We examine the geometry of a complete, negatively curved surface isometrically embedded in R3. We are especially interested in the behavior of the ends of the surface and its limit set at infinity. Various constructions are developed, and a classification theorem is obtained, showing that every possible end type for a topologically finite surface with at least one bowl end arises, as well as al...

In this paper, we shall show that the following translation \(I^M\) from propositional fragment \(\bf L_1\) of Leśniewski's ontology to modal logic KTB\) is sound: for any formula \(\phi\) and \(\psi\) L_1\), it defined as (M1) \(I^M(\phi \vee \psi) = I^M(\phi) I^M(\psi)\), (M2) \(I^M(\neg \phi) \neg I^M(\phi)\), (M3) \(I^M(\epsilon ab) \Diamond p_a \supset . \wedge \Box p_b .\wedge p_a\), wher...

In this paper, we study the restriction estimate for a certain surface of finite type in $\mathbb{R}^3$, and partially improves results Buschenhenke-M\"{u}ller-Vargas. The key ingredients proof include so called generalized rescaling technique based on decomposition adapted to geometry, decoupling inequality reduction dimension arguments.

Let (,) be a measurable space with -finite continuous measure, ()=. A linear operator T:L1()+L()L1()+L() is called the Dunford-Schwartz if ||T(f)||1||f||1 (respectively, ||T(f)||||f||) for all fL1() fL()). {Tt}t0is strongly in L1() semigroup of operators, then each At(f)=1t∫0tTs(f)ds∈L1(Ω){{{A_t(f)} ={\frac{1}{t}} {\int_0^t} {T_s(f)} ds \in L_1(\Omega)}} has unique extension to operator, which ...

A heterostructure composed of $N$ parallel homogeneous layers is studied in the limit as their widths $l_1, \ldots , l_N$ shrink to zero. The problem investigated one dimension and piecewise constant potential Schr\"{o}dinger equation given by strengths $V_1, V_N$ functions l_N$, respectively. key point derivation conditions on $V_1(l_1), V_N(l_N)$ for realizing a family one-point interactions ...

We define a broad class of local Lagrangian intersections which we call quasi-minimally degenerate (QMD) before developing techniques for studying their Floer homology. In some cases, one may think such as modeled on minimally functions defined by Kirwan. One major result this paper is: if $L_0,L_1$ are two submanifolds whose intersection decomposes into QMD sets, there is spectral sequence con...