Positivity最新文献

We provide fundamental results on positive solutions to parametrized systems of generalized polynomial inequalities (with real exponents and positive parameters), including generalized polynomial equations. In doing so, we also offer a new perspective on fewnomials and (generalized) mass-action systems. We find that geometric objects, rather than matrices, determine generalized polynomial systems: a bounded set/"polytope" P (arising from the coefficient matrix) and two subspaces representing monomial differences and dependencies (arising from the exponent matrix). The dimension of the latter subspace, the monomial dependency d, is crucial. As our main result, we rewrite polynomial inequalities in terms of d binomial equations on P, involving d monomials in the parameters. In particular, we establish an explicit bijection between the original solution set and the solution set on P via exponentiation. (i) Our results apply to any generalized polynomial system. (ii) The dependency d and the dimension of P indicate the complexity of a system. (iii) Our results are based on methods from linear algebra and convex/polyhedral geometry, and the solution set on P can be further studied using methods from analysis such as sign-characteristic functions (introduced in this work). We illustrate our results (in particular, the relevant geometric objects) through three examples from real fewnomial and reaction network theory. For two mass-action systems, we parametrize the set of equilibria and the region for multistationarity, respectively, and even for univariate trinomials, we offer new insights: We provide a "solution formula" involving discriminants and "roots".

In this paper, we study the positive solutions for nonlocal differential equations with concave and convex coefficients:

where (0<p<1le q.) Using the fixed point index theory and fixed point theorems on cones, existence and multiplicity results are obtained, when the nonlinear term f(t, x) is continuous, has a singularity at (x=0), changes sign, respectively.

In this paper, we first introduce some types of set relations on the power set of n-dimensional Euclidean spaces which are proposed by Kuroiwa–Tanaka–Ha and Jahn–Ha. We also mention new types of cancellation laws of set relations. Second, we introduce a complete lattice-valued problem on the power set of n-dimensional Euclidean spaces proposed by Hamel et al. Applying nonlinear scalarizing technique in complete lattice, we present a new type of minimal element theorem and generalized Ekeland’s variational principles in complete lattice optimization problem. We also present an existence theorem of minimal solutions related to the famous Takahashi’s minimization theorem in complete lattice optimization problem.

In this paper we provide a representation of a certain class of C*-valued positive sesquilinear and linear maps on non-unital quasi *-algebras, thus extending the results from Bellomonte (GNS-construction for positive (C^*-)valued sesquilinear maps on a quasi (*-)algebra, Mediterr. J. Math., 21 166 (22 pp) (2024)) to the case of non-unital quasi *-algebras. Also, we illustrate our results on the concrete examples of non-unital Banach quasi *-algebras, such as the standard Hilbert module over a commutative C*-algebra, Schatten p-ideals and noncommutative (L^2)-spaces induced by a semifinite, nonfinite trace. As a consequence of our results, we obtain a representation of all bounded positive linear C*-valued maps on non-unital C*-algebras. We also deduce some norm inequalities for these maps. Finally, we consider a noncommutative (L^2)-space equipped with the topology generated by a positive sesquilinear form and we construct a topologically transitive operator on this space.

In this paper, a subgradient projection method for quasiconvex minimization problems is provided. By employing strong subdifferentials, it is proved that the generated sequence of the proposed algorithm converges to the solution of the minimization problem of a proper, lower semicontinuous, and strongly quasiconvex function (in the sense of Polyak in Soviet Math 7:72–75, 1966), under the same assumptions as those required for convex functions with the convex subdifferentials. Furthermore, a quasi-linear convergence rate of the iterates, extending similar results for the general quasiconvex case, is also provided.

In this paper we introduce and study a new class of operators related to norm bounded sets on Banach Lattices and which brings together several classes of operators (as o-weakly compact, b-weakly compact, M-weakly compact, L-weakly compact and almost Dunford–Pettis operators). As applications, we find some new lattice approximation properties of these classes of operators.

The purpose of this paper is to establish several characterizations of almost order (L) sets (respectively, almost (L) sets). These characterizations generalize and correct those obtained recently by K. El Fahri and F.Z. Oughajji. In addition, we show that the almost (L) sets enjoy some interesting lattice approximation properties. Among other things, we show that a Banach lattice E has weakly sequentially continuous lattice operations if and only if the convex solid hull of every (L) set of ( E^{prime }) is an (L) set. Moreover, we study the domination property for absolutely weakly sequentially continuous operators.

In this paper, we propose a new class of generalized Nash-population games (GNPGs) which can be used to capture the desired features of both population games (PGs) and generalized Nash games within the same framework. We introduce the concept of generalized inertial Nash equilibrium (GINE) for the GNPG and show the existence of GINE by using the method of the system of variational inequalities and fixed point theorems both in the compact and noncompact cases. Moreover, we introduce a slightly altruistic generalized inertial Nash equilibrium (SAGINE) as a refinement concept of the GINE and prove that the GNPG has at least an SAGINE under some mild assumptions.

In the present manuscript, we present examples of regular upper semi-Fredholm (resp. non upper semi-Fredholm) operators on Banach lattices having non upper semi-Fredholm (resp. upper semi-Fredholm) modulus. We give also an example of a regular upper semi-Fredholm operator on Banach lattices with no modulus.

We investigate the spectrum and the essential spectra of weighted automorphisms of the polydisc algebra (mathbb {A}^n). In the case (n=2) we provide a detailed and, in most cases, complete description of these spectra.