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A number of previous papers have used the coupled-mode method to assess three-dimensional scattering by cylindrically symmetric anomalies (seamounts, hills) or anomalies which are invariant in a horizontal direction (wedges, ridges). This paper makes an extension to combinations of these two anomaly types. The upper and lower depth boundaries of the anomalies may be flat or irregular, and the sound source may be anywhere in the medium. After a discretization of the anomalies of the two types with laterally homogeneous rings and strips, respectively, an adaptation of the coupled-mode method yields the solution of the pertinent Helmholtz equation. The adaptation involves a combination of Fourier-series summations to handle the ring anomalies and adaptive wavenumber integrations to handle the strip structure. For each anomaly, recursively computed reflection matrices relate the expansion coefficients for incoming and outgoing normal modes. Iterative solution of a linear equation system for the amplitudes of the scattered cylindrical waves from the ring anomalies, involving formulas for transformation between plane and cylindrical waves, yields an expansion of the field. Related expansions allow isolation of partial waves, multiply scattered among the anomalies. The paper includes examples from underwater acoustics and atmospheric acoustics. [ABSTRACT FROM AUTHOR]

The L-fractional derivative is defined as a certain normalization of the well-known Caputo derivative, so alternative properties hold: smoothness and finite slope at the origin for the solution, velocity units for the vector field, and a differential form associated to the system. We develop a theory of this fractional derivative as follows. We prove a fundamental theorem of calculus. We deal with linear systems of autonomous homogeneous parts, which correspond to Caputo linear equations of non-autonomous homogeneous parts. The associated L-fractional integral operator, which is closely related to the beta function and the beta probability distribution, and the estimates for its norm in the Banach space of continuous functions play a key role in the development. The explicit solution is built by means of Picard's iterations from a Mittag–Leffler-type function that mimics the standard exponential function. In the second part of the paper, we address autonomous linear equations of sequential type. We start with sequential order two and then move to arbitrary order by dealing with a power series. The classical theory of linear ordinary differential equations with constant coefficients is generalized, and we establish an analog of the method of undetermined coefficients. The last part of the paper is concerned with sequential linear equations of analytic coefficients and order two. [ABSTRACT FROM AUTHOR]

The numerical solution of initial-value problems (IVP) for ordinary differential equations (ODE) is at this time a mature subject, with many high-quality codes freely available. Second-order linear equations without singularities are an especially simple class of problems to solve, even more so if only a single scalar equation such as the Mathieu equation y ′ ′ + (a - 2 q cos 2 x) y = 0 is being considered. Nonetheless, the topic is not yet exhausted, and this paper considers the case of writing an efficient arbitrary-precision code for the solution of such equations. For this purpose, an implicit Hermite–Obreshkov method attains nearly spectral accuracy at a cost only polynomial in the number of bits of accuracy requested. This is interesting for the Mathieu equation in particular because the solutions can be highly oscillatory of variable frequency and be highly ill-conditioned. This paper reports on the details of the prototype Maple implementation of the method and summarizes the approximation theoretic results justifying the choice of a balanced Hermite–Obreshkov method including its backward stability and decent Lebesgue constants. This method may be of especial interest for the solution of so-called D-finite equations, for which Taylor series coefficients up to degree m are available at cost only O(m), instead of the more usual O (m 2) . This paper celebrates the happy occasion of the 90th birthday of John C. Butcher. [ABSTRACT FROM AUTHOR]

This is the second paper in a series of papers addressing the characteristic gluing problem for the Einstein vacuum equations. We solve the codimension-10 characteristic gluing problem for characteristic data which are close to the Minkowski data. We derive an infinite-dimensional space of gauge-dependent charges and a 10-dimensional space of gauge-invariant charges that are conserved by the linearized null constraint equations and act as obstructions to the gluing problem. The gauge-dependent charges can be matched by applying angular and transversal gauge transformations of the characteristic data. By making use of a special hierarchy of radial weights of the null constraint equations, we construct the null lapse function and the conformal geometry of the characteristic hypersurface, and we show that the aforementioned charges are in fact the only obstructions to the gluing problem. Modulo the gauge-invariant charges, the resulting solution of the null constraint equations is C m + 2 for any specified integer m ≥ 0 in the tangential directions and C 2 in the transversal directions to the characteristic hypersurface. We also show that higher-order (in all directions) gluing is possible along bifurcated characteristic hypersurfaces (modulo the gauge-invariant charges). [ABSTRACT FROM AUTHOR]

