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Lung cancer is the biggest cause of cancer mortality worldwide and a major impediment to extending life expectancy. In comparison to other cancers, it has a relatively poor survival rate. In this paper, we have developed a mathematical model for lung cancer based on biological phenomena using nonlinear ordinary differential equations and analyzed it both analytically and numerically. According to the findings, CD8+ T cells and dendritic cells have a role in tumor cell variety. Surgery and chemotherapy have been used as treatment options, and we have observed that three doses of chemotherapy after surgery had the greatest results after examining several treatment options. During the treatment period, the cycle of each chemotherapy has been taken every 4 weeks, and the first dose has been taken after 28 days of surgery. Finally, we have evaluated the various starting dates for the best treatment choice and discovered that the patient who begins treatment sooner has a better probability of surviving. [ABSTRACT FROM AUTHOR]

Nowadays, skin cancer is a worldwide panic. It is related to ultraviolet radiation. In this paper, we have formulated a SIRS type mathematical model to show the effects of ultraviolet radiation on skin cancer. At first, we have showed the boundedness and positivity of the model solutions to verify the model's existence and uniqueness. The boundedness and positivity gave the solutions of our model bounded and positive, which was very important for real-world situation because in real world, population cannot be negative. Then, we have popped out all the equilibrium points of our model and verified the stability of the equilibrium points. This stability test expressed some physical situation of our model. The disease-free equilibrium point is locally asymptotically stable if R 0 < 1 and if R 0 > 1 , then it is unstable. Again, the endemic equilibrium point is stable, if R 0 > 1 and unstable if R 0 < 1. In order to understand the dynamical behavior of the model's equilibrium points, we examined the phase portrait. We also have observed the sensitivity of the model parameters. After this, we have investigated the different scenarios of bifurcations of the model's parameters. At the set of Hopf bifurcation parameters when infection rate due to UV rays is less than α 1 = 0.01 , proper control may eradicate the existence of disease. From transcritical bifurcation, we can say when recovery rate greater than 1.9, then the disease of skin cancer can be eliminated and when recovery rate less than 1.9 then the disease of skin cancer cannot be eradicated. Finally, numerical analysis is done to justify our analytical findings. [ABSTRACT FROM AUTHOR]

Tuberculosis (TB) and coronavirus (COVID-19) are both infectious diseases that globally continue affecting millions of people every year. They have similar symptoms such as cough, fever, and difficulty breathing but differ in incubation periods. This paper introduces a mathematical model for the transmission dynamics of TB and COVID-19 coinfection using a system of nonlinear ordinary differential equations. The well-posedness of the proposed coinfection model is then analytically studied by showing properties such as the existence, boundedness, and positivity of the solutions. The stability analysis of the equilibrium points of submodels is also discussed separately after computing the basic reproduction numbers. In each case, the disease-free equilibrium points of the submodels are proved to be both locally and globally stable if the reproduction numbers are less than unity. Besides, the coinfection disease-free equilibrium point is proved to be conditionally stable. The sensitivity and bifurcation analysis are also studied. Different simulation cases were performed to supplement the analytical results. [ABSTRACT FROM AUTHOR]

