# Editorial backlog

1. Андронова О.А., Войтицкий В. И. О спектральных свойствах одной краевой задачи с поверхностной диссипацией энергии
Status: accepted в т.9 №2
Abstract.
В работе изучается спектральная задача в ограниченной области $\Omega \subset R^{m}$, зависящая от ограниченного операторного коэффициента S$>$0 и параметра диссипации $\alpha >0$. В общем случае установлены достаточные условия, при которых задача имеет дискретный спектр, состоящий из счётного числа изолированных конечнократных собственных значений с предельной точкой на бесконечности, а также условия при которых из системы корневых элементов можно выделить полную подсистему в $L_{2}^{} (\Omega )$. В модельной одномерной и двумерной задаче установлена локализация собственных значений и найдены критические значения $\alpha$.
Date of submission: 01 February 2016 г.

2. Parfenov A.I. Dicrete Holder estimates for a certain kind of parametrix. II
Status: accepted в т.9 №2
Abstract.
In the first part of the paper we have introduced a certain parametrix and its respective potential. The parametrix corresponds to a uniformly elliptic second order differential operator having locally H\"older continuous coefficients in the half-space. Here we show the potential to be an approximate left inverse of the differential operator modulo hyperplane integrals, with the error estimated by the local H\"older norms. As a corollary, we evaluate approximately the potential whose density and differential operator originate from the straightening of the special Lipschitz domain. This corollary is meant for the future derivation of approximate formulas for harmonic functions.
Date of submission: 14 Mart 2016 г.

3. Arabov M.K., Mukhamadiev E.M., Nurov I.D., Sobirov H.I. SIGNS OF EXISTENCE OF LIMITING CYCLES IN THE SECOND ORDER DIFFERENTIAL EQUATIONS
Status: accepted в т.9 №2
Abstract.
This article takes consideration into the discovery of the limiting cycles in neighborhood of stationary point of the non - smooth second order differential equation. New conditions are found for coefficient of the equation which ensure the existence of a limiting cycle. On the basis of taken results was made sector division in a plane. Created a package of programs for drawing phase portraits in appropriate sectors.
Date of submission: 19 Aprel 2016 г.

4. Klyachin A.A. On continuity and differentiability of the maximum values of functions
Status: reviewing
Abstract.
This article discusses the functions which are the maximum values of continuous functions on compact subsets of families. These functions are used, for example, in the study of the geometric structure of the equilibrium of different surfaces -- minimal surfaces, surfaces of constant mean curvature, etc. In this paper we find conditions under which such functions are continuous and differentiable.
Date of submission: 17 May 2016 г.

5. Oreshina M.N. Spectral decomposition of a normal operator in a real Hilbert space
Status: reviewing
Abstract.
Unbounded normal operators acting in a real Hilbert space are considered. In this article we carry over the classic results of the spectral theory to the case of such operators. The questions connected with the complexification and decomplexification of normal operators are discussed. We present two real variants of the spectral decomposition and the real functional calculus theorems for unbounded normal operators acting in a real Hilbert space.
Date of submission: 22 May 2016 г.

6. Шафигуллин И.К. Нижняя оценка константы Харди для произвольной области в $\mathbb{R}^n$.
Status: accepted в т.0 №0
Abstract.
В работе получены отличные от нуля нижние оценки константы Харди для произвольных областей, не совпадающих со всем пространством. Данные оценки являются точными по порядку, при $n \rightarrow \infty$, где $n$ --- размерность пространства.
Date of submission: 25 May 2016 г.

7. Klishchuk B.A., Salimov R.R. LOWER BOUNDS FOR AREAS OF IMAGES OF DISCS
Status: reviewing
Abstract.
In this article we consider Q-homeomorphisms with respect to the p-modulus on the complex plane with p > 2. It is obtained a lower area estimate for image of discs under such mappings. We solved the extremal problem about minimization of the area functional of images of discs.
Date of submission: 16 June 2016 г.

