A Fractional Analog of the Duhamel Principle

Mathematics Subject Classification: 35CXX, 26A33, 35S10

Explicit Solutions of Nonlocal Boundary Value Problems, Containing Bitsadze-Samarskii Constraints

MSC 2010: 44A35, 35L20, 35J05, 35J25

Nonlocal Boundary Value Problems for Two-Dimensional Potential Equation on a Rectangle

Иван Димовски, Юлиан Цанков - Предложено е разширение на принципa на Дюамел. За намиране на явно решение на нелокални гранични задачи от този тип е развито операционно смятане основано върху некласическа двумерна конволюция. Пример от такъв тип е задачата на Бицадзе-Самарски.

Operational Methods in the Environment of a Computer Algebra System

This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.

Explicit Solution of Bitsadze-Samarskii Problem

Иван Димовски, Юлиан Цанков - В статията е намерено точно решение на задачата на Бицадзе-Самрски (1) за уравнението на Лаплас, като е използвано операционно смятане основано на некласическа двумернa конволюция. На това точно решение може да се гледа като начин за сумиране на нехармоничния ред по синуси на решението, получен по метода на Фурие.

Exact Solutions of Nonlocal Boundary Value Problems for One- and Two-Dimensional Heat Equation

Иван Хр. Димовски, Юлиан Ц. Цанков - Предложен е метод за намиране на явни решения на клас двумерни уравнения на топлопроводността с нелокални условия по пространствените променливи. Методът е основан на директно тримерно операционно смятане. Класическата дюамелова конволюция е комбинирана с две некласически конволюции за операторите ∂xx и ∂yy в една тримерна конволюция. Съответното операционно смятане използва мултипликаторни частни. Мултипликаторните частни позволяват да се продължи принципът на Дюамел за пространствените променливи и да се намерят явни решения на разглежданите гранични задачи. Общите разглеждания са приложени в случая на гранични условия от типа на Йонкин. Намерени са експлицитни решения в затворен вид.

Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations

MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05

Macrocycles mimic the extended peptide conformation recognized by aspartic, serine, cysteine and metallo proteases

It has been previously demonstrated that aspartic, serine, metallo and cysteine proteases bind to their inhibitors and substrate analogues in a single conformation, the saw-tooth or extended beta-strand. Consequently a generic approach to the development of protease inhibitors is the use of constraints that conformationally restrict putative inhibitor molecules to an extended form. In this way the inhibitor is pre-organized for binding to a protease and does not need to rearrange its structure. One constraining device that has proven to be effective for such pre-organization is macrocyclization. This article illustrates the general principle that macrocycles, especially those composed of 3-4 amino acids and usually 13-17 ring atoms, can effectively mimic the extended conformation of short peptide sequences. Such structure-stabilising macrocycles are stable to degradation by proteases, valuable components of potent protease inhibitors, and in many cases they are also bioavailable.

The "ethical anthropic principle" and the religious ethics of Levinas

Why did Levinas choose Isaiah 45:7 ("I make peace and create evil: I the Lord do all that") as a superscription of his essay on evil? This article explores the role of evil in Levinas's religious ethics. The author discusses the structure of evil as revealed phenomenologically and juxtaposes it to the structure of subjectivity found in the writings of Levinas. The idea of the "ethical anthropic principle," modeled upon the cosmic anthropic principle, is then used to link evil to the responsibility of the subject. The link is subsequently extended to God. This is proposed as one way of understanding the meaning of Isaiah 45:7. © 2001 Journal of Religious Ethics, Inc.

Statistical mechanics in the extended Gaussian ensemble

The extended Gaussian ensemble (EGE) is introduced as a generalization of the canonical ensemble. This ensemble is a further extension of the Gaussian ensemble introduced by Hetherington [J. Low Temp. Phys. 66, 145 (1987)]. The statistical mechanical formalism is derived both from the analysis of the system attached to a finite reservoir and from the maximum statistical entropy principle. The probability of each microstate depends on two parameters ß and ¿ which allow one to fix, independently, the mean energy of the system and the energy fluctuations, respectively. We establish the Legendre transform structure for the generalized thermodynamic potential and propose a stability criterion. We also compare the EGE probability distribution with the q-exponential distribution. As an example, an application to a system with few independent spins is presented.

