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There are many consensus measures that can be computed using Likert data. Although these measures should work with any number n of choices on the Likert scale, the measurements have been most widely studied and demonstrated for n = 5. One measure of consensus introduced by Akiyama et al. for n = 5 and theoretically generalized to all n depends on both the mean and variance and gives results that can differentiate between some group consensus behavior patterns better than other measures that rely on either just the mean or just the variance separately. However, this measure is more complicated and not easy to apply and understand. This paper addresses these two common problems by introducing a new computational method to find the measure of consensus that works for any number of Likert item choices. The novelty of the approach is that it uses computational methods in n-dimensional space. Numerical examples in three-dimensional (for n=6) and four-dimensional (for n=7) spaces are provided in this paper to assure the agreement of the computational and theoretical approach outputs. [ABSTRACT FROM AUTHOR]

The FRP-confined concrete-encased steel column is a new form of hybrid column, which integrates advantages of all the constituent materials. Its structural performance, including load carrying capacity, ductility, and corrosion resistance, has been demonstrated to be excellent by limited experimental investigation. Currently, no systematic procedure, particularly for that with reinforced structural steel of arbitrary shapes, has been proposed for the sectional analysis and design for such novel hybrid columns under biaxial loading. The present paper aims at filling this research gap by proposing an approach for the rapid section analysis and providing rationale basis for FRP-confined concrete-encased arbitrarily shaped steel columns. A robust iterative scheme has been used with a traditional so-called fiber element method. The presented numerical examples demonstrated the validity and accuracy of the proposed approach. [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]

Hölder’s inequality and its various extensions are playing very important roles in many branches of modern mathematics and physics. In this paper, we present some extensions of Hölder’s inequality via pseudo-integral. Moreover, some related Hölder type inequalities are also given. [ABSTRACT FROM AUTHOR]

Let TX be the full transformation semigroup on a set X. For a fixed nonempty subset Y of a set X, let TX,Y be the semigroup consisting of all full transformations from X into Y. In a paper published in 2008, Sanwong and Sommanee proved that the set FX,Y=α∈TX,Y:Xα=Yα is the largest regular subsemigroup of TX,Y. In this paper, we describe the maximal inverse subsemigroups of FX,Y and completely determine all the maximal regular subsemigroups of its ideals. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the full-duplex (FD) decode-and-forward (DF) cooperative relaying system, whereas the relay node can harvest energy from radiofrequency (RF) signals of the source and then utilize the harvested energy to transfer the information to the destination. Specifically, a hybrid time-power switching-based relaying method is adopted, which leverages the benefits of time-switching relaying (TSR) and power-splitting relaying (PSR) protocols. While energy harvesting (EH) helps to reduce the limited energy at the relay, full-duplex is one of the most important techniques to enhance the spectrum efficiency by its capacity of transmitting and receiving signals simultaneously. Based on the proposed system model, the performance of the proposed relaying system in terms of the ergodic capacity (EC) is analyzed. Specifically, we derive the exact closed form for upper bound EC by applying some special function mathematics. Then, the Monte Carlo simulations are performed to validate the mathematical analysis and numerical results. [ABSTRACT FROM AUTHOR]

Summary: Microgrids (MGs) can operate in two modes: grid‐connected and islanded. Islanding can be scheduled or unintentional. MG should be able to maintain its stability in case of unintentional islanding. Therefore, it is necessary to provide the required spinning reserve for stable islanding. In this paper, a two‐stage scheduling strategy is proposed to determine the required reserve for stable islanding by considering uncertainties of load and renewable generations. The proposed strategy uses advantages of the load as a reserve provider to compensate the deficiency of DGs and batteries in providing the required reserve. A novel objective function is proposed to determine the optimal amount of demand which considered as reserve. The objective function minimizes the sum of reserve preparation costs, expected cost of calling load reserve, and expected cost of emergency load curtailment. Another significant feature of the proposed model is its modularity that enables the model to be integrated with any other scheduling model. The effectiveness of the proposed model is evaluated by mathematical analysis and numerical simulations. [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]

This paper is an improvement over the previous work on New Sorting Algorithm first proposed by Sundararajan and Chakraborty (2007). Here we have taken the pivot element as the middle element of the array. We call this improved version Middle Pivot Element Algorithm (MPA) and it is found that MPA is much faster than the two algorithms RPA (Random Pivot element Algorithm) and FPA (First Pivot element Algorithm) in which the pivot element was selected either randomly or as the first element, respectively. [ABSTRACT FROM AUTHOR]

