Abstract In this paper we present a result of a general nature related to arbitrary enough smooth real functions. It is a simple principle (in the spirit of 17th century) which permits to give (for the first time) bounds for the number of zeros of similar functions. It is interesting that there is a version of the principle (for real functions) similar to the classical Nevanlinna deficiency relation

Abstract In this paper we consider the concept of statistical causality in continuous time between filtrations associated with stopping times, which is based on Granger’s definition of causality. Especially, we consider a generalization of a causality relationship ‘‘\({\mathbf{H}}\) is a cause of \({\mathbf{E}}\) within \({\mathbf{F}}\)’’ from fixed to stopping time. Then we apply the given concept

Abstract In this paper we obtain recovery formulas for coefficients of multiple Ciesielski series by means of its sum, if the square partial sums of a Ciesielski series converge in measure to a function \(f\) and the majorant of partial sums satisfies some necessary condition.

Abstract For a \(d\)-dimensional convex body we define new integral geometric concepts: conditional moments of the random chord length and conditional moments of the distance of two independent uniformly distributed points in the body. In addition, the relations between the concepts are found in this article.

Abstract A multidimensional convolution-type integral equations with concave nonlinearity is investigated. This equation arises in the mathematical theory of the geographic distribution of an epidemic. The combination of well-known multidimensional methods and operator methods for constructing invariant cone segments for such operators with methods of the theory of convolution-type integral operators

Abstract In this paper, the boundedness and compactness of embedding from Campanato spaces \(\mathcal{L}_{p,\lambda}\) into tent spaces \(\mathcal{T}_{p,s}(\mu)\) are investigated. As an application, we give a characterization for the boundedness of the Volterra integral operator \(J_{g}\) from \(\mathcal{L}_{p,\lambda}\) to general function spaces \(F(p,p-1-\lambda,s)\). Meanwhile, the operator \(I_{g}\)

Abstract We study the Fredholm property of semielliptic operators in anisotropic weighted spaces in \(\mathbb{R}^{n}\). In this paper necessary conditions are obtained for fulfillment of a priori estimates for such operators. Necessary and sufficient conditions are obtained for the Fredholm property of semielliptic operators with variable coefficients that have certain rate at infinity.

Abstract The action of the fractional integration operator in weighted Lebesgue classes and mixed-norm spaces is studied in the unit ball from \({\mathbb{R}}^{n}\). Some results of Hardy, Littlewood, and Flett are refined and generalized.

Abstract This paper discusses the location of zeros of polynomials in a polynomial sequence \(\{P_{n}(z)\}_{n=1}^{\infty}\) generated by a three-term recurrence relation of the form \(P_{n}(z)+B(z)P_{n-1}(z)+A(z)P_{n-k}(z)=0\) with \(k>2\) and the standard initial conditions \(P_{0}(z)=1\), \(P_{-1}(z)=P_{-k+1}(z)=0,\) where \(A(z)\) and \(B(z)\) are arbitrary coprime real polynomials. We show that

Abstract In the paper, we have exhaustively studied the uniqueness of meromorphic function sharing two values with its \(k\)th derivative counterpart. We have obtained a series of results each of which will improve and extend a number of existing results relevant to the content of the paper. We have also pointed out some gaps in one theorem in a paper due to Chen et al. (Pure Mathematics, 8(4), 378–382

Abstract We study uniqueness problems in terms of shared values or shared sets for a large class of entire functions representable as Dirichlet series in some right half-plane. In this article, we obtain a result that extends a recent result due to Oswald and Steuding [Ann. Univ. Sci. Budapest., Sect. Comput. 48 (2018), 117–128 (2018)]. Our result is also a variant of a result of Yuan, Li, and Yi [Lith

