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Recent rank-based attacks have reduced the security of Rainbow, which is one of the multi-layer UOV signatures, below the NIST security requirements by speeding up iterative kernel-finding operations using classical mathematics techniques. If quantum algorithms are applied to perform these iterative operations, the rank-based attacks may be more threatening to multi-layer UOV, including Rainbow. In this paper, we propose a quantum rectangular MinRank attack called the Q-rMinRank attack, the first quantum approach to key recovery attacks on multi-layer UOV signatures. Our attack is a general model applicable to multi-layer UOV signature schemes, and in this paper, we provide examples of its application to Rainbow and the Korean TTA standard, HiMQ. We design two quantum oracle circuits to find the kernel in consideration of the depth-width trade-off of quantum circuits. One is to reduce the width of the quantum circuits using qubits as a minimum, and the other is to reduce the depth using parallelization instead of using a lot of qubits. By designing quantum circuits to find kernels with fewer quantum resources and complexity by adding mathematical techniques, we achieve quadratic speedup for the MinRank attack to recover the private keys of multi-layer UOV signatures. We also estimate quantum resources for the designed quantum circuits and analyze quantum complexity based on them. The width-optimized circuit recovers the private keys of Rainbow parameter set V with only 1089 logical qubits. The depth-optimized circuit recovers the private keys of Rainbow parameter set V with a quantum complexity of 2 174 , which is lower than the complexity of 2 221 recovering the secret key of AES-192, which provides the same security level as parameter set III. [ABSTRACT FROM AUTHOR]

This note tries to answer issues raised in Bhardwaj and Kumar (J Optim Theory Appl 163(2): 685-696, 2014). The research summarizes that the results obtained in Khan et al. (J Optim Theory Appl 159: 536-546, 2013) are sound and correct and it fulfills all the necessary requirements of its scope and objectives. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of computing the rank of a block-structured symbolic matrix (a generic partitioned matrix) A = (A α β x α β) , where A α β is a 2 × 2 matrix over a field F and x α β is an indeterminate for α = 1 , 2 , ⋯ , μ and β = 1 , 2 , ⋯ , ν . This problem can be viewed as an algebraic generalization of the bipartite matching problem and was considered by Iwata and Murota (SIAM J Matrix Anal Appl 16(3):719–734, 1995). Recent interests in this problem lie in the connection with non-commutative Edmonds' problem by Ivanyos et al. (Comput Complex 27:561–593, 2018) and Garg et al. (Found. Comput. Math. 20:223–290, 2020), where a result by Iwata and Murota implicitly states that the rank and non-commutative rank (nc-rank) are the same for this class of symbolic matrices. The main result of this paper is a simple and combinatorial O ((μ ν) 2 min { μ , ν }) -time algorithm for computing the symbolic rank of a (2 × 2) -type generic partitioned matrix of size 2 μ × 2 ν . Our algorithm is inspired by the Wong sequence algorithm by Ivanyos et al. for the nc-rank of a general symbolic matrix, and requires no blow-up operation, no field extension, and no additional care for bounding the bit-size. Moreover it naturally provides a maximum rank completion of A for an arbitrary field F . [ABSTRACT FROM AUTHOR]

Theory of quasi-orthogonal polynomials is significantly related to constructing vector Padé approximations. The present paper introduces an efficient procedure to compute adjacent families of quasi-orthogonal polynomials as defined in Sadaka (Appl. Numer. Math. 21:57–70, 1996) and Sadaka (Appl. Numer. Math. 24:483–499, 1997). The derived algorithm uses short recursive relations whose coefficients are written in terms of lower triangular block determinants. The strategy of computing such determinants is given and analyzed. [ABSTRACT FROM AUTHOR]

This paper provides results in the area of the analytical derivation of the efficient set of a mean-variance portfolio selection problem that has more than three criteria. By "analytical" we mean derived by formula as opposed to being computed by algorithm. By "more than three criteria", we mean that beyond the mean and variance of regular portfolio selection, the problems addressed have two or more additional linear objectives. The additional objectives might include sustainability, dividend yield, liquidity, and R&D as extra objectives like these are being seen with greater frequency. While not all multiple criteria portfolio selection problems lend themselves to an analytical derivation, a certain class does and the problems in this class are covered by the mathematics of this paper. [ABSTRACT FROM AUTHOR]

A recursive algorithm for the determinant evaluation of general opposite-bordered tridiagonal matrices has been proposed by Jia et al. (J Comput Appl Math 290:423–432, 2015). Since the algorithm is a symbolic algorithm, it never suffers from breakdown. However, it may be time-consuming when many symbolic names emerge during the symbolic computation. In this paper, without using symbolic computation, first we present a novel breakdown-free numerical algorithm for computing the determinant of an n-by-n opposite-bordered tridiagonal matrix, which does not require any extra memory storage for the implementation. Then, we present a cost-efficient algorithm for the determinants of opposite-bordered tridiagonal matrices based on the use of the combination of an elementary column operation and Sylvester's determinant identity. Furthermore, we provide some numerical results with simulations in Matlab implementation in order to demonstrate the accuracy and efficiency of the proposed algorithms, and their competitiveness with other existing algorithms. The corresponding results in this paper can be readily obtained for computing the determinants of singly-bordered tridiagonal matrices. [ABSTRACT FROM AUTHOR]

