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Calculating molecular properties using quantum devices can be performed through the quantum linear response (qLR) or, equivalently, the quantum equation of motion (qEOM) formulations. Different parameterizations of qLR and qEOM are available, namely naïve, projected, self-consistent, and state-transfer. In the naïve and projected parameterizations, the metric is not the identity, and we show that it depends on redundant orbital rotations. This dependency may lead to divergences in the excitation energies for certain choices of the redundant orbital rotation parameters in an idealized noiseless setting. Furthermore, this leads to a significant variance when calculations include statistical noise from finite quantum sampling. [ABSTRACT FROM AUTHOR]

Motivated by the various applications of the trapping diffusion-influenced reaction theory in physics, chemistry, and biology, this paper deals with irreducible Cartesian tensor (ICT) technique within the scope of the generalized method of separation of variables (GMSV). We provide a survey from the basic concepts of the theory and highlight the distinctive features of our approach in contrast to similar techniques documented in the literature. The solution to the stationary diffusion equation under appropriate boundary conditions is represented as a series in terms of ICT. By means of proved translational addition theorem, we straightforwardly reduce the general boundary value diffusion problem for N spherical sinks to the corresponding resolving infinite set of linear algebraic equations with respect to the unknown tensor coefficients. These coefficients exhibit an explicit dependence on the arbitrary three-dimensional configurations of N sinks with different radii and surface reactivities. Our research contains all relevant mathematical details such as terminology, definitions, and geometrical structure, along with a step by step description of the GMSV algorithm with the ICT technique to solve the general diffusion boundary value problem within the scope of Smoluchowski's trapping model. [ABSTRACT FROM AUTHOR]

We derive equations of motion for bivariational wave functions with orthogonal adaptive basis sets and specialize the formalism to the coupled cluster Ansatz. The equations are related to the biorthogonal case in a transparent way, and similarities and differences are analyzed. We show that the amplitude equations are identical in the orthogonal and biorthogonal formalisms, while the linear equations that determine the basis set time evolution differ by symmetrization. Applying the orthogonal framework to the nuclear dynamics problem, we introduce and implement the orthogonal time-dependent modal vibrational coupled cluster (oTDMVCC) method and benchmark it against exact reference results for four triatomic molecules as well as a reduced-dimensional (5D) trans-bithiophene model. We confirm numerically that the biorthogonal TDMVCC hierarchy converges to the exact solution, while oTDMVCC does not. The differences between TDMVCC and oTDMVCC are found to be small for three of the five cases, but we also identify one case where the formal deficiency of the oTDMVCC approach results in clear and visible errors relative to the exact result. For the remaining example, oTDMVCC exhibits rather modest but visible errors. [ABSTRACT FROM AUTHOR]

A fully numerical homogenization technique for the retrieval of the effective surface susceptibilities of a periodic composite metasurface is developed in this work. We utilize the so-called dual field-flux finite element formulation scheme to accurately calculate the eigenmodes of a composite periodic metasurface, a scheme that possesses a crucial advantage: The capability of evaluating all field components and their derivatives accurately and with the same order of approximation is a requirement for our proposed technique. Next, we derive the generalized sheet transition condition equations for a general bianisotropic metasurface, which correlate the field components on either sides of the metasurface with its surface susceptibilities. At this point, we establish a new field averaging scheme for the acquisition of the average field components of the modes supported by the metasurface. Combining this computational information, we derive a set of linear algebraic equations based on the GSTCs and the average electromagnetic fields and numerically solve it, so as to obtain the effective surface susceptibilities of a bianisotropic metasurface. Comparison with the results of other techniques in the literature shows very good agreement, relatively to the resonance behavior of the returned values and their position at the frequency spectrum. The advantages that distinguish the proposed technique over other related methods are its foundation on the intrinsic modal information of the eigenmodes supported by the metasurface and its independence of any wave excitation schemes or involvement of analytical polarizability calculations. [ABSTRACT FROM AUTHOR]

Summary: In this article we deal with the problem of determining a non‐homogeneous N$$ N $$‐valued heat conductivity profile in a steady‐state heat conduction boundary‐value problem with mixed Dirichlet‐Neumann boundary conditions over a bounded domain in ℝn$$ {\mathbb{R}}^n $$, from the knowledge of the temperature field over the whole domain. In a previous work we developed a method based on a variational approach of the PDE leading to an optimality equation which is then projected into a finite dimensional space. Discretization of the optimality equation then yields a linear although severely ill‐posed equation which is then regularized via appropriate ad‐hoc penalizers based upon a‐priori information about the conductivities of all materials present. This process results in a generalized Tikhonov‐Phillips functional whose global minimizer yields our approximate solution to the inverse problem. In our previous work we showed that this approach yields quite satisfactory results in the cases of two different conductivities. We considered here an appropriate extension of that approach for the N$$ N $$ materials case and show a few numerical examples for the case N=3$$ N=3 $$ in which the method is able to produce very good reconstructions of the exact solution. [ABSTRACT FROM AUTHOR]

The advantages and disadvantages of application of Padé approximants to regression analysis with two independent covariates are discussed. The main difficulty of using Padé function is nonlinearity of data fitting. Possible approaches to overcoming the problem are discussed. New formulation of residuals is suggested in the method of least squares. It leads to a system of linear equations in case of rational functions. The possibility of using ridge regularization technique to avoid overfitting is demonstrated in this approach. To illustrate the efficiency of the suggested method, several practical cases from physics and reliability theory are considered. [ABSTRACT FROM AUTHOR]

