Search

In this paper, infrared thermography is applied to the quantitative characterization of optically semi-transparent media by using a newly introduced mathematical model. The method is specifically aimed to the detection and evaluations in graphic features buried beneath the surface of some particular kind of cultural heritage artefacts, such as books and documents. A numerical approach based on the finite element method, is proposed for solving the model equations. The computed thermographic signal depends on different inspected material physical properties, which have been selectively evaluated by comparing the theoretical results with the experimental ones in specifically designed test samples. Thereafter, the model is applied to the analysis of the results obtained in the case of graphic elements buried within samples constituted by the same previously characterized materials.

We propose a time-fractional compartmental model (SEI A I S HRD) comprising of the susceptible, exposed, infected (asymptomatic and symptomatic), hospitalized, recovered and dead population for the COVID-19 pandemic. We study the properties and dynamics of the proposed model. The conditions under which the disease-free and endemic equilibrium points are asymptotically stable are discussed. Furthermore, we study the sensitivity of the parameters and use the data from Tennessee state (as a case study) to discuss identifiability of the parameters of the model. The non-negative parameters in the model are obtained by solving inverse problems with empirical data from California, Florida, Georgia, Maryland, Tennessee, Texas, Washington and Wisconsin. The basic reproduction number is seen to be slightly above the critical value of one suggesting that stricter measures such as the use of face-masks, social distancing, contact tracing, and even longer stay-at-home orders need to be enforced in order to mitigate the spread of the virus. As stay-at-home orders are rescinded in some of these states, we see that the number of cases began to increase almost immediately and may continue to rise until the end of the year 2020 unless stricter measures are taken.

Highlights • It is proposed a model based on non-local operators capable of reproduce several of the equations traditionally used in research on population dynamics, as well as having additional features, useful for describing the phenomenon of pattern formation. • The combination of two of the parameters present in the model, namely, α and β, determines the existence of a phase space, characterized by regions with and without patterns. • The patterns formed will have M peaks and M valleys, with M ≥ 2. • There are (α, β) combinations which lead to the formation of degenerate states, where the system seems not to forget its initial conditions. • The model allows the study of real systems, such is the case of bacterial populations subjected to inhomogeneous growth conditions. • The parameter β represents a macroscopic measure of changes that occur at an individual level in the concentrations of proteins in bacteria, as a product of significant variations in the environment., Self-organization evolution of a population is studied considering generalized reaction-diffusion equations. We proposed a model based on non-local operators that has several of the equations traditionally used in research on population dynamics as particular cases. Then, employing a relatively simple functional form of the non-local kernel, we determined the conditions under which the analyzed population develops spatial patterns, as well as their main characteristics. Finally, we established a relationship between the developed model and real systems by making simulations of bacterial populations subjected to non-homogeneous lighting conditions. Our proposal reproduces some of the experimental results that other approaches considered previously had not been able to obtain.

This work presents a proof of convergence of a discrete solution to a continuous one. At first, the continuous problem is stated as a system of equations which describe the filtration process in the pressing section of a paper machine. Two flow regimes appear in the modeling of this problem. The model for the saturated flow is presented by the Darcy’s law and the mass conservation. The second regime is described by the Richards’ approach together with a dynamic capillary pressure model. The finite volume method is used to approximate the system of PDEs. Then, the existence of a discrete solution to the proposed finite difference scheme is proven. Compactness of the set of all discrete solutions for different mesh sizes is proven. The main theorem shows that the discrete solution converges to the solution of the continuous problem. At the end we present numerical studies for the rate of convergence.

It is shown that the main theorem of Arslan’s paper (Theorem 2, 2011), as stated, is incorrect. Under additional conditions, we present a short proof of the corrected version of the theorem. We also give a proof of a theorem of Rao and Shanbhag (1991) [2], employed by Arslan, without the use of the Kolmogorov Consistency Theorem.

An integrated model for ranking scientific publications together with authors and journals recently presented in [Bini, Del Corso, Romani, ETNA 2008] is closely analyzed. The model, which relies on certain adjacency matrices H,K and F obtained from the relations of citation, authorship and publication, provides the ranking by means of the Perron vector of a stochastic matrix obtained by combining H,K and F. Some perturbation theorems concerning the Perron vector previously introduced by the authors are extended to more general cases and a counterexample to a property previously addressed by the authors is presented. The theoretical results confirm the consistency and effectiveness of our model. Some paradigmatic examples are reported together with some results obtained on a real set of data.

This paper reviews minimax best equivariant estimation in these invariant estimation problems: a location parameter, a scale parameter and a (Wishart) covariance matrix. We briefly review development of the best equivariant estimator as a generalized Bayes estimator relative to right invariant Haar measure in each case. Then we prove minimaxity of the best equivariant procedure by giving a least favorable prior sequence based on non-truncated Gaussian distributions. The results in this paper are all known, but we bring a fresh and somewhat unified approach by using, in contrast to most proofs in the literature, a smooth sequence of non truncated priors. This approach leads to some simplifications in the minimaxity proofs., 21 pages

