Related papers: A sufficient and necessary condition for $\mathcal…

This is the second in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. The research in this article aims to find conditions of an algorithmic nature that are necessary and sufficient to…

In this paper we give some sufficient conditions of analyticity and univalence for functions defined by an integral operator. Next, we refine the result to a quasiconformal extension criterion with the help of the Becker's method. Further,…

In extending Stein's method to new target distributions, the first step is to find a Stein operator that suitably characterises the target distribution. In this paper, we introduce a widely applicable technique for proving sufficiency of…

We present a necessary and sufficient condition for Alt's system to be represented by a continuous utility function. Moreover, we present a necessary and sufficient condition for this utility function to be concave. The latter condition can…

Let $\Phi$ be a real valued function of one real variable, let $L$ denote an elliptic second order formally self-adjoint differential operator with bounded measurable coefficients, and let $P$ stand for the Poisson operator for $L$. A…

We generalize a result by Alberti, showing that, if a first-order linear differential operator $\mathcal{A}$ belongs to a certain class, then any $L^1$ function is the absolutely continuous part of a measure $\mu$ satisfying…

We consider the class of integral operators $Q_\f$ on $L^2(\R_+)$ of the form $(Q_\f f)(x)=\int_0^\be\f (\max\{x,y\})f(y)dy$. We discuss necessary and sufficient conditions on $\phi$ to insure that $Q_{\phi}$ is bounded, compact, or in the…

Let $C$ be an affine plane curve. We consider additive functions $f: K\rightarrow K$ for which $f(x)f(y)=0$, whenever $(x,y)\in C$. We show that if $K=\mathbb{R}$ and $C$ is the hyperbola with defining equation $xy=1$, then there exist…

We study the necessary and sufficient conditions on Abelianizable first class constraints. The necessary condition is derived from topological considerations on the structure of gauge group. The sufficient condition is obtained by applying…

We derive necessary and sufficient conditions for a continuous bounded function $f: R\to C$ to be a characteristic function of a probability measure. The Cauchy transform $K_f$ of $f$ is used as analytic continuation of $f$ to the upper and…

Approximate stationarity conditions provide necessary optimality conditions without requiring additional assumptions by demanding that a perturbed stationarity system possesses solutions as the involved perturbations tend to zero. Together…

In 2014, Michal Lewicki and Andrzej Olbry\'s proved that if a real valued function $f$ defined on the real line satisfies the conditional functional equation \[ f(tx + (1-t)y) = t f(x) + (1-t) f(y),\qquad x\leq y, \] called…

In the paper, we provide a new method to study the oscillatory singular integral operator $T_{Q,A}$ with nonstandard kernel defined by \[T_{Q,A} f(x)=\text { p.v. } \int_{\mathbb{R}^{n}} f(y)…

We consider general symmetric systems of first order linear partial differential operators on domains $\Omega \subset \mathbb{R}^d$, and we seek sufficient conditions on the coefficients which ensure essential self-adjointness. The…

We discuss the (first- and second-order) optimality conditions for nonlinear programming under the relaxed constant rank constraint qualification. This condition generalizes the so-called linear independence constraint qualification.…

We study some logical interrelationships between fundamental properties in (relativistic) quantum theories. An operational no-signalling condition is first introduced in the context of quantum mechanics, where we prove its equivalence to an…

A well-known theorem of Paulsen says that if $\mathcal{A}$ is a unital operator algebra and $\phi:\mathcal{A}\to B(\mathcal{H})$ is a unital completely bounded homomorphism, then $\phi$ is similar to a completely contractive map $\phi'$.…

Existence of an increasing quasi-concave value function consistent with given preference information is an important issue in various fields including Economics, Multiple Criteria Decision Making, and Applied Mathematics. In this paper, we…

We prove that for a homogeneous linear partial differential operator $\mathcal A$ of order $k \le 2$ and an integrable map $f$ taking values in the essential range of that operator, there exists a function $u$ of special bounded variation…

Making use of the method of subordination chains, we obtain some sufficient conditions for the univalence of an integral operator. In particular, as special cases, our results imply certain known univalence criteria. A refinement to a…