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In this paper, we investigate the secrecy performance of a dual-hop hybrid radio frequency–visible light communication (RF–VLC) system in which we consider a single source antenna (S) transmitting data signals via RF channel through decode and forward (DF) relay (R) toward an authorized receiving antenna (D) at the destination via VLC channel. In this system, we assume that the eavesdropper (E) attempts to eavesdrop the RF channel (S,R) during transmission of the signal. The relay decodes the incoming RF signal into corresponding optical signal and retransmits toward destination via VLC channel (R,D). The RF and VLC channels of the hybrid system are modelled using generalized-K fading distribution and generalized Lambertian radiant intensity distribution respectively. Also the receiver is assumed to be mobile and its mobility is defined by random waypoint (RWP) model. The channels statistics are used to derive the exact analytical expressions for average secrecy capacity and intercept probability in terms of Meijer's G-function. The derived closed form analytical expressions are the efficient tool to illustrate the impact of variation in different channel parameters on the secrecy performance, namely, shadowing parameters of RF channel, field of view (FOV), semiangle, and the order of Lambertian emission of the VLC channel. Further, numerical analysis is carried out to support the mathematical analysis of the RF–VLC hybrid system. [ABSTRACT FROM AUTHOR]

Millimeter (mmWave) and sub-terahertz communication is a key technology to support high data rate requirements of 5G and B5G mobile networks. However this field is still in its initial development stage because of the various technical difficulties in its practical implementation due to inherently distinct propagation properties of mmWave/sub-terahertz frequencies. A thorough investigation of mmWave/sub-terahertz communication link is required in order to successfully deploy these frequency bands in 5G and B5G mobile networks. This paper investigates the effect of atmospheric conditions like dry air, humidity, rain, snow, fog and foliage on the performance of the mmWave/sub-terahertz link. The work also presents a mathematical analysis of the coverage of mmWave/sub-terahertz communication link and investigates the effect of various parameters like frequency, bandwidth, transceiver antenna gain, path loss coefficient (LOS, NLOS case) and system noise on its performance. [ABSTRACT FROM AUTHOR]

This review explores several rarely discussed examples illustrating constructivism principles, generative and selective features of neuronal regulation of behaviour. First, the review highlights Walter Freeman's experiments and mathematical analysis that uncovered the existence of anticipatory attractors, i.e. non-random dynamical patterns in neurodynamics. Since Freeman's work did not extend to neurochemistry, this paper then points to the proposed earlier neurochemical framework summarizing the managerial roles of monoaminergic, cholinergic and opioid receptor systems likely contributing to anticipatory attractors in line with functional constructivism. As a third example, neurochemistry's evidence points to the "Throw & Catch" (T&C) principle in neurodynamics. This principle refers to the pro-active, neurochemically expensive, massive but topical increase of potentials ("Throw") within electrodynamics and neurotransmission in the brain whenever there is an uncertainty in selection of degrees of freedom (DFs). The T&C also underlines the relay-like processes during the selection of DFs. The "Throw" works as an internally generated "flashlight" that, contrarily to the expectations of entropy reduction, increases entropy and variance observed in processes related to orientation and action-formation. The discussed examples highlight the deficiency of structures-oriented projects and excitation-inhibition concepts in neuroscience. The neural regulation of behaviour appears to be a fluid, constructive process, constantly upgrading the choice of behavioural DFs, to ensure the compatibility between the environmental and individual's individuals' needs and capacities. [ABSTRACT FROM AUTHOR]

Self-phase modulation (SPM) is one of the major non-linear effect in single-tone radio over fiber system which limits the long-distance transmission as it leads to the broadening of pulse spectrum. In this paper, the mathematical and parametric analysis was carried out to understand the origination and upgradation of SPM and based on results achieved, a rigorous evaluation has been conducted to decrease the impact of SPM. The effect of SPM has been evaluated in terms of optical spectrums, eye diagrams, eye-opening and Q-factor by utilizing four important parameters specifically launched power, fiber effective area, bit rate and fiber attenuation using OptiSystem simulator which reveals insight information for the elimination of non-linear effects. [ABSTRACT FROM AUTHOR]

In this paper, we consider the inverse scattering problem of identifying a two-layered cavity by internal acoustic measurements under the condition that the interior interface has a mixed transmission boundary condition. We focus on the mathematical analysis of recovering the shape of the interior interface by using the linear sampling method, including reconstructing the surface conductivity by the same measurements. [ABSTRACT FROM AUTHOR]