In this paper we address, from a purely numerical point of view, the question, raised in [20, 21], and partly considered in [22, 9, 3], whether a certain function, referred to as "Euler Integral", is a quasi-integral along the trajectories of the three-body problem. Differently from our previous investigations, here we focus on the region of the "unperturbed separatrix", which turns to be complicated by a collision singularity. Concretely, we reduce the Hamiltonian to two degrees of freedom and, after fixing some energy level, we discuss in detail the resulting three-dimensional phase space around an elliptic and an hyperbolic periodic orbit. After measuring the strength of variation of the Euler Integral (which are in fact small), we detect the existence of chaos closely to the unperturbed separatrix. The latter result is obtained through a careful use of the machinery of covering relations, developed in [13, 24, 23]., This paper is supported by the the ERC project 677793 Stable and Chaotic Motions in the Planetary Problem (2016-2022)

In this paper, we are concerned with the mathematical analysis of a host–pathogen model with diffusion, hyperinfectivity and nonlinear incidence. We define the basic reproduction number ℜ0 by the spectral radius of the next generation operator, and study the relation between ℜ0 and the principal eigenvalue of the problem linearized at the disease-free steady state (DFSS). Under some assumptions, we show the threshold property of ℜ0: if ℜ01, then the system is uniformly persistent and a positive steady state (PSS) exists. Moreover, for the special case where all parameters are constants, we show that the PSS is GAS for ℜ0>1. Numerical simulation suggests that the spatial heterogeneity could enhance the intensity of epidemic, whereas the diffusion effect could reduce it.

*Maldar, Samet ( Aksaray, Yazar ) *Atalan, Yunus ( Aksaray, Yazar ), In this paper, we revisit two recently published papers on the iterative approximation of fixed points by Kumam et al. (2019) [17] and Maniu (2020) [19] and reproduce convergence, stability, and data dependency results presented in these papers by removing some strong restrictions imposed on parametric control sequences. We confirm the validity and applicability of our results through various non-trivial numerical examples. We suggest a new method based on the iteration algorithm given by Thakur et al. (2014) [28] to solve the two-point second-order boundary value problems. Furthermore, based on the above mentioned iteration algorithm and S-iteration algorithm, we propose two new gradient type projection algorithms and applied them to supervised learning. In both applications, we present some numerical examples to demonstrate the superiority of the newly introduced methods in terms of convergence, accuracy, and computational time against some earlier methods.

We present a Volume Integral formulation for the solution of large scale eddy-current problems coupled with low-rank approximation techniques. Two alternative approaches are introduced to map the problem unknowns into a subset of grid elements forming a base of global or mixed (global and local) cycles, respectively, and guarantee the well-posedness of the problem both in simply and multiply connected domains. The paper shows that the adoption of mixed cycles is computationally more efficient than global ones. In particular, integral formulations based on global cycles cannot be safely coupled with low-rank approximation techniques, which, however, are crucial to increase the size of the largest solvable problem, like the ones involving conducting structures in magnetic confinement fusion devices. The aim of this paper is to demonstrate how such bottleneck can be overcome by considering local and global cycles differently, on the basis of the cohomology theory. An improved, efficient, and robust algorithm for computing a base of global cycles is described in detail. In particular, the presented algorithm is able to almost minimize the cohomology basis length, i.e. the number of mesh edges forming such a basis, in order to allow an efficient solution of large scale problems . Furthermore, a novel and general method to handle global and local cycles together, in the context of low-rank approximated matrices, is shown to be efficient for the solution of large scale eddy-current problems in multiply connected domains. Along the manuscript, pseudo-codes are given, which clarify the proposed methods and help to implement them by Volume Integral Equation practitioners.

We discuss several approaches involving the reconstruction of discontinuous one-dimensional functions using parameter-dependent multiquadric radial basis function (MQ-RBF) local interpolants combined with weighted essentially non-oscillatory (WENO) techniques, both in the computation of the locally optimized shape parameter and in the combination of RBF interpolants. We examine the accuracy of the proposed reconstruction techniques in smooth regions and their ability to avoid Gibbs phenomena close to discontinuities. In this paper, we propose a true MQ-RBF–WENO method that does not revert to the classical polynomial WENO approximation near discontinuities, as opposed to what was proposed in Guo and Jung (2017) [12,13]. We present also some numerical examples that confirm the theoretical approximation orders derived in the paper.

The paper deals with a two-person zero-sum differential game for a dynamical system which motion is described by a delay differential equation under an initial condition defined by a piecewise continuous function. For the value functional of this game, we derive the Hamilton-Jacobi type equation with coinvariant derivatives. It is proved that, if the solution of this equation satisfies certain smoothness conditions, then it coincides with the value functional. On the other hand, it is proved that, at the points of coinvariant differentiability, the value functional satisfies the derived Hamilton-Jacobi equation. Therefore, this equation can be called the Hamilton-Jacobi-Bellman-Isaacs equation for time-delay systems. © 2019. The Authors. Published by Elsevier Ltd. All rights reserved.

