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Let C(X) denote the ring of all real-valued continuous functions on a topological space X; and C∞(X) be the subring of all functions C(X) which vanish at infinity. In [2], the paper "Rings of continuous functions vanishing at infinity," (Comment. Math. Univ. Carolin.45(3) (2004), 519–533), by A.R. Aliabad, F. Azarpanah, and M. Namdari, it is shown that for every completely regular Hausdorff space X, whenever C∞(X) ≠ (0), then there exists a locally compact space Y such that C∞(X) ≅ C∞(Y). In fact, the space Y may be considered as a nonempty open locally compact subspace of X. In the present paper, analogous results are derived in a pointfree context in which topological spaces are replaced by frames. [ABSTRACT FROM AUTHOR]

This paper presents the global Borel-Pompieu- and the global Cauchy-type integral formulas for the quaternionic slice regular functions using the relationship between this function space and a non-constant coefficient differential operator given by G := ∥ x → ∥ 2 ∂ 0 + x → ∑ k = 1 3 x k ∂ k , according to [González-Cervantes JO. On cauchy integral theorem for quaternionic slice regular functions. Complex Anal Oper Theory. 2019;13(6):2527–2539; Colombo F, González-Cervantes JO, Sabadini I. A non-constant coefficients differential operator associated to slice monogenic functions. Trans Am Math Soc. 2013;365:303–318]. This association allows to show a behavior of the theory of slice regular functions similar to the well known theories of the hypercomplex analysis. [ABSTRACT FROM AUTHOR]

The aim of this paper is to provide some practical aspects of point and interval estimates of the global maximum of a function using extreme value theory. Consider a real-valued function f:D→ defined on a bounded interval D such that f is either not known analytically or is known analytically but has rather a complicated analytic form. We assume that f possesses a global maximum attained, say, at u*∈D with maximal value x*=max u f(u)≐f(u*). The problem of seeking the optimum of a function which is more or less unknown to the observer has resulted in the development of a large variety of search techniques. In this paper we use the extreme-value approach as appears in Dekkers et al. [A moment estimator for the index of an extreme-value distribution, Ann. Statist. 17 (1989), pp. 1833-1855] and de Haan [Estimation of the minimum of a function using order statistics, J. Amer. Statist. Assoc. 76 (1981), pp. 467-469]. We impose some Lipschitz conditions on the functions being investigated and through repeated simulation-based samplings, we provide various practical interpretations of the parameters involved as well as point and interval estimates for x*. [ABSTRACT FROM AUTHOR]

The nature-inspired algorithms (NIAs) have shown efficiency to solve many complex real-world optimisation problems. The efficiency of NIAs is measured by their ability to find adequate results within a reasonable amount of time, rather than an ability to guarantee the optimal solution. This paper presents a solution for lower order system modelling using spider monkey optimisation (SMO) algorithm to obtain a better approximation for lower order systems and reflects almost original higher order system's characteristics. Further, a local search strategy, namely, power law-based local search is incorporated with SMO. The proposed strategy is named as power law-based local search in SMO (PLSMO). The efficiency, accuracy and reliability of the proposed algorithm is tested over 20 well-known benchmark functions. Then, the PLSMO algorithm is applied to solve the lower order system modelling problem. [ABSTRACT FROM AUTHOR]

In this paper, for a frameL, we characterize modified sobriety in stratifiedL-topological spaces and strongL-topological spaces internally using certain classes of stratifiedL-filters. While the first characterization using completely primeL-filters is trivial and applies to all stratifiedL-topological spaces, the other one using irreducibleL-filters generalizes an approach of R.E. Hoffmann to the lattice-valued case but is restricted to either the case that the lattice is a complete Boolean algebra or to the case of completely distributive lattices and strongL-topological spaces. [ABSTRACT FROM AUTHOR]

It is well known that simple examples are really encouraging in the understanding of rearrangements of infinite series. In this paper a similar role is played by simple examples in the case of infinite products. Perhaps the equivalence of the absolute convergence of the infinite product [image omitted] and the absolute convergence of the infinite series [image omitted], when each an is positive, has led the authors of many texts not discussing the rearrangements of infinite products. Iterated products of double products seem to have a similar spirit of rearrangements of products, although they are not the same. Therefore, learning about iterated products of double products will help the understanding of the rearrangements of products. In the absence of simple examples, existence theorems lend little confidence to understanding. In this article several inspiring examples are presented to show that infinite products indeed behave very differently from finite products as is the case with infinite sums. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability of the tower level set ... of a finite valued increasing convex-along-rays (ICAR) function f defined on ... In monotonic analysis, ICAR functions play the role of usual convex functions in classical convex analysis. We show that each ICAR function f is locally Lipschitz on int dom f and that the pointwise convergence of a sequence of ICAR functions implies its uniform convergence on each compact subset of ... The latter allows us to establish stability results for ICAR functions in some sense similar to those for convex functions. [ABSTRACT FROM AUTHOR]

This paper deals with an improvement of the Trudinger-Moser inequality associated to the embedding of the standard Sobolev space H0¹(Ω) into Orlicz spaces for Ω a smooth bounded domain in R². The inequality proved here gives in particular precise informations on a previous result obtained by Lions and can be very useful in the study of lack of compactness of the embedding of H0¹(Ω) into {exp(4πu²) ∈ L¹(Ω)}. We also provide a general asymptotic analysis for sequences of solutions to elliptic PDE's with critical Sobolev growth which blow up at some point. We obtain in particular a result which is well-known in higher dimensions: the concentration points are located at critical points of the regular part of the Green function of the linear operator involved in the equation. [ABSTRACT FROM AUTHOR]