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Transformation of number sequences (convergence acceleration) is one of the classical chapters of numerical analysis. These algorithms are used both for solution of practical problems and for the development of more advanced numerical methods. At the same time, numerical methods have found numerous applications in the number theory. One of the classical problems of number theory is the proof of irrationality of some fundamental constants, where the high rate of convergence of sequences of rational numbers plays a crucial role. However, as far as we know, the applications of (classical) convergence acceleration algorithms to the proofs of irrationality do not exist. This study is an attempt to fill this gap and to draw attention to this direction of research. Bibl. 37. [ABSTRACT FROM AUTHOR]

To solve the problem of instability and failure of a roadway in the Dianping coal mine working face under the condition of traditional gob-side entry retaining, a mechanical model was established for analysis. The reasons for the damage are as follows: (1) the mining height is high, and the hard thick old roof exhibits large space for rotation and subsidence; (2) the retained roadway includes a large section; and (3) the mining impact is strong, and the adaptability of traditional cable is poor. Therefore, the technologies of "roof-cutting type gob-side entry retaining" were proposed and the principle was analyzed. Numerical simulation analysis of displacement and stress field under two processes was performed. The results indicated that the peak value of side abutment pressure decreased from 20.54 to 18.24 MPa due to the roof cutting (a decrease of 11%). The advance stress was less than the stress value under traditional conditions. When compared with the traditional conditions, the deformation of the roadway decreased by more than 50%. Finally, field monitoring was performed, and the results showed that under the condition of roof cutting, the deformation corresponded to the most severe within the range of 30–80 m behind the working face. After 80 m, the deformation gradually stabilized, and the maximum convergence between the roof and floor was 210 mm. Along the inclined direction, the stress of the hydraulic support in the middle part was the highest, the stress in the uncut side was second highest, and that in the roof-cutting side was the lowest. The periodic weighting interval on the roof-cutting side was the highest, and the transverse influence range of the roof cutting along the working face corresponded to 29.5 m. [ABSTRACT FROM AUTHOR]

The mechanical model of the basic roof fracture structure is established on the basis of key block theory to study the roof breaking mechanism of gob-side entry retaining under roof cutting and pressure relief, and the analytical formula of roof support resistance is derived when the key block of the basic roof is stable. The influence of roof cutting angle and cutting height on roof support resistance is also analyzed. Determining the cutting seam parameters of the retained roadway roof is necessary to identify the support resistance of the roadway roof due to the correlation between the roof cutting parameters and the support resistance. Taking the II 632 haulage drift of the Hengyuan coal mine as the engineering background, FLAC3D numerical simulation is used in this paper to analyze the influence of different roof cutting angles and cutting heights on the surrounding rock structure evolution of retained roadways. Results show that the roof cutting angle and cutting height respond to the support resistance of the retained roadway roof, and the support resistance required by the roof increases with the roof cutting angle and cutting height. This condition ensures that the side roof of the gob can be cut off smoothly, and the support resistance required by the roof of retained roadways is within a reasonable range. Through theoretical and numerical simulation analysis, the reasonable roof cutting height of II 632 haulage drift is 8 m and the roof cutting angle is 15°. The theoretical analysis and numerical simulation results reveal that the required support resistance to maintain the stability of the roadway roof is 0.38 MPa. The supporting scheme of the roof of the II 632 haulage drift in the Hengyuan coal mine is then designed. Finally, the field industrial test is used for verification. The borehole imaging results show that the overall line of the retained roadway roof is small based on the description of field monitoring results. The deformation of the surrounding rock surface of the retained roadway is less than 100 mm, and the roadway is 40 m from the lagging working face. The deformation rate of surrounding rock decreases with the increase in distance from the working face. The integrity of the retained roadway roof is good, and the deformation of the surrounding rock is effectively controlled. [ABSTRACT FROM AUTHOR]