In this paper, a generalized finite difference method (GFDM) based on the Peridynamic differential operator (PDDO) is investigated. The weighted moving least square (MLS) procedure involved in the GFDM is replaced by the PDDO. PDDO is capable to recast differentiation operators through an integration procedure which has the following advantages: the method is free of using any particular treatment near sharp gradients and where the solution is governed by a steep variation of field variables; it facilitates the imposition of boundary conditions compared to certain meshless methods as its formulation does not need a symmetric kernel function ; it is free of any particular correction function and parameter tunings; the method is easy to implement and we shall show that it generates a well-conditioned stiffness matrix for both structured and unstructured discretization . In this paper, the method is applied to 2D Helmholtz-type problems including time-harmonic acoustic problems, though the extension to 3D is straightforward. We also present a simple and efficient way to equip the method in the solution of unbounded domains . Moreover, a comprehensive study on the accuracy, convergence, and behavior of the method through a patch test is conducted. The test may be considered as a way to find the optimal region of the required integrations. We shall benefit from the advantage of the method in terms of accurate calculation of derivatives to determine the flow of acoustic energy, in a frequency problem domain, without employing any particular singular basis functions.

We provide evidence of the existence of KAM quasi-periodic attractors for a dissipative model in Celestial Mechanics. We compute the attractors extremely close to the breakdown threshold. We consider the spin-orbit problem describing the motion of a triaxial satellite around a central planet under the simplifying assumption that the center of mass of the satellite moves on a Keplerian orbit, the spin-axis is perpendicular to the orbit plane and coincides with the shortest physical axis. We also assume that the satellite is non-rigid; as a consequence, the problem is affected by a dissipative tidal torque that can be modeled as a time-dependent friction, which depends linearly upon the velocity. Our goal is to fix a frequency and compute the embedding of a smooth attractor with this frequency. This task requires to adjust a drift parameter. The goal of this paper is to provide numerical calculations of the condition numbers and verify that, when they are applied to the numerical solutions, they will lead to the existence of the torus for values of the parameters extremely close to the parameters of breakdown. Computing reliably close to the breakdown allows to discover several interesting phenomena, which we will report in [CCGdlL20a]. The numerical calculations of the condition numbers presented here are not completely rigorous, since we do not use interval arithmetic to estimate the round off error and we do not estimate rigorously the truncation error, but we implement the usual standards in numerical analysis (using extended precision, checking that the results are not affected by the level of precision, truncation, etc.). Hence, we do not claim a computer-assisted proof, but the verification is more convincing that standard numerics. We hope that our work could stimulate a computer-assisted proof., 33 pages, 1 figure

In the analysis of the fluid queues, it is necessary to obtain the nonnegative solution of a nonsymmetric algebraic Riccati matrix equation. Under suitable conditions, this solution can be obtained transforming algebraic Riccati equations into unilateral quadratic matrix equations. In this paper, we use an efficient iterative scheme to approximate a solution of this quadratic matrix equation. We improve the efficiency and the accuracy of Newton’s method, widely used in the literature. Moreover, a local convergence result is proved. Finally, we apply this efficient method to approximate the solution of a particular noisy Wiener–Hopf problem and we compare it with Newton’s method. Moreover, a predictor–corrector iterative scheme is constructed that improve the accessibility of the aforesaid method.

Taking into account axial symmetry in the covariance function of a Gaussian random field is essential when the purpose is modelling data defined over a large portion of the sphere representing our planet. Axially symmetric covariance functions admit a convoluted spectral representation that makes modelling and inference difficult. This motivates the interest in devising alternative strategies to attain axial symmetry, an appealing option being longitudinal integration of isotropic random fields on the sphere. This paper provides a comprehensive theoretical framework to model longitudinal integration on spheres through a nonparametric Bayesian approach. Longitudinally integrated covariances are treated as random objects, where the randomness is implied by the randomised spectrum associated with the covariance function. After investigating the topological support induced by our construction, we give the posterior distribution a thorough inspection. A Bayesian nonparametric model for the analysis of data defined on the sphere is described and implemented, its performance investigated by means of the analysis of both simulated and real data sets.

In this paper, we explore a set of new heuristic strategies integrated within the column generation algorithm to solve the Capacitated Vehicle Routing Problem with 2-Dimensional Loading constraints. These heuristics rely on constructive procedures that iteratively build a solution using the solutions of a mixed integer linear programming model. The pricing subproblem is also heuristically solved, using strategies relying on variable neighborhood search algorithms proposed in literature. Column generation approaches for the 2L-CVRP are not quite explored. This paper aims to contribute with new strategies to tackle this problem. All the approaches were implemented and an exhaustive computational study is performed., This work has been supported by FEDER funding through the Programa Operacional Factores de Competitividade COMPETE and through the Portuguese Science and Technology Foundation (FCT): project UID/CEC/00319/2013 and grant SFRH/BD/73584/2010.

The aim of this paper is to present the implementation of 3D fractional viscoelastic constitutive theory presented in Alotta et al., 2016 [1]. Fractional viscoelastic models exactly reproduce the time dependent behaviour of real viscoelastic materials which exhibit a long “fading memory”. From an implementation point of view, this feature implies storing the stress/strain history throughout the simulations which may require a large amount of memory. We propose here a number of strategies to effectively limit the memory required. The form of the constitutive equations are summarized and the finite element implementation in a Newton-Raphson integration scheme is described in detail. The expressions that are needed to be coded in user-defined material subroutines for quasi static and dynamic implicit and explicit analysis (UMAT and VUMAT) in the commercial finite element software ABAQUS are readily provided. In order to demonstrate the accuracy of the numerical implementation we report a number of benchmark problems validated against analytical results. We have also analysed the behaviour of a viscoelastic plate with a hole in order to show the efficiency of these types of models. The source codes for the UMAT and VUMAT are provided as online supplements to this paper.

