The one-level functional equation of multi-rate loss systems

AbstractThe paper is concerned with some aspects of the theory of elementary volume from the measure-theoretical standpoint. It is shown that there exists a nontrivial solution of Cauchy's functional equation, nonmeasurable with respect to every translation invariant measure on the real line, extending the one-dimensional Lebesgue measure.

Download Full-text

Zeta functions on tori using contour integration

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s021988781550019x ◽

2015 ◽

Vol 12 (02) ◽

pp. 1550019

Author(s):

Emilio Elizalde ◽

Klaus Kirsten ◽

Nicolas Robles ◽

Floyd Williams

Keyword(s):

Functional Equation ◽

Eisenstein Series ◽

Zeta Functions ◽

Contour Integration ◽

Alternative Proof ◽

Functional Determinant ◽

Dedekind Eta Function ◽

Limit Formula ◽

Complex Tori ◽

The One

A new, seemingly useful presentation of zeta functions on complex tori is derived by using contour integration. It is shown to agree with the one obtained by using the Chowla–Selberg series formula, for which an alternative proof is thereby given. In addition, a new proof of the functional determinant on the torus results, which does not use the Kronecker first limit formula nor the functional equation of the non-holomorphic Eisenstein series. As a bonus, several identities involving the Dedekind eta function are obtained as well.

Download Full-text

Performance Evaluation of the Threshold Call Admission Policy in Multi-rate Loss Systems

Journal of Telecommunications and Information Technology ◽

10.26636/jtit.2020.142120 ◽

2020 ◽

Vol 2 ◽

pp. 51-60

Author(s):

Ioannis D. Moscholios ◽

Iskanter-Alexandros Chousainov ◽

Panagiotis I. Panagoulias ◽

Panagiotis G. Sarigiannidis ◽

Michael D. Logothetis

Keyword(s):

Performance Evaluation ◽

Admission Policy ◽

Call Admission ◽

Loss Systems ◽

Rate Loss

Download Full-text

On quantum separation of variables beyond fundamental representations

SciPost Physics ◽

10.21468/scipostphys.10.2.026 ◽

2021 ◽

Vol 10 (2) ◽

Author(s):

Jean Michel Maillet ◽

Giuliano Niccoli

Keyword(s):

Functional Equation ◽

Transfer Matrix ◽

Separation Of Variables ◽

Operator Family ◽

Transfer Matrices ◽

Conserved Charges ◽

Transfer Matrix Spectrum ◽

Lax Operator ◽

The One ◽

Matrix Spectrum

We describe the extension, beyond fundamental representations of the Yang-Baxter algebra, of our new construction of separation of variables bases for quantum integrable lattice models. The key idea underlying our approach is to use the commuting conserved charges of the quantum integrable models to generate bases in which their spectral problem is separated, i.e. in which the wave functions are factorized in terms of specific solutions of a functional equation. For the so-called “non-fundamental” models we construct two different types of SoV bases. The first is given from the fundamental quantum Lax operator having isomorphic auxiliary and quantum spaces and that can be obtained by fusion of the original quantum Lax operator. The construction essentially follows the one we used previously for fundamental models and allows us to derive the simplicity and diagonalizability of the transfer matrix spectrum. Then, starting from the original quantum Lax operator and using the full tower of the fused transfer matrices, we introduce a second type of SoV bases for which the proof of the separation of the transfer matrix spectrum is naturally derived. We show that, under some special choice, this second type of SoV bases coincides with the one associated to Sklyanin’s approach. Moreover, we derive the finite difference type (quantum spectral curve) functional equation and the set of its solutions defining the complete transfer matrix spectrum. This is explicitly implemented for the integrable quantum models associated to the higher spin representations of the general quasi-periodic Y(gl_{2})Y(gl2) Yang-Baxter algebra. Our SoV approach also leads to the construction of a QQ-operator in terms of the fused transfer matrices. Finally, we show that the QQ-operator family can be equivalently used as the family of commuting conserved charges enabling to construct our SoV bases.

Download Full-text

Functional Equations and μ-Spherical Functions

Georgian Mathematical Journal ◽

10.1515/gmj.2008.1 ◽

2008 ◽

Vol 15 (1) ◽

pp. 1-20

Author(s):

Mohamed Akkouchi ◽

Belaid Bouikhalene ◽

Elhoucien Elqorachi

Keyword(s):

Functional Equation ◽

Topological Group ◽

Functional Equations ◽

Compact Subgroup ◽

Aequationes Math ◽

Gelfand Pair ◽

Locally Compact ◽

The Matrix ◽

The One ◽

Locally Compact Topological Group

Abstract We will study the properties of solutions 𝑓, {𝑔𝑖}, {ℎ𝑖} ∈ 𝐶𝑏(𝐺) of the functional equation where 𝐺 is a Hausdorff locally compact topological group, 𝐾 a compact subgroup of morphisms of 𝐺, χ a character on 𝐾, and μ a 𝐾-invariant measure on 𝐺. This equation provides a common generalization of many functional equations (D'Alembert's, Badora's, Cauchy's, Gajda's, Stetkaer's, Wilson's equations) on groups. First we obtain the solutions of Badora's equation [Aequationes Math. 43: 72–89, 1992] under the condition that (𝐺,𝐾) is a Gelfand pair. This result completes the one obtained in [Badora, Aequationes Math. 43: 72–89, 1992] and [Elqorachi, Akkouchi, Bakali and Bouikhalene, Georgian Math. J. 11: 449–466, 2004]. Then we point out some of the relations of the general equation to the matrix Badora functional equation and obtain explicit solution formulas of the equation in question for some particular cases. The results presented in this paper may be viewed as a continuation and a generalization of Stetkær's, Badora's, and the authors' works.