Š. Schwarz in his paper [SCHWARZ, Š.: Zur Theorie der Halbgruppen, Sborník prác Prírodovedeckej fakulty Slovenskej univerzity v Bratislave, Vol. VI, Bratislava, 1943, 64 pp.] proved the existence of maximal subgroups in periodic semigroups and a decade later he brought into play the maximal subsemigroups and thus he embodied the idempotents in the structural description of semigroups [SCHWARZ, Š.: Contribution to the theory of torsion semigroups, Czechoslovak Math. J. 3(1) (1953), 7–21]. Later in his papers he showed that a proper description of these structural elements can be used to (re)prove many useful and important results in algebra and number theory. The present paper gives a survey of selected results scattered throughout the literature where an semigroup approach based on tools like idempotent, maximal subgroup or maximal subsemigroup either led to a new insight into the substance of the known results or helped to discover new approach to solve problems. Special attention will be given to some disregarded historical connections between semigroup and ring theory. [ABSTRACT FROM AUTHOR]

This paper explores the hyperbolic heat transfer effects in processes involving high heating rates. The behavior of the model is analyzed in detail under different boundary conditions and the circumstances under which a non-Fourier law could be used to describe thermal conduction processes established from physical mathematical analysis. Finally, the model developed here is coupled to a previous population balance framework to predict the bubbling phenomenon that occurs during the fast pyrolysis of biomass. We found that a transient overheating occurs in the central zone of the generated liquid phase due to the high heating rates that take place during that process. [ABSTRACT FROM AUTHOR]

The paper deals with the thermal decomposition of organometallic compound ferrocene carboxaldehyde [(C5H4CHO)Fe(C5H5)] in oxidative atmosphere, which leads to pure hematite nanoparticles, studied with non-isothermal thermogravimetry (TG) protocol. Deconvolution method with Fraser-Suzuki fit function is adopted to resolve the complex multistep TG profiles into six different reaction steps. Step-wise reaction kinetic parameters (activation energy, reaction mechanism function, reaction rate) are estimated based on the mathematical analysis of the multi-heating rate TG data primarily following model-free (integral isoconversional) approach and using master-plot method. The estimated kinetic parameters are utilised to reconstruct the conversion plots which successfully resemble the experimentally observed ones. A plausible reaction process leading to hematite on thermal decomposition of ferrocene carboxaldehyde as the end product is discussed. A comparative discussion on the thermal decomposition of two ferrocene derivatives have been made. The novelty of the present work lies in successful deconvolution of complex TG profiles and hence obtaining the step-wise reaction kinetic parameters demonstrating different reaction mechanisms involved in the thermal synthesis of hematite nanoparticles starting from ferrocene carboxaldehyde which have no prior reporting. Further, a satisfactory agreement between the reconstructed and experimental decomposition profiles establishes the correctness of the applied modelling approach as well as the methodology adopted. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the stability of the system of partial differential equations modelling scalar image velocimetry. We first revisit a successful numerical technique to reconstruct velocity vectors u from images of a passive scalar field ψ by minimizing a cost functional that penalizes the difference between the reconstructed scalar field ϕ and the measured scalar field ψ, under the constraint that ϕ is advected by the reconstructed velocity field u , which again is governed by the Navier–Stokes equations. We investigate the stability of the reconstruction by applying this method to synthetic scalar fields in two-dimensional turbulence that are generated by numerical simulation. Then we present a mathematical analysis of the nonlinear coupled problem and prove that, in the two-dimensional case, smooth solutions of the Navier–Stokes equations are uniquely determined by the measured scalar field. We also prove a conditional stability estimate showing that the map from the measured scalar field ψ to the reconstructed velocity field u, on any interior subset, is Hölder continuous. [ABSTRACT FROM AUTHOR]

In this paper, we present sufficient conditions for the third-order nonlinear advanced difference equations of the form Δ(a(n)Δ(b(n)Δy(n))) = p(n)f (y(Δ(n))) to have property B or to be oscillatory. These conditions are based on monotonic properties and estimates of nonoscillatory solutions of corresponding canonical type equations. The obtained results extended and improve known results mentioned in the literature. [ABSTRACT FROM AUTHOR]

We continue the investigations in this paper which were considered in its first part. In particular, the problem of optimal filtration of one components of solution of nonlinear evolutionary differential equation in a Hilbert space H perturbing by Gaussian random process under observation of the second components of the same equation is considered. Using the results of the first part of this paper, here the algorithm for the calculation of an optimal estimate in the filtration problem is obtained. [ABSTRACT FROM AUTHOR]