The paper is concerned with a nonlinear impulsive control system with trajectories of bounded variation. Necessary conditions of optimality in a form of the Maximum Principle are derived for a class of infinite horizon impulsive optimal control problems. For the overtaking optimality criterion under the assumption that all gradients of the payoff function are bounded, we construct a transversality condition for the adjoint variable in terms of limit points of the gradient of the payoff function. In the case when this limit point is unique, this condition supplements the system of the Maximum Principle and determines a unique solution of the adjoint system. This solution can be written explicitly with the use of the (Cauchy type) formula proposed earlier by S.M. Aseev and A.V. Kryazhimskii. The key idea of the proof is the application of the convergence of subdifferentials within Halkin’s scheme.

The a posteriori analysis of the realized motions (in other words, trajectories and controls) is an important part of the theory of optimal control and decision making. This paper is devoted to solving inverse problems of reconstruction of realized controls for control systems using known inaccurate measurements of the realized trajectories. A new method for solving inverse problems is suggested for a class of control systems with dynamics linear in controls and non-linear in state coordinates where the dimension of the control parameter is greater than or equal to the dimension of the state variable. This method relies on necessary optimality conditions in auxiliary variational problems. An illustrating example is exposed. © 2018 Russian Foundation for Basic Research, RFBR Russian Foundation for Basic Research, RFBR: 17-01-00074 Ural Branch, Russian Academy of Sciences, UB RAS: 18-1-1-10.

In this paper we present application of i-smooth analysis to approach-evasion linear differential game with delay. The main goal is to show that according to the methodology of i-smooth analysis one can realize extremal shift procedure by the finite dimensional component of the system state. © 2018 Russian Foundation for Basic Research, RFBR: 17-01-00636 The research was supported by the Russian Foundation for Basic Research (project 17-01-00636).

In this paper, we introduce a numerical scheme for fractional differential equations with feedback control. Due to the possibility of dealing with a feedback control as a functional delay, we construct a numerical method based on Euler method accompanied with piecewise constant interpolation. The method is based on the idea of separating the current state and the prehistory function. The convergence of the method is stated and proved. Numerical experiments are given to clarify the good agreement between numerical and theoretical results.

The paper deals with the Cauchy problem for Hamilton—Jacobi equation with discontinuous w.r.t. state variable Hamiltonian. In this case we use the notion of M-solution proposed by Subbotin. We consider the sequence of auxiliary Cauchy problems for Hamilton— Jacobi equations with Lipschitz continuous w.r.t. phase variable Hamiltonians. We show that the sequence of distances between of graphs of solutions for auxiliary Cauchy problems and graph of M-solution tends to zero in metrics L1.

In this paper we establish a construction of Euclidean 9-designs (i.e., the fourth order rotatable designs) on the unit ball. A classical, popular approach for this is to use the corner vectors of the hyperoctahedron such as the vertices, the midpoints of the edges, the barycentres of the faces and so on. As an improvement of this, we propose to use the corner vectors of the hyperoctahedral group, plus their “internally dividing points”. We give a classification of Euclidean 9-designs on two spheres, and several examples of the fourth order optimal rotatable designs in low dimensions.

Made available in DSpace on 2021-06-25T15:07:00Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-08-01 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Fuzzy initial value problems describing classical mechanical vibrations are the focus of this paper. In particular, this work considers systems described by nth-order linear ordinary differential equations whose initial conditions are uncertain and given by interactive fuzzy numbers. The concept of interactivity arises from the concept of joint possibility distribu-tion ( J). An approach based on the sup -J extension principle, which is a generalization of Zadeh & rsquo;s extension principle, is presented. This theory is applied to two major examples of oscillatory systems: the forced vibration of an uncoupled mass-spring-damper system and the free vibration of a coupled undamped mass-spring system. In both cases, we have that the solution via sup -J extension, where the fuzzy initial conditions are given by linearly correlated fuzzy numbers, is contained in the solution via Zadeh & rsquo;s extension. (c) 2021 Elsevier Inc. All rights reserved. Univ Austral Chile, Ctr Basic Sci Teaching Engn, Valdivia, Chile Sao Paulo State Univ, Dept Math, Rio Claro, Brazil Univ Austral Chile, Inst Acoust, Valdivia, Chile Univ Estadual Campinas, Dept Appl Math, Campinas, Brazil Natl Ctr Res Energy & Mat, Dept Integrated Sci Teaching Ctr, Campinas, Brazil Sao Paulo State Univ, Dept Math, Rio Claro, Brazil CNPq: 142414/20174 CNPq: 306546/20175 FAPESP: 2016/260407 CAPES: 001

In the first part of the paper we develop a constructive procedure to obtain the Taylor expansion, in terms of the energy, of the period function for a non-degenerated center of any planar analytic Hamiltonian system. We apply it to several examples, including the whirling pendulum and a cubic Hamiltonian system. The knowledge of this Taylor expansion of the period function for this system is one of the key points to study the number of zeroes of an Abelian integral that controls the number of limit cycles bifurcating from the periodic orbits of a planar Hamiltonian system that is inspired by a physical model on capillarity. Several other classical tools, like for instance Chebyshev systems are applied to study this number of zeroes. The approach introduced can also be applied in other situations., 23 pages

