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IEEEWhile the zeitgeist of today prescribes localization as a key to eliminate the excessive transportation for manufacturing firms, firm-level practical and workable guidelines that go beyond maxims are scant. Laden with analytical methods, this paper offers a phronetic, customizable framework based on Lean Six Sigma (LSS). The framework mimics Define-Measure-Analyze-Improve-Control (DMAIC) process. The early phases of the framework, ex-ante, prescribe the use of a variety tools and techniques from Lean Six sigma (LSS) and employ fuzzy analytic hierarchy process (FAHP) to extract the vital few root-causes that may impede localization. The latter phases suggest the use of design of experiments (DOE) to evaluate the root-causes, ex-post. The paper outlines a clear and established procedure and demonstrates each analytical phase using evidence from a two-year real-world application in steel industry.

The work handles a Fredholm integro-differential equation involving boundary layers. A fitted second-order difference scheme has been created on a uniform mesh utilizing interpolating quadrature rules and exponential basis functions. The stability and convergence of the proposed discretization technique are analyzed and one example is solved to display the advantages of the presented technique.

In the present paper, we introduce the fractional q-integral of Riemann-Liouville integral type Szász-Mirakyan-Kantorovich operators. Korovkin-type approximation theorem is given and the order of convergence of these operators are obtained by using Lipschitz-type maximal functions, second order modulus of smoothness and Peetre's K-functional. Weighted approximation properties of these operators in terms of modulus of continuity have been investigated. Then, for these operators, we give a Voronovskaya-type theorem. Moreover, bivariate fractional q- integral Riemann-Liouville fractional integral type Szász-Mirakyan-Kantorovich operators are constructed. The last section is devoted to detailed graphical representation and error estimation results for these operators.

Recently, the construction of 2D empirical wavelets based on partitioning the Fourier domain with the watershed transform has been proposed. If such approach can build partitions of completely arbitrary shapes, for some applications, it is desirable to keep a certain level of regularity in the geometry of the obtained partitions. In this paper, we propose to build such partition using Voronoi diagrams. This solution allows us to keep a high level of adaptability while guaranteeing a minimum level of geometric regularity in the detected partition.

In this work, q-analogue of the telegraph differential equation is investigated. The approximation solution of q-analogue of the telegraph differential equation is founded by using the Laplace transform collocation method (LTCM). Then, the exact solution is compared with the approximation solution for q-analogue of the telegraph differential equation. The results showed that the method is useful and effective for q-analogue of the telegraph differential equation.

We introduce a new method to approximate integrals ∫ R d f ( x ) d x \int _{\mathbb {R}^d} f(\boldsymbol {x}) \,\mathrm {d}\boldsymbol {x} which simply scales lattice rules from the unit cube [ 0 , 1 ] d [0,1]^d to properly sized boxes on R d \mathbb {R}^d , hereby achieving higher-order convergence that matches the smoothness of the integrand function f f in a certain Sobolev space of dominating mixed smoothness. Our method only assumes that we can evaluate the integrand function f f and does not assume a particular density nor the ability to sample from it. In particular, for the theoretical analysis we show a new result that the method of adding Bernoulli polynomials to a function to make it “periodic” on a box without changing its integral value over the box is equivalent to an orthogonal projection from a well chosen Sobolev space of dominating mixed smoothness to an associated periodic Sobolev space of the same dominating mixed smoothness, which we call a Korobov space. We note that the Bernoulli polynomial method is often not used because of its excessive computational complexity and also here we only make use of it in our theoretical analysis. We show that our new method of applying scaled lattice rules to increasing boxes can be interpreted as orthogonal projections with decreasing projection error. Such a method would not work on the unit cube since then the committed error caused by non-periodicity of the integrand would be constant, but for integration on the Euclidean space we can use the certain decay towards zero when the boxes grow. Hence we can bound the truncation error as well as the projection error and show higher-order convergence in applying scaled lattice rules for integration on Euclidean space. We illustrate our theoretical analysis by numerical experiments which confirm our findings.

