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Formerly the geometry was based on shapes, but since the last centuries this founding mathematical science deals with transformations, projections, and mappings. Projective geometry identifies a line with a single point, like the perspective on the horizon line and, due to this fact, it requires a restructuring of the real mathematical and numerical analysis. In particular, the problem of interpolating data must be refocused. In this paper, we define a linear structure along with a metric on a projective space, and prove that the space thus constructed is complete. Then, we consider an iterated function system giving rise to a fractal interpolation function of a set of data. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is the numerical analysis of a class of mathematical models that describe the contact between a thermo-piezoelectric body and a conductive foundation. Under the assumption of a static process, the material's behavior is modeled with a linear thermo-electro-elastic constitutive law and the frictional contact with Signorini's and Tresca's laws. A variational problem is derived and the existence of a unique weak solution is proved by combining arguments from the theory of variational inequalities with linear strongly monotone Lipschitz continuous operators. A successive iteration technique to linearize the problem by transforming it into an incremental recursive form is proposed, and its convergence is established. An Augmented Lagrangian variant, known as the Alternating Direction Multiplier Method (ADMM), is employed to split the original problem into two subproblems, resolve them sequentially, as well as update the dual variables at each iteration. To illustrate the performance of the proposed approach, several numerical simulations on two-dimensional test problems are carried out. [ABSTRACT FROM AUTHOR]

In this note we will show that finitely generated condition is necessary in Theorem 1.2 of the above mentioned paper. [ABSTRACT FROM AUTHOR]

In this paper, we have considered a deterministic mathematical model to analyze effective interventions for meningitis and pneumonia coinfection as well as to make a rational recommendation to public healthy, policy or decision makers and programs implementers. We have introduced the epidemiology of infectious diseases, the epidemiology of meningitis, the epidemiology of pneumonia, and the epidemiology of infection of meningitis and pneumonia. The positivity and boundedness of the sated model was shown. Our model elucidate that, the disease free equilibrium points of each model are locally asymptotically stable if the corresponding reproduction numbers are less than one and globally asymptotically stable if the corresponding reproduction numbers are greater than one. Additionally, we have analyzed the existence and uniqueness of the endemic equilibrium point of each sub models, local stability and global stability of the endemic equilibrium points for each model. By using standard values of parameters we have obtained from different studies, we found that the effective reproduction numbers of meningitis R e f f (m) = 9 and effective reproduction numbers of pneumonia R e f f (p) = 11 that lead us to the effective reproduction number of the meningitis and pneumonia co-infected model is m a x R e f f m , R e f f (p) = 9 . Applying sensitivity analysis, we identified the most influential parameters that can change the behavior of the solution of the meningitis pneumonia coinfection dynamical system are α 1 , α 2 and π . Biologically, decrease in α 1 and increasing in π is a possible intervention strategy to reduce the infectious from communities. Finally, our numerical simulation has shown that vaccination against those diseases, reducing contact with infectious persons and treatment have the great effect on reduction of these silent killer diseases from the communities. [ABSTRACT FROM AUTHOR]

In this paper, the reliability performance analysis of coupled cyber-physical systems under different network types is investigated. To study the underlying network model, their interactions, and relationships and how cascading failures occur in the interdependent cyber-physical systems, we propose a practical model for interdependent cyber-physical systems using network percolation theory. Besides, for different network models, we also study the effect of cascading failures effect and reveal mathematical analysis of failure propagation in such systems. Then we analyze the reliability of our proposed model caused by random attacks or failures by calculating the size of giant functioning components in interdependent cyber-physical systems. In order to gain an insight into the proposed analysis model, numerical simulation analysis is also provided. The results show that there exists a threshold for the proportion of faulty nodes, beyond which the cyber-physical systems collapse. We also determine the critical values for different system parameters. In this way, the reliability analysis based on network percolation theory can be effectively utilized for anti-attack and protection purposes in coupled cyber-physical systems. [ABSTRACT FROM AUTHOR]

