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In this paper, we develop a new method for studying the inhomogeneous vector Riemann–Hilbert boundary value problem (which is also called the Riemann boundary value problem) in the Wiener algebra of order two. The method consists in reducing the Riemann problem to a truncated Wiener–Hopf equation (to a convolution equation on a finite interval). The idea of the method was proposed by the author in a previous work. Here the method is applied to the inhomogeneous Riemann boundary value problem and to matrix functions of a more general form. The efficiency of the method is shown in the paper: new sufficient conditions for the existence of a canonical factorization of the matrix function in the Wiener algebra of order two are obtained. In addition, it was established that for the correct solvability of the inhomogeneous vector Riemann boundary value problem, it is necessary and sufficient to prove the uniqueness of the solution to the corresponding truncated homogeneous Wiener–Hopf equation.

The discriminant group of a minimal equicontinuous action of a group $G$ on a Cantor set $X$ is the subgroup of the closure of the action in the group of homeomorphisms of $X$, consisting of homeomorphisms which fix a given point. The stabilizer and the centralizer groups associated to the action are obtained as direct limits of sequences of subgroups of the discriminant group with certain properties. Minimal equicontinuous group actions on Cantor sets admit a classification by the properties of the stabilizer and centralizer direct limit groups. In this paper, we construct new families of examples of minimal equicontinuous actions on Cantor sets, which illustrate certain aspects of this classification. These examples are constructed as actions on rooted trees. The acting groups are countable subgroups of the product or of the wreath product of groups. We discuss applications of our results to the study of attractors of dynamical systems and of minimal sets of foliations., 20 pages, 1 figure. The condition of finite generation in Thm 1.9 was replaced by countability. The proof of Thm 1.9 has been simplified. The notation used in 5 has been modified. Several minor corrections across the paper

This is the first of two papers in which we investigate the properties of the displacement functions of automorphisms of free groups (more generally, free products) on Culler-Vogtmann Outer space and its simplicial bordification - the free splitting complex - with respect to the Lipschitz metric. The theory for irreducible automorphisms being well-developed, we concentrate on the reducible case. Since we deal with the bordification, we develop all the needed tools in the more general setting of deformation spaces, and their associated free splitting complexes. In the present paper we study the local properties of the displacement function. In particular, we study its convexity properties and the behaviour at bordification points, by geometrically characterising its continuity-points. We prove that the global-simplex-displacement spectrum of $Aut(F_n)$ is a well-ordered subset of $\mathbb R$, this being helpful for algorithmic purposes. We introduce a weaker notion of train tracks, which we call {\em partial train tracks} (which coincides with the usual one for irreducible automorphisms) and we prove that, for any automorphism, points of minimal displacement - minpoints - coincide with the marked metric graphs that support partial train tracks. We show that any automorphism, reducible or not, has a partial train track (hence a minpoint) either in the outer space or its bordification. We show that, given an automorphism, any of its invariant free factors is seen in a partial train track map. In a subsequent paper we will prove that level sets of the displacement functions are connected, and we will apply that result to solve certain decision problems., 50 pages. Originally part of arXiv:1703.09945 . We decided to split that paper following the recommendations of a referee. Updated subsequent to acceptance by Transactions of the American Mathematical Society

Embedded software is increasingly being used with high reliability. However, the fault localization of embedded software is still largely dependent on the experience of engineers. Besides, faults in embedded software programs are not independent individuals; they are related to each other and affect each other, which may lead to more complex interaction behavior. These uncertainties render the traditional methods for single-fault localization with limited practical value. This paper has proposed a multiple-fault localization method to be applied to the embedded software, with emphasis on the cache-based program spectra-acquiring method and the hybrid clustering-based fault partition method. Through case studies on 108 groups of the subject program, it has been proved that the hybrid clustering-based fault partition method has significantly improved the effectiveness of multiple-fault localization in comparison with the traditional fault localization methods. Experiments on three embedded software programs in engineering have revealed that the cache-based program spectra-acquiring method saves nearly half of the running-time cost compared with the traditional spectrum-acquiring method based on real-time transmission. Therefore, the multiple-fault localization method proposed in this paper can be applied in embedded software debugging and testing in engineering.

Based on Katznelson–Tzafriri Theorem on power bounded operators, we prove in this paper a theorem, which applies to the most of the classical Banach algebras of harmonic analysis associated with locally compact groups, to deal with the problems when a given Banach algebra A is Arens regular and when A is an ideal in its bidual. In the second part of the paper, we study the topological center of the bidual of a class of Banach algebras with a multiplier bounded approximate identity.

