*Khan N.U., Usman T.*CERTAIN GENERATING FUNCTIONS OF HERMITE-BERNOULLI-LEGENDRE POLYNOMIALS**Status:**In this paper, we introduce a new class of generating functions for Hermite- Bernoulli-Legendre polynomials and investigate certain implicit summation formulas by using different analytical means and applying generating function. We also introduce bi- lateral series associated with the newly-introduced generating function by appropriately specializing a number of known or new partly unilateral and partly bilateral generating functions.*reviewing*

Abstract.**Date of submission:**27 January 2017 г.

*Rathod A.*Nevanlinna’s Five-values Theorems for Algebroid Functions**Status:**By using the second main theorem of the algebroid function, we inves- tigate the problem on two algebroid functions partially sharing five or more values and that improve and generalize the previous results given by Xuan and Gao.*accepted в т.0 №0*

Abstract.**Date of submission:**06 Aprel 2017 г.*Stepanova I.V.*Symmetries of heat and mass transfer equations in viscous fluids**Status:**The paper is devoted to description of results of application of classical Lie-Ovsyannikov theory to study of heat and mass transfer equations in viscous liquids. Group properties of equations of convective and molecular heat and mass transfer are under consideration. The author analyzed 124 papers and monographs be concerning to mentioned problem.*reviewing*

Abstract.**Date of submission:**10 Aprel 2017 г.*Zhukova N.I.*The influence of stratification on groups of conformal transformations of pseudo-Riemannian orbifolds**Status:**Groups of conformal transformations of*accepted в т.0 №0*

Abstract.*n*n -dimensional pseudo-Riemannian orbifolds (N,*g*)(N,g) are investigated for*n*≥3n≥3 . It is shown that a conformal pseudo-Riemannian geometry is induced on each stratum of that orbifold. For*k*∈{0,1}∪{3,...,*n*−1}k∈{0,1}∪{3,...,n−1} exact estimates of dimensions of the conformal transformation groups of*n*n -dimensional pseudo-Rieman\-ni\-an orbifolds admitting*k*k -dimensional strata with essential conformal trans\-for\-ma\-tion groups are obtained.**Date of submission:**08 May 2017 г.*Kachalov V.I.*Pseudoholomorphic functions and their application**Status:**An analysis of asymptotic methods for solving singularly perturbed problems shows that the solutions obtained by means of these solutions depend in two ways on the small parameter: regularly and singularly. This dependence is particularly clearly demonstrated by the method of regularization of S.A.\,Lomov. Moreover, the regularized solu\-tions of singularly perturbed equations can converge in the usual sense. In this connection, it became necessary to study a special class of functions, pseudoholomorphic functions. This is a very important part of the analy\-sis, it is intended to substantiate the main points of the so-called analytic theory of singular perturbations. On the other hand, the relevance of the theory in question is also dictated by the fact that pseudoholomorphic functions, unlike holomorphic functions, are determined when the condi\-tions of the implicit function theorem are violated.*reviewing*

Abstract.**Date of submission:**16 May 2017 г.*Trynin A.Yu.*Uniform convergence of sync-approximations on the functional class**Status:**We obtain a uniform convergence inside the interval (0, \ pi) of the values of the Lagrange-Sturm-Liouville operators for functions from the class. The class is defined by means of one-way moduli of continuity and change*accepted в т.0 №0*

Abstract.**Date of submission:**18 May 2017 г.*Bobodzhanov A.A., Safonov V.F.*Regularized asymptotics of solutions of integro-differential partial differential equations with rapidly varying kernels**Status:**The method of Lomov regularization is generalized to partial differential equations with integral operators, the kernel of which contains a rapidly varying exponential factor. The case when the upper limit of the integral operator coincides with the differentiation variable is investigated. For such problems, an algorithm for constructing regularized asymptotics develops. In contrast to the work of Imanaliev M.I., where for analogous problems with slowly varying nuclei only the limit transition is investigated when the small parameter tends to zero, an asymptotic solution of any order (with respect to the parameter) is constructed here.*reviewing*