For a Schr\"odinger operator on the plane $\mathbb{R}^2$ with electric potential $V$ and Aharonov--Bohm magnetic field we obtain an upper bound on the number of its negative eigenvalues in terms of the $L^1(\mathbb{R}^2)$-norm of $V$. Similar to Calogero's bound in one dimension, the result is true under monotonicity assumptions on $V$. Our proof method relies on a generalisation of Calogero's bound to operator-valued potentials. We also establish a similar bound for the Schr\"odinger operator (without magnetic field) on the half-plane when a Dirchlet boundary condition is imposed and on the whole plane when restricted to antisymmetric functions., Comment: 14 pages

We present a new class of Lipschitz operators on Euclidean lattices that we call lattice Lipschitz maps, and we prove that the associated McShane and Whitney formulas provide the same extension result that holds for the real valued case. Essentially, these maps satisfy a (vector-valued) Lipschitz inequality involving the order of the lattice, with the peculiarity that the usual Lipschitz constant becomes a positive real function. Our main result shows that, in the case of Euclidean space, being lattice Lipschitz is equivalent to having a diagonal representation, in which the coordinate coefficients are real-valued Lipschitz functions. We also show that in the linear case the extension of a diagonalizable operator from the values in their eigenvectors coincide with the operator obtained both from the McShane and the Whitney formulae. Our work on such extension/representation formulas is intended to follow current research on the design of machine learning algorithms based on the extension of Lipschitz functions.

In this study, we derive Gelfand-Levitan-Marchenko type main integral equation of the inverse problem for singular Sturm-Liouville equation which has discontinuous coefficient. Then we prove the unique solvability of the main integral equation.

In this study, a new family of odd nakagami exponential (NE-G) distributions is introduced and investigated as a new generator of continuous distributions. Quantile, hazard rate function, moments, incomplete moments, order statistics, and entropies are only a few of the statistical features that are investigated. A unique model is presented and thoroughly examined. To estimate model parameters based on describing real-life data sets, the maximum likelihood method is applied. The bias and mean square error of maximum likelihood estimators are investigated using a comprehensive simulation exercise. Finally, the new family adaptability is demonstrated via application to real-world data sets.

We study a new version of the weak subgradient method, recently developed by Dinc Yalcin and Kasimbeyli for solving nonsmooth, nonconvex problems. This method is based on the concept of using any weak subgradient of the objective of the problem at the currently generated point with a version of the dynamic stepsize in order to produce a new point at each iteration. The target value needed in the dynamic stepsize is defined using a path based target level (PBTL) algorithm to ensure the optimal value of the problem is reached. We analyze the convergence and give an estimate of the convergence rate of the proposed method. Furthermore, we demonstrate the performance of the proposed method on nonsmooth, nonconvex test problems, and give the computational results by comparing them with the approximately optimal solutions.

In this paper, we define and explore the new family of exponentially convex functions which are called exponentially s–convex functions. We attain the amazing examples and algebraic properties of this newly introduced function. In addition, we find a novel version of Hermite-Hadamard type inequality in the support of this newly introduced concept via the frame of classical and fractional calculus (non-conformable and Riemann-Liouville integrals operator). Furthermore, we investigate refinement of Hermite-Hadamard type inequality by using exponentially s–convex functions via fractional integraloperator. Finally, we elaborate some Ostrowski type inequalities in the frame of fractional calculus. These new results yield us some generalizations of the prior results.

In this paper, we study the problem of two-dimensional free surface flows past an inclined plate of an infinite length. The Riabouchinsky model is considered. The fluid is assumed to be inviscid and incompressible and the flow to be steady and irrotational. For this study, the effects of gravity and surface tension are negligible. This problem is solved by using two methods. The first method allow us to compute analytical solution by employing Schwarz-Christoffel mapping. The other is numerically using the series truncation method. The obtained results showed a good agreement between the numerical solution and the exact solution.

