Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the growth of solutions of two types of complex difference-differential equations, and obtain two results. Improvements and extensions of some results in references are presented. Examples show that our results are precise.
In this work, with the help of the topological degree of continuous functions, we firstly discuss the normality of families of holomorphic functions sharing continuous functions with their first derivatives.
In this paper, we study the Riemann problem with the initial data containing the Dirac delta function for the Aw-Rascle traffic model with Chaplygin pressure. Under the generalized Rankine-Hugoniot relation and the entropy condition, we constructively obtain the global existence and uniqueness of generalized solutions including delta shock waves that explicitly exhibit four kinds of different structures. Moreover, it can be found that the solutions constructed here are stable for some perturbations of the initial data.
This research is a continuation of a recent paper [15]. Shared value problems related to a meromorphic function f(z) and its q-difference operator Δq, cf are studied. It is shown, for instance, that if f(z) is of zero order and shares four values IM with its q-difference operator Δq, cf = f(qz+c)-f(z), then f(z)=Δq, cf. Moreover, we also consider problems on sharing values of f(z) and Δq, cf when their orders are not an integer or infinite.
In view of Nevanlinna theory, we study the growth and poles of solutions of some systems of complex composite functional equations. The lower bounds for Nevalinna lower order, counting function of poles and maximum modulus for meromorphic functions of such systems are obtained which are generalization for some results given by Gao.
In this paper, the concept of generalized implicit complementarity problem is introduced and the existence theorems of solution of the generalized implicit complementarity problem are proved in Banach spaces.
For the bounded weak solution of a class of semilinear subelliptic equations under the natural growth, we prove an interior HÖlder continuity estimate by way of establishing the modified Moser-Nash iterations and weak Harnack inequality.
The complex dynamics of a SIRS epidemic model with saturate incidence rate, birth pulse, pulse vaccination and vertical transmission was studied. First, a Poincar\'e map was formulated, the existence and stability of the infection-free periodic solution were obtained with the help of the fixed point of the map and its eigenvalues. Then transcritical bifurcation, supercritical bifurcation and flip bifurcation were discussed in detail. Finally, numerical results, which are in good agreement with the theoretical analysis, were presented.
This article is devoted to studying the higher order linear differential equations f(k)+Ak-2f(k-2)+…+A1f'+A0f=0, where Aj(z)~(j=0,1, …, k-2) are meromorphic functions with at most finitely many poles. We show that small perturbations of such equations lead to solutions whose zeros must have infinite exponent of convergence. Extends some results of Alotaibi etc.
Rellich Lemma is a very important part of the electromagnetic related inverse problems theory, and this paper gives a new proof of Rellich Lemma. The proof is much simpler and it mainly uses fundamental theory of ordinary differential equations and unique continuation theory. We studied the properties of the solutions of Helmholtz equation through the proof.
By using Neumann series of inverse matrix,discrete coupled algebraic Riccati equation with unknown matrix inverse in discrete-time jump linear quadratic control problems can be transformed into the high degree polynomial matrix equations.Then Newton's method is applied to find different constrained solution of polynomial matrix equations, and the modified conjugate gradient method is used to solve different constrained solution or different constrained least square solution of linear matrix equations derived from each iterative step of Newton's method.In this way, a double iterative method is established to solve for different constrained solution of discrete coupled algebraic Riccati equation.Different constrained solution of discrete coupled algebraic Riccati equation is only required by double iterative algorithm.But it may not be unique.Besides there are not additional limits to its coefficient matrix of discrete coupled algebraic Riccati equation.The effectiveness of the double iterative method is demonstrated by numerical examples.
A family of rings Rk,q is defined. Cyclic codes over a family of rings are studied. It is proved that the images of cyclic codes over these rings under Gray map are 2k-quasi-cyclic codes.
A finite group G is said to be an almost simple related to L if and only if L≤G≤Aut(L) for some simple group L. Further, if L is a sporadic simple group, then say that G is an almost sporadic simple group related to L. In this paper, we prove that all almost sporadic simple groups can be determined uniquely by their orders and no more than two special conjugacy class lengths.
Under a more general parameter distribution, estimates on solutions of a new weakly singular Wendroff integral inequality with two nonlinear terms are discussed. Our results are more concise and also generalize some existing results with different distribution of the parameters. An application example to estimate the bounds of solutions of a differential equation is also given.
Let f(z) be a transcendental meromorphic function, and let 0<δ< 1, if
lim—r→∞log T(r+1/r,f )/log T(r, f)<+∞,
then there exist an (n=1, 2, …), such that the set {a: ?1)(a, f)>δ} is a subset of
∩∞j=1∪∞n=j {a:|a-an|<e-enσ},
which means {a:Δ1)(a, f)>δ} is a set of finite μ-measure.
The low pass filters play important role in construction of wavelets with MRA. But construction of wavelets of MRA in high dimensional case is very complicate in view of their different dilation matrices. In this paper, we discuss the low pass filters of MRA multivariate wavelets with the uniform dilation matrix 2I2=(2 0 0 2) (These filters are called dyadic bivariate filters). We character dyadic bivariate filters by using dyadic bivariate filter multipliers and prove that the set of all dyadic bivariate low pass filters is path-connected under the norm L2(T2) topology.