Published in 1999, Christodoulou proved that the naked singularities of a self-gravitating scalar field are not stable in spherical symmetry and therefore the cosmic censorship conjecture is true in this context. The original proof is by contradiction and sharp estimates are obtained strictly depending on spherical symmetry. In this paper, appropriate a priori estimates for the solution are obtained. These estimates are more relaxed but sufficient for giving another robust argument in proving the instability, in particular not by contradiction. In a companion paper, we are able to prove certain instability theorems of the spherically symmetric naked singularities of a scalar field under gravitational perturbations without symmetries. The argument given in this paper plays a central role. [ABSTRACT FROM AUTHOR]

In this paper, we study properties of functions and sequences with a semi-heavy tail, that is, functions and sequences of the form w(x) = e−βxf(x), β > 0, resp., wn = cnfn, 0 < c < 1, where the function f(x), resp., the sequence (fn), is regularly varying. Among others, we give a representation theorem and study convolution properties. The paper includes several examples and applications in probability theory. [ABSTRACT FROM AUTHOR]

In this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solution. Furthermore, the Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively the local and global stability results. We also establish the Hopf-bifurcation to show the existence of a branch of nontrivial periodic solutions. Finally, numerical simulations have been accomplished to validate our analytical findings. [ABSTRACT FROM AUTHOR]

In this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solution. Furthermore, the Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively the local and global stability results. We also establish the Hopf-bifurcation to show the existence of a branch of nontrivial periodic solutions. Finally, numerical simulations have been accomplished to validate our analytical findings. [ABSTRACT FROM AUTHOR]

A correction to the article "Critical examination of recent assertions by Logo (2013) about the paper 'Analytical and numerical solutions for a reliability based benchmark example'" that was published in the October 31, 2103 issue is presented.

This paper aims to study two-factor uncertain term structure model where the volatility of the uncertain interest rate is driven by another uncertain differential equation. In order to solve this model, the nested uncertain differential equation method is employed. This paper is also devoted to the study of the numerical solutions for the proposed nested uncertain differential equation using the α-path methods. We also use the built two-factor term structure model to value the bond price with the help of proposed numerical method. Finally, we give a numerical example where the price of a zero-coupon bond is calculated based on the α-path methods. [ABSTRACT FROM AUTHOR]

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic problem which models the evolution of the concentration of surfactants is analyzed from the numerical point of view. Both bulk and surface diffusions are taken into account into the model, and the relationship between both concentrations, in the bulk and at the surface, is considered by using the well-known Langmuir-Hinshelwood equation. Two convective terms are also included. The variational formulation is then written as a coupled system of parabolic partial differential equations, for which an existence and uniqueness result is stated in an earlier paper (Fernández et al. in SIAM J Math Anal 48(5):3065-3089, 2016). Then, fully discrete approximations are introduced by using the classical finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. An a priori error estimates result is proved, from which the linear convergence of the approximation is derived under suitable additional regularity conditions. Finally, some numerical simulations are presented in order to show the accuracy of the algorithm and the behaviour of the solution in real situations. [ABSTRACT FROM AUTHOR]

The development of efficient methods for detecting quasiperiodic oscillations and computing the corresponding invariant tori is a subject of great importance in dynamical systems and their applications in science and engineering. In this paper, we prove the convergence of a new Newton-like method for computing quasiperiodic normally hyperbolic invariant tori carrying quasiperiodic motion in smooth families of real-analytic dynamical systems. The main result is stated as an a posteriori KAM-like theorem that allows controlling the inner dynamics on the torus with appropriate detuning parameters, in order to obtain a prescribed quasiperiodic motion. The Newton-like method leads to several fast and efficient computational algorithms, which are discussed and tested in a companion paper (Canadell and Haro in J Nonlinear Sci, 2017. doi:), in which new mechanisms of breakdown are presented. [ABSTRACT FROM AUTHOR]

