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The topology of a polymer profoundly influences its behavior. However, its effect on imbibition dynamics remains poorly understood. In the present work, capillary filling (during imbibition and following full imbibition) of star polymer melts was investigated by molecular dynamics simulations with a coarse-grained model. The reversal of imbibition dynamics observed for linear-chain systems was also present for star polymers. Star polymers with short arms penetrate slower than the prediction of the Lucas–Washburn equation, while systems with long arms penetrate faster. The radius of gyration increases during confined flow, indicating the orientation and disentanglement of arms. In addition, the higher the functionality of the star polymer, the more entanglement points are retained. Besides, a stiff region near the core segments of the stars is observed, which increases in size with functionality. The proportion of different configurations of the arms (e.g., loops, trains, tails) changes dramatically with the arm length and degree of confinement but is only influenced by the functionality when the arms are short. Following full imbibition, the different decay rates of the self-correlation function of the core-to-end vector illustrate that arms take a longer time to reach the equilibrium state as the functionality, arm length, and degree of confinement increase, in agreement with recent experimental findings. Furthermore, the star topology induces a stronger effect of adsorption and friction, which becomes more pronounced with increasing functionality. [ABSTRACT FROM AUTHOR]

Approximation properties of multivariate quasi-projection operators Q j (f , Φ , Φ ̃) generated by vectors of compactly supported functions Φ , Φ ̃ are studied. Error estimates in L 2 -norm are obtained for a wide class of such operators. For refinable function vectors Φ , Φ ̃ quasi-projection operators are related to dual multiwavelet systems. Although the general scheme for the construction of dual multiwavelet frames in the multivariate case is known, its realization in practice is a difficult task because of the necessity of providing some additional properties. The notion of frame-like multiwavelets is a relaxed version of multiwavelet frames. Frame-like multiwavelets retain frame-type decompositions waiving the usual frame condition. This simplifies the problem of frame-like multiwavelets construction. Approximation properties of frame-like multiwavelets are established. Algorithms for constructing frame-like multiwavelets with the desired approximation order are suggested. [ABSTRACT FROM AUTHOR]

When scanning a document printed on both sides by using an electronic scanner, the printed material on the back (front) side may be transmitted to the front (back) side. This phenomenon is called show-through. The problem to remove the show-through from scanned images is called the show-through removal in the literature. In this paper, we propose a new method of show-through removal based on the following principle. The proposed method uses two scanned images with the front side and with the back side as input images. The proposed method is based on Ahmed's Blind Image Deconvolution method discovered in 2013, which succeeded in formulating Blind Image Deconvolution as a nuclear norm minimization. Since the structure of show-through removal resembles that of Blind Image Deconvolution, we discovered that the show-through removal can be reformulated into a nuclear norm minimization in the space of outer product matrix constructed from an image vector and a point spread function vector of blurring. Using this key idea, we constructed the proposed method as follows. First, our cost function consists of the following three terms. The first term is the data term and the second term is the nuclear norm derived from the above reformulation. The third term is a regularization term to overcome the underdetermined nature of show-through removal problem and the existence of noise in the measured images. The regularization term consists of Total Variation imposed on the images. The resulting nuclear norm minimization problem is solved by using Accelerated Proximal Gradient method and Singular Value Projection with some problem-specific modifications, which converges fast and requires a simple implementation. We show results of simulation studies as well as results of real image experiments to demonstrate the performances of the proposed method. [ABSTRACT FROM AUTHOR]

This article introduces the functional tensor singular value decomposition (FTSVD), a novel dimension reduction framework for tensors with one functional mode and several tabular modes. The problem is motivated by high-order longitudinal data analysis. Our model assumes the observed data to be a random realization of an approximate CP low-rank functional tensor measured on a discrete time grid. Incorporating tensor algebra and the theory of reproducing kernel Hilbert space (RKHS), we propose a novel RKHS-based constrained power iteration with spectral initialization. Our method can successfully estimate both singular vectors and functions of the low-rank structure in the observed data. With mild assumptions, we establish the non-asymptotic contractive error bounds for the proposed algorithm. The superiority of the proposed framework is demonstrated via extensive experiments on both simulated and real data. for this article are available online. [ABSTRACT FROM AUTHOR]

Summary: The problem of interval observer design for systems described by nonlinear models with uncertainties is considered. The problem is solved based on special mathematical technique (the algebra of functions) which allows obtaining solution for systems containing non‐smooth nonlinearities. The relations to design interval observer insensitive or having minimal sensitivity to the disturbance and estimating the prescribed nonlinear function of the state vector of the original system are derived. Theoretical results are illustrated by example. [ABSTRACT FROM AUTHOR]