Although the performance of popular optimization algorithms such as the Douglas-Rachford splitting (DRS) and the ADMM is satisfactory in small and well-scaled problems, ill conditioning and problem size pose a severe obstacle to their reliable employment. Expanding on recent convergence results for DRS and ADMM applied to nonconvex problems, we propose two linesearch algorithms to enhance and robustify these methods by means of quasi-Newton directions. The proposed algorithms are suited for nonconvex problems, require the same black-box oracle of DRS and ADMM, and maintain their (subsequential) convergence properties. Numerical evidence shows that the employment of L-BFGS in the proposed framework greatly improves convergence of DRS and ADMM, making them robust to ill conditioning. Under regularity and nondegeneracy assumptions at the limit point, superlinear convergence is shown when quasi-Newton Broyden directions are adopted.

In this paper we consider a linear thermoelastic system of Timoshenko typewhere the heat conduction is given by the linearized law of Gurtin-Pipkin. Anexistence and uniqueness result is proved by the use of a semigroup approach. We establish an exponential stability result without any assumption on the wave speeds once here we have a fully damped system.

In this paper, we will study the convergence properties of the method designed for the convection-diffusion problem. We will prove that the analytical and numerical methods give the same result. Merging the ideas in previous research, we introduce a numerical algorithm on a uniform mesh that requires no exact solution to the local convection-diffusion problem. We display how to obtain the numerical solution of the local Boundary Value Problem (BVP) in a suitable way to ensure that the resulting numerical algorithm recaptures the same convergence properties when using the exact solution of the local BVP. We prove that the proposed algorithm nodally converges to the exact solution.

In this paper we investigate the existence, the boundedness and theasymptotic behavior of the positive solutions of the fuzzy differenceequation \[z_{n+1}=\dfrac{Az_{n-1}}{1+z_{n-2}^{p}},~n\in\mathbb{N}_{0}\]where (zn)(zn) is a sequence of positive fuzzy numbers, AA and the initialconditions z−jz−j (j=0,1,2) (j=0,1,2) are positive fuzzy numbers and pp is a positive integer.

Controlling soft continuum manipulators is a challenging task due to the structural compliance of these systems which results in underactuation. While a variety of control approaches have been proposed for regulation tasks, tracking control requires further investigation. To this end, a new dynamic tube-Model Predictive Control formulation is presented, which includes an ancillary control law constructed analytically with an energy-shaping approach. Two different models are considered: (i) a rigid-link model with direct-torque actuation, which is representative of miniature soft continuum manipulators supplied by digital pressure regulators; (ii) an extended model that includes the pressure dynamics of the fluid, which is representative of fluidic actuation by means of a variable flow rate. The effectiveness of the proposed algorithm is demonstrated with numerical simulations considering bounded external disturbances, either constant or time-varying.

© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.With the growing state/action space, learning a satisfactory policy for regular Reinforcement Learning (RL) algorithms such as flat Q-learning becomes quickly infeasible. One possible solution to handle such cases is to employ hierarchical RL (HRL). In this work, we present two methods to autonomously construct (1) skills (ASKA) and (2) arbitrarily elaborate superskills or complexes through defining an arbitrary number of hierarchies in HRL (ASKAC) over a graph-based iteratively-growing environment model. We employ dynamic community detection (DCD) in detecting subgoals since DCD considers local changes only over the partially growing graphs and lowers the time complexity of the subgoal detection where groups of environment states (i.e., subenvironments) are modeled by communities from the graph theory. DCD’s drawback is oversegmentation where it mispartitions a subenvironment further into smaller components. To maintain the robustness of ASKAC against DCD’s possible oversegmentation we introduce the concept of skill coupling. Skill coupling does not only robustly solve the oversegmentation issue, but it also improves HRL by building up more elaborate complexes (i.e., skill compositions) obtained at an arbitrary number of hierarchies and reduces the number of decisions leading to the goal employing these complexes. In addition to the experiments that investigate the effect of parameters, proposed methods are experimentally evaluated in grid world and taxi driver benchmark environments.

