含参广义集值强向量平衡问题的稳定性

本文借助集合极限的性质和弱f-性假设证明了含参广义集值强向量平衡问题解集映射的下半连续性,其方法不同于最近文献(Zhao,2016和Meng,2018).此外,建立了含参广义集值强向量平衡问题解集连通性的充分条件,并举例验证了所得结果的正确性.本文得结果推广和改进了已有文献(Gong,2008,Xu,2009,Chen,2010,Xu,2013和Zhao,2013)中相应结果.     

Isomorphisms of spaces with large distortion

Let K and S be locally compact Hausdorff spaces and let X be a strictly convex Banach space of finite dimension at least 2. In this paper, we prove that if there exists an isomorphism T from onto satisfying then K and S are homeomorphic. Here denotes the Schäffer constant of X. Even for the classical cases , and , this result is the X‐valued Banach–Stone theorem via isomorphism with the largest distortion that is known so far, namely . On the other hand, it is well known that this result is not true for , even though K and S are compact Hausdorff spaces.     

The prescribed Ricci curvature problem on three‐dimensional unimodular Lie groups

Let G be a three‐dimensional unimodular Lie group, and let T be a left‐invariant symmetric (0,2)‐tensor field on G. We provide the necessary and sufficient conditions on T for the existence of a pair consisting of a left‐invariant Riemannian metric g and a positive constant c such that , where is the Ricci curvature of g. We also discuss the uniqueness of such pairs and show that, in most cases, there exists at most one positive constant c such that is solvable for some left‐invariant Riemannian metric g.     

Well‐posedness of fractional integro‐differential equations in vector‐valued functional spaces

We study the well‐posedness of the fractional differential equations with infinite delay on Lebesgue–Bochner spaces and Besov spaces , where A and B are closed linear operators on a Banach space X satisfying ,  and . Under suitable assumptions on the kernels a and b, we completely characterize the well‐posedness of in the above vector‐valued function spaces on by using known operator‐valued Fourier multiplier theorems. We also give concrete examples where our abstract results may be applied.     

Fractional powers of the noncommutative Fourier's law by the S‐spectrum approach

Let e_?, for ? = 1,2,3, be orthogonal unit vectors in and let be a bounded open set with smooth boundary ?Ω. Denoting by a point in Ω, the heat equation, for nonhomogeneous materials, is obtained replacing the Fourier law, given by the following: into the conservation of energy law, here a, b, are given functions. With the S‐spectrum approach to fractional diffusion processes we determine, in a suitable way, the fractional powers of T. Then, roughly speaking, we replace the fractional powers of T into the conservation of energy law to obtain the fractional evolution equation. This method is important for nonhomogeneous materials where the Fourier law is not simply the negative gradient. In this paper, we determine under which conditions on the coefficients a, b, the fractional powers of T exist in the sense of the S‐spectrum approach. More in general, this theory allows to compute the fractional powers of vector operators that arise in different fields of science and technology. This paper is devoted to researchers working in fractional diffusion and fractional evolution problems, partial differential equations, and noncommutative operator theory.     

How vector feeding preference through an infectious host relates to the seasonal transmission rates in a mathematical vector‐host model

Vector‐borne diseases, such as leishmaniasis, dengue, malaria, and yellow fever, transmitted by microparasites show periodic fluctuations in their prevalence. The novelty of this research is to assess the relationship between the vector feeding preference for an infectious host and the annual seasonal transmission through a vector‐host mathematical model. For the first time, numerical simulations illustrate that by increasing the vector feeding preference value in the transmission dynamics, periodic fluctuations accentuate and the endemic equilibrium average increases in vector and host populations. Moreover, increasing the vector feeding preference value, the amplitude strengthens for the infectious host and vector populations. This periodic behavior shows a similar pattern with the Peruvian incidence data from 2000 to 2016 for Andean cutaneous leishmaniasis provided by the Ministry of Health of Peru (MINSA). In addition, using the Floquet theory, the time average method and the linear operator method provides for the first time that the basic reproduction number for a nonautonomous system depends explicitly on the vector feeding preference for the infectious host. The nonautonomous model system shows that is a threshold parameter for the local stability of the disease‐free periodic solution. Therefore, the vector feeding preference is an important factor that should be considered and attended to for future research. Public and veterinary health in Peru and other countries should consider the vector feeding preference for specific host to vector control.     

Parallel Translation on K¨ahler Manifolds

In this paper, the author establishs a real-valued function on K¨ahler manifolds by holomorphic sectional curvature under parallel translation. The author proves if such functions are equal for two simply-connected, complete K¨ahler manifolds, then they are holomorphically isometric.     

Mean curvature flow with free boundary – Type 2 singularities

In this paper we give sufficient conditions that guarantee the mean curvature flow with free boundary on a pinched cylinder develops a Type 2 curvature singularity. We additionally prove that Type 0 singularities may only occur at infinity.     

Semiample and k-ample vector bundles

Abstract

The main result of this paper is that tensor products of semiample vector bundles over compact complex manifolds are semiample. An easy proof yields the analogous result for direct sums. We also show that tensor products of semiample vector bundles with k-ample vector bundles in the sense of Sommese are k-ample. On the other hand, we show that it is not generally true that tensor products of nef and k-ample vector bundles for positive k are still k-ample. Results of Sommese on k-ampleness are consequently strengthened. As an application of our main theorem we extend to k-ample the vanishing theorem of Ein-Lazarsfeld.