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New oscillatory properties for the oscillation of unbounded solutions to a class of thirdorder neutral differential equations with several deviating arguments are established. Several oscillation results are established by using generalized Riccati transformation and a integral average technique under the case of unbounded neutral coefficients. Examples are given to prove the significance of new theorems. [ABSTRACT FROM AUTHOR]

The article discusses a series of events in Bonn Mathematics "Tea Time with Women in Mathematics" that offers female students and researchers the opportunity to become part of a network to exchange experiences in mathematics. Topics discussed include analysis of partial differential equations; declaration on equal opportunities, diversity and scientific collaboration; new trends in algorithmic randomness and computable analysis; mathematical models; and mathematical analysis.

Abstract We study the differential identities of the algebra U T 2 of 2 × 2 upper triangular matrices over a field of characteristic zero. We let the Lie algebra L = Der (U T 2) of derivations of U T 2 (and its universal enveloping algebra) act on it. We study the space of multilinear differential identities in n variables as a module for the symmetric group S n and we determine the decomposition of the corresponding character into irreducibles. If V is the variety of differential algebras generated by U T 2 , we prove that unlike the other cases (ordinary identities, group graded identities) V does not have almost polynomial growth. Nevertheless we exhibit a subvariety U of V having almost polynomial growth. [ABSTRACT FROM AUTHOR]

In this paper, we use Schauder and Banach fixed point theorems to study the existence, uniqueness and stability of bounded nonhomogeneous iterative functional differential equations of the form x' (t) = λ1x(t) + λ2x[2](t)+...+λnx[n](t)+f(t). [ABSTRACT FROM AUTHOR]

Existence results of infinitely many solutions for a fourth-order differential equation are established. This equation depends on two real parameters. The approach is based on an infinitely many critical points theorem. [ABSTRACT FROM AUTHOR]

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We present new criteria for asymptotic stability of two classes of nonlinear neutral delay differential equations. By using two auxiliary functions on a contraction condition, we extend the results in [12]. Also we give two examples that illustrate our results. [ABSTRACT FROM AUTHOR]

We study parametric estimation in the Cox-Ingersoll-Ross model and establish the stochastic differential equations for the parameters involved in it. [ABSTRACT FROM AUTHOR]

Uncertain differential system is a type of differential system involving uncertain processes. Stability analysis has been widely studied but no work has been dedicated to attractivity analysis of uncertain differential systems. In this paper, some concepts of attractivity for uncertain differential systems are presented. Then the corresponding sufficient and necessary conditions are given. Furthermore, the stability of the solutions and α-path of uncertain differential systems are studied. [ABSTRACT FROM AUTHOR]

In this paper, we will give a sufficient condition for self-amalgamation of a strongly irreducible Heegaard splitting along any essential subsurface to be unstabilized. [ABSTRACT FROM AUTHOR]

The existence of solutions for a second-order periodic-integrable boundary value problem is discussed by a variational method, and the application to the forced oscillation equation is given. [ABSTRACT FROM AUTHOR]

The spatiotemporal nonlinear Schrödinger equation with power-law nonlinearity in -symmetric potentials is investigated, and two families of analytical three-dimensional spatiotemporal structure solutions are obtained. The stability of these solutions is tested by the linear stability analysis and the direct numerical simulation. Results indicate that solutions are stable below some thresholds for the imaginary part of -symmetric potentials in the self-focusing medium, while they are always unstable for all parameters in the self-defocusing medium. Moreover, some dynamical properties of these solutions are discussed, such as the phase switch, power and transverse power-flow density. The span of phase switch gradually enlarges with the decrease of the competing parameter k in -symmetric potentials. The power and power-flow density are all positive, which implies that the power flow and exchange from the gain toward the loss domains in the cell. [ABSTRACT FROM AUTHOR]

In this paper, we show that the chordal Loewner differential equation with C° driving function generates a C°1/2 slit for 1/2 < ° ≼ 2, except when ° = 3/2 the slit is only proved to be weakly C1,1. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to prove the existence of radial positive solutions for a nonpositone problem in an annulus when the nonlinearity is superlinear and has more than one zero. [ABSTRACT FROM AUTHOR]