Noise in cellular systems is often modeled and simulated with Gillespie's stochastic simulation algorithm (SSA), but the low efficiency of the SSA limits its application to large biochemical networks. To improve the efficiency of stochastic simulations, Haseltine and Rawlings (HR) proposed a hybrid algorithm, which combines ordinary differential equations for traditional deterministic models and the SSA for stochastic models. In this paper, accuracy of the HR hybrid method is studied based on a linear chain reaction system. Mathematical analysis and numerical results both show that the HR hybrid method is accurate if either the quantity of reactant molecules in fast reactions is above a certain threshold, or the reaction rates of fast reactions are much larger than those of slow reactions. This analysis also shows that the HR hybrid method approximates the chemical master equation well for a much greater region in system parameter space than the slow-scale SSA and the stochastic quasi-steady-state assumption methods. [ABSTRACT FROM AUTHOR]

In this paper, we study Jarzynski's equality and fluctuation theorems for diffusion processes. While some of the results considered in the current work are known in the (mainly physics) literature, we review and generalize these nonequilibrium theorems using mathematical arguments, therefore enabling further investigations in the mathematical community. On the numerical side, variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on Jarzynski's equality. [ABSTRACT FROM AUTHOR]

This paper introduces a notion of controllability for nonlinear Hilfer fractional stochastic system with multiple delays in control and Poisson jumps. A proper new series of sufficient conditions are derived for the considered system to be controllable by using fixed point technique, fractional calculus and stochastic analysis approach. The obtained result generalizes many results on controllability of stochastic systems and fractional stochastic systems. Finally, an example is provided to show the effectiveness of the achieved theoretical results. [ABSTRACT FROM AUTHOR]

Packing and covering linear programs (PC-LP s) form an important class of linear programs (LPs) across computer science, operations research, and optimization. Luby and Nisan (in: STOC, ACM Press, New York, 1993) constructed an iterative algorithm for approximately solving PC-LP s in nearly linear time, where the time complexity scales nearly linearly in N, the number of nonzero entries of the matrix, and polynomially in ε , the (multiplicative) approximation error. Unfortunately, existing nearly linear-time algorithms (Plotkin et al. in Math Oper Res 20(2):257–301, 1995; Bartal et al., in: Proceedings 38th annual symposium on foundations of computer science, IEEE Computer Society, 1997; Young, in: 42nd annual IEEE symposium on foundations of computer science (FOCS'01), IEEE Computer Society, 2001; Koufogiannakis and Young in Algorithmica 70:494–506, 2013; Young in Nearly linear-time approximation schemes for mixed packing/covering and facility-location linear programs, 2014. arXiv:1407.3015; Allen-Zhu and Orecchia, in: SODA, 2015) for solving PC-LP s require time at least proportional to ε - 2 . In this paper, we break this longstanding barrier by designing a packing solver that runs in time O ~ (N ε - 1) and covering LP solver that runs in time O ~ (N ε - 1.5) . Our packing solver can be extended to run in time O ~ (N ε - 1) for a class of well-behaved covering programs. In a follow-up work, Wang et al. (in: ICALP, 2016) showed that all covering LPs can be converted into well-behaved ones by a reduction that blows up the problem size only logarithmically. [ABSTRACT FROM AUTHOR]

This paper investigates a polyhedral approach to handle symmetries in mixed-binary programs. We study symretopes, i.e., the convex hulls of all binary vectors that are lexicographically maximal in their orbit with respect to the symmetry group. These polytopes turn out to be quite complex. For practical use, we therefore develop an integer programming formulation with ternary coefficients, based on knapsack polytopes arising from a single lexicographic order enforcing inequality. We show that for these polytopes, the optimization as well as the separation problem of minimal cover inequalities can be solved in almost linear time. We demonstrate the usefulness of this approach by computational experiments, showing that it is competitive with state-of-the-art methods and is considerably faster for specific problem classes. [ABSTRACT FROM AUTHOR]