In the paper, we have considered a nonlinear compartmental mathematical model that assesses the effect of treatment on the dynamics of HIV/AIDS and pneumonia coinfection in a human population at different infection stages. Our model revealed that the disease-free equilibrium points of the HIV/AIDS and pneumonia submodels are both locally and globally asymptotically stable whenever the associated basic reproduction numbers ( R H and R P ) are less than unity. Both the submodel endemic equilibrium points are locally and globally asymptotically stable whenever the associated basic reproduction numbers ( R P and R H ) are greater than unity. The full HIV/AIDS-pneumonia coinfection model has both locally and globally asymptotically stable disease-free equilibrium points whenever the basic reproduction number of the coinfection model R H P is less than unity. Using standard values of parameters collected from different kinds of literature, we found that the numerical values of the basic reproduction numbers of the HIV/AIDS-only submodel and pneumonia-only submodel are 17 and 7, respectively, and the basic reproduction number of the HIV/AIDS-pneumonia coinfection model is max 7 , 17 = 17. Applying sensitive analysis, we identified the most influential parameters to change the behavior of the solution of the considered coinfection dynamical system are the HIV/AIDS and pneumonia transmission rates β 1 and β 2 , respectively. The coinfection model was numerically simulated to investigate the stability of the coinfection endemic equilibrium point, the impacts of transmission rates, and treatment strategies for HIV/AIDS-only, pneumonia-only, and HIV/AIDS-pneumonia coinfected individuals. Finally, we observed that numerical simulations indicate that treatment against infection at every stage lowers the rate of infection or disease prevalence. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model that describes the transmission dynamics of schistosomiasis for humans, snails, and the free living miracidia and cercariae. The model incorporates the treated compartment and a preventive factor due to water sanitation and hygiene (WASH) for the human subpopulation. A qualitative analysis was performed to examine the invariant regions, positivity of solutions, and disease equilibrium points together with their stabilities. The basic reproduction number, R 0 , is computed and used as a threshold value to determine the existence and stability of the equilibrium points. It is established that, under a specific condition, the disease-free equilibrium exists and there is a unique endemic equilibrium when R 0 > 1. It is shown that the disease-free equilibrium point is both locally and globally asymptotically stable provided R 0 < 1 , and the unique endemic equilibrium point is locally asymptotically stable whenever R 0 > 1 using the concept of the Center Manifold Theory. A numerical simulation carried out showed that at R 0 = 1 , the model exhibits a forward bifurcation which, thus, validates the analytic results. Numerical analyses of the control strategies were performed and discussed. Further, a sensitivity analysis of R 0 was carried out to determine the contribution of the main parameters towards the die out of the disease. Finally, the effects that these parameters have on the infected humans were numerically examined, and the results indicated that combined application of treatment and WASH will be effective in eradicating schistosomiasis. [ABSTRACT FROM AUTHOR]

In this paper, the analyses of traffic evolution on the road network of a roundabout having three entrances and three exiting legs are conducted from macroscopic point of view. The road networks of roundabouts are modeled as a merging and diverging types 1 × 2 and 2 × 1 junctions. To study traffic evolution at junction, two cases have been considered, namely, demand and supply limited cases. In each case, detailed mathematical analysis and numerical tests have been presented. The analysis in the case of demand limited showed that rarefaction wave fills the portion of the road network in time. In the contrary, in supply limited case, traffic congestion occurs at merging junctions and shock wave propagating back results in reducing the performance of a roundabout to control traffic dynamics. Also, we illustrate density and flux profiles versus space discretization at different time steps via numerical simulation with the help of Godunov scheme. [ABSTRACT FROM AUTHOR]

The integrals evaluated are the products of multivariable Aleph-functions with algebraic functions, Jacobi polynomials, Legendre functions, Bessel-Maitland functions, and general class of polynomials. The main results of our paper are quite general in nature and competent at yielding a very large number of integrals involving polynomials and various special functions occurring in the problem of mathematical analysis and mathematical physics. [ABSTRACT FROM AUTHOR]

Weak convergence of semi-Markov processes in the diffusive approximation scheme is studied in the paper. This problem is not new and it is studied in many papers, using convergence of random processes. Unlike other studies, we used in this paper concept of the compensating operator. It enables getting sufficient conditions of weak convergence under the conditions on the local characteristics of output semi-Markov process. [ABSTRACT FROM AUTHOR]