We provide a new definition for reproducing kernel space with weighted integral and present a method to construct and calculate the reproducing kernel for the space. The new reproducing kernel space is an enlarged reproducing kernel space, which contains the traditional reproducing kernel space. The proposed method of this paper is a universal method and is suitable for the case of that the weight is variable. Obviously, this new method will generalize a number of applications of reproducing kernel theory to many areas. [ABSTRACT FROM AUTHOR]

This paper presents a nonlinear projection neural network for solving interval quadratic programs subject to box-set constraints in engineering applications. Based on the Saddle point theorem, the equilibrium point of the proposed neural network is proved to be equivalent to the optimal solution of the interval quadratic optimization problems. By employing Lyapunov function approach, the global exponential stability of the proposed neural network is analyzed. Two illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper. [ABSTRACT FROM AUTHOR]

This paper considers a Stackelberg game model in a dual-channel supply chain, which is composed of a manufacturer and a retailer. The manufacturer and retailer consider fairness concern in the market competition, and the manufacturer takes market share and profit as his/her business objectives. The entropy complexity and dynamic characteristic of the dual-channel system are analyzed through mathematical analysis and numerical simulation, such as local stability, bifurcation, entropy, and chaos. The results show that, with the increase of price adjustment speed, the dual-channel supply chain is more complex and falls into a chaotic state in which system entropy increases; the stability of the dual-channel supply chain will be robust with the increase of weight of market share and weaken with the increase of the fairness concern level of the manufacturer and retailer. The high level of fairness concern of the manufacturer and retailer is always disadvantageous to the leading manufacturer but not always bad for the follower retailer. The performance of the dual-channel supply chain is improved with a high level of the manufacturer's fairness concern and reduced with a high level of the retailer's fairness concern. We also find the retailer will gain more profits in the chaotic state than the stable state in the Stackelberg game model. The variable feedback control method is applied to control the chaos of the dual-channel supply chain, and choosing appropriate control parameters can make the dual-channel supply chain system return to the stable state from the chaotic state, or delay the system to enter the bifurcation state. The research results can provide a guideline for enterprise decision-making. [ABSTRACT FROM AUTHOR]

Unfortunately, situations such as flood, hurricanes, chemical accidents, and other events occur frequently more and more. To improve the efficiency and practicality of evacuation management plan, an integrated optimization model of one-way traffic network reconfiguration and lane-based non-diversion routing with crossing elimination at intersection for evacuation is constructed in this paper. It is an integrated model aiming at minimizing the network clearance time based on Cell Transmission Model. A hybrid algorithm with modified genetic algorithm and tabu search method is devised for approximating optimal problem solutions. To verify the effectiveness of the proposed model and solving method, two cases are illustrated in this paper. Through the first example, it can be seen that the proposed model and algorithm can effectively solve the integrated problems, and compared with the objective value of the original network, the network clearance time of the final solution reduces by 47.4%. The calculation results for the realistic topology and size network of Ningbo in China, which locates on the east coast of the Pacific Ocean, justify the practical value of the model and solution method, and solutions under different settings of reduction amount of merging cell capacity embody obvious differences. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Regret decision theory is a classic theory for decision problem. Recently, Yager proposed a generalized regret based decision‐making method, which calculates the effective regret associated with an alternative by aggregating this alternative's all regrets across all the possible states of nature. The generalized regret based decision‐making method that can be applied in many fields is understandable and effective. However, as Yager pointed, an issue limits the application of this method, that is, the generalized regret based decision‐making method is lack of indifference to irrelevant alternatives. In this paper, we analyze the cause of this issue, that is, unreasonable alternatives may change other alternatives' regrets by changing the maximal payoff under the occurrence of a state of nature. Furthermore, a new method based on original model is proposed to reduce the impact of unreasonable alternatives according to a parameter called impact factor defined to measure an alternative's quality. Finally, several numerical examples are illustrated to show this new method's effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, we study the unbounded upper triangular operator matrix with diagonal domain. Some sufficient and necessary conditions are given under which upper semi-Weyl spectrum (resp. upper semi-Browder spectrum) of such operator matrix is equal to the union of the upper semi-Weyl spectra (resp. the upper semi-Browder spectra) of its diagonal entries. As an application, the corresponding spectral properties of Hamiltonian operator matrix are obtained. [ABSTRACT FROM AUTHOR]