In this paper, we study the wave equation on infinite graphs. On one hand, in contrast to the wave equation on manifolds, we construct an example for the non-uniqueness for the Cauchy problem of the wave equation on graphs. On the other hand, we obtain a sharp uniqueness class for the solutions of the wave equation. The result follows from the time analyticity of the solutions to the wave equation in the uniqueness class. In the last part, we extend the result to a wide class of linear evolution equations. [ABSTRACT FROM AUTHOR]

Kaczmarz algorithm is an iterative projection method for solving system of linear equations that arise in science and engineering problems in various application domains. In addition to classical Kaczmarz, there are randomized and parallel variants. The main challenge of the parallel implementation is the dependency of each Kaczmarz iteration on its predecessor. Because of this dependency, frequent communication is required which results in a substantial overhead. In this study, a new distributed parallel method that reduces the communication overhead is proposed. The proposed method partitions the problem so that the Kaczmarz iterations on different blocks are less dependent. A frequency parameter is introduced to see the effect of communication frequency on the performance. The communication overhead is also decreased by allowing communication between processes only if they have shared non‐zero columns. The experiments are performed using problems from various domains to compare the effects of different partitioning methods on the communication overhead and performance. Finally, parallel speedups of the proposed method on larger problems are presented. [ABSTRACT FROM AUTHOR]

In many industries’ applications, one deals with pipes conveying fluid. Besides, the implementation of advanced materials in manufacturing of new-brand structures is developing. Consequently, in this paper, one of the most important dynamics analyzes that an advanced pipe conveying fluid may meet it is addressed. For the first time, linear and nonlinear dynamics of a pipe reinforced with graphene nanoplatelets (GPL pipe) that conveys pulsating flow is presented. The Euler–Bernoulli beam model follows the plug flow model in order to formulate the problem. The method of multiple scales (MMS) applied to the discretized couple nonlinear gyroscopic governing equations with the aim of specifying the instability region and the steady-state response of the GPL pipe subjected to the principal parametric resonance of one of its modes, as a consequence of pulsating flow. Respectively, the Floquet theory and the Runge–Kutta fourth-order (RK4) method are applied to the linear governing equations and nonlinear governing equations for the sake of confirming the current MMS results. It is deduced that a small amount usage of GPL reinforcement phase improves substantially the resistance against static instability, and the critical fluid excitation amplitude fraction, meanwhile declines the instability region bandwidth, and the steady-state response of the pipe. In contrary, it is confirmed that a heavier fluid makes reverse the preceding statements with respect to a lighter fluid. The aforementioned findings shed light on the essential design keys that outstandingly affect the mechanics of the GPL pipe conveying pulsating fluid that lead and conduct forthcoming studies and open new horizons for designers in industry implementations. [ABSTRACT FROM AUTHOR]

This study aims to examine the phenomenological consequences of the constant-roll condition on the f(R,ϕ,X) gravity in the context of a non-canonical scalar field. In this regard, two periods of inflation are investigated, specifically the slow-roll and quintessence phases, within the context of the non-canonical scalar field. We will make two assumptions: first, the slow-roll condition is imposed on the first slow-roll parameters, and second, the scalar field evolves according to the constant-roll condition. We provide a comprehensive explanation of the gravitational equations of motion that govern the behavior of the cosmological system. We consider the constant-roll condition and use a specifically chosen potential to simplify analytical calculations. By doing so, we express the slow-roll indices and the resulting observational indices of the theory as functions of the e-foldings number. Our analysis demonstrates that the existence of constant-roll inflation with non-canonical scalar fields aligns with observed results across a wide range of model parameters. Furthermore, we establish an equation that combines the fundamental equations of the theory. By using a differential operator, we convert this equation into a linear form, yielding the effective equation of state (EoS) parameter. The value of this parameter is dependent upon the exponential α parameter of the kinetic term, as well as to the first slow-roll parameter and the constant-roll parameter σ. Under the assumption of a fixed σ field, we demonstrate that the early universe has the ability to experience a two-stage inflation, as described by the EoS parameter. [ABSTRACT FROM AUTHOR]

Airborne pollen, a significant natural pollutant, restricts outdoor activities and impacts quality of life for sensitive individuals with pulmonary disorders. This study examines trends in airborne pollen concentrations and explores whether air pollution, pollen concentration, or both impact patient counts. The annual pollen trend in Jaipur shows peaks in pollen concentration in March (due to trees, 66%), September (due to weeds, 45%), and December (due to grass, 50%). Among the fifteen taxa examined, Holoptelea integrifolia is the largest pollen emitter in Jaipur, followed by Poaceae, among others. The count of patients arriving for clinical consultations in a hospital shows a strong and positive correlation with weed (Asteraceae spp. and Argemone mexicana) and grass pollen. A linear regression equation is developed (R2 value = 0.835) for forecasting consulting patient counts based on Cassia siamea pollen concentration. This can assist hospital administration in resource management, especially during peak allergy seasons. [ABSTRACT FROM AUTHOR]

Long-term cyclic loading can have a significant effect on the modulus of sand, and the influence on saturated coral sand has yet to be established. In this paper, the significant influence of non-plastic fines content (FC) and relative density (D r) on dynamic elastic modulus (E) of saturated coral sand has been evaluated by a series of cyclic triaxial drainage tests. The results show that the dynamic elastic modulus increases rapidly at the beginning of loading; then the growth slows down and finally stabilizes. In general, the development of E is influenced collectively by FC, D r and cyclic stress ratio (CSR). The initial dynamic elastic modulus E d-1 and steady-state dynamic elastic modulus E d-s increase with the increase of D r, and decrease as FC increases. The linear fitting equations are given by introducing the equivalent skeleton void ratio esk*. Furthermore, the relative dynamic elastic modulus E r is defined as the ratio of E d-N to E d-s, and the prediction equation for E r was developed to provide a basis for the engineering mechanical parameters of coral sands under long-term loads. [ABSTRACT FROM AUTHOR]

