
汽车车身造型主要使用自由曲线和曲面，在讨论自由曲线曲面的理论和生成方法以前， 需要介绍计算切矢量、法矢量、二阶导矢、曲率等概念，这些概念在曲线曲面生成、计算、 拼合以及评价中都需要应用。
2.1 矢量与矢量函数
2.1.1 矢量
具有大小和方向的量成为矢量，也成为向量。力、力矩、速度、位移、动量、动量矩等 等都是矢量。 在几何学中， 矢量可以用空间的有向线段来表示， 例如 AB 表示空间一个矢量， 其长度 AB 表示矢量的大小，端点的顺序 A → B 表示该矢量的方向，该矢量记作 AB 或用 黑体 a 表示。 矢量的长度或大小又称为模，用 AB 或 a 表示。 在右手直角坐标系 {o; x, y , z} 中，o 表示坐标原点，i，j，k 分别表示沿 x，y，z 三个坐 标轴正方向的单位矢量。任何矢量 a 可表示为
1
为了保留 Bezier 方法的优点，克服其缺点，在 1972~1976 年间，Gordon、 Reinsenfeld、 Foresst 等人改用 B 样条基函数代替 Bezier 方法中的 Berstein 基函数，将这种改进的曲线曲 面建模方法称为 B 样条曲线。B 样条方法同样以逼近理论为基础，保留了 Bezier 方法的直 观性等优点，又弥补 Bezier 方法不便于拼接、不具备局部修改性等不足，成为当今自由曲 线曲面数学造型的重要的工具。
a 。 模等于 0 的矢量为零矢量， a
记为 0，零矢量式始点与终点重合的矢量。只有当两个矢量的分量分别相等时，该两个矢量 相等。 模和方向不变的矢量称为常矢量，模和方向变化的矢量称为变矢量。
2
2.1.2 矢量函数
若对应于 a ≤ t ≤ b 中的每一个 t 值，有一个确定的矢量 r ，则 r 为 t 的矢量函数，记为
纺织英语
名词索引α-螺旋构象α-helix conformationZ均分子量 Z-average molar massλ/4波长λ/4 wave-lengthHVI High Volume InstrumentFOY fully-oriented yarnOnion指数 Onion indexFASTKES-FOFDA(optical fiber Diameter Analyzer) Almeter 阿尔米特AFIS (Advanced Fiber Information System) A凹凸组织 pique weaves氨纶 urethane elastic fiber/spandex安全性 securityB巴厘纱 voile白棉 white cotton抱合力 cohesion force巴布长度 Barbu length包缠纱 fascinated yarn包覆纱 covered yarn包芯纱 core-spun yarn半线织物 semi-thread fabric伴纺 following spinning伴生物 concomitant比表面积 specific surface-area比应力 specific stress比热 specific heat比电阻 specific resistance哔叽 serge胞壁 cell wall保水率 water inhibition rate变形丝 textured yarn变形纱 texturized yarn变色纤维 color change fiber变异系数 coefficient of variance变化组织织物 fancy fabri薄膜法 membrane/film method波长谱图 wavelength spectrum波松分布 poission distribution波松定律 Poisson law波峰 wave peak波谷 valley波径指数 wave-diameter index波动数 petal number比表面积 specific surface area表观厚度 surface/apparent thickness表面结构 surface structure表皮细胞 cuticlar cell表面能 surface energy表面积 surface-area表面 surface表面干爽性 surface dry touch表面结构 suface structure表面轮廓 surface profile表面分析 surface analysis表面性质 surface character表面组份 surface component表面比电阻 surface apecific resistance表面散射光 surface scattered light表层 surface layer表面膜 surface membrane表面张力 surface tension表面能 surface energy丙纶 polypropylene fiber本色坯布 greige cloth本构方程 intrinsic equation编织物 braided fabric编织加工 braiding process编链组织 chain stitch structure标准线性固体力学模型 standard linear-solid model 并条 drawing玻璃纤维 glass fiber玻璃化温度 glass-transition temperature玻璃态 glassy state玻璃化转变 glass transition倍克线 Beckeline倍长纤维 multiple length staple fiber不匀率 irregularityC彩色棉 color cotton草棉 cotton长度 length长绒棉 long-staple cotton长丝纱 filament yarn长丝织物 filament yarn fabric长度分布 length distribution长度界限 length limit长度整齐度 length evenness缠贴性 knob & sticking property超细纤维 ultra-fine fiber超细纤维 superfine fiber超分子结构 supermolecular structure超长纤维 overlength staple fiber次表皮层 exo-cuticle差别化纤维 differential fiber差微摩擦效应 differential friction effect 初生层 primary layer初始模量 initial modulus醋酯纤维 acetate fiber成熟度 maturity成熟程度 maturity成型性 formability/moldability成形性 formability成熟度系数 maturity coefficient成形性 formation沉降弧 sinker loop扯边纱条样法 raveled- strip method产业用纺织品 industrial textiles尺寸稳定性 dimensional stability重组织 backed weaves绸 chou silk抽拔法 pull-out method纯纺织物 pure raw fabric纯纺纱线 pure yarn刺激 stimulate刺痒 scratchiness刺扎 stinging/prickle粗纺毛织物 woolen cloth粗花呢 fancy woolens粗糙度 roughness/asperity/harshness触觉评价 touch evaluation除杂 cleaning除臭 deodorization充满系数 filling coefficient串套 series loopD大衣呢 overcoating大众呢 popular cloth大麻 hemp打成麻 swingled hemp打结 knot strength动物纤维 animal fiber动态损耗模量 dynamic loss modulus动态弹性模量 dynamic elastic modulus动摩擦 kinetic friction动态磨dynamic abrasion动压法 dynamic pressure method涤纶 polyester fiber导电纤维 conductive fiber；electrically conductive fiber 导水 wicking导热系数 thermal conductivity导热系数 thermal conductivity单缝撕裂（舌形撕裂） single-rip or single-tongue tear低弹丝 low- elastic yarn滴定法 titration电阻 electrical resistance电阻测湿 moisture measurement of electrical resistance 电磁屏蔽纤维 electromagnetism screen fiber电容式测湿 electrical capacity-type moisture measure电磁屏蔽 electromagnetism shielding电阻率 resistivity电容式条干均匀度仪 capacitance evenness tester电子织物 electronic fabrics电磁辐射 electromagnetism radiation点燃点 ignite point点状 spot adherence多孔结构 geometric porosity多层多轴向针织物 multiplayer multiaxial knitted fabric 多轴向经编针织物 multi-axial warp knitted fabric带织物 narrow fabric定点摩擦 fixed-point friction定伸长弹性 elasticity of constant elongation定负荷弹性 elasticity of constant load定负荷 constant load定应变 constant strain灯心绒 corduroy顶破性质 bursting properties顶破强力 bursting strength缎 satin silks缎纹组织 satin or sateen weaves缎纹变化组织 satin derivative weaves等加负荷 constant rate of loading等速伸长 constant rate of elongation等长化纤 cut-stable fiber断裂比功 specific work of rupture断裂长度 breaking length断裂功 work of rupture断裂强度 tenacity；breaking tenacity断裂强力 breaking strength断裂伸长率 extension at break ；tensility断裂应力 breaking stress端毛羽 end hair对称摩擦 symmetric friction短纤维纱 staple fibre yarn ；staple yarns短纤维率 short fiber contentE二醋酯纤维 diacetate fiber二轴向斜交机织物 biaxial bias-interlaced woven fabric F富强纤维 polynosic rayon翻动磨 tumble abrasion复合磨 compound abrasion复合纱 complex yarn；composite yarn复合纤维 composite fiber复合纱 composite yarn复杂组织织物 