In some recent papers, a method was developed of reducing coupled fixed point problems in (ordered) metric and various generalized metric spaces to the respective results for mappings with one variable. In this paper, we apply the mentioned method and obtain some coupled fixed point results for mappings satisfying φ-weak contractive conditions in ordered b-metric spaces. Examples show how these...

Every odd prime number p has exactly (p+1)/2 different expressions as a sum ab + cd of two ordered products and such that min(a,b)>max(c,d). An easy corollary is proof Fermat’s Theorem expressing primes in 1+4N sums squares.

The exciting detection of a very high degree of linear polarization, P = 80%±20%, in the prompt γ-ray emission of the recent GRB 021206, provides strong evidence that synchrotron emission is the dominant radiation mechanism. Besides this immediate implication, there were also claims that this implies a magnetic field that is ordered on large scales within the ejecta, and must therefore be produ...

Based on a complete Heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a Cartesian-closed category, calledthe category of $L-$ordered fuzzifying convergence spaces, in whichthe category of $L-$fuzzifying topological spaces can be embedded.In addition, two new categories are introduced, which are called the...

Normally ordered forms of functions of boson operators are important in many contexts mainly concerning quantum field theory and quantum optics. Beginning with the seminal work of Katriel [Lett. Nuovo Cimento 10(13):565–567, 1974], in the last few years, normally ordered forms have been shown to have a rich combinatorial structure [see P. B lasiak, quant-ph/0507206]. In this paper, we apply the...

Let A and B be simply ordered sets and A XB the cartesian product ordered by first differences. Sufficiency conditions are given on the sets A and B for the existence of fixed points in the set AXB (Theorem 2). Sufficiency conditions are given on the sets A, B, and C for the incomparability of the order types1 \A XB\ and \A XC\ (| CXA\ and | CXB\) (Corollary 2 of Theorem 7). The content of Theo...

OBJECTIVE Here we explored whether children with ADHD have a deficit in relational reasoning, a skill subtending the acquisition of many cognitive abilities and social rules. METHOD We analyzed the performance of a group of children with ADHD during a transitive inference task, a task requiring first to learn the reciprocal relationship between adjacent items of a rank ordered series (e.g., A...

Single-phase perovskites were formed in the (1−x)Ba(Zn1/3Nb2/3)O3–(x)La(Zn2/3Nb1/3)O3 system for compositions with 0.0 ≤ x ≤ 0.6. Although the stability of the trigonal ‘‘1:2’’ ordered structure of the Ba(Zn1/3Nb2/3)O3 end member is very limited (0.0 ≤ x < 0.05), low levels of lanthanum induce a transformation to a cubic, ‘‘1:1’’ ordered structure that has a broad range of homogeneity (0.05 ≤ x...

A Mendelsohn design M(k,v) is a pair (V,B) t where IV\=v and B is a set of cyclically ordered k-tuples of distinct elements of V, called blocks, such that every ordered pair of distinct elements of V belongs to exactly one block of B. A M( k, v) is called cyclic if it has an automorphism consisting of a single cycle of length v. The spectrum of existence of cyclic M(3,v)'s and M(4,v)'s is known...