Let $$S=\{p_{1},\ldots ,p_{t}\}$$ be a fixed finite set of prime numbers listed in increasing order. In this paper, we prove that the Diophantine equation $$(F_n^{(k)})^s=p_{1}^{a_{1}}+\cdots +p_{t}^{a_{t}}$$ , in integer unknowns $$n\ge 1$$ , $$s\ge 1,~k\ge 2$$ and $$a_i\ge 0$$ for $$i=1,\ldots ,t$$ such that $$\max \left\{ a_{i}: 1\le i\le t\right\} =a_t$$ has only finitely many effectively computable solutions. Here, $$F_n^{(k)}$$ is the nth k–generalized Fibonacci number. We compute all these solutions when $$S=\{2,3,5\}$$ . This paper extends the main results of [15] where the particular case $$k=2$$ was treated.

Based on the basic theory of the material point method (MPM), the factors affecting the computational efficiency are analyzed and discussed, and the problem of improving calculation efficiency is studied. This paper introduces a mirror reflection boundary condition to the MPM to solve axisymmetric problems; to improve the computational efficiency of solving large deformation problems, the concept of "dynamic background domain (DBD)" is also proposed in this paper. Taking the explosion and/or shock problems as an example, the numerical simulation are calculated, and the typical characteristic parameters and the CPU time are compared. The results show that the processing method introducing mirror reflection boundary condition and MPM with DBD can improve the calculation efficiency of the corresponding problems, which, under the premise of ensuring its calculation accuracy, provide useful reference for further promoting the engineering application of this method.

The classical result of L. Székelyhidi states that (under some assumptions) every solution of a general linear equation must be a polynomial function. It is known that Székelyhidi’s result may be generalized to equations where some occurrences of the unknown functions are multiplied by a linear combination of the variables. In this paper we study the equations where two such combinations appear. The simplest nontrivial example of such a case is given by the equation$$\begin{aligned} F(x + y) - F(x) - F(y) = yf(x) + xf(y) \end{aligned}$$F(x+y)-F(x)-F(y)=yf(x)+xf(y)considered by Fechner and Gselmann (Publ Math Debrecen 80(1–2):143–154, 2012). In the present paper we prove several results concerning the systematic approach to the generalizations of this equation.

This paper is devoted to the problem of where the critical points of a polynomial are relative to their zeros. Classical and new developments are surveyed along with illustrative examples. The paper finishes with a short proof of the sector theorem of Sendov and Sendov.

"The main object of this paper is to give sufficient conditions for the general integral operator Tn, to be univalent in the open disk U, when gi, hi, ki ∈ Gbi for all i = 1, n. This general integral operator was considered in a recent work [Barbatu, C. and Breaz, D., ˘ Classes of an univalent integral operator, Studia Univ. Babes¸-Bolyai Math., accepted]. The results derived in this paper are shown to follow upon specializing the parameters involved in our results. Several corollaries of the main results are also considered."

Since the appearance of Robbins’s paper (1948) the central limit theorem for a sum of a random number of independent identically distributed random variables is one of the most fundamental results in probability, and explains the appearance of the normal distribution in a whole host of diverse applications in mathematics, physics, biology and the social sciences. Compound random sums are extensions of classical random sums when the numbers of independent summands in sums are partial sums of independent identically distributed positive integer-valued random variables, assumed independent of summands of sums. The main aim of this paper is to introduce central limit theorems for normalized compound random sums of independent random variables and establish the convergence rates in types of small-o and large- $$\mathcal{O}$$ estimates, in term of Trotter-distance. The obtained results in this paper are extensions of several known ones.

In this paper we compute the rates of convergence of power series statistical convergence of sequences of positive linear operators. We also investigate some Korovkin type approximation properties of the $$q$$ -Meyer–Konig and Zeller operators and Durrmeyer variant of the $$q$$ -Meyer–Konig and Zeller operators via power series statistical convergence. We show that the approximation results obtained in this paper expand some previous approximation results of the corresponding operators.

In this paper we study some cube packing problems. In particular we are interested in compact subsets of $\mathbb{R}^n,n\geq 2$, which contain boundaries of cubes with all side lengths in $(0,1)$. We show here that such sets must have lower box dimension at least $n-0.5$ and we will also provide sharp examples. We also show here that such sets must be large in general in a precise sense which is also introduced in this paper., 9 pages. arXiv admin note: text overlap with arXiv:1711.06533

In this paper we study the isotypic decomposition of the regular module of a finite-dimensional Hopf algebra over an algebraically closed field of characteristic zero. For a semisimple Hopf algebra, the idempotents realizing the isotypic decomposition can be explicitly expressed in terms of characters and the Haar integral. In this paper we investigate Hopf algebras with the Chevalley property, which are not necessarily semisimple. We find explicit expressions for idempotents in terms of Hopf-algebraic data, where the Haar integral is replaced by the regular character of the dual Hopf algebra. For a large class of Hopf algebras, these are shown to form a complete set of orthogonal idempotents. We give an example which illustrates that the Chevalley property is crucial., Comment: 29 pages

Reinsurance plays a role of a stabilizer of the insurance industry and can be an effective tool to reduce the risk for the insurer. This paper aims to provide the optimal reinsurance design associated with the stop-loss reinsurance under the criterion of value-at-risk (VaR) risk measure. In this paper, the probability levels in the VaRs used by the both reinsurance parties are assumed to be different and the optimality results of reinsurance are derived by minimizing linear combination of the VaRs of the cedent and the reinsurer. The optimal parameter values of the stop-loss reinsurance policy are formally derived under the expectation premium principle.