In this paper, we study the performance improvement of free space optical (FSO) communication system with spatial diversity techniques employing hybrid pulse position modulation-binary phase shift keying-subcarrier intensity modulation (PPM-BPSK-SIM). The involvement of multiple photo-detectors in diversity based FSO systems offers an effective way to overcome scntillation. In this paper, we have simulated the bit error rate (BER) with respect to different parameters like average SNR, link distance at various weather conditions. The simulation results are verified in Matlab environment with the mathematical analysis. The simulation results show that higher order single input multiple output (SIMO) system achieves better BER performance and hybrid PPM-BPSK-SIM has significant improved performance than the common modulation schemes like PPM, BPSK-SIM. [ABSTRACT FROM AUTHOR]

We suggest in this paper a global Random Walk on Spheres (gRWS) method for solving transient boundary value problems, which, in contrast to the classical RWS method, calculates the solution in any desired family of m prescribed points. The method uses only N trajectories in contrast to mN trajectories in the conventional RWS algorithm. The idea is based on the symmetry property of the Green function and a double randomization approach. We present the gRWS method for the heat equation with arbitrary initial and boundary conditions, and the Laplace equation. Detailed description is given for 3D problems; the 2D problems can be treated analogously. Further extensions to advection-diffusion-reaction equations will be presented in a forthcoming paper. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of nontrivial solutions for critical Hardy–Schrödinger–Kirchhoff systems driven by the fractional p-Laplacian operator. Existence is derived as an application of the mountain pass theorem and the Ekeland variational principle. The main features and novelty of the paper are the presence of the Hardy terms as well as critical nonlinearities. [ABSTRACT FROM AUTHOR]

The aim of this paper is to consider the asymptotic behavior of boundary value problems in n-dimensional domains with periodically placed particles, with a general microscopic boundary condition on the particles and a p-Laplace diffusion operator on the interior, in the case in which the particles are of critical size. We consider the cases in which 1 < p < n, n ≥ 3. In fact, in contrast to previous results in the literature, we formulate the microscopic boundary condition in terms of a Robin type condition, involving a general maximal monotone graph, which also includes the case of microscopic Dirichlet boundary conditions. In this way we unify the treatment of apparently different formulations, which before were considered separately. We characterize the so called "strange term" in the homogenized problem for the case in which the particles are balls of critical size. Moreover, by studying an application in Chemical Engineering, we show that the critically sized particles lead to a more effective homogeneous reaction than noncritically sized particles. [ABSTRACT FROM AUTHOR]

Motivated by the work [9], in this paper we investigate the infinite boundary value problem associated with the semilinear PDE Lu = ƒ(u) + h(x) on bounded smooth domains Ω ⊆ ℝn, where L is a non-divergence structure uniformly elliptic operator with singular lower-order terms. In the equation, ƒ is a continuous non-decreasing function that satisfies the Keller–Osserman condition, while h is a continuous function in Ω that may change sign, and which may be unbounded on Ω. Our purpose is two-fold. First we study some sufficient conditions on ƒ and h that would ensure existence of boundary blow-up solutions of the above equation, in which we allow the lower-order coefficients to be singular on the boundary. The second objective is to provide sufficient conditions on ƒ and h for the uniqueness of boundary blow-up solutions. However, to obtain uniqueness, we need the lower-order coefficients of L to be bounded in Ω, but we still allow h to be unbounded on Ω. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of periodic solutions of fractional differential equations with periodic impulses. The first part of the paper is devoted to the uniqueness, existence and asymptotic stability results for periodic solutions of impulsive fractional differential equations with varying lower limits for standard nonlinear cases as well as for cases of weak nonlinearities, equidistant and periodically shifted impulses. We also apply our result to an impulsive fractional Lorenz system. The second part extends the study to periodic impulsive fractional differential equations with fixed lower limit. We show that in general, there are no solutions with long periodic boundary value conditions for the case of bounded nonlinearities. [ABSTRACT FROM AUTHOR]

In this paper, we study varieties and characterize convolution operators on the algebras related to the new structures of KPC-hypergroups, which are a generalization of the classical ones. [ABSTRACT FROM AUTHOR]