This paper is concerned with mathematical and numerical analysis of the system of radiative integral transfer equations. The existence and uniqueness of solution to the integral system is proved by establishing the boundedness of the radiative integral operators and proving the invertibility of the operator matrix associated with the system. A collocation-boundary element method is developed to discretize the differential-integral system. For the non-convex geometries, an element-subdivision algorithm is developed to handle the computation of the integrals containing the visibility factor. An efficient iterative algorithm is proposed to solve the nonlinear discrete system and its convergence is also established. Numerical experiment results are also presented to verify the effectiveness and accuracy of the proposed method and algorithm. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new hierarchy of large cardinals between I3 and I2, the iterability hierarchy, and we prove that every step of it strongly implies the ones below. [ABSTRACT FROM AUTHOR]

Intrusion detection systems (IDSs) are the fundamental parts of any network security infrastructure given their role as layers of defense against hackers. However, IDSs generate frequent instances of false alerts and miss a lot of real attacks that block the normal traffic and threaten the network security. It is not possible to identify a missed intrusion using one IDS, so multiple IDSs are used since they respond differently to the same packet trace and produce different alert sets. Actually, an attack missed by an IDS can be detected by another while inspecting the same network traffic. In this paper, we propose a multi-objective optimization process that aims to identify false negatives and false positives from the sets of alerts generated by multiple IDSs. In the first step, low-level alerts are clustered into meta-alerts to give a better understanding of the output of each IDS. Then, a filtering step is performed having as input the distinct meta-alert sets generated by different IDSs and as output the set of potential false negatives collecting the meta-alerts detected by some IDSs and missed by others. Meta-alerts generated by all IDSs are discarded since they cannot be missed attacks. Later, a clustering inter-IDS step is performed to group together similar meta-alerts generated by different IDSs. This clustering step aims to avoid the redundancy between the alerts generated by more than one IDS. Finally, a binary multi-objective optimization problem is used to detect false negatives and false positives. The proposed method is evaluated using a real network traffic, DARPA 1999 and NSL-KDD data sets. Experimental results show that the proposed process outperforms concurrent methods for false negatives and false positives detection. [ABSTRACT FROM AUTHOR]

Suppose that 0 → I → A → A/I → 0 is a tracially quasidiagonal extension of C* -algebras. In this paper, the authors give two descriptions of the K0, K1 index maps which are induced by the above extension and show that for any ϵ > 0, any τ in the tracial state space of A/I and any projection p¯∈A/I (any unitary u¯∈A/I, there exists a projection p ∈ A (a unitary u ∈ A) such that |τ(p¯)=τ(π(p))|<∈(|τ(u¯)=τ(π(u))|<∈). [ABSTRACT FROM AUTHOR]

In this paper, the synchronization for a kind of first order quasilinear hyperbolic system is taken into account. In this system, all the equations share the same positive wave speed. To realize the synchronization, a uniform constructive method is adopted, rather than an iteration process usually used in dealing with nonlinear systems. Furthermore, similar results on the exact boundary synchronization by groups can be obtained for a kind of first order quasilinear hyperbolic system of equations with different positive wave speeds by groups. [ABSTRACT FROM AUTHOR]

An accurate mathematical model has a vital role in controlling and synchronization of chaotic systems. But generally in real-world problems, parameters are mixed with mismatches and distortions. This paper proposes two simple but effective estimation methods to detect the unknown parameters of chaotic models. These methods focus on improving the performance of a recently proposed evolutionary algorithm called backtracking search optimization algorithm (BSA). In this research firstly, a new operator to generate initial trial population is proposed. Then a group search ability is provided for the BSA by proposing a shuffled BSA (SBSA). Grouping population into several sets can provide a better exploration of search space, and an independent local search of each group increases exploitation ability of the BSA. Also new proposed operator to generate initial trial population, by providing a deep search, increases considerably the quality of solutions. The superiority of the proposed algorithms is investigated on parameter identification of 10 typical chaotic systems. Practical experiences and nonparametric analysis of obtained results show that both of the proposed ideas to improve performance of original BSA are very effective and robust so that the BSA by aforementioned ideas produces similar and promising results over repeated runs. A considerably better performance of proposed algorithms based on average of objective functions demonstrates that the proposed ideas can evolve robustness and consistence of BSA. A comparison of the proposed algorithms in this study with respect to other algorithms reported in the literature confirms a considerably better performance of proposed algorithms. [ABSTRACT FROM AUTHOR]