The first aim of this paper is to investigate the growth of the entire function defined by the Laplace-Stieltjes transform converges on the whole complex plane. By introducing the concept of generalized order, we obtain two equivalence theorems of Laplace-Stieltjes transforms related to the generalized order, A * and λn. The second purpose of this paper is to study the problem on the approximation of this Laplace-Stieltjes transform. We also obtain some theorems about the generalized order, the error, and the coefficients of Laplace-Stieltjes transforms, which are generalization and improvement of the previous results.

In this paper we study multi-dimensional mean-field backward doubly stochastic differential equations (BDSDEs), that is, BDSDEs whose coefficients depend not only on the solution processes but also on their law. The first part of the paper is devoted to the comparison theorem for multi-dimensional mean-field BDSDEs with Lipschitz conditions. With the help of the comparison result for the Lipschitz case we prove the existence of a solution for multi-dimensional mean-field BDSDEs with an only continuous drift coefficient of linear growth, and we also extend the comparison theorem to such BDSDEs with a continuous coefficient.

In this paper, we introduce a Halpern algorithm and a nonconvex combination algorithm to approximate a solution of the split common fixed problem of quasi- ϕ -nonexpansive mappings in Banach space. In our algorithms, the norm of linear bounded operator does not need to be known in advance. As the application, we solve a split equilibrium problem in Banach space. Finally, some numerical examples are given to illustrate the main results in this paper and compare the computed results with other ones in the literature. Our results extend and improve some recent ones in the literature.

The original definition of cluster algebras by Fomin and Zelevinsky has been categorified and generalised in several ways over the course of the past 20 years, giving rise to cluster theory. This study lead to Iyama and Yang's generalised cluster categories $\mathcal{T}/\mathcal{T}^{fd}$ coming from $n$-Calabi-Yau triples $(\mathcal{T}, \mathcal{T}^{fd}, \mathcal{M})$. In this paper, we use some classic tools of homological algebra to give a deeper understanding of such categories $\mathcal{T}/\mathcal{T}^{fd}$. Let $k$ be a field, $n\geq 3$ an integer and $\mathcal{T}$ a $k$-linear triangulated category with a triangulated subcategory $\mathcal{T}^{fd}$ and a subcategory $\mathcal{M}=\text{add}(M)$ such that $(\mathcal{T}, \mathcal{T}^{fd}, \mathcal{M})$ is an $n$-Calabi-Yau triple. In this paper, we prove some properties of the triangulated categories $\mathcal{T}$ and $\mathcal{T}/\mathcal{T}^{fd}$. Our first result gives a relation between the Hom-spaces in these categories, using limits and colimits. Our second result is a Gap Theorem in $\mathcal{T}$, showing when the truncation triangles split. Moreover, we apply our two theorems to present an alternative proof to a result by Guo, originally stated in a more specific setup of dg $k$-algebras $A$ and subcategories of the derived category of dg $A$-modules. This proves that $\mathcal{T}/\mathcal{T}^{fd}$ is Hom-finite and $(n-1)$-Calabi-Yau, its object $M$ is $(n-1)$-cluster tilting and the endomorphism algebras of $M$ over $\mathcal{T}$ and over $\mathcal{T}/\mathcal{T}^{fd}$ are isomorphic. Note that these properties make $\mathcal{T}/\mathcal{T}^{fd}$ a generalisation of the cluster category., Comment: 17 pages. Final accepted version to appear in the Pacific Journal of Mathematics

A sequence $$(v_1,\ldots ,v_k)$$ of vertices in a graph G without isolated vertices is called a total dominating sequence if every vertex $$v_i$$ in the sequence totally dominates at least one vertex that was not totally dominated by $$\{v_1,\ldots , v_{i-1}\}$$ and $$\{v_1,\ldots ,v_k\}$$ is a total dominating set of G. The length of a shortest such sequence is the total domination number of G ( $$\gamma _{t}(G)$$ ), while the length of a longest such sequence is the Grundy total domination number of G ( $$\gamma _{gr}^t(G)$$ ). In this paper we study graphs with equal total and Grundy total domination numbers. We characterize bipartite graphs with both total and Grundy total dominations number equal to 4, and show that there is no connected chordal graph G with $$\gamma _{t}(G)=\gamma _{gr}^t(G)=4$$ . The main result of the paper is a characterization of bipartite graphs with $$\gamma _{t}(G)=\gamma _{gr}^t(G)=6$$ proved by establishing a surprising correspondence between the existence of such graphs and a classical but still open problem of the existence of certain finite projective planes.