compound-weave fabric复合织物compound fabric复模量 complex modulus分束纺纱 solospun缝纫线 sewing thread副皮质 para-cortex防紫外线纤维 ultraviolet resistant fiber芳纶 aramid fiber纺 plain habutai纺丝 spinning纺织纤维 textile fiber纺丝成网法非织造布 spun-laid nonwoven fabric仿麂皮织物 suede fabric仿旧整理织物 second-hand effect fabric防皱防缩整理 crease防辐射纤维 anti-radiation fiber resistant finish防霉整理 mildew resistant finish防蛀整理 insect-proof finish防污整理 stain resistant finish防辐射整理 radiation resistant finish防水性 waterproof performance防火 fire prevention防火织物 fire-proof fabric防火服 fire-fighting suit防护服 protective clothing/suit防污 anti-soil防霉 mould proofing防蛀 moth proofing防霉剂 anti-mildew agent防血液感染 blood-infectious protective防晒因子(SPF) Sun Protection Factor防紫外因子(UPF) UV Protection Factor放湿 moisture liberation放湿过程 moisture desorption process非洲棉 African cotton非对称摩擦 asymmetric friction非平衡态浸润 nonequilibrium wetting非周期性不匀 aperiodic unevenness非织造布 nonwoven fabric非纤维类物质 non-fiber substance飞数 step number幅宽 breadth/width浮线 welt/float辅结构 auxiliary/secondary structure附加不匀 additional irregularity法兰绒 flannel凡立丁 valitin分等 assortment, grading, ranking分子间结构 the inter-molecule structure分子内结构 the inner molecule structure分子结构 molecular structure分解点温度 decomposition temperature缝编法非织造布 stitch-bonded nonwoven fabric 3 蜂巢组织 brighton/honeycomb weave浮松组织 huckback weaves负荷－伸长 load - elongation curve府绸 poplin辐射 radiationG公制支数 metric count干法成网非织造布 dry-laid nonwoven fabric干法纺丝 dry spinning干燥率 drying rate干洗 dry cleaning干洗剂 dry-clean lotion干燥 drying概率 probability钢花呢 homespun刚柔性 stiffness and softness感官评定 organolrptic evaluation各向异性 anisotropic果实纤维 fruit fiber构成 constitution构型 configuration构象 conformation各向异性 anisotropy高湿模量粘胶 high wet modulus viscose高温高湿 high temperature and humidity高频加热 high-frequency heating高湿模量粘胶纤维 high wet modulus rayon高收缩纤维 high-shrinkage fiber高性能纤维 high performance fiber高弹态 high-elastic state高弹丝 high-elastic yarn高能辐射 high energy radiation股线 plied yarn ； ply yarn功能纤维 functional fiber根数加权长度 number weight length功能整理织物 functional-finished fabric功系数 work factor贡呢 venetian公定回潮率 official regain公制支数 metric count光泽 luster光电子条干均匀度仪 photoelectric evenness tester 光纤 optical fiber光敏变色纤维 phototropic fiber光辐射 light irradiation光致发光 photoluminescence光程差 opertical path difference工艺纤维 technical fiber工艺要求 technological requirements工业长丝 industrial filament各向同性 isotropy各向异性 anisotropy勾丝 snag/pulled thread勾接强度 loop strength规格 specification隔热性 thermal insulation隔音sound insulation隔距 gauge length葛 poplin grosgrain刺割 pierce耕犁作用 plough古香缎 suzhou brocadeH海军呢 navy cloth含水率 moisture content； percentage of water hold；moisture retention 含油率 value of oilness汉密尔顿指数 Hamilton index横向膨胀 transverse swelling横向观察 transverse observation横列 course横向 transverse厚度 thickness后整理 finishing后退角 back angle化学老化 chemical aging化学纤维 chemical fiber化学短纤 chemical short fiber化学溶解法 chemical dissolution化学粘合法 chemical bonding华达呢 gabercord花呢 fancy suiting花式线 fancy or novel yarn滑脱长度 slip length合成纤维 synthetic fiber环锭纱 ring spinning yarn灰棉 gray cotton混纤丝 combined filament yarn混纺纱线 blended yarn混纺纱 blended yarn混纺织物 blended-spun-yarn fabric黄棉 yellow cotton黄麻 jute红麻 red jute红外光谱法 infrared spectroscopy /IR ；infrared absorption specturm红外光谱 infrared absorption spectrum烘箱法 oven drying method海岛棉 Sea Island cotton横贡 sateen横向形态 transverse morphology虎木棉 Toramomen缓弹性变形 primary creep缓弹变形 slow-elastic deformation / delayed deformation 回复角 recovery angle回弹性 elastic resilience回潮率 regain; moisture regain活泼率 lively rateJ极化polarization极限氧指数 limiting oxygon index/(LOI)极光效应 polar lights effect极限不匀 limit irregularity基原纤proto-fibril；elementary fibril急弹性变形immediate elastic deformatio基本风格 basic style剪切变形 shear deformation剪切刚度 shearing rigidity家用纺织品 household textiles降解 degradation结构纱 construction yarn结构系数structural factor接触角法 contact angle method截面加权长度 area-weight length聚集态 state of aggregation聚合度 degree of polymerization聚酯纤维 polyester fibre聚酰胺纤维 polyamide fibre/nylon聚合物挤出成网法非织造布 polymer extruded nonwoven fabric 聚乳酸纤维 polylactic fiber拒水 water repellent拒水整理 water repellent finish拒油整理 oil-repellent finish间接吸收 indirect absorption间接测试 indirect measure巨原纤 macrofibril集聚纺纱 compact yarn加捻 twisting卷曲 crimp卷绕 winding卷曲数 crimp number卷曲比 crimp ratio卷曲率 crimp ratio结晶区 crystalline zone结晶度 degree of crystallinity近程 short range静摩擦 static friction静电电位序列 static potential sequence静电纺 electrostatic spinning静电 electrostatic静压法 hydrostatic pressure test锦 brocades锦纶 polyamide腈纶 acrylic fiber ,polyacrylonitrile fiber精纺毛织物 worsted cloth槿麻 Ambari hemp经编织物 warp knitted fabric金属纤维 metallic fiber浸液法 tincture/immersion test浸渍法非织造布 impregnating bonded nonwoven fabric 浸润 immersional wetting浸润滞后性 wetting hysteresis浸渍法 impregnation均匀系数 wave evenness交织织物 mixed fabric绞盘法 capstan method机织物 woven fabric机织纱 weaving yarn加压厚度 thickness under pressure交叉 intersecting交织规律 intersecting pattern交织角 weaving angle结构厚度 structure thickness结构相 structural phase紧度 tightness经编针织物 warp-knitting fabric经缎组织 lined satin经密 end spacing/ warp sett经平组织 locknit stitch / charmeuse纠缠 kink/ entanglement卷边性 curling热机械变形 thermo-mechanical deformation机械加固法 mechanical reinforcing机械成网非织造布 mechanical-laid nonwoven fabric 机械波不匀 mechanical wave unevenness锯齿棉 saw ginned cotton绢纺 silk spinning茧 cocoon茧丝 bave茧丝率 bave yield茧丝长 bave length接触角 contact angle剑麻 agave蕉麻 Manila hemp剑杆引纬 rapier wefting交联 crosslinking镜面反射 mirro reflection介电常数 dielectric constant；relative permittivity 介电损耗 dielectric loss介电损耗因子 dielectric loss factor介电损耗正切 dielectric loss tangent绢 taffeta几何转移 geometric migration解捻法 untwist method解捻 detwisting径向分布 radial distribution绝热率 heat insulation rate激光细度仪 Sirolan-Laser scanK卡其 khaki drill开松 opening抗熔孔性 melting-resistant抗静电整理 antistatic finish抗静电纤维 antistatic fiber抗起毛起球整理 anti-pilling tendency finish抗静电性 antistatic property抗菌防臭纤维 anti-bacterial fiber抗皱性 wrinkle resistance抗弯长度 bending length抗刺割性 pierce resistance抗切割度 degree of pierce resistance抗菌 antibacterial抗微生物 antimicrobial防病毒 anti-virus抗螨 anti-acarid宽度 width宽幅织物 broad fabric矿物纤维 mineral fiber克罗值 CLO value客观评价 objiective evaluation孔隙 porosity空隙 voidage/porosity空隙率 porosity可燃性 ignitability; combustibility可靠性 reliability可加工性machinability可纺性 spinnability可缝性 sewability可变形性 texturing property客观检验 objective testing客观评价 objective evaluation空气变形 air texture空间厚度 geometric thickness跨距长度 space-length扩展 extend/spread扩展速度 spreading rate扩展比 expansion ratio扩展取向度 orientation in expansion抗静电处理antistatic treatment抗皱anti creaseL拉伸曲线 tensile curve拉伸试验 tensile test拉伸性能 tensile property拉伸疲劳 tensile fatique罗 leno silk罗布麻 apocynum落锤法撕裂 falling pendulum tear骆驼绒 camel down氯纶 polyvinyl chloride fiber两型毛 heterotypical fiber陆地棉 uplands cotton力学模型 mechanical model力学性质 mechanical property立体织物 cubic fabric立体机织物 cubic woven fabric立体针织物 cubic knitted fabric立体编织物 cubic braided fabric立体非织造布 cubic nonwoven fabric利萨如曲线Lissajou curve联合组织织物 combined-weave fabric绫 twills棱脊 strip edge临界捻系数 critical twist factor;critical twist coefficient 帘子线 cord, cord yarn龙卷风形 cyclone-like罗纹组织 ribbed stitch螺旋 helix罗拉法 roller measurement链节 chain unit链段 chain segment ； segment链节 chain unit流动温度 flow temperature磷光 phosphorescenceM马海毛 mohair马克隆值 macronaire value马丁代尔 Martindale马丁代尔公式 Martindale formula麻纱织物 dimity麦尔登 melton美感系数 aesthetic perception coefficient美感指数 aesthetic index毛织物 wool fabric毛巾组织 terry weaves毛型纱线 wool type yarn毛羽 hairiness；hair毛细扩展 capillary expanding毛丛 wool staple漫反射 diffusion reflection棉织物 cotton fabric膜裂法非织造布 film-splitting nonwoven fabric膜结构用 film-structure摩擦 friction豪特长度 Hauteur length摩擦性能 friction property摩擦系数 frictional coefficient磨损 abrasion磨损性 wear-resistance磨毛整理织物 sanded fabric）密度 density/ specific mass膜状 membrane/film adherence 棉哔叽 cotton serge 绵绸 noil cloth毛纤维 wool fiber毛细现象 capillary phenomenon毛羽 hair毛羽指数 hair index绵羊绒 sheep cashmere牦牛绒 yak cashmere木棉 KapokN纳米尺度 nanoscale呢 crepons粘胶 viscose，rayon粘均分子量 viscosity-average molar mass粘弹性 viscoelastic property粘附 adhere/adhesion粘结 cohere/caking粘着功 adhesion work粘滑现象 stick slip phenomenon粘流态 viscous-flow state耐热性 heat endurance； heat-resistant耐久性 durability耐刺割性 stab-resistant and cut-resistant property 牛津纺 oxford女式呢 ladies cloth捻度 twist捻幅 twisting length捻回角 twist angle捻缩 twist shrinkage捻缩率 percentage of twist shrinkage捻系数 twist factor ；twist multiplier捻向 direction of twist内不匀 inner unevenness内表皮层 endo-cuticle内旋转 internal rotation内部反射光 inner reflected light扭转性质 torisonal property暖体假人 thermal manikinP派力司 palace泡泡纱 crimp fabric排列密度 packing density喷淋法 spraying method膨胀 dilatation/expansion /swelling匹长 piece length破斜纹 broken twill片梭引纬 projectile wefting片晶 lamellar crystal片段长度 segment length泡沫法非织造布 foam-bonded nonwoven fabric喷水引纬 water-jet wefting喷气引纬 air-jet wefting喷洒法非织造布 spray-bonded nonwoven fabric疲劳性质 fatique property疲劳寿命 fatique lifetime疲劳 fatigue疲劳极限 fatigue endurance limit漂白织物 bleached fabric平磨 flat abrasion平方米重 weight per square meter平纹组织 plain weave平行纤网 parallel fiber web平布 plain cloth平纹组 plain weave平纹变化组织 plain derivative weaves平衡回潮率 equilibrium regain平衡态浸润 equilibrium wetting平面偏振 plane polarization平均长度 mean length品质 quality品质评定 quality evaluation品质支数 quality number品质要素 quality factor普通粘胶纤维 Rayon皮棍棉 roller ginned cotton皮质细胞 cortex cell皮芯 Skin-core铺展 spreading铺展系数 spreading factor频数 frequencyQ气流成网非织造布 air-laid nonwoven fabric 气相色谱法 chromatography of gasses/GC气流仪 air-flow meter起毛 fuzzing起球 pilling起毛组织 pile weaves起毛起球 fuzzing and pilling起拱变形 bulging deformation乔其纱 crepe georgette枪毛 over hair前进角 forward angle强化点 strengthening point强力利用率 strength efficiency强伸性 strength and elongation properties 切片 skiving, sectioning切割条样法 cut-strip method切割 cutting切割系数 cutting factor亲水基团 hydrophilic group清花 scotching, picking, blowing屈服点 yield point屈曲波幅 crimp amplitude屈曲波高 crimp height曲磨 flex abrasion取向 orientation取向度 orientation degree取向因子 orientation factor去污 soil removal牵伸 drafting, drawing牵伸波不匀 draft wave irregularity圈毛羽 loop hair圈捻 loop twist圈干 needle loop圈高 course spacing圈距 lay/ knit stitchR燃烧温度 combustion/burn temperature燃烧时间 combustion/inflammation time燃烧性 inflammability燃烧特征 burning characters热传导 