Meshfree methods such as the Reproducing Kernel Particle Method and the Element Free Galerkin method have proven to be excellent choices for problems involving complex geometry, evolving topology, and large deformation, owing to their ability to model the problem domain without the constraints imposed on the Finite Element Method (FEM) meshes. However, meshfree methods have an added computational cost over FEM that come from at least two sources: increased cost of shape function evaluation and the determination of adjacency or connectivity. The focus of this paper is to formally address the types of adjacency information that arises in various uses of meshfree methods; a discussion of available techniques for computing the various adjacency graphs; propose a new search algorithm and data structure; and finally compare the memory and run time performance of the methods. [ABSTRACT FROM AUTHOR]

In order to obtain the measurability of a random attractor, the RDS is usually required to be continuous which, however, is hard to verify in many applications. In this paper, we introduce a quasi strong-to-weak (abbrev. quasi-S2W) continuity and establish a new existence theorem for random attractors. It is shown that such continuity is equivalent to the closed-graph property for mappings taking values in weakly compact spaces. Moreover, it is inheritable: if a mapping is quasi-S2W continuous in some space, then so it is automatically in more regular subspaces. Also, a mapping with such continuity must be measurable. These results enable us to study random attractors in regularity spaces without further proving the system’s continuity. In addition, applying the core idea to bi-spatial random attractor theory we establish new existence theorems ensuring that the bi-spatial attractors are measurable in regularity spaces. As an application, for a stochastic reaction-diffusion equation with general conditions we study briefly the random attractor in H1(Rd), the (L2(Rd),H1(Rd))-random attractor and the (L2(Rd),Lp(Rd))-random attractor, p>2, d∈N. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze two kinds of novel and symmetric energy-preserving formulae for the nonlinear oscillatory Hamiltonian system of second-order differential equations Aq″ (t)+ Bq(t) = f(q(t)), where A ∈ ℝm×m is a symmetric positive definite matrix, B ∈ ℝm×m is a symmetric positive semi-definite matrix that implicitly contains the main frequencies of the problem and f(q) = −∇qV (q) for a real-valued function V (q). The energy-preserving formulae can exactly preserve the Hamiltonian H(q′,q)=12q′TAq′+12qTBq+V(q). We analyze the properties of energy-preserving and convergence of the derived energy-preserving formula and obtain new efficient energy-preserving integrators for practical computation. Numerical experiments are carried out to show the efficiency of the new methods by the nonlinear Hamiltonian systems. [ABSTRACT FROM AUTHOR]

We give a constant factor approximation algorithm for the Asymmetric Traveling Salesman Problem on shortest path metrics of directed graphs with two different edge weights. For the case of unit edge weights, the first constant factor approximation was given recently by Svensson. This was accomplished by introducing an easier problem called Local-Connectivity ATSP and showing that a good solution to this problem can be used to obtain a constant factor approximation for ATSP. In this paper, we solve Local-Connectivity ATSP for two different edge weights. The solution is based on a flow decomposition theorem for solutions of the Held-Karp relaxation, which may be of independent interest. [ABSTRACT FROM AUTHOR]

Effective dimension, an indicator for the difficulty of high-dimensional integration, describes whether a function can be well approximated by low-dimensional terms or sums of low-order terms. Some problems in option pricing are believed to have low effective dimensions, which help explain the success of quasi-Monte Carlo (QMC) methods recently observed in financial engineering. This paper provides a way of studying the structure of effective dimensions by finding a proper space the function of interest belongs to and then determining the effective dimension of that space. To this end, we extend the definitions of effective dimensions to weighted function spaces with product-order-dependent weights and give bounds on norms and variances. Furthermore, we show that the proposed method is applicable to functions arising in option pricing and consequently offers some hints on the performance of QMC methods. [ABSTRACT FROM AUTHOR]