Abstract.**Date of submission:**19 May 2017 г.*Fedotov A.I.*Hermite-Fejer polynomials as an approximate solution of the singular integro-differential equations**Status:**An approximate method for solving singular integro-differen-tial equations in periodic case is justified. An approximate solution is sought in a form of Hermite-Fejer polynomials. The convergence of the method is proved and the errors are estimated.*reviewing*

Abstract.**Date of submission:**24 May 2017 г.*Kachalov V.I.*On the holomorphic regularization of strongly nonlinear singularly perturbed problems**Status:**The method of holomorphic regularization, which is a logical extension of the Lomov method, allows one to construct solutions of nonlinear singularly perturbed initial problems in the form of series converging in the usual sense in powers of a small parameter. The method itself is based on a generalization of the Poincare decomposition theorem: in the regular case, solutions depend holomorphically on a small parameter, in the singular case the first integrals inherit this dependence.*reviewing*

Abstract.**Date of submission:**29 May 2017 г.*Zikkos E.*A Taylor-Dirichlet series with no singularities on its abscissa of convergence**Status:**In this paper it is proved that given any non-negative real number*reviewing*

Abstract.*d*d , there exists a Taylor-Dirichlet series of the form∑*n*=1∞(∑*k*=0*μ**n*−1*c**n*,*k**z**k*)*e**λ**n**z*,*c**n*,*k*∈C∑n=1∞(∑k=0μn−1cn,kzk)eλnz,cn,k∈Cwith no singularities on its abscissa of convergence, such that its associated multiplicity-sequence Λ={

*λ**n*,*μ**n*}∞*n*=1Λ={λn,μn}n=1∞ has the following properties: \noindent (1) the terms of ΛΛ are positive real numbers and uniformly separated, \noindent (inf*n*∈N(*λ**n*+1−*λ**n*)>0)(infn∈N(λn+1−λn)>0) , \noindent (2) ΛΛ has density equal to*d*d , (lim*t*→∞∑*λ**n*≤*t**μ**n**t*=*d*<∞)(limt→∞∑λn≤tμnt=d<∞) , \noindent (3) the multiplicities of the terms of ΛΛ are unbounded, (*μ**n*≠*O*(1))(μn≠O(1)) . The proof is based on the fact that for this sequence ΛΛ its Krivosheev characteristic*S*ΛSΛ is negative. We remark that when*μ**n*=1μn=1 for all*n*∈Nn∈N the result is false by a well known theorem of P\'{o}lya.**Date of submission:**30 May 2017 г.*Vinnitskii B.V., Sharan V.L., Sheparovych I.B.*About some interpolation problem in the class of functions of exponential type in a half-plane**Status:**The conditions of solvability of the interpolation problem*reviewing*

Abstract.*f*(*λ**k*)=*d**k*f(λk)=dk are found in the class of functions of exponential type. This results are applied to research of some problem of the function's splitting.**Date of submission:**01 June 2017 г.*Klimentov S.B.*About Isomorphism of Some Integro-differential Operators**Status:**In this work representations of <> for solutions of the linear general elliptic system of the first order in the unit circle are considered. The isomorphism of corresponding operators is established in Banach spaces*accepted в т.0 №0*

Abstract.*C**k**α*(*D*¯¯¯¯)Cαk(D¯) and*W**k**p*(*D*¯¯¯¯)Wpk(D¯) ,*k*≥k≥ 1, 0<→*a**l**p**h**a*<0<→alpha< 1,*p*>p> 2. These results develop and supplement B.V. Boyarsky's works where representa\-tions of <> where obtained. Also this work supplements author’s results on representations of <> with more difficult operators.**Date of submission:**02 June 2017 г.*Poluboyarova N.M.*On the instability of extremals of the potential energy functional**Status:**In this paper study has been done on problem of stability and instability of the potential energy functional. By stability we mean the sign-definiteness of the second variation. The expression for the second variation of the functional is calculated. With the capacitive method it is obtain to make the feature of instability extremals. Proved that stability parabolic extremals are planes. We have written the equation of extremals and the second variation of the functional for n-dimensional surfaces of revolution.*reviewing*

Abstract.**Date of submission:**18 June 2017 г.*Berdellima A.*ON A CONJECTURE OF KHABIBULLIN ABOUT A PAIR OF INTEGRAL INEQUALITIES**Status:**It is known that in general Khabibullin’s conjecture is not true. Sharipov [8] constructed a counterexample when*accepted в т.9 №2*

