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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]

The paper details a comprehensive system for the treatment of the topic of limits—conceptually, computationally, and formally. The system addresses fundamental linguistic flaws in the standard presentation of limits, which attempts to force limit discussion into the language of individual real numbers and equality. The system of near-numbers properly fits the context of limits, allowing precise and unambiguous notation in limit computation. More importantly, the near-numbers are a set of concrete mathematical objects that provide a scaffold both for building an accurate intuitive understanding of the limit concept and for connecting that understanding to the formal definition of the limit. [ABSTRACT FROM AUTHOR]

The present paper is a continuation of [1]; therefore, we preserve the notation and continue the numbering of sections, formulas, and theorems. [ABSTRACT FROM AUTHOR]

An extremely simple proof of the K-K-M-S Theorem is given involving only Brouwer's fixed point theorem and some elementary calculus. A function is explicitly given such that a fixed point of it yields an intersection point of a balanced collection of sets together with balancing weights. Moreover, any intersection point of a balanced collection of sets together with balancing weights corresponds to a fixed point of the function. Furthermore, the proof can be used to show π-balanced versions of the K-K-M-S Theorem, with π-balancedness as introduced in Billera (1970). The proof makes clear that the conditions made with respect to π by Billera can be even weakened. [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 article, we investigate the chaotic behaviours in the fractional-order Lorenz system. By utilizing the fractional calculus techniques, we found that chaos exists in the fractional-order Lorenz system of order less than 3. The lowest order we found to have chaos in this system is 2.97. [ABSTRACT FROM AUTHOR]

The article reports on the nature of projectile motion in a uniform, downward gravitational field and resisted by a drag force due to the air through which it moves. It states that the nature of the projectile motion lies near the heart of the scientific revolution. The drag force is assumed to act in a direction opposite to that of the projectile's velocity and to depend only on its magnitude, therefore, Coriolis forces and Earth's curvature are ignored. The author notes that the projectile motion under quadratic drag was at the center of an episode in the calculus priority dispute.

Abstract  The χ calculus is a model of concurrent and mobile systems. It emphasizes that communications are information exchanges. In the paper, two constructions are incorporated into the framework of the chi calculus, which are asymmetric communication and mismatch condition widely used in applications. Since the barbed bisimilarity has proved its generality and gained its popularity as an effective approach to generating a reasonable observational equivalence, we study both the operational and algebraic properties of the barbed bisimilarity in this enriched calculus. The investigation supports an improved understanding of the bisimulation behaviors of the model. It also gives a general picture of how the two constructions affect the observational theory. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the author investigates two-species nonautonomous delay diffusive preypredator models with Michaelis-Menten functional response. Sufficient conditions are derived for permanence of the species. Further, the author also establishs the sufficient conditions that guarantee the arbitrary positive periodic solution of the systems is global attractive. [Copyright &y& Elsevier]

The article reports on the sharpening of Wielandt's characterization of the gamma function. It presents the two conditions that is satisfied with Euler's gamma function. According to the author, the two conditions by themselves do not characterize the gamma function and presents characterization of the gamma function through theorems that Wielandt discovered. He adds that a characterization in the real domain, found in 1922 by other scholars, is well known, while Wielandt's theorem is function-theoretic.

Exact solutions of some important non-linear partial differential equations in one and two dimensions are obtained using the tanh function method. The efficiency of the method is demonstrated by applying it to a variety of selected equations. [ABSTRACT FROM AUTHOR]

A fourth-order parabolic partial differential equation in one space variable which arises in the study of transverse vibrations of a uniform flexible beam is solved. The numerical solution is obtained by using a new three-level method based on a sextic spline in space and finite-difference discretization in time. Stability analysis of the method has been carried out. It is shown that we obtain a scheme of O ( k 2 + h 4 ) and O ( h 4 + h 2 k 2 ). The method is tested on a problem which has appeared in physical applications. Comparison with some known methods shows the superiority of the present method. [ABSTRACT FROM AUTHOR]

In this article, the author discusses on the optimal control of almost periodic motions under constraints.

The article presents an elementary proof of Joris's Theorem. It utilizes Rolle's theorem, L'Hospital's rule, and Taylor's formula from elementary calculus. Joris considers the conditions under which a quotient of smooth functions is again smooth. Let g(x) = f(x)m and h(x) = f(x)n. It is assumed that, since m and n are relatively prime, one of m or n is odd. Function f is continuous as the composition of the continuous functions. Function f is continuous as the composition of the continuous functions n√x and h. Let K = f -1 ({0}). Then K is closed, and 0 = R \ K is an open subset of R, hence the disjoint union of countably many open intervals. On each of these intervals, both n√x and h are smooth on O.