In this paper, a new type of non-self-mapping, called Berinde MT-cyclic contractions, is introduced and studied. Best proximity point theorems for this type of mappings in a metric space are presented. Some examples illustrating our main results are also given. Our results generalize and improve some known results in the literature. [ABSTRACT FROM AUTHOR]

Recently, social touch gesture recognition has been considered an important topic for touch modality, which can lead to highly efficient and realistic human-robot interaction. In this paper, a deep convolutional neural network is selected to implement a social touch recognition system for raw input samples (sensor data) only. The touch gesture recognition is performed using a dataset previously measured with numerous subjects that perform varying social gestures. This dataset is dubbed as the corpus of social touch, where touch was performed on a mannequin arm. A leave-one-subject-out cross-validation method is used to evaluate system performance. The proposed method can recognize gestures in nearly real time after acquiring a minimum number of frames (the average range of frame length was from 0.2% to 4.19% from the original frame lengths) with a classification accuracy of 63.7%. The achieved classification accuracy is competitive in terms of the performance of existing algorithms. Furthermore, the proposed system outperforms other classification algorithms in terms of classification ratio and touch recognition time without data preprocessing for the same dataset. [ABSTRACT FROM AUTHOR]

Vibration responses of building structure closely related to the structural health status. In this paper, wavelet singular spectrum entropy (WSSE) is proposed to evaluate the damage condition of building structure. A 1/3 scaled model of a Chinese ancient timber structure has been constructed, and three damage conditions and one restored condition of the structure are simulated. The acceleration responses for undamaged and the four simulated damaged and restored conditions are measured and analyzed by employing WSSE to identify the location at which the structure has incurred damage. Results show that (1) the relative variation rate of WSSE for the damaged position changes significantly; (2) the relative variation rate of WSSE of the point that is damaged more severely would become higher; and (3) signals of North-South and East-West directions are required for further identification. Moreover, a finite element modeling analysis of the timber structure under different damage conditions is performed, and the results verify the applicability of the method proposed. [ABSTRACT FROM AUTHOR]

Speed sensorless control schemes have potential benefits for industrial applications because they contribute to reducing process cost and they avoid using fragile sensors as encoders or resolvers in hostile environment. In addition, simplicity, reliability, and fast response of control structures to signal commands are much-needed features. In this paper, a new Speed Sensorless Direct Control (SSDC) technique allowing the achievement of these objectives is proposed. This technique combines Field Oriented Control (FOC) and Direct Torque Control (DTC) properties in the same approach. The estimated speed is reached only according to the measured current and voltage of the stator. DTC is extended to speed sensorless direct control with any notable modification. The proposed scheme is implemented to the induction machine benchmark and evaluated in real time under various possible scenarios of use. Experimental results show that the proposed SSDC has interesting capabilities to conduct induction motor in real time operation with good accuracy. [ABSTRACT FROM AUTHOR]

According to the application of range-free localization technology for wireless sensor networks (WSNs), an improved localization algorithm based on iterative centroid estimation is proposed in this paper. With this methodology, the centroid coordinate of the space enclosed by connected anchor nodes and the received signal strength indication (RSSI) between the unknown node and the centroid are calculated. Then, the centroid is used as a virtual anchor node. It is proven that there is at least one connected anchor node whose distance from the unknown node must be farther than the virtual anchor node. Hence, in order to reduce the space enclosed by connected anchor nodes and improve the location precision, the anchor node with the weakest RSSI is replaced by this virtual anchor node. By applying this procedure repeatedly, the localization algorithm can achieve a good accuracy. Observing from the simulation results, the proposed algorithm has strong robustness and can achieve an ideal performance of localization precision and coverage. [ABSTRACT FROM AUTHOR]