Due to the existence of abandoned roadways in the thick coal seam, the ground pressure would increase greatly due to the roof advanced breaking when the working face passed through the affected area of abandoned roadways. In order to solve this problem, a solution for roof presplit in the abandoned roadway was proposed. Based on the mining and geological conditions of Huasheng Hufeng coal mine, the roof vertical stress and vertical displacement with different roof presplit distance were analyzed by using FLAC3D numerical software. The research results indicated that the roof vertical stress and vertical displacement could be reduced effectively by roof presplit. When the roof presplit distance was 15 m, the maximum vertical stress and the maximum vertical displacement were both minimum. The maximum vertical stress was reduced by 14.55% and the maximum vertical displacement was reduced by 37.51% after roof presplit. The reasonable roof presplit distance of the working face was determined to be about 15 m by combining theoretical and numerical analysis. The engineering application results indicated that the maximum working resistance of the hydraulic support was reduced by 35.86% after roof presplit, and the engineering effect was good. The research results can provide technical guidance and theoretical support for the same type mines. [ABSTRACT FROM AUTHOR]

Highlights • We propose a new ASGD method, Acc-Prox-SVRG-BB, which uses the BB method to automatically compute step size for Acc-Prox-SVRG. We prove the convergence of Acc-Prox-SVRG-BB and show that its complexity achieves the same level as the best known stochastic gradient methods. • To reduce the difficulty of choosing the parameters in Acc-Prox-SVRG, we propose a new method, FISTA-Prox-SVRG, which incorporates Beck and Teboulle's APG (a.k.a FISTA) and Prox-SVRG in a mini-batch setting. • To further validate the effectiveness of the BB method in the ASGD methods, we combine the BB method with FISTA-Prox-SVRG. Numerical experiments show the efficacy of our proposed methods. Abstract Accelerated stochastic gradient descent (ASGD) methods, which incorporate accelerated proximal gradient (APG) and stochastic gradient (SG), have received considerable attention recently for solving regularized risk minimization problems in signal/image processing, statistics and machine learning. However, there has been a paucity of practical guidance proposed for resolving one of the major issues in ASGD: how to choose an appropriate step size. To solve this problem, we propose to use the Barzilai-Borwein (BB) method to automatically compute step size for the accelerated mini-batch Prox-SVRG (Acc-Prox-SVRG) method (the state of the art ASGD method), thereby obtaining a new accelerated method: Acc-Prox-SVRG-BB. We prove the convergence of Acc-Prox-SVRG-BB and show that its complexity is comparable with the best known stochastic gradient methods. In addition, we incorporate Beck and Teboulle's APG (FISTA) and Prox-SVRG in a mini-batch setting and obtain another new accelerated gradient descent method, FISTA-Prox-SVRG, which requires the selection of fewer unknown parameters than those required in Acc-Prox-SVRG. Finally, we introduce the BB method into FISTA-Prox-SVRG to further show the efficacy of the BB method. Numerical results demonstrate the advantage of our algorithms. [ABSTRACT FROM AUTHOR]

Abstract In this work, we present a new implicit numerical scheme for fractional subdiffusion equations. In this approach we use the Keller Box method [1] to spatially discretise the fractional subdiffusion equation and we use a modified L1 scheme (ML1), similar to the L1 scheme originally developed by Oldham and Spanier [2], to approximate the fractional derivative. The stability of the proposed method was investigated by using Von-Neumann stability analysis. We have proved the method is unconditionally stable when 0 < λ q < min (1 μ 0 , 2 γ) and 0 < γ ≤ 1, and demonstrated the method is also stable numerically in the case 1 μ 0 < λ q ≤ 2 γ and log 3 2 ≤ γ ≤ 1. The accuracy and convergence of the scheme was also investigated and found to be of order O (Δ t 1 + γ) in time and O (Δx 2) in space. To confirm the accuracy and stability of the proposed method we provide three examples with one including a linear reaction term. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we introduce a split-step theta Milstein (SSTM) method for n -dimensional stochastic delay differential equations (SDDEs). The exponential mean-square stability of the numerical solutions is analyzed, and in accordance with previous findings, we prove that the method is exponentially mean-square stable if the employed time-step is smaller than a given and easily computable upper bound. In particular, according to our investigation, larger time-steps can be used in the case θ ∈ (1 2 , 1 ] than in the case θ ∈ [ 0 , 1 2 ]. Numerical results are presented which reveal that the SSTM method is conditionally mean-square stable and that in the case θ ∈ (1 2 , 1 ] the interval of time-steps for which the SSTM method is theoretically shown to be mean-square stable is significantly larger than in the case θ ∈ [ 0 , 1 2 ]. It is worth mentioning that the SSTM method has never been employed or analyzed for the numerical approximation of SDDEs, at least to the very best of our knowledge. [ABSTRACT FROM AUTHOR]

