Uniqueness of diffusion generators for two types of particle systems with singular interactions

For two types of stochastic particle systems in we show non-explosion in finite time by proving that their respective generators are L¹(μ)-unique, where μ is their respective invariant (in these cases even symmetrizing) measure. We also prove the much harder L²(μ)-uniqueness in both models.     

Definition and detection of data-based uniqueness in evaluating bilinear (two-way) chemical measurements

Multivariate curve resolution methods, frequently used in analyzing bilinear data sets, result in ambiguous decomposition in general. Implementing the adequate constraints may lead to reduce the so-called rotational ambiguity drastically, and in the most favorable cases to the unique solution. However, in some special cases, non-negativity constraint as minimal information of the system is a sufficient condition to resolve profiles uniquely. Although, several studies on exploring the uniqueness of the bilinear non-negatively constrained multivariate curve resolution methods have been made in the literature, it has still remained a mysterious question. In 1995, Manne published his profile-based theorems giving the necessary and sufficient conditions of the unique resolution. In this study, a new term, i.e., data-based uniqueness is defined and investigated in details, and a general procedure is suggested for detection of uniquely recovered profile(s) on the basis of data set structure in the abstract space. Close inspection of Borgen plots of these data sets leads to realize the comprehensive information of local rank, and these argumentations furnish a basis for data-based uniqueness theorem. The reported phenomenon and its exploration is a new stage (it can be said fundament) in understanding and describing the bilinear (matrix-type) chemical data in general.     

On results of G. Brosch and T.C. Alzahary

We prove a uniqueness theorem for two non-constant meromorphic functions sharing three values which improves a recent result of T.C. Alzahary. As a consequence of our main result we also improve a theorem of G. Brosch.     

Uniqueness and value-sharing of entire functions

In this paper, we study the uniqueness problems on entire functions sharing one value with the same multiplicities. We generalize and unify some previous results of Fang and Hua [M.L. Fang, X.H. Hua, Entire functions that share one value, J. Nanjing Univ. Math. Biquarterly 13 (1) (1996) 44-48], Yang and Hua [C.C. Yang, X.H. Hua, Uniqueness and value-sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (2) (1997) 395-406] and Fang [M.L. Fang, Uniqueness and value-sharing of entire functions, Comput. Math. Appl. 44 (2002) 828-831].     

Nonlinear weighted best simultaneous approximation in Banach spaces

The present paper is concerned with the problem of weighted best simultaneous approximations in Banach spaces. The weighted best simultaneous approximations to sequences from S- and BS-suns in the Banach space are characterized in view of the Kolmogorov conditions. Applications are provided for weighted best simultaneous approximations from RS-sets and strict RS-sets. Our results obtained in the present paper extend and improve all earlier known results in this direction.     

Meromorphic solutions of equations over non-Archimedean fields

In this paper, we give some conditions to assure that the equation P(X)=Q(Y) has no meromorphic solutions in all K, where P and Q are polynomials over an algebraically closed field K of characteristic zero, complete with respect to a non-Archimedean valuation. In particular, if P and Q satisfy the hypothesis (F) introduced by H. Fujimoto, a necessary and sufficient condition is obtained when deg P=deg Q. The results are presented in terms of parametrization of a projective curve by three entire functions. In this way we also obtain similar results for unbounded analytic functions inside an open disk.      

Almost periodic solution for n-species Lotka–Volterra competitive system with delay and feedback controls

In this paper, a n-species Lotka–Volterra competition system with delay and feedback controls is investigated. By means of the theory of comparison theorem and suitable Lyapunov functional, some sufficient conditions for the existence and uniqueness of almost positive periodic solutions of this system is obtained.     

Solvability of the boundary value problem for stationary magnetohydrodynamic equations under mixed boundary conditions for the magnetic field

The global solvability of the boundary value problem for stationary magnetohydrodynamic equations under the Dirichlet boundary condition for the velocity and mixed boundary conditions for the magnetic field is proved.     

Existence and uniqueness of maximal strong solution of a 1D blood flow in a network of vessels

We study the well-posedness of a system of one-dimensional partial differential equations modeling blood flows in a network of vessels with viscoelastic walls. We prove the existence and uniqueness of maximal strong solution for this type of hyperbolic/parabolic model. We also prove a stability estimate under suitable nonlinear Robin boundary conditions.