This paper studies a discriminant problem of location-scale family in case of prediction from type II censored samples. Three model selection approaches and two types of predictors are, respectively, proposed to predict the future order statistics from censored data when the best underlying distribution is not clear with several candidates. Two members in the location-scale family, the normal distribution and smallest extreme value distribution, are used as candidates to illustrate the best model competition for the underlying distribution via using the proposed prediction methods. The performance of correct and incorrect selections under correct specification and misspecification is evaluated via using Monte Carlo simulations. Simulation results show that model misspecification has impact on the prediction precision and the proposed three model selection approaches perform well when more than one candidate distributions are competing for the best underlying distribution. Finally, the proposed approaches are applied to three data sets. [ABSTRACT FROM AUTHOR]

Nowadays, multi-agent networks are ubiquitous in the real world. Over the last decade, consensus has received an increasing attention from various disciplines. This paper investigates cluster consensus for discrete-time multi-agent networks. By utilizing a special coupling matrix and the Kronecker product, a criterion based on linear matrix inequality (LMI) is obtained. It is shown that the addressed discrete-time multi-agent networks achieve cluster consensus if a certain LMI is feasible. Finally, an example is given to demonstrate the effectiveness of the proposed criterion. [ABSTRACT FROM AUTHOR]

The aim of this present paper is to establish the Poincaré-Bertrand formula for the double-layer potential on piecewise Lyapunov curve of integration. [ABSTRACT FROM AUTHOR]

This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions. Firstly, the problem is reduced to an equivalent problem which is easy to handle using variational iteration method. Secondly, variational iteration method is used to solve the reduced problem. Using this method a rapid convergent sequence can be produced which tends to the exact solution of the problem. Furthermore, variational iteration method does not require the discretization of the problem. Two numerical examples are presented to illustrate the strength of the method. [ABSTRACT FROM AUTHOR]

A novel filled function is given in this paper to find a global minima for a nonsmooth constrained optimization problem. First, a modified concept of the filled function for nonsmooth constrained global optimization is introduced, and a filled function, which makes use of the idea of the filled function for unconstrained optimization and penalty function for constrained optimization, is proposed. Then, a solution algorithm based on the proposed filled function is developed. At last, some preliminary numerical results are reported. The results show that the proposed approach is promising. [ABSTRACT FROM AUTHOR]

This paper studies the boundedness, global asymptotic stability, and periodicity of positive solutions of the equation xn = f(xn-2)/g(xn-1), n ϵ ℕ0, where f, g ϵ C[(0,∞), (0,∞)]. It is shown that if f and g are nondecreasing, then for every solution of the equation the subsequences {x2n} and {x2n-1} are eventually monotone. For the case when f(x) = a + βx and g satisfies the conditions g(0) = 1, g is nondecreasing, and x/g(x) is increasing, we prove that every prime periodic solution of the equation has period equal to one or two. We also investigate the global periodicity of the equation, showing that if all solutions of the equation are periodic with period three, then f(x) = c1/x and g(x) = c2x, for some positive c1 and c2. [ABSTRACT FROM AUTHOR]

Kupershmidt and Tuenter have introduced reflection symmetries for the q-Bernoulli numbers and the Bernoulli polynomials in (2005), (2001), respectively. However, they have not dealt with congruence properties for these numbers entirely. Kupershmidt gave a quantization of the reflection symmetry for the classical Bernoulli polynomials. Tuenter derived a symmetry of power sum polynomials and the classical Bernoulli numbers. In this paper, we study the new symmetries of the q-Bernoulli numbers and polynomials, which are different from Kupershmidt's and Tuenter's results. By using our symmetries for the q-Bernoulli polynomials, we can obtain some interesting relationships between q-Bernoulli numbers and polynomials. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study the distribution of Genocchi polynomials. Finally, we construct the Genocchi zeta function which interpolates Genocchi polynomials at negative integers. [ABSTRACT FROM AUTHOR]

Multispectral bioluminescence tomography (BLT) attracts increasingly more attention in the area of optical molecular imaging. In this paper, we analyze the properties of the solutions to the regularized and discretized multispectral BLT problems. First, we show the solution existence, uniqueness, and its continuous dependence on the data. Then, we introduce stable numerical schemes and derive error estimates for numerical solutions. We report some numerical results to illustrate the performance of the numerical methods on the quality of multispectral BLT reconstruction. [ABSTRACT FROM AUTHOR]