We study the existence and nonexistence of traveling waves of the reaction‐diffusion equations that describes a diffusive SEIR model with nonlocal reaction between the infected subpopulation and the susceptible subpopulation, where the total population is not constant. The existence of traveling waves depends on the basic reproduction number R0 of the corresponding ordinary differential equations and the minimal wave speed c∗. The main difficulty is the lack of order‐preserving property of our general system. Its proof is showed by constructing a closed and convex set and applying Schauder fixed point theorem. The proof of nonexistence result is obtained by two‐side Laplace transform. Finally, we present some numerical results of the minimal wave speed. [ABSTRACT FROM AUTHOR]

Abstract We study the cutting planes system CP+ ∀ red for quantified Boolean formulas (QBF), obtained by augmenting propositional Cutting Planes with a universal reduction rule, and analyse the proof-theoretic strength of this new calculus. While in the propositional case, Cutting Planes is of intermediate strength between resolution and Frege, our findings here show that the situation in QBF is slightly more complex: while CP+ ∀ red is again weaker than QBF Frege and stronger than the CDCL-based QBF resolution systems Q-Res and QU-Res , it turns out to be incomparable to even the weakest expansion-based QBF resolution system ∀ Exp+Res. A similar picture holds for a semantic version semCP+ ∀ red. Technically, our results establish the effectiveness of two lower bound techniques for CP+ ∀ red : via strategy extraction and via monotone feasible interpolation. [ABSTRACT FROM AUTHOR]

The paper presents explicit interval multistep methods of Milne type, which may be considered as alternative methods to other known explicit interval multistep methods (of Adams-Bashforth and Nyström). It is proved that enclosures of solutions (in the form of intervals) obtained by these methods contain the exact solutions of the initial value problem. Numerical examples show that the widths of intervals obtained by proposed methods are smaller than those obtained by explicit interval multistep methods known so far. [ABSTRACT FROM AUTHOR]

In this article, we focus on a generalized problem of linear non-autonomous fractional nabla difference equations. Firstly, we define the equations and describe how this family of problems covers other linear fractional difference equations that appear in the literature. Then, by using matrix theory we provide a new practical formula of solutions for these type of equations. Finally, numerical examples are given to justify our theory. [ABSTRACT FROM AUTHOR]

This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady state solutions. Absorbing and reflecting boundary conditions are considered, and illustrated through several examples. Reflecting boundary conditions involve fractional derivatives. The Caputo fractional derivative is shown to be unsuitable for modeling fractional diffusion, since the resulting boundary value problem is not positivity preserving. [ABSTRACT FROM AUTHOR]

In this article, we studied the Caputo and Riemann–Liouville type discrete fractional difference initial value problems with discrete Mittag-Leffler kernels. The existence and uniqueness of the solution is proved by using Banach contraction principle. The linear type equations are used to prove new discrete fractional versions of the Gronwall’s inequality. The nabla discrete Laplace transform is used to obtain solution representations. The proven Gronwall’s inequality under a new defined α -Lipschitzian is used to prove that small changes in the initial conditions yield small changes in solutions. Numerical examples are discussed to demonstrate the reliability of the theoretical results. [ABSTRACT FROM AUTHOR]