In this paper we investigate the effect of a topological defect, such as a screw dislocation in an α - T 3 Aharonov–Bohm quantum ring and scrutinized the effects of an external transverse magnetic field and Rashba spin-orbit coupling therein. The screw dislocation yields an effective flux which reshape the periodic oscillations in the persistent current in both charge and spin sectors, with a period equal to one flux quantum. Moreover, they suffer a phase shift proportional to the degree of dislocation, and include scattering effects due to the dislocation present in the system. Such tunable oscillation of the spin persistent current highlights applications of our system as potential spintronic devices. Further, the behaviour of the current induced by the Burgers vector ( b z ) which denotes the strength of the dislocation is investigated in the absence and presence of an external magnetic field. In both the scenarios, an almost linear decrease in the current profile as a function of the Burgers vector is observed. Notably, without the external magnetic field, the Burgers current suffers a back flow for α = 1 (dice lattice), while in the presence of the external magnetic field, for other values of α (e.g., α = 0.5 ) this back flow occurs for a specific value of b z . Additionally, the presence of the distortion induces a chirality effect, giving rise to an additional chiral current even in the absence of an external field. Furthermore, in the absence of field, the Burgers spin current initially rises, attains a maximum before diminishing as b z is enhance for all values of α . However, such a non-monotonicity in the Burgers spin current is conspicuously non-existent in the presence of an external field. The chiral current discussed above may hold important applications to spintronics. [ABSTRACT FROM AUTHOR]

We present existing results and properties for the solutions of some vector equilibrium problems with set-valued functions in the case of a vector space ordered by a cone with some "interiority" properties. Some applications concerning the existence of equilibrium for abstract economies and vector optimization problems are given. [ABSTRACT FROM AUTHOR]

The paper studies quasilinear interpolation by minimal splines constructed on nonuniform grids with multiple nodes. Asymptotic representations for normalized splines are obtained. The sharpness of biorthogonal approximation and the order of accuracy of quasilinear interpolation with respect to the grid stepsize are established. Results of numerical experiments on approximating some test functions, which demonstrate the effect of choosing a generating vector function in constructing the corresponding minimal spline, are presented. [ABSTRACT FROM AUTHOR]

Cut-generating linear programs (CGLPs) play a key role as a separation oracle to produce valid inequalities for the feasible region of mixed-integer programs. When incorporated inside branch-and-bound, the cutting planes obtained from CGLPs help to tighten relaxations and improve dual bounds. However, running the CGLPs at the nodes of the branch-and-bound tree is computationally cumbersome due to the large number of node candidates and the lack of a priori knowledge on which nodes admit useful cutting planes. As a result, CGLPs are often avoided at default settings of branch-and-cut algorithms despite their potential impact on improving dual bounds. In this paper, we propose a novel framework based on machine learning to approximate the optimal value of a CGLP class that determines whether a cutting plane can be generated at a node of the branch-and-bound tree. Translating the CGLP as an indicator function of the objective function vector, we show that it can be approximated through conventional data classification techniques. We provide a systematic procedure to efficiently generate training data sets for the corresponding classification problem based on the CGLP structure. We conduct computational experiments on benchmark instances using classification methods such as logistic regression. These results suggest that the approximate CGLP obtained from classification can improve the solution time compared with that of conventional cutting plane methods. Our proposed framework can be efficiently applied to a large number of nodes in the branch-and-bound tree to identify the best candidates for adding a cut. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoc.2022.0241. [ABSTRACT FROM AUTHOR]

This note contains reflections on a type of factorization that came up in the work of analytic operator valued functions by I.C. Gohberg and E.I. Sigal (cf. [14] , [10] , [11]). The determining characteristic of the factorizations in question is that they are obtained by the extraction of elementary factors of the form I − P + λ P where P is an idempotent in the underlying Banach algebra. It will be demonstrated here that there is a fundamental difference between the finite dimensional (matrix) case and the situation where infinite dimensional Banach algebras are taken into consideration. [ABSTRACT FROM AUTHOR]

In the framework of the first-order differential structure introduced by Gigli, we obtain a Gauss–Green formula on regular bounded open sets in doubling metric measure spaces supporting a weak Poincaré inequality, valid for BV functions and vector fields with integrable divergence. Then, we study least gradient functions in metric measure spaces and provide an Euler–Lagrange-type formulation of the least gradient problem, using this formula as the main tool. [ABSTRACT FROM AUTHOR]

This article concentrates on the fixed‐time synchronization (FTS) and energy cost (EC) problems of delayed coupled neural networks (NNs). A switching controller is proposed and some sufficient conditions are advanced to ensure FTS of delayed coupled NNs based on the comparison theorem. Following that, the required EC is estimated during the control process. The main results of FTS and EC for considered NNs are obtained based on the Lyapunov functions in the sense of vector 1‐norm, 2‐norm, and ∞$$ \infty $$‐norm, respectively. Under the same controller parameters, this article shows that the minimum estimation of settling time and EC are sometimes not in one norm sense. Finally, numerical examples are given to show the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