© 2023 John Wiley & Sons, Ltd.Approximate computing enhances the performance and energy efficiency of applications, while still achieving acceptable accuracy. Some of the multithreaded applications can tolerate the accuracy loss when critical sections are approximately executed, which in turn will eliminate the synchronization overhead of these applications and increase their performance. In this study, our objective is to explore the behavior of the critical sections and selectively skip the ones yielding performance improvements with an acceptable accuracy loss. We have observed the behavior of 62 critical sections of 4 selected applications. We have grouped them depending on their effects on program execution and skipped or approximated them accordingly. Our experimental study indicates that skipping 76% of the critical sections offers 2.5 (Formula presented.) performance gain with 16% accuracy loss for Raytrace whereas 1.4 (Formula presented.) performance improvement with 17% accuracy loss is obtained for Radiosity on average when 36% of the critical sections are skipped. For Water_NSquared the performance gain is 1.1 (Formula presented.) with 9% accuracy loss on average with 79% of critical sections skipped. For the Ocean_CP application we see a performance improvement of 1.6 (Formula presented.) with accuracy loss 1% when we skip 38% of critical sections.

The goal of this paper is to develop some differential equation formulas for the extended generalized Mittag-Leffler function (EGMLF) using Caputo type Marichev-Saigo-Maeda (MSM) fractional derivative operators involving the third Appell function as kernel, with the results viewed in the context of extended Wright hypergeometric type function. Furthermore, we highlight their relation to previously known results.

© 2023 John Wiley & Sons, Ltd.Redundant multithreading (RMT) is an effective thread-level replication method to improve the reliability requirements of applications. Although it significantly improves the robustness of applications, it comes with additional performance overhead since the redundant threads might share the same core resources. In our previous study [Efficient selective replication of critical code regions for SDC mitigation leveraging redundant multithreading. J Supercomput 2021;77:14130-14160], we presented an efficient software-level RMT approach, where we execute the most critical code regions with three threads to correct errors. In this study, we focus on further improving the performance of our software-level RMT method by presenting a set of different thread-to-core mapping alternatives. We provide different static mapping methods, which require preliminary information about the applications, such as execution time, instruction-per-cycle (IPC), or cache usage patterns, and a set of dynamic mapping methods, which map threads to cores dynamically at runtime without requiring any additional information. The dynamic mapping methods decide which threads are mapped to which cores at each scheduling point based on the IPC, cache miss rate, or cache access values of each thread as well as each core. Experimental results show that the dynamic mapping method, which maps threads to cores based on IPC values, outperforms all other static and dynamic methods. It also outperforms our baseline model, where the operating system handles the thread-to-core mappings by 8%, 7%, and 20% based on average speedup, harmonic speedup, and mean slowdown metrics.

ispartof: pages:103-122 ispartof: SMART CARD RESEARCH AND ADVANCED APPLICATIONS, CARDIS 2022 vol:13820 pages:103-122 ispartof: 21st International Conference on Smart Card Research and Advanced Applications (CARDIS) location:ENGLAND, Birmingham date:7 Nov - 9 Nov 2022 status: published

We apply methods from algebraic geometry to study uniform matrix product states. Our main results concern the topology of the locus of tensors expressed as uMPS, their defining equations and identifiability. By an interplay of theorems from algebra, geometry and quantum physics we answer several questions and conjectures posed by Critch, Morton and Hackbusch., Comment: 24 pages

Cities have proliferated and experienced increasing environmental issues in the modern world. The concept of environmental sustainability is one of the main problems to solve. Therefore, it is fundamental to establish statistical methods to measure environmental sustainability. The first aim of this study is to measure the environmental sustainability performance of 42 cities in Turkey by Data Envelopment Analysis. The second aim is to solve the imbalance in the efficiency values obtained using Synthetic Minority Oversampling Technique methods. After all, we expose the multiple relationships between input and output variables and efficiency using the Decision trees classifiers approach. As a result of the analyses, three internal factors were found to influence the environmental efficiency levels: residential sales, population intensity, and the number of completed industrial sites. It has been determined that the number of completed industrial sites and the increase in residential sales distorted environmental efficiency.

An analytical solution is obtained for the diffraction problem. In an infinite cylindrical duct, the sound waves are emanating by a ring source. The duct is rigid for z < l and perforated for z > l. The mixed boundary value problem is defined by a Wiener Hopf equation, by using the Fourier transform technique. Then the numerical solution is obtained. The influence of the parameters of the problem on the diffraction phenomenon is displayed graphically. The present study can be used as a model for different applications. Reducing noise in exhaust systems, ventilation systems are some of these applications.

