A link between Wilson’s and d’Alembert’s functional equations

If \({f, g : G \to \mathbb{C}}\), f ≠ 0, is a solution of Wilson’s functional equation on a group G, then g is a d’Alembert function.     

Reich’s problem concerning Halpern’s convergence

We discuss Halpern’s convergence for nonexpansive mappings in Hilbert spaces. We prove that one of the conditions in [R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. (Basel), 58 (1992), 486–491] is the weakest sufficient condition among the conditions known to us. We also improve a necessary condition, which is close to Wittmann’s. This is one step to solve the problem raised by Reich in 1974 and 1983. Received: 15 July 2008     

Sur Une Classe D’Espaces D’Interpolation

Sans résumé Les A. ont été soutenus par l’Interpol.     

L’Extension Abelienne D’une Categorie semi-abelienne

We show that if (K,L) is a semi-abelian category, there exists an abelian categoryK ^x with the followings properties:

GENERALIZEDSCHWARZ’SLEMMAFORANALYTICOPERATORFUNCTIONS

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Continuous approximations of Gol’dshtik’s model

We consider continuous approximations to the Gol’dshtik problem for separated flows in an incompressible fluid. An approximated problem is obtained from the initial problem by small perturbations of the spectral parameter (vorticity) and by approximating the discontinuous nonlinearity continuously in the phase variable. Under certain conditions, using a variational method, we prove the convergence of solutions of the approximating problems to the solution of the original problem.     

Warfield’s Duality and Malcev’s Matrix

In this work, we investigate relations between Malcev’s matrices of a torsion-free group G of finite rank and Malcev’s matrices of groups Hom(R,G) and Hom(G,R), where G is a locally free group and R is a torsion-free group of rank 1.     

Bergmann’s Dilemma and Internalism’s Escape

Michael Bergmann has argued that internalist accounts of justification face an insoluble dilemma. This paper begins with an explanation of Bergmann??s dilemma. Next, I review some recent attempts to answer the dilemma, which I argue are insufficient to overcome it. The solution I propose presents an internalist account of justification through direct acquaintance. My thesis is that direct acquaintance can provide subjective epistemic assurance without falling prey to the quagmire of difficulties that Bergmann alleges all internalist accounts of justification cannot surmount.     

A Significant ‘False Perception’ of Wittgenstein’s Draft on Mind’s Eye

If we read the Tractatus logico-philosophicus according to the decimal numbering of its propositions, we may understand, finally, the section about the self and the limits of language and world. Proposition 5.64 follows 5.63 (not 5.634); 5.634 follows 5.633 (not 5.6331); and so on. Thus, it becomes clear that the picture of the visual field (TLP 5.6331) cannot be what scholars have always quoted and discussed, i.e. a draft of an eye inside its field of sight. Actually, Wittgenstein’s original drafts depict (to criticise it) the ordinary way of representing the visual field. Following him, the field of vision is ‘without limits’; it does not have a form that implies the existence of an eye, as far as the phenomenological experience does not have a form that implies the existence of an ‘I’. As a result, the current reproductions of the 5.6331 image must be rectified, and all references to this similitude should be radically amended.     

Generalizations of Sherman’s Inequality Via Fink’s Identity and Green’s Function

Ukrainian Mathematical Journal - New generalizations of Sherman’s inequality for n-convex functions are obtained with the help of Fink’s identity and Green’s function. By using...     

D’Alembert’s and Wilson’s functional equations on step 2 nilpotent groups

Summary. We describe the set of solutions of Wilsons functional equation on any step 2 nilpotent group and how the set of classical solutions in certain cases must be supplemented by 4-dimensional spaces of solutions.     

Principio d’azione stazionaria nell’elettrodinamica dei fluidi

Sunto Si deducono da un unico principio d’azione stazionaria entrambe le equazioni spa zio-temporali che reggono il campo elettromagnetico in un corpo generico. Nel caso di un fluido, si aggiunge alla precedente azione elettromagnetica quella meccanica e dall’azione totale si trae, col procedimento diHilbert, il tensore energetico totale e quindi quello diAbraham, dovuto al solo campo elettromagnetico. Dalla stazionarietà dell’azione totale si ricavano tutte le leggi indefinite, elettromagnetiche e meccaniche, che reggono il moto dei fluidi elettrizzati, cioè le leggi rigorose dell’elettromagnetofluidodinamica. Ad Antonio Signorini nel suo 70^o compleanno.     