In this paper we study a connective commutative differential graded algebra (CDGA) which is piecewise Noetherian. The principal aim is to analyze a dualizing complex of CDGA’s and investigate a Gorenstein CDGA. We also establish many other results which can be expected to play basic roles in the study of a CDGA, such as the Auslaner-Buchsbaum formula and Bass formula without any unnecessary assumptions. The key notion is the sup-projective (sppj) and inf-injective (ifij) resolutions introduced by the author, which are DG-versions of the projective and injective resolutions for ordinary modules. In the paper, we show that sppj and ifij resolutions are powerful tools to study DG-modules.

This paper concerns on two types of integral boundary value problems of a nonlinear fractional differential system, i . e ., nonlocal strip integral boundary value problems and coupled integral boundary value problems. With the aid of the monotone iterative method combined with the upper and lower solutions, the existence of extremal system of solutions for the above two types of differential systems is investigated. In addition, a new comparison theorem for fractional differential system is also established, which is crucial for the proof of the main theorem of this paper. At the end, an example explaining how our studies can be used is also given.

The main aim of this paper is to give refinement of bounds of fractional integral operators involving extended generalized Mittag-Leffler functions. A new definition, namely, strongly α , m -convex function is introduced to obtain improvements of bounds of fractional integral operators for convex, m -convex, and α , m -convex functions. The results of this paper will provide simultaneous generalizations as well as refinements of various published results.

This paper concerns the density of the Hartman--Watson law. Yor (1980) obtained an integral formula that gives a closed-form expression of the Hartman--Watson density. In this paper, based on Yor's formula, we provide alternative integral representations for the density. As an immediate application, we recover in part a Dufresne's result (2001) that exhibits remarkably simple representations for the laws of exponential additive functionals of Brownian motion., Comment: 21 pages; this is an abridged version of the previous one, accepted for publication in the Journal of Theoretical Probability, with shortened Section 4

Typhoons can have disastrous effects on power systems. They may lead to a large number of power outages for distribution network users. Therefore, this paper establishes a model to predict the power outage quantity of distribution network users under a typhoon disaster. Firstly, twenty-six explanatory variables (called global variables) covering meteorological factors, geographical factors, and power grid factors are considered as the input variables. On this basis, the correlation between each explanatory variable and response variable is analyzed. Secondly, we established a global variable model to predict the power outage quantity of distribution network users based on Random Forest (RF) algorithm. Then the importance of each explanatory variable is mined to extract the most important variables. To reduce the complexity of the model and ease the burden of data collection, eight variables are eventually selected as important variables. Afterward, we predict the power outage quantity of distribution network users again using the eight important variables. Thirdly, we compare the prediction accuracy of a model called the No-model that has been used before, Linear Regression (LR), Support Vector Regression (SVR), Decision Tree Regression (DTR), RF-global variable model, and RF-important variable model. Simulation results show that the RF-important variable model proposed in this paper has a better effect. Since fewer variables can save prediction time and make the model simplified, it is recommended to use the RF-important variable model.

A dynamical system $$ {\displaystyle \begin{array}{ll}{u}_{tt}-\Delta u-\nabla 1\mathrm{n}\;\rho \cdot \nabla u=0& in\kern0.6em {\mathrm{\mathbb{R}}}_{+}^3\times \left(0,T\right),\\ {}{\left.u\right|}_{t=0}={\left.{u}_t\right|}_{t=0}=0& in\kern0.6em \overline{{\mathrm{\mathbb{R}}}_{+}^3},\\ {}{\left.{u}_z\right|}_{z=0}=f& for\kern0.36em 0\le t\le T,\end{array}} $$ is under consideration, where ρ = ρ(x, y, z) is a smooth positive function; f = f(x, y, t) is a boundary control; u = uf (x, y, z, t) is a solution. With the system one associates a response operator R : f ↦ uf|z = 0. The inverse problem is to recover the function ρ via the response operator. A short representation of the local version of the BC-method, which recovers ρ via the data given on a part of the boundary, is provided. If ρ is constant, the forward problem is solved in explicit form. In the paper, the corresponding representations for the solutions and response operator are derived. A way to use them for testing the BC-algorithm, which solves the inverse problem, is outlined. The goal of the paper is to extend the circle of the BC-method users, who are interested in numerical realization of methods for solving inverse problems.