This paper deals with the modeling of fault for analog circuits. A two-dimensional (2D) fault model is first proposed based on collaborative analysis of supply current and output voltage. This model is a family of circle loci on the complex plane, and it simplifies greatly the algorithms for test point selection and potential fault simulations, which are primary difficulties in fault diagnosis of analog circuits. Furthermore, in order to reduce the difficulty of fault location, an improved fault model in three-dimensional (3D) complex space is proposed, which achieves a far better fault detection ratio (FDR) against measurement error and parametric tolerance. To address the problem of fault masking in both 2D and 3D fault models, this paper proposes an effective design for testability (DFT) method. By adding redundant bypassing-components in the circuit under test (CUT), this method achieves excellent fault isolation ratio (FIR) in ambiguity group isolation. The efficacy of the proposed model and testing method is validated through experimental results provided in this paper. [ABSTRACT FROM AUTHOR]

This paper deals with a nonlinear differential equation, by using the fixed point theory. The existence of the periodic solution of the nonlinear differential equation is obtained; these results are new. [ABSTRACT FROM AUTHOR]

Nonclassical slicing and symmetry reduction can act as efficient structural abstract methods for pruning state space when dealing with verification problems. In this paper, we mainly address theoretical and algorithmic aspects for nonclassical slicing and symmetry reduction over prime event structures. We propose sliced and symmetric quotient reduction models of event structures and present their corresponding algorithms. To construct the underlying foundation of the proposed methodologies, we introduce strong and weak conflict concepts and a pair of mutually inverse operators and extend permutation group based symmetry notion of event structures. We have established a unified mathematical framework for slicing and symmetry reduction, and further investigated the translation, isomorphism, and equivalence relationship and other related basic facts from a theoretical point of view. The framework may provide useful guidance and theoretical exploration for overcoming verification challenges. This paper also demonstrates their practical applications by two cases. [ABSTRACT FROM AUTHOR]

Let G = (V, E) be a connected simple graph and let M be a nonempty subset of V. The M-distance pattern of a vertex u in G is the set of all distances from u to the vertices in M. If the distance patterns of all vertices in V are distinct, then the set Mis a distance pattern distinguishing set of G. A graph G with a distance pattern distinguishing set is called a distance pattern distinguishing graph. Minimum number of vertices in a distance pattern distinguishing set is called distance pattern distinguishing number of a graph. This paper initiates a study on the problem of finding distance pattern distinguishing number of a graph and gives bounds for distance pattern distinguishing number. Further, this paper provides an algorithm to determine whether a graph is a distance pattern distinguishing graph or not and hence to determine the distance pattern distinguishing number of that graph. [ABSTRACT FROM AUTHOR]

This paper investigates finite-time synchronization of the singular hybrid coupled networks. The singular systems studied in this paper are assumed to be regular and impulse-free. Some sufficient conditions are derived to ensure finite-time synchronization of the singular hybrid coupled networks under a state feedback controller by using finite-time stability theory. A numerical example is finally exploited to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigating the limit properties of distances and the existence and uniqueness of fixed points, best proximity points and existence, and uniqueness of limit cycles, to which the iterated sequences converge, of single-valued, and socalled, contractive precyclic self-mappings which are proposed in this paper. Such self-mappings are defined on the union of a finite set of subsets of uniformly convex Banach spaces under generalized contractive conditions. Each point of a subset is mapped either in some point of the same subset or in a point of the adjacent subset. In the general case, the contractive condition of contractive precyclic self-mappings is admitted to be point dependent and it is only formulated on a complete disposal, rather than on each individual subset, while it involves a condition on the number of iterations allowed within each individual subset before switching to its adjacent one. It is also allowed that the distances in-between adjacent subsets can be mutually distinct including the case of potential pairwise intersection for only some of the pairs of adjacent subsets. [ABSTRACT FROM AUTHOR]

The purpose of this paper is using Korpelevich's extragradient method to study the existence problem of solutions and approximation solvability problem for a class of systems of finite family of general nonlinear variational inequality in Banach spaces, which includes many kinds of variational inequality problems as special cases. Under suitable conditions, some existence theorems and approximation solvability theorems are proved. The results presented in the paper improve and extend some recent results. [ABSTRACT FROM AUTHOR]