This paper proposes an innovative statistical method to measure the impact of the class/school on student achievements in multiple subjects. We propose a semiparametric model for a bivariate response variable with random coefficients, that are assumed to follow a discrete distribution with an unknown number of support points, together with an Expectation-Maximization algorithm—called BSPEM algorithm—to estimate its parameters. In the case study, we apply the BSPEM algorithm to data about Italian middle schools, considering students nested within classes, and we identify subpopulations of classes, standing on their effects on student achievements in reading and mathematics. The proposed model is extremely informative in exploring the correlation between multiple class effects, which are typical of the educational production function. The estimated class effects on reading and mathematics student achievements are then explained in terms of various class and school level characteristics selected by means of a LASSO regression. [ABSTRACT FROM AUTHOR]

In this paper, we combine the S-iteration process introduced by Agarwal et al. (J. Nonlinear Convex Anal., 8(1), 61–79 2007) with the proximal point algorithm introduced by Rockafellar (SIAM J. Control Optim., 14, 877–898 1976) to propose a new modified proximal point algorithm based on the S-type iteration process for approximating a common element of the set of solutions of convex minimization problems and the set of fixed points of nearly asymptotically quasi-nonexpansive mappings in the framework of CAT(0) spaces and prove the △-convergence of the proposed algorithm for solving common minimization problem and common fixed point problem. Our result generalizes, extends and unifies the corresponding results of Dhompongsa and Panyanak (Comput. Math. Appl., 56, 2572–2579 2008), Khan and Abbas (Comput. Math. Appl., 61, 109–116 2011), Abbas et al. (Math. Comput. Modelling, 55, 1418–1427 2012) and many more. [ABSTRACT FROM AUTHOR]

We will refer to the paper "Convergence rates for Kaczmarz-type algorithms", published in Numerical Algorithms, 79(1)(2018), 1-17. It was observed by Dr. Mokhtar Abbasi (Department of Mathematics, University of Qom, Iran) that in the proof of Theorem 7, related to the linear convergence rate of the MREK algorithm it exists an inequality which is not always true. [ABSTRACT FROM AUTHOR]

Let $${\mathcal {F}}$$ be a family of graphs. Given an n-vertex input graph G and a positive integer k, testing whether G has a vertex subset S of size at most k, such that $$G-S$$ belongs to $${\mathcal {F}}$$ , is a prototype vertex deletion problem. These type of problems have attracted a lot of attention in recent times in the domain of parameterized complexity. In this paper, we study two such problems; when $${\mathcal {F}}$$ is either the family of forests of cacti or the family of forests of odd-cacti. A graph H is called a forest of cacti if every pair of cycles in H intersect on at most one vertex. Furthermore, a forest of cacti H is called a forest of odd cacti, if every cycle of H is of odd length. Let us denote by $${\mathcal {C}}$$ and $${{\mathcal {C}}}_\mathsf{odd}$$ , the families of forests of cacti and forests of odd cacti, respectively. The vertex deletion problems corresponding to $${\mathcal {C}}$$ and $${{\mathcal {C}}}_\mathsf{odd}$$ are called Diamond Hitting Set and Even Cycle Transversal, respectively. In this paper we design randomized algorithms with worst case run time $$12^k n^{\mathcal {O}(1)}$$ for both these problems. Our algorithms considerably improve the running time for Diamond Hitting Set and Even Cycle Transversal, compared to what is known about them. [ABSTRACT FROM AUTHOR]

The aim of this study is to propose a high-accuracy and high-efficiency sleep staging algorithm using single-channel electroencephalograms (EEGs). The process consists four parts: signal preprocessing, feature extraction, feature selection, and classification algorithms. In the preconditioning of EEG, wavelet function and IIR filter are used for noise reduction. In feature selection, 15 feature algorithms in time domain, time-frequency domain, and nonlinearity are selected to obtain 30 feature parameters. Feature selection is very important for eliminating irrelevant and redundant features. Feature selection algorithms as Fisher score, Sequential Forward Selection (SFS), Sequential Floating Forward Selection (SFFS), and Fast Correlation-Based Filter Solution (FCBF) were used. The paper establishes a new ensemble learning algorithm based on stacking model. The basic layers are k-Nearest Neighbor (KNN), Random Forest (RF), Extremely Randomized Trees (ERT), Multi-layer Perceptron (MLP), and Extreme Gradient Boosting (XGBoost) and the second layer is a Logistic regression. Comparing classification of RF, Gradient Boosting Decision Tree (GBDT), and XGBoost, the accuracies and kappa coefficients are 96.67% and 0.96 using the proposed method. It is higher than other classification algorithms.The results show that the proposed method can accurately sleep staging using single-channel EEG and has a high ability to predict sleep staging. Graphical abstract. [ABSTRACT FROM AUTHOR]

