A unique graph of minimal elastic energy

Nonlinear functionals that appear as a product of two integrals are considered in the context of elastic curves of variable length. A technique is introduced that exploits the fact that one of the integrals has an integrand independent of the derivative of the unknown. Both the linear and the nonlinear cases are illustrated. By lengthening parameterized curves it is possible to reduce the elastic energy to zero. It is shown here that for graphs this is not the case. Specifically, there is a unique graph of minimal elastic energy among all graphs that have turned 90 degrees after traversing one unit.

     

Boundedness of Solutions for Elliptic Variational Inequalities

Ｂｏｕｎｄｅｄｎｅｓｓ　ｏｆ　Ｓｏｌｕｔｉｏｎｓ　ｆｏｒ　Ｅｌｌｉｐｔｉｃ　Ｖａｒｉａｔｉｏｎａｌ　ＩｎｅｑｕａｌｉｔｉｅｓＢｏｕｎｄｅｄｎｅｓｓｏｆＳｏｌｕｔｉｏｎｓｆｏｒＥｌｌｉｐｔｉｃＶａｒｉａｔｉｏｎａｌＩｎｅｑｕａｌｉｔｉｅｓ￥ＹｅＲｕｉｆ...     

钢筋混凝土板的弯曲问题解法

本以含高阶项的试函数，用Galerkin法求得了周边固支的钢筋混凝土板在均布荷载作用下的挠度表达式，所得结果在特殊情况下与[1]的各向同性均质板在均布荷载下的结果相符合．     

四元数体上的Schur不等式及改进

本文证明了四元数矩阵Ａ的右特征值的实部、虚部的模和右特征值的模在四元数的相似之下唯一确定的，由此在四元数体上推广和改进了Ｓｃｈｕｒ不等式。     

KH2PO4和(CH3NHCH2COOH)CaCl2在高压下的状态方程与相变

 在活塞圆筒式p-V关系测量装置上，研究了KH₂PO₄（KDP）和(CH₃NHCH₂COOH)CaCl₂［Tris-sarcosine calcium chloride（TSCC）］在室温下、4.5 GPa内的p-V关系。实验结果表明：KDP在2.1 GPa左右有一个相变；TSCC在0.8 GPa和3.2 GPa左右各有一个相变。本工作还给出了它们在相变前后的状态方程，以及它们的格临爱森参数γ₀、体积模量B₀和B₀的压力导数B₀'。     

Stresses in an elastic plate lying over a base due to strip-loading

The closed-form analytic expressions for the stresses at any point of an elastic plate coupling in different ways to a base as a result of a two-dimensional shear strip-loading are obtained. The contact between the horizontal layer and the base is either smooth-rigid or rough-rigid or welded. The variations of the shear stresses with the horizontal distance have been studied numerically. It is found that the effect of different boundary conditions on the stress field is significant and the stresses for an elastic layer lying over an elastic half-space differ considerably from those of an entire homogeneous elastic half-space.     

Novel functional polymers: Poly(dimethyl siloxane)–polyamide multiblock copolymers. XI. The effects of sequence regularity on the thermal and mechanical properties

Poly(aramid silicone) (PAS) multiblock copolymers were synthesized by the low‐temperature solution polycondensation of isophthaloyl dichloride (IPC) and two diamines, diamino poly(dimethyl siloxane) (PDMS; number‐average molecular weight = 1680) and 3,4′‐diaminodiphenylether (3,4′‐DAPE), in tetrahydrofuran/dimethylacetamide (2/1 v/v). Two synthetic methods for the control of the PAS sequence were used: a one‐step synthesis that presumably gave PAS with a random sequence and the polymerization of 3,4′‐DAPE with a presynthesized dimer, IPC–PDMS–IPC (two‐step synthesis), that presumably gave PAS with an alternating sequence of 3,4′‐DAPE and PDMS segments. In a ¹H NMR study of the amide protons of the 3,4′‐DAPE component in PAS, the relative length of the 3,4′‐DAPE segment of randomly sequenced PAS to that of ideally sequenced PAS could be estimated. The glass‐transition temperatures of the 3,4′‐DAPE and PDMS segments of random PAS were 152–234 and ?104 to ?117 °C, respectively, whereas the alternating PAS sequences showed no glass transition for the 3,4′‐DAPE segments. A tensile test indicated that randomly sequenced PAS behaved like a rubber‐toughened material at lower PDMS contents and like a thermoplastic elastomer at higher PDMS contents, whereas the alternately sequenced PAS behaved like a very soft rubber, showing a high value of elongation at the breaking point. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 841–852, 2003     

LAPLACE-STIELTJES变换所定义的解析函数的下级

对于Ｌａｐｌａｃｅ－Ｓｔｉｅｌｔｊｅｓ变换所定义的整函数或在半平面内解析的函数，分别定义了下级，适当引进序列０≤λｎ↑＋∞，建立该变换的最大模与“最大项”之间的关系，并由这些关系推导了两类下级的充分必要条件     

Second order elastic anomalies in barium titanate from orthorhombic to rhombohedral phase transition

The anomalies in second order elastic constants have been derived for barium titanate for the phase transition from orthorhombic to rhombohedral state. The equilibrium values of order parameter, strain variables and fluctuations in order parameter have been derived using stability conditions and Landau-Khalatnikov equations respectively. Expression for shift in specific heat is obtained. All the anomalies in second order elastic constants have been derived and relations among them reported. The numerical values of anomalies in the individual constants are calculated and their variation is represented graphically. Changes in elastic constants occur over a range of temperature of the order 10⁻²K.     

Second order elastic anomalies in barium titanate from cubic to tetragonal phase transition

The anomalies of the second order elastic constants have been derived for barium titanate for the phase transition from cubic to tetragonal. The equilibrium values of the components of the order parameter and the strain variables have been obtained from the stability conditions. The fluctuations in the order parameter have been derived from the Landau-Khalatnikov equations. Expression for the shift in the zero point energy in the tetragonal phase is obtained and is shown to be proportional to (T −T _c)². The anomalies for all the second order elastic constants have been derived and relations among them reported. It is shown that the second order elastic anomalies suffer a discontinuity at the transition temperature.