The first step in the analysis of a structure is to generate its configuration. Different means are available for this purpose. The use of graph products is an example of such tools. In this paper, the use of product graphs is extended for the formation of different types of structural models. Here weighted graphs are used as the generators and the connectivity properties of different models are expressed in terms of the properties of their generators through simple algebraic relationships. In this paper by using graph product concepts and spatial structured matrices, a new algebraic closed form is proposed for mathematical formulation and presentation of structures. For clarification some examples are included. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to investigate the problems of the well-posedness for a system of mixed quasivariational-like inequalities in Banach spaces. First, we generalize the concept of a-well-posedness to the system of mixed quasivariational-like inequalities, which includes symmetric quasi-equilibrium problems as a special case. Second, we establish some metric characterizations of a-well-posedness for the system of mixed quasivariational-like inequalities. Under some suitable conditions, we prove that the a-well-posedness is equivalent to the existence and uniqueness of solution for the system of mixed quasivariational-like inequalities. The corresponding concept of a-well-posedness in the generalized sense is also considered for the system of mixed quasivariational-like inequalities having more than one solution. The results presented in this paper generalize and improve some known results in the literature. [ABSTRACT FROM AUTHOR]

The techniques for parametrizing nonsingular cubic surfaces have shown to be of great interest in recent years. This paper is devoted to the rational parametrization of nonsingular cubic blending surfaces. We claim that these nonsingular cubic blending surfaces can be parametrized using the symbolic computation due to their excellent geometric properties. Especially for the specific forms of these surfaces, we conclude that they must be F3, F4, or F5 surfaces, and a criterion is given for deciding their surface types. Besides, using the algorithm proposed by Berry and Patterson in 2001, we obtain the uniform rational parametric representation of these specific forms. It should be emphasized that our results in this paper are invariant under any nonsingular real projective transform. Two explicit examples are presented at the end of this paper. [ABSTRACT FROM AUTHOR]

Some properties of the weak subdifferential are considered in this paper. By using the definition and properties of the weak subdifferential which are described in the papers (Azimov and Gasimov, 1999; Kasimbeyli and Mammadov, 2009; Kasimbeyli and Inceoglu, 2010), the author proves some theorems connecting weak subdifferential in nonsmooth and nonconvex analysis. It is also obtained necessary optimality condition by using the weak subdifferential in this paper. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study the convergence properties of Generalized Fibonacci Sequences and the series of partial sums associated with them. When the proper values of an s×s real matrix A are real and different, we give a necessary and sufficient condition for the convergence of the matrix sequence A,A2,A3,… to a matrix B. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the motion of two associated ruled surfaces in Euclidean 3-space E3. In particular, the motion of Bishop Frenet offsets of ruled surfaces is investigated. Additionally, the characteristic properties for such ruled surfaces are given. Finally, an application is presented and plotted using computer aided geometric design. [ABSTRACT FROM AUTHOR]

This paper is concerned with the scattering problem of time-harmonic acoustic plane waves by an impenetrable obstacle buried in a piecewise homogeneous medium. The so-called generalized impedance boundary condition is imposed on the boundary of the obstacle. Firstly, the well posedness of the solution to the direct scattering problem is established by using the boundary integral method. Then a uniqueness result for the inverse scattering problem is proved; that is, both of the obstacle’s shape and the impedances (μ, λ) can be uniquely determined from far field measurements. Furthermore, a mathematical basis is given to reconstruct the shape of the obstacle by using a modified linear sampling method. [ABSTRACT FROM AUTHOR]

An (a,s)-vertex-antimagic edge labeling (or an (a,s)-VAE labeling, for short) of G is a bijective mapping from the edge set E(G) of a graph G to the set of integers 1,2,…,|E(G)| with the property that the vertex-weights form an arithmetic sequence starting from a and having common difference s, where a and s are two positive integers, and the vertex-weight is the sum of the labels of all edges incident to the vertex. A graph is called (a,s)-antimagic if it admits an (a,s)-VAE labeling. In this paper, we investigate the existence of (a,1)-VAE labeling for disconnected 3-regular graphs. Also, we define and study a new concept (a,s)-vertex-antimagic edge deficiency, as an extension of (a,s)-VAE labeling, for measuring how close a graph is away from being an (a,s)-antimagic graph. Furthermore, the (a,1)-VAE deficiency of Hamiltonian regular graphs of even degree is completely determined. More open problems are mentioned in the concluding remarks. [ABSTRACT FROM AUTHOR]