Equatorial Kelvin waves (KWs) are associated with a variety of equatorial atmospheric phenomena, namely, tropical convection, cloud and precipitation variability, tropical cyclogenesis, the onset of monsoon season over Africa and India, and even the quasi‐biennial oscillation and the Madden–Julian oscillation. As such, if operational forecasts are to improve near the Tropics, it is important that they correctly represent KWs. This article aims at developing a novel methodology for identifying KWs in real‐time operational forecasts at specific longitudes using only the meridional structures of the solutions to the free Laplace tidal equations, known as Hough vector functions. The main advantages of this newly proposed methodology are that (a) it can identify KWs at a specific longitude and (b) very low computational cost is needed to apply it to real‐time operational forecasts. The application of the method to 2015–2017 European Centre for Medium‐range Weather Forecasts (ECMWF) analysis and operational forecast data reveals a systematic bias in the representation of KWs by the ECMWF operational forecast model. [ABSTRACT FROM AUTHOR]

In this paper, we study a nonlinear scalarization function for a variable domination structure in an arbitrary linear space without assuming any particular topology. Conditions are provided under which the nonlinear scalarization function possesses several useful properties such as finiteness, properness, positive homogeneity, subadditivity, (strict) monotonicity, convexity or continuity. These properties are employed to characterize approximate efficiency in linear spaces. [ABSTRACT FROM AUTHOR]

Detailed deterministic derivation of kinetic equations for relativistic plasmas is given. Focus is made on the dynamic of one-coordinate distribution functions of various tensor dimensions, but the closed set of kinetic equations is constructed of three functions: the scalar distribution function, the vector distribution function of dipole moment, and the vector distribution function of velocity (or the dipole moment in the momentum space). All two-coordinate distribution functions are discussed as well. They are presented together with their limits existing in the self-consistent field approximation. The dynamics of the small amplitude spin-electron-acoustic waves in the dense degenerate plasmas is studied within the kinetic model. This work presents the deterministic approach to the derivation and interpretation of the kinetic equations. So, no probability is introduced during the transition from the level of individual particles to the collective functions. The problem of thermalization is not considered, but we can see that the structure of kinetic equations is kept for the system before and after thermalization. Hence, the kinetic equations can be used to approach this item. [ABSTRACT FROM AUTHOR]

We introduce the topologically twisted index for four-dimensional N = 1 gauge theories quantized on AdS 2 × S 1 . We compute the index by applying supersymmetric localization to partition functions of vector and chiral multiplets on AdS 2 × T 2 , with and without a boundary: in both instances we classify normalizability and boundary conditions for gauge, matter and ghost fields. The index is twisted as the dynamical fields are coupled to a R-symmetry background 1-form with non-trivial exterior derivative and proportional to the spin connection. After regularization, the index is written in terms of elliptic gamma functions, reminiscent of four-dimensional holomorphic blocks, and crucially depends on the R-charge. [ABSTRACT FROM AUTHOR]

An algorithm for obtaining the Chaundy-Bullard identity for a vector partition function with weight that uses computer algebra methods is proposed. To automate this process in Maple, an algorithm was developed and implemented that calculates the values of the vector partition function with weight by finding non-negative solutions of systems of linear Diophantine equations that are used to form the identities involved. The algorithm's input data is represented by the set of integer vectors that form a pointed lattice cone and by some point from this cone, and the Chaundy-Bullard identity for the vector partition function with weight is its output. The code involved is stored in the depository and is ready-to-use. An example demonstrating the algorithm's operation is given. [ABSTRACT FROM AUTHOR]

This paper discusses a type of mixed-delay quaternion-valued neural networks (QVNNs) under impulsive and stochastic disturbances. The considered QVNNs model are treated as a whole, rather than as complex-valued neural networks (NNs) or four real-valued NNs. Using the vector Lyapunov function method, some criteria are provided for securing the mean-square exponential stability of the mixed-delay QVNNs under impulsive and stochastic disturbances. Furthermore, a type of chaotic QVNNs under stochastic and impulsive disturbances is considered using a previously established stability analysis method. After the completion of designing the linear feedback control law, some sufficient conditions are obtained using the vector Lyapunov function method for determining the mean-square exponential synchronization of drive–response systems. Finally, two examples are provided to demonstrate the correctness and feasibility of the main findings and one example is provided to validate the use of QVNNs for image associative memory. [ABSTRACT FROM AUTHOR]

We propose a method for imaging in scattering media when large and diverse datasets are available. It has two steps. Using a dictionary learning algorithm the first step estimates the true Green's function vectors as columns in an unordered sensing matrix. The array data comes from many sparse sets of sources whose location and strength are not known to us. In the second step, the columns of the estimated sensing matrix are ordered for imaging using the multidimensional scaling algorithm with connectivity information derived from cross-correlations of its columns, as in time reversal. For these two steps to work together, we need data from large arrays of receivers so the columns of the sensing matrix are incoherent for the first step, as well as from sub-arrays so that they are coherent enough to obtain connectivity needed in the second step. Through simulation experiments, we show that the proposed method is able to provide images in complex media whose resolution is that of a homogeneous medium. [ABSTRACT FROM AUTHOR]