8. MAHDAVIAN RAD H., NIKNAM A. Multi-Tuple Derivations and Automatic Continuity
Status: reviewing
Abstract.
Let A be an algebra and m a natural number. A linear operator d : A → A is called a multi-tuple derivation of degree m if there exist families {δ u },{ε u } of linear operators on A, where u ∈ Z,1 ≤ u ≤ m − 1, such that d(ab) = d(a)b + ad(b) + m−1 ∑ u=0 (δ u (a)ε u (b) + ε u (a)δ u (b)) for all a,b ∈ A. We study some algebraic properties of these mappings and give a formula for calculat- ing d n (ab). After that, we state a few theorems and corollaries regarding the concept automatic continuity. Also we define a new terminology named higher multi-tuple derivation and prove that under certain conditions, it is continuous on semi-simple Banach algebras.
Date of submission: 17 June 2016 г.

9. Rani N., Vamshee Krishna D., Venkateswarlu B. Third Hankel determinant for the inverse of reciprocal of bounded turning functions has a positive real part of order alpha
Status: accepted в т.0 №0
Abstract.
In this paper we obtain the best possible upper bound to the third Hankel determinants for the functions belonging to the class of reciprocal of bounded turning functions using Toeplitz determinants
Date of submission: 29 June 2016 г.

10. Khubiev K.U. Analog of Tricomi problems for characteristicly loaded hyperbolic-parabolic equations with variable coefficients
Status: accepted в т.9 №2
Abstract.
In this paper the analog of Tricomi problem for loaded equation of hyperbolic-parabolic type with variable coefficients is considered. The existence and uniqueness theorem of solution the problems is proved. The uniqueness of solution is proved by maximum principle and the solution existence is proved by integral equation methods.
Date of submission: 07 July 2016 г.

11. Balkizov Zh.A. The first boundary problem for parabolic-hyperbolic equation of third order with degeneration of the type and order in the domain of hyperbolicity
Status: accepted в т.9 №2
Abstract.
We investigated an analog of the Tricomi problem for a parabolic-hyperbolic equation of third order with multiple characteristics, containing terms with lower derivatives. Under certain conditions specified functions and parameters that are included in this equation, a theorem on the existence and uniqueness of solutions of the problem. The uniqueness of the solution of the problem is proved by using the generalized method of Tricomi existence - the method of integral equations.
Date of submission: 07 July 2016 г.

12. Khasanov Yu.Kh., Shakiriv I.A. BILATERAL EVALUATION OF THE NORM OF THE FOURIER OPERATOR
Status: reviewing
Abstract.
The lower and the upper uniform estimates of the Lebesgue constants of the classical Fourier operator are not final. A new and more simple integral representation received for it, then on the basis of which the problem of its top assessment is completely solved and the known lower assessment is improved.
Date of submission: 14 July 2016 г.

13. Горбацевич V.V. О геометрии решения приближенных уравнений и их симметриях
Status: reviewing
Abstract.
The article is devoted to the development of the geometric approach to the theory of approximate equations (including ODE and PDE) and their symmetries. We introduce dual Lie algebras, manifolds over dual numbers and dual Lie group. We describe some constructions for these objects. On the basis of these constructions it is shown how it is possible to formulate basic concepts and methods in the theory of approximate equations and their symmetry. The proofs of many general results here can be obtained almost automatically from classical one's, unlike used now in studying of the approximate equations methods.
Date of submission: 14 July 2016 г.

14. Salo T.M., Skaskiv O.B. The minimum modulus of gap power series and h-measure of exceptional sets
Status: reviewing
Abstract.
For an entire function of the form $f(z)=\sum_{k=0}^{+\infty}f_kz^{n_k}$, where $(n_k)$ is a strictly increasing sequence of non negative integers, we establish conditions when the relations $$M_f(r)=(1+o(1)) m_f(r),\quad M_f(r)=(1+o(1))\mu_f(r)$$ is true as $r\to+\infty$ outside some set $E$ such that $\text{\rm h-meas }(E)=\int_{E}\frac{dh(r)}{r}<+\infty$, where $h(r)$ is positive continuous function increasing to $+\infty$ on $[0,+\infty)$ with non-decreasing derivative, and $M_f(r)=\max\{|f(z)|\colon |z|=r\},\ m_f(r)=\min\{|f(z)|\colon |z|=r\},\ \mu_f(r)=\max\{|f_k|r^{n_k}\colon k\geq 0\}$ the maximum modulus, the minimum modulus and the maximum term of $f,$ respectively.
Date of submission: 22 July 2016 г.