By presenting Riordanmatrix as a triangle, the central coefficients are entries in the central column. Starting at the central column, the r-shifted central coefficients are entries in column r of the right part of the triangle. This paper aims to characterize the r-shifted central coefficients of Riordan matrices. Here we will concentrate on four elements of the subgroups of the Riordan group, that is, the Bell subgroup, the associated subgroup, the derivative subgroup, and the hitting time subgroup. Some examples are presented to show how we deduce the generating functions for interesting sequences by using different means of calculating these r-shifted central coefficients. Besides, we make some extensions in the Bell subgroup. [ABSTRACT FROM AUTHOR]

Project planning, defining the limitations and resources by leveling the resources available, have a great importance for the management projects. All these activities directly affect the duration and the cost of the project. To get a competitive value on the market, the project must be completed at the optimum time. In other to be competitive enough the optimum or near optimum solutions of time cost tradeoff and the resource leveling and resource constrained scheduling problems should be obtained in the planning phase of the project. One important aspect of the projectmanagement is activity crashing, that is, reducing activity time by addingmore resources such as workers and overtime. It is important to decide the optimal crash plan to complete the project within the desired time period. The comparison of fuzzy simulated annealing and the genetic algorithm based on the crashing method is introduced in this paper to evaluate project networks and determine the optimum crashing configuration that minimizes the average project cost, caused by being late and crashing costs in the presence of vagueness and uncertainty. The evaluation results based on a real case study indicate that the method can be reliably applied to engineering projects. [ABSTRACT FROM AUTHOR]

Two families of third-order iterative methods for finding multiple roots of nonlinear equations are developed in this paper. Mild conditions are given to assure the cubic convergence of two iteration schemes (I) and (II). The presented families include many third-ordermethods for findingmultiple roots, such as the known Dong'smethods andNeta'smethod. Some new concrete iterative methods are provided. Each member of the two families requires two evaluations of the function and one of its first derivative per iteration. All these methods require the knowledge of the multiplicity. The obtainedmethods are also compared in their performance with various other iteration methods via numerical examples, and it is observed that these have better performance than the modified Newton method, and demonstrate at least equal performance to iterative methods of the same order. [ABSTRACT FROM AUTHOR]

In 2012, Abdo and Dimitrov defined the total irregularity of a graph G = (V, E) as irrt (G) = (1/2)Σ u, VϵV dG(U) - dG (V), where d G (U) denotes the vertex degree of a vertex u ϵ V. In this paper, we investigate the total irregularity of bicyclic graphs and characterize the graph with the maximal total irregularity among all bicyclic graphs on n vertices. [ABSTRACT FROM AUTHOR]

This paper considers several estimators for estimating the stochastic restricted ridge regression estimators. A simulation study has been conducted to compare the performance of the estimators. The result from the simulation study shows that stochastic restricted ridge regression estimators outperform mixed estimator. A numerical example has been also given to illustrate the performance of the estimators. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new relaxed extragradient algorithms for the split feasibility problem. Our relaxed extragradient algorithm is new and it generalized some results for solving the split feasibility problem. [ABSTRACT FROM AUTHOR]