Abstract.*n*=2n=2 and*α*=2α=2 . In this paper we develop a method of how to construct a counterexample for the more general case*n*>2n>2 and*α*>1/2α>1/2 .**Date of submission:**24 June 2017 г.*Garayev M., Guediri H., Sadrawi H.*New Characterizations of Bloch spaces, Bers-type and Zygmund-type spaces and Related Questions**Status:**We give in terms of Berezin symbols new characterizations of\ the Bloch spaces BB and B0,B0, Bers-type and the Zygmund-type spaces of analytic functions on the unit disc DD of the complex plane C.C. Moreover, we discuss some properties of Toeplitz operators on the Bergman space*reviewing*

Abstract.*L*2*a*(D).La2(D). A new characterization of\ some function space with variable exponents is also given.**Date of submission:**29 June 2017 г.*Kopachevsky N.D., Tsvetkov D.O.*Малые движения идеальной стратифицированной жидкости со свободной поверхностью, полностью покрытой крошеным льдом**Status:**Let a rigid immovable vessel be partially filled with an ideal incompressible stratified fluid. We assume that in an equilibrium state the density of a fluid is a function of the vertical variable*reviewing*

Abstract.*x*3,x3, i.e.,*ρ*0=*ρ*0(*x*3).ρ0=ρ0(x3). In this case the gravitational field with constant acceleration*g*⃗=−*g**e*⃗3g→=−ge→3 acts on the fluid, here*g*>0g>0 and*e*⃗3e→3 is unit vector of the vertical axis*O**x*3,Ox3, which is directed opposite to*g*⃗.g→. Let ΩΩ be the domain filled with a fluid in equilibrium state,*S*S be rigid wall of the vessel adherent to the fluid, ΓΓ be a free surface completely covered with a crumbled ice. The initial boundary value problem is reduced to the Cauchy problemA*d*2*x**d**t*2+C*x*=*f*(*t*),*x*(0)=*x*0,*x*′(0)=*x*1,0<<A=A∗∈L(H),0≤C=C∗∈L(H).Ad2xdt2+Cx=f(t),x(0)=x0,x′(0)=x1,0<<A=A∗∈L(H),0≤C=C∗∈L(H).in some Hilbert space HH . The theorem on strong solvability of initial boundary value problem is proved.

**Date of submission:**29 June 2017 г.*Baskakov A.G., Uskova N.B.*Linear differential operator with an involution as generator of group of operators**Status:**We consider mixed problem for first order differential equation with involution. By the method of similar operators, he differential operator, which defined by this differential equation, is transformed in orthogonal direct sum of operators. By the main theorem we construct group of operators and we describe the weak solutions of this problem. We use this theorem for Fourier method.*accepted в т.0 №0*

Abstract.**Date of submission:**29 June 2017 г.*Andriyan S.M., Kroyan A.K., Khachatryan K.A.*On Solvability of a Class of Nonlinear Integral Equations in*p*p -adic String Theory**Status:**In this paper a class of nonlinear integral equations, which has direct application in the*accepted в т.0 №0*

Abstract.*p*p -adic string theory, is studied. The existence of a nontrivial continuous odd and bounded solution on the whole axis is proved. With some additional conditions, the uniqueness of the constructed solution in the certain class of continuous functions is established as well.**Date of submission:**15 July 2017 г.*RamReddy T., Shalini D., Vamshee Krishna D.*THIRD ORDER HANKEL DETERMINANT FOR STAR LIKE FUNCTIONS OF ORDER*α*α**Status:**The objective of this paper is to obtain best possible upper bound to the third Hankel determinant for the class of starlike functions of order*reviewing*

Abstract.*α*α (0≤*α*<10≤α<1 ), using Toeplitz determinants.**Date of submission:**17 July 2017 г.*Muravnik A.B.*On Qualitative Properties of Solutions of Quasilinear Parabolic Equations Admitting Degenerations at Infinity**Status:**We consider the Cauchy problem для for quasilinear parabolic equations of the kind*reviewing*