One of the quasi-Newton update formulae, namely the Davidon-Fletcher-Powell method, is crucial for resolving nonlinear programming optimization problems. In order to achieve a Newton-like condition that depends on the function values and gradient vectors at each iteration, we construct an alternative positive-definite Hessian approximation in this study. The essential theorems are established to study algorithm convergence. The proposed approach is then tested on well-known test problems and then compared to the standard DFP method. The numerical outcomes demonstrate the effectiveness of the newly developed method. [ABSTRACT FROM AUTHOR]

For the solid-on-solid (SOS) model with an external field and with spin values from the set of all integers on a Cayley tree, each (gradient) Gibbs measure corresponds to a boundary law (an infinite-dimensional vector function defined on vertices of the Cayley tree) satisfying a nonlinear functional equation. Recently some translation-invariant and height-periodic (non-normalizable) solutions to the equation are found. Here, our aim is to find non-height-periodic and non-normalizable boundary laws for the SOS model. By such a solution one can construct a non-probability Gibbs measure. We find explicitly several non-normalizable boundary laws. Moreover, we reduce the problem to solving of a nonlinear, second-order difference equation. We give analytic and numerical analyses of the difference equation. [ABSTRACT FROM AUTHOR]

Apple latent spherical virus (ALSV) is widely used as a virus-induced gene silencing (VIGS) vector for function genome study. However, the application of ALSV to soybeans is limited by the resistance of many varieties. In this study, the genetic locus linked to the resistance of a resistant soybean variety Heinong 84 was mapped by high-throughput sequencing-based bulk segregation analysis (HTS–BSA) using a hybrid population crossed from Heinong 84 and a susceptible variety, Zhonghuang 13. The results showed that the resistance of Heinong 84 to ALSV is controlled by two genetic loci located on chromosomes 2 and 11, respectively. Cleaved amplified polymorphic sequence (CAPS) markers were developed for identification and genotyping. Inheritance and biochemical analyses suggest that the resistance locus on chromosome 2 plays a dominant dose-dependent role, while the other locus contributes a secondary role in resisting ALSV. The resistance locus on chromosome 2 might encode a protein that can directly inhibit viral proliferation, while the secondary resistance locus on chromosome 11 may encode a host factor required for viral proliferation. Together, these data reveal novel insights on the resistance mechanism of Heinong 84 to ALSV, which will benefit the application of ALSV as a VIGS vector. [ABSTRACT FROM AUTHOR]

We investigate the uniqueness problems of meromorphic functions and their difference operators by using a new method. It is proved that if a non-constant meromorphic function f shares a non-zero constant and ∞ counting multiplicities with its difference operators Δcf(z) and Δ c 2 f (z) , then Δ c f (z) ≡ Δ c 2 f (z) . In particular, we give a difference analogue of a result of Jank–Mues–Volkmann. Our method has two distinct features: (i) It converts the relations between functions into the corresponding vectors. This makes it possible to deal with the uniqueness problem by linear algebra and combinatorics. (ii) It circumvents the obstacle of the difference logarithmic derivative lemma for meromorphic functions of infinite order, since this method does not depend on the growth of the functions. Furthermore, the idea in this paper can also be applied to the case for several variables. [ABSTRACT FROM AUTHOR]

As we have easier access to massive data sets, functional analyses have gained more interest. However, such data sets often contain large heterogeneities, noises, and dimensionalities. When generalizing the analyses from vectors to functions, classical methods might not work directly. This paper considers noisy information reduction in functional analyses from two perspectives: functional clustering to group similar observations and thus reduce the sample size and functional variable selection to reduce the dimensionality. The complicated data structures and relations can be easily modeled by a Bayesian hierarchical model due to its flexibility. Hence, this paper proposes a nonparametric Bayesian functional clustering and peak point selection method via weighted Dirichlet process mixture (WDPM) modeling that automatically clusters and provides accurate estimations, together with conditional Laplace prior, which is a conjugate variable selection prior. The proposed method is named WDPM‐VS for short, and is able to simultaneously perform the following tasks: (1) Automatic cluster without specifying the number of clusters or cluster centers beforehand; (2) Cluster for heterogeneously behaved functions; (3) Select vibrational peak points; and (4) Reduce noisy information from the two perspectives: sample size and dimensionality. The method will greatly outperform its comparison methods in root mean squared errors. Based on this proposed method, we are able to identify biological factors that can explain the breast cancer racial disparities. [ABSTRACT FROM AUTHOR]