Let Φ be a unital positive linear map between unital C*-algebra A and B(H) the algebra of all bounded linear operators on a Hilbert space H. Kadison's inequality say that Φ(A)2Φ≤(A2) for each self-adjoint element A in A. In this paper, we extent Kadison's inequality via Furuta inequality to several operators.
A Hilbert space operator T is said to satisfy a-Browder's theorem if σa(T)\σawTπa00(T), where σa(T) and σaw(T) denote the approximate point spectrum and the Weyl essential approximate point spectrum respectively, and πa00(T)={λ∈iso σa(T), 0<dim N(T-λI)<∞}. If σa(T)\σaw(T)=πa00(T), we say T satisfies a-Weyl's theorem.T∈B(H) is said to have the stability of the a-Browder's (a-Weyl's) theorem if T+K satisfies the a-Browder's (a-Weyl's) theorem for all compact operators K. In this note, we investigate the stability of the a-Browder's theorem and the a-Weyl's theorem, and we characterize those operators for which the a-Browder's theorem and the a-Weyl's theorem are stable under compact perturbations.
In this paper, we consider the multiplicity of the eigenvalue and the completeness of the eigen and root vector system of a class of Hamiltonian operators. The geometric multiplicity, algebraic index and algebraic multiplicity of each eigenvalue is completely determined. Based on the above properties and the symplectic orthogonality of the associated eigen and root vectors, the necessary and sufficient condition for the eigen or root vector system to be complete is obtained. Moreover, the obtained results are tested for several problems, for example, the plate bending, plane elasticity, Stokes flow.
In this paper some iterative schemes to approximate a common fixed point of one-parameter nonexpansive cosine family are investigated in Hilbert spaces. By using the theory of cosine families, a series of new convergence theorems are established under some mild conditions for the explicit, implicit and viscosity iteration processes, respectively. Our results show that the above three iterative methods are applicable to the nonexpansive cosine families; and the implicit and viscosity iterations are superior the explicit iteration in convergence.
By means of critical points theory, we prove the existence of infinitely many solutions for two classes of perturbed symmetric elliptic equations involving p-Laplacian
In this paper, the left and right inverse eigenpairs problem and associated approximation problem on the given disk of eigenvalues of reflexive matrices are studied. Under special conditions, the general solutions of the left and right inverse eigenpairs problem are presented, and the expression of the solution for the optimal approximation problem is obtained.
The following random graph process Gt is introduced. Assuming that at the time-step 1 and 2 there has been a graph G1=G2 consisting of vertices v1, v2 and 2 edges between them. At time-step t≥3, Gt is defined as follows: (i) each vertex v∈Gt-1 is inactive with probability α0, independently its and other vertices' statuses before t-1. The inactiveness of v means it can not being connected by more edges; (ii) with probability 1-β a new vertex vt is added along with one edge connected to it. Then a vertex wi is chosen with probability proportional to its degree. If wi is active then connect vt to wi. Otherwise, the edge of vt is connected to itself; (iii) with probability β a vertex is deleted preferentially from the network. It is proved that there is a phase transition on expected degree distribution when 2β//(1-α0) is in the vicinity of 1. In the supercritical regime (2β/(1-α0)>1), its expected fraction of vertices with degree k decays exponentially. While in the subcritical regime (2β/(1-α0)<1), the expected fraction of vertices with degree k decreases asymptotically as a power law.
In this paper, the three-species predator-prey model with diffusion and cross-diffusion is discussed. By applying the method of upper and lower solutions, the existence of positive solutions of this model is obtained. And then the non-existence of positive solutions of the model is considered.
Let R be a ring, and let J(R) be the Jacobson radical of R. An element of a ring R is called strongly J-clean provided that it can be written as the sum of an idempotent and an element in J(R) that commute. For a commutative local ring R with 2∈J(R), we get a necessary and sufficient condition under which a 2×2 matrix over RG is strongly J-clean where G={ 1, g} is a group. An application to strong cleanness is also obtained
This paper is to research the transport equations of an age structured proliferating cell populations in Lp-space (1≤p<+∞). It is to prove that the C0 semigroups by the transport operators is compact, and it is to obtain that the spectrum of the transport operators is countable and consists of, at most, isolate eigenvalues with finite algebraic multiplicity with -∞ as the only possible limit point.
The bilinear element approximation is discussed for a class of nonlinear dispersion-dissipative wave equations. Based on the high acuraccy analysis of the element and interpolation post-processing technique, the optimal order error estimate, superclose property and superconvergence result in H1 norm are deduced for semi-discrete scheme under the proper regularity property hypothesis of the exact solution. At the same time, the extrapolation result with three order is obtained by constructing a new extrapolation scheme. Finally, a fully-discrete scheme is established and the superclose property is studied.
In this paper, the authors generalize the Roper-Suffridge extension operator, and discuss that the generalized operators preserve some properties of subclasses of biholomorphic mappings. From the definition, they prove the fact that the generalized operators preserve spirallikeness of type β and order α and strongly spirallikeness of type β, and as the special case, they obtain that the generalized operators preserve starllikeness of order α and strongly starllikeness on the corresponding domain, and they also research the distortion of the generalized operators.
Wish all the best wishes for youRecommendationWish all the best wishes for youRecommendation