Abstract.*ρ*(*x*)*u**t*=Δ*u*+*g*(*u*)|∇*u*|2,ρ(x)ut=Δu+g(u)|∇u|2, where the positive coefficient*ρ*ρ admits a degeneration at infinity, while the coefficient*g*g either is a continuous function or admits power singularities such that the power does not exceed one. The long-time behavior of (classical) solutions of the specified problem is investigated.**Date of submission:**21 July 2017 г.*Ehrgashev T.G.*Third Double-Layer Potential for a Generalized Bi-Axially Symmetric Helmholtz Equation**Status:**The double-layer potential plays an important role in solving boundary value problems for elliptic equations, and in the study of which for a certain equation, the properties of the fundamental solutions of the given equation are used. All the fundamental solutions of the generalized bi-axially symmetric Helmholtz equation were known, and only for the first one was constructed the theory of potential. Here, in this paper, we aim at constructing theory of double-layer potentials corresponding to the third fundamental solution. By using some properties of one of Appell's hypergeometric functions in two variables, we prove limiting theorems and derive integral equations concerning a denseness of double-layer potentials.*accepted в т.0 №0*

Abstract.**Date of submission:**31 July 2017 г.*Bandura A.I., Skaskiv O.B.*Exhaustion by balls and entire functions of bounded**L**L -index in joint variables**Status:**We prove criteria of boundedness of*reviewing*

Abstract.**L**L -index in joint variables which describe local behavior of partial derivatives on sphere in C*n*.Cn. Some obtained results are new even for entire functions of bounded index in joint variables, i. e.**L**(*z*)≡1,L(z)≡1, because we used an exhaustion of C*n*Cn by balls instead an exhaustion of C*n*Cn by polydiscs.**Date of submission:**08 Avgust 2017 г.*Baskakov A.G., Dikarev E.E.*Spectral Theory of Functions in Research of Partial Differential Operators**Status:**Spectral properties of differential operators with constant coefficients defined on subspaces of space of bounded continuous functions are studied. Necessary and sufficient conditions of invertibility are obtained under condition of regularity at the infinity (ellipticity type conditions) of polynomial which describes such operators. Spectrum, images and kernels are described. Conditions of compactness of resolvent of differential operators are obtained. Main results are obtained by methods of harmonic analysis and spectral theory of Banach modules.*accepted в т.0 №0*

Abstract.**Date of submission:**10 Avgust 2017 г.*Rubinshtein A.I.*On the Bary-Stechkin Theorem**Status:**We concider the problem on the modulus of continuity for the analogue conjugate functions in the case of functions in the case of functions defined on the diadic group. It is shown that for this case no analogue a Bary--Stechkin theorem.*reviewing*

Abstract.**Date of submission:**18 Avgust 2017 г.*Das S.*ON THE ZEROS OF A POLYNOMIALS**Status:**In this paper we extend a classical result due to Cauchy [6] for moduli of all zeros of a polynomial of degree*reviewing*

Abstract.*n*n . our result is best possible and sharpen some well-known results. In many cases the new bounds are much better than some other known bounds.**Date of submission:**30 Avgust 2017 г.*Gadylshin T.R., Mukminov F.Kh.*Perturbation of second order nonlinear equations by the delta-like potential**Status:**Boundary value problems for one-dimensional quasyilinear second order equation are considered, perturbed by the Delta-shaped potential*reviewing*

Abstract.*ε*−1*Q*(*ε*−1*x*)ε−1Q(ε−1x) , where*Q*(*ξ*)Q(ξ) --- finite function, 0<*ε*≪10<ε≪1 . By the method of integral inequalities solutions to these boundary value problems are built with accuracy*O*(*ε*)O(ε) . To prove the existence of a solution the source and limit problems the fixed point theorem is used. For linear boundary value problem all types of boundary conditions are considered.**Date of submission:**16 September 2017 г.*Salakhudinov R.G.*Some properties of domain functionals on level sets**Status:**For a plane domain*reviewing*