In this paper, we consider a version of energy minimisation technique applied to images of a 2D fluid flow. The two Navier–Stokes equations describe the static flow of a 2D fluid in terms of velocity field, (u, v), pressure field, p and forcing field, f. Apart from these two Navier–Stokes equations, we have the incompressibility condition to evaluate the three parameters. While implementing this system, random noise (usually non-Gaussian) creeps into the random force field $$\underline{f}(x,y)$$ f ̲ ( x , y ) . We denote this random field by $$\delta \underline{f}(x,y)$$ δ f ̲ ( x , y ) having zero mean and non-trivial second and third moments. We assume that these two moments are known except for some unknown parameters $$\underline{\theta }$$ θ ̲ (like mean, variance, co-variance, skewness, etc.) which we wish to estimate. In the proposed technique, we first calculate the approximate shift in the average fluid energy defined as a quadratic function of the velocity field. The energy method then requires that $$\underline{\theta }$$ θ ̲ should be such that this average increases in the energy due to the random forcing component be minimised. We should, however, note that the standard statistical approach to force field estimation is to calculate the velocity field as a function of the force field and then adopt the statistical moment matching technique. Such an approach assumes spatial ergodicity of the velocity field. This approach to force field estimation is more accurate from the statistical moment matching view point but works only if velocity measurements are made. The former technique of energy minimisation does not require any velocity measurements. Both of these techniques are discussed in this paper and MATLAB simulations presented.

This work has been motivated by recent papers that quantify the density of values of generic quadratic forms and other polynomials at integer points, in particular ones that use Rogers' second moment estimates. In this paper we establish such results in a very general framework. Given any subhomogeneous function (a notion to be defined) $f: \mathbb{R}^n \to \mathbb{R}$, we derive a necessary and sufficient condition on the approximating function $\psi$ for guaranteeing that a generic element $f\circ g$ in the $G$-orbit of $f$ is $\psi$-approximable; that is, $|f\circ g(\mathbf{v})| \le \psi(\|\mathbf{v}\|)$ for infinitely many $\mathbf{v} \in \mathbb{Z}^n$. We also deduce a sufficient condition in the case of uniform approximation. Here, $G$ can be any closed subgroup of $\rm{ASL}_n(\mathbb{R})$ satisfying certain axioms that allow for the use of Rogers-type estimates., Comment: 26 pages; misprints corrected, concluding remarks added

The study in this paper is made on the nonlinear fractional differential equation whose nonlinearity involves the explicit fractional order D0+β u(t). The corresponding Green's function is derived first, and then the completely continuous operator is proved. Besides, based on the Schauder's fixed point theorem and the Krasnosel'skii's fixed point theorem, the sufficient conditions for at least one or two existence of positive solutions are established. Furthermore, several other sufficient conditions for at least three, n or 2n-1 positive solutions are also obtained by applying the generalized AveryHenderson fixed point theorem and the Avery-Peterson fixed point theorem. Finally, several simulation examples are provided to illustrate the main results of the paper. In particularly, a novel efficient iterative method is employed for simulating the examples mentioned above, that is, the interesting point of this paper is that the approximation graphics for the solutions are given by using the iterative method.

In order to construct global solutions to two-dimensional (2D for short) Riemann problems for nonlinear hyperbolic systems of conservation laws, it is important to study various types of wave interactions. This paper deals with two types of wave interactions for a 2D nonlinear wave system with a nonconvex equation of state: Rarefaction wave interaction and shock-rarefaction composite wave interaction. In order to construct solutions to these wave interactions, the authors consider two types of Goursat problems, including standard Goursat problem and discontinuous Goursat problem, for a 2D self-similar nonlinear wave system. Global classical solutions to these Goursat problems are obtained by the method of characteristics. The solutions constructed in the paper may be used as building blocks of solutions of 2D Riemann problems.

The Monte Carlo method to solve the Cauchy problem for large systems of linear differential equations is proposed in this paper. Firstly, a quick overview of previously obtained results from applying the approach towards the Fredholm-type integral equations is made. In the main part of the paper, the method is applied towards a linear ODE system that is transformed into an equivalent system of the Volterra-type integral equations, which makes it possible to remove the limitations due to the conditions of convergence of the majorant series. The following key theorems are stated. Theorem 1 provides the necessary compliance conditions that should be imposed upon the transition propability and initial distribution densities that initiate the corresponding Markov chain, for which equality between the mathematical expectation of the estimate and the functional of interest would hold. Theorem 2 formulates the equation that governs the estimate’s variance. Theorem 3 states the Markov chain parameters that minimize the variance of the estimate of the functional. Proofs are given for all three theorems. In the practical part of this paper, the proposed method is used to solve a linear ODE system that describes a closed queueing system of ten conventional machines and seven conventional service persons. The solutions are obtained for systems with both constant and time-dependent matrices of coefficients, where the machine breakdown intensity is time dependent. In addition, the solutions obtained by the Monte Carlo and Runge–Kutta methods are compared. The results are presented in the corresponding tables.