J. Jakubík noted in [JAKUBÍK, J.: Modular Lattice of Locally Finite Length, Acta Sci. Math. 37 (1975), 79–82] that F. Šik in the unpublished manuscript proved that in the class of upper semimodular lattices of locally finite length, modularity is equivalent to the lack of cover-preserving sublattices isomorphic to S7. In the present paper we extend the scope of Šik's theorem to the class of upper semimodular, upper continuous and strongly atomic lattices. Moreover, we show that corresponding result of Jakubík from [JAKUBÍK, J.: Modular Lattice of Locally Finite Length, Acta Sci. Math. 37 (1975), 79–82] cannot be strengthened is analogous way. [ABSTRACT FROM AUTHOR]

The article is a short reaction to the Zámečník's paper The nature of the explanation in the synergetic linguistics () which claims that the synergetic linguistics lacks full-fledged explanation and praises the Menzerath-Altmann Law for its explanatory power. However, this paper shows that the synergetic linguistic explanatory mechanism is comparable to the mechanism of Menzerath-Altmann Law and that it aims to follow the explanatory logic of white-box models in other sciences like ecology. The quantitative linguistic laws in general often lack clear information about the known principles from which they are derived, what stochastic process they represent and what the interpretation of their parameters is, but it does not mean that they are intrinsically wrong and that we are in a critical need for a paradigm shift. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new kind of conformable stochastic impulsive differential systems (CSIDS) involving discrete distribution of Bernoulli. For random discontinuous trajectories, we modify the tracking error of piecewise continuous variables by a zero-order holder. First, the improved P-type and PDα-type learning laws of the random iterative learning control (ILC) scheme are designed through global and local averaging operators. Next, we establish sufficient conditions for convergence of the tracking error in the expectation sense and prove the main results by using the impulsive Gronwall inequality and mathematical analysis tools. Finally, the theoretical results are verified by two numerical examples, and the tracking performance is compared for different conformable order of α. [ABSTRACT FROM AUTHOR]

Arone and the second author showed that when the dimensions are in the stable range, the rational homology and homotopy of the high-dimensional analogues of spaces of long knots can be calculated as the homology of a direct sum of finite graph-complexes that they described explicitly. They also showed that these homology and homotopy groups can be interpreted as the higher-order Hochschild homology, also called Hochschild–Pirashvili homology. In this paper, we generalize all these results to high-dimensional analogues of spaces of string links. The methods of our paper are applicable in the range when the ambient dimension is at least twice the maximal dimension of a link component plus two, which in particular guarantees that the spaces under study are connected. However, we conjecture that our homotopy graph-complex computes the rational homotopy groups of link spaces always when the codimension is greater than two, i.e. always when the Goodwillie–Weiss calculus is applicable. Using Haefliger’s approach to calculate the groups of isotopy classes of higher-dimensional links, we confirm our conjecture at the level of π 0 {\pi_{0}}. [ABSTRACT FROM AUTHOR]

We define a “period-ring-valued beta function” and give a reciprocity law on its special values. The proof is based on some results of Rohrlich and Coleman concerning Fermat curves. We also have the following application. Stark’s conjecture implies that the exponentials of the derivatives at s = 0 s=0 of partial zeta functions are algebraic numbers which satisfy a reciprocity law under certain conditions. It follows from Euler’s formulas and properties of cyclotomic units when the base field is the rational number field. In this paper, we provide an alternative proof of a weaker result by using the reciprocity law on the period-ring-valued beta function. In other words, the reciprocity law given in this paper is a refinement of the reciprocity law on cyclotomic units. [ABSTRACT FROM AUTHOR]

Gromov’s compactness theorem for pseudo-holomorphic curves is a foundational result in symplectic geometry. It controls the compactness of the moduli space of pseudo-holomorphic curves with bounded area in a symplectic manifold. In this paper, we prove the analog of Gromov’s compactness theorem in non-archimedean analytic geometry. We work in the framework of Berkovich spaces. First, we introduce a notion of Kähler structure in non-archimedean analytic geometry using metrizations of virtual line bundles. Second, we introduce formal stacks and non-archimedean analytic stacks. Then we construct the moduli stack of non-archimedean analytic stable maps using formal models, Artin’s representability criterion and the geometry of stable curves. Finally, we reduce the non-archimedean problem to the known compactness results in algebraic geometry. The motivation of this paper is to provide the foundations for non-archimedean enumerative geometry. [ABSTRACT FROM AUTHOR]