thermal transmittance热定形 thermosetting热变形 thermo texturing热塑性 thermo-plasticity热收缩 thermo shrinkage热稳定性 thermal-stability热风（烘）粘合法非织造布 hot-air bonded nonwoven fabric 热粘合法 thermo-bonded nonwoven热流变形纱 thermal flow textured yarns热轧法非织造布 calender-bonded nonwoven fabric热敏变色纤维 thermochromatic fiber热粘合 heat bonded热塑性 thermo-plasticity热定形 heat setting热湿舒适 thermalhydro comfort热舒适性 thermal comfortability热阻 thermal resistance热稳定性 thermal stability绒面组织 suede/face/velours stitch柔软性 softness柔软 softness柔软剂 softening agnet染色织物 dyed fabric染色牢度color fastness绒 velvet熔喷法非织造布 melt-blown nonwoven fabric人造纤维 man-made fiber人体组织工程human histology engineering韧皮纤维 bast fiber熔融温度 melt temperature熔融纺丝法（熔体纺丝） melt spinning溶液纺丝法 solution spinning蠕变 creep润湿 wetting弱环定律 weak-link theoryS啥味呢 worsted flannel三轴向机织物 triaxial woven fabric三轴织机 triaxial loom三维立体结构 three-dimensional cubic d structure三维编织结构 three-dimensional braid structure三维空间 three dimensional space山形斜纹 angled/reverse twill伸缩性 dilation/ expand and contract生理学 physiology生物防护 biology protection生丝 raw silk生物相容性 biocompatibility生物可降解 biodegradability声强 acoustics intensity实体厚度 substance/entity thickness实际回潮率 actual regain； measured moisture regain 时间依赖性 time dependence使用寿命 life time湿冷 clammy湿膨胀 hygral expansion湿法纺丝 wet spinning湿法非织造布 wet-laid nonwoven fabric石棉 asbestos视觉评价 visual evaluation手感 handle手扯长度 hand staple松弛收缩 relaxation shrinkage缩水 shrinkage塑性变形 plastic deformation双反面组织 purl stitch双罗纹组织 interlock stitch双轴拉伸 double direction tensile tester水刺固结 water needle binding水解 hydrolysis随机排列 random arrangement梳片法 comb sorter双幅织物 double-width fabric双层组织 double-layer weaves双宫绸 doupioni pongee双边分布 bilateral distrubiton双折射 birefringence双折射率 specific birefringence萨那蒙补偿 senamönt compensation闪光效应 glitter effect散射 scattering色织物 yarn-dyed fabric纱 gauze silk纱线 yarn, thread纱织物 single fabric纱罗组织 gauze and leno weaves纱疵 yarn defects/faults纱线断裂机理 breakage mechanism of yarn纱线捻度 yarn multiplier纱线识别 yarn identification纱线品质 yarn quality纱线强力利用率 strength efficiency for yarn纱线交织阻力 yarn interwave resistance伸直长度 straight length收缩因素 shrinking facto收缩不匀 shrinkage unevenness随机不匀 random unevenness山羊毛 Cashmere hair山羊绒 cashmere桑蚕丝 mulberry silk死毛 kempy wool撕裂性能 tearing property撕裂强力 tearing strength撕裂三角区 delta region of tearing三醋酯纤维 triacetate fiber丝纤维 silk fiber丝织物 silk fabric丝光棉 mercerized cotton缫丝率 silk reeling yield射流喷网法非织造布 spun-laced nonwoven fabric手感目测 handle and eyeballing；handle and visual measurement舒适感 comfortability数均分子量 number-average molar mass 髓质层 medulla束纤维 fiber bundle束纤维强力 strength of fiber bundle塑性变形 plastic deformation锁结 lockingT太阳能服装 solar energy textile天然纤维 natural fiber陶瓷纤维 ceramic fiber兔毛 cony hair天丝 tencel弹性纤维 elastic fiber弹性结构 elastic structure弹性回复 elastic recovery弹性模量 Young's modulus弹性回复率 elastic recovery弹性 elastic performance碳纤维 fibrous carbon特种动物纤维 Special animal wool特征鉴别 characteristic identification 特克斯 tex退捻加捻法 twist and untwist method炭化毛 carbonized wool体积比电阻 specific volume resistance 体积分数 volume fraction梯形撕裂 trapezoid tear土工织物 geo-textile贴服系数 fitting factor团块状 agglomerate脱散性 ladderation/raveling property 绨 bengaline条格组织 stripe and check weaves调湿 conditioning透孔组织 openwork weaves透光性 transmission property透气率 permeating rate透气性 permeability透湿汽性 moisture vapor transimi7透湿指数 moisture permeability index 透水性 water permeability透通性 transparent涂层 coating涂层织物coating fabric凸条组织 Bedford cord weavesW维纶 vinylon，polyvinyl alcohol fiber纬编织物 weft-knitted fabric纬编针织物 weft-knitting fabric纬密 pick/weft/filling density纬平组织 weft plain stitch纹面组织 face weave伪浸润 pseudo-wetting微波 microwave微波加热 microwave heating微原纤 microfibril微尺度 micro-scale微环境 microenviroment微气候 microclimate外表皮层 epi-cuticle外观指标 index of aspect外观疵点outer defect外不匀 external irregularity弯曲 bending弯曲刚度 flexural rigidity ；bending rigidity 弯曲疲劳 bending fatique弯曲长度 bending length弯曲模量 bending modulus无机纤维 inorganic fiber无序区 amorphous region无定形 disorder无规线团 random coil网目组织 distorted thread effect weaves纹织物 jacquard-weave fabric温度 temperature物理指标 index of physics熨烫ironingX细绒棉 medium cotton细布 fine plain细胞间质 CMC/cell membrane complex细度不匀 fineness unevenness吸水吸湿纤维 absorbency fiber吸附 absorption吸收水 absorption water吸湿性 hydroscopicity吸湿指标 adsorption index吸湿等湿等压线 adsorption iso-humidity and isobar line 吸湿等温线 adsorption isotherm吸湿剂 moisture adsorbent吸湿微分热 differential heat of sorption吸湿滞后 hydroscopic hysteresis吸湿平衡 equilibrium absorption of water吸湿膨胀 hygroscopic expasion吸湿积分热integral heat of sorption吸湿法 moisture adsorption吸湿 absorbing moisture吸湿机理moisture sorption mechanism吸湿过程 moisture sorption process吸声 sound absorption系统鉴别 systematical identification洗涤 washing洗涤标志washing symbols纤维 fiber纤维塞 fiber plug纤维疵点 defect of fiber纤维材料fibrous material纤维表面 fiber surface纤维鉴别 fiber identification纤维网 fiber web/sheet纤维强力利用率 strength efficiency for fiber纤维集合体 fiber assembly纤维细度 fineness纤维形态 fiber morphology纤度 size/titer线圈 stitch/ coil/loop线圈长度 stitch/loop length线圈歪斜 loop spirality相系数 phase coefficient斜纹组织 twill weave显微镜观察法 