In the paper flows of shock waves in multiphase media are described. Gas suspensions are considered as a multiphase medium—liquid drops or solid particles suspended in a gas. In this work, a continual approach in mathematical modeling of the dynamics of multiphase media is applied. The continual approach involves solving the complete hydrodynamic system of equations for each of the mixture components. The system of equations for the dynamics of each phase includes equation of continuity of density (average density for the dispersed phase), equations of conservation of momentum and energy. The carrier medium is described as a viscous, compressible heat-conducting gas. The mathematical model takes into account the velocity and thermal interaction of the phases of the mixture. The system of equations was solved by the MacCormack explicit finite-difference method of the second order of accuracy. To obtain a monotonic numerical solution, a nonlinear correction scheme was applied to the grid function. The influence of parameters of a disperse phase on speed and the shape of the reflected shockwave was numerically studied in the paper. Results of numerical calculations of the distribution of a shock wave from clean gas to a gas suspension, with the subsequent reflection from a firm surface, are given. Calculations allowed to establish that the intensity of a shock wave, reflected from a firm surface, in a gas suspension increases with a decrease of the number of dispersed particles. It is established that in polydisperse gas suspensions existence of fine fraction leads to an increase in the intensity of the reflected shock wave.

This paper systematically investigates the impact of porous media disorder and its coupling with flow rates, favorable and unfavorable viscosity ratios, as well as surface tensions on the dynamics of interfaces development during two-phase drainage flow. A special attention is paid to establishing relationship between the dynamics of fluid–fluid and fluid–solid interfacial lengths, the pore selectivity and the displacement efficiency using imaging of fluids distribution in porous media. As samples of study, we used artificially generated models of porous media with different disorder parameters and with two-types of pore-channels systems "— hexagonal and square. In our methodology, the disorder defines the range of grain size distribution and is applied to control the pore size range. For two-phase flow simulation, the lattice Boltzmann equations and the color-gradient model are applied. It was established the linear relationships between fluid–fluid and fluid–solid interfacial length and saturation of the invaded fluid. During numerical simulations at different disorders, the lack of disorder effect on the fluid–fluid interface dynamics and negative disorder impact on the fluid–solid interface dynamics was found. When varying the flow parameters, it was identified that the increase in the fluid–fluid interface dynamics is accompanied by a decrease in the fluid–solid interface dynamics. For all displacement mechanisms considered in this paper, except capillary fingering, an inverse relationship between pore selectivity and pore number, involved in displacement, was detected. We found a shift of pore selectivity towards higher values with increasing disorder which negatively impacts on the displacement efficiency. In capillary fingering regime, a strong tendency to minimize fluid–fluid interfacial length with surface tension explains the lack of relationship between pore selectivity and pore number which leads to bad predictable displacement efficiency in this regime.

This paper is the 2nd in a series of planned papers that provide 1st bijective proofs of alternating sign matrix (ASM) results. Based on the main result from the 1st paper, we construct a bijective proof of the enumeration formula for ASMs and of the fact that ASMs are equinumerous with descending plane partitions. We are also able to refine these bijections by including the position of the unique $1$ in the top row of the matrix. Our constructions rely on signed sets and related notions. The starting point for these constructions were known “computational” proofs, but the combinatorial point of view led to several drastic modifications. We also provide computer code where all of our constructions have been implemented.

In this paper we deal with the martingales in variable Lebesgue space over a probability space. We first prove several basic inequalities for conditional expectation operators and give several norm convergence conditions for martingales in variable Lebesgue space. The main aim of this paper is to investigate the boundedness of weak-type and strong-type Doob’s maximal operators in martingale Lebesgue space with a variable exponent. In particular, we present two kinds of weak-type Doob’s maximal inequalities and some necessary and sufficient conditions for strong-type Doob’s maximal inequalities. Finally, we provide two counterexamples to show that the strong-type inequality does not hold in general variable Lebesgue spaces with p > 1.

The aim of this paper is to characterize the solutions Φ : G → M 2(ℂ) of the following matrix functional equations Φ ( x y ) + Φ ( σ ( y ) x ) 2 = Φ ( x ) Φ ( y ) , x , y , ∈ G , {{\Phi \left( {xy} \right) + \Phi \left( {\sigma \left( y \right)x} \right)} \over 2} = \Phi \left( x \right)\Phi \left( y \right),\,\,\,\,\,\,x,y, \in G, and Φ ( x y ) − Φ ( σ ( y ) x ) 2 = Φ ( x ) Φ ( y ) , x , y , ∈ G , {{\Phi \left( {xy} \right) - \Phi \left( {\sigma \left( y \right)x} \right)} \over 2} = \Phi \left( x \right)\Phi \left( y \right),\,\,\,\,\,\,x,y, \in G, where G is a group that need not be abelian, and σ : G → G is an involutive automorphism of G. Our considerations are inspired by the papers [13, 14] in which the continuous solutions of the first equation on abelian topological groups were determined.

