The Experts below are selected from a list of 13542 Experts worldwide ranked by ideXlab platform
Xia Chun - One of the best experts on this subject based on the ideXlab platform.
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A PERTURBATION SOLUTION OF LONGITUDINALLY TWISTED NATURAL VIBRATION OF ELASTIC BAR UNDER THERMAL STATE
2001Co-Authors: Xia ChunAbstract:The longitudinally twisted natural vibration of an elastic bar under the thermal state is studied by using a first- order perturbation solution of the second- order Linear Homogeneous Equation with big parameters,and the characteristic Equation of its vibration frequency is derived.Actual calculations indicate thatthe perturbation solution is both exact and simple.
Lin Zi-jie - One of the best experts on this subject based on the ideXlab platform.
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A PERTURBATION SOLUTION TO LONGITUDINAL TWISTED NATURAL VIBRATION OF ELASTIC BAR IN THERMAL STATE
Journal of Changde Teachers University, 2000Co-Authors: Lin Zi-jieAbstract:The longitudinal twisted natural vibration of elastic bar under thermal state is studied by using first order perturbation solution to second order Linear Homogeneous Equation with big parameter,and the characteristic Equation of its vibration frequency is derivated.Actual caculation indicates that the perturbation solution is exact and simple.
V. E. Slyusarchuk - One of the best experts on this subject based on the ideXlab platform.
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Strengthening of the kneser theorem on zeros of the solutions of the Equation $$y'' + p(x)y = 0$$
Ukrainian Mathematical Journal, 1996Co-Authors: V. E. SlyusarchukAbstract:We establish conditions for a second-order Linear Homogeneous Equation to be nonoscillatory on a semiaxis and conditions under which its solutions have infinitely many zeros.
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Strengthening of the kneser theorem on zeros of the solutions of the Equation \(y'' + p(x)y = 0\)
Ukrainian Mathematical Journal, 1996Co-Authors: V. E. SlyusarchukAbstract:We establish conditions for a second-order Linear Homogeneous Equation to be nonoscillatory on a semiaxis and conditions under which its solutions have infinitely many zeros.
Alan Jeffrey - One of the best experts on this subject based on the ideXlab platform.
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25 – Partial Differential Equations and Special Functions
Handbook of Mathematical Formulas and Integrals, 2004Co-Authors: Alan JeffreyAbstract:Publisher Summary This chapter focuses on partial differential Equations (PDE) and special functions. The chapter presents a classification of Equations; discusses the method of separation of variables; and reviews the Sturm-Liouville problem and special functions. A boundary value problem for a PDE arises when its solution is required to satisfy conditions on a boundary in space. If, however, one of the independent variables is the time t and the solution is required to satisfy certain conditions when t = 0, this leads to an initial value problem for the PDE. Many physical situations involve a combination of both of these situations, and they then lead to an initial boundary value problem. When a PDE subject to auxiliary conditions gives rise to a solution that is unique (except possibly for an arbitrary additive constant), and depends continuously on the data in the auxiliary conditions, it is said to be well posed or properly posed. The method of separation of variables is a technique for the determination of the solution of a boundary value or an initial value problem for a Linear Homogeneous Equation that involves attempting to separate the spatial behavior of a solution from its time variation (temporal behavior).
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Partial Differential Equations and Special Functions
Handbook of Mathematical Formulas and Integrals, 1995Co-Authors: Alan JeffreyAbstract:This chapter focuses on partial differential Equations (PDE) and special functions. The chapter presents a classification of Equations; discusses the method of separation of variables; and reviews the Sturm-Liouville problem and special functions. A boundary value problem for a PDE arises when its solution is required to satisfy conditions on a boundary in space. If, however, one of the independent variables is the time t and the solution is required to satisfy certain conditions when t = 0, this leads to an initial value problem for the PDE. Many physical situations involve a combination of both of these situations, and they then lead to an initial boundary value problem. When a PDE subject to auxiliary conditions gives rise to a solution that is unique (except possibly for an arbitrary additive constant), and depends continuously on the data in the auxiliary conditions, it is said to be well posed or properly posed. The method of separation of variables is a technique for the determination of the solution of a boundary value or an initial value problem for a Linear Homogeneous Equation that involves attempting to separate the spatial behavior of a solution from its time variation (temporal behavior).
Nathan Johns - One of the best experts on this subject based on the ideXlab platform.
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Establishing Conditions on the Degree of Regularity of Linear Homogeneous Equations
arXiv: Combinatorics, 2017Co-Authors: Nathan JohnsAbstract:In 1933, Rado conjectured that for any positive integer n, there is always a Linear Homogeneous Equation with degree of regularity n. In proving this conjecture, Alexeev and Tsimerman, and independently Golowich, found that some Equations in n variables have degree of regularity n-1 for any value of n. Their work left many questions as to how and which other properties of Equations are closely tied to the degree of regularity, and if there is a simpler or more effective way of thinking about it. In this paper, we answer some of these questions, prove that various families of Linear Homogeneous Equations in n variables have degree of regularity n-1, and establish some conditions under which this property holds.