Abstract: Periodic travelling wave solutions of reaction–diffusion equations were studied by many authors. The type reaction–diffusion system is a notable special model that admits explicit periodic travelling wave solutions and was introduced by Kopell and Howard in 1973. There are now similar systems which are investigated by means of autonomous dynamics. In contrast, there are few papers which are concerned with non-autonomous cases. For this reason, we apply Mawhin’s continuation theorem to derive the existence of periodic travelling wave solutions for non-autonomous systems, and we describe the ‘disappearance’ of periodic travelling wave solutions under special situations. Our main result is also illustrated by examples. [Copyright &y& Elsevier]

Motivated by the concept of complete pairs, which was introduced by Krein and Langer, we present the concepts of an almost complete pair of matrices and a complete triple of matrices. It is proved that an almost complete pair of matrices can be extended to a complete triple. An application of the result to differential equations is also given. [ABSTRACT FROM AUTHOR]

Abstract: We present some curious formulae for infinite products of twisted -functions. [Copyright &y& Elsevier]

Background: Expanding access to highly active antiretroviral therapy (HAART) has become an important approach to HIV prevention in recent years. Previous studies suggest that concomitant changes in risk behaviours may either help or hinder programs that use a Treatment as Prevention strategy. Analysis: We consider HIV-related risk behaviour as a social contagion in a deterministic compartmental model, which treats risk behaviour and HIV infection as linked processes, where acquiring risk behaviour is a prerequisite for contracting HIV. The equilibrium behaviour of the model is analysed to determine epidemic outcomes under conditions of expanding HAART coverage along with risk behaviours that change with HAART coverage. We determined the potential impact of changes in risk behaviour on the outcomes of Treatment as Prevention strategies. Model results show that HIV incidence and prevalence decline only above threshold levels of HAART coverage, which depends strongly on risk behaviour parameter values. Expanding HAART coverage with simultaneous reduction in risk behaviour act synergistically to accelerate the drop in HIV incidence and prevalence. Above the thresholds, additional HAART coverage is always sufficient to reverse the impact of HAART optimism on incidence and prevalence. Applying the model to an HIV epidemic in Vancouver, Canada, showed no evidence of HAART optimism in that setting. Conclusions: Our results suggest that Treatment as Prevention has significant potential for controlling the HIV epidemic once HAART coverage reaches a threshold. Furthermore, expanding HAART coverage combined with interventions targeting risk behaviours amplify the preventive impact, potentially driving the HIV epidemic to elimination. [ABSTRACT FROM AUTHOR]

We generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions [ABSTRACT FROM AUTHOR]

Results on Colombeau product of distributions x-r-1/2+ and x-r-1/2- are derived. They are obtained in Colombeau differential algebra G(R) of generalized functions that contains the space D' (R) of Schwartz distributions as a subspace and has a notion of "association" that is a faithful generalization of the weak equality in D' (R). [ABSTRACT FROM AUTHOR]

We show that any traced "-autonomous category is compact closed. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we consider non-linear differential equations which are closely related to the generating functions of Frobenius–Euler polynomials. From our non-linear differential equations, we derive some new identities between the sums of products of Frobenius–Euler polynomials and Frobenius–Euler polynomials of higher order. [Copyright &y& Elsevier]

In this paper, we obtain some applications of first order differential subordination and superordination results involving the operator Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed for certain normalized p-valent analytic functions associated with that operator. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the property of linearly dependence of solutions and for higher order linear differential equation where () are entire periodic coefficients and () is the dominant coefficient, is investigated. [Copyright &y& Elsevier]

Abstract: Sufficient criteria are established for the existence of -periodic solutions of a family of Lazer–Solimini equations with state-dependent delay. The method of proof relies on a combination of Leray–Schauder degree and a priori bounds. [Copyright &y& Elsevier]

Abstract: The purpose of this work is to introduce the concept of pseudo-exactness for second-order linear ordinary differential equations (ODEs), and then to try to solve some specific ODEs. [Copyright &y& Elsevier]

In this paper, we apply the first integral method to study the exact solutions of different coupled nonlinear Maccari's systems [ABSTRACT FROM AUTHOR]