A new method is developed for finding exact solitary wave solutions of a generalized Korteweg–de Vries equation with p$p$‐power nonlinearity coupled to a linear Schrödinger equation arising in many different physical applications. This method yields 22 solution families, with p=1,2,3,4$p=1,2,3,4$. No solutions for p>1$p>1$ were known previously in the literature. For p=1$p=1$, four of the solution families contain bright/dark Davydov solitons of the 1st and 2nd kind, obtained in recent literature by basic ansatz applied to the ordinary differential equation (ODE) system for traveling waves. All of the new solution families have interesting features, including bright/dark peaks with (up to) p$p$ symmetric pairs of side peaks in the amplitude and a kink profile for the nonlinear part in the phase. The present method is fully systematic and involves several novel steps that reduce the traveling wave ODE system to a single nonlinear base ODE for which all polynomial solutions are found by symbolic computation. It is applicable more generally to other coupled nonlinear dispersive wave equations  as well as to nonlinear ODE systems of generalized Hénon–Heiles form. [ABSTRACT FROM AUTHOR]

At present paper, we study the pathwise behavior of the solutions of 2D non-autonomous stochastic Navier-Stokes equation driven by a linear non-degenerate noise. When the stochastic external force is an H − 1 / 2 -valued Q -Wiener process and the deterministic non-autonomous external force is normal function in L l o c 2 (R ; V ′) , we establish the existence of uniform random attractor for the equation in H. We also obtain the regularity of uniform random attractor for the equation driven by the H -valued Q -Wiener process with the deterministic non-autonomous external force being normal in L l o c 2 (R ; H). Finally, we investigate the existence of uniform random attractor for the equation driven by an H -valued cylindrical Wiener process in H and V , respectively. [ABSTRACT FROM AUTHOR]

We consider an abstract linear wave equation with a time-dependent dissipation that decays at infinity with the so-called scale invariant rate, which represents the critical case. We do not assume that the coefficient of the dissipation term is smooth, and we investigate the effect of its oscillations on the decay rate of solutions. We prove a decay estimate that holds true regardless of the oscillations. Then we show that oscillations that are too fast have no effect on the decay rate, while oscillations that are in resonance with one of the frequencies of the elastic part can alter the decay rate. In the proof we first reduce ourselves to estimating the decay of solutions to a family of ordinary differential equations, then by using polar coordinates we obtain explicit formulae for the energy decay of these solutions, so that in the end the problem is reduced to the analysis of the asymptotic behavior of suitable oscillating integrals. [ABSTRACT FROM AUTHOR]

The so-called Frobenius number in the famous linear Diophantine problem of Frobenius is the largest integer such that the linear equation a 1 x 1 + ⋯ + a k x k = n ( a 1 , ... , a k are given positive integers with gcd (a 1 , ... , a k) = 1) does not have a non-negative integer solution (x 1 , ... , x k). The generalized Frobenius number (called the p -Frobenius number) is the largest integer such that this linear equation has at most p solutions. That is, when p = 0 , the 0 -Frobenius number is the original Frobenius number. In this paper, we introduce and discuss p -numerical semigroups by developing a generalization of the theory of numerical semigroups based on this flow of the number of representations. That is, for a certain non-negative integer p , p -gaps, p -symmetric semigroups, p -pseudo-symmetric semigroups, and the like are defined, and their properties are obtained. When p = 0 , they correspond to the original gaps, symmetric semigroups and pseudo-symmetric semigroups, respectively. [ABSTRACT FROM AUTHOR]

Algebraic expressions for averaging linear and nonlinear stiffness tensors from general anisotropy to different effective symmetries (11 Laue classes elastically representing all 32 crystal classes, and two non‐crystalline symmetries: isotropic and cylindrical) have been derived by automatic symbolic computations of the arithmetic mean over the set of rotational transforms determining a given symmetry. This approach generalizes the Voigt average to nonlinear constants and desired approximate symmetries other than isotropic, which can be useful for a description of textured polycrystals and rocks preserving some symmetry aspects. Low‐symmetry averages have been used to derive averages of higher symmetry to speed up computations. Relationships between the elastic constants of each symmetry have been deduced from their corresponding averages by resolving the rank‐deficient system of linear equations. Isotropy has also been considered in terms of generalized Lamé constants. The results are published in the form of appendices in the supporting information for this article and have been deposited in the Mendeley database. [ABSTRACT FROM AUTHOR]

Purpose: To estimate the astigmatic power of the crystalline lens and the whole eye without phakometry using a set of linear equations and to provide estimates for the astigmatic powers of the crystalline lens surfaces. Methods: Linear optics expresses astigmatic powers in the form of matrices and uses paraxial optics and a 4 × 4 ray transfer matrix to generalise Bennett's method comprehensively to include astigmatic elements. Once this is established, the method is expanded to estimate the contributions of the front and back lens surfaces. The method is illustrated using two examples. The first example is of an astigmatic model eye and compares the calculated results to the original powers. In the second example, the method is applied to the biometry of a real eye with large lenticular astigmatism. Results: When the calculated powers for the astigmatic model eye were compared to the actual powers, the difference in the power of the eye was 0.030.130.04TD (where T represents the matrix transpose) and for the crystalline lens, the difference was 0.080.290.08TD (power vector format). A second example applies the method to a real eye, obtaining lenticular astigmatism of −5.84 × 175. Conclusions: The method provides an easy‐to‐code way of estimating the astigmatic powers of the crystalline lens and the eye. [ABSTRACT FROM AUTHOR]