15. Berdellima A. KHABIBULLIN’S CONJECTURE: Khabibullin’s Theorem, a Counterexample and Further Observations
Status: accepted в т.9 №2
Abstract.
We prove a restricted variant of Khabibullin’s Theorem, construct a counterex- ample to the conjecture when $n = 2$ and $\alpha > 1/2$ and explore some relations of the integral inequalities with the beta and Cauchy distribution
Date of submission: 26 July 2016 г.

16. Ахмадуллин R.Z. О НЕРАВЕНСТВЕ РОБИНА ДЛЯ ГИПОТЕЗЫ РИМАНА
Status: reviewing
Abstract.
Рассмотрена гипотеза Римана о распределении нулей дзета-функции в формулировке, не использующем понятия комплексного переменного. Получены необходимые и достаточные условия, при которых неравенство выполнено для всех натуральных чисел N, за исключением их некоторого конечного количества.
Date of submission: 28 July 2016 г.

17. Mitrokhin S.I. Об исследовании дифференциального оператора с суммируемым потенциалом с разрывной весовой функцией
Status: reviewing
Abstract.
В работе предлагается новый подход к исследованию дифференциальных операторов с разрывной весовой функцией. Изучены спектральные свойства дифференциального оператора, заданного на конечном отрезке, с разделенными граничными условиями, с суммируемым потенциалом, с условиями <<сопряжения>> в точке разрыва весовой функции. При больших значениях спектрального параметра получена асимптотика фундаментальной системы решений соответствующего дифференциального уравнения, с помощью которой выведено уравнение на собственные значения изучаемого дифференциального оператора. Изучена индикаторная диаграмма и найдена асимптотика собственных значений исследуемого оператора.
Date of submission: 25 Avgust 2016 г.

18. Khushtova F.G. The first boundary value problem in the half-strip for a differential equation with Bessel operator and partial derivative of Riemann-Liouville
Status: reviewing
Abstract.
We study the first boundary value problem in the half-strip for a differential equation with Bessel operator and partial derivative of Riemann-Liouville. The representation of the solution in the case of the zero side condition found in terms of the integral transform with the Wright's function at the kernel. Uniqueness of the solution is proved in the class of functions that satisfy the analogue of Tikhonov's condition.
Date of submission: 16 September 2016 г.

19. Khrystiyanyn A.Y., Lukivska D.V. Quasi-elliptic functions
Status: reviewing
Abstract.
We investigate quasi-elliptic functions (i. e. certain generalization of elliptic functions). For this class of functions analogues of $\wp$, $\zeta$ and $\sigma$ Weierstrass functions are constructed and relation between quasi-elliptic and $p$-loxodromic functions is obtained.
Date of submission: 27 September 2016 г.

20. Nurmagomedov A.A., Rasulov N.K., Umalatov A.A. Estimations to Function Lebega of Fourier Sums by Polynomials Orthogonal on Non-uniform grids
Status: reviewing
Abstract.
We study to function Lebega of Fourier private sums by polynomials forming orthonormal system on non-uniform grids from segments $[-1, 1]$ are investigated. In particular, we find a order of the growing for discrete function Lebega.
Date of submission: 28 October 2016 г.

21. Krivosheyeva O.A. Invariant subspaces with spectrum of zero density
Status: reviewing
Abstract.
In the paper it is shown that every analytic solution of the homogeneous convolution equation with the characteristic function of a minimal exponential type in the domain of its existence is represented as the series of exponential polynomials which converges uniformly on compact subsets of this domain.
Date of submission: 31 October 2016 г.