This paper deals with a class of singular nonlinear polyharmonic equations on the unit ball B in ℝn (n ≥ 2) where the combined effects of a singular and a sublinear term allow us by using the Schauder fixed point theorem to establish an existence result for the following problem: (-∇)mu = φ(·,u) + ψ(·,u) in B (in the sense of distributions), u > 0, lim∣x∣→1 u(x)/(1-∣x∣)m-1 = 0. Our approach is based on estimates for the polyharmonic Green function on B with zero Dirichlet boundary conditions. [ABSTRACT FROM AUTHOR]

This paper deals with a class of nonlinear elliptic equations in an unbounded domain D of ℝn, n ≥ 3, with a nonempty compact boundary, where the nonlinear term satisfies some appropriate conditions related to a certain Kato class K∞(D). Our purpose is to give some existence results and asymptotic behaviour for positive solutions by using the Green function approach and the Schauder fixed point theorem. [ABSTRACT FROM AUTHOR]

The paper investigates the stability and passivity analysis problems for a class of uncertain neural networks with time-delay via delta operator approach. Both the parameter uncertainty and the generalized activation functions are considered in this paper. By constructing an appropriate Lyapunov-Krasovskii functional, some new stability and passivity conditions are obtained in terms of linear matrix inequalities (LMIs). The main characteristic of this paper is to obtain novel stability and passivity analysis criteria for uncertain neural networks with time-delay in the delta operator system framework. A numerical example is presented to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to deal with the shared set and uniqueness of meromorphic functions on annulus. The set of this paper is different from the set of the paper by Cao and Deng, and our theorems are improvement of the results given by Cao and Deng. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study representations of 3-dimensional simple multiplicative Hom-Lie algebras (g; [-,- ]; α) (whose structure is of A1-type). In this paper we can see that a finite dimensional representation of (g; [[-,- ]; α) is not always completely reducible, and a representation of (g; [-,-]; α) is irreducible if and only if it is a regular Lie-type representation. [ABSTRACT FROM AUTHOR]

This paper is concerned with the existence of solutions for the discrete second-order boundary value problem Δ2u(t - 1) + λ 1u(t) + g(Δu(t)) = f(t), tε{1,2,...,T}, u(0) = u(T + 1) = 0, where T > 1 is an integer, f : {1,...,T} ➙ R, g : R ➙ R is bounded and continuous, and λ 1 is the first eigenvalue of the eigenvalue problem Δ2u(t - 1) + λu(t) = 0, t ε T, u(0) = u(T + 1) =0. [ABSTRACT FROM AUTHOR]

The paper deals with nonlinear differential systems with random parameters in a general form. A newmethod for construction of the Lyapunov functions is proposed and is used to obtain sufficient conditions for L2-stability of the trivial solution of the considered systems [ABSTRACT FROM AUTHOR]

The main object of the present paper is to discuss some extensions of certain integral operators and to obtain their order of convexity. Several other closely related results are also considered. [ABSTRACT FROM AUTHOR]

The aim of this article is to obtain more general forms than the papers of (Jun et al. (2010); Jun et al. (in press)). The notions of N-subalgebras of types (∊, qk), (∊,∊ ∨qk), and (q,∊ ∨qk) are introduced, and the concepts of qk-support and∊ ∨qk-support are also introduced. Several related properties are investigated. Characterizations of N-subalgebra of type (∊,∊ ∨qk) are discussed, and conditions for an N-subalgebra of type (∊,∊ ∨qk) to be an N-subalgebra of type (∊, ∊) are considered. [ABSTRACT FROM AUTHOR]

Recently, Xiao et al. proposed a nonsmooth equations-based method to solve the l₁-norm minimization problem (2011). The advantage of this method is its simplicity and lower storage. In this paper, based on new nonsmooth equations reformulation, we investigate new nonsmooth equations-based algorithms for solving l₁-norm minimization problems. Under mild conditions, we show that the proposed algorithms are globally convergent. The preliminary numerical results demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper is concerned with the convergence, global superconvergence, local superconvergence, and stability of collocation methods for u'(t) = au(t) + bu([t]). The optimal convergence order and superconvergence order are obtained, and the stability regions for the collocation methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained, and some numerical experiments are given. [ABSTRACT FROM AUTHOR]

Using fixed point methods we establish some existence theorems of positive (nontrivial) solutions for a class of Hadamard fractional boundary value problems with sign-changing nonlinearity. [ABSTRACT FROM AUTHOR]