"Available online 28 December 2020", Hybrid-Trefftz finite elements are well suited for modeling the response of materials under highly transient loading. Their approximation bases are built using functions that satisfy exactly the differential equations governing the problem. This option embeds relevant physical information into the approximation basis and removes the well-known sensitivity of the conventional finite elements to high solution gradients and short wavelength excitations. Despite such advantages, no public software using hybrid-Trefftz finite elements to model wave propagation through solid and porous media exists to date. This paper covers the formulation and implementation of hybrid-Trefftz finite elements for single-phase, biphasic and triphasic media, subjected to dynamic loads. The formulation is cast in a unified framework, valid for the three types of materials alike, and independent of the nature (harmonic, periodic or transient) of the applied load. Displacement, traction, elastic and absorbing boundary conditions are accommodated. The implementation is made in three novel, open-source and user-friendly computational modules which are freely distributed online., This work was partly funded by Fundação para a Ciência e a Tecnologia (MCTES) through national funds (PIDDAC) under the R&D Units “Institute for Sustainability and Innovation in Structural Engineering (ISISE)” and “Civil Engineering Research and Innovation for Sustainability (CERIS)”, references UIDB/04029/2020 and UIDB/04625/2020, respectively, and through research project CEN-DynaGEO, reference PTDC/EAM-GTC/29923/2017.

A proper coloring of a given graph is an assignment of a positive integer number (color) to each vertex such that two adjacent vertices receive different colors. This paper studies the Minimum Sum Coloring Problem (MSCP), which asks for finding a proper coloring while minimizing the sum of the colors assigned to the vertices. We propose the first branch-and-price algorithm to solve the MSCP to proven optimality. The newly developed exact approach is based on an Integer Programming (IP) formulation with an exponential number of variables which is tackled by column generation. We present extensive computational experiments, on synthetic and benchmark DIMACS graphs from the literature, to compare the performance of our newly developed branch-and-price algorithm against three compact IP formulations. On synthetic graphs, our algorithm outperforms the compact formulations in terms of: ( i ) number of solved instances, ( i i ) running times and ( i i i ) exit gaps obtained when optimality is not achieved. For the DIMACS instances, our algorithm is competitive with the best compact formulation and provides very strong dual bounds.

Accurate and precise measurement of channel temperature for RF devices and especially for high power density devices such as MESFETs and GaAs High Electron Mobility Transistors (HEMTs) is essential for understanding the physics behind device degradation. In high power density devices, self-heating effects (SHEs) and channel to base plate temperature gradients are very high. This paper proposes an automated experimental setup using ordinary lab instruments for the measurement of channel temperature of MESFETs and HEMTs in terms of thermal resistance (θth) and thermal capacitance (Cth). The automated experimental setups utilize ordinary lab equipment instead of using specialized high-end tools. With ambient temperature, DC bias conditions, and RF power levels, channel temperature is calculated using θth and Cth parameters. The proposed technique is applied on three different HEMTs and the results were similar for all of them which reflect accuracy of the technique.

The aim of this work consists of finding a suitable numerical method for the solution of the mathematical model describing the prostate tumor growth, formulated as a system of time-dependent partial differential equations (PDEs), which plays a key role in the field of mathematical oncology. In the literature on the subject, there are a few numerical methods for solving the proposed mathematical model. Localized prostate cancer growth is known as a moving interface problem, which must be solved in a suitable stable way. The mathematical model considered in this paper is a system of time-dependent nonlinear PDEs that describes the interaction between cancer cells, nutrients, and prostate-specific antigen (PSA). Here, we first derive a non-dimensional form of the studied mathematical model using the well-known non-dimensionalization technique, which makes it easier to implement different numerical techniques. Afterward, the analysis of the numerical method describing the two-dimensional prostate tumor growth problem, based on radial basis function-generated finite difference (RBF-FD) scheme, in combination with a first-order time discretization has been done. The numerical technique we use, does not need the use of any adaptivity techniques to capture the features in the interface. The discretization leads to solving a linear system of algebraic equations solved via the biconjugate gradient stabilized (BiCGSTAB) algorithm with zero-fill incomplete lower–upper (ILU) preconditioner. Comparing the results obtained in this investigation with those reported in the recent literature, the proposed approach confirms the ability of the developed numerical scheme. Besides, the effect of choosing constant parameters in the mathematical model is verified by many simulations on rectangular and circular domains.

Pulsed thermography has proven to be a useful tool to detect subsurface features in ancient bookbindings and, in particular, to provide the IR image of texts buried beneath the end - leaves of the books. In this paper the theory is presented to analyze the influence of the geometrical and physical parameters involved in the processes leading to the distortion in the IR image of the detected buried graphical features. The distortion is mainly due to the lateral diffusion of the heat generated at the ink feature after the absorption of an excitation light. A comprehensive analysis taking into account the three dimensional heat diffusion process, in an optically semi-transparent medium, is considered. Numerical results are reported showing the behavior of the contrast and of a distortion parameter of the buried inked feature detected by the IR imaging in the various considered cases.