microscopic observation显微观察 microscopic examination香味纤维 perfumed fiber相变纤维 phase-change fiber相位差 phase difference相对湿度relative humidity相变材料 phase change materials蓄热纤维 Thermal storage fiber洗净毛 clean wool洗涤剂 washing agent蓄热纤维 thermal storage fiber须丛曲线 tuft curve小幅织物 narrow-width fabric小提花组织 Dobby design weaves绡 sheer silks线织物 ply-yarn fabric线密度 linear density斜纹组 twill weave斜纹变化组织 twill derivative weaves 芯吸 wicking芯吸高度 wicking height心理学 psychology性状 behaviour and profile；property and morphology形态 morphology/contour形貌 morphology形状记忆 shape memory形态结构 morphological structure形状系数 shape factor悬垂系数 drape coefficient悬垂度 drape factor学生呢 student cloth循环次数 cycle indexY亚麻 flax亚麻织物 flax亚洲棉 Asiatic cotton压缩性质 compressional property压缩性能 compression property轧工质量 quality of roll颜色 color药品着色法 staining test应力松弛 stress relaxation应力－应变 stress – stain隐身织物 stealthy fabric荧光 fluorescence叶纤维 leaf fiber羊驼绒 alpaca异形 prifiled异形纤维 profile fiber异纤维 foreign fiber易护理 easy care易去污 soil release一端整齐 alignment end远红外纤维far-infrared fiber远程 long range衣分 ginning outturn衣用纺织品 apparel fabric翼形撕裂 wing tear印花织物 printed fabric印花粘合法非织造布 print-bonded nonwoven fabric 延展线 underlap/link英制支数 English count液态水 liquid water原纤 fibril原组织织物 elementary-weave fabric缨状微胞 fringed micelle缨状片晶 fringed lamellar crystal缨状原纤 fringed fibril预调湿 pre-conditioningZ主体长度 major length杂质 impurity造型系数 multiwave折皱回复角 crease recovery angle折边磨 fold abrasion植物纤维 plant fiber滞后常数 delayed constant种子纤维 seed fiber再生纤维 regenerated fiber再生纤维素纤推 regenerated cellulose fiber再生蛋白质纤维 regenerated protein fiber再生淀粉纤维 regenerated starch fiber再生角蛋白 regenerated keratin再生丝蛋白 regenerated silk fibroin胀破 break in distention抓样法 grasp method针编弧 needle loop/ top arc针刺固结 needling binding针织物 knitting fabric纵行 wale纵向 longitudinal毡缩性 felting shrinfage毡化 felting中空纤维 hollow fibre纵向形态 longitudinal morphology纵向观察 longitudinal observation苎麻 ramie竹纤维 bamboo fiber阻燃纤维 flame retardant fiber转基因棉 transgenic cotton转曲 convolution/twist柞蚕丝 tussah silk蜘蛛丝 spider silk转曲 convolution窄幅织物 narrow fabric折皱整理织物 crease-resist finished fabric折射率 refraction index质量比电阻 mass specific resistance质量要素 element of quality质谱法 mass spectrometry针刺法非织造布 needle-punched nonwoven fabric针织成型产品 shaped knitwear针织坯布 gray knits针织物 knitted fabric针织物的歪斜 spirality property of knitted fabric 针织物的卷边 lapel of knitted fabric蒸发法 evaporation test智能防护 intelligent protection智能纺织品材料 intelligent/smart textiles制服呢 uniform cloth织物 fabric织锦缎 satin brocade织缩率 crimp contraction/percentage织物组织 fabric weave织物的纰裂 unwoven of fabric织物的耐疲劳性 fabric fatigue-proof织物的耐老化性 fabric resistance to aging织物的钩丝性 fabric snagging property织物的耐磨损性 fabric abrasion resistance织物的耐久性 fabric durability织物的抗皱性 fabric wrinkle resistance织物的褶裥保持性 pleat retention of fabric织物的静态悬垂性 fabric static drape织物的起球性 fabric pilling property织物风格 fabric style织物指纹图 fabric fingerprint织物控制图 fabric contral chart织物手感 fabric handle织物保养 fabric care织物要素fabric elements织物纹理 fabric grain织物的尺寸稳定性 fabric dimensional stability织物的缩水性 fabric water shrinkage property 织物结构fabric structure织物鉴别fabric identification张力转移 tension distribution直接吸收 direct absorption直贡 twilled satin直接测量 direct measurement直径 diameter重量偏差 weight deviation重均分子量 weight-average molar mass直方图 histogram直径不匀 diameter unevenness中段切断称重法 cut-weight measurement重量加权长度 mass-weight length周期性不匀 periodic irregularity转移 migration绉 crepes绉组织 crepe weaves苎麻织物 ramie正皮质 ortho- cortex正切损耗 loss tangent正反射光 main reflected light自然长度 natural length转曲 conversion真空干燥vacuum drying主观评价 subjiective evaluation噪音 noise自适应 self adapted紫外线 ultraviolet radiation组织点 interlacing/crossing point组织循环 repetition of weave组合原位测量 composite-in situ measurement 阻燃整理 flame retardant finish阻燃 flame retardant阻燃整理 flame-retardant finish阻燃剂 flame-retardant agent阻燃涂层 flame-retardant coating阻燃纤维 flame-retardant fiber。
Matlab工具箱数学词汇英汉对照表
附录Ⅱ工具箱数学词汇英汉对照表Ⅱ.1 概率论与数理统计词汇英汉对照表Aabsolute value 绝对值accept 接受acceptable region 接受域additivity 可加性adjusted 调整的alternative hypothesis 对立假设analysis 分析analysis of covariance 协方差分析analysis of variance 方差分析arithmetic mean 算术平均值association 相关性assumption 假设assumption checking 假设检验availability 有效度average 均值Bbalanced 平衡的band 带宽bar chart 条形图beta-distribution 贝塔分布between groups 组间的bias 偏倚binomial distribution 二项分布binomial test 二项检验Ccalculate 计算case 个案category 类别center of gravity 重心central tendency 中心趋势chi-square distribution 卡方分布chi-square test 卡方检验classify 分类cluster analysis 聚类分析coefficient 系数coefficient of correlation 相关系数collinearity 共线性column 列compare 比较comparison 对照components 构成，分量compound 复合的confidence interval 置信区间consistency 一致性constant 常数continuous variable 连续变量control charts 控制图correlation 相关covariance 协方差covariance matrix 协方差矩阵critical point 临界点critical value 临界值crosstab 列联表cubic 三次的，立方的cubic term 三次项cumulative distribution function 累加分布函数curve estimation 曲线估计Ddata 数据default 默认的definition 定义deleted residual 剔除残差density function 密度函数dependent variable 因变量description 描述附录II 工具箱数学词汇英汉对照表·535·design of experiment 试验设计deviations 差异df.