This paper introduces a new three-parameter distribution which is obtained by combining the Lomax and Lindley distributions in a serial system and is called the Lomax-Lindley distribution. The new distribution is quite flexible to model lifetime data. This distribution provides a simple form for hazard rate function which can be increasing, decreasing, bathtub-shaped and unimodal for different choices of the parameter values. Some statistical properties of the Lomax-Lindley distribution such as quantiles, moments, order statistics, Renyi entropy and mean deviations are discussed. The maximum likelihood estimators of its unknown parameters are obtained and the approximate confidence intervals of the parameters are provided. A Monte Carlo simulation study is conducted to investigate the performance of the maximum likelihood estimators and their corresponding confidence intervals. Finally, two real data sets having bathtub-shaped and unimodal hazard rate functions are analyzed and it is shown that the proposed distribution can provide a better fit than other distributions for both lifetime data.

In hydrologic risk analysis, the use of exceedance statistics are very important. In this sense, we construct a random threshold model based on bivariate order statistics. The exact distribution of exceedance statistics is calculated under some well-known copulas such as independent and Farlie-Gumbel-Morgenstern (FGM) copulas. Furthermore, numerical results are provided for expected value and variance of exceedance statistics under independent and Farlie-Gumbel-Morgenstern copulas. The application of the model in hydrology is also discussed.

In this study, we implement a variant of infeasible interior-point algorithm for solving monotone linear complementarity problems (LCP). We first reformulate the monotone LCP as an minimization problem. Then a descent iterative method is applied to the latter. The descent direction is computed via the Newton method. However, for maintaining the positivity of iterates, a novel and efficient strategy is proposed. Some numerical results are reported to show the efficiency of our proposed approach.

In this paper, we investigate the resolvent operator of the singular q-Sturm-Liouville problem defined as −(1/q)Dq⁻¹[Dqy(x)]+[r(x)-λ]y(x)=0−(1/q)Dq⁻¹Dqy(x)+r(x)y(x)=λy(x),with the boundary condition y(0,λ)cosβ+Dq⁻¹y(0,λ)sinβ=0y(0,λ)cosβ+Dq⁻¹y(0,λ)sinβ=0,where λ∈Cλ∈C, $r$ is a real function defined on $[0,∞)$, continuous at zero and r∈Lq,loc¹(0,∞)r∈Lq,loc¹(0,∞). We give an integral representation for the resolvent operator and investigate some properties of this operator. Furthermore, we obtain a formula for the Titchmarsh-Weyl function of the singular $q$-Sturm-Liouville problem.

Media monitoring plays an important role in the success of companies by protecting their corporate, staff, and brand reputation. With the emergence of ICT, monitoring has emerged as an inevitable means of covering various fields of media: newspapers, online news, broadcast news (TV, radio), and social networks. Companies need a 360-degree view of media sources in near real-time that reports what's going on. In this paper, we proposed a unified system for processing news and detecting advertisements in TV streams. The system architecture is completely described, and the automatic processing has been detailed. Our contributions include a TV stream segmentation method, a news topics segmentation method, and an advertisements classification model. These methods have been evaluated and given promising results. However, more improvements can be made in the future.

The study of interaction between predator and prey species is one of the important subjects in mathematical biology. Optimal strategy control plays a vital role in preserving animals from extinction. Harvesting of species is a vital issue for the conservation biologists. In this work, we investigate the bifurcation and chaos control of the two species interaction model of fractional order in discrete time with harvesting of both prey and predator species. Existence results and the stability conditions of the system are analyzed using the fixed points and jacobian matrix. The chaotic behavior of the system is discussed with bifurcation diagrams. Linear control and hybrid control methods are used in controlling the chaos of the system. Numerical experiments with different phase portraits are simulated for the better understanding of the qualitative behavior of the considered model.