Forest census allows getting precise data for logging planning and elaboration of the forest management plan. Species identification blunders carry inadequate forest management plans and high risks inside forest concessions. Hence, an identification protocol prevents the exploitation of non-commercial or endangered timber species. The current Peruvian legislation allows the incorporation of non-technical experts, called “materos”, during the identification. Materos use common names given by the folklore and traditions of their communities instead of formal ones, which generally lead to misclassifications. In the real world, logging companies hire materos instead of botanists due to cost/time limitations. Given such a motivation, we explore an end-to-end software solution to automatize the species identification. This paper introduces the Peruvian Amazon Forestry Dataset, which includes 59,441 leaves samples from ten of the most profitable and endangered timber-tree species. The proposal contemplates a background removal algorithm to feed a pre-trained CNN by the ImageNet dataset. We evaluate the quantitative (accuracy metric) and qualitative (visual interpretation) impacts of each stage by ablation experiments. The results show a 96.64% training accuracy and 96.52% testing accuracy on the VGG-19 model. Furthermore, the visual interpretation of the model evidences that leaf venations have the highest correlation in the plant recognition task. © 2021

This paper focuses on the modelling and simulation of gas networks to be used in an integrated multi-carrier energy scenario. A topological approach is followed, where a simplified graph-based description of the gas network is adopted and a systematic analysis of the metrics of three real test cases is carried out with the aim of discovering relevant network features. The governing equations of the basic building blocks such as pipelines, compressors and pressure reduction stations are readily derived under the assumptions of steady-state operation and isothermal behaviour, allowing a good matching between model compactness and accuracy. In addition, a circuit-based interpretation of model equations and well-established tools for circuit analysis are used. The obtained results proved that the proposed approach offers a feasible tool for gas networks, which can be readily integrated in a co-simulation framework.

The paper presents a system for noise measurements in infrared photodetectors characterized by low shunt resistances based on a two-channel ultra-low-noise voltage amplifier with paralleled discrete JFETs at the input stages. Using cross correlation method, a background noise well below of 10−19 V2/Hz can be obtained at frequencies above 10 Hz. To facilitate the estimation of the noise in such a wide frequency range (5 decades), we also developed a software based on the QLSA library. As a result of these efforts, the equivalent input voltage noise of the system is below 10−19 V2/Hz at 10 Hz and 10−20 V2/Hz for frequencies above a few hundred Hz. The system effectiveness is demonstrated by noise measurements at room temperature on advanced InAsxSb1-x photodetectors characterized by an active area of 1 mm2 and a shunt resistance below 10 Ω.

We observe that the iterated tangent group of a Lie group may be realized as a double cross product of the 2nd order tangent group, with the Lie algebra of the base Lie group. Based on this observation, we derive the 2nd order Euler-Lagrange equations on the 2nd order tangent group from the 1st order Euler-Lagrange equations on the iterated tangent group. We also present in detail the 2nd order Lagrangian dynamics on the 2nd order tangent group of a double cross product group., Comment: Revisions has been made to shorten the text... the discussion on discrete dynamics has been spared for a separate paper

This paper studies the SEIRD epidemic model for COVID-19. First, I show that the model is poorly identified from the observed number of deaths and confirmed cases. There are many sets of parameters that are observationally equivalent in the short run but lead to markedly different long run forecasts. Second, I show that the basic reproduction number R 0 can be identified from the data, conditional on epidemiologic parameters, and propose several nonlinear SUR approaches to estimate R 0 . I examine the performance of these methods using Monte Carlo studies and demonstrate that they yield fairly accurate estimates of R 0 . Next, I apply these methods to estimate R 0 for the US, California, and Japan, and document heterogeneity in the value of R 0 across regions. My estimation approach accounts for possible underreporting of the number of cases. I demonstrate that if one fails to take underreporting into account and estimates R 0 from the reported cases data, the resulting estimate of R 0 may be biased downward and the resulting forecasts may exaggerate the long run number of deaths. Finally, I discuss how auxiliary information from random tests can be used to calibrate the initial parameters of the model and narrow down the range of possible forecasts of the future number of deaths.

Computer system vulnerabilities, computer viruses, and cyber attacks are rooted in software vulnerabilities. Reducing software defects, improving software reliability and security are urgent problems in the development of software. The core content is the discovery and location of software vulnerability. However, traditional human experts-based approaches are labor-consuming and time-consuming. Thus, some automatic detection approaches are proposed to solve the problem. But, they have a high false negative rate. In this paper, a deep learning based static taint analysis approach is proposed to automatically locate Internet of Things (IoT) software vulnerability, which can relieve tedious manual analysis and improve detection accuracy. Deep learning is used to detect vulnerability since it considers the program context. Firstly, the taint from the difference file between the source program and its patched program selection rules are designed. Secondly, the taint propagation paths are got using static taint analysis. Finally, the detection model based on two-stage Bidirectional Long Short Term Memory (BLSTM) is applied to discover and locate software vulnerabilities. The Code Gadget Database is used to evaluate the proposed approach, which includes two types of vulnerabilities in C/C++ programs, buffer error vulnerability (CWE-119) and resource management error vulnerability (CWE-399). Experimental results show that our proposed approach can achieve an accuracy of 0.9732 for CWE-119 and 0.9721 for CWE-399, which is higher than that of the other three models (the accuracy of RNN, LSTM, and BLSTM is under than 0.97) and achieve a lower false negative rate and false positive rate than the other approaches. This work was supported in part by the National Key R&D Plan under Grant CNS 2016QY06X1205 ,in part by the Basic Research Business Fees of Central Colleges under Grant CNS 20826041B4252 , in part by the National Natural Science Foundation (NSFC) under Grant CNS 61572115 , and in part by the Science and Technology Project of State Grid Corporation of China under Grant CNS 522722180007 . Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not reflect the views of the funding agencies.