The Particle Swarm Optimization (PSO) Algorithm is a popular optimization method that is widely used in various applications, due to its simplicity and capability in obtaining optimal results. However, ordinary PSOsmay be trapped in the local optimal point, especially in high dimensional problems. To overcome this problem, an efficient Global Particle Swarm Optimization (GPSO) algorithm is proposed in this paper, based on a new updated strategy of the particle position. This is done through sharing information of particle position between the dimensions (variables) at any iteration. The strategy can enhance the exploration capability of the GPSO algorithm to determine the optimum global solution and avoid traps at the local optimum. The proposed GPSO algorithmis validated on a 12-benchmarkmathematical function and compared with three different types of PSO techniques. The performance of this algorithm is measured based on the solutions' quality, convergence characteristics, and their robustness after 50 trials. The simulation results showed that the new updated strategy in GPSO assists in realizing a better optimum solution with the smallest standard deviation value compared to other techniques. It can be concluded that the proposed GPSO method is a superior technique for solving high dimensional numerical function optimization problems. [ABSTRACT FROM AUTHOR]

Thefirst main idea of this paper is to develop thematrix sequences that represent Padovan and Perrin numbers. Then, by taking into account matrix properties of these new matrix sequences, some behaviours of Padovan and Perrin numbers will be investigated. Moreover, some important relationships between Padovan and Perrin matrix sequences will be presented. [ABSTRACT FROM AUTHOR]

For a graph G = (V,E), a bijection f from V(G) U E(G) {1, 2, . . ., |V(G)| + |E(G)|} is called (a, d)-edge-antimagic total ((a, d)- EAT) labeling of G if the edge-weights w(xy) = f(x) + f(y) + f(xy), xy ε E(G), form an arithmetic progression starting from a and having a common difference d, where a > 0 and d = 0 are two fixed integers. An (a, d)-EAT labeling is called super (a, d)-EAT labeling if the vertices are labeled with the smallest possible numbers; that is,f(V) = {1, 2, . . ., |V(G)|}. In this paper, we study super (a, d)-EAT labeling of cycles with some pendant edges attached to different vertices of the cycle. [ABSTRACT FROM AUTHOR]

There are occasions when an average value of a graph parameter gives more useful information than the basic global value. In this paper, we introduce the concept of the average covering number of a graph (the covering number of a graph is the minimum number of vertices in a set with the property that every edge has a vertex in the set). We establish relationships between the average covering number and some other graph parameters, find the extreme values of the average covering number among all graphs of a given order, and find the average covering number for some families of graphs. [ABSTRACT FROM AUTHOR]

The aim of this paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of int-soft positive implicative ideals is introduced, and related properties are investigated. Relations between an int-soft ideal and an int-soft positive implicative ideal are established. Characterizations of an int-soft positive implicative ideal are obtained. Extension property for an int-soft positive implicative ideal is constructed. The Λ-product and Λproduct of int-soft positive implicative ideals are considered, and the soft intersection (resp., union) of int-soft positive implicative ideals is discussed. [ABSTRACT FROM AUTHOR]

This paper deals with a generalized form of nonlinear retarded Gronwall-Bellman type integral inequality in which the maximum of the unknown function of two variables is involved. This form includes both a nonconstant term outside the integrals and more than one distinct nonlinear integrals. Requiring neither monotonicity nor separability of given functions, we apply a technique of monotonization to estimate the unknown function. Our result can be used to weaken conditions for some known results. We apply our result to a boundary value problem of a partial differential equation with maxima for uniqueness. [ABSTRACT FROM AUTHOR]

In a communication network, the vulnerability parameters measure the resistance of the network to disruption of operation after the failure of certain stations or communication links. A vertex subversion strategy of a graph G, say S, is a set of vertices in G whose closed neighborhood is removed from G. The survival subgraph is denoted by G/S. The neighbor rupture degree of G, Nr(G), is defined to be Nr(G) = max{ω(G/S)-|S|-c(G/S) : S ⊂ V(G),ω(G/S) ≥ 1}, where S is any vertex subversion strategy of G, ω(G/S) is the number of connected components in G/S and c(G/S) is the maximum order of the components of G/S (G. Bacak Turan, 2010). In this paper we give some results for the neighbor rupture degree of the graphs obtained by some graph operations. [ABSTRACT FROM AUTHOR]