We consider the chordal Loewner differential equation for multiple slits in the upper half-plane and relations between the pointwise Hölder continuity of the driving functions and the generated hulls. The first result generalizes a result of Lind that gives a sufficient condition for driving functions to generate simple curves. The second result translates the property that the hulls locally look like straight lines at their starting points into a condition for the driving functions. [ABSTRACT FROM AUTHOR]

Abstract: It is the goal of this paper to study the boundedness, the persistence and the asymptotic behavior of the positive solutions of the system of two difference equations of exponential form where are positive constants, and the initial values are positive real values. [Copyright &y& Elsevier]

It has been shown that every n-person, perfect information game with no chance moves and bounded, lower semicontinuous payoffs has a subgame perfect-equilibrium in pure strategies. Here the same is proved when the payoffs are bounded and upper semicontinuous. [ABSTRACT FROM AUTHOR]

The article examines the coefficients of the expansion of smooth functions of several variables in the bases of the spaces Lp([0,1]d). It discusses the normalized basis in Lp([0,1]d) and the series of Fourier coefficients in the trigonometric system. It also discusses the Faber-Schauder system, Haar system, and Rademacher function.

We introduce a new kind of equation, stochastic differential equations with self-exciting switching. Firstly, we give some preliminaries for this kind of equation, and then, we get the main results of our paper; that is, we gave the sufficient condition which can guarantee the existence and uniqueness of the solution. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we extend the Tanaka finiteness theorem and inequality for the number of symmetries to arbitrary distributions (differential systems) and provide several applications. [Copyright &y& Elsevier]

In this paper, Numerical solution of Partial Diferential-Algebraic Equa- tions(PDAEs) is considered by Multivariate Padè Approximations. We applied these method to one example. First Partial Diferential-Algebraic Equation(PDAE) has been converted to power series by two-dimensional diferential transformation,Then the numerical solution of equation was put into Multivariate Padè series form. Thus we obtained numerical solution of Partial Diferential-Algebraic Equa- tion(PDAE). [ABSTRACT FROM AUTHOR]

Abstract. In this paper, we obtain some applications of first order differential subordination and superordination results for some analytic functions defined by convolution. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence of multiple positive solutions for the 2n-th order m-point boundary value problems: {x(2n)(t) = f(t, x(t), x" (t), ⋯ , x(2(n-1))(t)), 0 ≤ t ≤ 1, x(2i+1)(0) = Σj=1m-2 αijx(2i+1)(ξj), x(2i)(1) = Σj=1m-2 βijx(2i)(ξj), 0 ≤ i ≤ n - 1, where αij , βij (0 ≤ i ≤ n - 1, 1 ≤ j ≤ m - 2) ∈ [0,∞), Σj=1m-2 αij Σj=1m-2 βij ∈ (0, 1), 0 < ξ1 < ξ2 < . . . < ξm-2 < 1. Using Leggett-Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. [ABSTRACT FROM AUTHOR]

Research on student learning in higher education suggests that threshold concepts within various disciplines have the capacity to transform students’ understanding. The present study explores students’ understanding in relation to particular threshold concepts in mathematics—integral and limit—and tries to clarify in what sense developing an understanding of those threshold concepts involves a transformation of understanding in relation to ways of thinking in mathematics. Drawing on data collected in interviews with students taking a basic course on calculus the analysis offers an initial characterisation of students’ understandings as algorithmic. It then proceeds to construct a more fine-grained theoretical account for how these understandings develop in the course of the interview, suggesting that the transformative aspects of threshold concepts may be conceptualised in terms of shifts in students’ contextualisations allowing the development of conceptions at different levels of abstraction simultaneously interacting to shape students’ awareness of the ways of thinking and practising in the subject. [ABSTRACT FROM AUTHOR]

The theorem of Mukhin, Tarasov, and Varchenko (formerly the Shapiro conjecture for Grassmannians) asserts that all (a priori complex) solutions to certain geometric problems in the Schubert calculus are actually real. Their proof is quite remarkable, using ideas from integrable systems, Fuchsian differential equations, and representation theory. There is now a second proof of this result, and it has ramifications in other areas of mathematics, from curves to control theory to combinatorics. Despite this work, the original Shapiro conjecture is not yet settled. While it is false as stated, it has several interesting and not quite understood modifications and generalizations that are likely true, and the strongest and most subtle version of the Shapiro conjecture for Grassmannians remains open. [ABSTRACT FROM AUTHOR]