In this paper, we consider a risk model by introducing a temporal dependence between the claim numbers under periodic environment, which generalizes several discrete-time risk models. The model proposed is based on the Poisson INAR(1) process with periodic structure. We study the moment-generating function of the aggregate claims. The distribution of the aggregate claims is discussed when the individual claim size is exponentially distributed. [ABSTRACT FROM AUTHOR]

A code for computing the p-variation of a piecewise monotone function is introduced. The code is publicly available in the R environment package under the name pvar. The algorithm is based on some properties of the p-variation of a piecewise monotone function proved in this paper. The mathematical results may have their own interest. [ABSTRACT FROM AUTHOR]

Abstract: The Maxwell system is considered in a three-dimensional domain G having several cylindrical ends. The coefficients are variable and stabilizing at infinity with exponential rate. The limit coefficients are independent of the axial coordinate in the corresponding cylinder. A scattering matrix is defined on the waveguide continuous spectrum outside of the thresholds. The matrix depends on the spectral parameter, is of finite size, which remains constant between neighbouring thresholds and changes when the parameter crosses a threshold. The scattering matrix is unitary. In the paper, we propose a method for approximate computation of the scattering matrix. Moreover, we prove the existence of finite one-side limits of this matrix at every threshold. [ABSTRACT FROM AUTHOR]

In this paper, we modify the Langevin dynamics associated to the generalized Curie-Weiss model by introducing noisy and dissipative evolution in the interaction potential. We show that, when a zero-mean Gaussian is taken as single-site distribution, the dynamics in the thermodynamic limit can be described by a finite set of ODEs. Depending on the form of the interaction function, the system can have several phase transitions at different critical temperatures. Because of the dissipation effect, not only the magnetization of the systems displays a self-sustained periodic behavior at sufficiently low temperature, but, in certain regimes, any (finite) number of stable limit cycles can exist. We explore some of these peculiarities with explicit examples. [ABSTRACT FROM AUTHOR]

In this paper, we study the global existence and decay rates of the solutions near Maxwellian for non-linear Fokker-Planck equations in the whole space. The global existence is proved by combining uniform-in-time energy estimates with local solution constructed by Picard type iteration sequence. The decay rates of the nonlinear model is obtained by using the precise spectral analysis of the linearized Fokker-Planck operator as well as the energy method. The nonlinearity in the model brings new difficulty to the energy estimates, which is resolved by additional tailored weighted-in-v energy estimates suitable for Fokker-Planck operators. [ABSTRACT FROM AUTHOR]

In this paper, we study the truncated two-particle correlation function in particle systems with long range interactions. For Coulombian and soft potentials, we define and give well-posedness results for the equilibrium correlations. In the Coulombian case, we prove the onset of the Debye screening length in the equilibrium correlations, for suitable velocity distributions. Additionally, we give precise estimates on the effective range of interaction between particles. In the case of soft potential interaction the equilibrium correlations and their fluxes in the space of velocities are shown to be linearly stable. [ABSTRACT FROM AUTHOR]

In this paper we review, and extend to the non-isothermal case, some results concerning the application of the maximum entropy closure technique to the derivation of hydrodynamic equations for particles with spin-orbit interaction and Fermi-Dirac statistics. In the second part of the paper we treat in more details the case of electrons on a graphene sheet and investigate various asymptotic regimes. [ABSTRACT FROM AUTHOR]

In this paper we discuss the asymptotic stability of stationary solutions for the non-isentropic Euler-Maxwell system in R. It is known in the authors' previous works [17, 18, 19] that the Euler-Maxwell system verifies the decay property of the regularity-loss type. In this paper we first prove the existence and uniqueness of a small stationary solution. Then we show that the non-stationary problemhas a global solution in a neighborhood of the stationary solution under smallness condition on the initial perturbation. Moreover, we show the asymptotic convergence of the solution toward the stationary solution as time tends to infinity. The crucial point of the proof is to derive a priori estimates by using the energy method. [ABSTRACT FROM AUTHOR]

