Let f be a transcendental integral function and there exist a non-zero complex number c^* such that the zeros of f-c are of multiplicity >= 2. then there exists a direction H: argz=\theta\sb 0 (0\leq \theta\sb 0\leq 2\pi) such that for every positive \varepsilon,f and f share a non-zero finite complex number IM at most in {z|\arg z-\theta_0|<\varepsilon\}
Let X,Y be topological spaces, f:X-->Y,g:Y-->X. In this paper, follow conclutions are obtained:(1)f(Fix((g f)^n))=Fix((f g)^n), g(Fix((f g)^n))=Fix((g f)^n),and #Fix((g f)^n)=#Fix((f g)^n);(2)R((g f)^n)=R((f g)^n).where n is a natural number.
Based upon a generally projective Riccati equation method, which is a direct and unified algebraic method for constructing more general form travelling wave solutions of nonlinear partial differential equations (PDEs) and implemented in a computer algebraic system, the authors consider the (2+1)-dimensional dispersive long wave equations(DLWE). More and new general form solutions are obtained, including kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions.The properties of some new formal solitary wave solutions are shown by some figures.
In this paper, the authors first study the growth and regular growth of Dirichlet series of finite order in the plane and obtain two necessary and sufficient conditions; and then prove that the growth of random entire functions defined by random Dirichlet series of finite order in any horizontal straight line is almost surely equal to the growth of entire functions defined by their corresponding Dirichlet series.
(M, g) is assumed to be a Riemannian surface, the paper stated here firstly defines the Φ - Dirichlet integral of the functions on M, then reaches the main theorem about the bounded property of the Φ- subharmonic functions on M with finite Φ - Dirichlet integral.
The authors first establish the neutral type predator-prey system with Holling type II functional response, then by developing some new technique of analysis and using a continuation theorem based on coincidence degree theory, the authors study the global existence of positive periodic solution for the above model. A set of easily verifiable sufficient conditions is obtained. Example shows that our main results are feasible.
By studying the convergence of B-valued Bi-random Dirichlet series under the following conditions: (i) {X_n(\omega)} satisfying the strong law of large numbers and 0<\mathop{\underline{\lim}}\limits_{n\to\infty}\Big\|\frac{\sum\limits_{i=1}^nEX_i}{n}\Big\| \leq\mathop{\overline{\lim}}\limits_{n\to\infty}\Big\|\frac{\sum\limits_{i=1}^nEX_i}{n}\Big\|<+\infty. (ii){X_{n}}is independent and unequally distributed and \mathop{\underline{\lim}}\limits_{n\to\infty}E||X_n||>0,\quad \sup\limits_{n\geq 1}E||X_n||^p <+\infty\quad (p>1),some simple and explicit formulae of the absciassa of convergence are obtained.
Based on the homogeneous balance principle, a new and effective method is given.By this method, new exact Jacobi elliptic function solutions of KdV equation, Boussinesq equation, KGS equations are obtained.
The existence of general Lidstone boundary value problems with all order derivatives is considered. By making use of Leray-Schauder fixed point theorem, equivalent norm and the techniques of system on integral equations, two existence theorems of solutions and positive solutions are proved.These theorems are very convenient for the applications. In other words, the existence can be determined by considering the "height" of nonlinear term on a bounded set.
This paper uses some special treating methods of infinite series, analyses deeply the characters of some special functions about Γ function, reveals some profound regularities of the changes about the extreme value of F distribution density function when parameters change. This paper points out that the maximum of F distribution density function f_{m,n}(x) is monotone increasing when n increases, and the maximum of this density function is monotone decreasing, or decreases at the beginning and then increases when m increases.
The method constructing the Julia sets from a simple nonanalytic mapping developed by Michelitsch and Rossler is expanded. According to the complex mapping expanded by the author, a series of the generalized Julia sets for real index number are constructed. Using the experimental mathematics method and combining the theory of analytic functions of one complex variable with computer aided drawing, the fractal features and evolutions of the generalized Julia sets are studied. The results show: (i) the geometry structure of the generalized Julia sets depends on the parameters of α,R and c; (ii) the generalized Julia sets have symmetry and fractal feature; (iii) the generalized Julia sets for decimal index number have discontinuity and collapse, and their evolutions depend on the choice of the principal range of the phase angle.
In this paper, some criteria on the existence of point spectrum and residual spectrum for the upper triangular infinite dimensional Hamiltonian operators are obtained. Based on the above results, some concrete examples of infinite dimensional Hamiltonian operators with non-empty residual spectrum are constructed in L^2*L^2 to further justify the criterions' effectiveness.
A modified upwind difference procedure is formulated to treat the model of contamination by compressible nuclear waste without dispersion. Convergence analysis is processed and finally the l^2 error estimate is derived.
A method to search k -tight optimal infinite families of directed double loop networks is given. Two 3-tight optimal infinite families of directed double loop networks are obtained by using this method
Using the new equation of state density motivated by the generalized uncertainty relation, the authors derive the entropy of the black cylinder on the background of the cylindrically symmetric spacetime. When the new equation of state density is utilized to obtain that the entropy of the black cylinder is proportional to the horizon area, the divergence appearing in the brick wall model is removed, without any cutoff. It is shown that black cylinder's entropy is the entropy of quantum state on the surface of horizon. The black cylinder's entropy is a kind of quantum effect. It is the intrinsic property of the black cylinder. Via the method of quantum statistics, the authors directly derive the partition functions of Bosonic and Fermi field in black cylinder. The authors also avoid the difficult to solve the wave equation of various particles. The authors offer a new simple and direct way of calculating the entropy of black cylinders of different complicated spacetime.
Let Σ=Σ_{i=1}^{t}(n_i-1) and Λ=Σ_{j=1}^s(m_j-1). This paper considers the generalized Ramsey number R(K_{1,n_1},…, K_{1,n_t},m_1K_2,…, m_sK_2) for any Σ and Λ. And the authors get their exact values if 1<=Λ<=Σ and their upper bounds if Λ>= Σ
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