Abstract.*G*G we consider special functionals that are constructed with the help of domain functions, such as the distance function from a point to the boundary ∂*G*∂G , and the warping function of*G*G . Functionals that depend on the distance function are considered in the case of simply-connected domains. Functionals that depend on the distance function are considered in the case of simply-connected domains. Functionals depending on the warping function of a finitely connected domain are also studied. We prove that isoperimetric monotonicity properties with respect to a free parameter of the functionals generate another monotonicity of the functionals. Namely, we consider the functionals as functions defined on subdomains of*G*G . Some special cases of inequalities were obtained earlier by Payne. We note that the inequalities have been successfully applied to justify new estimates of the torsional rigidity of simply connected and multiply connected domains. In particular, new functionals of the domain with monotonic property in both their arguments are constructed.In addition, exact estimates of the rate of change of the functionals are found, that is, exact estimates of the derivatives are obtained.**Date of submission:**26 September 2017 г.*Merzlyakov S. G.*Systems of convolution equations in complex domains**Status:**In this paper we study systems of convolution equations in spaces of vector-valued functions of one variable. For such systems an analogue of the interpolating function of Leot'ev is defined and a number of properties of this function are given. A theorem on the representation of arbitrary vector functions in a series of elementary solutions of a homogeneous system of convolution equations is proved.*reviewing*

Abstract.**Date of submission:**24 October 2017 г.*Rathod A.*CHARACTERISTIC FUNCTION AND DEFICIENCY OF ALGEBROID FUNCTIONS ON ANNULI**Status:**In this paper, the value distribution theory for meromorphic functions with maximal deficiency sum will be considered for algebroid functions on annuli and also the relationship between the deficiency of algebroid function on annuli and that of their derivatives is studied.*reviewing*

Abstract.**Date of submission:**26 October 2017 г.*Asylgareev A.S.*On the application of comparison theorems to the study of stability with probability 1 of stochastic differential equations**Status:**Comparison theorems for solutions of stochastic differential equations were proven. Based on the results obtained conditions of the stability with probability 1 of the perturbed solution of a stochastic differential equation were shown. The approach stated in the article is based on the fact that the solution of a stochastic differential equation can be represented as a deterministic function of a random argument. Due to the fact that this technique is based on properties of the individual trajectory, the results obtained in this work can be reformulated for deterministic analogs of stochastic differential equations.*reviewing*

Abstract.**Date of submission:**03 November 2017 г.*Petrosova M.A., Tikhonov I.V., Sherstyukov V.B.*A rate of growth of the coefficients in the Bernstein polynomials of the standard module function on a symmetric interval**Status:**We study the Bernstein polynomials for the standard module function on a symmetric interval. The question is a~rate of growth of the coefficients in these polynomials with an explicit algebraic representation. Particular attention is paid to the behaviour of the maximum coefficient for which exact exponential asymptotics and corresponding two-sided estimates are established. It is shown that the coefficients ``neighboring'' with the maximum have the same rate of growth. The asymptotics for the sum of absolute values of all coefficients is obtained.*reviewing*

Abstract.**Date of submission:**17 December 2017 г.*Krivosheyeva O.A.*A basis in a invariant subspace of analytical functions**Status:**A representation of functions from an invariant subspace in convex domain in complex plane are studied. A sufficient condition for the existence of a basis in the invariant subspace consisting of linear combinations of eigenfunctions and associated functions of differential operator in this subspace are received. Linear combinations are built on the system of exponential monomials, which are divided into relatively small groups. It is applies a method that uses interpolating function of A. F. Leontiev. Herewith is given a complete description of the space of coefficients of the series which provide a representation of functions from invariant subspace. Also is found the necessary conditions for the representation functions from an arbitrary invariant subspaces admitting spectral synthesis in an arbitrary convex domain. It is used the method of constructing of special series of exponential polynomials developed by the author earlier.*reviewing*