Download Full-text

Note on Selection of Coordinate Systems for Geodynamics

International Astronomical Union Colloquium ◽

10.1017/s0252921100051174 ◽

1975 ◽

Vol 26 ◽

pp. 395-407

Author(s):

S. Henriksen

Keyword(s):

Sea Level ◽

The Other ◽

Coordinate Systems ◽

Mean Sea Level ◽

The Earth ◽

The One ◽

Static Systems ◽

Selection Of

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.

Download Full-text

Nucleation of Disorder in Fe3Al Alloys

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100061574 ◽

1967 ◽

Vol 25 ◽

pp. 312-313

Author(s):

P. R. Swann ◽

W. R. Duff ◽

R. M. Fisher

Keyword(s):

Electron Microscopy ◽

Transmission Electron Microscopy ◽

Annealing Temperature ◽

Antiphase Domain ◽

Effect Of Temperature ◽

Domain Structures ◽

Transmission Electron ◽

Domain Boundaries ◽

Higher Temperature ◽

The One

Recently we have investigated the phase equilibria and antiphase domain structures of Fe-Al alloys containing from 18 to 50 at.% Al by transmission electron microscopy and Mössbauer techniques. This study has revealed that none of the published phase diagrams are correct, although the one proposed by Rimlinger agrees most closely with our results to be published separately. In this paper observations by transmission electron microscopy relating to the nucleation of disorder in Fe-24% Al will be described. Figure 1 shows the structure after heating this alloy to 776.6°C and quenching. The white areas are B2 micro-domains corresponding to regions of disorder which form at the annealing temperature and re-order during the quench. By examining specimens heated in a temperature gradient of 2°C/cm it is possible to determine the effect of temperature on the disordering reaction very precisely. It was found that disorder begins at existing antiphase domain boundaries but that at a slightly higher temperature (1°C) it also occurs by homogeneous nucleation within the domains. A small (∼ .01°C) further increase in temperature caused these micro-domains to completely fill the specimen.

Download Full-text

Fundamental Research into Thin Films in a Developing Country

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100095753 ◽

1972 ◽

Vol 30 ◽

pp. 500-501

Author(s):

J.A. Eades ◽

E. Grünbaum

Keyword(s):

Thin Films ◽

Growth Process ◽

Empirical Process ◽

Nucleation And Growth ◽

Research Groups ◽

Film Research ◽

Fundamental Research ◽

Controlled Deposition ◽

The One ◽

The University

In the last decade and a half, thin film research, particularly research into problems associated with epitaxy, has developed from a simple empirical process of determining the conditions for epitaxy into a complex analytical and experimental study of the nucleation and growth process on the one hand and a technology of very great importance on the other. During this period the thin films group of the University of Chile has studied the epitaxy of metals on metal and insulating substrates. The development of the group, one of the first research groups in physics to be established in the country, has parallelled the increasing complexity of the field.The elaborate techniques and equipment now needed for research into thin films may be illustrated by considering the plant and facilities of this group as characteristic of a good system for the controlled deposition and study of thin films.

Download Full-text

STM studies of crystal growth

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100086179 ◽

1991 ◽

Vol 49 ◽

pp. 374-375

Author(s):

M. G. Lagally

Keyword(s):

Crystal Growth ◽

Molecular Beam ◽

Chemical Vapor ◽

Sputter Deposition ◽

Field Of View ◽

Scanning Tunneling ◽

Wide Field ◽

Tunneling Microscopy ◽

Wide Field Of View ◽

The One

It has been recognized since the earliest days of crystal growth that kinetic processes of all Kinds control the nature of the growth. As the technology of crystal growth has become ever more refined, with the advent of such atomistic processes as molecular beam epitaxy, chemical vapor deposition, sputter deposition, and plasma enhanced techniques for the creation of “crystals” as little as one or a few atomic layers thick, multilayer structures, and novel materials combinations, the need to understand the mechanisms controlling the growth process is becoming more critical. Unfortunately, available techniques have not lent themselves well to obtaining a truly microscopic picture of such processes. Because of its atomic resolution on the one hand, and the achievable wide field of view on the other (of the order of micrometers) scanning tunneling microscopy (STM) gives us this opportunity. In this talk, we briefly review the types of growth kinetics measurements that can be made using STM. The use of STM for studies of kinetics is one of the more recent applications of what is itself still a very young field.

Download Full-text