Head-controlled assistive telerobot with extended physiological proprioception capability

People with disabilities such as quadriplegia can use mouth-sticks and head-sticks as extension devices to perform desired manipulations. These extensions provide extended proprioception which allows users to directly feel forces and other perceptual cues such as texture present at the tip of the mouth-stick. Such devices are effective for two principle reasons: because of their close contact with the user's tactile and proprioceptive sensing abilities; and because they tend to be lightweight and very stiff, and can thus convey tactile and kinesthetic information with high-bandwidth. Unfortunately, traditional mouth-sticks and head-sticks are limited in workspace and in the mechanical power that can be transferred because of user mobility and strength limitations. We describe an alternative implementation of the head-stick device using the idea of a virtual head-stick: a head-controlled bilateral force-reflecting telerobot. In this system the end-effector of the slave robot moves as if it were at the tip of an imaginary extension of the user's head. The design goal is for the system is to have the same intuitive operation and extended proprioception as a regular mouth-stick effector but with augmentation of workspace volume and mechanical power. The input is through a specially modified six DOF master robot (a PerForceTM hand-controller) whose joints can be back-driven to apply forces at the user's head. The manipulation tasks in the environment are performed by a six degree-of-freedom slave robot (the Zebra-ZEROTM) with a built-in force sensor. We describe the prototype hardware/software implementation of the system, control system design, safety/disability issues, and initial evaluation tasks.

The equivalence principle revisited

A precise fomulation of the strong Equivalence Principle is essential to the understanding of the relationship between gravitation and quantum mechanics. The relevant aspects are reviewed in a context including General Relativity but allowing for the presence of torsion. For the sake of brevity, a concise statement is proposed for the Principle: An ideal observer immersed in a gravitational field can choose a reference frame in which gravitation goes unnoticed. This statement is given a clear mathematical meaning through an accurate discussion of its terms. It holds for ideal observers (time-like smooth non-intersecting curves), but not for real, spatially extended observers. Analogous results hold for gauge fields. The difference between gravitation and the other fundamental interactions comes from their distinct roles in the equation of force.

Extended 2D generalized dilaton gravity theories

We show that an anomaly-free description of matter in (1+1) dimensions requires a deformation of the 2D relativity principle, which introduces a non-trivial centre in the 2D Poincare algebra. Then we work out the reduced phase space of the anomaly-free 2D relativistic particle, in order to show that it lives in a noncommutative 2D Minkowski space. Moreover, we build a Gaussian wave packet to show that a Planck length is well defined in two dimensions. In order to provide a gravitational interpretation for this noncommutativity, we propose to extend the usual 2D generalized dilaton gravity models by a specific Maxwell component, which guages the extra symmetry associated with the centre of the 2D Poincare algebra. In addition, we show that this extension is a high energy correction to the unextended dilaton theories that can affect the topology of spacetime. Further, we couple a test particle to the general extended dilaton models with the purpose of showing that they predict a noncommutativity in curved spacetime, which is locally described by a Moyal star product in the low energy limit. We also conjecture a probable generalization of this result, which provides strong evidence that the noncommutativity is described by a certain star product which is not of the Moyal type at high energies. Finally, we prove that the extended dilaton theories can be formulated as Poisson-Sigma models based on a nonlinear deformation of the extended Poincare algebra.

Extended arm polyphenylene dendrimers

In order to eliminate the de Gennes packing problem, which usually limits the attainable size of dendrimers, a new branching unit containing para-tetraphenylene ethynyl arms has been synthesized and utilized in the preparation of dendrimers of the Müllen type. The divergent principle of synthesis, based on the Dilthey reaction, could be carried up to sixth generation which contains 2776 benzene rings and possesses a diameter in the 27 nm range ("exploded dendrimer"). Monodispersity and dimensions of this and the lower generation species have been studied by MALDI-TOF MS (including the very recent superconducting tunnel junction detector), by size-exclusion chromatography, dynamic light scattering, transmission electron microscopy, and atomic force microscopy. Interesting features, apart from the huge dimension, are the low density and high porosity of these giant molecules which cause extensive aggregation in the gas phase, flattening on solid support (AFM) and the ready incorporation of guest molecules in the condensed phase. Since the synthesis of the para-tetraphenylene arms is quite elaborate, similar dendrimers containing para-terphenylene arms have been prepared; they are accessible more economically ("semi-exploded dendrimers"). It has been shown that they in several aspects mimic the features of the "exploded dendrimers". In order to take advantage of the presence of large internal cavities in this dendrimer type, dendrons containing -C≡C- triple bonds have also been incorporated. Surprisingly, they are readily hydrogenated under the condition of heterogeneous catalysis (Pd/C) which demonstrates the large size of the cavities. As revealed by a quartz microbalance study the post-hydrogenation dendrimers are less prone to incorporate guest molecules than before hydrogenation. Obviously, the more flexible nature of the former reduces porosity, it also leads to significant shrinkage. An interesting perspective is the use of homogeneous hydrogenation catalysts of variable size with the aim of determining the dimension of internal free space.

The Optimal Response to Default: Renegotiation or Extended Maturity?

This paper reinforces the argument of Harding and Sirmans (2002) that the observed preference of lenders for extended maturity rather than renegotiation of the principle in the case of loan default is due to the superior incentive properties of the former. Specifically, borrowers have a greater incentive to avoid default under extended maturity because it reduces the likelihood that they will be able to escape paying off the full loan balance. Thus, although extended maturity leaves open the possibility of foreclosure, it will be preferred to renegotiation as long as the dead weight loss from foreclosure is not too large.