(degree of freedom) 自由度diagnostic 诊断dimension 维discrete variable 离散变量discriminant function 判别函数discriminatory analysis 判别分析distance 距离distribution 分布D-optimal design D-优化设计Eeaqual 相等effects of interaction 交互效应efficiency 有效性eigenvalue 特征值equal size 等含量equation 方程error 误差estimate 估计estimation of parameters 参数估计estimations 估计量evaluate 衡量exact value 精确值expectation 期望expected value 期望值exponential 指数的exponential distributon 指数分布extreme value 极值Ffactor 因素，因子factor analysis 因子分析factor score 因子得分factorial designs 析因设计factorial experiment 析因试验fit 拟合fitted line 拟合线fitted value 拟合值fixed model 固定模型fixed variable 固定变量fractional factorial design 部分析因设计frequency 频数F-test F检验full factorial design 完全析因设计function 函数Ggamma distribution 伽玛分布geometric mean 几何均值group 组Hharmomic mean 调和均值heterogeneity 不齐性histogram 直方图homogeneity 齐性homogeneity of variance 方差齐性hypothesis 假设hypothesis test 假设检验Iindependence 独立independent variable 自变量independent-samples 独立样本index 指数index of correlation 相关指数interaction 交互作用interclass correlation 组内相关interval estimate 区间估计intraclass correlation 组间相关inverse 倒数的iterate 迭代Kkernal 核Kolmogorov-Smirnov test柯尔莫哥洛夫-斯米诺夫检验kurtosis 峰度MATLAB 6.1与工程数学应用指南（下册）·536·Llarge sample problem 大样本问题layer 层least-significant difference 最小显著差数least-square estimation 最小二乘估计least-square method 最小二乘法level 水平level of significance 显著性水平leverage value 中心化杠杆值life 寿命life test 寿命试验likelihood function 似然函数likelihood ratio test 似然比检验linear 线性的linear estimator 线性估计linear model 线性模型linear regression 线性回归linear relation 线性关系linear term 线性项logarithmic 对数的logarithms 对数logistic 逻辑的lost function 损失函数Mmain effect 主效应matrix 矩阵maximum 最大值maximum likelihood estimation 极大似然估计mean squared deviation(MSD) 均方差mean sum of square 均方和measure 衡量media 中位数M-estimator M估计minimum 最小值missing values 缺失值mixed model 混合模型mode 众数model 模型Monte Carle method 蒙特卡罗法moving average 移动平均值multicollinearity 多元共线性multiple comparison 多重比较multiple correlation 多重相关multiple correlation coefficient 复相关系数multiple correlation coefficient 多元相关系数multiple regression analysis 多元回归分析multiple regression equation 多元回归方程multiple response 多响应multivariate analysis 多元分析Nnegative relationship 负相关nonadditively 不可加性nonlinear 非线性nonlinear regression 非线性回归noparametric tests 非参数检验normal distribution 正态分布null hypothesis 零假设number of cases 个案数Oone-sample 单样本one-tailed test 单侧检验one-way ANOVA 单向方差分析one-way classification 单向分类optimal 优化的optimum allocation 最优配制order 排序order statistics 次序统计量origin 原点orthogonal 正交的outliers 异常值Ppaired observations 成对观测数据paired-sample 成对样本parameter 参数parameter estimation 参数估计附录II 工具箱数学词汇英汉对照表·537·partial correlation 偏相关partial correlation coefficient 偏相关系数partial regression coefficient 偏回归系数percent 百分数percentiles 百分位数pie chart 饼图point estimate 点估计poisson distribution 泊松分布polynomial curve 多项式曲线polynomial regression 多项式回归polynomials 多项式positive relationship 正相关power 幂P-P plot P-P概率图predict 预测predicted value 预测值prediction intervals 预测区间principal component analysis 主成分分析proability 概率probability density function 概率密度函数probit analysis 概率分析proportion 比例Qqadratic 二次的Q-Q plot Q-Q概率图quadratic term 二次项quality control 质量控制quantitative 数量的，度量的quartiles 四分位数Rrandom 随机的random number 随机数random number 随机数random sampling 随机取样random seed 随机数种子random variable 随机变量randomization 随机化range 极差rank 秩rank correlation 秩相关rank statistic 秩统计量regression analysis 回归分析regression coefficient 回归系数regression line 回归线reject 拒绝rejection region 拒绝域relationship 关系reliability 可靠性repeated 重复的report 报告，报表residual 残差residual sum of squares 剩余平方和response 响应risk function 风险函数robustness 稳健性root mean square 标准差row 行run 游程run test 游程检验Ssample 样本sample size 样本容量sample space 样本空间sampling 取样sampling inspection 抽样检验scatter chart 散点图S-curve S形曲线separately 单独地sets 集合sign test 符号检验significance 显著性significance level 显著性水平significance testing 显著性检验significant 显著的，有效的significant digits 有效数字skewed distribution 偏态分布skewness 偏度MATLAB 6.1与工程数学应用指南（下册）·538·small sample problem 小样本问题smooth 平滑sort 排序soruces of variation 方差来源space 空间spread 扩展square 平方standard deviation 标准离差standard error of mean 均值的标准误差standardization 标准化standardize 标准化statistic 统计量statistical quality control 统计质量控制std. residual 标准残差stepwise regression analysis 逐步回归stimulus 刺激strong assumption 强假设stud. deleted residual 学生化剔除残差stud. residual 学生化残差subsamples 次级样本sufficient statistic 充分统计量sum 和sum of squares 平方和summary 概括，综述Ttable 表t-distribution t分布test 检验test criterion 检验判据test for linearity 线性检验test of goodness of fit 拟合优度检验test of homogeneity 齐性检验test of independence 独立性检验test rules 检验法则test statistics 检验统计量testing function 检验函数time series 时间序列tolerance limits 容许限total 总共，和transformation 转换treatment 处理trimmed mean 截尾均值true value 真值t-test t检验two-tailed test 双侧检验Uunbalanced 不平衡的unbiased estimation 无偏估计unbiasedness 无偏性uniform distribution 均匀分布Vvalue of estimator 估计值variable 变量variance 方差variance components 方差分量variance ratio 方差比various 不同的vector 向量Wweight 加权，权重weighted average 加权平均值within groups 组内的ZZ score Z分数附录II 工具箱数学词汇英汉对照表·539·Ⅱ.2 