The strong ℋ -tensors have important applications in many areas of science and engineering, e.g., the determination of positive definiteness for an even-order homogeneous polynomial form in the real field. In this paper, we propose two iterative algorithms with non-parameter for identifying strong ℋ -tensors, which overcome the drawback of choosing the best value of parameter 𝜖 in some existing algorithms given by Li et al. and Liu et al. (J. Comput. Appl. Math., 255, 1–14, 2014 and Comput. Appl. Math. 36, 1623–1635, 2017). Some numerical experiments are performed to illustrate the feasibility and effectiveness of our algorithms. [ABSTRACT FROM AUTHOR]

In this paper we consider a class of structured nonsmooth difference-of-convex (DC) minimization in which the first convex component is the sum of a smooth and nonsmooth functions while the second convex component is the supremum of possibly infinitely many convex smooth functions. We first propose an inexact enhanced DC algorithm for solving this problem in which the second convex component is the supremum of finitely many convex smooth functions, and show that every accumulation point of the generated sequence is an (α , η) -D-stationary point of the problem, which is generally stronger than an ordinary D-stationary point. In addition, inspired by the recent work (Pang et al. in Math Oper Res 42(1):95–118, 2017; Wen et al. in Comput Optim Appl 69(2):297–324, 2018), we propose two proximal DC algorithms with extrapolation for solving this problem. We show that every accumulation point of the solution sequence generated by them is an (α , η) -D-stationary point of the problem, and establish the convergence of the entire sequence under some suitable assumption. We also introduce a concept of approximate (α , η) -D-stationary point and derive iteration complexity of the proposed algorithms for finding an approximate (α , η) -D-stationary point. In contrast with the DC algorithm (Pang et al. 2017), our proximal DC algorithms have much simpler subproblems and also incorporate the extrapolation for possible acceleration. Moreover, one of our proximal DC algorithms is potentially applicable to the DC problem in which the second convex component is the supremum of infinitely many convex smooth functions. In addition, our algorithms have stronger convergence results than the proximal DC algorithm in Wen et al. (2018). [ABSTRACT FROM AUTHOR]

Research on graph searching has recently gained interest in computer science, mathematics, and physics. This paper studies fast searching of a fugitive in a graph, a model that was introduced by Dyer et al. (in: Fleischer, Xu (eds.) Algorithmic aspects in information and management, Springer, New York, 2008). We provide lower bounds and upper bounds on the fast search number (i.e., the minimum number of searchers required for capturing the fugitive) of complete k-partite graphs. We also investigate some special classes of complete k-partite graphs, such as complete bipartite graphs and complete split graphs. We solve the open problem of determining the fast search number of complete bipartite graphs, and present upper and lower bounds on the fast search number of complete split graphs. [ABSTRACT FROM AUTHOR]

The paper concerns worst-case compliance optimization by finding the structural topology with minimum compliance for the loading due to the worst possible acceleration of the structure and attached non-structural masses. A main novelty of the paper is that it is shown how this min-max problem can be formulated as a non-linear semi-definite programming (SDP) problem involving a small-size constraint matrix and how this problem is solved numerically. Our SDP formulation is an extension of an eigenvalue problem seen previously in the literature; however, multiple eigenvalues naturally arise which makes the eigenvalue problem non-smooth, whereas the SDP problem presented in this paper provides a computationally tractable problem. Optimized designs, where the uncertain loading is due to acceleration of applied masses and the weight of the structure itself, are shown in two and three dimensions and we show that these designs satisfy optimality conditions that are also presented. [ABSTRACT FROM AUTHOR]

The power graph $${\fancyscript{P}}(G)$$ of a group $$G$$ is the graph which has a vertex set of the group elements and two elements are adjacent if one is a power of the other. Chakrabarty, Ghosh, and Sen proved the main properties of the undirected power graph of a finite group. The aim of this paper is to generalize some results of their work and presenting some counterexamples for one of the problems raised by these authors. It is also proved that the power graph of a $$p$$ -group is $$2$$ -connected if and only if the group is a cyclic or generalized quaternion group and if $$G$$ is a nilpotent group which is not of prime power order then the power graph $${\fancyscript{P}}(G)$$ is $$2$$ -connected. We also prove that the number of edges of the power graph of the simple groups is less than or equal to the number of edges in the power graph of the cyclic group of the same order. This partially answers to a question in an earlier paper. Finally, we give a complete classification of groups in which the power graph is a union of complete graphs sharing a common vertex. [ABSTRACT FROM AUTHOR]