This paper extends the definition of the complexity factor for a charged self‐gravitating structure in the background of f(R,T)$f(\mathbf {R},\mathbf {T})$ gravity. For this purpose, the modified Einstein‐Maxwell field equations and the mass function in terms of interior charge are calculated corresponding to a static sphere. The Reissner‐Nordström exterior spacetime and match it with the spherical interior at the hypersurface to determine the junction conditions are adopted then. The curvature tensor is also decomposed orthogonally, resulting in several scalar functions. Only YTF$\mathbf {Y}_{TF}$ encompasses all the required parameters and fulfills the proposed criteria to be the complexity factor for the considered setup is noticed. Moreover, some constraints to minimize the degrees of freedom in the field equations are chosen. To achieve this, complexity‐free constraint with four additional conditions depending on the matter sector that lead to different models is employed. The stability of the developed models is also analyzed in the presence and absence of charge through the standard model R+2ξ3T$\mathbf {R}+2\xi _3\mathbf {T}$ by varying the values of the model parameter ξ3$\xi _3$. The presence of charge in compact models corresponding to Pr=0$\mathrm{P}_r=0$, a polytropic and a linear equation of state make them stable for specific values of ξ3$\xi _3$ is concluded. This paper extends the definition of the complexity factor for a charged self‐gravitating structure in the background of f (R, T) gravity. For this purpose, the modified Einstein‐Maxwell field equations and the mass function in terms of interior charge are calculated corresponding to a static sphere. The Reissner‐Nordström exterior spacetime and match it with the spherical interior at the hypersurface to determine the junction conditions are adopted then. The curvature tensor is also decomposed orthogonally, resulting in several scalar functions. Only YTF encompasses all the required parameters and fulfills the proposed criteria to be the complexity factor for the considered setup is noticed. Moreover, some constraints to minimize the degrees of freedom in the field equations are chosen. To achieve this, complexity‐free constraint with four additional conditions depending on the matter sector that lead to different models is employed. The stability of the developed models is also analyzed in the presence and absence of charge through the standard model R + 2ξ3T by varying the values of the model parameter ξ3. The presence of charge in compact models corresponding to Pr = 0, a polytropic and a linear equation of state make them stable for specific values of ξ3 is concluded. [ABSTRACT FROM AUTHOR]

Combining multiple devices for localization has important applications in the military field. This paper exploits the land-based short-wave platforms and satellites for fusion localization. The ionospheric reflection height error and satellite position errors have a great impact on the short-wave localization and satellite localization accuracy, respectively. In this paper, an iterative constrained weighted least squares (ICWLS) algorithm is proposed for these two kinds of errors. The algorithm converts the nonconvex equation constraints to linear constraints using the results of the previous iteration, thus ensuring convergence to the globally optimal solution. Simulation results show that the localization accuracy of the algorithm can reach the corresponding Constrained Cramér–Rao Lower Bound (CCRLB). Finally, the localization results of the two methods are fused using Kalman filtering. Simulations show that the fused localization accuracy is improved compared to the single-means localization. [ABSTRACT FROM AUTHOR]

In this paper, we would like to consider the Cauchy problem for semilinear σ$$ \sigma $$‐evolution equations with time‐dependent damping for any σ≥1$$ \sigma \ge 1 $$. Motivated strongly by the classification of damping terms in some previous papers, the first main goal of the present work is to make some generalizations from σ=1$$ \sigma =1 $$ to σ>1$$ \sigma >1 $$ and simultaneously to investigate decay estimates for solutions to the corresponding linear equations in the so‐called effective damping cases. For the next main goals, we are going not only to prove the global well‐posedness property of small data solutions but also to indicate blow‐up results for solutions to the semilinear problem. In this concern, the novelty which should be recognized is that the application of a modified test function combined with a judicious choice of test functions gives blow‐up phenomena and upper bound estimates for lifespan in both the subcritical case and the critical case, where σ$$ \sigma $$ is assumed to be any fractional number. Finally, lower bound estimates for lifespan in some spatial dimensions are also established to find out their sharp results. [ABSTRACT FROM AUTHOR]

We consider general classes of Euler type linear and half‐linear difference equations, which are conditionally oscillatory. Applying the adapted Riccati technique, we improve known oscillation criteria for these equations. More precisely, our presented main criterion is the full oscillatory counterpart of a non‐oscillation criterion. Thus, in this paper, we enlarge the set of conditionally oscillatory Euler type difference equations. We highlight that our results are new even for linear equations with periodic coefficients. This fact is documented by simple examples of such equations at the end of this paper. [ABSTRACT FROM AUTHOR]

With its complex nonlinear dynamic behavior, the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression, and has attracted a lot of attention. In this paper, an asymmetric tristable design is proposed to improve the vibration suppression efficiency of nonlinear energy sinks (NESs) for the first time. The proposed asymmetric tristable NES (ATNES) is composed of a pair of oblique springs and a vertical spring. Then, the three stable states, symmetric and asymmetric, can be achieved by the adjustment of the distance and stiffness asymmetry of the oblique springs. The governing equations of a linear oscillator (LO) coupled with the ATNES are derived. The approximate analytical solution to the coupled system is obtained by the harmonic balance method (HBM) and verified numerically. The vibration suppression efficiency of three types of ATNES is compared. The results show that the asymmetric design can improve the efficiency of vibration reduction through comparing the chaotic motion of the NES oscillator between asymmetric steady states. In addition, compared with the symmetrical tristable NES (TNES), the ATNES can effectively control smaller structural vibrations. In other words, the ATNES can effectively solve the threshold problem of TNES failure to weak excitation. Therefore, this paper reveals the vibration reduction mechanism of the ATNES, and provides a pathway to expand the effective excitation amplitude range of the NES. [ABSTRACT FROM AUTHOR]

