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The aim of the present article is to establish the connection between the existence of the limit along the normal and an admissible limit at a fixed boundary point for holomorphic functions of several complex variables.
We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating…
We are interested in belief revision involving conditional statements where the antecedent is almost certainly false. To represent such problems, we use Ordinal Conditional Functions that may take infinite values. We model belief change in…
We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…
In this paper we discuss the existence of solutions to vectorial differential inclusions. We investigate sufficient conditions for existence, more flexible than those available in the literature, so that important applications can be fitted…
Simulations of specifications are introduced as a unification and generalization of refinement mappings, history variables, forward simulations, prophecy variables, and backward simulations. A specification implements another specification…
An $integral$ of a group $G$ is a group $H$ whose commutator subgroup is isomorphic to $G$. This paper continues the investigation on integrals of groups started in the work arXiv:1803.10179. We study: (1) A sufficient condition for a bound…
Interval linear programming provides a tool for solving real-world optimization problems under interval-valued uncertainty. Instead of approximating or estimating crisp input data, the coefficients of an interval program may perturb…
This article is devoted to obtain new sufficient conditions for an extremum in problems of classical calculus of variations. The concept of a set of integrands is introduced. Using this concept, first and second order sufficient conditions…
In this study, new master theorems and general formulas of integrals are presented and implemented to solve some complicated applications in different fields of science. The proposed theorems are considered to be generators of new problems,…
Interval arithmetic is a simple way to compute a mathematical expression to an arbitrary accuracy, widely used for verifying floating-point computations. Yet this simplicity belies challenges. Some inputs violate preconditions or cause…
When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…
The aim of this paper is to exhibit a necessary and sufficient condition of optimality for functionals depending on fractional integrals and derivatives, on indefinite integrals and on presence of time delay. We exemplify with one example,…
This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their…
The aim of this paper is first to give necessary and sufficient condition of existence (of free boundaries) for both Laplacian and bi-Laplacian operators in the case where the overdetermined condition is not constant. second, by using some…
Instrumental variables allow for quantification of cause and effect relationships even in the absence of interventions. To achieve this, a number of causal assumptions must be met, the most important of which is the independence assumption,…
We provide new results on the existence of extremal solutions for discontinuous differential equations with a deviated argument which can be either delayed or advanced. The boundary condition is allowed to be discontinuous and to depend…
The present paper is a continuation of the author's previous works, in which necessary and sufficient local extrema at a stationary point of a polynomial or a power series (and thus of an analytic function) are given. It is known that for…
It is shown that a finite number of conditions are {\em not} sufficient to determine the locality of transformations between two probability distributions of pure states as well as the locality of transformations between two $d\times d$…
This paper is concerned with the existence of positive solutions of second-order impulsive differential equations with integral boundary conditions on an infinite interval. As an application, an example is given to demonstrate our main…