Bipolar fuzzy soft set theory, which is a very useful hybrid set in decision making problems, is a mathematical model that has been emphasized especially recently. In this paper, the concepts of (α,β)-cuts, first type semi-strong (α,β)-cuts, second type semi-strong (α,β)-cuts, strong (α,β)-cuts, inverse (α,β)-cuts, first type semi-weak inverse (α,β)-cuts, second type semi-weak inverse (α,β)-cuts and weak inverse (α,β)-cuts of bipolar fuzzy soft sets were introduced together with some of their properties. In addition, some distinctive properties between (α,β)-cuts and inverse (α,β)-cuts were established. Moreover, some related theorems were formulated and proved. It is further demonstrated that both (α,β)-cuts and inverse (α,β)-cuts of bipolar fuzzy soft sets were useful tools in decision making.

Many complex applications require the solution of initial-value problems where some components change fast, while others vary slowly. Multirate schemes apply different step sizes to resolve different components of the system, according to their dynamics, in order to achieve increased computational efficiency. The stiff components of the system, fast or slow, are best discretized with implicit base methods in order to ensure numerical stability. To this end, linearly implicit methods are particularly attractive as they solve only linear systems of equations at each step. This paper develops the Multirate GARK-ROS/ROW (MR-GARK-ROS/ROW) framework for linearly-implicit multirate time integration. The order conditions theory considers both exact and approximative Jacobians. The effectiveness of implicit multirate methods depends on the coupling between the slow and fast computations; an array of efficient coupling strategies and the resulting numerical schemes are analyzed. Multirate infinitesimal step linearly-implicit methods, that allow arbitrarily small micro-steps and offer extreme computational flexibility, are constructed. The new unifying framework includes existing multirate Rosenbrock(-W) methods as particular cases, and opens the possibility to develop new classes of highly effective linearly implicit multirate integrators.

Radiation of sound waves by a semi-infinite circular cylindrical pipe with non-uniform lining is analyzed by using the Jones\" method in conjunction with the mode matching technique. This mixed method of formulation gives rise to a scalar Wiener-Hopf equation. The inner surface of the duct is coated by acoustically absorbing different linings. In the present study, different linings with partial rigidity make the problem more interesting when it is compared with the uniform lining. The solution of the considered problem involves three infinite sets of coefficients satisfying three infinite systems of linear algebraic equations. Numerical solutions of these systems are obtained for various values of the parameters of the problem and their effects on the radiation phenomenon are shown graphically. The solution is compared graphically with a similar study existing in the literature. A perfect agreement is observed between the both results.

Wildfires are an example of a phenomenon that can be investigated using point process theory. We analyze public data from the National Forestry Commission. It consists of wildfire records, specifically their coordinates and dates of occurrence in Mexico State from 2010 to 2018. The spatial component was examined, and we found that wildfires tend to cluster. Afterwards, a time series analysis was conducted. This shows that the data comes from a stationary stochastic process. Finally, some spatio-temporal features that demonstrate the point process' regular behavior in space and time were investigated. This research could be a reference to describe wildfire behavior in a specific space and time.

In order to solve the problems of serious axial and tangential leakage and low torque density in the magnetic circuit axial permanent magnet gear (APMG), an external regulating ring is introduced on the basis of APMG to form a dual-excitation and modulation APMG structure, namely DEM-APMG. The low speed rotor of DEM-APMG is clamped between the inner and outer magnetizing rings to generate dual-excitation field (i.e. dual excitation). At the same time, the inner and outer magnetizing rings modulate the low speed rotor dual-directionally modulation (i.e. dual modulation). The axial and tangential leakage flux of APMG can be converted into useful harmonics to increase the output torque and torque density on the basis of APMG. In this study, mathematical analysis is used to describe the air gap magnetic density and electromagnetic torque model of a DEM-APMG, which essentially describes the root cause of the increase in torque density. Using 3D finite element static and dynamic simulations, the transmission characteristics of the APMG and DEM-APMG are compared and analyzed. Results show that the maximum static torque of the DEM-APMG high-speed and low-speed rotors with the same outer diameter increase by 22.7% and 23.8%, respectively, compared with APMG, 26% and 29%, respectively, in steady-state operation, and the torque density increases by 24%. The influence of the primary structural parameters on the transmission characteristics is also investigated using the control variable method. Results show that the duty cycle of the magnet adjusting block, the axial length of the high-speed permanent magnet and the low-speed permanent magnet have the strongest effect on the torque density of the DEM-APMG. When the axial length of the high-speed permanent magnet and low-speed permanent magnet is 8mm, and the duty cycle is 0.4, the torque density can reach the optimal value of 156kNm/m3.