This paper presents a reliable approach for solving linear systems of ordinary and fractional differential equations. First, the FDEs or ODEs of a system with initial conditions to be solved are transformed to Volterra integral equations. Then Taylor expansion for the unknown function and integration method are employed to reduce the resulting integral equations to a new system of linear equations for the unknown and its derivatives. The fractional derivatives are considered in the Riemann-Liouville sense. Some numerical illustrations are given to demonstrate the effectiveness of the proposed method in this paper. [ABSTRACT FROM AUTHOR]

In the literature, most known sequence transformations can be written as a ratio of two determinants. But, it is not always this case. One exception is that the sequence transformation proposed by Brezinski, Durbin, and Redivo-Zaglia cannot be expressed as a ratio of two determinants. Motivated by this, we will introduce a new algebraic tool—pfaffians, instead of determinants in the paper. It turns out that Brezinski-Durbin-Redivo-Zaglia’s transformation can be expressed as a ratio of two pfaffians. To the best of our knowledge, this is the first time to introduce pfaffians in the expressions of sequence transformations. Furthermore, an extended transformation of high order is presented in terms of pfaffians and a new convergence acceleration algorithm for implementing the transformation is constructed. Then, the Lax pair of the recursive algorithm is obtained which implies that the algorithm is integrable. Numerical examples with applications of the algorithm are also presented. [ABSTRACT FROM AUTHOR]

Hessenberg matrices frequently arise in many application areas and have been attracted much attention in recent years. In the current paper, we present two numerical algorithms of $$O(n^2)$$ for computing the determinant of an n-by- n general Hessenberg matrix. The algorithms are all suited for implementation using Computer Algebra Systems such as MATLAB and MAPLE. Some numerical examples are provided in order to demonstrate the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Tukey depth function is one of the most famous multivariate tools serving robust purposes. It is also very well known for its computability problems in dimensions $$p \ge 3$$ . In this paper, we address this computing issue by presenting two combinatorial algorithms. The first is naive and calculates the Tukey depth of a single point with complexity $$O\left( n^{p-1}\log (n)\right) $$ , while the second further utilizes the quasiconcave of the Tukey depth function and hence is more efficient than the first. Both require very minimal memory and run much faster than the existing ones. All experiments indicate that they compute the exact Tukey depth. [ABSTRACT FROM AUTHOR]

We analyze the convergence rate of the alternating direction method of multipliers (ADMM) for minimizing the sum of two or more nonsmooth convex separable functions subject to linear constraints. Previous analysis of the ADMM typically assumes that the objective function is the sum of only two convex functions defined on two separable blocks of variables even though the algorithm works well in numerical experiments for three or more blocks. Moreover, there has been no rate of convergence analysis for the ADMM without strong convexity in the objective function. In this paper we establish the global R-linear convergence of the ADMM for minimizing the sum of any number of convex separable functions, assuming that a certain error bound condition holds true and the dual stepsize is sufficiently small. Such an error bound condition is satisfied for example when the feasible set is a compact polyhedron and the objective function consists of a smooth strictly convex function composed with a linear mapping, and a nonsmooth $$\ell _1$$ regularizer. This result implies the linear convergence of the ADMM for contemporary applications such as LASSO without assuming strong convexity of the objective function. [ABSTRACT FROM AUTHOR]

Previous research has reported the validity and reliability of a range of field-based tests of children's cardiorespiratory fitness. These two criteria are critical in ensuring the integrity and credibility of data derived through such tests. However, the criterion of scalability has received little attention. Scalability determines the degree to which tests developed on small samples in controlled settings might demonstrate real-world value, and is of increasing interest to policymakers and practitioners. The present paper proposes a method by which the scalability of cardiorespiratory field-based tests suitable for school-aged children might be assessed. We developed an algorithm to estimate scalability based on a six-component model; delivery, evidence of operating at scale, effectiveness, costs, resource requirements and practical implementation. We tested the algorithm on data derived through a systematic review of research that has used relevant fitness tests. A total of 229 studies that had used field based cardiorespiratory fitness tests to measure children's fitness were identified. Initial analyses indicated that the 5-min run test did not meet accepted criteria for reliability, whilst the 6-min walk test likewise failed to meet the criteria for validity. Of the remainder, a total of 28 studies met the inclusion criteria, 22 reporting the 20-m shuttle-run and seven the 1-mile walk/run. Using the scalability algorithm we demonstrate that the 20-m shuttle run test is substantially more scalable than the 1-mile walk/run test, with tests scoring 34/48 and 25/48, respectively. A comprehensive analysis of scalability was prohibited by the widespread non-reporting of data, for example, those relating to cost-effectiveness. Of all sufficiently valid and reliable candidate tests identified, using our algorithm the 20-m shuttle run test was identified as the most scalable. We hope that the algorithm will prove useful in the examination of scalability in either new data relating to existing tests or in data pertaining to new tests. [ABSTRACT FROM AUTHOR]