We establish new oscillation criteria for second-order delay differential equations with mixed nonlinearities of the form Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. are continuous functions defined on [0, ∞), and p(t) > 0, p'(t) ≥ 0, and a1 >…> αm > α m+1 >…> α n > 0. No restriction is imposed on the potentials pi(t), qi(t), and e(t) to be nonnegative. These oscillation criteria extend and improve the results given in the recent papers. An interesting example illustrating the sharpness of our results is also provided. [ABSTRACT FROM AUTHOR]

Sufficient conditions for the existence of solutions of nonlinear boundary value problems for higher-order functional difference equations with p-Laplacian are established by making of continuation theorems. We allow f to be at most linear, superlinear, or sublinear in obtained results. [ABSTRACT FROM AUTHOR]

This study is part of a project concerned with the analysis of how students work with two-variable functions. This is of fundamental importance given the role of multivariable functions in mathematics and its applications. The portion of the project we report here concentrates on investigating the relationship between students’ notion of subsets of Cartesian three-dimensional space and the understanding of graphs of two-variable functions. APOS theory and Duval’s theory of semiotic representations are used as theoretical framework. Nine students, who had taken a multivariable calculus course, were interviewed. Results show that students’ understanding can be related to the structure of their schema for R3 and to their flexibility in the use of different representations. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the pseudo-isochronicity for a class of septic differential systems. In this paper, we transform infinity into the origin so that the properties of infinity can be investigated with the methods developed for finite critical points. By calculating the singular point quantities and period constants of the origin, the problem of infinity being a pseudo-isochronous center has been solved in this case. [Copyright &y& Elsevier]

We analyse an ALOHA-type random multiple-access protocol where users have local interactions. We show that the fluid model of the system workload satisfies a certain differential equation. We obtain a sufficient condition for the stability of this differential equation and deduce from that a sufficient condition for the stability of the protocol. We discuss the necessary condition. Furthermore, for the underlying Markov chain, we estimate the rate of convergence to the stationary distribution. Then we establish an interesting and unexpected result showing that the main diagonal is locally unstable if the input rate is sufficiently small. Finally, we consider two generalisations of the model. [ABSTRACT FROM AUTHOR]

Abstract: We present sufficient conditions which guarantee that all positive solutions of some higher order rational difference equations are global asymptotically stable. The boundedness of the solutions and the existence of prime period two solutions of such equations are also investigated. [Copyright &y& Elsevier]

In this paper, shunting inhibitory cellular neural networks (SICNNs) with timevarying and distributed delays are considered. Without assuming the global Lipschitz conditions of activation functions, some new sufficient conditions for the existence and exponential stability of the almost periodic solutions are established. Finally, a numerical example is given to demonstrate the effectiveness of the obtained result. [ABSTRACT FROM AUTHOR]

Flocking, arguably one of the most fascinating concepts in nature, has in recent times established a growing stature within the field of robotics. In this paper, we control the collective motion of a flock of nonholonomic car-like vehicles in a constrained environment. A continuous centralized motion planner is proposed for split/rejoin maneuvers of the flock via the Lyapunov-based control scheme to anchor avoidance of obstacles intersecting the paths of flockmates. The control scheme inherently utilizes the artificial potential fields, within a new leader-follower framework, to accomplish the desired formations and reformations of the flock. The effectiveness of the proposed control laws are demonstrated through computer simulations. [ABSTRACT FROM AUTHOR]

In [12], a numerical comparison between the differential transform method and Adomian decomposition method for solving fourth-order boundary value problems was presented. In this article, we use the differential transformation method (DTM) to solve the linear and non-linear higher-order boundary value problems (HOBVPs). The method proved to be very successful and powerful in computing such elements. The specific problems chosen for this purpose is that of the different types of higher order (e.g. fifth, sixth, ninth, tenth and twelfth ) boundary value problems. The differential transformation (DT) solutions are compared with the theoretical solution. It is shown that the solutions obtained from the technique have a very high degree of accuracy. [ABSTRACT FROM AUTHOR]