Next Issue
Volume 4, March
Previous Issue
Volume 4, September

Table of Contents

Axioms, Volume 4, Issue 4 (December 2015) , Pages 423-553

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Readerexternal link to open them.
Order results
Result details
Select all
Export citation of selected articles as:
Open AccessReview
An Overview of the Pathway Idea and Its Applications in Statistical and Physical Sciences
Axioms 2015, 4(4), 530-553; https://doi.org/10.3390/axioms4040530 - 19 Dec 2015
Viewed by 1787
Abstract
Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter α, called the pathway parameter, one can connect generalized type-1 beta family of densities, generalized [...] Read more.
Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter α, called the pathway parameter, one can connect generalized type-1 beta family of densities, generalized type-2 beta family of densities, and generalized gamma family of densities, in the scalar as well as the matrix cases, also in the real and complex domains. It is shown that when the model is applied to physical situations then the current hot topics of Tsallis statistics and superstatistics in statistical mechanics become special cases of the pathway model, and the model is capable of capturing many stable situations as well as the unstable or chaotic neighborhoods of the stable situations and transitional stages. The pathway model is shown to be connected to generalized information measures or entropies, power law, likelihood ratio criterion or λ - criterion in multivariate statistical analysis, generalized Dirichlet densities, fractional calculus, Mittag-Leffler stochastic process, Krätzel integral in applied analysis, and many other topics in different disciplines. The pathway model enables one to extend the current results on quadratic and bilinear forms, when the samples come from Gaussian populations, to wider classes of populations. Full article
Show Figures

Figure 1

Open AccessArticle
On Limiting Behavior of Contaminant Transport Models in Coupled Surface and Groundwater Flows
Axioms 2015, 4(4), 518-529; https://doi.org/10.3390/axioms4040518 - 06 Nov 2015
Cited by 1 | Viewed by 1613
Abstract
There has been a surge of work on models for coupling surface-water with groundwater flows which is at its core the Stokes-Darcy problem. The resulting (Stokes-Darcy) fluid velocity is important because the flow transports contaminants. The analysis of models including the transport of [...] Read more.
There has been a surge of work on models for coupling surface-water with groundwater flows which is at its core the Stokes-Darcy problem. The resulting (Stokes-Darcy) fluid velocity is important because the flow transports contaminants. The analysis of models including the transport of contaminants has, however, focused on a quasi-static Stokes-Darcy model. Herein we consider the fully evolutionary system including contaminant transport and analyze its quasi-static limits. Full article
(This article belongs to the Special Issue Functional Differential Equations)
Open AccessArticle
Free Boolean Topological Groups
Axioms 2015, 4(4), 492-517; https://doi.org/10.3390/axioms4040492 - 03 Nov 2015
Cited by 4 | Viewed by 1809
Abstract
Known and new results on free Boolean topological groups are collected. An account of the properties that these groups share with free or free Abelian topological groups and properties specific to free Boolean groups is given. Special emphasis is placed on the application [...] Read more.
Known and new results on free Boolean topological groups are collected. An account of the properties that these groups share with free or free Abelian topological groups and properties specific to free Boolean groups is given. Special emphasis is placed on the application of set-theoretic methods to the study of Boolean topological groups. Full article
Open AccessArticle
Characterized Subgroups of Topological Abelian Groups
Axioms 2015, 4(4), 459-491; https://doi.org/10.3390/axioms4040459 - 16 Oct 2015
Cited by 3 | Viewed by 1737
Abstract
A subgroup H of a topological abelian group X is said to be characterized by a sequence v = (vn) of characters of X if H = {xX : vn(x) → 0 in T}. [...] Read more.
A subgroup H of a topological abelian group X is said to be characterized by a sequence v = (vn) of characters of X if H = {xX : vn(x) → 0 in T}. We study the basic properties of characterized subgroups in the general setting, extending results known in the compact case. For a better description, we isolate various types of characterized subgroups. Moreover, we introduce the relevant class of auto-characterized groups (namely, the groups that are characterized subgroups of themselves by means of a sequence of non-null characters); in the case of locally compact abelian groups, these are proven to be exactly the non-compact ones. As a by-product of our results, we find a complete description of the characterized subgroups of discrete abelian groups. Full article
Open AccessArticle
Locally Quasi-Convex Compatible Topologies on a Topological Group
Axioms 2015, 4(4), 436-458; https://doi.org/10.3390/axioms4040436 - 13 Oct 2015
Cited by 6 | Viewed by 1763
Abstract
For a locally quasi-convex topological abelian group (G,τ), we study the poset \(\mathscr{C}(G,τ)\) of all locally quasi-convex topologies on (G) that are compatible with (τ) (i.e., have the same dual as (G,τ) ordered by inclusion. [...] Read more.
For a locally quasi-convex topological abelian group (G,τ), we study the poset \(\mathscr{C}(G,τ)\) of all locally quasi-convex topologies on (G) that are compatible with (τ) (i.e., have the same dual as (G,τ) ordered by inclusion. Obviously, this poset has always a bottom element, namely the weak topology σ(G,\(\widehat{G})\) . Whether it has also a top element is an open question. We study both quantitative aspects of this poset (its size) and its qualitative aspects, e.g., its chains and anti-chains. Since we are mostly interested in estimates ``from below'', our strategy consists of finding appropriate subgroups (H) of (G) that are easier to handle and show that \(\mathscr{C} (H)\) and \(\mathscr{C} (G/H)\) are large and embed, as a poset, in \(\mathscr{C}(G,τ)\). Important special results are: (i) if \(K\) is a compact subgroup of a locally quasi-convex group \(G\), then \(\mathscr{C}(G)\) and \(\mathscr{C}(G/K)\) are quasi-isomorphic (3.15); (ii) if (D) is a discrete abelian group of infinite rank, then \(\mathscr{C}(D)\) is quasi-isomorphic to the poset \(\mathfrak{F}_D\) of filters on D (4.5). Combining both results, we prove that for an LCA (locally compact abelian) group \(G \) with an open subgroup of infinite co-rank (this class includes, among others, all non-σ-compact LCA groups), the poset \( \mathscr{C} (G) \) is as big as the underlying topological structure of (G,τ) (and set theory) allows. For a metrizable connected compact group \(X\), the group of null sequences \(G=c_0(X)\) with the topology of uniform convergence is studied. We prove that \(\mathscr{C}(G)\) is quasi-isomorphic to \(\mathscr{P}(\mathbb{R})\) (6.9). Full article
Open AccessArticle
Yang–Baxter Equations, Computational Methods and Applications
Axioms 2015, 4(4), 423-435; https://doi.org/10.3390/axioms4040423 - 09 Oct 2015
Cited by 5 | Viewed by 1627
Abstract
Computational methods are an important tool for solving the Yang–Baxter equations (in small dimensions), for classifying (unifying) structures and for solving related problems. This paper is an account of some of the latest developments on the Yang–Baxter equation, its set-theoretical version and its [...] Read more.
Computational methods are an important tool for solving the Yang–Baxter equations (in small dimensions), for classifying (unifying) structures and for solving related problems. This paper is an account of some of the latest developments on the Yang–Baxter equation, its set-theoretical version and its applications. We construct new set-theoretical solutions for the Yang–Baxter equation. Unification theories and other results are proposed or proven. Full article
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations 2015)
Previous Issue
Next Issue
Back to TopTop