The Connected Facility Location (CFL) is a network design problem that arises from a combination of the Uncapacitated Facility Location (FL) and the Steiner Tree (ST) problems. The Online Connected Facility Location problem (OCFL) is an online version of the CFL. San Felice et al. (2014) presented a randomized algorithm for the OCFL and proved that it is $$\mathrm {O}(\log ^2 n)$$ -competitive, where n is the number of clients. That algorithm combines the sample-and-augment framework of Gupta, Kumar, Pál, and Roughgarden with previous algorithms for the Online Facility Location (OFL) and the Online Steiner Tree (OST) problems. In this paper we use a more precise analysis to show that the same algorithm is $$\mathrm {O}(\log n)$$ -competitive. Since there is a lower bound of $$\mathrm {\Omega }(\log n)$$ for this problem, our result achieves the best possible competitive ratio, asymptotically. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of fast and efficient indexing techniques for sequences evolving in non-Euclidean spaces. This problem has several applications in the areas of human activity analysis, where there is a need to perform fast search, and recognition in very high dimensional spaces. The problem is made more challenging when representations such as landmarks, contours, and human skeletons etc. are naturally studied in a non-Euclidean setting where even simple operations are much more computationally intensive than their Euclidean counterparts. We propose a geometry and data adaptive symbolic framework that is shown to enable the deployment of fast and accurate algorithms for activity recognition, dynamic texture recognition, motif discovery. Toward this end, we present generalizations of key concepts of piece-wise aggregation and symbolic approximation for the case of non-Euclidean manifolds. We show that one can replace expensive geodesic computations with much faster symbolic computations with little loss of accuracy in activity recognition and discovery applications. The framework is general enough to work across both Euclidean and non-Euclidean spaces, depending on appropriate feature representations without compromising on the ultra-low bandwidth, high speed and high accuracy. The proposed methods are ideally suited for real-time systems and low complexity scenarios. [ABSTRACT FROM AUTHOR]

This paper presents the analysis of multi-channel electrogastrographic (EGG) signals using the continuous wavelet transform based on the fast Fourier transform (CWTFT). The EGG analysis was based on the determination of the several signal parameters such as dominant frequency (DF), dominant power (DP) and index of normogastria (NI). The use of continuous wavelet transform (CWT) allows for better visible localization of the frequency components in the analyzed signals, than commonly used short-time Fourier transform (STFT). Such an analysis is possible by means of a variable width window, which corresponds to the scale time of observation (analysis). Wavelet analysis allows using long time windows when we need more precise low-frequency information, and shorter when we need high frequency information. Since the classic CWT transform requires considerable computing power and time, especially while applying it to the analysis of long signals, the authors used the CWT analysis based on the fast Fourier transform (FFT). The CWT was obtained using properties of the circular convolution to improve the speed of calculation. This method allows to obtain results for relatively long records of EGG in a fairly short time, much faster than using the classical methods based on running spectrum analysis (RSA). In this study authors indicate the possibility of a parametric analysis of EGG signals using continuous wavelet transform which is the completely new solution. The results obtained with the described method are shown in the example of an analysis of four-channel EGG recordings, performed for a non-caloric meal. [ABSTRACT FROM AUTHOR]

In this paper, a new multi-objective uniform-diversity differential evolution (MUDE) algorithm is proposed and used for Pareto optimum design of mechanisms. The proposed algorithm uses a diversity preserving mechanism called the ε-elimination algorithm to improve the population diversity among the obtained Pareto front. The proposed algorithm is firstly tested on some constrained and unconstrained benchmarks proposed for the special session and competition on multi-objective optimizers held under IEEE CEC 2009. The inverted generational distance (IGD) measure is used to assess the performance of the algorithm. Secondly, the proposed algorithm has been used for multi-objective optimization of two different combinatorial case studies. The first case contains a two-degree of freedom leg mechanism with springs. Three conflicting objective functions that have been considered for Pareto optimization are namely, leg size, vertical actuating force, and the peak crank torque. The second case is a two-finger robot gripper mechanism with two conflicting objectives which are the difference between the maximum and minimum gripping force and the transmission ratio of actuated and experienced gripper forces. Comparisons of obtained Pareto fronts using the method of this work with those obtained in other references show significant improvements. [ABSTRACT FROM AUTHOR]

In this paper, multi-objective particle swarm optimization with preference information (MOPSO-PI) has been proposed. In the proposed algorithm, the information entropy is employed for measuring the probability distribution of particles; the user's preference information is represented as the ranking of each particle through the possible matrix. The optimal procedure is guided by the preference information since the global best performance of particle is randomly chosen among non-dominated solutions with higher ranking value in each iteration. Finally, the MOPSO-PI is applied to optimize the steelmaking process; the power supply curve obtained reduces the electric energy consumption, shortens the smelting time and prolongs the lifespan of the furnace lining. The application results show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a generalized version of the classic projective reconstruction theorem which helps to choose or assess depth constraints for projective depth estimation algorithms. The theorem shows that projective reconstruction is possible under a much weaker constraint than requiring all estimated projective depths to be nonzero. This result enables us to present classes of depth constraints under which any reconstruction of cameras and points projecting into given image points is projectively equivalent to the true camera-point configuration. It also completely specifies the possible wrong configurations allowed by other constraints. We demonstrate the application of the theorem by analysing several constraints used in the literature, as well as presenting new constraints with desirable properties. We mention some of the implications of our results on iterative depth estimation algorithms and projective reconstruction via rank minimization. Our theory is verified by running experiments on both synthetic and real data. [ABSTRACT FROM AUTHOR]