This article proposes an identification method of continuous-time fractional-order Hammerstein model using smoothed functional algorithm with a norm-limited update vector (NL-SFA). In particular, the standard smoothed functional algorithm (SFA) based method is modified by implementing a limit function in the update vector of the standard SFA based method to solve the issue of high tendency of divergence during the identification process. As a result of this, the proposed NL-SFA based method is applied to identify the variables of the linear and non-linear subsystems in the Hammerstein model. While most of the actual linear subsystems can be naturally expressed in a continuous-time domain, the implementation of the fractional-order could also reduce the computational complexity in finding a more accurate reduced-order model. Moreover, three experiments of the Hammerstein model identification based on a numerical example, an actual twin-rotor system, and an actual flexible manipulator system were carried out in this study to verify the effectiveness of the proposed NL-SFA-based method. The numerical and experimental results were analyzed to correspond to the measurement of the objective function and variable identification error and time-domain and frequency-domain responses. Conclusively, the proposed NL-SFA-based method can provide stable convergence and significantly better accuracy of the Hammerstein model in the numerical example, the actual twin-rotor system, and the flexible manipulator system compared to the standard SFA. Moreover, the proposed NL-SFA also provides slightly competitive identification accuracy with the existing norm-limited simultaneous perturbation stochastic approximation (NL-SPSA) and the average multi-verse optimizer sine cosine algorithm (AMVO-SCA) based methods. [ABSTRACT FROM AUTHOR]

Closed form expressions in real Clifford geometric algebras Cl0,3,Cl3,0,Cl1,2$$ C{l}_{0,3},C{l}_{3,0},C{l}_{1,2} $$, and Cl2,1$$ C{l}_{2,1} $$ are presented in a coordinate‐free form for exponential function when the exponent is a general multivector. The main difficulty in solving the problem is connected with an entanglement (or mixing) of vector and bivector components ai$$ {a}_i $$ and ajk$$ {a}_{jk} $$ in a form (ai−ajk)2,i≠j≠k$$ {\left({a}_i-{a}_{jk}\right)}^2,i\ne j\ne k $$. After disentanglement, the obtained formulas simplify to the well‐known de Moivre‐type trigonometric/hyperbolic function for vector or bivector exponentials. The presented formulas may find wide application in solving GA differential equations, in signal processing, automatic control and robotics. [ABSTRACT FROM AUTHOR]

The most difficult decision problems arise when several parties with several criteria must reach a consensus. This problem can be modelled as a game with vector-valued payoffs. If the players are allowed to use mixed strategies, there can be many Nash equilibria, and therefore many outcomes. The role of negotiation is to choose a specific outcome, or to restrict the set of outcomes to a small subset. One promising approach to negotiation support is scalarization of the vector payoff function. Here we apply Germeier scalarizing function, also known as the Rawlsian function, to mixed-strategy multicriteria games. After developing the mathematical background, we extend to these games the principle of Best Guaranteed Value, the value that a player may count on regardless of the other players' actions. We suggest that a good outcome for negotiation in a multicriteria game is a Nash equilibrium outcome that provides each player with the payoffs that are better than its Best Guaranteed Value. We describe all such outcomes, thereby defining a new negotiation support mechanism. [ABSTRACT FROM AUTHOR]

The contraction condition in the Banach contraction principle forces a function to be continuous. Many authors overcome this obligation and weaken the hypotheses via metric spaces endowed with a partial order. In this paper, we present some coupled fixed point theorems for the functions having mixed monotone properties on ordered vector metric spaces, which are more general spaces than partially ordered metric spaces. We also define the double monotone property and investigate the previous results with this property. In the last section, we prove the uniqueness of a coupled fixed point for non-monotone functions. In addition, we present some illustrative examples to emphasize that our results are more general than the ones in the literature. [ABSTRACT FROM AUTHOR]

This work develops a new robust multi‐objective model predictive control (MoMPC) strategy for constrained non‐linear systems with bounded disturbances. The multiple objectives are always contradictory, and the presence of disturbances may result in the violation of state constraints and instability of the controlled system. Firstly, the conflict between multiple objectives is reconciled by minimizing the distance of the cost function vector to the vector of independently minimised objectives obtained by solving a set of steady‐state optimisation problems. Then the contractive state set, which takes into account the effect of disturbances on system states, is constructed to guarantee the robust satisfaction of state constraints. Finally, a stability constraint updated online by solving an auxiliary optimization problem is established to ensure the robust stability of the system under MoMPC. An isothermal chemical reactor system is employed to verify the effectiveness of the controller proposed here. [ABSTRACT FROM AUTHOR]

The three-dimensional (3D) visualization of geological structures and the dynamic simulation of geological evolutionary processes are helpful when studying the formation of renowned geological features. However, most of the existing 3D modeling software is based on raster models, which are unable to generate smooth geological boundaries. This work proposes a 3D temporally dynamic (i.e., four-dimensional (4D)) modeling method using parametric functions and vector data structures, which can dynamically build geological evolutionary vector models of well-known geological features. First, we extract the typical features of different kinds of geological formations and represent them using different parameters. Next, we select appropriate parametric functions to simulate these geological formations according to the characteristics of the individual structures. Then, we design and develop 4D vector modeling software to simulate the geological evolution of these features. Finally, we simulate an area with complex geological structures and select six real-world geological features, such as the Piqiang Fault in China and the Eye of the Sahara in the Sahara Desert, as case studies. The modeling results show that a regional geological evolutionary model that contains smooth boundaries can be established within minutes using this method. This work will support studies into the formation of renowned geological features in terms of providing visualizations and will make the representation of geological processes more intuitive in 3D. [ABSTRACT FROM AUTHOR]