The objects of consideration are thin linearly elastic Kirchhoff–Love-type open circular cylindrical shells having a functionally graded macrostructure and a tolerance-periodic microstructure in circumferential direction. The first aim of this contribution is to formulate and discuss a new mathematical averaged non-asymptotic model for the analysis of selected stability problems for such shells. As a tool of modelling we shall apply the tolerance averaging technique. The second aim is to derive and discuss a new mathematical averaged asymptotic model. This model will be formulated using the consistent asymptotic modelling procedure. The starting equations are the well-known governing equations of linear Kirchhoff–Love second-order theory of thin elastic cylindrical shells. For the functionally graded shells under consideration, the starting equations have highly oscillating, non-continuous and tolerance-periodic coefficients in circumferential direction, whereas equations of the proposed models have continuous and slowly-varying coefficients. Moreover, some of coefficients of the tolerance model equations depend on a microstructure size. It will be shown that in the framework of the tolerance model not only the fundamental cell-independent, but also the new additional cell-dependent critical forces can be derived and analysed. [ABSTRACT FROM AUTHOR]

We deal, for the classical N -body problem, with the existence of action minimizing half entire expansive solutions with prescribed asymptotic direction and initial configuration of the bodies. We tackle the cases of hyperbolic, hyperbolic-parabolic and parabolic arcs in a unified manner. Our approach is based on the minimization of a renormalized Lagrangian action on a suitable functional space. With this new strategy, we are able to confirm the already-known results of the existence of both hyperbolic and parabolic solutions, and we prove for the first time the existence of hyperbolic-parabolic solutions for any prescribed asymptotic expansion in a suitable class. Associated with each element of this class we find a viscosity solution of the Hamilton-Jacobi equation as a linear correction of the value function. Besides, we also manage to give a precise description of the growth of parabolic and hyperbolic-parabolic solutions. [ABSTRACT FROM AUTHOR]

We formulate and analyze a fully discrete approximate solution of the linear Schrödinger equation on the unit square written as a Schrödinger-type system. The finite element Galerkin method is used for the spatial discretization, and the time stepping is done with an alternating direction implicit extrapolated Crank-Nicolson method. We demonstrate the existence and uniqueness of the approximation, and prove that the scheme is of optimal accuracy in the L 2 , H 1 and L ∞ norms in space and second-order accurate in time. Numerical results are presented which support the theory. [ABSTRACT FROM AUTHOR]

Piezothermoelasticity and wave interaction studies hold immense significance in designing functional devices ranging from transducers to sensors for a variety of purposes like energy harvesting and structural health monitoring. These applications catalyze interest in this article which addresses the problem of reflection of plane wave at the boundary of piezothermoelastic half-space. Through this study, the effect of impedance parameter on amplitude and energy ratios of the reflected waves is studied. Four wave modes are indicated upon reflection and a linear system of equations is formed to obtain a closed-form expression for amplitude and energy ratios. These equations are solved by suitable mathematical tools leading to expression for amplitude ratios as a function of incidence angle. For a suitable piezothermoelastic medium, the ratios are plotted against incidence angle and the findings are compared for two well-known theories of thermoelasticity, namely, Lord–Shulman (LS theory) and Green–Lindsay (GL theory). The analytical outcomes suggest approximate values of impedance and incidence angle for preferred energy division between reflected waves. It is recognized that adding impedance increases the amplitude of the quasi-longitudinal (qP) wave and decreases that of the quasi-transverse wave, making it suitable for devices that require a more robust qP wave signal detection. [ABSTRACT FROM AUTHOR]

We consider Kantorovich modifications of linking operators and Stancu modifications of the classical Bernstein operators. For the modified operators we determine the limits of iterates and the invariant measures. In order to find the limits we have to solve systems of linear equations and to this end we use a suitable iterative algorithm. [ABSTRACT FROM AUTHOR]

In this article, we present a formally fourth‐order accurate hybrid‐variable (HV) method for the Euler equations in the context of method of lines. The HV method seeks numerical approximations to both cell averages and nodal solutions and evolves them in time simultaneously; and it is proved in previous work that these methods are supraconvergent, that is, the order of the method is higher than that of the local truncation error. Taking advantage of the supraconvergence, the method is built on a third‐order discrete differential operator, which approximates the first spatial derivative at each grid point using only the information in the two neighboring cells. Analyses of stability, accuracy, and pointwise convergence are conducted in the one‐dimensional case for the linear advection equation; whereas extension to nonlinear systems including the Euler equations is achieved using characteristic decomposition and the incorporation of a residual‐consistent viscosity to capture strong discontinuities. Extensive numerical tests are presented to assess the numerical performance of the method for both 1D and 2D problems. [ABSTRACT FROM AUTHOR]

The paper presents error estimates within a unified abstract framework for the analysis of FEM for boundary value problems with linear diffusion‐convection‐reaction equations and boundary conditions of mixed type. Since neither conformity nor consistency properties are assumed, the method is called completely discrete. We investigate two different stabilized discretizations and obtain stability and optimal error estimates in energy‐type norms and, by generalizing the Aubin‐Nitsche technique, optimal error estimates in weaker norms. [ABSTRACT FROM AUTHOR]