On Andrunakievich’s chain and Koethe’s problem

In 1969 Andrunakievich asked whether one gets a ring without nonzero nil left ideals from an arbitrary ring R by factoring out the ideal A(R) which is the sum of all nil left ideals of R. Recently, it was shown that this problem is equivalent to Koethe’s problem. In this context one may consider the chain of ideals, which starts with A ₁(R) = A(R) ⊆ A ₂(R), where A ₂(R)/A ₁(R) = A(R/A ₁(R)), and extends by repeating this process. We study the properties of this chain and show that, assuming a negative solution of Koethe’s problem, this chain can terminate at any given ordinal number.     

Kantorovich’s majorants principle for Newton’s method

We prove Kantorovich’s theorem on Newton’s method using a convergence analysis which makes clear, with respect to Newton’s method, the relationship of the majorant function and the non-linear operator under consideration. This approach enables us to drop out the assumption of existence of a second root for the majorant function, still guaranteeing Q-quadratic convergence rate and to obtain a new estimate of this rate based on a directional derivative of the derivative of the majorant function. Moreover, the majorant function does not have to be defined beyond its first root for obtaining convergence rate results. The research of O.P. Ferreira was supported in part by FUNAPE/UFG, CNPq Grant 475647/2006-8, CNPq Grant 302618/2005-8, PRONEX–Optimization(FAPERJ/CNPq) and IMPA. The research of B.F. Svaiter was supported in part by CNPq Grant 301200/93-9(RN) and by PRONEX–Optimization(FAPERJ/CNPq).     

Auditing Shaked and Shanthikumar’s ‘excess wealth’

A notion called “excess wealth” was introduced by Shaked and Shanthikumar around 1998 (Probab. Eng. Inf. Sci. 12:1–23, 1998). Subsequent to this, much has been written on it, mostly by Shaked and his colleagues; see Sordo (Insur. Math. Econ. 45(3):466–469, 2009) for a recent review. These works have appeared in the literatures of reliability theory and stochastic orderings. Since the term excess wealth connotes a measure of income inequality—much like its dual, poverty—it should have had an impact in economics and the econometric literature. This, it appears is not the case, at least to the extent that it should be. The purpose of this paper is to investigate the above disconnect by looking at the notion of excess wealth more carefully, but keeping in mind the angle of economics and income. Our conclusion is that an alternative definition of excess wealth better encapsulates what one means by a colloquial use of the term. Our motivation for being attracted to this topic arises from two angles. The first is that the stochastics of diagnostic and threat detection tests, in which we have an interest, has a strong bearing on indices of concentration like the Lorenz Curve, the Gini index, and the entropy. Thus the notion of excess wealth, which conveys a sense of income concentration should also be relevant to diagnostics. The second motivation is to honor Moshe Shaked, a prolific researcher and a friend of the first author, by developing a paper based on an idea that is co-attributed to him.     

Dedekind’s and Frege’s views on logic

A contextual and comparative analysis shows that Dedekind and Frege do not understand the terms “logic” and “arithmetic” in the same way. More specifically the meaning and the scope of the corresponding concepts are essentially different for them. Consequently Dedekind and Frege have different conceptions of the relationship between arithmetic and logic.     

Stationary points of O’Hara’s knot energies

In this article we study the regularity of stationary points of the knot energies E ^(α) introduced by O’Hara (Topology 30(2):241–247, 1991; Topol Appl 48(2):147–161, 1992; Topol Appl 56(1):45–61, 1994) in the range ${\alpha\in(2,3)}$ . In a first step we prove that E ^(α) is C ¹ on the set of all regular embedded curves belonging to ${{H^{(\alpha+1)/2,2}(\mathbb {R}{/}\mathbb {Z}, \mathbb {R}^n)}}$ and calculate its derivative. After that we use the structure of the Euler-Lagrange equation to study the regularity of stationary points of E ^(α) plus a positive multiple of the length. We show that stationary points of finite energy are of class C ^∞—so especially all local minimizers of E ^(α) among curves with fixed length are smooth.     

A note on Stone’s,Baire’s,Ky Fan’s and Dugundji’s theorem in tvs-cone metric spaces

Recently, Ayse Sonmez [A. Sonmez, On paracompactness in cone metric spaces, Appl. Math. Lett. 23 (2010) 494–497] proved that a cone metric space is paracompact when the underlying cone is normal. Also, very recently, Kieu Phuong Chi and Tran Van An [K.P. Chi, T. Van An, Dugundji’s theorem for cone metric spaces, Appl. Math. Lett. (2010) doi:10.1016/j.aml.2010.10.034] proved Dugundji’s extension theorem for the normal cone metric space. The aim of this paper is to prove this in the frame of the tvs-cone spaces in which the cone does not need to be normal. Examples are given to illustrate the results.