Abstract In this paper, we consider the entire solutions of nonlinear difference equation \(f^{3}+q(z)\Delta f=p_{1}e^{\alpha_{1}z}+p_{2}e^{\alpha_{2}z}\), where \(q\) is a polynomial, and \(p_{1},p_{2},\alpha_{1},\) and \(\alpha_{2}\) are nonzero constants with \(\alpha_{1}\neq\alpha_{2}\). It is showed that if \(f\) is a nonconstant entire solution of \(\rho_{2}(f)<1\) to the above equation, then

Abstract The following Artin theorem about alternative linear algebras defined on the commutative, associative ring with unity is well-known: in an alternative linear algebra, if \((a,b,c)=0\), then the subalgebra generated by the elements \(a\), \(b\), and \(c\) is associative. In this paper a wide generalization of this classical result is proposed using the concepts of hyperidentity and coidentity

Abstract In work of Movsisyan and Gevorgyan Mov1 , it was proved that the reversible algebra \((Q,\Sigma)\) satisfying the following second-order formula $$\forall X,Y,\exists X^{\prime},Y^{\prime}\forall x,y,z(X(Y^{\prime}(x,y),z)=Y(x,X^{\prime}(y,z))),$$ is linear over the group. In the current work a more general result is proved that the regular and division algebra \((Q,\Sigma)\) with the mentioned

Abstract The Fourier transform associated with the normalized logarithm of the modulus of the Riemann Zeta Function is considered. The formulas linking the Fourier transform and the zeros of the Riemann function are established that lead to the necessary and sufficient condition of satisfaction of the Riemann hypothesis.

Abstract In this paper we study the properties of the Lebesgue constant of the conjugate transforms. For conjugate Fejér means we will find necessary and sufficient condition on \(t\) for which the estimation \(E\left|\widetilde{\sigma}_{n}^{\left(t\right)}f\right|\leq cE\left|f\right|\) holds. We also prove that for dyadic irrational \(t\), \(L\log L\) is the maximal Orlicz space for which the estimation

Abstract In this paper, we present functional Strassen’s law of the iterated logarithm for Csörgő–Révész (C–R) increments of a fractional Brownian motion in Hölder norm with respect to \((r,p)\)-capacity. The method of the proof for our main results is based on the large deviation for the fractional Brownian motion.

Abstract The problem, posed by N.N. Luzin in 1915, on the convergence of trigonometric series to \({+}\infty\) on the set of positive measure, was solved by S.V. Konyagin in 1988. There naturally arises the question of N.N. Luzin for double trigonometric series. In the present paper the theorem is proved which contains the answer to this problem.

Abstract In this paper we prove that a planar set \(\mathcal{X}\) of at most \(mn-1\) points, where \(m\leq n\), is \(\kappa\)-dependent if and only if there exists a number \(r\), \(1\leq r\leq m-1\), and an essentially \(\kappa\)-dependent subset \(\mathcal{Y}\subset\mathcal{X}\), \(\#\mathcal{Y}\geq rs\), where \(r+s-3=\kappa\), belonging to an algebraic curve of degree \(r\), and not belonging

Abstract In this paper our aim is to establish new integral representations for the Fox–Wright function \({}_{p}\Psi_{q}[^{(\alpha_{p},A_{p})}_{(\beta_{q},B_{q})}|z]\) when \(\mu=\sum_{j=1}^{q}\beta_{j}-\sum_{k=1}^{p}\alpha_{k}+\frac{p-q}{2}=-m,\;\;m\in\mathbb{N}_{0}.\) In particular, closed-form integral expressions are derived for the four parameter Wright function under a special restriction on

Abstract In the present paper a formula for calculation of the density function \(f_{\rho}(x)\) of the distance between two independent points randomly and uniformly chosen in a bounded convex body \(D\) is given. The formula permits to find an explicit form of density function \(f_{\rho}(x)\) for body with known chord length distributions. In particular, we obtain an explicit expression for \(f_{\rho}(x)\)

Abstract The paper continues the research to reconstruct a convex body in \({\mathbb{R}}^{n}\) from the distribution of characteristics of its \(k\)-dimensional sections (\(k