The mixed principal eigenvalue of p -Laplacian (equivalently, the optimal constant of weighted Hardy inequality in L space) is studied in this paper. Several variational formulas for the eigenvalue are presented. As applications of the formulas, a criterion for the positivity of the eigenvalue is obtained. Furthermore, an approximating procedure and some explicit estimates are presented case by case. An example is included to illustrate the power of the results of the paper. [ABSTRACT FROM AUTHOR]

In the first part (Bourgade et al., Local circular law for random matrices, preprint, arXiv:1206.1449, ) of this article series, Bourgade, Yau and the author of this paper proved a local version of the circular law up to the finest scale $$N^{-1/2+ {\varepsilon }}$$ for non-Hermitian random matrices at any point $$z \in \mathbb {C}$$ with $$||z| - 1| > c $$ for any constant $$c>0$$ independent of the size of the matrix. In the second part (Bourgade et al., The local circular law II: the edge case, preprint, arXiv:1206.3187, ), they extended this result to include the edge case $$ |z|-1={{\mathrm{o}}}(1)$$ , under the main assumption that the third moments of the matrix elements vanish. (Without the vanishing third moment assumption, they proved that the circular law is valid near the spectral edge $$ |z|-1={{\mathrm{o}}}(1)$$ up to scale $$N^{-1/4+ {\varepsilon }}$$ .) In this paper, we will remove this assumption, i.e. we prove a local version of the circular law up to the finest scale $$N^{-1/2+ {\varepsilon }}$$ for non-Hermitian random matrices at any point $$z \in \mathbb {C}$$ . [ABSTRACT FROM AUTHOR]

A sample X1,...,Xn consisting of independent identically distributed vectors in ℝp with zero mean and a covariance matrix Σ is considered. The recovery of spectral projectors of high-dimensional covariance matrices from a sample of observations is a key problem in statistics arising in numerous applications. In their 2015 work, V. Koltchinskii and K. Lounici obtained nonasymptotic bounds for the Frobenius norm ∥Pr−P^r∥2 of the distance between sample and true projectors and studied asymptotic behavior for large samples. More specifically, asymptotic confidence sets for the true projector Pr were constructed assuming that the moment characteristics of the observations are known. This paper describes a bootstrap procedure for constructing confidence sets for the spectral projector Pr of the covariance matrix Σ from given data. This approach does not use the asymptotical distribution of ∥Pr−P^r∥2 and does not require the computation of its moment characteristics. The performance of the bootstrap approximation procedure is analyzed. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and stability of Hilfer-type fractional differential equations (dynamic equations) on time scales. We obtain sufficient conditions for existence and uniqueness of solutions by using classical fixed point theorems such as Schauder's fixed point theorem and Banach fixed point theorem. In addition, Ulam stability of the proposed problem is also discussed. As in application, we provide an example to illustrate our main results. [ABSTRACT FROM AUTHOR]

The Ehrenfest diffusion model is a well-known classical physical model consisting of two urns and n balls. There is a group theoretical interpretation of the model by using the Gelfand pair (Z/2Z≀Sn,Sn) by Diaconis and Shahshahani (Z Wahrsch Verw Gebiete 57(2):159-179, 1981). This interpretation is still valid for an r-urns generalization. Then the corresponding Gelfand pair is (Sr≀Sn,Sr-1≀Sn). However, in these models, there are no restrictions for ball movements, i.e., each ball can freely move to any urns. In this paper, interactions between urns arising from actions of finite groups are introduced. Degree of freedom of ball movements are restricted by finite group actions. We then show that the cutoff phenomenon occurs in some particular (yet significant and interesting) cases. [ABSTRACT FROM AUTHOR]

