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11.
An asymptotic formula is obtained for the number of representations of an element of a finite field as a weighted sum of two prescribed powers of primitive elements. This generalises previous work on sums of primitive elements, including that relating to some conjectures of Golomb. 相似文献
12.
CHEN Falai & YANG Wu Department of Mathematics University of Science Technology of China Hefei China 《中国科学A辑(英文版)》2005,48(9):1260-1273
Wu's elimination method is an important method for solving multivariate poly- nomial equations.In this paper,we apply interval arithmetic to Wu's method and convert the problem of solving polynomial equations into that of solving interval polynomial equa- tions.Parallel results such as zero-decomposition theorem are obtained for interval poly- nomial equations.The advantages of the new approach are two-folds:First,the problem of the numerical instability arisen from floating-point arithmetic is largely overcome.Second, the low efficiency of the algorithm caused by large intermediate coefficients introduced by exact compaction is dramatically improved.Some examples are provided to illustrate the effectiveness of the proposed algorithm. 相似文献
13.
We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game (Section 1 and Appendix). Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game (which is two-dimensional but without labels), by a simple and natural interpretation (Section 2). Jervell proposed another type of a combinatorial game, by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show (Section 3) that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φω (0) (while that of PA or of Kirby-Paris' Game is φ1 (0) = ?0) in the Veblen hierarchy of ordinals. 相似文献
14.
15.
Yi-rang Yuan 《应用数学学报(英文版)》2007,23(2):255-268
For a coupled system of multiplayer dynamics of fluids in porous media,the characteristic finiteelement domain decomposition procedures applicable to parallel arithmetic are put forward.Techniques suchas calculus of variations,domain decomposition,characteristic method,negative norm estimate,energy methodand the theory of prior estimates are adopted.Optimal order estimates in L~2 norm are derived for the error inthe approximate solution. 相似文献
16.
In this paper, we apply Adomian decomposition method (shortly, ADM) to develop a fast and accurate algorithm of a special second-order ordinary initial value problems. The ADM does not require discretization and consequently of massive computations. This paper is particularly concerned with the ADM and the results obtained are compared with previously known results using the Quintic C2-spline integration methods. The numerical results demonstrate that the ADM is relatively accurate and easily implemented. 相似文献
17.
We discuss equivalent definitions of holomorphic second-order cusp forms and prove bounds on their Fourier coefficients. We
also introduce their associated L-functions, prove functional equations for twisted versions of these L-functions and establish a criterion for a Dirichlet series to originate from a second order form. In the last section we
investigate the effect of adding an assumption of periodicity to this criterion.
2000 Mathematics Subject Classification Primary—11F12, 11F66
G. Mason: Research supported in part by NSF Grant DMS 0245225.
C. O’Sullivan: Research supported in part by PSC CUNY Research Award No. 65453-00 34. 相似文献
18.
The exterior of a cross-linked polymer gel resembles a polymer brush. Such gel including its brush can be swollen by a good solvent. The detachment of the solvent–vapor (L–V) interface from the brush is controlled by the adsorption of polymer segments onto this interface and is to a very good approximation not influenced by long-range van der Waals contributions. A wetting transition in this system coincided with the adsorption–desorption transition for chains onto such L–V interface and has various unusual features. There are several indications that in practice this system should feature a second-order wetting transition. 相似文献
19.
20.
In this paper, we aim to investigate the difference equation
\begin{align*}
\Delta^{2}y(t-1)+|y(t)|=0, \ \ \ \ \ t\in[1,T]_{\mathbb{Z}}
\end{align*}
with different boundary conditions $y(0)=0$ or $\Delta y(0)=0$ and $y(T+1)=B$ or $\Delta y(T)=B$,\ where\ $T\geq 1$ is an integer and $B\in\mathbb{R}$. We will show that how the values of $T$ and $B$ influence the existence and uniqueness of the solutions to the about problem. In details, for the different problems, the $TB$-plane explicitly divided into different parts according to the number of the solutions to the above problems. These parts of $TB$-plane for the value of $T$ and $B$ guarantee the uniqueness, the existence and the nonexistence of solutions respectively. 相似文献