Abstract The paper considers measures in the space \(\mathbb{E}\) of planes in \(\mathbb{R}^{3}\), and combinatorial decompositions for their values on ‘‘Buffon sets’’ in \(\mathbb{E}\). These decompositions, written in terms of a ‘‘wedge function’’ depending on the measure, have been known since long in Combinatorial Integral Geometry, yet their explicit expressions have been well established only

Abstract In this paper, we derive an \(L^{p}\) version of the de Rham theorem. The key is an \(L^{p}\) version of the Nec̆as inequality. Using this result and the variational method, we show the existence of a solution to the Maxwell–Stokes type system.

Abstract It is proven that, if the Riemann sums of a trigonometric series are bounded everywhere, perhaps, except for some countable set and converge in measure to a bounded function \(f\), then this series is the Fourier series of the function \(f\). This implies the generalizations of the Cantor and Young theorems.

Abstract The integrable function universal for classes \(L^{p}[0,1]\), \(p\in\left(0,1\right)\) with respect to the Walsh system is constructed in terms of signs. The Fourier–Walsh series of this function converges everywhere in \((0,1)\) and in the metrics \(L^{p}[0,1]\), \(p\in(0,1)\), and its Fourier coefficients by the Walsh system are in decreasing order. After selecting the appropriate signs

Abstract In the paper the formulas are provided for the derivatives of Cauchy-type integral \(K[u]\) which are smooth on the skeleton of the polydisk of functions \(u\). These formulas express the derivatives of the order \(m\) of \(K[u]\) through the derivatives of lower order (Theorem 2.1). They are used for estimating the smoothness of the derivatives of the Cauchy-type integral in terms of Hölder

Abstract In this paper we generalize the concept of the Szegö kernel by putting the weight of integration in the definition of the inner product in the Szegö space. We give some sufficient conditions for the weight in order for the Szegö kernel of the correspoding space to exist. We give examples of weights on unit ball for which there is no Szegö kernel of the corresponding Szegö space. Then using

Abstract In this paper, at first we study boundedness and compactness criterions for generalized composition operator from the Lipschitz space into the Zygmund space. Then we estimate the essential norm of this operator.

Abstract Landesman-Lazer’s type efficient sufficient conditions are established for the solvability of the two-point boundary value problem \(u^{(4)}(t)=p(t)u(t)+f(t,u(t))+h(t)\) for \(a\leq t\leq b\), \(u^{(i)}(a)=0\), \(u^{(i)}(b)=0,\quad(i=0,1)\), where \(h,p\in L([a,b];R)\) and \(f\in K([a,b]\times R;R)\), in the case where the linear problem \(w^{(4)}(t)=p(t)w(t)\), \(w^{(i)}(a)=0\), \(w^{(i)}(b)=0\)

Abstract The complete description of weakly invertible elements in weighted \(L^{p}\) spaces of entire Fock-type functions is obtained in the paper.

erratum

Abstract \(\mathbb{I}_{n}\) (or \(\tilde{\mathbb{I}}_{n}\), respectively) denotes the set of polynomials in \(n\) variables \(P(\xi)=P(\xi_{1},\xi_{2},...,\xi_{n})\) with real coefficients such that \(|P(\xi)|\rightarrow\infty\) as \(|\xi|\rightarrow\infty\) (respectively, \(\tilde{P}(\xi):=\sum_{\nu}|D^{\nu}P(\xi)|\rightarrow\infty\) as \(|\xi|\rightarrow\infty\). The necessary and sufficient conditions

Abstract In this article, we study the existence results of large positive weak solution for nonlinear system with singular weights (1.4), where \(\Omega\) is a bounded domain of \(R^{n}\) with boundary \(\partial\Omega\), \(0\in\Omega\), \(10\). Here, there is no any sign-changing conditions on \(a\) or \(b\). The proof of the main results is based on the sub-supersolutions method. Application and

Abstract In this work we obtain a sufficient condition for analytic functions to belong to certain subclasses of p-valently starlike functions of order \(\beta\) and p-valently close-to-convex functions of order \(\beta\). Further, we get a generalization of some of the well-known results.