In this paper, the author investigates particular disconjugate even‐order linear difference equations with two terms and classify them based on the properties of their recessive solutions at plus and minus infinity. The main theorem described states that the studied equation is (k−p+1)$(k-p+1)$‐critical whenever a specific second‐order linear difference equation is p$p$‐critical. In the proof, the author derived closed‐form solutions for the studied equation wherein the solutions of the said second‐order equation appear. Furthermore, the solutions were organized, in order to determine recessive solutions, into a linear chain by sequence ordering that compares the solutions at ±∞$\pm \infty$. [ABSTRACT FROM AUTHOR]

Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to select a meaningful solution is to introduce a regularizer. While for most applications the regularizer is convex, in many cases it is neither smooth nor strongly convex. In this paper, we propose and study two new iterative regularization methods, based on a primal-dual algorithm, to regularize inverse problems efficiently. Our analysis, in the noise free case, provides convergence rates for the Lagrangian and the feasibility gap. In the noisy case, it provides stability bounds and early stopping rules with theoretical guarantees. The main novelty of our work is the exploitation of some a priori knowledge about the solution set: we show that the linear equations determined by the data can be used more than once along the iterations. We discuss various approaches to reuse linear equations that are at the same time consistent with our assumptions and flexible in the implementation. Finally, we illustrate our theoretical findings with numerical simulations for robust sparse recovery and image reconstruction. We confirm the efficiency of the proposed regularization approaches, comparing the results with state-of-the-art methods. [ABSTRACT FROM AUTHOR]

F-concavity is a generalization of power concavity and, actually, the largest available generalization of the notion of concavity. We characterize the F-concavities preserved by the Dirichlet heat flow in convex domains on {\mathbb R}^n, and complete the study of preservation of concavity properties by the Dirichlet heat flow, started by Brascamp and Lieb in 1976 and developed in some recent papers. More precisely, we discover hot-concavity, which is the strongest F-concavity preserved by the Dirichlet heat flow; we show that log-concavity is the weakest F-concavity preserved by the Dirichlet heat flow; quasi-concavity is also preserved only for n=1; we prove that if F-concavity is strictly weaker than log-concavity and n\ge 2, then there exists an F-concave initial datum such that the corresponding solution to the Dirichlet heat flow is not even quasi-concave, hence losing any reminiscence of concavity. Furthermore, we find a sufficient and necessary condition for F-concavity to be preserved by the Dirichlet heat flow. We also study the preservation of concavity properties by solutions of the Cauchy–Dirichlet problem for linear parabolic equations with variable coefficients and for nonlinear parabolic equations such as semilinear heat equations, the porous medium equation, and the parabolic p-Laplace equation. [ABSTRACT FROM AUTHOR]

In this paper, we for the first time prove local solvability and stability of the inverse Sturm‐Liouville problem with complex‐valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The proof method is constructive. It is based on the reduction of the inverse problem to a linear equation in the Banach space of bounded infinite sequences. We prove that, under a small perturbation of the spectral data, the main equation of the inverse problem remains uniquely solvable. Furthermore, we derive new reconstruction formulas for obtaining the problem coefficients from the solution of the main equation and get stability estimates for the recovered coefficients. [ABSTRACT FROM AUTHOR]

The optimal control problems of degenerate parabolic equations have many applications in economics, physics, climatology, and so on. Motivated by the applications, we consider the optimal control problems of a class of nonlinear degenerate parabolic equations in this paper. The main result is that we deduce the first order necessary condition for the optimal control problem of nonlinear degenerate parabolic equations by variation method. Moreover, we investigate the uniqueness of the solutions to the optimal control problems. For the linear equations, we obtain the global uniqueness, while for the nonlinear equations, we obtain only the local uniqueness. Finally, we give a numerical example to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper we construct new families of extremal copositive matrices in arbitrary dimension by an algorithmic procedure. Extremal copositive matrices are organized in relatively open subsets of real-algebraic varieties, and knowing a particular such matrix A allows in principle to obtain the variety in which A is embedded by solving the corresponding system of algebraic equations. We show that if A is a matrix associated to a so-called COP-irreducible graph with stability number equal 3, then by a trigonometric transformation these algebraic equations become linear and can be solved by linear algebra methods. We develop an algorithm to construct and solve the corresponding linear systems and give examples where the variety contains singularities at the initial matrix A. For the cycle graph C 7 we completely characterize the part of the variety which consists of copositive matrices. [ABSTRACT FROM AUTHOR]

This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each sub-iterate is minimized over a certain two-dimensional subspace. Convergence properties of the proposed method are studied in detail. The approach is further developed to solve (regularized) normal equations arising from the discretization of ill-posed problems. The results of numerical experiments are reported to illustrate the performance of exact and inexact variants of the method on several test problems from different application areas. [ABSTRACT FROM AUTHOR]