Does every Boolean tautology have a short propositional-calculus proof? Here, a propositional-calculus (i.e., Frege) proof is any proof starting from a set of axioms and deriving new Boolean formulas using a fixed set of sound derivation rules. Establishing any superpolynomial-size lower bound on Frege proofs (in terms of the size of the formula proved) is a major open problem in proof complexity and among a handful of fundamental hardness questions in complexity theory. Noncommutative algebraic formulas, on the other hand, constitute a quite weak computational model, for which exponential-size lower bounds were shown back in 1991 by Nisan [Proceedings of STOC, 1991, pp. 410{418], using a particularly transparent argument. In this work we show that Frege lower bounds in fact follow from size lower bounds on noncommutative formulas computing certain families of polynomials (and that such lower bounds on noncommutative formulas must exist, unless NP = coNP). More precisely, we demonstrate a natural association between tautologies T to families of noncommutative polynomials P such that if T has a polynomial-size Frege proof, then some noncommutative polynomial in P can be computed by a polynomial-size noncommutative algebraic formula, and conversely, when T is a formula in disjunctive normal form, if some polynomial in P has a polynomial-size noncommutative algebraic formula over GF(2), then T has a Frege proof of quasipolynomial size. The argument is a characterization of Frege proofs as noncommutative formulas: we show that the Frege system is (quasi-) polynomially equivalent to a noncommutative ideal proof system(IPS), following the recent work of Grochow and Pitassi [Proceedings of FOCS, 2014, pp. 110{119] that introduced a propositional proof system in which proofs are algebraic circuits and the work in [I. Tzameret, Inform. Comput., 209 (2011), pp. 1269{1292] that considered adding the commutator as an axiom in algebraic propositional proof systems. This also gives a characterization of propositional Frege proofs in terms of (noncommutative) algebraic formulas that is tighter than (the formula version of IPS) in Grochow and Pitassi [Proceedings of FOCS, 2014, pp. 110{119]. [ABSTRACT FROM AUTHOR]

Inherent part of evolutionary algorithms that are based on Darwin’s theory of evolution and Mendel’s theory of genetic heritage, are random processes since genetic algorithms and evolutionary strategies are used. In this paper, we present extended experiments (of our previous) of selected evolutionary algorithms and test functions showing whether random processes really are needed in evolutionary algorithms. In our experiments we used differential evolution and SOMA algorithms with functions 2ndDeJong, Ackley, Griewangk, Rastrigin, SineWave and StretchedSineWave. We use n periodical deterministic processes (based on deterministic chaos principles) instead of pseudo-random number generators (PRGNs) and compare performance of evolutionary algorithms powered by those processes and by PRGNs. Results presented here are numerical demonstrations rather than mathematical proofs. We propose the hypothesis that a certain class of deterministic processes can be used instead of PRGNs without lowering the performance of evolutionary algorithms. [ABSTRACT FROM AUTHOR]

In this paper we investigate strictly convex central configurations of the planar five-body problem, and prove some necessary conditions for such configurations. In particular, given such a central configuration with multiplier λ and total mass M, we show that all exterior edges are less than r0 =(M/λ)1/3, at most two interior edges are less than or equal to r0, and its subsystem with four masses cannot be a central configuration. We also obtain some other necessary conditions for strictly convex central configurations with five bodies, and show numerical examples of strictly convex central configurations with five bodies that have either one or two interior edges less than or equal to r0. Our work develops some formulae in a classic work by W. L. Williams in 1938 and we rectify some unsupported assumptions there. [ABSTRACT FROM AUTHOR]

This paper addresses the combination of unreliable evidence sources which provide uncertain information in the form of basic probability assignment (BPA) functions. We proposed a novel evidence combination rule based on credibility and non-specificity of belief functions. Following a review of all existing non-specificity measures in evidence theory, a non-specificity measure for evidence theory is discussed. It is claimed that the non-specificity degree of a BPA is related to its ability of pointing to one and only one element. Based on the difference between the largest belief grades and other belief grades, a non-specificity measure is defined. Properties of the proposed non-specificity measure are put forward and proved mathematically. Illustrative examples are employed to show the properties of non-specificity measure. After providing a procedure for the evaluation of evidence credibility, we propose a novel evidence combination rule. Numerical example and application in target identification are applied to demonstrate the performance of our proposed evidence combination rule. [ABSTRACT FROM AUTHOR]

