The Field of Definition of Function Fields and a Problem in the Reducibility of Polynomials in Two Variables
ثبت نشده
چکیده
Introduction Let K be a number field, ax the ring of integers of K. Suppose we are given a projective curve 2, and a morphism 4 : Z 4 Pf(C) (where Pf(C) is the projective line) such that 4 and Z are both defined over K. We denote by K(Z) the field of functions of Z defined over K, and from this data we obtain a permutation representation T of the Galois group G(K(Z) "/K(Pt(C))) (where K(Z) A is the normal closure of K(Z) over K @ ' ( C ) ) ) . In Section 1 we investigate (for our needs) the combinatorial and group theoretical aspects of the situation where
منابع مشابه
First Principles Derivation of Displacement and Stress Function for Three-Dimensional Elastostatic Problems, and Application to the Flexural Analysis of Thick Circular Plates
In this study, stress and displacement functions of the three-dimensional theory of elasticity for homogeneous isotropic bodies are derived from first principles from the differential equations of equilibrium, the generalized stress – strain laws and the geometric relations of strain and displacement. It is found that the stress and displacement functions must be biharmonic functions. The deriv...
متن کاملUniqueness of meromorphic functions ans Q-differential polynomials sharing small functions
The paper concerns interesting problems related to the field of Complex Analysis, in particular, Nevanlinna theory of meromorphic functions. We have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a small function. Outside, in this paper, we also consider the uniqueness of $q-$ shift difference - differential polynomials of mero...
متن کاملOperational matrices with respect to Hermite polynomials and their applications in solving linear differential equations with variable coefficients
In this paper, a new and efficient approach is applied for numerical approximation of the linear differential equations with variable coeffcients based on operational matrices with respect to Hermite polynomials. Explicit formulae which express the Hermite expansion coeffcients for the moments of derivatives of any differentiable function in terms of the original expansion coefficients of the f...
متن کاملGENERAL SOLUTION OF ELASTICITY PROBLEMS IN TWO DIMENSIONAL POLAR COORDINATES USING MELLIN TRANSFORM
Abstract In this work, the Mellin transform method was used to obtain solutions for the stress field components in two dimensional (2D) elasticity problems in terms of plane polar coordinates. the Mellin transformation was applied to the biharmonic stress compatibility equation expressed in terms of the Airy stress potential function, and the boundary value problem transformed to an algebraic ...
متن کاملElzaki transform method for finding solutions to two-dimensional elasticity problems in polar coordinates formulated using Airy stress functions
In this paper, the Elzaki transform method is used for solving two-dimensional (2D) elasticity problems in plane polar coordinates. Airy stress function was used to express the stress compatibility equation as a biharmonic equation. Elzaki transform was applied with respect to the radial coordinate to a modified form of the stress compatibility equation, and the biharmonic equation simplified t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011