Abstract For weighted \(L^{p}\)-classes of holomorphic functions in the unit disc, a family of weighted integral representations with a weighted function of type \(|w|^{2\varphi}\cdot(1-|w|^{2\rho})^{\beta}\) and with reproducing Mittag–Leffler kernels are obtained.

Abstract In this paper, we prove some factorization theorems of Cesàro and Copson spaces on an arbitrary time scale \(\mathbb{T}\), which offer enhancements of dynamic Copson’s and Hardy’s inequalities. Our results enhance, among others, the best-known forms of dynamic Hardy’s inequality. The main results will be proved by employing the time scales Hölder’s inequality and the derived time scales power

Abstract In this paper, we introduce \(n\)-variables mappings which are mixed additive-quadratic in each variable. We show that such mappings can be described by a equation, namely, by a multi-mixed additive-quadratic functional equation. The main goal is to extend the applications of a fixed point method to establish the Hyers-Ulam stability for the multi-mixed additive-quadratic mappings.

Abstract This note is framed in the field of complex analysis and deals with some types of interpolating sequences for Lipschitz functions in the unit disk. We introduce recursion between each point of a sequence and the next. We also add interpolation by the derivative, linking its values to those that the function takes. On the supposition that the sequences are quite contractive and lie in a Stolz

Abstract In this work we introduce the notion of the excess risk in the setup of estimation of the Gaussian mean when the observations are corrupted by outliers. It is known that the sample mean loses its good properties in the presence of outliers [5, 6]. In addition, even the sample median is not minimax-rate-optimal in the multivariate setting. The optimal rate of the minimax risk in this setting

Abstract In this paper we have found the necessary and sufficient conditions for the power integrability with a weight of the sum of the sine and cosine series whose coefficients belong to a subclass of \(\gamma RBVS\) class.

Abstract In this paper, the existing results concerning difference operator sharing two sets have been extended up to the most general form, namely linear difference operator. Furthermore, we have been able to find out the specific form of the function. A considerable number of examples have been exhibited throughout the paper pertinent with different issues.

Abstract The Heun functions satisfy linear ordinary differential equations of second order with certain singularities in the complex plane. The first order derivatives of the Heun functions satisfy linear second order differential equations with one more singularity. In this paper we compare these equations with linear differential equations isomonodromy deformations of which are described by the Painlevé

Abstract In this paper we obtain, that if the partial sums \(\sigma_{q_{k}}(x)\) of a Franklin series converge in measure to a function \(f\), the ratio \(\frac{q_{k+1}}{q_{k}}\) is bounded and the majorant of partial sums satisfies to a necessary condition, then the coefficients of the series are restored by the function \(f\).

Abstract This paper deals with the problem of finding some upper bound estimates for the maximal modulus of the polar derivative of a complex polynomial on a disk under certain constraints on the zeros and on the functions involved. A variety of interesting results follow as special cases from our results.

Abstract In this paper we prove the Noether theorem with the multiplicities described by PD operators. Despite the known analog versions in this case the provided conditions are necessary and sufficient. We also prove the Cayley–Bacharach theorem with PD multiplicities. As far as we know this is the first generalization of this theorem for multiple intersections.

Abstract In the present paper a formula for calculation of the density function \(f_{\rho}(x)\) of the distance between two independent points randomly and uniformly chosen in a bounded convex body \(D\) is given. The formula permits to find an explicit form of density function \(f_{\rho}(x)\) for body \(D\) with known chord length distributions. In particular, we obtain an explicit expression for

Abstract This work is concerned with the solvability of multi-point boundary value problems for fractional differential equations with nonlinear growth at the resonance. Existence results are obtained with the use of the coincidence degree theory. As an application, we discuss an example to illustrate the obtained results.

