scholarly journals Bi-interior Ideal Elements in ∧e-semigroups

2021 ◽  
Vol 14 (1) ◽  
pp. 43-52
Author(s):  
Niovi Kehayopulu
Keyword(s):  
General Setting ◽  
General Topology ◽  
Abstract Form ◽  
Ordered Semigroups ◽  
Abstract Formulation

All the results on semigroups obtained using only sets, can be written in an abstract form in a more general setting. Let us consider a recent paper to justify what we say. The bi-interior ideals of semigroups introduced and studied by M. Murali Krishna Rao in Discuss. Math. Gen. Algebra Appl. in 2018, follow for more general statements about ordered semigroups. The same holds for every result of this sort on semigroups based on right (left) ideals, bi-ideals, quasi-ideals, interior ideals etc. for which we use sets. As a result, we have an abstract formulation of the results on semigroups obtained by sets that is in the same spirit with the abstract formulation of general topology (the so-called topology without points) initiated by Koutsk ́y, Nöbeling and, even earlier, by Chittenden, Terasaka, Nakamura, Monteiro and Ribeiro. As a consequence, results on ordered Γ-hypersemigroups and on similar simpler structures can be obtained.

scholarly journals Regular Wallman compactifications of rim-compact spaces

1981 ◽  
Vol 31 (3) ◽  
pp. 312-324
Author(s):  
Olav Njåstad
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
General Setting ◽  
General Topology ◽  
Locally Compact ◽  
Compact Spaces ◽  
Closed Sets ◽  
The Family ◽  
Locally Compact Hausdorff Space ◽  
Regular Closed

AbstractA compact Hausdorff space is regular Wallman if it possesses a separating ring of regular closed sets, an s-ring. It was proved by P. C. Baayen and J. van Mill [General Topology and Appl. 9 (1978), 125–129] that if a locally compact Hausdorff space possesses an s-ring, then every Hausdorff compactification with zero-dimensional remainder is regular Wallman.In this paper the reasoning leading to this result is modified to work in a more general setting. Iet αX be a Hausdorff compactification of a space X, and let be the family of those closed sets in αX whose boundaries are contained in X. A main result is the following: If contains an s-ring for some Hausdorff compactification γX, then every larger Hausdorff compactification αX for which is a base for the closed sets on αX — X, is regular Wallman. Various consequences concerning compactifications of a class of rim-compact spaces (called totally rim-compact spaces) are discussed.

scholarly journals Directed unions of local monoidal transforms and GCD domains

2019 ◽  
Vol 19 (04) ◽  
pp. 2050061
Author(s):  
Lorenzo Guerrieri
Keyword(s):  
Prime Ideal ◽  
Local Ring ◽  
Maximal Ideal ◽  
General Setting ◽  
Regular Local Ring ◽  
Dimension Formula

Let [Formula: see text] be a regular local ring of dimension [Formula: see text]. A local monoidal transform of [Formula: see text] is a ring of the form [Formula: see text], where [Formula: see text] is a regular parameter, [Formula: see text] is a regular prime ideal of [Formula: see text] and [Formula: see text] is a maximal ideal of [Formula: see text] lying over [Formula: see text] In this paper, we study some features of the rings [Formula: see text] obtained as infinite directed union of iterated local monoidal transforms of [Formula: see text]. In order to study when these rings are GCD domains, we also provide results in the more general setting of directed unions of GCD domains.

scholarly journals Demographic Dynamics in Multitype Populations with Migrations

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 246
Author(s):  
Manuel Molina-Fernández ◽  
Manuel Mota-Medina
Keyword(s):  
Mathematical Modeling ◽  
Population Dynamics ◽  
Branching Process ◽  
Probability Model ◽  
Biological Systems ◽  
Research Work ◽  
General Setting ◽  
Process Theory ◽  
Multitype Branching Process ◽  
Demographic Dynamics

This research work deals with mathematical modeling in complex biological systems in which several types of individuals coexist in various populations. Migratory phenomena among the populations are allowed. We propose a class of mathematical models to describe the demographic dynamics of these type of complex systems. The probability model is defined through a sequence of random matrices in which rows and columns represent the various populations and the several types of individuals, respectively. We prove that this stochastic sequence can be studied under the general setting provided by the multitype branching process theory. Probabilistic properties and limiting results are then established. As application, we present an illustrative example about the population dynamics of biological systems formed by long-lived raptor colonies.