In this paper, Ulam’s-type stabilities are studied for a class of first-order impulsive differential equations with bounded variable delays on compact interval with finite number of impulses. Results of stability are proved via newly established integral inequality of Bellman–Grönwall–Bihari type with delay for discontinuous functions. Using this inequality for the first time and assumption of α $\alpha$ -H o ¨ $\ddot{o}$ lder’s condition instead of common Lipschitz condition is novelty of this paper. Moreover, solution is obtained in quasi–Banach spaces which is best suited for obtaining results under the assumptions of α $\alpha$ -H o ¨ $\ddot{o}$ lder’s condition. [ABSTRACT FROM AUTHOR]

By virtue of the excellent aerodynamic performances, conformal phased arrays have been attracting considerable attention. However, for the synthesis of patterns with low/ultra-low sidelobes of the conventional conformal arrays, the obtained dynamic range ratios of amplitude excitations could be quite high, which results in stringent requirements on various error tolerances for practical implementation. Time-modulated array (TMA) has the advantages of low sidelobe and reduced dynamic range ratio requirement of amplitude excitations. This paper takes full advantages of conformal antenna arrays and time-modulated arrays. The active-element-pattern, including element mutual coupling and platform effects, is employed in the whole design process. To optimize the pulse durations and the switch-on instants of the time-modulated elements, multiobjective invasive weed optimization (MOIWO) algorithm based on the nondominated sorting of the solutions is proposed. A S-band 8-element cylindrical conformal array is designed and a S-band 16-element cylindrical-parabolic conformal array is constructed and tested at two different steering angles. [ABSTRACT FROM AUTHOR]

In this paper, we discuss some important and interesting remarks on the concept of occasionally weakly compatible (owc) mappings, which is an active and interesting area of research in the present era. Also, we discuss here the lapses of several authors in quoting the definition of owc maps and provide the corrected proof by including some additional conditions on their results. [ABSTRACT FROM AUTHOR]

After graduating in geodesy at the Faculty of Civil Engineering of the Slovak University of Technology in Bratislava in 1954, you started your work at the Geodetic Institute in Bratislava, where you stayed from 1954 until 1962. This time both were from the Faculty of Natural Sciences of Comenius University, the first in mathematical analysis in 1957 and the second in probability & mathematical statistics in 1964. You are an honorary member of the Learned Society of Slovakia, and in 2002 you were awarded the honorary degree Dr.h.c. of the Faculty of Civil Engineering of the Slovak University of Technology. [Extracted from the article]

In a previous paper we introduced a family of differential-reflection operators ΛA,ε acting on smooth functions defined on R, where the spectral problem for the operators ΛA,ε has been studied. Here A is a Sturm-Liouville function with additional hypotheses and -1 ⩽ ε ⩽ 1. Via the eigenfunctions of ΛA,ε, we introduce in this paper a generalized Fourier transformFA,ε. An Lp-harmonic analysis for FA,ε is developed when 0 < p ⩽ 2/1+ √1- 1+1-ε2 . In particular, an Lp-Schwartz space isomorphism theorem for FA,ε is proved. [ABSTRACT FROM AUTHOR]

In this paper, an inverse problem of determining the unknown coefficient of a multidimensional nonlinear time-dependent Schrödinger equation that has a complex number at nonlinear part is considered. The inverse problem is reformulated as a variational one which aims to minimize the observation functional. This paper presents existence and uniqueness theorems of solutions of the constituted variational problem, the gradient of the observation functional and a necessary condition for the solution of the variational problem. [ABSTRACT FROM AUTHOR]

This paper contributes to the classification of flag transitive cF4-geometries. Here, under some mild extra conditions, we determine those geometries in which the point-residue is a building of type F4(2) and we show that the automorphism groups are ²2E6(2) : 2 or 3.²E6(2) : 2 orE6(2):2 or 226 : F4(2). This work was started by Corinna Wiedorn. In this paper we follow her ideas and just show that the corresponding amalgams are uniquely determined. [ABSTRACT FROM AUTHOR]

In this paper, we explore a general method to derive Hp →→ Lp boundedness from Hp →→ Hp boundedness of linear operators, an idea originated in the work of Han and Lu in dealing with the multiparameter flag singular integrals ([[Discrete Littlewood-Paley-Stein theory and multi-parameter Hardy spaces associated with the flag singular integrals]]). These linear operators include many singular integral operators in one parameter and multiparameter settings. In this paper, we will illustrate further that this method will enable us to prove the Hp →→ Lp boundedness on product spaces of homogeneous type in the sense of Coifman and Weiss ([[Lecture Notes in Math. 242: 1971]]) where maximal function characterization of Hardy spaces is not available. Moreover, we also provide a particularly easy argument in those settings such as one parameter or multiparameter Hardy spaces and where the maximal function characterization exists. The key idea is to prove ||ƒƒ|| Lp ≤≤ C ||ƒƒ || Hp for ƒƒ ∈∈ Lq ∩∩ Hp (1 < q < ∞∞, 0 < p ≤≤ 1). It is surprising that this simple result even in this classical setting has been absent in the literature. [ABSTRACT FROM AUTHOR]