Björner, Lovász and Shor introduced a chip-firing game on a finite graph $$G$$ as follows. We put some chips on each vertex of $$G$$ , we say that a vertex is ready if it has at least as many chips as its degree, in which case we can fire it and the result is that it distributes one chip to each of its neighbors, this may cause other vertices to be ready, and so on. This game continues until no vertex can be fired. In this paper, we study chip-firing games on complete graphs. We obtain a sufficient and necessary condition for chip-firing games on complete graphs to be finite. [ABSTRACT FROM AUTHOR]

In the present paper, we study the extrinsic and intrinsic geometry of submanifolds of an almost contact metric manifold admitting a quarter-symmetric metric connection. We deduce Gauss, Codazzi and Ricci equations corresponding to the quarter-symmetric metric connection and show some applications of these equations. Finally, we give an example verifying the results. [ABSTRACT FROM AUTHOR]

Let $$G$$ be a graph with degree sequence $$d_1,d_2,\ldots ,d_n$$ . Given a positive integer $$p$$ , denote by $$e_p(G)=\sum _{i=1}^n d_i^p$$ . Caro and Yuster introduced a Turán-type problem for $$e_p(G)$$ : given an integer $$p$$ , how large can $$e_p(G)$$ be if $$G$$ has no subgraph of a particular type. They got some results for the subgraph of particular type to be a clique of order $$r+1$$ and a cycle of even length, respectively. Denote by $$ex_p(n,H)$$ the maximum value of $$e_p(G)$$ taken over all graphs with $$n$$ vertices that do not contain $$H$$ as a subgraph. Clearly, $$ex_1(n,H)=2ex(n,H)$$ , where $$ex(n,H)$$ denotes the classical Turán number. In this paper, we consider $$ex_p(n, C_5)$$ and prove that for any positive integer $$p$$ and sufficiently large $$n$$ , there exists a constant $$c=c(p)$$ such that the following holds: if $$ex_p(n, C_5)=e_p(G)$$ for some $$C_5$$ -free graph $$G$$ of order $$n$$ , then $$G$$ is a complete bipartite graph having one vertex class of size $$cn+o(n)$$ and the other $$(1-c)n+o(n)$$ . [ABSTRACT FROM AUTHOR]

Let $${\mathcal {F}}$$ denote the class of all functions univalent in the unit disk $$\Delta \equiv \{\zeta \in {\mathbb {C}}\,:\,\left| \zeta \right| <1\}$$ and convex in the direction of the real axis. The paper deals with the subclass $${\mathcal {F}}^{(n)}$$ of these functions $$f$$ which satisfy the property $$f(\varepsilon z)=\varepsilon f(z)$$ for all $$z\in \Delta $$ , where $$\varepsilon =e^{2\pi i/n}$$ . The functions of this subclass are called $$n$$ -fold symmetric. For $${\mathcal {F}}^{(n)}$$ , where $$n$$ is odd positive integer, the following sets, $$\bigcap _{f\in {\mathcal {F}}^{(n)}} f(\Delta )$$ -the Koebe set and $$\bigcup _{f\in {\mathcal {F}}^{(n)}} f(\Delta )$$ -the covering set, are discussed. As corollaries, we derive the Koebe and the covering constants for $${\mathcal {F}}^{(n)}$$ . [ABSTRACT FROM AUTHOR]

Take three integers $$m\ge 0,\,k\ge 1$$ , and $$n\ge 2$$ . Let $$a\ (\not \equiv 0)$$ be a holomorphic function in a domain $$D$$ of $$\mathbb {C}$$ such that multiplicities of zeros of $$a$$ are at most $$m$$ and divisible by $$n+1$$ . In this paper, we mainly obtain the following normality criterion: Let $${{{\fancyscript{F}}}}$$ be the family of meromorphic functions on $$D$$ such that multiplicities of zeros of each $$f\in {{\fancyscript{F}}}$$ are at least $$k+m$$ and such that multiplicities of poles of $$f$$ are at least $$m+1$$ . If each pair $$(f,g)$$ of $${{\fancyscript{F}}}$$ satisfies that $$f^{n}f^{(k)}$$ and $$g^{n}g^{(k)}$$ share $$a$$ (ignoring multiplicity), then $${{\fancyscript{F}}}$$ is normal. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a concept of graph convergence for the $$H(\cdot ,\cdot )$$ -co-accretive mapping in Banach spaces and prove an equivalence theorem between graph convergence and resolvent operator convergence for the $$H(\cdot ,\cdot )$$ -co-accretive mapping. Further, we consider a system of generalized variational inclusions involving $$H(\cdot ,\cdot )$$ -co-accretive mapping in real $$q$$ -uniformly smooth Banach spaces. Using resolvent operator technique, we prove the existence and uniqueness of solution and suggest an iterative algorithm for the system of generalized variational inclusions under some suitable conditions. Further, we discuss the convergence of iterative algorithm using the concept of graph convergence. Our results can be viewed as a refinement and generalization of some known results in the literature. [ABSTRACT FROM AUTHOR]