Some comparison theorems for the spectral radius of double splittings of different matrices under suitable conditions are presented, which are superior to the corresponding results in the recent paper by Miao and Zheng (2009). Some comparison theorems between the spectral radius of single and double splittings of matrices are established and are applied to the Jacobi and Gauss-Seidel double SOR method. [ABSTRACT FROM AUTHOR]

We give new results of a cyclic generalized weakly C-contraction in partial metric space. The results of this paper extend, generalize, and improve some fixed point theorems in the literature. [ABSTRACT FROM AUTHOR]

For a,b > 0 with a≠b, the Schwab-Borchardt mean SB(a,b) is defined as SB(a,b) = {√b² - a² /cos-1 (a/b) if a b. In this paper, we find the greatest values of α1 and α2 and the least values of β1 and β2 in [0, 1/2] such that H(α1 a+(1- α1 )b, α1b+(1-α1 )a) < SAH (a,b) < H(β1 a+(1-β1 )b, β1b+(1-β1 )a) and H(α2 a+(1-α2 )b, α2b+(1-α2 )a) < SAH (a,b) < H(β2 a+ (1-β2 )b, β2b+(1-β2 )a). Similarly, we also find the greatest values of α3 and α4 and the least values of β3 and β4 in [1/2, 1] such that C(α3 a+(1-α3 )b, α3b+(1-α3 )a) < SCA (a,b) < C(β3 a+(1-β3 )b, β3b+(1-β3 )a) and C(α4 a+(1-α4 )b, α4b+(1-α4 )a) < SAC (a,b) < C(β4 a+(1-β4 )b, β4b+(1-β4 )a). Here, H(a,b) = 2ab/(a+b), A(a,b) = (a+b)/2, and C(a,b) = (a 2 +b 2 )/(a+b) are the harmonic, arithmetic, and contraharmonic means, respectively, and SHA (a,b) = SB(H,A), SAH (a,b) = SB(A,H), SCA (a,b) = SB(C,A), and SAC (a,b) = SB(A, C) are four Neuman means derived from the Schwab-Borchardt mean. [ABSTRACT FROM AUTHOR]

Let G be a simple graph. The incidence energy (IE for short) of G is defined as the sum of the singular values of the incidencematrix. In this paper, a new upper bound for IE of graphs in terms of themaximum degree is given. Meanwhile, bounds for IE of the line graph of a semiregular graph and the paraline graph of a regular graph are obtained. [ABSTRACT FROM AUTHOR]

The edge-neighbor-rupture degree of a connected graph G is defined to be ENR(G) = max{ɷ(G - S) - |S| - m(G - S) : S s E(G), ɷ(G - S) = 1}, where S is any edge-cut-strategy of G, ɷ(G - S) is the number of the components of G-S, and m(G - S) is the maximumorder of the components of G-S. In this paper, the edge-neighbor-rupture degree of some graphs is obtained and the relations between edge-neighbor-rupture degree and other parameters are determined. [ABSTRACT FROM AUTHOR]

Thecontribution of the flowsignal is generally addressed by the weight function in the researches of the electromagnetic flowmeters, and various mathematical technologies were concentrated on the methodologies for solving the value of the weight function. However, it is still difficult to avoid the abstruse mathematical theories and the complex calculation when the solution domain is irregular in shape. This paper treats the problemwithin the intuitive physical perspective, and the approach, inwhich the proportion of the current is considered as the substitute for the weight function with the hypothetic current excitation source, is presented. A simple mathematical modeling of the current is built by means of the resistive network without the redundant assumption, and the strict mathematical derivation for the conventional asymmetric flow in the circular flowmeter is made to verify the feasibility and the correctness of the approach. The distributions of the weight function in various situations are obtained with the simulation employed, using the resistive network modeling, and the advantages of the approach are discussed. [ABSTRACT FROM AUTHOR]