Abstract For some large classes of differential equations of the first order we give bounds for Ahlfors-Shimizu characteristics of meromorphic solutions in the complex plane of these equations. The considered equations largely generalize algebraic ones for which the obtained results imply the known Goldberg theorem. Characteristics of meromorphic solutions in a given domain weren’t studied at al. We

Abstract One of the main problems in prediction theory of second-order stationary processes, called direct prediction problem, is to describe the asymptotic behavior of the best linear mean squared one-step ahead prediction error variance in predicting the value \(X(0)\) of a stationary process \(X(t)\) by the observed past of finite length \(n\) as \(n\) goes to infinity, depending on the regularity

Abstract In this paper, we investigate the following two Painlevé III equations: \(\overline{w}\underline{w}(w^{2}-1)=w^{2}+\mu\) and \(\overline{w}\underline{w}(w^{2}-1)=w^{2}-\lambda w\), where \(\overline{w}:=w(z+1)\), \(\underline{w}:=w(z-1)\) and \(\mu\) (\(\mu\neq-1\)) and \(\lambda\notin\{\pm 1\}\) are constants. We discuss the questions of existence of rational solutions, of Borel exceptional

Abstract By using lemmas of Dubinin and Osserman some results for rational functions with fixed poles and restricted zeros are proved. The obtained results strengthen some known results for rational functions and, in turn, produce refinements of some polynomial inequalities as well.

Abstract A finite group \(G\) is said to be a generalized Frobenius group with kernel\(F\), if \(F\) is a proper nontrivial normal subgroup of \(G\) and for every element \(Fx\) of prime order of the quotient group \(G/F\) the coset \(Fx\) of the group \(G\) over \(F\) has only \(p\)-elements for some prime \(p\) depending on \(x\). This article considers generalized Frobenius groups with insoluble

Abstract A group is called an \(n\)-torsion group if it has a system of defining relations of the form \(r^{n}=1\) for some elements \(r\), and for any of its finite order element \(a\) the defining relation \(a^{n}=1\) holds. In this paper, we prove that all the finite subgroups of the relatively free \(n\)-torsion groups are cyclic groups. Notice that for each rank \(m>1\) and for any odd \(n\geq

Abstract In this paper, we study the problem of normality of meromorphic functions with multiple values and obtain three normality criteria. Examples are given to illustrate that the conditions in our results are necessary.

Abstract For most of the cases of bounded measurement errors fuzzification of calculations can be used. In the case of reconstructing convex body by random line segments we introduce a fuzzy convex body concept and define orientation dependent distribution of the length of line segment. We consider several properties of the latter.

Abstract In this paper we prove that the quadratic partial sums of a multiple Franklin series with indices \(2^{\nu}\), \(\nu=1,2,...\), cannot converge to \(+\infty\) on a set of positive measure.

Abstract The paper is devoted to the study of a class of integral equations with a symmetric kernel and with convex nonlinearity on the positive semiaxis. Existence and uniqueness theorems for a nonnegative and bounded solution are proved. The qualitative properties of the constructed solution are investigated. At the end of the paper, some particular examples for the above mentioned class of equations

Abstract In this paper, by using variational methods and critical point theory we investigate the existence of solutions for the following fractional Kirchhoff-type equation: $$\begin{cases}S\left(\int\limits_{\mathbb{R}}{|{}_{-\infty}D_{t}^{\alpha}u(t)|}^{2}dt\right){}_{t}D_{\infty}^{\alpha}({}_{-\infty}D_{t}^{\alpha}u(t))+l(t)u(t)=f(t,u(t)),\quad t\in\mathbb{R},\\ u\in H^{\alpha}(\mathbb{R}),\end{cases}$$

In this paper we construct an integrable function of two variables for which the double Fourier-Walsh series converges both by rectangles and by spheres. Besides, we show that the coefficients of the series on the spectrum are positive and are arranged in decreasing order in all directions. Also, it is proved that after a suitable choice of signs for the Fourier coefficients of the series the spherical