Inequalities involving multipliers using the sequences {cn} and {dn} of positive real numbers are introduced for complex-valued harmonic univalent functions. By specializing {cn} and {dn}, we determine representation theorems, distortion bounds, convolutions, convex combinations, and neighbourhoods for such functions. The theorems presented, in many cases, confirm or generalize various well-kno...

The objective of this paper is to deal with the fuzzy conic programming problems. The aim here is to derive weak and strong duality theorems for a general fuzzy conic programming. Toward this end, The convexity-like concept of fuzzy mappings is introduced and then a specific ordering cone is established based on the parameterized representation of fuzzy numbers. Under this setting, duality theo...

We prove several results concerning the existence of potentially crystalline lifts of prescribed Hodge–Tate weights and inertial types of a given representation r : GK → GLn(Fp), where K/Qp is a finite extension. Some of these results are proved by purely local methods, and are expected to be useful in the application of automorphy lifting theorems. The proofs of the other results are global, m...

The paper investigates technical meta-logical notions and theorems relating to definitions and relative definability and shows how these are relevant to the concerns of knowledge representation. In particular they can be used to identify sets of primitives that are sufficent to fully describe a given domain. Fundamental definability theorems of Tarski are examined, and it is shown how these can...

Let f : M ! E m be an immersion of a manifold in a Euclidean space. called the cubic representation of the submanifold. The purpose of this article is to investigate the geometry of the cubic representation of a spherical submanifold. Several theorems in this respect are obtained.

Parikh theorem was originally stated and proved by Rohkit Parikh in MIT research report in 1961. Many different proofs of this classical theorems were produced then; our goal is to give another proof using Chomsky-Schutzenberger representation theorem. We present the proof which doesn't use any formal language theory tool at all except the representation theorem, just some linear algebra.

In the paper, authors discuss some extended results involving Catalan numbers and establish an integral representation of in terms $(\alpha,k)$-gamma $(\alpha,k)$-beta function. We refer to available literature by giving special values parameters obtained theorems.

We extend the notion of cointegration for time series taking values in a potentially infinite dimensional Banach space. Examples such include stochastic processes $C[0,1]$ equipped with supremum distance and those finite vector space non-Euclidean distance. then develop versions Granger–Johansen representation theorems I(1) I(2) autoregressive (AR) To achieve this goal, we first note that an AR...

We prove robust representation theorems for monetary measures of risk in a situation of uncertainty, where no probability measure is given a priori. They are closely related to a robust extension of the Savage representation of preferences on a space of financial positions which is due to Gilboa and Schmeidler. We discuss the problem of computing the monetary measure of risk induced by the subj...

It is shown that every two-variable adjunction in categories enriched a commutative quantale serves as base for constructing Isbell adjunctions between functor categories, and Kan are precisely constructed from suitable associated adjunctions. Representation theorems established fixed points of these