Line structured light (LSL) measurement systems can obtain high accuracy profiles, but the overall clarity relies greatly on the sampling interval of the scanning process. Photometric stereo (PS), on the other hand, is sensitive to tiny features but has poor geometrical accuracy. Cooperative measurement with these two methods is an effective way to ensure precision and clarity results. In this paper, an LSL-PS cooperative measurement system is brought out. The calibration methods used in the LSL and PS measurement system are given. Then, a data fusion algorithm with adaptive weights is proposed, where an error function that contains the 3D point cloud matching error and normal vector error is established. The weights, which are based on the angles of adjacent normal vectors, are also added to the error function. Afterward, the fusion results can be obtained by solving linear equations. From the experimental results, it can be seen that the proposed method has the advantages of both the LSL and PS methods. The 3D reconstruction results have the merits of high accuracy and high clarity. [ABSTRACT FROM AUTHOR]

Many articles have recently been devoted to Mahler equations, partly because of their links with other branches of mathematics such as automata theory. Hahn series (a generalization of the Puiseux series allowing arbitrary exponents of the indeterminate as long as the set that supports them is well ordered) play a central role in the theory of Mahler equations. In this paper, we address the following fundamental question: is there an algorithm to calculate the Hahn series solutions of a given linear Mahler equation? What makes this question interesting is the fact that the Hahn series appearing in this context can have complicated supports with infinitely many accumulation points. Our (positive) answer to the above question involves among other things the construction of a computable well‐ordered receptacle for the supports of the potential Hahn series solutions. [ABSTRACT FROM AUTHOR]

In this paper, we design a decoupled, linear, unconditionally stable and fully discrete numerical scheme for a ferrohydrodynamics system with second‐order temporal accuracy. This scheme is based on a second‐order backward difference formula for time derivative terms and linearization extrapolation for nonlinear terms, which produces a series of decoupled linear equations and solves effectively this nonlinear and multiphysical coupled system. Meanwhile, we show that the scheme is unconditionally stable. Finally, some numerical experiments are provided to verify the theoretical finding and illustrate the accuracy and efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical formulation of a transient problem for an anisotropic plate on an elastic-inertial foundation. The plate features local fixations of various types, located along its perimeter. The plate's contour can be arbitrary. It is subjected to a load with a time-varying amplitude. An original method for solving the posed problem has been developed and implemented. By applying integral transformations, a fundamental solution for an unlimited anisotropic plate has been constructed. This solution is used to formulate resolving integral representations for investigating the transient dynamics of the plate with local supports. Integral representations for transient displacements, moments, and rotation angles of the plate sections have been obtained using the method of compensating loads. The time-dependent compensating loads are determined from the solution of a system of Volterra integral equations of the first kind. By employing the quadrature method at each time step, the problem of compensating loads is reduced to solving a system of linear algebraic equations. A comparison of the obtained results with solutions derived using the finite element method is conducted. Graphical results of the calculations and an evaluation of the convergence of the proposed method are provided. [ABSTRACT FROM AUTHOR]

In this paper, we discuss an efficient spectral approach for solving a class of second kind VIEs with highly oscillatory kernels possessing the stationary point. First, we use one variable transform to convert the highly oscillatory problem into the long-time one, and then split the long-time problem into a linear system of integral equations by using a dilation approach. Next on each interval we study the characteristic of the original solution and then propose an efficient spectral-Galerkin method for solving the linear system of integral equations. We prove that the proposed algorithm requires to solve the number O (log 2 ⁡ ω) of linear algebra equations of order n + 1 and reaches the convergence order O (n − r) , where r denotes the degree of the regularity of the original solution and ω denotes the wave number. Moreover, we give the approach of computing the highly oscillatory integrals produced in the spectral-Galerkin method. At last, two numerical examples are provided to verify the efficiency of our proposed method. [ABSTRACT FROM AUTHOR]

The purpose of this study is to propose a computationally effective algorithm for the numerical evaluation of a fractional-order system of singular Lane-Emden type equations arising in physical problems. The fractional operator considered is in the sense of the Liouville-Caputo derivative. The presented matrix collocation method is based upon a combination of the quasilinearization method (QLM) and the shifted Legendre functions (SLFs) and is called QLM-SLFs method. By applying first the QLM to the nonlinear underlying system, we get a family of linear equations. Hence, a spectral matrix collocation scheme relied on the SLFs is designed to solve the resulting sequence of linear system of equations at very few iterations. The uniform convergence of the shifted Legendre expansion series solution is established. To illustrate the effectiveness of the proposed QLM-SLFs technique in the present paper, three test examples are carried out. The applicability and validity of the proposed method are testified through comparisons with the outcomes of other existing procedures in the literature. The proposed QLM-SLFs method is efficient and easy to implement. The approximation obtained by the method also converges quickly to the solutions of the underlying model problem. In comparison with available existing computational procedures, the QLM-SLFs approach shows that the use of Legendre functions together with QLM provides solutions with high accuracy and exponential convergence rate. [ABSTRACT FROM AUTHOR]