In this paper, we mainly introduce a partitioned scheme based on Gauge-Uzawa finite element method for the 2D time-dependent incompressible magnetohydrodynamics (MHD) equations. It is a fully decoupled projection method which combines the Gauge and Uzawa methods within a variational formulation. Firstly, the temporal discretization is based on backward Euler technique for the linear term and semi-implicit scheme for the nonlinear term. Secondly, the spatial approximation of fluid velocity, hydrodynamic pressure, and magnetic field apply the mixed element method. Finally, the validity, reliability, and accuracy of the proposed algorithms are supported by numerical experiments. [ABSTRACT FROM AUTHOR]

A method to define trivariate spline quasi-interpolation operators (QIOs) is developed by blending univariate and bivariate operators whose linear functionals allow oversampling. In this paper, we construct new operators based on univariate B-splines and bivariate box splines, exact on appropriate spaces of polynomials and having small infinity norms. An upper bound of the infinity norm for a general blending trivariate spline QIO is derived from the Bernstein-Bézier coefficients of the fundamental functions associated with the operators involved in the construction. The minimization of the resulting upper bound is then proposed and the existence of a solution is proved. The quadratic and quartic cases are completely worked out and their exact solutions are explicitly calculated. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of solutions for the minimization problem of the shell weight for a given minimal frequency of the shell vibrations as well as for the maximization problem of the minimal frequency for a given shell weight. We consider an optimal control problem governed by an eigenvalue problem for a system of differential equations with variable coefficients. The form of the shell is considered as a control. Some of the coefficients are non-measurable. Earlier, we introduced certain special weighted functional spaces. By using these spaces, we establish the continuity of the considered minimal frequency functional and obtain the existence of solutions of both optimal control problems. At the end, we prove the Lipschitz continuity of the eigenvalue problem. [ABSTRACT FROM AUTHOR]

We study the uniqueness and explicit derivation of the relaxed optimal solutions, corresponding to the minimization of weighted sum of potential energies for a mixture of two isotropic conductive materials on an annulus. Recently, it has been shown by Burazin and Vrdoljak that even for multiple-state problems, if the domain is spherically symmetric, then the proper relaxation of the problem by the homogenization method is equivalent to a simpler relaxed problem, stated only in terms of local proportions of given materials. This enabled explicit calculation of a solution on a ball, while problems on an annulus appeared to be more tedious. In this paper, we discuss the uniqueness of a solution of this simpler relaxed problem, when the domain is an annulus and we use the necessary and sufficient conditions of optimality to present a method for explicit calculation of the unique solution of this simpler proper relaxation, which is demonstrated on an example. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to investigate EQ-algebras with internal states and state morphism good EQ-algebras. To begin with, we introduce the notion of EQ-algebras with internal states (simplify, SEQ-algebras) and discuss the relation between SEQ-algebras and state EQ-algebras. In the following, we study state filters (simplify, S-filters) and state prefilters (simplify, S-prefilters) of SEQ-algebras and discuss subdirectly irreducible SEQ-algebras. We focus on algebraic structures of the set SPF(E,σ) of all S-prefilters on a SEQ-algebra and obtain that SPF(E,σ) forms a complete Brouwerian lattice, when E is an ℓEQ-algebra or good. Moreover, for ℓEQ-algebras, SPF(E,σ) forms a Heyting algebra if σ is faithful and preserves →. Then, we introduce the σ-co-annihilator of a non-empty set A on a SEQ-algebra. As applications, we give a characterization for minimal prime S-prefilters of state morphism good EQ-algebras and characterize the representable state morphism good EQ-algebras by minimal prime S-prefilters. [ABSTRACT FROM AUTHOR]

In this paper, we propose a sentential logic naturally associated, in the sense of Abstract Algebraic Logic, with the variety of distributive nearlattices. We show that the class of algebras canonically associated (in the sense of Abstract Algebraic Logic) with this logic is the variety of distributive nearlattices. We also present several properties of this sentential logic. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an algorithm for presentation of an inner estimation of the solution set of a complex interval linear system, where the coefficient matrix is a crisp complex-valued matrix and the right-hand-side vector is an interval complex-valued vector. Also, we show that under some certain conditions, the obtained inner estimation is, in fact, an algebraic solution. [ABSTRACT FROM AUTHOR]