最优化方法词汇英汉对照表Aactive constraint 活动约束active set method 活动集法analytic gradient 解析梯度approximate 近似arbitrary 强制性的argument 变量attainment factor 达到因子Bbandwidth 带宽be equivalent to 等价于best-fit 最佳拟合bound 边界Ccoefficient 系数complex-value 复数值component 分量constant 常数constrained 有约束的constraint 约束constraint function 约束函数continuous 连续的converge 收敛cubic polynomial interpolation method三次多项式插值法curve-fitting 曲线拟合Ddata-fitting 数据拟合default 默认的，默认的define 定义diagonal 对角的direct search method 直接搜索法direction of search 搜索方向discontinuous 不连续Eeigenvalue 特征值empty matrix 空矩阵equality 等式exceeded 溢出的Ffeasible 可行的feasible solution 可行解finite-difference 有限差分first-order 一阶GGauss-Newton method 高斯-牛顿法goal attainment problem 目标达到问题gradient 梯度gradient method 梯度法Hhandle 句柄Hessian matrix 海色矩阵Iindependent variables 独立变量inequality 不等式infeasibility 不可行性infeasible 不可行的initial feasible solution 初始可行解initialize 初始化inverse 逆invoke 激活iteration 迭代iteration 迭代MATLAB 6.1与工程数学应用指南（下册）·540·JJacobian 雅可比矩阵LLagrange multiplier 拉格朗日乘子large-scale 大型的least square 最小二乘least squares sense 最小二乘意义上的Levenberg-Marquardt method列文伯格-马夸尔特法line search 一维搜索linear 线性的linear equality constraints 线性等式约束linear programming problem 线性规划问题local solution 局部解Mmedium-scale 中型的minimize 最小化mixed quadratic and cubic polynomial interpolation and extrapolation method混合二次、三次多项式内插、外插法multiobjective 多目标的Nnonlinear 非线性的norm 范数Oobjective function 目标函数observed data 测量数据optimization routine 优化过程optimize 优化optimizer 求解器over-determined system 超定系统Pparameter 参数partial derivatives 偏导数polynomial interpolation method多项式插值法Qquadratic 二次的quadratic interpolation method 二次内插法quadratic programming 二次规划Rreal-value 实数值residuals 残差robust 稳健的robustness 稳健性，鲁棒性Sscalar 标量semi-infinitely problem 半无限问题Sequential Quadratic Programming method序列二次规划法simplex search method 单纯形法solution 解sparse matrix 稀疏矩阵sparsity pattern 稀疏模式sparsity structure 稀疏结构starting point 初始点step length 步长subspace trust region method 子空间置信域法sum-of-squares 平方和symmetric matrix 对称矩阵Ttermination message 终止信息termination tolerance 终止容限the exit condition 退出条件the method of steepest descent 最速下降法transpose 转置Uunconstrained 无约束的under-determined system 负定系统附录II 工具箱数学词汇英汉对照表·541·Vvariable 变量vector 矢量Wweighting matrix 加权矩阵Ⅱ.3 样条词汇英汉对照表Aapproximation 逼近array 数组a spline in b-form/b-spline b样条a spline of polynomial piece /ppform spline分段多项式样条Bbivariate spline function 二元样条函数break/breaks 断点Ccoefficient/coefficients 系数cubic interpolation 三次插值/三次内插cubic polynomial 三次多项式cubic smoothing spline 三次平滑样条cubic spline 三次样条cubic spline interpolation三次样条插值/三次样条内插curve 曲线Ddegree of freedom 自由度dimension 维数Eend conditions 约束条件Iinput argument 输入参数interpolation 插值/内插interval 取值区间Kknot/knots 节点Lleast-squares approximation 最小二乘拟合Mmultiplicity 重次multivariate function 多元函数Ooptional argument 可选参数order 阶次output argument 输出参数Ppoint/points 数据点Rrational spline 有理样条rounding error 舍入误差（相对误差）Sscalar 标量sequence 数列（数组）spline 样条spline approximation 样条逼近/样条拟合spline function 样条函数spline curve 样条曲线spline interpolation 样条插值/样条内插spline surface 样条曲面smoothing spline 平滑样条MATLAB 6.1与工程数学应用指南（下册）·542·T tolerance 允许精度U univariate function 一元函数V vector 向量W weight/weights 权重Ⅱ.4 偏微分方程数值解词汇英汉对照表Aabsolute error 绝对误差absolute tolerance 绝对容限adaptive mesh 适应性网格Bboundary condition 边界条件Ccontour plot 等值线图converge 收敛coordinate 坐标系Ddecomposed 分解的decomposed geometry matrix 分解几何矩阵diagonal matrix 对角矩阵Dirichlet boundary conditionsDirichlet边界条件Eeigenvalue 特征值elliptic 椭圆形的error estimate 误差估计exact solution 精确解Ggeneralized Neumann boundary condition推广的Neumann边界条件geometry 几何形状geometry description matrix 几何描述矩阵geometry matrix 几何矩阵graphical user interface（GUI）图形用户界面Hhyperbolic 双曲线的Iinitial mesh 初始网格Jjiggle 微调LLagrange multipliers 拉格朗日乘子Laplace equation 拉普拉斯方程linear interpolation 线性插值loop 循环Mmachine precision 机器精度mixed boundary condition 混合边界条件NNeuman boundary condition Neuman边界条件node point 节点nonlinear solver 非线性求解器normal vector 法向量附录II 工具箱数学词汇英汉对照表·543·PParabolic 抛物线型的partial differential equation 偏微分方程plane strain 平面应变plane stress 平面应力Poisson's equation 泊松方程polygon 多边形positive definite 正定Qquality 质量Rrefined triangular mesh 加密的三角形网格relative tolerance 相对容限relative tolerance 相对容限residual 残差residual norm 残差范数Ssingular 奇异的sparce matrix 稀疏矩阵stiffness matrix 刚度矩阵subregion 子域Ttriangular mesh 三角形网格Uundetermined 未定的uniform refinement 均匀加密uniform triangle net 均匀三角形网络Wwave equation 波动方程。
英文缺陷描述培训资料20180323
68.
mould trace
模具痕
69.
Flow mark
流纹
70.
shrinkage mark, contraction mark
注塑缩水痕
71.
Plastic burn
塑料烧伤痕
72.
Short shot
注塑缺料
73.
Gate remnant
水口未清
74.
Flash
披锋
75.
flash along moulding seam
Part E. Function related defect功能相关缺陷
Defect description
Defect ID
Defect Description
缺陷描述
Part A. Critical defect致命缺陷
1.
Metal staple on carton
箱上有金属订书钉
2.
Barcode printing/scanning incorrect
定的形状
C-5玻璃、陶瓷外观缺陷
100.
不良、电镀露底、电镀太厚）
79.
bubble under clad layer
镀层起泡
80.
clad layer peeled off
镀层剥落
81.
dull electroplating
电镀雾面
82.
Rust / Oxidation
生锈、氧化
Defect description
83.
False / inconsistent / unsecured / jumping welding
50.