In this paper, we study the time evolution of three-states spin-1 non-Hermitian systems. The state vector of the wave function for Schrödinger equation is obtained analytically by using the Cayley–Hamilton theorem. We note that the behavior of the non-Hermitian three-states system corresponds to the Hermitian three-state system. Furthermore, the fluctuation between three-state spin-1 is periodically oscillating when the eigenvalues of the non-Hermitian system are real. Moreover, if the eigenvalues are imaginary, we explore that from our analysis and analytical solution that the probabilities' amplitudes always grow with time for all physical parameters in the three-state, i.e. including the -symmetry non-Hermitian system. It means that the Schrödinger equation becomes the growth exponential. [ABSTRACT FROM AUTHOR]

The primary objective of this paper is to explore contact CR-warped product submanifolds of Sasakian space forms equipped with a semi-symmetric metric connection. We thoroughly examine these submanifolds and establish various key findings. Furthermore, we derive an inequality relating the Ricci curvature to the mean curvature vector and warping function. [ABSTRACT FROM AUTHOR]

In this study, we focus on the estimation of the regression function in the single-index model based on B-splines using penalization techniques. We adopt a spherical coordinates reparameterization of an index vector to deal with an identification problem of the single-index model. To provide a spatially adaptive method, two types of penalties are applied to the estimation of the index vector and the regression function. A special penalty called the localized penalty is introduced to handle the sparsity of the index vector using the spherical coordinates, and the total variation penalty is considered to deal with the smoothing function. Using a coordinate descent algorithm with a grid search of the two tuning parameters, the entire solution paths of the index coefficients and the regression functions for tuning parameters can be obtained efficiently. The performance of the proposed estimator is studied through both numerical simulations and real data sets. An R software package pbssim is available. [ABSTRACT FROM AUTHOR]

In this paper, we consider the Radon transform for vector-valued functions. We propose an implementation of a nondestructive magnetic-induction research, which allows one to obtain an image of the internal structure of a magnetized sample by measuring the density of the flux penetrating it. [ABSTRACT FROM AUTHOR]

Cooperation plays an important role in dynamic games related to resource management problems. To construct cooperative behavior in asymmetric (when players possess different discount factors) and multicriteria (when players have vector payoff functions) dynamic games, the standard approaches are not applicable. The paper presents methods based on bargaining schemes to determine cooperative and noncooperative equilibria in such games. Cooperative strategies and payoffs in asymmetric dynamic games are obtained via the Nash bargaining scheme, while modified bargaining schemes are applied for multicriteria dynamic games. To illustrate the presented approaches, a dynamic bioresource management problems (fish war problem) with asymmetric players and vector payoff functions is investigated. [ABSTRACT FROM AUTHOR]

Bolometric light curves play an important role in understanding the underlying physics of various astrophysical phenomena, as they allow for a comprehensive modelling of the event and enable comparison between different objects. However, constructing these curves often requires the approximation and extrapolation from multicolour photometric observations. In this study, we introduce vector Gaussian processes as a new method for reduction of supernova light curves. This method enables us to approximate vector functions, even with inhomogeneous time-series data, while considering the correlation between light curves in different passbands. We applied this methodology to a sample of 29 superluminous supernovae (SLSNe) assembled using the Open Supernova Catalog. Their multicolour light curves were approximated using vector Gaussian processes. Subsequently, under the blackbody assumption for the SLSN spectra at each moment of time, we reconstructed the bolometric light curves. The vector Gaussian processes developed in this work are accessible via the python library gp-multistate-kernel on GitHub. Our approach provides an efficient tool for analysing light curve data, opening new possibilities for astrophysical research. [ABSTRACT FROM AUTHOR]

This paper introduces a novel concept of the impulsive delayed Mittag–Leffler-type vector function, an extension of the Mittag–Leffler matrix function. It is essential to seek explicit formulas for the solutions to linear impulsive fractional differential delay equations. Based on explicit formulas of the solutions, the finite-time stability results of impulsive fractional differential delay equations are presented. Finally, we present four examples to illustrate the validity of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the new concept of an impulsive delayed vector function, which helps us to build the representation of an exact solution for the linear impulsive oscillating differential delay systems (IODDSs). Second, we derive some sufficient conditions to guarantee the existence and uniqueness of solution by Schauder's and Banach's fixed point theorems for a new class of nonlinear IODDSs. Finally, we obtain the Ulam‐Hyers stability (UHs) and Ulam‐Hyers‐Rassias stability (UHRs) for nonlinear IODDSs, and two examples are presented to illustrate the main results of our study. [ABSTRACT FROM AUTHOR]

Starting from a simple Gauss–Markov model, this paper presents notes about criteria for the estimability of parametric functions of the vector of interest in linear models. The results obtained for the transformed models are compared with known results from the literature. [ABSTRACT FROM AUTHOR]