We prove the uniform L1→L1,∞ and HE1→L1 boundedness of oscillatory singular integral operators whose kernels are the products of an oscillatory factor with bilinear phase and a Calderón-Zygmund kernel K(x,y) satisfying a Hölder condition. This Hölder condition appreciably weakens the C1 condition imposed in existing literature. [ABSTRACT FROM AUTHOR]

This paper is an extension to the recent results presented by M. Sabatini about the existence and uniqueness of limit cycles of a certain class of planar differential systems in order to include other new classes. A concrete example exhibiting the applicability of the result is introduced. [ABSTRACT FROM AUTHOR]

This paper presents a general and comprehensive description of Optimization Methods, and Algorithms from a novel viewpoint. It is shown, in particular, that Direct Methods, Iterative Methods, and Computer Science Algorithms belong to a well-defined general class of both Finite and Infinite Procedures, characterized by suitable descent directions. [ABSTRACT FROM AUTHOR]

We consider generalized Melvin-like solutions associated with nonexceptional Lie algebras of rank 4 (namely, A4, B4, C4, and D4) corresponding to certain internal symmetries of the solutions. The system under consideration is a static cylindrically symmetric gravitational configuration in D dimensions in presence of four Abelian 2-forms and four scalar fields. The solution is governed by four moduli functions Hs(z) (s=1,…,4) of squared radial coordinate z=ρ2 obeying four differential equations of the Toda chain type. These functions turn out to be polynomials of powers (n1,n2,n3,n4)=(4,6,6,4),(8,14,18,10),(7,12,15,16),(6,10,6,6) for Lie algebras A4, B4, C4, and D4, respectively. The asymptotic behaviour for the polynomials at large distances is governed by some integer-valued 4×4 matrix ν connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in A4 case) the matrix representing a generator of the Z2-group of symmetry of the Dynkin diagram. The symmetry properties and duality identities for polynomials are obtained, as well as asymptotic relations for solutions at large distances. We also calculate 2-form flux integrals over 2-dimensional discs and corresponding Wilson loop factors over their boundaries. [ABSTRACT FROM AUTHOR]

The aim of this paper, firstly, is to construct generating functions of q-Euler numbers and polynomials of higher order by applying the fermionic p-adic q-Volkenborn integral, secondly, to define multivariate q-Euler zeta function (Barnes-type Hurwitz q-Euler zeta function) and l-function which interpolate these numbers and polynomials at negative integers, respectively. We give relation between Barnes-type Hurwitz q-Euler zeta function and multivariate q-Euler l-function. Moreover, complete sums of products of these numbers and polynomials are found. We give some applications related to these numbers and functions as well. [ABSTRACT FROM AUTHOR]

We present an integer valued degree theory for locally compact perturbations of Fredholm maps of index zero between (open sets in) Banach spaces (quasi-Fredholm maps, for short). The construction is based on the Brouwer degree theory and on the notion of orientation for nonlinear Fredholm maps given by the authors in some previous papers. The theory includes in a natural way the celebrated Leray-Schauder degree. [ABSTRACT FROM AUTHOR]

This paper is concerned with pointwise estimates for the gradient of the heat kernel Kt, t > 0, of the Laplace operator on a Riemannian manifold M. Under standard assumptions on M, we show that ∇Kt satisfies Gaussian bounds if and only if it satisfies certain uniform estimates or estimates in Lp for some 1 ≤ p ≤ ∞. The proof is based on finite speed propagation for the wave equation, and extends to a more general setting. We also prove that Gaussian bounds on ∇Kt are stable under surjective, submersive mappings between manifolds which preserve the Laplacians. As applications, we obtain gradient estimates on covering manifolds and on homogeneous spaces of Lie groups of polynomial growth and boundedness of Riesz transform operators. [ABSTRACT FROM AUTHOR]

The aim of this paper is twofold. First, several basic mathematical concepts involved in the construction and study of Bregman type iterative algorithms are presented from a unified analytic perspective. Also, some gaps in the current knowledge about those concepts are filled in. Second, we employ existing results on total convexity, sequential consistency, uniform convexity and relative projections in order to define and study the convergence of a new Bregman type iterative method of solving operator equations. [ABSTRACT FROM AUTHOR]