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951.
Polynomial functions (in particular, permutation polynomials) play an important role in the design of modern cryptosystem. In this note the problem of counting the number of polynomial functions over finite commutative rings is discussed. Let A be a general finite commutative local ring. Under a certain condition, the counting formula of the number of polynomial functions over A is obtained. Before this paper, some results over special finite commutative rings were obtained by many authors. 相似文献
952.
953.
The authors establish a general monotonicity formula for the following elliptic system
△ui+fi(x,ui,…,um)=0 in Ω,
where Ω belong to belong to R^n is a regular domain, (fi(x, u1,... ,um)) = △↓F(x,→↑u), F(x,→↑u ) is a given smooth function of x ∈ R^n and →↑u = (u1,…,um) ∈ R^m. The system comes from understanding the stationary case of Ginzburg-Landau model. A new monotonicity formula is also set up for the following parabolic system
δtui-△ui-fi(x,ui,…,um)=0 in(ti,t2)×R^n,
where t1 〈 t2 are two constants, (fi(x,→↑u ) is given as above. The new monotonicity formulae are focused more attention on the monotonicity of nonlinear terms. The new point of the results is that an index β is introduced to measure the monotonicity of the nonlinear terms in the problems. The index β in the study of monotonieity formulae is useful in understanding the behavior of blow-up sequences of solutions. Another new feature is that the previous monotonicity formulae are extended to nonhomogeneous nonlinearities. As applications, the Ginzburg-Landau model and some different generalizations to the free boundary problems are studied. 相似文献
△ui+fi(x,ui,…,um)=0 in Ω,
where Ω belong to belong to R^n is a regular domain, (fi(x, u1,... ,um)) = △↓F(x,→↑u), F(x,→↑u ) is a given smooth function of x ∈ R^n and →↑u = (u1,…,um) ∈ R^m. The system comes from understanding the stationary case of Ginzburg-Landau model. A new monotonicity formula is also set up for the following parabolic system
δtui-△ui-fi(x,ui,…,um)=0 in(ti,t2)×R^n,
where t1 〈 t2 are two constants, (fi(x,→↑u ) is given as above. The new monotonicity formulae are focused more attention on the monotonicity of nonlinear terms. The new point of the results is that an index β is introduced to measure the monotonicity of the nonlinear terms in the problems. The index β in the study of monotonieity formulae is useful in understanding the behavior of blow-up sequences of solutions. Another new feature is that the previous monotonicity formulae are extended to nonhomogeneous nonlinearities. As applications, the Ginzburg-Landau model and some different generalizations to the free boundary problems are studied. 相似文献
954.
In this article, authors begin with establishing representation formulas and properties for functions on Carnot groups. Then, some unique continuation results to solutions of sub-Laplace equations with potentials are proved. 相似文献
955.
956.
本文研究了Hilbert型级数不等式.利用改进的Euler-Maclaurin求和公式及权系数的方法,并引进两对共轭指数,获得一个具有最佳常数系数的Hilbert型不等式,该不等式是联系若干Hilbert型不等式的加强推广式.作为应用,给出该不等式的等价形式及若干有意义的特殊结果. 相似文献
957.
958.
Abdelhai Elazzouzi Aziz Ouhinou 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(7):1980-2000
In this work, the dynamic behavior of solutions is investigated for a class of partial functional differential equations with infinite delay. We suppose that the undelayed homogeneous part generates an analytic semigroup and the delayed part is continuous with respect to fractional powers of the generator. Firstly, a variation of constants formula is obtained in the corresponding α-norm space, which is mainly used to establish a reduction principle of complexity of the considered equation. The reduction principle proves that the dynamics of the considered equation is governed by an ordinary differential equation in finite dimensional space. As an application, we investigate the existence of periodic, almost periodic and almost automorphic solutions for the original equation. 相似文献
959.
Thomas Strömberg 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1802-1811
We present comparison, uniqueness and existence results for unbounded solutions of a viscous Hamilton-Jacobi or eikonal equation. The equation includes an unbounded potential term V(x) subject to a quadratic upper bound. The results are obtained through a tailor-made change of variables in combination with the Hopf-Cole transformation. An integral representation formula for the solution of the Cauchy problem is derived in the case where V(x)=ω2|x|2/2. 相似文献
960.
G(o)del逻辑和L*逻辑中公式的真度分布 总被引:1,自引:0,他引:1
研究了G\"{o}del逻辑系统和$L^\ast$逻辑系统中公式的真度的分布情况. 结果表明在G\"{o}del逻辑系统和$L^\ast$逻辑系统中含有$n$个原子命题的公式($n$元公式)的真度集分别为$\{\frac{i}{(n+ 1)!}\vert 0 \le i \le (n + 1)! ,i \in N\}$和$\{\frac{i}{(n + 1)!}\vert 0\le i \le 2^n(n + 1)!,i \in N\}.$ 进而得到了G\"{o}del逻辑系统和$L^\ast$逻辑系统中公式的真度集均为[0,1]上的有理数集. 最后,还给出了两系统中公式的相似度,伪距离的分布情况. 相似文献