The Splitting Problem for Coalgebras: A Direct Approach

In this note we give a new and elementary proof of a result of Năstăsescu and Torrecillas (J. Algebra, 281:144–149, 2004) stating that a coalgebra C is finite dimensional if and only if the rational part of any right module M over the dual algebra is a direct summand in M (the splitting problem for coalgebras). Research supported by a CNCSIS BD-type grant, and by the bilateral project BWS04/04 “New Techniques in Hopf Algebra Theory and Graded Ring Theory” of the Flemish and Romanian governments.     

对称扭杆弹簧系统隔振性能研究2000-04-03收稿.

对扭杆弹簧隔振系统的研究表明,扭臂的质量对系统的性能有比较大的影响。虽然系统可获得长的共振周期,但由于扭臂的质量不为零,地基振动的加速度被直接耦合进系统,从而严重地降低了系统的隔振性能。     

温度对高应变率扭-拉复合加载下形状记忆合金本构关系影响的研究

利用分离式扭-拉复合加载Hopkinson杆装置,在20℃和500℃下研究了温度对高应变率扭-拉复合加载下铁基形状记忆合金本构的影响,试验结果表明：该材料在高应变率扭-拉复合加载下的名义剪切屈服强度、剪切强度极限和名义拉伸屈服极限、拉伸强度极限均随温度的升高而降低,拉伸和扭转之间具有相互藕合作用。     

Torsion of an Elastomeric Cylinder Undergoing Microstructural Changes

A constitutive theory which accounts for scission and cross linking processes in polymers during deformation is used to analyze the torsion of a circular bar. In each increment of deformation at a material element of the torsion bar, some volume fraction of material undergoes scission and then re-cross links to form a new network with a new reference state. The scission process reduces the ability of the material to transmit stress. The newly formed networks restore the ability of the material to transmit stress. The total stress is assumed to be the superposition of the stress in the remainder of the original material, determined by its deformation from its original configuration, and the stress in each newly formed network, determined by the deformation in that network from the configuration at which it formed.The interaction of this material response with the inhomogeneous deformation during torsion is studied. The analysis shows the evolution of regions of original and modified material, the softening effects associated with the process of scission and re-cross linking and the occurrence of residual stress and deformation on removal of load.     

Elliptic curves and their torsion subgroups over number fields of type (2, 2, ..., 2)

Suppose thatE: y ² =x(x + M) (x + N) is an elliptic curve, whereM N are rational numbers (#0, ±1), and are relatively prime. LetK be a number field of type (2,...,2) with degree 2′. For arbitrary n, the structure of the torsion subgroup E(K) _tors of theK-rational points (Mordell group) ofE is completely determined here. Explicitly given are the classification, criteria and parameterization, as well as the groups E(K) _tors themselves. The order of E( K)_tors is also proved to be a power of 2 for anyn. Besides, for any elliptic curveE over any number field F, it is shown that E( L)_tors = E( F) _tors holds for almost all extensionsL/F of degree p(a prime number). These results have remarkably developed the recent results by Kwon about torsion subgroups over quadratic fields.     

Characterizations of some homogeneous Hopf real hypersurfaces in a nonflat complex space form by extrinsic shapes of trajectories

We characterize some homogeneous Hopf real hypersurfaces in a nonflat complex space form by studying trajectories for Sasakian magnetic fields whose extrinsic shapes are tangentially of order 2.     

Improvement of the standard method for solving the problem of internal rotation in molecules with symmetrical tops

Drawbacks of the standard method for solving the problem of internal rotation (IR) in molecules with symmetrical tops were examined. The drawbacks can be eliminated by taking into account the higher harmonics of the IR potentials. A new calculation procedure based on the approximation of the lower portion of the potential curve by the equationV(φ)=1/2V _n ^* (1-cosn φ), which describes adequately the arrangement of the torsion levels, was proposed. The successfull implementation of the proposed procedure showed that the procedures used currently are incorrect as well as the Herschbach procedure, which includes a systematic error at each iteration step. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 239–244, February, 1999.     

Behaviors of three BCC metals during non-proportional multi-axial loadings: experiments and modeling

Non-proportional torsion–tension and biaxial-compressive experimental results are presented on tantalum, tantalum alloy with 2.5% tungsten, and AerMet 100 steel. These test results form a comprehensive set of data to show the material behaviors at finite strain and wide strain-rate range. Using the parameter set determined from uniaxial constant strain-rate compressive and tensile tests, the capability of a new constitutive model (Khan, A.S., Liang, R., 1999. Behaviors of three BCC metal over a wide range of strain rates and temperatures: experiments and modeling. International Journal of Plasticity 15, 1089–1109) is shown to accurately predict complex loading paths of current experimental results. Using von Mises equivalent strain, stress, and strain rate, the constitutive model gives excellent predictions of these non-proportional experimental results.     

考虑弯扭形变的薄壁箱形梁的非线性后屈曲

在大位移和扭转的前提下,通过一中等弯曲扭转的位移场描述了薄壁箱形梁在偏心载荷作用下的静稳定性问题.该非线性公式可用于分析简支薄壁箱形梁在不同载荷作用下的屈曲和后屈曲行为.采用伽辽金方法将非线性微分系统离散,并通过牛顿-拉普森增量迭代法求解得代数方程组.数值计算结果表明,当前屈曲位移不可忽略时,经典的横向屈曲预测是保守的...