In this paper, by applying the supplementary variable method (SVM), some high-order, conformal structure-preserving, linearized algorithms are developed for the damped nonlinear Schrödinger equation. We derive the well-determined SVM systems with the conformal properties and they are then equivalent to nonlinear equality constrained optimization problems for computation. The deduced optimization models are discretized by using the Gauss type Runge-Kutta method and the prediction-correction technique in time as well as the Fourier pseudo-spectral method in space. Numerical results and some comparisons between this method and other reported methods are given to favor the suggested method in the overall performance. It is worthwhile to emphasize that the numerical strategy in this work could be extended to other conservative or dissipative system for designing high-order structure-preserving algorithms. [ABSTRACT FROM AUTHOR]

This paper is dedicated to the full discretization of linear wave equations, where the space discretization is carried out with a discontinuous Galerkin method on spatial meshes which are locally refined or have a large wave speed on only a small part of the mesh. Such small local structures lead to a strong Courant–Friedrichs–Lewy (CFL) condition in explicit time integration schemes causing a severe loss in efficiency. For these problems, various local time-stepping schemes have been proposed in the literature in the last years and have been shown to be very efficient. Here, we construct a quite general class of local time integration methods preserving a perturbed energy and containing local time-stepping and locally implicit methods as special cases. For these two variants we prove stability and optimal convergence rates in space and time. Numerical results confirm the stability behavior and show the proved convergence rates. [ABSTRACT FROM AUTHOR]

Research shows the salient place of mathematical teaching talk, including the mathematical-linguistic practices of naming and explaining, in the enactment of students' mathematical talk and learning with understanding in the classroom. Our study was developed to examine the noticing of two groups of secondary-school mathematics teachers in one-day workshops with tasks about these practices. The two workshops were mathematically content-specific, with teaching and learning accounts and prompts aimed at guiding focused attention to naming and explaining in the teaching of linear equations and probability. Thematic text analyses led to identify three foci of the two groups' noticing: (i) missing practices of mathematical naming in own teaching talk; (ii) relative impact of mathematical explaining in teaching talk; and (iii) tensions around mathematical naming and explaining in teaching talk. Our results show that the social construction of teacher noticing is a feature of noticing development that can be documented in the context of one-day workshops. Whereas time for individual thinking and responses to the tasks created a context of support for noticing development, participation in the group discussions allowed the teachers to notice nuances of mathematical naming and explaining in teaching talk unaddressed in the task prompts. The group discussions thus amplified and opened up the opportunities to develop some focused noticing on the content of the workshops, specifically in connection with the teachers' own teaching practice. [ABSTRACT FROM AUTHOR]

The finite set model predictive control (FCS-MPC) method for quasi-Z-source inverter-permanent magnet synchronous motor (QZSI-PMSM) system suffers from the problems of unclear linkage between control objectives, complex control system, and poor control performance. A three-phase duty cycle modulation-based model predictive control (TDCM-MPC) strategy without cost function is proposed. In this strategy, the control objectives are converted firstly to make a connection between the control variables of inverterside and motor-side, and based on it construct a system of nonhomogeneous linear equations to calculate the three-phase duty cycle. In addition, the three-phase duty cycles may have a secondary correction according to the size of the capacitor voltage error to realize the overall control of the four control variables. Finally, the driving pulse is generated based on space vector modulation (SVM) to obtain smaller steady-state ripples. The experimental results show that, compared with the conventional FCS-MPC, the proposed TDCM-MPC strategy reduces the computation of the control system and can obtain better control performance. [ABSTRACT FROM AUTHOR]

Cryptanalysis of modern symmetric ciphers may be done by using linear equation systems with multiple right hand sides, which describe the encryption process. The tool was introduced by Raddum and Semaev (Des Codes Cryptogr 49(1):147–160, 2008) where several solving methods were developed. In this work, the probabilities are ascribed to the right hand sides and a statistical attack is then applied. The new approach is a multivariate generalisation of the correlation attack by Siegenthaler (IEEE Trans Comput C 49(1):81–85, 1985). A fast version of the attack is provided too. It may be viewed as an extension of the fast correlation attack in Meier and Staffelbach (J Cryptol 1(3):159–176, 1989), based on exploiting so called parity-checks for linear recurrences. Parity-checks are a particular case of the relations that we introduce in the present work. The notion of a relation is irrelevant to linear recurrences. We show how to apply the method to some LFSR-based stream ciphers including those from the Grain family. The new method generally requires a lower number of the keystream bits to recover the initial states than other techniques reported in the literature. [ABSTRACT FROM AUTHOR]

In this work, numerous rogue wave solution strategy (MRWSS) agreeing to the Hirota bilinear hypothesis is utilized. The said strategy to build different soliton wave solutions for the generalized Hirota-Satsuma-Ito (GHSI) condition is considered. These numerous soliton wave solutions incorporate first-order, second-order, third-order, and fourth-order waves solutions and so on, which are all depending on the starting theory of chosen capacities. For the lump solution with one most extreme or least esteem, the properties of the Hessian lattice are examined. Besides, the arrangements are contained the lump-two kink arrangements, cross-kink wave arrangements, periodic wave arrangements, and periodic-kink wave arrangements. The various classes of arrangements are gotten. We make utilize of the direct superposition procedure to find out N-soliton wave arrangements to the said condition. The appropriateness and viability of the obtained arrangements is detailed through the reenactment comes about within the shape of 3-D, density, and 2-D charts. The gotten comes about in this work are anticipated to open modern viewpoints for the traveling wave theory. [ABSTRACT FROM AUTHOR]

