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In this paper, we present an Expert System dealing with the diagnosis of fibromyalgia. Being fibromyalgia a very hard illness to diagnose, we think that our system may be useful for non-specialists (like family doctors) or specialists that would like to compare their own diagnoses with the one provided by our system. Our system has the peculiarity of being based on a previous mathematical result which...
Let K be a quadratic field, and let ζK its Dedekind zeta function. In this paper we introduce a factorization of ζK into two functions, L1 and L2, defined as partial Euler products of ζK, which lead to a factorization of Riemann’s ζ function into two functions, p1 and p2. We prove that these functions satisfy a functional equation which has a unique solution, and we give series of very...
We specify representations of the spaces $${\mathcal{O}_M}$$ and $${\mathcal{O}'_M}$$ and show that they are not appropriate to conclude that $${\mathcal{O}_M}$$ is ultrabornological. We investigate topological properties, multipliers and convolutors of Kučera’s spaces occurring in his proof (Int J Math Math Sci 8(4):813–816, 1985) of the fact that $${\mathcal{O}_M}$$ is ultrabornological...
Rus (Approx. Convexity 3:171–178, 2005) introduced the concept of cyclic contraction mapping. Păcurar and Rus (Nonlinear Anal. 72:1181–1187, 2010) proved some fixed point results for cyclic $${\phi }$$ -contraction mappings on a metric space. Karapinar (Appl. Math. Lett. 24:822–825, 2011) obtained a unique fixed point of cyclic weak $${\phi }$$ - contraction mappings and studied well-posedness...
We introduce the countably measure determined compact spaces, originally due to M. Talagrand, which form a class that is strictly located between the class of compacta carrying a strictly positive Radon probability and the class of those spaces which carry a strictly positive Radon probability of countable (Maharam) type. Some properties of these compact spaces are studied and also some applications...
An automorphism of a bordered compact Klein surface induces a permutation of its boundary components and we study the corresponding representations of groups of automorphisms of such surfaces in the corresponding finite symmetric groups. The principal result gives a characterization of those abstract representations of a finite group G in symmetric groups which, up to the natural equivalence, proceed...
We introduce a cardinal function that assigns to each topological space Y a cardinal number ℓΣ (Y) that measures how the space is determined by its compact subsets via upper semicontinuous compact valued maps defined on metric spaces. By doing so we extend and take to a different dimension the study of the so-called countably K-determined spaces (or Lindelöf Σ-spaces) and their associates Gul’ko compacta...
Let {Xni, i ≥ 1, n ≥ 1} be an array of rowwise negatively orthant dependent random variables. Some sufficient conditions for complete convergence for arrays of rowwise negatively orthant dependent random variables are presented without assumptions of identical distribution. As an application, the Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of negatively orthant dependent...
If a separable Banach space X contains an isometric copy of every separable reflexive Fréchet smooth Banach space, then X contains an isometric copy of every separable Banach space. The same conclusion holds if we consider separable Banach spaces with Fréchet smooth dual space. This improves a result of G. Godefroy and N.J. Kalton.
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