Global Perturbation of Nonlinear Eigenvalues

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Julián López-Gómez ◽  
Juan Carlos Sampedro
Keyword(s):  
Perturbation Theory ◽  
Spectral Parameter ◽  
Classical Theory ◽  
General Setting ◽  
Perturbation Parameter ◽  
Linear Operators ◽  
Fredholm Operators ◽  
Index Zero ◽  
Finite Dimensional ◽  
Nonlinear Eigenvalues

Abstract This paper generalizes the classical theory of perturbation of eigenvalues up to cover the most general setting where the operator surface 𝔏 : [ a , b ] × [ c , d ] → Φ 0 ⁢ ( U , V ) {\mathfrak{L}:[a,b]\times[c,d]\to\Phi_{0}(U,V)} , ( λ , μ ) ↦ 𝔏 ⁢ ( λ , μ ) {(\lambda,\mu)\mapsto\mathfrak{L}(\lambda,\mu)} , depends continuously on the perturbation parameter, μ, and holomorphically, as well as nonlinearly, on the spectral parameter, λ, where Φ 0 ⁢ ( U , V ) {\Phi_{0}(U,V)} stands for the set of Fredholm operators of index zero between U and V. The main result is a substantial extension of a classical finite-dimensional theorem of T. Kato (see [T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Class. Math., Springer, Berlin, 1995, Chapter 2, Section 5]).

scholarly journals Representation and Presentation of Culinary Tradition as Cultural Heritage

Heritage ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 612-640
Author(s):  
Nikolaos Partarakis ◽  
Danai Kaplanidi ◽  
Paraskevi Doulgeraki ◽  
Effie Karuzaki ◽  
Argyro Petraki ◽  
...  
Keyword(s):  
Social Sciences ◽  
Knowledge Representation ◽  
Cultural Heritage ◽  
Systematic Approach ◽  
Semantic Representation ◽  
Ethnographic Research ◽  
Abstract Form ◽  
Web Based ◽  
Social Sciences And Humanities ◽  
Authoring Environment

This paper presents a knowledge representation framework and provides tools to allow the representation and presentation of the tangible and intangible dimensions of culinary tradition as cultural heritage including the socio-historic context of its evolution. The representation framework adheres to and extends the knowledge representation standards for the Cultural Heritage (CH) domain while providing a widely accessible web-based authoring environment to facilitate the representation activities. In strong collaboration with social sciences and humanities, this work allows the exploitation of ethnographic research outcomes by providing a systematic approach for the representation of culinary tradition in the form of recipes, both in an abstract form for their preservation and in a semantic representation of their execution captured on-site during ethnographic research.

scholarly journals High Order Semi-implicit Multistep Methods for Time-Dependent Partial Differential Equations

2021 ◽  
Author(s):  
Giacomo Albi ◽  
Lorenzo Pareschi
Keyword(s):  
Multistep Methods ◽  
General Setting ◽  
Reaction Diffusion ◽  
Strong Stability ◽  
High Order ◽  
Iterative Solvers ◽  
Time Dependent ◽  
Linear Multistep Methods ◽  
Advection Diffusion Equation ◽  
Separation Of Scales

AbstractWe consider the construction of semi-implicit linear multistep methods that can be applied to time-dependent PDEs where the separation of scales in additive form, typically used in implicit-explicit (IMEX) methods, is not possible. As shown in Boscarino et al. (J. Sci. Comput. 68: 975–1001, 2016) for Runge-Kutta methods, these semi-implicit techniques give a great flexibility, and allow, in many cases, the construction of simple linearly implicit schemes with no need of iterative solvers. In this work, we develop a general setting for the construction of high order semi-implicit linear multistep methods and analyze their stability properties for a prototype linear advection-diffusion equation and in the setting of strong stability preserving (SSP) methods. Our findings are demonstrated on several examples, including nonlinear reaction-diffusion and convection-diffusion problems.

‘Who Ya Gonna Call …?’ Ethical and legal dilemmas in specialist children centres and district general hospitals

2021 ◽  
pp. 147775092110366
Author(s):  
Harika Avula ◽  
Mariana Dittborn ◽  
Joe Brierley
Keyword(s):  
Intensive Care ◽  
Clinical Ethics ◽  
Ethical Issues ◽  
General Setting ◽  
Daily Practice ◽  
Paediatric Intensive Care ◽  
Ethical Challenges ◽  
Legal Cases ◽  
Ethics Support ◽  
The Uk

The field of Paediatric Bioethics, or ethical issues applied to children's healthcare, is relatively new but has recently gained an increased professional and public profile. Clinical ethics support to health professionals and patients who face ethical challenges in clinical practice varies between and within institutions. Literature regarding services available to paediatricians is sparse in specialist tertiary centres and almost absent in general paediatrics. We performed a mixed-methods study using online surveys and focus groups to explore the experiences of ethical and legal dilemmas and the support structures available to (i) paediatric intensive care teams as a proxy for specialist children's centres and (ii) paediatricians working in the general setting in the UK. Our main findings illustrate the broad range of ethical and legal challenges experienced by both groups in daily practice. Ethics training and the availability of ethics support were variable in structure, processes, funding and availability, e.g., 70% of paediatric intensive care consultants reported access to formal ethics advice versus 20% general paediatricians. Overall, our findings suggest a need for ethics support and training in both settings. The broad experience reported of ethics support, where it existed, was good – though improvements were suggested. Many clinicians were concerned about their relationship with children and families experiencing a challenging ethical situation, partly as a result of high-profile recent legal cases in the media. Further research in this area would help collect a broader range of views to inform clinical ethics support's development to better support paediatric teams, children and their families.

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