The issue of microplastic pollution has escalated in significance and urgency due to the global infiltration of minuscule plastic particles into terrestrial and marine ecosystems. Microplastics are generated through a variety of processes, including the decomposition of larger plastics, industrial operations, and the incorporation of microbeads into personal care items. These substances have been detected in sediments, lakes, rivers, oceans, and even the air we breathe. The detrimental impacts of microplastics on the well-being of wildlife are extensively documented. These particles present hazards to marine organisms such as seabirds, fish, and sea turtles via ingestion or entanglement. Moreover, they might function as vectors through which detrimental substances infiltrate the food chain. To adequately tackle this matter, it is imperative to adopt a multidisciplinary strategy that encompasses policy interventions aimed at restricting plastic production and consumption, advancements in waste management technologies, public awareness initiatives promoting sustainable lifestyles, and ongoing research to comprehensively comprehend the problem's magnitude and ecological repercussions. The assurance of a cleaner environment for future generations is contingent upon our collective efforts to mitigate microplastic pollution. [ABSTRACT FROM AUTHOR]

In this research, a novel approach is applied to obtain the solution for the non-homogeneous system of fuzzy fractional differential equations. The fuzzy fractional initial value problem is split into sets of classical fractional initial value problems. Such a fractional initial value problem is constructed by taking the forcing term derived from each of fuzzy set and the initial value obtained from each of fuzzy intervals. The solution to the fuzzy fractional initial value problem is defined as the collection of all solutions of the classical fractional initial value problems, and its degree of membership is the smallest value among the degrees of membership obtained from forcing terms and initial values in the associated fuzzy sets. Specifically, a solution is constructed as a fuzzy collection of real vector functions, instead of a vector of fuzzy-valued functions. The numerical example has been used to illustrate the proposed approach in detail. The benefits of the proposed methodology over the existing methodology, as well as its applicability to the real world, are clearly demonstrated. [ABSTRACT FROM AUTHOR]

The paper is devoted to the formal description of the running time of the user task on some virtual nodes in the computing network. Based on the probability theory framework, this time represents a random value with a finite mean and variance. For any class of user task, these moments are the functions of the node resources, task numerical characteristics, and the parameters of the current node state. These functions of the vector arguments can be treated as some surfaces in the multidimensional Euclidean spaces, so the proposed models are called the stochastic time complexity surfaces. The paper also presents a class of functions suitable for the description of both the mean and variance. They contain unknown parameters which should be estimated. The article includes the statement of the parameter identification problem given the statistical results of the node stress testing, recommendations concerning the test planning, and preprocessing of the raw experiment data. To illustrate the performance of the proposed model, the authors design it for an actual database application—the prototype of the passengers' personal data anonymization system. Its application functions are classified into two user task classes: the data anonymization procedures and fulfillment of the statistical queries. The authors identify the stochastic time complexity surfaces for both task types. The additional testing experiments confirm the high performance of the suggested model and its applicability to the solution of the practical providers' problems. [ABSTRACT FROM AUTHOR]

The article is a natural continuation of the systematic research of the properties of the generalized concept of differentiability for functions with a domain X ⊂ R n that is not necessarily open, at points that allow a neighbourhood ray in the domain. In the new context, the well-known Lagrange's mean value theorem for scalar functions is stated and proved, even for the case when the differential is not unique at all points of the observed segment in the domain. Likewise, it has been proven that its variant is valid for vector functions as well. Additionally, the paper provides a proof of the generalization of the mean value theorem for continuous scalar functions continuously differentiable in the interior of a compact domain. [ABSTRACT FROM AUTHOR]

In order to ensure zero steady-state error in multi-area hybrid power systems, load frequency control is implemented in the power system. However, variations in load due to cyclic amplitude deviation create frequency fault leading to unscheduled tie-line power. Hence a novelOperational Load Forecasting Approach is utilized in which objective function in support vector regression predicts load demand and generation based on temporalcharacteristicsand utilize parallel processing to tolerate the acceptable error margin. Moreover, the uncertainties of active power generation in islanding mode make the estimation of frequency response deviation under decentralized islanding modes difficult. Hence a novelDifferential ControllerAlgorithm has been proposed in which the sigmoidal range function determines the optimal amplitude value from individual areasand the controller predicts the high load demand area that exceeds the threshold limit and isolatesthat area until the deviation is rectified. Low tie-line power, frequency, and settling time deviations were accomplished using the proposed methodologies as they were simulated using the Simulink platform. [ABSTRACT FROM AUTHOR]