Moderate deviation principle is achieved by the weak convergence approach for a stochastic Schrödinger type equation with linear drift term and noise driven by a Q-Wiener process. The central limit theorem is also shown for the equation to further analyze its asymptotic behavior. [ABSTRACT FROM AUTHOR]

In this paper, we survey the developments of the symplectic aspects about the gauged linear sigma model, invented by Witten 30 years ago. [ABSTRACT FROM AUTHOR]

This research proposes the application of fractional‐order sliding mode control (FOSMC) at the primary controller level to improve the stability of an islanded microgrid by adjusting its voltage and frequency. The control strategies used in the microgrid are performed in two levels (primary and secondary) in the islanded mode. Practically, most previous studies have worked to improve the primary controller. Droop control is one of the most commonly used methods at the primary level and is adopted in this study as well. The sliding mode control (SMC) strategy is normally used to control linear equations. Thus, the non‐linear microgrid equations were transformed into some linear ones using the input‐output feedback linearization technique. Further, a fractional sliding surface was acquainted. The sliding surface and FOSMC were designed to reject system uncertainties and organize the voltage and frequency. Design parameters were chosen using the Lyapunov stability theorem. The validation of the proposed method using Simulink‐MATLAB confirms its effectiveness in enhancing level power sharing, regulating frequency, and maintaining voltage stability across the system. [ABSTRACT FROM AUTHOR]

This study presents, a numerical method for the solutions of the generalized nonlinear Benjamin-Bona-Mahony-Burgers' equation, with variable order local time fractional derivative. This derivative is expressed as a product of two functions, the usual integer order time derivative, and a function of time having a fractional exponent. Then, forward difference approximation is used for time derivative. The unknown solution of the differential problem and corresponding derivatives are estimated using Haar wavelet approximations (HWA). The collocation procedure is then implemented in HWA, to transform the given model to the system of linear algebraic equations for the determination of unknown constant coefficient of the Haar wavelet series, which update the derivatives and the numerical solutions. The sufficient condition is established for the stability of the proposed technique, and then verified computationally. To check the performance of the scheme, few illustrative examples in one and two dimensions along with l ∞ and l 2 error norms are also given. Besides this, the computational convergence rate is calculated for both type equations. Additionally, computed solutions are compared with available results in literature. Simulations and graphical data discloses, that suggested scheme works well for such complex problems. [ABSTRACT FROM AUTHOR]

In this article, the mathematical study of the problem of identifying the space-dependent source term, in transport processes given by an n -dimensional linear parabolic equation, from space-dependent noisy measurements taken at an arbitrary fixed time is conducted. The problem is analytically solved using Fourier techniques, and it is shown that this solution is not stable. Three families of uniparametric regularization operators are proposed to address the instability of the solution. Each of them is designed to compensate for the factor that causes the instability of the inverse operator. Additionally, a selection rule for the regularization parameter is included, and an error bound for each estimation of Hölder type is obtained. Numerical examples of different characteristics are presented to demonstrate the benefits of the proposed strategies. [ABSTRACT FROM AUTHOR]

Background: This research aims to compare the differences in kinematic parameters associated with cross and uppercut punches between Sanda athletes (SA) and Boxing athletes (BA) to analyze their impacts on peak punching speed. Methods: The punches of BA (n = 20) and SA (n = 20) were compared utilizing a three-dimensional (3D) framework and high-speed cameras in terms of 13 key parameters. An independent samples t-test (α = 0.05) was employed to analyze the differences in punching between BA and SA. Meanwhile, a stepwise multiple linear regression equation was developed to analyze the influence of selected parameters on peak punching speed. Results: The results reveal that, among the 13 kinematic parameters, the six cross-related parameters and four uppercut-related parameters are significantly different (both p ≤ 0.05). The results of multivariate regression analysis unveils that the peak punching speed for the cross are influenced by the anteroposterior position of the center of gravity (in BA) and the maximum angular velocity of the shoulder (in SA). In contrast, for both BA and SA, the maximum angular velocity of the shoulder plays a critical impact on uppercut. Conclusions: These findings indicate that trunk and upper limbs significantly influence the peak punching speed, which provides suggestions for daily training regimen of SA and BA as well as their coaches. [ABSTRACT FROM AUTHOR]

ABSTRACT A novel Wiener‐type dynamic neural network (Wiener‐type DNN) method for large signal modeling of power amplifiers (PAs) is proposed in this paper. In this method, the proposed model structure for the PA contains two Wiener‐type DNNs to describe the input impedance and the amplification efficiency, respectively. The Wiener‐type DNN includes a simplified linear dynamic equation module and a nonlinear static equation module. For the simplification process of the linear dynamic equation, it is proposed to process fundamental frequency components of the large signal harmonic data of the PA by vector fitting. The neural network is used to implement the static equation in the Wiener‐type DNN. The formulas for training the proposed Wiener‐type DNN model of the PA using large signal data are derived. The training algorithm of the PA model is proposed to improve the training efficiency. A Motorola MOSFET PA example and a Freescale lateral double‐diffused MOSFET PA example are present to validate the proposed Wiener‐type DNN method. For the Motorola MOSFET PA, a dynamic neural network (DNN) model and a time‐delay deep neural network (TDDNN) are established for comparison. For the Freescale PA, the DNN model is used for comparison experiment. The comparison figures show that the Wiener‐type DNN model has better convergence properties than the DNN model in the nonlinear region of the PA. The established accurate PA model is conducive to the design of subsequent communication circuits. [ABSTRACT FROM AUTHOR]