This paper employs a numerical method for the numerical treatment of the time fractional Fokker–Planck equation. This method is based on applying the spectral Petrov–Galerkin method. We utilize suitable combinations for the shifted Chebyshev polynomial of the fifth-kind as basis functions. The key idea of the suggested strategy is to transform the governed boundary-value problem into a set of linear algebraic equations using the spectral Petrov–Galerkin method. Several approaches are available to solve the resultant linear system. An in-depth investigation is conducted on the convergence and error analysis of the expansion of the shifted Chebyshev polynomial function of the fifth kind. Many examples are provided to illustrate the precision of the suggested approach. [ABSTRACT FROM AUTHOR]

Conjugate gradient (CG) methods are a popular class of iterative methods for solving linear systems of equations and nonlinear optimization problems. In this paper, a new hybrid conjugate gradient (CG) method is presented and analyzed for solving unconstrained optimization problems, where the parameter β k \beta_{k} is a convex combination of β k WYL \beta_{k}^{\mathrm{WYL}} and β k CD \beta_{k}^{\mathrm{CD}} . Under the strong Wolfe line search, the new method possesses the sufficient descent condition and the global convergence properties. The preliminary numerical results show the efficiency of our method in comparison with other CG methods. Furthermore, the proposed algorithm HWYLCD was extended to solve the problem of a mode function. [ABSTRACT FROM AUTHOR]

In this paper, we study the improved block splitting (IBS) iteration method and its accelerated variant, the accelerated improved block splitting (AIBS) iteration method, for solving linear systems of equations stemming from the discretization of the complex Helmholtz equation. We conduct a comprehensive convergence analysis and derive optimal iteration parameters aimed at minimizing the spectral radius of the iteration matrix. Through numerical experiments, we validate the efficiency of both iteration methods. [ABSTRACT FROM AUTHOR]

Benchmark instances for the unbounded knapsack problem are typically generated according to specific criteria within a given constant range R, and these instances can be referred to as the unbounded knapsack problem with bounded coefficients (UKPB). In order to increase the difficulty of solving these instances, the knapsack capacity C is usually set to a very large value. While current efficient algorithms primarily center on the Fast Fourier Transform (FFT) and (min,+)-convolution method, there is a simpler method worth considering. In this paper, based on the basic Unbounded-DP algorithm, we utilize a recent branch and bound (B&B) result and basic theory of linear Diophantine equation, and propose an improved Unbounded-DP algorithm with time complexity of O (R 4) and space complexity of O (R 3) . Additionally, the algorithm can also solve the All-capacities unbounded knapsack problem within the complexity O (R 4 + C) . In particular, the proof techniques required by the algorithm are primarily covered in the first-year mathematics curriculum, which is convenient for subsequent researchers to grasp. [ABSTRACT FROM AUTHOR]

The symmetric successive overrelaxation (SSOR) and symmetric accelerated overrelaxation (SAOR) are conventional iterative methods for solving linear equations. In this paper, novel approaches are presented by combining a splitting–linearizing method with SSOR and SAOR for solving a system of nonlinear equations. The nonlinear terms are decomposed at two sides through a splitting parameter, which are linearized around the values at the previous step, obtaining a linear equation system at each iteration step. The optimal values of parameters are determined to minimize the reciprocal of the maximal projection, which are sought in preferred ranges using the golden section search algorithm. Numerical tests assess the performance of the developed methods, namely, the optimal splitting symmetric successive over-relaxation (OSSSOR), and the optimal splitting symmetric accelerated over-relaxation (OSSAOR). The chief advantages of the proposed methods are that they do not need to compute the inverse matrix at each iteration step, and the computed orders of convergence by OSSSOR and OSSAOR are between 1.5 and 5.61; they, without needing the inner iterations loop, converge very fast with saving CPU time to find the true solution with a high accuracy. [ABSTRACT FROM AUTHOR]