The notion of strongly quotient graph (SQG) was introduced by Adiga et al. (2007). In this paper, we obtain some better results for the distance energy and the distance Estrada index of any connected strongly quotient graph (CSQG) as well as some relations between the distance Estrada index and the distance energy. We also present some bounds for the distance energy and the distance Estrada index of CSQG whose diameter does not exceed two. Additionally, we show that our results improve most of the results obtained by Güngör and Bozkurt (2009) and Zaferani (2008). [ABSTRACT FROM AUTHOR]

We investigate a periodic predator-prey systemsubject to impulsive perturbations, in which a disease can be transmitted among the prey species only, in this paper. With the help of the theory of impulsive differential equations and Lyapunov functional method, sufficient conditions for the permanence, global attractivity, and partial extinction of system are established, respectively. It is shown that impulsive perturbations contribute to the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results. [ABSTRACT FROM AUTHOR]

This paper was concerned to simulate both wet and dry bed dam break problems. A high-resolution finite volume method (FVM) was employed to solve the one-dimensional (1D) and two-dimensional (2D) shallow water equations (SWEs) using an unstructured Voronoi mesh grid. In this attempt, the robust local Lax-Friedrichs (LLxF) scheme was used for the calculating of the numerical flux at cells interfaces. The model named V-Break was run under the asymmetry partial and circular dam break conditions and then verified by comparing the model outputs with the documented results. Due to a precise agreement between those output and documented results, theV-Break could be considered as a reliablemethod for dealing with shallow water (SW) and shock problems, especially those having discontinuities. In addition, statistical observations indicated a good conformity between the V-Break and analytical results clearly. [ABSTRACT FROM AUTHOR]

The concepts of preinvex and invex are extended to the interval-valued functions. Under the assumption of invexity, the Karush- Kuhn-Tucker optimality sufficient and necessary conditions for interval-valued nonlinear programming problems are derived. Based on the concepts of having no duality gap in weak and strong sense, the Wolfe duality theorems for the invex interval-valued nonlinear programming problems are proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper studies the stability of complex-valued nonlinear differential system. The stability criteria of complex-valued nonlinear autonomous system are established. For the general complex-valued nonlinear non-autonomous system, the comparison principle in the context of complex fields is given. Those derived stability criteria not only provide a new method to analyze complex-valued differential system, but also greatly reduce the complexity of analysis and computation. [ABSTRACT FROM AUTHOR]

Modeling and testing for parallel software systems are very difficult, because the number of states and execution sequences expands significantly caused by parallel behaviors. In this paper, a model reduction method based on Coloured Petri Net (CPN) is shown, which could generate a functionality-equivalent and trace-equivalent model with smaller scale. Model-based testing for parallel software systems becomesmuch easier after the model is reduced by the reduction method. Specifically, a formal model for software system specification is constructed based on CPN. Then the places in the model are divided into input places, output places, and internal places; the transitions in the model are divided into input transitions, output transitions, and internal transitions. Internal places and internal transitions could be reduced if preconditions are matching, and some other operations should be done for functionality equivalence and trace equivalence. If the place and the transition are in a parallel structure, then many execution sequences will be removed from the state space. We have proved the equivalence and have analyzed the reduction effort, so that we could get the same testing result with much lower testing workload. Finally, some practices and a performance analysis show that the method is effective. [ABSTRACT FROM AUTHOR]

This paper introduces a new series of three-dimensional chaotic systems with cross-product nonlinearities. Based on some conditions, we analyze the globally exponentially or globally conditional exponentially attractive set and positive invariant set of these chaotic systems. Moreover, we give some known examples to show our results, and the exponential estimation is explicitly derived. Finally, we construct some three-dimensional chaotic systems with cross-product nonlinearities and study the switching system between them. [ABSTRACT FROM AUTHOR]

This paper considers the existence of positive solutions of the boundary value problems Vn +λ(V +Vp -Vq) = 0 and V(-1) = V(1) = 0, where p > r > q > -1 and λ is a positive parameter. Using a time-map approach, we obtain the exact number of positive solutions in different cases. [ABSTRACT FROM AUTHOR]