We consider algebraic models of sequential programs where the semantics of operators is defined on the base of a semigroup. In the paper, for the first time an example is constructed of a solvable semigroup with indecomposable neutral element for which the stopping problem for a Turing machine reduces to the problem of equivalence of programs over a given semigroup. All known examples of models of insoluble problem of equivalence of programs were based on groups. Thus, in the paper we succeeded in refining the boundary between soluble and insoluble cases of the problem of equivalence of programs in algebraic models. The obtained result supports also the importance of some sufficient conditions of solubility of the problem of equivalence of programs. [ABSTRACT FROM AUTHOR]

This paper presents a new proof that if kαα is irrational then the sequence {⌊⌊ αα ++ log k n⌋⌋} n≥≥1 is not k-regular. Unlike previous proofs, the methods used do not rely on automata or language theoretic concepts. The paper also proves the stronger statement that if kαα is irrational then the generating function in k non-commuting variables associated with {⌊⌊ αα ++ log k n⌋⌋} n≥≥1 is not algebraic. [ABSTRACT FROM AUTHOR]

Let j be the modular invariant. For the primes p ≦ 23 the q-expansion coefficients of Um( j – 744) are multiplicative as it was a Hecke eigenform modulo a power of p which increases with m. This was conjectured by Atkin on the basis of extensive numerical experiments, and is proved in this paper. The cases p = 5, 7 and 11 are under special consideration in this paper. [ABSTRACT FROM AUTHOR]

This paper deals with the mathematical analysis of a general class of epidemiological models with multiple infectious stages for the transmission dynamics of a communicable disease. We provide a theoretical study of the model. We derive the basic reproduction number R 0 $\mathcal R_0$ that determines the extinction and the persistence of the infection. We show that the disease-free equilibrium is globally asymptotically stable whenever R 0 ≤ 1 $\mathcal R_0 \leq 1$ , while when R 0 > 1 $\mathcal R_0 \gt 1$ , the disease-free equilibrium is unstable and there exists a unique endemic equilibrium point which is globally asymptotically stable. A case study for tuberculosis (TB) is considered to numerically support the analytical results. [ABSTRACT FROM AUTHOR]

A mathematical study of an Oldroyd 4-constant fluid for a blade coating process is studied in this paper. The results for plane as well as exponential coaters are analyzed. Suitable dimensionless variables are used to convert the model governing equations into dimensionless form. Lubrication approximation theory is applied to simplify the dimensionless form of governing partial differential equations. The well-known numerical technique known as the shooting method is used to solve the non-linear boundary value problem. Influence of the involved rheological parameters on the blade coating process is analyzed. From an engineering point of view, load on the blade and pressure are important outcomes of the present study as they ensure the thickness and quality of coating and enhance the life of the substrate. The effects of material parameters on load, thickness, velocity, pressure and pressure gradient are discussed. Obtained results for velocity, pressure gradient and pressure distribution are shown graphically, whereas load and thickness are expressed in a tabulated form. [ABSTRACT FROM AUTHOR]

In this paper, we present upper and lower linear bounds for the Shannon function for length of checking tests for repetition-free functions in the basis {0, 1, &, ∨, ¬}. The research was supported by Russian Foundation for Basic Research, grants 04-01-00359 and 05-01-01000. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a relaxed splitting preconditioner for saddle point problems. Spectral properties of the preconditioned matrix are analyzed and compared with the closely related preconditioner in recent paper [New preconditioners for saddle point problems, Appl. Math. Comput. 172 (2006), 762-771] by Pan et al. Numerical experiments are given to illustrate the efficiency of the proposed precoditioner. [ABSTRACT FROM AUTHOR]

In this paper, we establish the least upper bound of the product Bi( K) Bi( K*) for width-integrals of index i of a convex body K. Further, the least upper bound of the product A p, i( K) A q, i( K*) for mixed width-integrals of index p ( q) is given. [ABSTRACT FROM AUTHOR]