Simple Summary: The metabolic profile implies simultaneous determination of carbohydrate, fat, protein, and mineral metabolism parameters as well as endocrinological parameters in the blood of cows. Blood is exposed to a variety of preanalytical factors during sampling, transport to the laboratory, and laboratory preparation for analysis, which may cause hemolysis of the sample. As hemolysis affects the values of the metabolic profile, the analyzed blood parameters may falsely increase or decrease, and the metabolic status of the cows may be misinterpreted. Preventing hemolysis is important because severe hemolysis requires discarding the sample and resampling, which is very resource-intensive. In this paper, three levels of hemolysis were determined for each blood parameter tested: (a) a hemolysis level that does not affect the values of the parameters and allows the results to be issued without restriction; (b) a hemolysis level that affects the values of the parameters but remains within the acceptable biological variability and permits the results to be issued along with a note in the form of a correction formula; and (c) a hemolysis level at which the obtained values of the parameters or the entire sample must be discarded. The results are presented graphically using interferograms, which can be easily implemented in every laboratory after validation. Hemolysis is a common cause of errors in laboratory tests as it affects blood parameters and leads to a positive or negative bias. This study aims to examine the relationship between the level of hemolysis (expressed as cell-free hemoglobin concentration, g/L) and the variability of metabolic and endocrine parameters and to determine the threshold level of hemolysis that causes an analytically and clinically significant bias for the twenty most frequently examined blood parameters in cows. Paired blood samples of 10 mL each were obtained from 30 cows. One was subjected to mechanical trauma and plasma was extracted directly from the other. Hemolyzed and non-hemolyzed samples from the same animal were mixed to obtain final samples with cell-free hemoglobin concentrations of 0, 1, 2, 4, 6, 8, and 10 g/L. Metabolic and endocrine parameters were measured in the samples and their deviation and the linear equation between the level of hemolysis and the deviation were determined. The following threshold values of hemolysis were determined, which correspond to the acceptable analytical (lower value) and clinical (upper value) levels of parameter variability: BHB 0.96 and 4.81; NEFA 0.39 and 3.31; GLU 0.38 and 3.90; ALB 1.12 and 6.11; TPROT 1.40 and 6.80; UREA 6.62 and 20.1; TBIL 0.75 and 5.65; AST 0.11 and 2.18; GGT 1.71 and 8.90, LDH 0.01 and 0.11, ALP 0.97 and 2.95; TGC 1.56 and 15.5; CHOL 1.29 and 8.56; Ca 5.68 and 25.7; P 0.57 and 8.43; Mg 1.10 and 8.47; INS 1.15 and 3.89; T3 8.19 and 15.6; T4 8.97 and 18.5; and CORT 2.78 and 11.22 g/L cell-free hemoglobin. Three decision levels are available for each metabolic and endocrine parameter: if hemolysis is below the lower (analytical) threshold value, results can be reported without restriction; if hemolysis is between the lower and upper thresholds, the results can be issued with guidance in the form of corrective linear equations; and if hemolysis is above the upper (clinical) threshold, the results and sample must be discarded. This method contributes to an optimal approach to hemolysis interference with metabolic profile parameters in blood samples from cows. [ABSTRACT FROM AUTHOR]

In this paper, we extend SMSNS [Pourbagher M, Salkuyeh DK. On the solution of a class of complex symmetric linear systems. Appl Math Lett. 2018;76:14–20.] iteration method for solving a class of complex symmetric system of linear equations. We propose a successive-overrelaxation (SOR) acceleration scheme for SMSNS (SMSNSSOR), discuss the convergence conditions of it and give the optimal parameters which make the fast convergence. Numerical results demonstrate that SMSNSSOR iteration method is feasible and effective for solving complex symmetric systems, and performs better than some other usually used iteration methods. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study a class of conformable impulsive delay differential equations (CIDDEs). We first define a conformable impulsive delayed matrix function, and construct an explicit solution for linear CIDDEs by virtue of variation of constants method. Subsequently, based on impulsive delayed Grammian matrix, we study the relative controllability for the addressed linear equations. Moreover, with the help of Krasnoselskii's fixed point theorem, relative controllability for the considered semilinear equations is proposed. Finally, two examples with numerical simulations are given to illustrate the main results. [ABSTRACT FROM AUTHOR]

The greedy block Kaczmarz (GBK) method has been successfully applied in areas such as data mining, image reconstruction, and large-scale image restoration. However, the computation of pseudo-inverses in each iterative step of the GBK method not only complicates the computation and slows down the convergence rate, but it is also ill-suited for distributed implementation. The leverage score sampling free pseudo-inverse GBK algorithm proposed in this paper demonstrated significant potential in the field of image reconstruction. By ingeniously transforming the problem framework, the algorithm not only enhanced the efficiency of processing systems of linear equations with multiple solution vectors but also optimized specifically for applications in image reconstruction. A methodology that combined theoretical and experimental approaches has validated the robustness and practicality of the algorithm, providing valuable insights for technical advancements in related disciplines. [ABSTRACT FROM AUTHOR]

The Levenberg–Marquardt (LM) method is one of the most significant methods for solving nonlinear equations as well as symmetric and asymmetric linear equations. To improve the method, this paper proposes a new adaptive LM algorithm by modifying the LM parameter, combining the trust region technique and the non-monotone technique. It is interesting that the new algorithm is constantly optimized by adaptively choosing the LM parameter. To evaluate the effectiveness of the new algorithm, we conduct tests using various examples. To extend the convergence results, we prove the convergence of the new algorithm under the Hölderian local error bound condition rather than the commonly used local error bound condition. Theoretical analysis and numerical results show that the new algorithm is stable and effective. [ABSTRACT FROM AUTHOR]

