Mediterranean Journal of Mathematics最新文献

We focus on investigating the differential geometric properties of cuspidal edge in the three-sphere from a viewpoint of duality. Using Legendrian duality, we study a special kind of flat surface along cuspidal edge in three-dimensional sphere space. This kind of surface is dual to the singular set of the cuspidal edge surface. Thus, we call it the flat (Delta )-dual surface. Flatness of a surface can be defined by the degeneracy of the dual surface. It is similar to the case for the Gauss map of a flat surface in Euclidean space. Moreover, classifications of singularities of the flat (Delta )-dual surface are shown. We also investigate the dual relationships of singularities between flat (Delta )-dual surface and flat approximations of the original cuspidal edge surface. At last, we consider a global geometry of the singular set of a cuspidal edge surface using the flat (Delta )-dual surface.

We study the topological algebra identification of the multiplier algebra of a certain algebra E and that of a closed left ideal in E. The case when one of the algebras is a Segal topological algebra in the other is considered. We also study this problem in the context of locally (C^{*})-algebras.

We introduce a notion of proper morphism for schematic finite spaces and prove the analog of Grothendieck’s finiteness theorem for it. The techniques we employ, which further develop the theory of schematic spaces and proschemes, are ultimately founded on descent properties of flat epimorphisms of rings that are applicable in other situations in order to weaken finite presentation requirements.

By utilizing Krasnoselskii’s fixed point theorem, we examine a specific class of first-order neutral nonlinear differential equations and establish criteria for the existence of positive periodic solutions. The theoretical framework developed in this study is substantiated by an illustrative example.

In this work, ruled surfaces in 3-dimensional Riemannian manifolds are studied. We determine the expressions for the extrinsic and sectional curvatures of a parametrized ruled surface, where the former one is shown to be non-positive. We also quantify the set of ruling vector fields along a given base curve which allows us to define a relevant reference frame that we refer to as Sannia frame. The fundamental theorem of existence and equivalence of Sannia ruled surfaces in terms of a system of invariants is given. The second part of the article tackles the concept of the striction curve, which is proven to be the set of points where the so-called Jacobi evolution function vanishes on a ruled surface. This characterisation of striction curves provides independent proof for their existence and uniqueness in space forms and disproves their existence or uniqueness in some other cases.

In this paper, an exploration is undertaken into positivity and positivity-definiteness within the Cauchy product and self-product, which encompass normalized linear functionals applied to the space of real polynomials. We reveal that for two normalized linear functionals, (mathscr {U}) and (mathscr {V}), the positivity-definiteness of (mathscr {V}mathscr {U}) and the positivity of (mathscr {V}mathscr {U}^{-1}) imply the positive-definiteness of (mathscr {V}). Additionally, if (mathscr {U}^2) is positive-definite (resp. positive), and (mathscr {V}^2) is positive, then (mathscr {U}mathscr {V}) is positive-definite (resp. positive). The extension of the integer Cauchy power to the real powers of a linear functional introduces the concept of the index of positivity for linear functionals. We establish some properties of the index map. Finally, we determine the index of positivity for various linear functionals, including the Dirac mass at any real point and some linear functionals with semi-classical character.

Two generalized integrals of the beta family are the prime focus of this paper. By taking into account the generalized integral of the beta family, the series and integral representations are created through generalized special functions. Also covered are the fractional maps of Saigo, Riemann–Liouville, and Kober operators with the extended beta function. Results for classical beta function and extended beta functions were proved as special cases.

We study existence of solutions for the singular system of Schrödinger-Maxwell equations

Here (r > 1), (0< theta < 1), and (f(x) ge 0) belongs to suitable Lebesgue spaces. We will also prove that the solution ((u,psi )) is a saddle point of a suitable functional.

In this paper, we study the Makar–Limanov invariant and its modifications in the case of not necessary normal affine toric varieties. We prove the equality of the Makar–Limanov invariant and the modified Makar–Limanov invariant in this case.

In this paper, we study conformally flat almost Kenmotsu 3-manifolds such that (text {tr} , h^2) is a constant and (nabla _{xi }h=-2alpha hvarphi ) for some constant (alpha ). Moreover, we classify conformally flat H-almost Kenmotsu 3-manifolds.