We consider an adaptive isogeometric method (AIGM) based on (truncated) hierarchical B-splines and continue the study of its numerical properties. We prove that our AIGM is optimal in the sense that delivers optimal convergence rates as soon as the solution of the underlying partial differential equation belongs to a suitable approximation class. The main tool we use is the theory of adaptive methods, together with a local upper bound for the residual error indicators based on suitable properties of a well selected quasi-interpolation operator on hierarchical spline spaces. [ABSTRACT FROM AUTHOR]

We present some results concerning the controllability of a hyperbolic linear equation with constraints on the gradient, we're interested in an internal subregion of the system evolution domain Ω. We analyse the controllability problem with constraints (also called the enlarged controllability) with distributed control that ensures the transfer of our system to a final desired gradient between two prescribed profiles f1 and f2. The proofs use a sub-differential approach, the Lagrangian one, and finally numerical results are illustrated. [ABSTRACT FROM AUTHOR]

We prove that a second order backward difference semi-discretization approximation for the integro-differential equations with the multi-term kernels preserves the weighted asymptotic integrabilities of continuous solutions. The method of proof extend and simulate numerically those introduced by Hannsgen and Wheeler, relying on deep frequency domain techniques. [ABSTRACT FROM AUTHOR]

Gaussian elimination with no pivoting and block Gaussian elimination are attractive alternatives to the customary but communication intensive Gaussian elimination with partial pivoting 1 provided that the computations proceed safely and numerically safely , that is, run into neither division by 0 nor numerical problems. Empirically, safety and numerical safety of GENP have been consistently observed in a number of papers where an input matrix was pre-processed with various structured multipliers chosen ad hoc. Our present paper provides missing formal support for this empirical observation and explains why it was elusive so far. Namely we prove that GENP is numerically unsafe for a specific class of input matrices in spite of its pre-processing with some well-known and well-tested structured multipliers, but we also prove that GENP and BGE are safe and numerically safe for the average input matrix pre-processed with any nonsingular and well-conditioned multiplier. This should embolden search for sparse and structured multipliers, and we list and test some new classes of them. We also seek randomized pre-processing that universally (that is, for all input matrices) supports (i) safe GENP and BGE with probability 1 and/or (ii) numerically safe GENP and BGE with a probability close to 1. We achieve goal (i) with a Gaussian structured multiplier and goal (ii) with a Gaussian unstructured multiplier and alternatively with Gaussian structured augmentation. We consistently confirm all these formal results with our tests of GENP for benchmark inputs. We have extended our approach to other fundamental matrix computations and keep working on further extensions. 1 Hereafter we use the acronyms GENP , BGE , and GEPP . [ABSTRACT FROM AUTHOR]

In this paper, we consider linear control systems on Lie groups and compare three different approaches to local controllability for these systems: Hermes-Sussmann conditions, Hermes condition, and ad-rank condition. We prove that the ad-rank condition can be deduced from the Hermes-Sussmann conditions. We also prove that the Hermes condition and the ad-rank condition are equivalent in case of systems with scalar control. As application, we provide a criterion for global controllability for restricted linear systems on the Heisenberg group. [ABSTRACT FROM AUTHOR]

In this paper, we present an investigation of quantale algebras ( Q-algebras for short) as lattice-valued quantales ( Q-quantales for short). First, we prove that the set of all fuzzy ideals of a commutative ring with appropriate operations is a [0, 1]-quantale. Furthermore, we discuss some properties of localic nuclei on Q-algebras, and show that the category of Q-algebras with the quantale structures being frames is a full reflective subcategory of the category of Q-algebras. From this result, we can conclude that the category of L-frames is a full reflective subcategory of the category of L-quantales, where L is a frame. Finally, we build and characterize the Q-quantale completions of a Q-ordered semigroup. [ABSTRACT FROM AUTHOR]