The article is devoted to the analysis of optimal control problems with infinite time horizon. These problems arise in economic growth models and in stabilization problems for dynamic systems. The problem peculiarity is a quality functional with an unbounded integrand which is discounted by an exponential index. The problem is reduced to an equivalent optimal control problem with the stationary value function. It is shown that the value function is the generalized minimax solution of the corresponding Hamilton-Jacobi equation. The boundary condition for the stationary value function is replaced by the property of the Hölder continuity and the sublinear growth condition. A backward procedure on infinite time horizon is proposed for construction of the value function. This procedure approximates the value function as the generalized minimax solution of the stationary Hamilton-Jacobi equation. Its convergence is based on the contraction mapping method defined on the family of uniformly bounded and Hölder continuous functions. After the special change of variables the procedure is realized in numerical finite difference schemes on strongly invariant compact sets for optimal control problems and differential games. Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND license

This paper is devoted to a family of Newton-like methods with frozen derivatives used to approximate a locally unique solution of an equation. We perform a convergence study and an analysis of the efficiency. This analysis gives us the opportunity to select the most efficient method in the family without the necessity of their implementation. The method can be applied to many type of problems, including the discretization of ordinary differential equations, integral equations, integro-differential equations or partial differential equations. Moreover, multi-step iterative methods are computationally attractive.

We highlight the existence of a topological horseshoe arising from a a--priori stable model of the binary asteroid dynamics. The inspection is numerical and uses correctly aligned windows, as described in a recent paper by A. Gierzkiewicz and P. Zgliczy\'nski, combined with a recent analysis of an associated secular problem., Comment: 20 pages, 10 figures

In this paper, an evolution law for the modulus of the Short Time Fourier Transform, referred as spectrogram, of a frequency modulated multicomponent signal is proposed. Based on this result, an iterative reallocating method for the enhancement of spectrogram resolution is proposed. Compared to the standard reassignment method, the presented procedure allows us to obtain a time–frequency representation which better localizes the individual modes of a multicomponent signal even in the non separable case. The proposed method is computationally advantageous and robust to modes interference, then it could be employed for accurate instantaneous frequency estimation, which is a fundamental goal in applications dealing with non stationary signals such as radar, surveillance and audio signals.

Reaction networks are mainly used to model the time-evolution of molecules of interacting chemical species. Stochastic models are typically used when the counts of the molecules are low, whereas deterministic models are often used when the counts are in high abundance. The mathematical study of reaction networks has increased dramatically over the last two decades as these models are now routinely used to investigate cellular behavior. In 2011, the notion of “tiers” was introduced to study the long time behavior of deterministically modeled reaction networks that are weakly reversible and have a single linkage class. This “tier” based argument was analytical in nature. Later, in 2014, the notion of a strongly endotactic network was introduced in order to generalize the previous results from weakly reversible networks with a single linkage class to this wider family of networks. The point of view of this later work was more geometric and algebraic in nature. The notion of strongly endotactic networks was later used in 2018 to prove a large deviation principle for a class of stochastically modeled reaction networks. In the current paper we provide an analytical characterization of strongly endotactic networks in terms of tier structures. By doing so, we not only shed light on the connection between the two points of view, but also make available a new proof technique for the study of strongly endotactic networks. We show the power of this new technique in two distinct ways. First, we demonstrate how the main previous results related to strongly endotactic networks, both for the deterministic and stochastic modeling choices, can be quickly obtained from our characterization. Second, we demonstrate how new results can be obtained by proving that a sub-class of strongly endotactic networks, when modeled stochastically, is positive recurrent. Finally, and similarly to recent independent work by Agazzi and Mattingly, we provide an example which closes a conjecture in the negative by showing that stochastically modeled strongly endotactic networks can be transient (and even explosive).

The inverse stochastic resonance (ISR) phenomenon consists of an unexpected depression in the response of a system under external noise, e.g., as observed in the mean firing rate in some pacemaker neurons subject to moderate values of noise. A possible cause for such unexpected reaction is the occurrence of a bistable regime controlling these neurons dynamics. We here explore theoretically the emergence of ISR in a general bistable model system, and thus determine the specific conditions the potential function driving the dynamics must accomplish. We conclude that such an intriguing, and apparently widely observed, phenomenon ensues in the case of an asymmetric potential function when the high activity minimum state of the system is metastable having a larger basin of attraction than the low activity state which is the global minimum of the system. We then discuss on the relevance of such a picture to understand the ISR features and to predict its appearance in nature. In addition, we report on existence of another intriguing, non-standard stochastic resonance in our model even in the absence of any weak signal input. Depending on the shape of the potential function, this new phenomenon shows up together with ISR precisely within the theoretical framework we present in this paper. © 2019 Elsevier B.V., Ministry of Education, Science and Technology Agencia Estatal de Investigación: FIS2017-84256-P Federación Española de Enfermedades Raras, We acknowledge the Spanish Ministry for Science and Technology and the “Agencia Española de Investigación” ( AEI ) for financial support under grant FIS2017-84256-P (FEDER funds). We also thank fruitful comments from P. L. Garrido.