Interest in facial recognition hypotheses and algorithms has grown steadily over the last few decades. Video monitoring, criminal identification, building access control, and unmanned and autonomous vehicles are only a few examples of concrete applications that are becoming increasingly attractive to industry. Various techniques are being developed, including local, holistic, and hybrid approaches, which use only a few face image characteristics or the entire facial features to provide a face image description. Many methods have good results, if there are sufficiently representative training samples per person, in the face recognition system. Facial part finding and extraction show the utmost vital role in face and age recognition. In this research work a new algorithm is proposed for Face and Age Recognition (FAR) by using Discrete Wavelet Transform (DWT), Radial Basis Function Support Vector Machine (RBF-SVM) classifier, and Rotational Local Binary Pattern (RLBP). RLBP is utilized for the selection and extraction of features from the face image. In this algorithm, extract the face component like Nose, Mouth, Left and Right eye. In the preprocessing stage median filter is used to remove noises from the face image. By using this, there is an improvement in the feature extraction procedure. In pattern recognition, a basic errand is finding a picture from the picture parts. For the implementation of results FG-NET ((Face and Gesture Recognition Network) and AT&T datasets are used. The detection rate of face recognition has reached up to 92-98% and the detection rate for age recognition is 87%. The proposed algorithm is compared with SVM shows better over previous algorithms and also estimate the value of accuracy. [ABSTRACT FROM AUTHOR]

This paper is concerned with a version of the Lebesgue dominated convergence theorem (DCT) which has been stated for the Kurzweil–Stieltjes integral of real functions. Our objective in this work is to analyze the extension of this result to include vector functions with values in Banach spaces. We establish that the mentioned convergence theorem for the Kurzweil–Stieltjes integral can be formulated in weaker versions for reflexive and separable Banach spaces, and spaces having the Schur property, nonetheless it is not verified in the general case. [ABSTRACT FROM AUTHOR]

Due to properties such as interpolation, smoothness, and spline connections, Hermite subdivision schemes employ fast iterative algorithms for geometrically modeling curves/surfaces in CAGD and for building Hermite wavelets in numerical PDEs. In this paper, we introduce a notion of generalized Hermite (dyadic) subdivision schemes and then we characterize their convergence, smoothness and underlying matrix masks with or without interpolation properties. We also introduce the notion of linear-phase moments for achieving the polynomial-interpolation property. For any given integer m ∈ N , we constructively prove that there always exist convergent smooth generalized Hermite subdivision schemes with linear-phase moments such that their basis vector functions are spline functions in C m (R d) and have linearly independent integer shifts. As by-products, our results resolve convergence, smoothness, and existence of Lagrange, Hermite, or Birkhoff subdivision schemes. Even in dimension one our results significantly generalize and extend many known results on extensively studied univariate Hermite subdivision schemes. To illustrate the theoretical results in this paper, we provide examples of convergent generalized Hermite subdivision schemes with symmetric matrix masks having short support and smooth basis vector functions with or without interpolation property. [ABSTRACT FROM AUTHOR]

Binary code similarity analysis is widely used in the field of vulnerability search where source code may not be available to detect whether two binary functions are similar or not. Based on deep learning and natural processing techniques, several approaches have been proposed to perform cross-platform binary code similarity analysis using control flow graphs. However, existing schemes suffer from the shortcomings of large differences in instruction syntaxes across different target platforms, inability to align control flow graph nodes, and less introduction of high-level semantics of stability, which pose challenges for identifying similar computations between binary functions of different platforms generated from the same source code. We argue that extracting stable, platform-independent semantics can improve model accuracy, and a cross-platform binary function similarity comparison model N_Match is proposed. The model elevates different platform instructions to the same semantic space to shield their underlying platform instruction differences, uses graph embedding technology to learn the stability semantics of neighbors, extracts high-level knowledge of naming function to alleviate the differences brought about by cross-platform and cross-optimization levels, and combines the stable graph structure as well as the stable, platform-independent API knowledge of naming function to represent the final semantics of functions. The experimental results show that the model accuracy of N_Match outperforms the baseline model in terms of cross-platform, cross-optimization level, and industrial scenarios. In the vulnerability search experiment, N_Match significantly improves hit@N, the mAP exceeds the current graph embedding model by 66%. In addition, we also give several interesting observations from the experiments. The code and model are publicly available at https://www.github.com/CSecurityZhongYuan/Binary-Name_Match. [ABSTRACT FROM AUTHOR]

Given a probability space (Ω , A , P) , a complete separable Banach space X with the σ -algebra B (X) of all its Borel subsets, an operator Λ : Ω → L (X , X) and ξ : Ω → X we consider the B (X) ⊗ A -measurable function f : X × Ω → X given by f (x , ω) = Λ (ω) x + ξ (ω) and investigate the continuous dependence of a weak limit π f of the sequence of iterates (f n (x , ·)) n ∈ N of f, defined by f 0 (x , ω) = x , f n + 1 (x , ω) = f (f n (x , ω) , ω n + 1) for x ∈ X and ω = (ω 1 , ω 2 , ⋯) . Moreover for X taken as a Hilbert space we characterize π f via the functional equation φ f (u) = ∫ Ω φ f (Λ (ω) u) φ ξ (u) P (d ω) with the aid of its characteristic function φ f . We also indicate the continuous dependence of a solution of that equation. [ABSTRACT FROM AUTHOR]