In this paper we consider the branched transportation problem in two dimensions associated with a cost per unit length of the form 1 + β ⁢ θ {1+\beta\,\theta} , where θ denotes the amount of transported mass and β > 0 {\beta>0} is a fixed parameter (notice that the limit case β = 0 {\beta=0} corresponds to the classical Steiner problem). Motivated by the numerical approximation of this problem, we introduce a family of functionals ( { ℱ ε } ε > 0 {\{\mathcal{F}_{\varepsilon}\}_{\varepsilon>0}}) which approximate the above branched transport energy. We justify rigorously the approximation by establishing the equicoercivity and the Γ-convergence of { ℱ ε } {\{\mathcal{F}_{\varepsilon}\}} as ε ↓ 0 {\varepsilon\downarrow 0}. Our functionals are modeled on the Ambrosio–Tortorelli functional and are easy to optimize in practice. We present numerical evidences of the efficiency of the method. [ABSTRACT FROM AUTHOR]

In the present paper, it is shown that if a prime ring R admits a generalized derivation f associated with a nonzero derivation d such that either f ⁢ ([ x m , y n ]) + [ x m , y n ] ∈ Z ⁢ (R) for all ⁢ x , y ∈ R f([x^{m},y^{n}])+[x^{m},y^{n}]\in Z(R)\quad\text{for all }x,y\in R or f ⁢ ([ x m , y n ]) - [ x m , y n ] ∈ Z ⁢ (R) for all ⁢ x , y ∈ R , f([x^{m},y^{n}])-[x^{m},y^{n}]\in Z(R)\quad\text{for all }x,y\in R, then R is commutative. We apply this purely ring theoretic result to obtain commutativity of Banach algebras and prove that if A is a prime Banach algebra which admits a continuous linear generalized derivation f associated with a nonzero continuous linear derivation d such that either f ⁢ ([ x m , y n ]) - [ x m , y n ] ∈ Z ⁢ (A) {f([x^{m},y^{n}])-[x^{m},y^{n}]\in Z(A)} or f ⁢ ([ x m , y n ]) + [ x m , y n ] ∈ Z ⁢ (A) {f([x^{m},y^{n}])+[x^{m},y^{n}]\in Z(A)} for an integer m = m ⁢ (x , y) > 1 {m=m(x,y)>1} and sufficiently many x , y {x,y} in A, then A is commutative. A similar result is obtained for a unital prime Banach algebra A which admits a nonzero continuous linear generalized derivation f associated with a continuous linear derivation d such that d ⁢ (Z ⁢ (A)) ≠ 0 {d(Z(A))\neq 0} satisfying either f ⁢ ((x ⁢ y) m) - x m ⁢ y m ∈ Z ⁢ (A) {f((xy)^{m})-x^{m}y^{m}\in Z(A)} or f ⁢ ((x ⁢ y) m) - y m ⁢ x m ∈ Z ⁢ (A) {f((xy)^{m})-y^{m}x^{m}\in Z(A)} for each x ∈ G 1 {x\in G_{1}} and y ∈ G 2 {y\in G_{2}} , where G 1 , G 2 {G_{1},G_{2}} are open sets in A and m = m ⁢ (x , y) > 1 {m=m(x,y)>1} is an integer: then A is commutative. [ABSTRACT FROM AUTHOR]

Let (X , *) {(X,*)} be a hypergroup and let w 0 {w_{0}} be a fixed measure on X. In this paper we study the two functional equations 〈 δ x * δ y * ω 0 , g 〉 + 〈 δ x * δ y ˇ * ω 0 , g 〉 = 2 ⁢ g ⁢ (x) ⁢ g ⁢ (y) , x , y ∈ X , \langle\delta_{x}*\delta_{y}*\omega_{0},g\rangle+\langle\delta_{x}*\delta_{% \check{y}}*\omega_{0},g\rangle=2g(x)g(y),\quad x,y\in X, and 〈 δ x * δ y ˇ * ω 0 , f 〉 - 〈 δ x * δ y * ω 0 , f 〉 = 2 ⁢ f ⁢ (x) ⁢ f ⁢ (y) , x , y ∈ X , \langle\delta_{x}*\delta_{\check{y}}*\omega_{0},f\rangle-\langle\delta_{x}*% \delta_{y}*\omega_{0},f\rangle=2f(x)f(y),\quad x,y\in X, where g , f : X → ℂ {g,f:X\to\mathbb{C}} are continuous and bounded functions to be determined. We express the solutions of the two functional equations in terms of multiplicative maps on (X , *) {(X,*)}. As an application we give the solution of the two functional equations on polynomial and Sturm–Liouville hypergroups. [ABSTRACT FROM AUTHOR]

