A geometric definition of mass

An invariant definition of mass is given, within the context of a geometric unified theory, in terms of the geometric connection and the matter current. This geometric mass corresponds to the concept of self energy and leads to the mass parameter in Dirac's equation.     

The conjugacy vector of ap-group of maximal class

We find the conjugacy vector, i.e., we determine the number of conjugacy classes which compose the sets of the elements with centralizers of equal order, for several general families ofp-groups of maximal class which include those of order up top ⁹. As a consequence, we obtain the number of conjugacy classes,r(G), for the groups in these families. Also, we provide upper and lower bounds forr(G) and characterize when they are attained. Examples are given showing that the bounds are actually attained. This work has been supported by DGICYT grant PB91-0446 and by the University of the Basque Country.     

A fuzzy approach to cooperative n-person games

The object of this paper is to provide a systematic treatment of bargaining procedures as a basis for negotiation. An innovative fuzzy logic approach to analyze n-person cooperative games is developed. A couple of indices, the Good Deal Index and the Counterpart Convenience Index are proposed to characterize the heuristic of bargaining and to provide a solution concept. The indices are examined theoretically and experimentally by analyzing three case studies. The results verify the validity of the approach.     

Formulation of Aluminum Chloride Phthalocyanine in Pluronic™ P‐123 and F‐127 Block Copolymer Micelles: Photophysical properties and Photodynamic Inactivation of Microorganisms

Aluminum Chloride Phthalocyanine (AlPcCl) can be used as a photosensitizer (PS) for Photodynamic Inactivation of Microorganisms (PDI). The AlPcCl showed favorable characteristics for PDI due to high quantum yield of singlet oxygen (Φ_Δ) and photostability. Physicochemical properties and photodynamic inactivation of AlPcCl incorporated in polymeric micelles of tri‐block copolymer (P‐123 and F‐127) against microorganisms Staphylococcus aureus, Escherichia coli and Candida albicans were investigated in this work. Previously, it was observed that the AlPcCl undergoes self‐aggregation in F‐127, while in P‐123 the PS is in a monomeric form suitable for PDI. Due to the self‐aggregation of AlPcCl in F‐127, this formulation did not show any effect on these microorganisms. On the other hand, AlPcCl formulated in P‐123 was effective against S. aureus and C. albicans and the death of microorganisms was dependent on the PS concentration and illumination time. Additionally, it was found that the values of PS concentration and illumination time to eradicate 90% of the initial population of microorganisms (IC₉₀ and D₉₀, respectively) were small for the AlPcCl in P‐123, showing the effectiveness of this formulation for PDI.     

Global $$L^q$$-Gevrey Functions and Their Applications

The goal of this paper is to introduce a class of \(C^\infty \) functions derivatives of which satisfy quantitative size estimates. The estimates, called global \(L^q\) Gevrey estimates, first arose in the work of Boggess and Raich ( J. Fourier Anal. Appl. 19:180–224, 2013) when they investigated how to capture a particular type of exponential decay through estimates on the Fourier transform. In the present work, we refine the notion of global \(L^q\)-Gevrey functions and include a discussion of the function theory as well as the relationship to Gevrey classes and known function spaces. In addition, we present explicit examples of global \(L^q\)-Gevrey functions and ways to generate new global \(L^q\)-Gevrey functions from old ones. We conclude with three applications: The first is solving a Carleman-type problem for constructing functions derivatives of which are a given sequence of global \(L^q\)-Gevrey functions. The other two applications concern extensions of a given global \(L^q\)-Gevrey function: the first is constructing an almost analytic extension, and the second is building an approximate solution to a first-order complex vector field coefficients of which are global \(L^q\)-Gevrey functions.