In this paper, we investigate the demonic transitive closure of fuzzy relations in the sense of demonic operators. To address this, we focus on the demonic order refinement of fuzzy relations, which has a special treatment associated with the membership function of fuzzy relations. We look closely at the transitive closure of fuzzy relations with the use of angelic operators (the usual operators ∪, ∩ and ◦) and reform it by applying the demonic operators (˜⊔, ˜⊓ and ˜□ ). In order to carry out this task, we adopt existing algorithms and reformulate them in the means of demonic operators.

The dynamic transitions of the Brusselator model has been recently analyzed in Y. Choi et’al (2021) and T. Ma, S. Wang (2011). Our aim in this paper is to address the relation between the pattern formation and dynamic transition results left open in those papers. We consider the problem in the setting of a 2D rectangular box where an instability of the homogeneous steady state occurs due to the perturbations in the direction of several modes becoming critical simultaneously. Our main results are two folds: (1) a rigorous characterization of the types and structure of the dynamic transitions of the model from basic homogeneous states and (2) the relation between the dynamic transitions and the pattern formations. We observe that the Brusselator model exhibits different transition types and patterns depending on the nonlinear interactions of the pattern of the critical modes.

Let 𝑅 = 𝐹𝑞+u𝐹𝑞+𝑢^2𝐹𝑞, 𝑢^3=0 be a finite chain ring. In this paper, we give the structure of constacyclic codes over 𝑅 and obtain self-orthogonal codes over 𝐹𝑞 by using the Gray map from 𝑅𝑛 to 𝐹𝑞^(3𝑛). As an application, we present a construction of quantum codes from the codes obtained from this class.

In this work, a finite element scheme is proposed using a method of Euler-Taylor-Galerkin described in Páez et al. (2016), for a non-linear model which describes the behavior of a new chemo-fluidic oscillator, Donea (1984). This model is expressed by the coupling of an ordinary differential equation describing the hydrogel dynamics, the non-linear transport equation and an auxiliary equation determining the flux volume. The numerical solution is constructed by taking a semi-discretization in time of the transport equation, employing forward-time Taylor series expansions including time derivatives of second order and third order, avoiding instabilities problems. In this semi discrete equation, the spatial variable is approximated by the finite element formulation according to Galerkin. Some simulations are carried out taking different initial conditions for the concentration of the hydrogel. The numerical results describe the oscillatory behavior of the system as in Donea (1984), where MatLab tools are used as black box.

The main goal of this paper is to classify the first transitions of a class of 1D second order reaction diffusion equation with a non-self-adjoint linear part and semilinear nonlinearity on a bounded interval subject to homogeneous boundary conditions. The emphasis is on the interaction of the nonlinear terms, the boundary conditions and the strength of the first order derivative term which makes the linear operator non-self-adjoint. The equations admit a trivial steady state solution which loses stability as a control parameter exceeds a threshold. According to our results, the first transitions of the system are either continuous, jump or mixed type. We compare our results with a recent study where only self adjoint linear operator was considered. In the Dirichlet, Neumann and periodic boundary condition cases, the first transition occurs via a transcritical/pitchfork bifurcation and the dynamics remain unchanged between the self-adjoint and non-self-adjoint cases. However, for the periodic case, with imposed zero mean condition, in the non-self adjoint case, the first transition is always accompanied by a Hopf bifurcation with a stable/unstable bifurcated limit cycle which is different than the self-adjoint case. Finally, we apply our results to determine the first transitions of some well-known reaction diffusion equations such as the Kolmogorov-Fisher, Chaffee-Infante equation and the Burger\"s equation.

Threshold Implementations are known countermeasures defending against side-channel attacks via the use of masking techniques. While sufficient properties are known to defend against first-order side-channel attacks, it is not known how to achieve higher-order security. This work generalizes the Threshold Implementation notion of uniformity and proves it achieves second-order protection. The notion is applied to create a second-order masking of the Present cipher with a low randomness cost.