Abstract.**Date of submission:**27 December 2017 г.*Gorbatkov S.A., Polupanov D.V.*ИССЛЕДОВАНИЕ УСТОЙЧИВОСТИ РЕШЕНИЯ НЕЛИНЕЙНОЙ КРАЕВОЙ ЗАДАЧИ ДЛЯ ПАРАБОЛИЧЕСКОГО УРАВНЕНИЯ**Status:**Получено аналитическое решение задачи анализа устойчивости решений нелинейной начально-краевой задачи теплопроводности в твердых телах, описываемой параболическим уравнением. Использован разработанный ранее авторами итеро-аппроксимативный метод (ИАМ) и метод функций Ляпунова. ИАМ позволяет выразить решение на каждом шаге итерации в виде рядов по собственным функциям линейной части параболического оператора задачи и создает все предпосылки для применения математического аппарата функций Ляпунова. Приведены результаты расчетов устойчивости теплофизического процесса в трехмерном металлическом теле с переменными по объему теплофизическими свойствами при возмущении начального состояния.*reviewing*

Abstract.**Date of submission:**28 December 2017 г.*Singh G., Singh G.,*A New Subclass of Univalent Functions**Status:**In this paper, a new subclass*reviewing*

Abstract.*χ**t*(*A*,*B*)χt(A,B) of close-to-convex functions, defined by means of subordination is investigated. Some results such as coefficient estimates, inclusion relations, distortion theorems, radius of convexity and Fekete-Szego problem for this class are derived. The results obtained here is extension of earlier known work.**Date of submission:**02 January 2018 г.*Khakimova A.R.*К задаче описания обобщенных инвариантных многообразий нелинейных уравнений**Status:**В статье обсуждается задача построения обобщенных инвариантных многообразий для нелинейных уравнений в частных производных. Обобщенное инвариантное многообразие является аналогом понятия симметрии и имеет приложения в теории интегрируемости. Обобщенные инвариантные многообразия позволяют эффективно строить пары Лакса и операторы рекурсии для интегрируемых уравнений. В работе дано полное описание обобщенных инвариантных многообразий порядка (2,2)(2,2) для уравнения Кортевега-де Фриза. Показано как связано это многообразие с парой Лакса и с оператором рекурсии.*reviewing*

Abstract.**Date of submission:**15 January 2018 г.*Alhouzani M., Chuprunov A.N.*ПУАССОНОВСКИЕ ПРЕДЕЛЬНЫЕ ТЕОРЕМЫ В СХЕМАХ РАЗМЕЩЕНИЯ РАЗЛИЧИМЫХ ЧАСТИЦ**Status:**Рассматривается случайная величина - число ячеек, содержащих*reviewing*

Abstract.*r*r частиц, среди первых*K*K ячеек в равновероятной схеме размещения не более*n*n различимых частиц по*N*N различным ячейкам. Найдены условия, обеспечивающие сходимость этих случайных величин к пуассоновской случайной величине. Получено описание предельного распределения. Показано, что эти результаты переносятся на схему размещения различимых частиц по различным ячейкам.**Date of submission:**18 January 2018 г.*Borisov D.I.*On spectral gaps of a Laplacian in a strip with a bounded periodic perturbation**Status:**В работе рассматривается Лапласиан с краевым условием Дирихле в бесконечной плоской полосе, возмущённый ограниченным периодическим оператором. Основной полученный результат – отсутствие спектральных лакун в нижней части спектра при достаточно малом периоде потенциала. Верхняя оценка на период, гаран- тирующая данный результат, выписана явно в числовом виде. Также явно выписана длина части спектра, в которой гарантировано отсутствие лакун.*reviewing*

Abstract.**Date of submission:**25 January 2018 г.*Galkina V.S., Polyntseva S.V.*Two problems of identification of two lower coefficients in the many-dimensional parabolic equation of a special type**Status:**We consider two problems of identification of two lower coefficients of the many-dimensional parabolic equa\-tions of a special type. In the first problem the overdetermination conditions are given on the same hyperplane, and in the second problem this conditions are given on two various hyperplanes. The inverse problems are reduced to Cauchy's direct auxiliary problems by means of the overdetermination conditions. The resolvability of direct auxiliary problems are proved. The theorems of existence and uniqueness of classical solutions of the inverse problems are proved in the classes of smooth bounded functions. The solutions of the inverse problems are represented explicitly in terms of the solutions of the direct problems.*reviewing*

