共查询到20条相似文献,搜索用时 15 毫秒
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We get that for any element a∈Fq and any primitive element , there exists a primitive normal polynomial f(x)=xn−σ1xn−1+?+(−1)n−1σn−1x+(−1)nσn with σn−1=a, σn=b for n≥5. The estimates of hybrid extended Kloostermann sums over finite fields and some new variations of Cohen’s sieve techniques help to get the above result. 相似文献
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Shuji Saito 《Inventiones Mathematicae》1986,85(2):379-414
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A. É. Maevskii 《Mathematical Notes》2009,85(1-2):68-81
A deterministic algorithm for calculating the roots of polynomials in one variable with coefficients in the ring of polynomials in several variables over an arbitrary integral domain is constructed. An estimate for the arithmetic complexity of the algorithm in the worst case is obtained. 相似文献
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Numerical Algorithms - The motivation of this work stems from the numerical approximation of bounded functions by polynomials satisfying the same bounds. The present contribution makes use of the... 相似文献
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Timothy Meagher Bin Jiang Peng Jiang 《Numerical Methods for Partial Differential Equations》2020,36(5):1129-1144
An enhanced finite-difference time-domain (FDTD) algorithm is built to solve the transverse electric two-dimensional Maxwell's equations with inhomogeneous dielectric media where the electric fields are discontinuous across the dielectric interface. The new algorithm is derived based upon the integral version of the Maxwell's equations as well as the relationship between the electric fields across the interface. To resolve the instability issue of Yee's scheme (staircasing) caused by discontinuous permittivity across the interface, our algorithm revises the permittivities and makes some corrections to the scheme for the cells around the interface. It is also an improvement over the contour-path effective permittivity algorithm by including some extra terms in the formulas. The scheme is validated in solving the scattering of a dielectric cylinder with exact solution from Mie theory and is then compared with the above contour-path method, the usual staircasing and the volume-average method. The numerical results demonstrate that the new algorithm has achieved significant improvement in accuracy over other methods. Furthermore, the algorithm has a simple structure and can be merged into current FDTD software packages easily. The C++ source code for this paper is provided as supporting information for public access. 相似文献
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Marcin Studniarski 《Numerische Mathematik》1989,55(6):685-693
Summary We present an algorithm which enables us to calculate one particular subgradient of a convex functionf: 2 at a given point. Such a calculation is required in many existing numerical methods for convex nondifferentiable optimization. The novelty of our approach lies in the assumption that only the values off are computable and no analytical formula for the subdifferential is known. We include some numerical examples. 相似文献
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Sunsook Noh 《代数通讯》2013,41(2):613-624
Let υ be a prime divisor of a 2-dimensional regular local ring (R m) with algebraically closed residue field k. Zariski showed that a prime divisor υ of R is uniquely associated to a simple m-primary integrally closed ideal I of R, there exist finitely many simple υ-ideals including I, and all the other υ-ideals can be uniquely factored into products of simple υ-ideals. It is known that such an m-primary ideal I of R can be minimally generated by o(I) + 1 elements.Given a simple integrally closed ideal I of order one with arbitrary rank and its associated prime divisor υ, we find minimal generating sets of all the simple υ-ideals and describe factorizations of all the composite υ-ideals in terms of power products of simple υideals as explicitly as possible. 相似文献
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Shinji Mizuno 《Mathematical Programming》1984,28(3):329-336
We investigate the structure of the solution setS to a homotopy equationH(Z,t)=0 between two polynomialsF andG with real coefficients in one complex variableZ. The mapH is represented asH(x+iy, t)=h
1(x, y, t)+ih
2(x, y, t), whereh
1 andh
2 are polynomials from ℝ2 × [0,1] into ℝ and i is the imaginary unit. Since all the coefficients ofF andG are real, there is a polynomialh
3 such thath
2(x, y, t)=yh3(x, y, t). Then the solution setS is divided into two sets {(x, t)∶h
1(x, 0, t)=0} and {(x+iy, t)∶h
1(x, y, t)=0,h
3(x, y, t)=0}. Using this division, we make the structure ofS clear. Finally we briefly explain the structure of the solution set to a homotopy equation between polynomial systems with
real coefficients in several variables. 相似文献
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Summary One-dimensional stochastic Ising systems with a local mean field interaction (Kac potential) are investigated. It is shown that near the critical temperature of the equilibrium (Gibbs) distribution the time dependent process admits a scaling limit given by a nonlinear stochastic PDE. The initial conditions of this approximation theorem are then verified for equilibrium states when the temperature goes to its critical value in a suitable way. Earlier results of Bertini-Presutti-Rüdiger-Saada are improved, the proof is based on an energy inequality obtained by coupling the Glauber dynamics to its voter type, linear approximation. 相似文献
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Michel Cristofol Patricia Gaitan Hichem Ramoul Masahiro Yamamoto 《Applicable analysis》2013,92(11):2073-2081
In this article, we consider a nonlinear parabolic system with two components and prove a stability estimate of Lipschitz type in determining two coefficients of the system by data of only one component. The main idea for the proof is a Carleman estimate. 相似文献
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Horst Brunotte 《manuscripta mathematica》2009,129(4):523-524
A short proof of a theorem of Dubickas on roots of polynomials with positive rational coefficients is presented. 相似文献
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We continue our study on counting irreducible polynomials over a finite field with prescribed coefficients. We set up a general combinatorial framework using generating functions with coefficients from a group algebra which is generated by equivalence classes of polynomials with prescribed coefficients. Simplified expressions are derived for some special cases. Our results extend some earlier results. 相似文献
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A.D. Gadjiev 《Applied mathematics and computation》2010,216(3):890-901
A new generalization of Bernstein-Stancu type polynomials for one and two variables are constructed and the theorems on convergence and the degree of convergence are established. In addition some numerical examples, corresponding to obtaining results are given. 相似文献
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This paper deals with -periodicity and regularity of solutions to the one dimensional nonlinear wave equation with -dependent coefficients