In this paper, a link between the Hyers–Ulam stability and the Moore–Penrose inverse is established, that is, a closed operator has the Hyers–Ulam stability if and only if it has a bounded Moore–Penrose inverse. Meanwhile, the stability constant can be determined in terms of the Moore– Penrose inverse. Based on this result, some conditions for the perturbed operators having the Hyers– Ulam stab...

Let N = (R,+, ·, <, . . . ) be an o-minimal expansion of the standard structure of a real closed field R. A definably compact definable group G is a definable Borsuk-Ulam group if there exists an isovariant definable map f : V → W between representations of G, then dimV − dimV G ≤ dimW − dimW. We prove that if a finite group G satisfies the prime condition, then G is a definable Borsuk-Ulam gro...

We study the Fadell–Husseini index of the configuration space F (R, n) with respect to different subgroups of the symmetric group Sn. For p prime and k ≥ 1, we completely determine IndexZ/p(F (R, p);Fp) and partially describe Index(Z/p)k (F (R, p);Fp). In this process we obtain results of independent interest, including: (1) an extended equivariant Goresky–MacPherson formula, (2) a complete des...

The Borsuk-Ulam theorem of topology is applied to a problem in discrete mathematics. A bisection of a necklace with k colors of beads is a collection of intervals whose union captures half the beads of each color. Every necklace with fc colors has a bisection formed by at most k cuts. Higherdimensional generalizations are considered.

The total phenolic contents (TPC) and antioxidant activities of five popular Malay raw salads or Ulam were investigated using DPPH radical scavenging and reducing ferric ion antioxidant power (FRAP) assays. The Ulam studied were the leaves of Cosmos caudatus (Ulam Raja), Oenanthe javanica (Selom), Murraya koenigii (Curry Leaf), Centella asiatica (Pegaga) and the seeds of Parkia speciosa (Petai)...

The Ulam sequence is given by a1 = 1, a2 = 2, and then, for n ≥ 3, the element an is defined as the smallest integer that can be written as the sum of two distinct earlier elements in a unique way. This gives the sequence 1, 2, 3, 4, 6, 8, 11, 13, 16, . . . , which has a mysterious quasi-periodic behavior that is not understood. Ulam’s definition naturally extends to higher dimensions: for a se...

In this paper,we consider functional equations involving a two variables examine some of these equations in greater detail and we study applications of cauchy’s equation.using the generalized hyers-ulam-rassias stability of quaradic functional equations finding the solution of two variables(quaradic functional equations) 1.INTRODUCTION We achieve the general solution and the generalized Hyers-U...

In 1940 (and 1964) S. M. Ulam proposed the well-known Ulam stability problem. In 1941 D. H. Hyers solved the Hyers-Ulam problem for linear mappings. In 1992 and 2008, J. M. Rassias introduced the Euler-Lagrange quadratic mappings and the JMRassias “product-sum” stability, respectively. In this paper we introduce an Euler-Lagrange type quadratic functional equation and investigate the JMRassias ...

In the paper we discuss a stability in the sense of the generalized Hyers-Ulam-Rassias for functional equations ∆n(p, c)φ(x) = h(x), which is called generalized Newton difference equations, and give a sufficient condition of the generalized Hyers-Ulam-Rassias stability. As corollaries, we obtain the generalized Hyers-Ulam-Rassias stability for generalized forms of square root spirals functional...

We consider a PageRank model of opinion formation on Ulam networks, generated by the intermittency map and the typical Chirikov map. The Ulam networks generated by these maps have certain similarities with such scale-free networks as the World Wide Web (WWW), showing an algebraic decay of the PageRank probability. We find that the opinion formation process on Ulam networks have certain similari...