三线摆摆线质量对转动惯量精确测量的影响

三线摆法是测量转动惯量的常用方法, 理论上通常都是把摆线作理想处理(即摆线质量趋于0), 但在工程测量中, 被测工件往往较重, 摆线不再是轻质细线, 摆线质量势必会对空载悬盘的转动惯量测量产生影响. 本文应用哈密顿原理和变量替换, 导出三线摆摆线的变张力弦振动方程, 通过对摆线与悬盘连接点(x=0)的运动状态讨论, 推得摆线质量不能忽略情形下的对称式三线摆的转动惯量计算式, 并借助于MATLAB 软件快速便利地进行计算.     

A difference between continuous and absolutely continuous norms in Banach function spaces

On examples we show a difference between a continuous and absolutely continuous norm in Banach function spaces.     

Unique Continuation with Weak Type Lower Order Terms

This paper proves a unique continuation property for the elliptic differential inequality|u| A|u| + B|u|,where the coefficients A and B are functions in the Lorentz space with small weak type norm.     

Rigid sets and nonexpansive mappings

We introduce a new class of normed spaces (not necessarily finite dimensional), which contains the finite dimensional normed spaces with polyhedral norm. We study the properties of rigid sets of the spaces of this class and we apply the results to limit sets of the sequences of iterates of nonexpansive maps.

     

Spherical Bessel functions and explicit quadrature formula

An evaluation of the derivative of spherical Bessel functions of order at its zeros is obtained. Consequently, an explicit quadrature formula for entire functions of exponential type is given.

     

A note on the Gelfand-Mazur Theorem

Three Gelfand-Mazur type theorems are proved. One of these provides a -property analogue of Zalar's recent generalizations of the Froelich-Ingelstam-Smiley Theorems concerning unital multiplication in Hilbert spaces; the second illustrates that the assumption in Kaplansky's version of the Gelfand-Mazur Theorem can be weakened in the presence of a -norm; whereas the third provides a real analogue of a result due to Srinivasan.

     

New index transforms of the Lebedev–Skalskaya type

New index transforms, involving the real part of the modified Bessel function of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces. Inversion theorems are proved. As an interesting application, a solution of the initial value problem for the second-order partial differential equation, involving the Laplacian, is obtained. It is noted that the corresponding operators with the imaginary part of the modified Bessel function of the first kind lead to the familiar Kontorovich–Lebedev transform and its inverse.     

A bound for the optimal constant in an inequality of Ladyzhenskaya and Solonnikov

Ladyzhenskaya & Solonnikov (1976) introduced a representationtheorem in ³, which contained an integral inequality involvinga multiplicative dimensionless constant. The existence of theconstant was established but not its magnitude which dependsonly on the shape of the domain. In this paper, we derive anupper bound for the optimal constant when the underlying domainis star shaped.