PurposeThe purpose of this paper is to determine the structure of nilpotent (n+6)-dimensional n-Lie algebras of class 2 when n≥4.Design/methodology/approachBy dividing a nilpotent (n+6)-dimensional n-Lie algebra of class 2 by a central element, the authors arrive to a nilpotent (n+5) dimensional n-Lie algebra of class 2. Given that the authors have the structure of nilpotent (n+5)-dimensional n-Lie algebras of class 2, the authors have access to the structure of the desired algebras.FindingsIn this paper, for each n≥4, the authors have found 24 nilpotent (n+6) dimensional n-Lie algebras of class 2. Of these, 15 are non-split algebras and the nine remaining algebras are written as direct additions of n-Lie algebras of low-dimension and abelian n-Lie algebras.Originality/valueThis classification of n-Lie algebras provides a complete understanding of these algebras that are used in algebraic studies.

In this paper we consider the following problem: letXk, be a Banach space with a normalised basis (e(k, j))j, whose biorthogonals are denoted by${(e_{(k,j)}^*)_j}$, for$k\in\N$, let$Z=\ell^\infty(X_k:k\kin\N)$be theirl∞-sum, and let$T:Z\to Z$be a bounded linear operator with a large diagonal,i.e.,$$\begin{align*}\inf_{k,j} \big|e^*_{(k,j)}(T(e_{(k,j)})\big|>0.\end{align*}$$Under which condition does the identity onZfactor throughT? The purpose of this paper is to formulate general conditions for which the answer is positive.

This paper concerns the existence of transonic shock solutions to the 2-D steady compressible Euler system in an almost flat finite nozzle ( in the sense that it is a generic small perturbation of a flat one ), under physical boundary conditions proposed by Courant-Friedrichs in \cite{CourantFriedrichs1948}, in which the receiver pressure is prescribed at the exit of the nozzle. In the resulting free boundary problem, the location of the shock-front is one of the most desirable information one would like to determine. However, the location of the normal shock-front in a flat nozzle can be anywhere in the nozzle so that it provides little information on the possible location of the shock-front when the nozzle's boundary is perturbed. So one of the key difficulties in looking for transonic shock solutions is to determine the shock-front. To this end, a free boundary problem for the linearized Euler system will be proposed, whose solution will be taken as an initial approximation for the transonic shock solution. In this paper, a sufficient condition in terms of the geometry of the nozzle and the given exit pressure is derived which yields the existence of the solutions to the proposed free boundary problem. Once an initial approximation is obtained, a further nonlinear iteration could be constructed and proved to lead to a transonic shock solution., 53 pages

In this paper, by using linear forms in logarithms and the Baker–Davenport reduction procedure we prove that there are no even perfect numbers appearing in generalized Pell sequences. We also deduce some interesting results involving generalized Pell numbers, which we believe are of independent interest. This paper continues a previous work that searched for perfect numbers in the classical Pell sequence.

The paper aims to establish new results on Tauberian theorem for Cesàro summability of double sequences of fuzzy numbers, and thus to extend and unify several results in the available literature. Further, a number of special cases, corollaries and illustrative example in support of the investigation of this paper are also presented.

The motivation of this paper is to study the uniqueness problems of meromorphic functions concerning differential polynomials that share a small function. The results of the paper improve and generalize the recent results due to Fengrong Zhang and Linlin Wu [13]. We also solve an open problem as posed in the last section of [13].

The paper is devoted to the evaluation of energy efficiency of High Performance Computing systems used in a scientific supercomputer center. The authors propose a method for the comparison of energy efficiency of computing systems based on the power consumption and execution time of parallel programs. The paper presents a software tool that allows to determine the energy consumption profile of a parallel program automatically without changing its source code. The paper also presents the results of power consumption comparison of NAS Parallel Benchmarks (BT, EP, IS, and LU) tests on computing systems with codenames Intel microprocessors Broadwell, Cascade Lake, Knights Landing and Skylake).