22. Baizaev S., Rakhimova M.A. О некоторых функциональных уравнениях в пространствах Шварца и их приложениях
Status: reviewing
Abstract.
В статье изучается вопросы нетривиальной разрешимости функциональных уравнений вида $$(B+r^{2}E)u(r,\theta)=0$$ где $B -$ постоянная комплексная матрица порядка $n$, $E -$ единичная матрица порядка $n$, $(r,\theta) -$ полярные координаты в пространствах Шварца. Получены многообразия всех решений из указанных пространств и даны приложения результатов к задачам нахождения решений полиномиального роста ряда классов эллиптических систем и переопределенных систем.
Date of submission: 12 December 2016 г.

23. Garifullin R.N., Yamilov R.I. On the integrability of a discrete analogue of the Kaup–Kupershmidt equation
Status: accepted в т.0 №0
Abstract.
We study a new example of equation obtained as a result of a recent generalized symmetry classification of differential-difference equations defined on five points of one-dimensional lattice. We have established that in the continuous limit this new equation goes into the well-known Kaup–Kupershmidt equation. We have also proved its integrability by constructing an $L-A$ pair and conservation laws. Moreover, we present a possibly new scheme for deriving conservation laws from $L-A$ pairs.
Date of submission: 12 December 2016 г.

24. Ishkina Sh.Kh. Combinatorial bounds of overfitting for threshold classifiers
Status: reviewing
Abstract.
Tightening generalization bounds is a fundamental objective of statistical learning theory. However, accurate and computationally efficient bounds are still unknown even for very simple cases. In~this paper, we consider one-dimensional threshold decision rules. We~use the framework of combinatorial theory of overfitting, which is based on a single probabilistic assumption that all partitions of a~set of objects into an observed training sample and a~hidden test sample can occur with equal probability. We~propose a~polynomial algorithm for computing both probability of overfitting and complete cross-validation.
Date of submission: 21 December 2016 г.

25. Kalyakin L.A. Adiabatic approximation for a model of resonance capture
Status: accepted в т.9 №2
Abstract.
Две модельные задачи о захвате в резонанс анализируются методом усреднения, который приводит к адиабатическому приближению в главном члене асимптотики. Основной целью является приближенное описание области захвата в резонанс. Эта область зависит от дополнительного параметра, входящего в уравнения. Демонстрируется непригодность адиабатического приближения, когда область захвата становится узкой. В этом случае требуется значительное изменение метода усреднения.
Date of submission: 26 December 2016 г.

26. Galakhov E.I., Salieva O.A. Условия отсутствия решений некоторых неравенств и систем с функциональными параметрами и сингулярными коэффициентами на границе
Status: accepted в т.0 №0
Abstract.
We obtain sufficient conditions for nonexistence of positive solutions of some nonlinear elliptic inequalities and systems that contain the $p(x)$-Laplace operators with variable power exponents and coefficients possessing singularity on the boundary.
Date of submission: 28 December 2016 г.

27. Tunc C. A note on the qualitative properties of solutions of nonlinear retarded Volterra integro-differential equations
Status: reviewing
Abstract.
In this article, we construct new sufficient conditions for the asymptotically stability and boundedness of solutions to nonlinear Volterra integro-differential equations of first order with constant delay. Our analysis is based on the successful construction of suitable Lyapunov –Krasovskii functionals. The results of this paper are new and correct, and they improve that obtained in literature.
Date of submission: 30 December 2016 г.

28. Belaidi B., Saidani M. On The Growth of Solutions of Some Higher Order Linear Differential Equations With Meromorphic Coefficients
Status: reviewing
Abstract.
In this paper, we study the growth of meromorphic solutions of the differential equation ....
Date of submission: 06 January 2017 г.

29. Khan N.U., Usman T. CERTAIN GENERATING FUNCTIONS OF HERMITE-BERNOULLI-LEGENDRE POLYNOMIALS
Status: reviewing
Abstract.
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.
Date of submission: 27 January 2017 г.