Causal discovery is central to human cognition, and learning directed acyclic graphs (DAGs) is its foundation. Recently, many nature-inspired meta-heuristic optimization algorithms have been proposed to serve as the basis for DAG learning. However, a single meta-heuristic algorithm requires specific domain knowledge and empirical parameter tuning and cannot guarantee good performance in all cases. Hyper-heuristics provide an alternative methodology to meta-heuristics, enabling multiple heuristic algorithms to be combined and optimized to achieve better generalization ability. In this paper, we propose a multi-population choice function hyper-heuristic to discover the causal relationships encoded in a DAG. This algorithm provides a reasonable solution for combining structural priors or possible expert knowledge with swarm intelligence. Under a linear structural equation model (SEM), we first identify the partial v-structures through partial correlation analysis as the structural priors of the next nature-inspired swarm intelligence approach. Then, through partial correlation analysis, we can limit the search space. Experimental results demonstrate the effectiveness of the proposed methods compared to the earlier state-of-the-art methods on six standard networks. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of quasi-periodic response solutions (i.e., solutions that are quasi-periodic with the same frequencies as forcing term) for a class of forced reversible wave equations with derivative nonlinearity. The forcing frequency ω ∈ R 2 would be Liouvillean which is weaker than the usual Diophantine and Brjuno conditions. The derivative nonlinearity in the equation also leads to some difficulty in measure estimate. To overcome it, we also use the Töplitz–Lipschitz property of vector field. The proof is based on an infinite dimensional Kolmogorov–Arnold–Moser theorem for reversible systems. [ABSTRACT FROM AUTHOR]

In this paper, we use the parabolized stability equations (PSEs) to investigate heat effects on supersonic jet screech. The PSE is derived from the linear Euler equations, and the computations are performed on an empirical mean flow profile. Employing PSE, we can examine several important characteristics of the shear-layer instability waves, including the convection velocity, the growth rate, and the location where the instability waves attain the maximal total amplification. Equipped with these knowledge, we further explore their impacts on the jet screech. Specifically, using a newly proposed iteration scheme, we first identify a more suitable convective Mach number to predict the screech frequency in both heated and cold jets. Second, we find that the transition of the screech mode from the axisymmetric to the helical mode may be explained by the shift in the most amplified instability modes. Using this criterion, we can predict a transition Mach number for the mode staging. Third, by assuming that the effective source location is the position where the instability wave attains its maximal amplitude and using the newly obtained convective Mach number, we can predict the screech mode staging in cold and heated jets using Gao's model. The predictions agree well with the experimental data. Finally, we investigate the heat effects on screech amplitude. It is found that compared to cold jets, the difference between the frequency of the most amplified instability wave and the frequency of the jet screech is much bigger in heated jets, which may lead to a lower screech amplitude. [ABSTRACT FROM AUTHOR]

A key challenge in causal inference from observational studies is the identification and estimation of causal effects in the presence of unmeasured confounding. In this paper, we introduce a novel approach for causal inference that leverages information in multiple outcomes to deal with unmeasured confounding. An important assumption in our approach is conditional independence among multiple outcomes. In contrast to existing proposals in the literature, the roles of multiple outcomes in the conditional independence assumption are symmetric; hence, the name parallel outcomes. We show nonparametric identifiability with at least three parallel outcomes and provide parametric estimation tools under a set of linear structural equation models. Our proposal is evaluated through a set of synthetic and real data analyses. [ABSTRACT FROM AUTHOR]

In this paper, we focus on solving the generalized absolute value equations (GAVE). We present a new method named as modulus-based block triangular splitting iteration (MBTS) method based on the block matrix structure resulting from the transformation of the GAVE into two equations. This method is developed by decomposing the matrix into diagonal and triangular matrices, as well as applying a series of suitable combination and modification techniques. The advantage of the MBTS method is that it is not necessary to solve the inverse of the coefficient matrix of the linear equation system during each iteration, which greatly improves the computational speed and reduces its storage requirements. In addition, we present some convergent theorems proving by different techniques and the estimate of the required number of iteration steps. Furthermore, in the accompanying corollaries, we provide some estimations for choosing appropriate parameter values. Finally, we validated the effectiveness and efficiency of our newly developed method through two numerical examples of the GAVE. [ABSTRACT FROM AUTHOR]