Let T be the bilinear Fourier multiplier operator with associated multiplier σ satisfying the Sobolev regularity that $$\mathop {\sup }\limits_{k \in \mathbb{Z}} {\left\| {{\sigma _k}} \right\|_{{W^s}\left( {{\mathbb{R}^{2n}}} \right)}} < \infty $$ for some s ∈ ( n, 2 n]. In this paper, it is proved that the commutator generated by T and CMO(ℝ) functions is a compact operator from $${L^{{p_1}}}\left( {{\mathbb{R}^n},{\omega _1}} \right) \times {L^{{p_2}}}\left( {{\mathbb{R}^n},{\omega _2}} \right)$$ to $${L^p}\left( {{\mathbb{R}^n},{\nu _{\vec \omega }}} \right)$$ for appropriate indices p , p , p ∈ (1,∞) with $$\frac{1}{p} = \frac{1}{{{p_1}}} + \frac{1}{{{p_2}}}$$ and weights ω , ω such that $$\vec \omega = \left( {{\omega _1},{\omega _2}} \right) \in {A_{\vec p/\vec t}}\left( {{\mathbb{R}^{2n}}} \right)$$ . [ABSTRACT FROM AUTHOR]

In this paper, we establish approximate representations of solutions to stochastic Volterra integral equations (SVIEs, for short), by virtue of solutions to a family of stochastic differential equations. As an application, we present two algorithms for solving SVIEs: stochastic theta method and splitting method, and prove the global 1/2 order convergence rates in L 2 norm. [ABSTRACT FROM AUTHOR]

We present numerical results and computer assisted proofs of the existence of periodic orbits for the Kuramoto--Sivashinky equation. These two results are based on writing down the existence of periodic orbits as zeros of functionals. This leads to the use of Newton's algorithm for the numerical computation of the solutions and, with some a posteriori analysis in combination with rigorous interval arithmetic, to the rigorous verification of the existence of solutions. This is a particular case of the methodology developed in [J.-L. Figueras, J.-P. Lessard, M. Gameiro and R. de la Llave, preprint, arXiv:1605.01086, 2016] for several types of orbits. An independent implementation, cover- ing overlapping but different ground, using different functional setups, appears in [J.-P. Lessard and M. Gameiro, A Posteriori Verification of Invariant Objects of Evolution Equations: Periodic Orbits in the Kuramoto-Sivashinsky PDE, manuscript]. [ABSTRACT FROM AUTHOR]

We exhibit a large class of Banach function spaces which fail to have the Radon-Nikodym property. [ABSTRACT FROM AUTHOR]

The aim of this paper is to analyze the delay-dependent stability of symmetric Runge--Kutta methods, including the Gauss methods and the Lobatto IIIA, IIIB, and IIIS methods, for the linear neutral delay integro-differential equations. By means of the root locus technique, the structure of the root locus curve is given and the numerical stability region of symmetric Runge--Kutta methods is obtained. It is proved that, under some conditions, the analytical stability region is contained in the numerical stability region. Finally, some numerical examples are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This work demonstrates an innovative numerical method for counting and locating eigenvalues with the Evans function. Utilizing the geometric phase in the Hopf bundle, the technique calculates the winding of the Evans function about a contour in the spectral plane, describing the eigenvalues enclosed by the contour for the Hocking–Stewartson pulse of the complex Ginzburg–Landau equation. Locating eigenvalues with the geometric phase in the Hopf bundle was proposed by Way (2009), and proven by Grudzien et al. (2016). Way demonstrated his proposed method for the Hocking–Stewartson pulse, and this manuscript redevelops this example as in the proof of the method in Grudzien et al. (2016), modifying his numerical shooting argument, and introduces new numerical results concerning the phase transition. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the crossing change operation along exchangeable double curves of a surface-knot diagram. We show that under certain condition, a finite sequence of Roseman moves preserves the property of those exchangeable double curves. As an application for this result, we also define a numerical invariant for a set of surface-knots called du-exchangeable set. [ABSTRACT FROM AUTHOR]