Scenario optimization is a broad methodology to perform optimization based on empirical knowledge. One collects previous cases, called “scenarios”, for the set-up in which optimization is being performed, and makes a decision that is optimal for the cases that have been collected. For convex optimization, a solid theory has been developed that provides guarantees of performance, and constraint satisfaction, of the scenario solution. In this paper, we open a new direction of investigation: the risk that a performance is not achieved, or that constraints are violated, is studied jointly with the complexity (as precisely defined in the paper) of the solution. It is shown that the joint probability distribution of risk and complexity is concentrated in such a way that the complexity carries fundamental information to tightly judge the risk. This result is obtained without requiring extra knowledge on the underlying optimization problem than that carried by the scenarios; in particular, no extra knowledge on the distribution by which scenarios are generated is assumed, so that the result is broadly applicable. This deep-seated result unveils a fundamental and general structure of data-driven optimization and suggests practical approaches for risk assessment.

In this paper, an alternative approach is provided in the well-posedness analysis of elliptic variational–hemivariational inequalities in real Hilbert spaces. This includes the unique solvability and continuous dependence of the solution on the data. In most of the existing literature on elliptic variational–hemivariational inequalities, well-posedness results are obtained by using arguments of surjectivity for pseudomonotone multivalued operators, combined with additional compactness and pseudomonotonicity properties. In contrast, following (Han in Nonlinear Anal B Real World Appl 54:103114, 2020; Han in Numer Funct Anal Optim 42:371–395, 2021), the approach adopted in this paper is based on the fixed point structure of the problems, combined with minimization principles for elliptic variational–hemivariational inequalities. Consequently, only elementary results of functional analysis are needed in the approach, which makes the theory of elliptic variational–hemivariational inequalities more accessible to applied mathematicians and engineers. The theoretical results are illustrated on a representative example from contact mechanics.

We establish a theory of $Q$-valued functions minimizing a suitable generalization of the Dirichlet integral. In a second paper the theory will be used to approximate efficiently area minimizing currents $\mathrm{mod}(p)$ when $p=2Q$, and to establish a first general partial regularity theorem for every $p$ in any dimension and codimension., 37 pages. First part of a two-papers work aimed at establishing a first general partial regularity theory for area minimizing currents modulo p, for any p and in any dimension and codimension. v3 is the final version, to appear on Comm. Pure Appl. Math

This paper provides a rigorous derivation of a counterexample of Bourgain, related to a well-known question of pointwise a.e. convergence for the solution of the linear Schrödinger equation, for initial data in a Sobolev space. This counterexample combines ideas from analysis and number theory, and the present paper demonstrates how to build such counterexamples from first principles, and then optimize them.

In this paper, to model cascading failures, a new stochastic failure model is proposed. In a system subject to cascading failures, after each failure of the component, the remaining component suffers from increased load or stress. This results in shortened residual lifetimes of the remaining components. In this paper, to model this effect, the concept of the usual stochastic order is employed along with the accelerated life test model, and a new general class of stochastic failure models is generated.

In this paper, we consider the operator sheaf $$ -\Delta +V+\varepsilon {\mathrm{\mathcal{L}}}_{\varepsilon}\left(\lambda \right)+{\lambda}^2 $$ in the space L2(ℝ2), where the real-valued potential V depends only on the first variable x1, e is a small positive parameter, λ is the spectral parameter, $$ {\mathrm{\mathcal{L}}}_{\varepsilon}\left(\lambda \right) $$ is a localized operator bounded with respect to the Laplacian −Δ, and the essential spectrum of this operator is independent of e and contains certain critical points defined as isolated eigenvalues of the operator $$ -\frac{d^2}{dx_1^2}+V\left({x}_1\right) $$ in L2(ℝ). The basic result obtained in this paper states that for small values of e, in neighborhoods of critical points mentioned, isolated eigenvalues of the sheaf considered arise. Sufficient conditions for the existence or absence of such eigenvalues are obtained. The number of arising eigenvalues is determined, and in the case where they exist, the first terms of their asymptotic expansions are found.

PurposeThe purpose of this current paper is to deal with the study of non-constant entire solutions of some non-linear complex differential equations in connection to Brück conjecture, by using the theory of complex differential equation. The results generalize the results due to Pramanik et al.Design/methodology/approach39B32, 30D35.FindingsIn the current paper, we mainly study the Brück conjecture and the various works that confirm this conjecture. In our study we find that the conjecture can be generalized for differential monomials under some additional conditions and it generalizes some works related to the conjecture. Also we can take the complex number a in the conjecture to be a small function. More precisely, we obtain a result which can be restate in the following way: Let f be a non-constant entire function such that σ2(f)<∞, σ2(f) is not a positive integer and δ(0, f)>0. Let M[f] be a differential monomial of f of degree γM and α(z), β(z)∈S(f) be such that max{σ(α), σ(β)} <σ(f). If M[f]+β and fγM−α share the value 0 CM, then M[f]+βfγM−α=c,where c≠0 is a constant.Originality/valueThis is an original work of the authors.