Abstract.**Date of submission:**29 January 2018 г.*Amanov D.*Boundary value problem for fourth order equation of mixed type in a rectangular domain**Status:**In the present paper, we study a boundary value problem for fourth order equation of mixed type in a rectangular domain and prove the existence of the unique solution of this problem. In the theory of boundary value problems for mixed type equations usually two conjugation conditions are in use, in general. In this case, for the solvability of boundary value problem governed by mixed type equation containing a hyperbolic equation in a rectangular domain a certain condition (on the sizes of the sides of the rectangle) appears. However, in this paper, we give three conjugation conditions so that such condition does not appear.*reviewing*

Abstract.**Date of submission:**15 February 2018 г.*Gekkieva S.Kh., Kerefov M.A.*First boundary-value problem for Aller – Lykov moisture transfer equation with time fractional derivative**Status:**In this paper we consider the first boundary value problem for the Aller – Lykov moisture transfer equation with the Riemann – Liouville fractional derivative with respect to time. The equation under study presents generalization for the Aller – Lykov equation employing the idea of the fractal speed change in humidity that explains the existence of moisture flows opposing the humidity potential. The existence of a solution to the first boundary-value problem is proved by the Fourier method. With the method of energy inequalities, an a priori estimate is obtained for the solution to the problem in terms of the Riemann – Liouville fractional derivative that implies the uniqueness of the solution.*reviewing*

Abstract.**Date of submission:**20 February 2018 г.*Biswas T.*RELATIVE ORDER AND RELATIVE TYPE ORIENTED GROWTH PROPERTIES OF GENERALIZED ITERATED ENTIRE FUNCTIONS**Status:**The main aim of this paper is to study some growth properties of generalized iterated entire functions in the light of their relative orders, relative types and relative weak types.*reviewing*

Abstract.**Date of submission:**21 February 2018 г.*Poptsova M.N., Habibullin I.T.*Algebraic Properties of Quasilinear Two-Dimensional Lattices**Status:**In the article a classification method for nonlinear integrable equations with three independent variables is discussed based on the notion of the integrable reductions. We call the equation integrable if it admits a large class of reductions being Darboux integrable systems of hyperbolic type equations with two independent variables. The most natural and convenient object to be studied within the frame of this scheme is the class of two dimensional lattices generalizing the well-known Toda lattice. In the present article we deal with the quasilinear lattices of the form*reviewing*

Abstract.*u**n*,*x**y*=*α*(*u**n*+1,*u**n*,*u**n*−1)*u**n*,*x**u**n*,*y*+*β*(*u**n*+1,*u**n*,*u**n*−1)*u**n*,*x*+*γ*(*u**n*+1,*u**n*,*u**n*−1)*u**n*,*y*+*δ*(*u**n*+1,*u**n*,*u**n*−1)un,xy=α(un+1,un,un−1)un,xun,y+β(un+1,un,un−1)un,x+γ(un+1,un,un−1)un,y+δ(un+1,un,un−1) . We specify the coefficients of the lattice assuming that there exist cutting off conditions which reduce the lattice to a Darboux integrable hyperbolic type system of the arbitrarily high order. Under some extra assumption on the structure of the characteristic Lie ring we described the class of the lattices integrable in the sense indicated above.**Date of submission:**27 February 2018 г.*Абдуллаева З.~Ш., Фаязов К.С.*Условная корректность внутренней краевой задачи для псевдо-дифференциального уравнения с меняющимся направлением времени**Status:**We consider a problem with data inside of the regularity domain for a pseudo-differential equation, spectral problems related to like thise equations. The uniqueness of the solution of the problem is proved, and the conditional stability of the solution of the problem on the set of correctness is obtained. Using the results of the generalized spectral problem, the form of the solution of the unknown problem is constructed and the incorrectness is proved, namely, the lack of stability of the solution from the data. The conditional stability of the solution on the set of correctness is proved by the methods of functional analysis. The obtained estimates characterizing the conditional stability of the solution of the required problem.*reviewing*