We take up a systematic study of all steps to derive a proof of [5, Lemma 2] from that of [1, Lemma 6.8.3]. [ABSTRACT FROM AUTHOR]

In this paper, we present a general procedure for solving of homogeneous equations that describe penetration and diffusion of X-rays in plane geometry. Starting from Van Kampen's and Case's observation that it suffices that 'solutions' be distributions, elementary solutions of a homogeneous equation are found. We also prove that general solutions can be obtained by superposition of elementary solutions. [ABSTRACT FROM AUTHOR]

We construct all the irreducible representations of spin quiver Hecke algebras for orthosymplectic Lie superalgebras o s p ( 1 | 2 n ) , and show that their highest weights are given by the dominant words. We use the dominant Lyndon words to construct the cuspidal modules and show that the irreducible representations are the simple heads of standard representations constructed by induction from the cuspidal modules. [ABSTRACT FROM AUTHOR]

3D numerical thermal simulation on conjugate heat transfer in hollow roofs is conducted by self-compiled program based on the finite volume method to improve insulation performance. Eight kinds of hollow roofs with different box fillers are optimized by regularly designing partitions to divide air-filled cavity. In addition, the effect of box filler materials on thermal behavior is considered. The numerical results demonstrate that: horizontal partitions decrease the equivalent thermal conductivity by 13.65%–40.42%, whose effect is more remarkable for higher void roofs, whereas vertical partitions cause few effects. Besides, different box filler materials can bring about slight variation no more than 3%. [ABSTRACT FROM AUTHOR]

We prove that every finite union of rectangles with edges parallel to the axes in Rd admits a Riesz basis of exponentials. [ABSTRACT FROM AUTHOR]

In this paper, a variational integrator is constructed for Gross–Pitaevskii equations in Bose–Einstein condensate. The discrete multi-symplectic geometric structure is derived. The discrete mass and energy conservation laws are proved. The numerical tests show the effectiveness of the variational integrator, and the performance of the proved discrete conservation law. [ABSTRACT FROM AUTHOR]

We prove that viscosity solutions of the degenerate prescribed curvature equation F [ u ] = F ( κ 1 , …, κ n ) ≡ 0 in Ω, u = g on ∂ Ω are unique for a broad class of differential operators F . [ABSTRACT FROM AUTHOR]

In this study, failure analysis of a large span longwall drift under water-rich roofs was presented relying on field observations and numerical simulations. We had sought to find the key points that caused the drift roof collapse and water inrush. The numerical results were similar with that observed from field situations, and they both determined the origins of the roof failure problem. Wrong location selection and unreasonable excavation and support schemes were verified to be the most important factors that caused roof failure of the drift. Subsequently, a new excavation location with poor roof aquifer was recommended. A two staged excavation procedure was employed. Firstly, a small span roadway was excavated and reinforced, then the roadway was widened to the design width. After the first pass, boreholes were drilled to dewater the roof aquifer, and chemical glue material was grouted into the roof to cement the pre-existing discontinuities and induced fractures. Such control techniques had been undertaken in the new longwall drift. Both numerical modeling and field measurement verified that the proposed method could guarantee the large span drift stability during excavation and longwall preparation period. The interest of this study resides in combining the integrated methods to evaluate the state of failure in a highly detailed manner and determine simultaneously control techniques for the thorny problem under study. [ABSTRACT FROM AUTHOR]

In this paper, we present spectral methods in order to solve wave equation subject to a locally distributed nonlinear damping. Thanks to the efficiency and the accuracy of spectral method, we can check that discrete energy decreases to zero as time goes to infinity, uniformly with respect to the mesh size when the damping is supported in a suitable subset of the domain of consideration. We prove the convergence of the full Fourier–Galerkin discretization. Thus, we apply our schemes to illustrate the uniform discrete energy decay rates of the solution for a wide range of damping functions. [ABSTRACT FROM AUTHOR]