There are many articles in the literature dealing with the first-order and the second-order differential subordination and differential superordination problems for analytic functions in the unit disk, but there are only a few articles dealing with the third-order differential subordination problems. The concept of third-order differential subordination in the unit disk was introduced by Antonino and Miller, and studied recently by Tang and Deniz. Let $$\Omega $$ be a set in the complex plane $$\mathbb {C}$$ , let $$\mathfrak {p}(z)$$ be analytic in the unit disk $$\mathbb {U}=\{z:z\in \mathbb {C}\quad \text {and} \quad |z|<1\}$$ , and let $$\psi : \mathbb {C}^4\times \mathbb {U}\rightarrow \mathbb {C}$$ . In this paper, we investigate the problem of determining properties of functions $$\mathfrak {p}(z)$$ that satisfy the following third-order differential superordination: As applications, we derive some third-order differential superordination results for analytic functions in $$\mathbb {U}$$ , which are associated with a family of generalized Bessel functions. The results are obtained by considering suitable classes of admissible functions. New third-order differential sandwich-type results are also obtained. [ABSTRACT FROM AUTHOR]

In this paper, we use a result of N. S. Feldman to show that there are no supercyclic subnormal tuples in infinite dimensions. Also, we investigate some spectral properties of hypercyclic tuples of operators. Besides, we prove that if $$T$$ is a supercyclic $$\ell $$ -tuple of commuting $$n\times n$$ complex matrices, then $$\ell \ge n$$ and also there exists a supercyclic $$n$$ -tuple of commuting diagonal $$n\times n$$ matrices. Furthermore, we see that if $$T=(T_{1},\ldots ,T_{n})$$ is a supercyclic $$n$$ -tuple of commuting $$n\times n$$ complex matrices, then $$T_{j}$$ 's are simultaneously diagonalizable. [ABSTRACT FROM AUTHOR]

In this paper, we characterize the congruence lattice of a symmetric extended De Morgan algebra $$L$$ . We show that the congruence lattice of the algebra $$L$$ is a pseudocomplemented lattice, and that such a congruence lattice is a Stone lattice if and only if the lattice of the compact congruences on $$L$$ forms a complete Boolean lattice. In particular, we prove that the congruence lattice of $$L$$ is a Boolean lattice if and only if, it is a relative Stone lattice, which is the case, if and only if $$L$$ is finite. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the Morgenstern type bivariate-generalized exponential distribution. This distribution is an extension of Morgenstern type bivariate exponential distribution (MTBED), and the marginal distributions are generalized exponential distribution. We study some properties of this bivariate distribution. Also, some distributional properties of concomitants of order statistics as well as record values for the MTBED are studied. Recurrence relations between moments of concomitants are also obtained. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the central limit theorem and the law of the iterated logarithm for Galton-Watson branching processes with time-dependent immigration in varying environments. [ABSTRACT FROM AUTHOR]

The b-chromatic index $$\varphi '(G)$$ of a graph $$G$$ is the largest integer $$k$$ such that $$G$$ admits a proper $$k$$ -edge coloring in which every color class contains at least one edge incident to some edge in all the other color classes. The b-chromatic index of trees is determined and equals either to a natural upper bound $$m'(T)$$ or one less, where $$m'(T)$$ is connected with the number of edges of high degree. Some conditions are given for which graphs have the b-chromatic index strictly less than $$m'(G)$$ , and for which conditions it is exactly $$m'(G)$$ . In the last part of the paper, regular graphs are considered. It is proved that with four exceptions, the b-chromatic index of cubic graphs is $$5$$ . The exceptions are $$K_4$$ , $$K_{3,3}$$ , the prism over $$K_3$$ , and the cube $$Q_3$$ . [ABSTRACT FROM AUTHOR]

Cohen-Macaulayness of bipartite graphs is investigated by several mathematicians and has been characterized combinatorially. In this paper, we give some different combinatorial conditions for a bipartite graph which are equivalent to Cohen-Macaulayness of the graph. We prove that a bipartite graph is Cohen-Macaulay if and only if it is well covered and has a unique perfect matching. We also provide a fast algorithm to check Cohen-Macaulayness of a given bipartite graph. [ABSTRACT FROM AUTHOR]