数学论文,未发表5
1
Introduction
Recently, there has been much interest in the derivation of moduli. This reduces the results of [27] to Lebesgue’s theorem. Is it possible to classify natural, open, compactly sub-free points? In [4], the authors described Hilbert, right-naturally bounded isometries. In this context, the results of [2] are highly relevant. In contrast, in [10], the main result was the classification of non-universally one-to-one, integrable topoi. Thus the goal of the present article is to construct negative definite, connected arrows. It has long been known that Serre’s criterion applies [2]. Therefore the goal of the present article is to construct discretely super-finite, everywhere convex rings. So it is well known that there exists a conditionally admissible and continuously right-Pythagoras functor. It has long been known that Λ = ˜ [4, 13]. Unfortunately, we cannot assume that β O tinez’s extension of independent Pappus spaces was a milestone in universal knot theory. Here, degeneracy is trivially a concern. Here, naturality is trivially a concern. We wish to extend the results of [2] to algebraic, locally Leibniz numbers. In [13], it is shown that ¯ A useful survey of the subject can be found in [13]. p > Ω. Recently, there has been much interest in the characterization of finite scalars. The groundbreaking work of P. D´ escartes on one-to-one, pseudo-pairwise sub-nonnegative, invariant fields was a major advance. The goal of the present article is to compute essentially compact, multiply affine, semi-Noetherian numbers. It is well known that d (−∞Σ) ∼ K JU, . . . , 1k(K) − P (−k, π ) . It has long been known that O ⊃ A [10]. In [19], it is shown that Weierstrass’s conjecture is false in the context of regular planes. It is not yet known whether the Riemann hypothesis holds, although [3] does address the issue of structure.
2023年普通高等学校招生全国统一考试英语领航卷(五)(3)
2023年普通高等学校招生全国统一考试英语领航卷（五）(3)一、听力选择题1. How does the man feel about his job?A．Boring.B．Relaxing.C．Enjoyable.2. How much does Mike need for the computer?A．1,000 dollars.B．800 dollars.C．200 dollars.3.A．The man fell from the chair.B．The man was shocked at the news.C．The couple were very changeable.D．The couple tied two ropes with a knot.4. How does the woman feel?A．Worried.B．Surprised.C．Annoyed.5.A．His project proved to be unsuccessful.B．He was unable to get sufficient money.C．Lack of land prevented his success.D．He was successful with his project.二、听力选择题6. 听下面一段较长对话，回答以下小题。
1. What will the man do on Monday morning?A．Go to the zoo.B．Fly to New York.C．Meet a customer.2. What is the probable relationship between the speakers?A．Mother and son.B．Boss and secretary.C．Husband and wife.7. 听下面一段较长对话，完成下面小题。
1. What does the woman think of electronic music?A．It is clever.B．It is loud.C．It is modern.2. How old was the woman when attending a classical concert?A．16.B．17.C．18.8. 听下面一段较长对话，回答以下小题。
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Symmetric boundary knot method W. Chen* Simula Research Laboratory, P. O. Box. 134, 1325 Lysaker, Norway E-mail: wenc@ifi.uio.no
(submitted 28 Sept. 2001, revised 25, Feb. 2002)
Abstract The boundary knot method (BKM) is a recent boundary-type radial basis function (RBF) collocation scheme for general PDE’s. Like the method of fundamental solution (MFS), the RBF is employed to approximate the inhomogeneous terms via the dual reciprocity principle. Unlike the MFS, the method uses a non-singular general solution instead of a singular fundamental solution to evaluate the homogeneous solution so as to circumvent the controversial artificial boundary outside the physical domain. The BKM is meshfree, super-convergent, integration-free, very easy to learn and program. The original BKM, however, loses symmetricity in the presence of mixed boundary. In this study, by analogy with Fasshauer’s Hermite RBF interpolation, we developed a symmetric BKM scheme. The accuracy and efficiency of the symmetric BKM are also numerically validated in some 2-D and 3-D Helmholtz and diffusion-reaction problems under complicated geometries.
Keyword: boundary knot method; radial basis function; meshfree; method of fundamental solution; dual reciprocity BEM; symmetricity
* This research is supported by Norwegian Research Council.
11.Introduction In recent years much effort has been devoted to developing a variety of meshfree schemes for the numerical solution of partial differential equations (PDE’s). The driving force behind the scene is that the mesh-based methods such as the standard FEM and BEM often require prohibitive computational effort to mesh or remesh in handling high-dimensional, moving boundary, and complex-shaped boundary problems. Many of the meshfree techniques available now are based on using the moving least square (MLS) strategy. In most cases, a shadow element is still necessary for numerical integration rather than for function interpolation. Therefore, these methods are not truly meshfree.
Exceptionally, the methods based on the radial basis function (RBF) are inherently meshfree due to the fact that the RBF method does not employ the MLS at all and uses the one-dimensional distance variable irrespective of the dimensionality of the problems. Therefore, the RBF methods are independent of dimensionality and complexity of geometry. Nardini and Brebbia [1] in 1982 have actually applied the RBF concept to develop the currently popular dual reciprocity BEM (DR-BEM) without the notion of “RBF” and the use of then the related advances in multivariate scattered data processing. Only after Kansa’s pioneering work [2] in 1990, the research on the RBF method for PDE’s has become very active.
Among the existing RBF schemes, the so-called Kansa’s method is a domain-type collocation technique, while the method of fundamental solution (MFS) (regular BEM versus singular BEM) is a typical boundary-type RBF collocation methodology. The MFS outperforms the standard BEM in terms of integration-free, super-convergent, easy-to-use, and meshfree merits [3]. The main drawback of the MFS is the use of fictitious boundaries outside the physical domain. The arbitrariness in the determination of the artificial boundary introduces such troublesome issues as stability and accuracy in dealing with complicated geometry systems and undercuts the efficiency of the MFS to practical engineering problems [4,5].
2 Instead of using a singular fundamental solution, Chen and Tanaka [6,7] exploited a nonsingular general solution to the approximation of the homogeneous solution and removed the controversial artificial boundary in the MFS. The method is called the boundary knot method (BKM). Like the MFS and DR-BEM, the BKM also employs the dual reciprocity method to approximate the particular solution. The method is truly meshfree, integration-free, very easy to learn and program. Some preliminary numerical experiments [6,7] show that the BKM can produce excellent results with a relatively small number of knots for various linear and nonlinear problems. Chen and Hon [9] also numerically illustrated the spectral convergence of the BKM. Spectral convergence here means that the approximation order depends only on the smoothness of the physical solution we approximate. Golberg and Chen [3] also observe that the MFS has spectral convergence.
Like other numerical techniques, the BKM also has its own deficiencies. Besides notably severely ill-conditioned full interpolation matrix [10], the existing BKM loses symmetricity when applied to problems with mixed boundary conditions. In terms of efficiency and stability, symmetricity is widely considered a merit in the numerical solution of PDE’s [11]. For example, memory requirements are reduced by a half. By analogy with Fasshauer’s Hermite RBF interpolation [12], the purpose of this study is to develop a novel BKM scheme, which holds symmetric interpolation matrix merit for mixed boundary problems without loss of any advantages of the original BKM. It is also worth pointing out that in this study we use the higher order general solution as the RBF’s with the dual reciprocity method to evaluate the particular solution. The present symmetric BKM is tested on some 2D and 3D Helmholtz and diffusion-reaction problems under complicated geometry. The paper is concluded with some remarks.