Recently, by using methods of hypercomplex function theory, the authors have shown that a certain sequence S of rational numbers (Vietoris’ sequence) combines seemingly disperse subjects in real, complex and hypercomplex analysis. This sequence appeared for the first time in a theorem by Vietoris (1958) with important applications in harmonic analysis (Askey/Steinig, 1974) and in the theory of stable holomorphic functions (Ruscheweyh/Salinas, 2004). A non-standard application of Clifford algebra tools for defining Clifford-holomorphic sequences of Appell polynomials was the hypercomplex context in which a one-parametric generalization S(n),n≥1, of S (corresponding to n=2) surprisingly showed up. Without relying on hypercomplex methods this paper demonstrates how purely real methods also lead to S(n). For arbitrary n≥1 the generating function is determined and for n=2 a particular case of a recurrence relation similar to that known for Catalan numbers is proved., The work of the first and third authors was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e Tecnologia”), within project PEst-OE/MAT/UI4106/2013. The work of the second author was supported by Portuguese funds through the CMAT - Centre of Mathematics and FCTwithin the Project UID/MAT/00013/2013

In this paper we introduce and analyze a mixed virtual element method (mixed-VEM) for a pseudostress-displacement formulation of the linear elasticity problem with non homogeneous Dirichlet boundary conditions. We follow a previous work by some of the authors, and employ a mixed formulation that does not require symmetric tensor spaces in the finite element discretization. More precisely, the main unknowns here are given by the pseudostress and the displacement, whereas other physical quantities such as the stress, the strain tensor of small deformations, and the rotation, are computed through simple postprocessing formulae in terms of the pseudostress variable. We first recall the corresponding variational formulation, and then summarize the main mixed-VEM ingredients that are required for our discrete analysis. In particular, we utilize a well known local projector onto a suitable polynomial subspace to define a calculable version of our discrete bilinear form, whose continuous version requires information of the variables on the interior of each element. Next, we show that the global discrete bilinear form satisfies the hypotheses required by the Babuška–Brezzi theory. In this way, we conclude the well-posedness of our mixed-VEM scheme and derive the associated a priori error estimates for the virtual solutions as well as for the fully computable projections of them. Furthermore, we also introduce a second element-by-element postprocessing formula for the pseudostress, which yields an optimally convergent approximation of this unknown with respect to the broken H(div)-norm. In addition, this postprocessing formula can also be applied to the postprocessed stress tensor. Finally, several numerical results illustrating the good performance of the method and confirming the theoretical rates of convergence are presented. En este artículo presentamos y analizamos un método de elementos virtuales mixtos (VEM mixto) para una formulación de pseudoesfuerzo-desplazamiento del problema de elasticidad lineal con condiciones de frontera de Dirichlet no homogéneas. Seguimos un trabajo previo de algunos de los autores y empleamos una formulación mixta que no requiere espacios tensoriales simétricos en la discretización de elementos finitos. Más precisamente, las principales incógnitas aquí vienen dadas por la pseudoesfuerzo y el desplazamiento, mientras que otras magnitudes físicas como la tensión, el tensor de deformación de pequeñas deformaciones y la rotación, se calculan mediante fórmulas simples de posprocesamiento en términos de la variable de pseudoesfuerzo. Primero recordamos la formulación variacional correspondiente y luego resumimos los principales ingredientes mixtos de VEM que se requieren para nuestro análisis discreto. En particular, utilizamos un proyector local bien conocido en un subespacio polinómico adecuado para definir una versión calculable de nuestra forma bilineal discreta, cuya versión continua requiere información de las variables en el interior de cada elemento. A continuación, mostramos que la forma bilineal discreta global satisface las hipótesis requeridas por la teoría de Babuška-Brezzi. De esta manera, concluimos la buena posición de nuestro esquema VEM mixto y derivamos las estimaciones de error a priori asociadas para las soluciones virtuales, así como para las proyecciones totalmente computables de las mismas. Además, también introducimos una segunda fórmula de posprocesamiento elemento por elemento para el pseudoesfuerzo, que produce una aproximación óptimamente convergente de esta incógnita con respecto a la norma H (div) rota. Además, esta fórmula de posprocesamiento también se puede aplicar al tensor de tensión posprocesado. Finalmente, se presentan varios resultados numéricos que ilustran el buen desempeño del método y que confirman las tasas teóricas de convergencia. Universidad de Concepción, Chile Universidad Nacional, Costa Rica Escuela de Matemática

In this paper, the process of the extended direct algebraic method (EDAM) is used to solve two fractional Boussinesq-like equations by means of conformable derivatives. Firstly, these fractional equations are changed into the ordinary differential equations by using the traveling wave transformation. Then new solutions are obtained by using EDAM. This dynamical model plays a key role in engineering and physics. The constructed solitons solution help researchers in understanding the physical phenomenon of this equation. The standard linear stability analysis is utilized and the stability of the model is investigated which substantiate that all results are stable and exact. Graphically, the movements of some solutions are depicted at appropriate values of parameters. The achieved results show simplicity, reliability, and power of the current schemes., Research Center of the Center for Female Scientific and Medical Colleges, Deanship of Scientific Research, King Saud University