A connected graph $$G$$ is said to be factor-critical if $$G-v$$ has a perfect matching for every vertex $$v$$ of $$G$$ . Lovász proved that every factor-critical graph has an ear decomposition. In this paper, the ear decomposition of the factor-critical graphs $$G$$ satisfying that $$G-v$$ has a unique perfect matching for any vertex $$v$$ of $$G$$ with degree at least 3 is characterized. From this, the number of maximum matchings of factor-critical graphs with the special ear decomposition is obtained. [ABSTRACT FROM AUTHOR]

An $$m\times n\,\{0,1\}$$ -matrix $$A$$ is said to be totally convertible if there exists a matrix $$B$$ obtained from $$A$$ by changing some 1's in $$A$$ to $$-1$$ 's such that for any submatrix $$A^{\prime }$$ of $$A$$ of order $$m$$ , the corresponding submatrix $$B^{\prime }$$ of $$B$$ satisfies $$\mathrm{per}(xI-A^{\prime })=\det (xI-B^{\prime })$$ . In this paper, motivated by the well-known Pólya's problem, our object is to characterize those totally convertible matrices. Associate a matrix $$A$$ with a bipartite graph $$G^{*}_A$$ . We first prove that a square matrix $$A$$ is totally convertible if and only if $$G^{*}_A$$ is Pfaffian, and then we generalize this result to an $$m\times n$$ $$\{0,1\}$$ -matrix. Moreover, the characterization of a totally convertible matrix provides an equivalent condition to compute the permanental polynomial of a bipartite graph by the characteristic polynomial of the skew adjacency matrix of its orientation graph. As applications, we give some explicit expressions of the permanental polynomials of two totally convertible matrices by the technique of Pfaffian orientation. [ABSTRACT FROM AUTHOR]

In this paper, we present some results on the existence of random coincidence points of expansive type completely random operators. Some applications to random fixed point theorems and random equations are given. [ABSTRACT FROM AUTHOR]

The energy of a simple graph $$G$$ , denoted by $$E(G)$$ , is defined as the sum of the absolute values of eigenvalues of $$G$$ . In this paper, we show that, among all subdivisions of graphs with $$n$$ vertices and chromatic number $$k$$ , the subdivision of the Turán graph $$T(n,k)$$ has the maximal energy. [ABSTRACT FROM AUTHOR]

In this paper we introduce and study the concepts of graded second (gr-second) and graded coprimary (gr-coprimary) modules which are different from second and coprimary modules over arbitrary-graded rings. We list some properties and characterizations of gr-second and gr-coprimary modules and also study graded prime submodules of modules with gr-coprimary decompositions. We also deal with graded secondary representations for graded injective modules over commutative-graded rings. By using the concept of $$\sigma $$ -suspension $$(\sigma )M$$ of a graded module $$M,$$ we prove that a graded injective module over a commutative graded Noetherian ring has a graded secondary representation. [ABSTRACT FROM AUTHOR]

This paper deals with equilibrium problems with nonlinear constraints. Exploiting a gap function which relies on a polyhedral approximation of the feasible region, we propose two descent methods. They are both based on the minimization of a suitable exact penalty function, but they use different rules for updating the penalization parameter and they rely on different types of line search. The convergence of both algorithms is proved under standard assumptions. [ABSTRACT FROM AUTHOR]

This paper presents a new proof method about the paper (Yuan et al. in Appl. Math. Model. 47:811–825, 2017). In the proof, the global convergence of the Polak–Ribière–Polak algorithm is established without these two assumptions d k T g k < 0 and g k + 1 d k ≤ − σ 1 g k T d k which are needed in the above paper. This means that this paper has the same results under weaker conditions. More dimension functions for practical problems are tested to show the performance of the modified algorithm and the normal algorithm. An application of the fact engineering model is done to show the effectiveness of the given conjugate gradient algorithm. [ABSTRACT FROM AUTHOR]

The problem in this paper is motivated by physical problems concerned with the case when a class of continuous and equimeasurable densities of a string is given then how to find minimal frequencies among these given densities, that is, what kind of densities minimize the frequencies. By taking Dirichlet eigenvalues into account, given a certain weight function ω, we will show the minimizer of the mth eigenvalue is the m-degree continuous symmetrical decreasing rearrangement of ω. The main result of this paper can be viewed as complementary to Schwarz’s work (Schwarz in J. Math. Mech. 10:401-422, 1961). [ABSTRACT FROM AUTHOR]

Due to the complex topological structure of the coronary artery and the uneven distribution of the contrast agent, the angiography images are inevitably blurred and has low contrast, which causes great difficulty in process of segmentation. For this problem, a two-steps segmentation algorithm based on Hessian matrix and level set is proposed in this paper. Firstly, potential blood vessels of coronary images are preliminary extracted via Hessian matrix eigenvalues feature vectors of the geometric features and the response function. Then a novel regularization and area constraint is introduced into the local data energy fitting functional. Finally, the precision of Coronary Artery image is obtained in the evolution of the level set function. Experiments show that our proposed algorithm has better performance to these comparison segmentation algorithms. [ABSTRACT FROM AUTHOR]