Quantum computing (QC) has been viewed as a groundbreaking development in the modern technological landscape. The field of QC technology has made significant strides in various applications in recent years, making it one of the most researched topics today. QC technology outperforms classical computers by running quantum algorithms (QA), which have demonstrated superiority in real-time decision-making over traditional computing solutions. QA has wide-ranging applications in areas such as cryptography, search, optimization, measurements, quantum system simulation, and solving large-scale linear equations. This current study presents a scientometric analysis of over 2800 QA publications from the Scopus database spanning the last decade (2014–2023). The findings of this study shed light on key research areas in QA, providing insights into geographical analysis, linkages, keyword co-occurrences, prominent institutions, journal co-citations, document co-citations, and future research directions for QA. Furthermore, document co-citation analysis and linkages are conducted for each QA domain. A review of the academic literature reveals significant issues in the QA knowledge domain. The information gathered from this study can help identify relevant applications, research challenges, and major issues, offering a comprehensive overview of QA research. This scientometric study examines the growth and categorization of QA and its domains over time, while also identifying trends in collaboration among leading nations and institutions, prestigious journals, and active research fields. Through collaboration analysis, the top 10 nations and universities supporting QA research were identified, showcasing their global leadership in the discipline. Additionally, the study determined the most highly esteemed journals in the field. [ABSTRACT FROM AUTHOR]

ABSTRACT It is becoming increasingly common for researchers to consider leveraging information from external sources to enhance the analysis of small‐scale studies. While much attention has focused on univariate survival data, correlated survival data are prevalent in epidemiological investigations. In this article, we propose a unified framework to improve the estimation of the marginal accelerated failure time model with correlated survival data by integrating additional information given in the form of covariate effects evaluated in a reduced accelerated failure time model. Such auxiliary information can be summarized by using valid estimating equations and hence can then be combined with the internal linear rank‐estimating equations via the generalized method of moments. We investigate the asymptotic properties of the proposed estimator and show that it is more efficient than the conventional estimator using internal data only. When population heterogeneity exists, we revise the proposed estimation procedure and present a shrinkage estimator to protect against bias and loss of efficiency. Moreover, the proposed estimation procedure can be further refined to accommodate the non‐negligible uncertainty in the auxiliary information, leading to more trustable inference conclusions. Simulation results demonstrate the finite sample performance of the proposed methods, and empirical application on the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial substantiates its practical relevance. [ABSTRACT FROM AUTHOR]

A geometric and physical model for melting ice sliding over inclined superhydrophobic (SH) surfaces with parallel ridges is presented. By analyzing the micro-shear flows of molten liquid films between the ice layer and SH surfaces, the hyperslip velocities of melting ice sliding are investigated. The stick-slip boundary condition of the SH surface is used to establish the dual-series equations analytically, and the numerical solutions are implemented by truncating Fourier series and transforming the dual-series equations into linear algebraic equations to determine the hyperslip velocities of melting ice sliding. The numerical results indicate that the non-dimensional hyperslip velocities increase nonlinearly from near 0 to approximately 1.1 for longitudinal sliding and from near 0 to approximately 0.55 for transverse sliding with an increasing air groove ratio (a). The hyperslip velocities increase with increasing δ at the beginning initially (δ < 1), after which they tend toward asymptotic solutions as δ = 1. The hyperslip velocity ratio (Wh/Uh) shows that longitudinal ridges are at least twice as effective as transverse ridges in enhancing the ice hyperslip velocity, with the velocities accounting for more than 60% of the ice sliding velocities for arbitrary θ at a = 0.95 and δ = 0.1. The relative deviations between the numerical and asymptotic solutions are less than 5% at δ = 1, with the maximum relative deviation occurring at a = 0.65 for arbitrary θ. [ABSTRACT FROM AUTHOR]

This paper is concerned with recovering the solution of a final value problem associated with a parabolic equation involving a non linear source and a non-local term, which to the best of our knowledge has not been studied earlier. It is shown that the considered problem is ill-posed, and thus, some regularization method has to be employed in order to obtain stable approximations. In this regard, we obtain regularized approximations by solving some non linear integral equations which is derived by considering a truncated version of the Fourier expansion of the sought solution. Under different Gevrey smoothness assumptions on the exact solution, we provide parameter choice strategies and obtain the error estimates. A key tool in deriving such estimates is a version of Grönwalls' inequality for iterated integrals, which perhaps, is proposed and analysed for the first time. [ABSTRACT FROM AUTHOR]

Integer linear programming (ILP) is often used to model and solve real-life problems. In practice, alternative solutions are very useful as they significantly increase flexibility for the decision-maker. In this study, an alternative method based on parameterization obtained from the Diophantine equation is developed to find all alternative solutions to ILP problems, and an easy-to-implement, efficient, and reliable algorithm is presented. The proposed method was used without being affected by the number of variables and constraints in the problem. Numerical examples are presented to demonstrate the usefulness of the proposed method. In addition, these examples are coded in the MAPLE programming language according to the proposed algorithm. [ABSTRACT FROM AUTHOR]

This study aims to explore the spatial distribution of false kelpfish (Sebastiscus marmoratus) in the mussel farming area, artificial reef areas of Gouqi Island (Shengsi, China), and natural areas using eDNA detection methods. Surface and bottom water samples were collected at 12 stations in November 2022 and April 2023, totaling 52 samples. We used species-specific primers and probes for quantitative PCR (qPCR) detection of Sebastiscus marmoratus eDNA. The eDNA concentrations differed seasonally (p < 0.05) and did not differ (p > 0.05) among the three sampling areas and two water layers. The greatest eDNA concentrations occurred in the surface layer during the spring. Higher concentrations of Sebastiscus marmoratus eDNA were also found in the mussel aquaculture area. Temperature exhibited a significant positive correlation with Sebastiscus marmoratus eDNA concentration (p < 0.05). Additionally, we developed linear equations predicting the relationship between environmental factors and environmental factors, providing a reference for future fishery resource surveys. [ABSTRACT FROM AUTHOR]