30. Shukla I. Simultaneous Quadruple Series Equations Involving Konhauser Biorthogonal Polynomials
Status: reviewing
Abstract.
Spencer and Fano [11] used the biorthogonal polynomials (for the case of k = 2) in carrying out calculations involving penetration of gamma rays through matter. In the present paper an exact solution of simultaneous quadruple series equations involving Konhauser – biorthogonal polynomials of first kind of different indices is obtained by multiplying factor technique due to Noble [13]. This technique has been modified by Thakare [12] to solve dual series equations involving orthogonal polynomials which led to disprove a possible conjecture of Askey [6] that dual series equations involving Jacobi polynomials of different indices cannot be solved. In this paper the solution of simultaneous quadruple series equations involving generalized Laguerre polynomials also have been discussed in a particular case.
Date of submission: 28 January 2017 г.

31. Malyutin K.G., Shevtsova T.V. The delta-subharmonic functions of finite $(\gamma,\varepsilon)$-growth
Status: reviewing
Abstract.
Let $\gamma(r)$ be growth function and $\varepsilon(r)>0$ be non-increasing function satisfying the condition $\varepsilon(r(1+\varepsilon(r)))\geqslant(\varepsilon(r))^\eta$ for some $\eta>1$ for all large $r$. We consider the class $\delta\mathcal{S}(\gamma,\varepsilon)$ delta-subharmonic functions $v$ in $\mathbb{C}$ such that the Nevanlinna characteristic $T(r,v)$ is estimated by the inequality $T(r,v)\leqslant\frac{a}{(\varepsilon(r))^{\alpha}}\gamma(r+\beta\varepsilon(r)r)$ for some positive constants $a,\ \alpha,\ \beta$. The necessary and sufficient conditions for a function $v$ in class $\delta\mathcal{S}(\gamma,\varepsilon)$ is obtained. These criteria are formulated in terms of $c_k (r, v)=\frac1{2\pi}\int_0 ^{2\pi}v(re^{i\theta})e^{-ik\theta}\,d\theta$, $k\in\mathbb Z$, the Fourier coefficients of the function $v$.
Date of submission: 28 January 2017 г.

32. Salimov R.B. The study of the behavior of the singular integral with the Hilbert kernel near a point of the new weak continuity of the density
Status: reviewing
Abstract.
We study the behavior of a singular integral with the Hilbert kernel near a fixed point, where the density vanishes as a negative exponent of the logarithm module of the distance from the fixed point to a variable one at the new conditions.
Date of submission: 08 February 2017 г.

33. Biswas T., Datta S.K. On some bounds involving relative Ritt type and relative Ritt weak type of entire functions represented by vector valued Dirichlet series
Status: reviewing
Abstract.
In this paper we wish to study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of relative Ritt type and relative Ritt weak type.
Date of submission: 13 February 2017 г.

34. Murtazina S.A., Fazlytdinov M.F., Shevtsova T.V., Yumagulov M.G. Operator methods for computing Lyapunov quantities in the problems on the local bifurcations of dynamical systems
Status: reviewing
Abstract.
This work proposes new formulas to calculate Lyapunov quantities in problems of major scripts of local bifurcations of dynamical systems. Considered a dynamical system, described by differential equations, and point mappings. The proposed formulas are obtained from the general operational method of the study of local bifurcations and do not require transition to normal forms and use theorems about the central diversity.
Date of submission: 06 Mart 2017 г.

35. Kononova A.A. On measures generating orthogonal polynomials with similar asymptotic behavior of the ratio near infinity
Status: reviewing
Abstract.
We consider perturbations of orthogonality measure of the system of polynomials that do not change (in some sense) the asymptotical behavior of the ratio of corresponding orthogonal polynomials. The support of the measure consists of the finite number of Jordan curves and may also contain a finite number of mass-points out of the polynomial convex hull of the support of the absolute continuous part of the measure. The problem is a generalization of the problem of compactness of the perturbation of Jacobi operator generated by the perturbation of its spectral measure. A condition, necessary (or necessary and sufficient under some additional restriction) for the stability of the asymptotical behavior of the corresponding orthogonal polynomials is found.
Date of submission: 09 Mart 2017 г.