In this article, we correct the proof of the main theorem of Gordji's paper [M. Eshaghi Gordji, n-Jordan homomorphisms, Bull. Aust. Math. Soc. 80 2009, 1, 159–164] by a different method and generalize Zelazko's theorem to 4-Jordan homomorphisms by considering an extra condition. [ABSTRACT FROM AUTHOR]

Sobol' sequences are widely used for quasi-Monte Carlo methods that arise in financial applications. Sobol' sequences have parameter values called direction numbers, which are freely chosen by the user, so there are several implementations of Sobol' sequence generators. The aim of this paper is to provide a comparative study of (non-commercial) high-dimensional Sobol' sequences by calculating financial models. Additionally, we implement the Niederreiter sequence (in base 2) with a slight modification, that is, we reorder the rows of the generating matrices, and analyze and compare it with the Sobol' sequences. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of mild solutions of impulsive fractional integrodifferential evolution equations with nonlocal conditions via the fixed point theorems and fractional cosine family combined with solutions operator theorems. Our results improve and generalize some classical results. Finally, an example is given to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, we consider an inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary conditions. The unknown source term is to be determined by additional boundary data. This problem is ill-posed since the dimensionality of the boundary is lower than the dimensionality of the inner domain. To overcome the ill-posed nature, using the a priori information (sourcewise representation), and based on the coupled complex boundary method, we propose a coupled complex boundary expanding compacts method (CCBECM). A finite element method is used for the discretization of CCBECM. The regularization properties of CCBECM for both the continuous and discrete versions are proved. Moreover, an a posteriori error estimate of the obtained finite element approximate solution is given and calculated by a projected gradient algorithm. Finally, numerical results show that the proposed method is stable and effective. [ABSTRACT FROM AUTHOR]

The closed subsets ℱ (X) of any topological space can be given a topology, called the Chabauty–Fell topology, in which ℱ(X) is quasi-compact. If X is a locally compact space, then ℱ(X) is Hausdorff. If X = G is a locally compact group, then the subset 𝒮𝒰ℬ(G) of closed subgroups is closed in ℱ (G), and the set of closed subgroups inherits its own compact topology, called the Chabauty topology. We develop some of the important properties of this topology. More precisely, the results contained in this paper deal with the following question: Given a locally compact topological group, when is ℱ(G) (resp. 𝒮𝒰ℬ(G) a totally disconnected space? [ABSTRACT FROM AUTHOR]

In this paper, we show that the third subgroup of the Andreadakis–Johnson filtration of the automorphism group of a free group coincides with the third group of the lower central series of the IA-automorphism group. [ABSTRACT FROM AUTHOR]

We investigate weighted Sobolev spaces on metric measure spaces (X , d , 𝔪) {(X,\mathrm{d},\mathfrak{m})}. Denoting by ρ the weight function, we compare the space W 1 , p ⁢ (X , d , ρ ⁢ 𝔪) {W^{1,p}(X,\mathrm{d},\rho\mathfrak{m})} (which always coincides with the closure H 1 , p ⁢ (X , d , ρ ⁢ 𝔪) {H^{1,p}(X,\mathrm{d},\rho\mathfrak{m})} of Lipschitz functions) with the weighted Sobolev spaces W ρ 1 , p ⁢ (X , d , 𝔪) {W^{1,p}_{\rho}(X,\mathrm{d},\mathfrak{m})} and H ρ 1 , p ⁢ (X , d , 𝔪) {H^{1,p}_{\rho}(X,\mathrm{d},\mathfrak{m})} defined as in the Euclidean theory of weighted Sobolev spaces. Under mild assumptions on the metric measure structure and on the weight we show that W 1 , p ⁢ (X , d , ρ ⁢ 𝔪) = H ρ 1 , p ⁢ (X , d , 𝔪) {W^{1,p}(X,\mathrm{d},\rho\mathfrak{m})=H^{1,p}_{\rho}(X,\mathrm{d},\mathfrak{% m})}. We also adapt the results in [23] and in the recent paper [27] to the metric measure setting, considering appropriate conditions on ρ that ensure the equality W ρ 1 , p ⁢ (X , d , 𝔪) = H ρ 1 , p ⁢ (X , d , 𝔪) {W^{1,p}_{\rho}(X,\mathrm{d},\mathfrak{m})=H^{1,p}_{\rho}(X,\mathrm{d},% \mathfrak{m})}. [ABSTRACT FROM AUTHOR]