The article studies quantitative characteristics of the mechanism of excitation of VLF chorus emissions by analyzing high-resolution data from the Van Allen Probes. A typical example of chorus with spectral forms in the lower frequency band (below half of the electron cyclotron frequency) in the region of the local minimum of the magnetic field behind the plasmapause in the middle magnetosphere is presented. A new method of analysis of quasi-harmonic signals recorded with high digitization frequency is proposed and implemented by the example of chorus in the lower frequency band. The results of wave field measurements in a high-resolution data channel are presented in the form of a rectangular event matrix, each row of which corresponds to one cycle of the wave process. In the event matrix, the rows corresponding to the fragments of the implementation that characterize the natural source of short electromagnetic pulses are selected. This made it possible to determine the complex eigenvalues of the characteristic equation of the source at the linear stage of chorus excitation. The values of the roots of the characteristic equation obtained by analyzing the data of chorus observations correspond to the implementation of chorus excitation by the amplification of noise electromagnetic pulses in a planar densification waveguide. [ABSTRACT FROM AUTHOR]

We use a recently proposed scheme of matrix extension of dispersionless integrable systems in the Abelian case, leading to linear equations related to the original dispersionless system. In the examples considered, these equations can be interpreted in terms of Abelian gauge fields on the geometric background defined by a dispersionless system. They are also connected with the linearization of the original systems. We construct solutions of these linear equations in terms of wave functions of the Lax pair for the dispersionless system, which is represented in terms of some vector fields. [ABSTRACT FROM AUTHOR]

Summary: We provide a simple recursive method for generating the finite sum of whole number powers of integers. Given that we know only the formula for the sum with power p – 1, this method generates the formula for the sum with power p by a simple polynomial integration and a solution to a linear equation in one variable. This method makes no use of Bernoulli's equation or Bernoulli numbers in either its implementation or justification. [ABSTRACT FROM AUTHOR]

We study point-line configurations through the lens of projective geometry and matroid theory. Our focus is on their realization spaces, where we introduce the concepts of liftable and quasi-liftable configurations, exploring cases in which an n-tuple of collinear points can be lifted to a nondegenerate realization of a point-line configuration. We show that forest configurations are liftable and characterize the realization space of liftable configurations as the solution set of certain linear systems of equations. Moreover, we study the Zariski closure of the realization spaces of liftable and quasi-liftable configurations, known as matroid varieties, and establish their irreducibility. Additionally, we compute an irreducible decomposition for their corresponding circuit varieties. Applying these liftability properties, we present a procedure to generate some of the defining equations of the associated matroid varieties. As corollaries, we provide a geometric representation for the defining equations of two specific examples: the quadrilateral set and the 3 × 4 grid. While the polynomials for the latter were previously computed using specialized algorithms tailored for this configuration, the geometric interpretation of these generators was missing. We compute a minimal generating set for the corresponding ideals. [ABSTRACT FROM AUTHOR]

Numerical models based on seepage-deformation coupling governing equations are often used to simulate soil hydrodynamics and deformation in unsaturated porous media. Among them, Picard iteration method with pressure head as the main variable is widely used because of its simplicity and ability to deal with partial saturation conditions. It is well known that the method is prone to convergence failure under some unfavorable flow conditions and is also computationally time-consuming. In this study, the soil–water characteristic curve (SWCC) of unsaturated soil described by the exponential function is used to linearize the coupling equations to overcome the repeated assembly of nonlinear ordinary differential equations. The finite element method with six-node triangular element is used to discretely linearize the coupling governing equations. Further, the classical Gauss–Seidel iterative method (GS) can be used to solve the linear equations generated from the linearized coupling equations. However, the convergence rate of GS seriously restricts the ill-condition of the linear equations, especially when the condition number of linear equations is much larger than 1.0. Thus, we propose an improved Gauss–Seidel iterative methods MP(m)-GSCMGI by combining multistep preconditioning and cascadic multigrid. The applicability of the proposed methods in simulating variably saturated flow and deformation in unsaturated porous media is verified by numerical examples. The results show that the proposed improved methods have faster convergence rate and computational efficiency than the conventional Picard and GS. The hybrid improved method MP(m)-GSCMGI can achieve more robust convergence and economical simulation. [ABSTRACT FROM AUTHOR]

Abstract\nHIGHLIGHTSThree-dimensional orthogonal woven composites (3DOWC) can be widely used in various industries, including aerospace, automotive and military. This research examines the linear free vibration behavior of 3DOWC, focusing on the effects of important parameters, such as thickness, dimensional ratio, and binder fiber volume fraction under different boundary conditions. To achieve this, Ritz theory is utilized to calculate the natural frequency of the system. First, the governing equations for the linear free vibrations of 3DOWC are derived. After forming the energy function of the system and minimizing it, the frequency equations of the system are obtained.The equations of motion were derived using energy relations and solved by Ritz method.Increasing the plate thickness led to reduction in natural frequency.Increase in plate length resulted decrease in natural frequency.Reducing the fiber density in the binder layer led to reduction in natural frequency.Four edges clamped boundary conditions, exhibited the highest natural frequency. [ABSTRACT FROM AUTHOR]