This article introduces patterns of ideals of numerical semigroups, thereby unifying previous definitions of patterns of numerical semigroups. Several results of general interest are proved. More precisely, this article presents results on the structure of the image of patterns of ideals, and also on the structure of the sets of patterns admitted by a given ideal. [ABSTRACT FROM AUTHOR]

Inspired by the theoretical results on optimal preconditioning stated by Ng, Chan, and Tang in the framework of Reflective boundary conditions (BCs), in this paper we present analogous results for Anti-Reflective BCs. Here a key technical difficulty is represented by the non-orthogonal character of the Anti-Reflective transform and indeed the proof proposed by Ng, Chan, and Tang does not work. Nevertheless, in both cases, the optimal preconditioner is the blurring matrix associated to the symmetrized Point Spread Function (PSF). The geometrical idea on which our proof is based is very simple and general, so it may be useful in the future to prove theoretical results for new proposed BCs. Numerical tests show that the optimal preconditioning strategy is effective when using both preconditioned conjugate gradient methods and recently introduced nonstationary preconditioned iterations. [ABSTRACT FROM AUTHOR]

• There are several significant contributions associated with the proposed approach. • From the experimental results, we have found out that the modified muffler is more effective than the others without modifications in terms of transmission loss reduction of around 10%. • The baffle plate in the muffler plays a major role in the reduction of transmission loss. • The numerical results in MATLAB shows that the redesigned muffler offers a lesser amplitude of noise. • The new muffler design would help in reducing the exhaust noise of the automobile. In many technical applications in the present era, acoustics noise is the most difficult issue for humans. Although reactive and absorptive types of mufflers are currently available for noise reduction, their performance is limited for a variety of reasons. This study involves measuring transmission loss in an automotive exhaust muffler and then adopting new design parameters to reduce transmission loss, which is important for a greener environment. The automotive mufflers chosen for this study are investigated and employed in a numerical study to compare with an experimental investigation of passive noise control for transmission loss in automobiles. The transmission losses are compared to the original muffler chamber specifications to find the change in transmission losses, and the muffler chambers are modified by integrating a baffle plate to minimise the automotive exhaust noise. The transmission loss in a muffler is experimentally controlled by a passive noise, and a numerical analysis is performed for comparison using commercial software MATLAB. The installation of the baffle plate reduces the transmission loss, both in the narrow band and octave band region, according to the experimental, numerical and theoretical data, with more reduction happening in the narrow band region than the octave band region in this passive noise control experimental work. [ABSTRACT FROM AUTHOR]

We prove an analog of the Wiman-type inequality for analytic functions in a polydisk ⅅ={ z ∈ ℂ : | z | < 1, j ∈ {1, ... p}}, p ∈ ℕ. The obtained inequality is sharp. [ABSTRACT FROM AUTHOR]

A real snowstorm often lasts for hours to several days. Simulating snow drifting on a roof through traditional transient method of computational fluid dynamics would be time consuming. Thus, a quasi-steady method is proposed in this paper to simulate redistribution of snow on roofs. The process of snow drifting is divided into several phases according to the characteristics of meteorological data. The erosion/deposition of snow in each phase is regarded as a steady state. In the numerical simulation, the angle of repose of snow is taken into account. The boundaries of snowpack are updated based on the calculated results of change rate of snow depth in the previous phase. The proposed numerical method was applied to predict snow redistribution on a flat roof. A scaled test was conducted in a wind tunnel to validate the accuracy of the numerical simulation, in which a kind of high-density particle, silica sand, was used to model snow particles. The snow redistributions obtained from the numerical simulation agree well with those from the test results. As the wind tunnel test, the numerical simulation also predicted deposition on a small windward area of the flat roof. Then the transport rate of snow or silica sand on roof surface was investigated. The influence of the threshold velocity of snow and silica sand on prototype duration was also studied. Finally the snow redistribution on a flat roof during a real snowstorm was simulated in this study to show the practicability of the proposed method. [ABSTRACT FROM AUTHOR]