This paper considers model order reduction based on low-rank decomposition of the cross Gramian for linear systems. The proposed approach uses the low-rank factors of the cross Gramian to generate approximate balanced model for the large-scale system. Then, the reduced-order model is obtained by truncating the states corresponding to the small approximate Hankel singular values. The low-rank factors are directly constructed from the expansion coefficients of impulse responses in the space spanned by Legendre polynomials by solving block tridiagonal linear systems. In contrast to balanced truncation related approaches which require to solve Sylvester equation to compute the full cross Gramian, the proposed method needs to solve sparse linear equations, and only one singular value decomposition is applied to a low-dimensional matrix. The stability preservation of the reduced model is briefly discussed. And in combination with the dominant subspace projection method, the reduction procedure is modified to alleviate the shortcoming, which may unexpectedly lead to unstable systems even though the original one is stable. Finally, numerical experiments are given to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Intensity inhomogeneity (IIH) and noise are ubiquitous in images acquired by a variety of imaging modalities, which pose an ongoing challenge for segmentation methods used in many applications. This paper proposes a level set evolution equation based on fractional derivative to address the IIH and noise issues in image segmentation, which integrates the information from the input and guidance images. The proposed model is a linear diffusion equation of level set function with nonlinear edge-stopping and guidance sources, in which the edge-stopping source is derived from the input image and a local statistical model (Bayesian formulation) in the level set framework, whereas the guidance source is derived from the guidance image and the fitting term of the popular Chan-Vese model. The guidance source ensures swift contour movement toward the boundary of the objects and enhances the robustness to noise and contour initialization, while the edge-stopping source is used to stop the evolving contour on the boundary of the objects later in the evolution. To tackle the challenge of obtaining accurate guidance images for many applications, an adaptive variable-order of fractional derivative robust to IIH and noise is introduced to generate the desired guidance image from the input image. The proposed diffusion equation with sources is solved numerically by the series splitting method and finite difference scheme. Experimental results on synthetic and real images show that the proposed model has higher performance in terms of accuracy and efficiency of segmentation, compared to several state-of-the-art level set models. • Propose guided active contours via level set evolution for noisy images with intensity inhomogeneity (IIH). • Design an adaptive order of fractional derivative that is basically not affected by IIH and noise. • Present a fractional derivative based method for generating guidance image from the input image. • Our model is experimentally very effective and efficient in segmenting images with IIH and noise. [ABSTRACT FROM AUTHOR]

This paper consists of two parts. The first one deals with the generation of an iterative algorithm to obtain an approximate solution of a linear equation of the second kind in a Banach space. This generation is based on a perturbed version of the geometric series theorem which, in particular, allows us to find a family of unisolvent linear Fredholm integral equations of the second kind, even when the associated linear operator has norm greater than or equal to 1. When we consider Fredholm equations of this type and linear Volterra integral equations of second kind, the numerical schemes obtained when appropriate Schauder bases are also introduced in the spaces where the equations operate, enable us to approximate their respective solutions iteratively. The second part of this work focuses on the design of a numerical method for solving an inverse problem associated with a linear equation of the second kind in a Banach space, a method which we apply to problems of parameter estimation related to the two classes of integral equations mentioned above. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the chaos in the Duffing equation with negative linear stiffness and a fractional damping term given by a Caputo fractional derivative of order α ranging from 0 to 2. We use two different numerical methods to compute the solutions, one of them new. We discriminate between regular and chaotic solutions by means of the attractor in the phase space and the values of the Lyapunov Characteristic Exponents. For this, we have extended a linear approximation method to this equation. The system is very rich with distinct behaviours. In the limits α to 0 or α to 2, the system tends to basically the same undamped system with a behaviour clearly different from the classical Duffing equation. [ABSTRACT FROM AUTHOR]

We consider the limit of solutions of scaled linear kinetic equations with a reflection-transmission-killing condition at the interface. Both the coefficient describing the probability of killing and the scattering kernel degenerate. We prove that the long-time, large-space limit is the unique solution of a version of the fractional in space heat equation that corresponds to the Kolmogorov equation for a symmetric stable process, which is reflected, or transmitted while crossing the interface and is killed upon the first hitting of the interface. The results of the paper are related to the work in Komorowski et al. (Ann Prob 48:2290–2322, 2020), where the case of a non-degenerate probability of killing has been considered. [ABSTRACT FROM AUTHOR]

LU and Cholesky matrix factorization algorithms are core subroutines used to solve systems of linear equations (SLEs) encountered when solving an optimization problem. Standard floating-point algorithms are highly efficient but remain susceptible to the accumulation of round-off errors, which can lead solvers to return feasibility and optimality claims that are actually invalid. This paper introduces a novel direct solution approach for solving sequences of closely related SLEs encountered in nonlinear programming efficiently and without round-off errors. Specifically, it introduces rank-one update algorithms for the round-off error–free factorization framework, a tool set built on integer-preserving arithmetic that has led to the development and implementation of extremely reliable subroutines for solving SLEs occurring in linear programming. The formal guarantees of the presented algorithms are established through the derivation of theoretical insights. Their advantages are supported with computational experiments, which demonstrate upward of 75× improvements over exact factorization runtimes on fully dense matrices with more than one million entries. A significant advantage of the featured integer-preserving framework is that the length of any matrix coefficient produced by its algorithms is bounded polynomially in the size of the inputs without having to resort to greatest common divisor operations, which are required by and thereby hinder an efficient implementation of exact rational arithmetic approaches. History: Accepted by Antonio Frangioni, Area Editor for Design & Analysis of Algorithms–Continuous. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2021.0331) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2021.0331). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

This paper concern to determine a local energy decay estimate for synchronizable solutions of a coupled system of linear wave equations. Here, it is shown that the energy for such solutions decays at a rate of t−n$$ {t}^{-n} $$ (n$$ n $$ is the space dimension) when the coupling matrix satisfy the positive C1$$ {C}_1 $$‐compatibility condition. [ABSTRACT FROM AUTHOR]