Abstract.**Date of submission:**28 February 2018 г.*Khusnullin I.Kh.*The perturbation of the quantum and the acoustic waveguide narrow potential**Status:**We consider boundary value problems in an n-dimensional cylinder, Modeling quantum and acoustic waveguides with a potential- which depend on two parameters, small and large. Small the parameter corresponds to the diameter of the carrier of the potential, and the large - its maximum value. The ratios of the parameters are as follows: the product of a small parameter by a square root of a large parameter tends to zero. In this formulation, the problem is different from the previously investigated topics, that the ratio of the parameters of the tax- wives are weaker, and different types of boundary conditions. The main content of the work is constructing a special transformation that translates the operator to an operator with a small localized perturbation. Moreover, this transformation does not change the spectrum of the original operation. Torah. The condition on the potential is obtained, under which from the edge of the non- an eigenvalue arises, as well as condition absence of such an intrinsic value. In case of occurrence, the principal terms of its asymptotics are constructed. Results are formulated as a theorem.*reviewing*

Abstract.**Date of submission:**01 Mart 2018 г.*Lyakhov L.N., Polovinkina M.V., Roshchupkin S.A.*On one Lizorkin's weighted class**Status:**A new class of test functions Φ+*reviewing*

Abstract.*γ*Φγ+ is introduced. This class is constructed by means of the mixed Fourier--Bessel--Kipriyanov--Katrahov transform on the principle of Lizorkin's space. Functional class Φ+*γ*Φγ+ \, (*γ*=(*γ*1,…,*γ**n*)γ=(γ1,…,γn) ,*γ**i*>0γi>0 ) consists of functions that are orthogonal to polynomials of arbitrary order (in the*L**γ*2L2γ scalar product with weight ∏|*x**i*|*γ**i*∏|xi|γi ) and only of them. We prove a theorem that the class Φ+*γ*Φγ+ is dense in the Lebesgue space*L**γ**p*Lpγ with this weight.**Date of submission:**12 Mart 2018 г.*Biswas D., Dutta S.*Mobius action by*S**L*(2;R)SL(2;R) on different homogeneous spaces**Status:**In this paper, we have considered all the possible subgroups of SL(2;R) (upto conjugacy) from dimension zero to three. For each of the classification, we have defined group action on the same line as Vladimir V. Kisil. M¨ obius transformation have been taken as the corresponding action. This action is defined on the homogeneous spaces of various dimensions generated by the subgroups.*reviewing*

Abstract.**Date of submission:**15 Mart 2018 г.*Aldweby H., Darus M., Elhaddad S.*A Subclass of Harmonic Univalent Functions Defined by a Generalized Differential Operator Involving*q*q -Mittag-Leffler function**Status:**The starlike class of complex-valued harmonic univalent functions is defined in this paper by using a rather generalized operator that involve q-Mittag-Leffler function. In a more precise approach, a necessary and sufficient coefficient for functions f is given to be included in this class. Growth bounds and neighborhoods are also consider.*reviewing*

Abstract.**Date of submission:**18 Mart 2018 г.*Aisagaliev A.S., Ayazbayeva A.M., Sigalovskiy M.A.*To the simplest problem of the calculus of variations**Status:**A constructive method for solving the simplest problem of the calculus of variations is developed on the basis of constructing the general solution of the Fredholm integral equation of the first kind.*reviewing*

Abstract.**Date of submission:**24 Mart 2018 г.*Chourdhary A., Raj K.*ORLICZ DIFFERENCE TRIPLE LACUNARY IDEAL SEQUENCE SPACES OVER N-NORMED SPACES**Status:**In the present article, we introduce and study some Lacunary I−convergent and Lacunary I−bounded triple difference sequence spaces defined by Orlicz function over n−normed spaces. We shall investigate some algebraic and topological properties of newly formed sequence spaces. We also make an effort to obtain some inclusion results between these spaces.*reviewing*

Abstract.**Date of submission:**26 Mart 2018 г.*Godase A.D.*ON GENERALIZED*k*k - LUCAS SEQUENCES**Status:**The k- Lucas sequence is companion sequence of k- Fibonacci sequence defined with the k- Lucas numbers which are defined with the recurrence relation L k,n = kL k,n−1 + L k,n−2 with the initial conditions L k,0 = 2 and L k,1 = k. In this paper, we introduce a new generalisation M k,n of k-Lucas sequence. We present generating functions and Binet formulas for generalized k-Lucas sequence, and establish binomial and congruence sums of generalized k-Lucas sequence.*reviewing*

Abstract.**Date of submission:**27 Mart 2018 г.