36. Halder S., Sahoo P. UNIQUENESS OF MEROMORPHIC FUNCTIONS CONCERNING DIFFERENTIAL POLYNOMIALS SHARING A SET
Status: reviewing
Abstract.
In this paper, we investigate the uniqueness of meromorphic functions whose certain nonlinear differential polynomials share a set of values with finite weight and obtain some results that generalize and improve the recent results due to H.Y. Xu [J. Computational Analysis and Applications, 16(2014), 942-954].
Date of submission: 27 Mart 2017 г.

37. Nuraliev F.A., Hayotov A.R., Shadimetov Kh.M. Optimal quadrature formulas with derivatives in Sobolev space
Status: reviewing
Abstract.
In the present paper the problem of construction of optimal quadrature formulas in the sense of Sard in the space $L_2^{(m)}(0,1)$ is considered. Here the quadrature sum consists of values of the integrand at nodes and values of the first and the third derivatives of the integrand at the end points of the integration interval. The coefficients of optimal quadrature formulas are found and the norm of the optimal error functional is calculated for arbitrary natural number $N\geq m-3$ and for any $m\geq 4$ using S.L. Sobolev method which is based on the discrete analogue of the differential operator $d^{2m}/dx^{2m}$. In particular, for $m=4,\ 5$ optimality of the classical Euler-Maclaurin quadrature formula is obtained. Starting from $m=6$ new optimal quadrature formulas are obtained. At the end of this work some numerical results are presented.
Date of submission: 30 Mart 2017 г.

38. Krivosheyev A.S., Kuzhaev A.F. On a Leontiev-Levin theorem
Status: reviewing
Abstract.
In this work we investigate relations between different densities of a positive sequence and variables related to them. The results are used to generalise classical proposition on completeness of exponential monomials systems with positive exponents in a convex domain when these exponents haven't density. That proposition was obtained by A.Leontiev and B.Levin independently. This generalisation is given for sufficiently wide class of convex domains, for example, with vertical or horizontal symmetry axes.
Date of submission: 30 Mart 2017 г.

39. Rathod A. Nevanlinna’s Five-values Theorems for Algebroid Functions
Status: reviewing
Abstract.
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.
Date of submission: 06 Aprel 2017 г.

40. Khashimov A.R. ЭНЕРГЕТИЧЕСКИЕ ОЦЕНКИ ДЛЯ РЕШЕНИЙ КРАЕВЫХ ЗАДАЧ УРАВНЕНИЯ ТРЕТЬЕГО ПОРЯДКА С КРАТНЫМИ ХАРАКТЕРИСТИКАМИ
Status: reviewing
Abstract.
В статье рассмотрена первая краевая задача для уравнения третьего порядка с кратными характеристиками. Для обобщенного решения уравнения установлена энергетические оценки типа аналога принципа Сен-Венана. С помощью этой оценки выявлены наибольшее класс единственности решений краевых задач в зависимости от геометрических характеристик области.
Date of submission: 07 Aprel 2017 г.

41. Kalinin S.I. $(0,1)$-convex functions
Status: reviewing
Abstract.
The paper is devoted to the class of so-called $(0, 1)$-convex functions on the interval. A geometric characterization of such functions is given, their properties are studied, in particular, the Jensen inequality and its analogue are established. Sufficient conditions for the $(0, 1)$-convexity and $(0, 1)$-concavity of a function in terms of derivatives are formulated.
Date of submission: 07 Aprel 2017 г.

42. Shabat A.B., Эфендиев M.H. О приложениях формулы Фаа-ди-Бруно
Status: reviewing
Abstract.
Two new modifications of the classical Faa-di-Bruno formula are constructed and applications of the obtained formulas in the theory of integrability of nonlinear partial differential equations
Date of submission: 08 Aprel 2017 г.

43. Stepanova I.V. Symmetries of heat and mass transfer equations in viscous fluids
Status: reviewing
Abstract.
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.
Date of submission: 10 Aprel 2017 г.