scholarly journals A new approach to temperate generalized Colombeau functions

2008 ◽  
Vol 84 (98) ◽  
pp. 109-121 ◽  
Author(s):  
Antoine Delcroix
Keyword(s):  
General Scheme ◽  
Regularity Theory ◽  
Generalized Functions ◽  
Natural Topology ◽  
Fourier Image ◽  
New Approach ◽  
Generalized Distributions ◽  
Nonlinear Generalized Functions ◽  
The Fourier Transform ◽  
Definition Of

A new approach to the algebra G? of temperate nonlinear generalized functions is proposed, in which G? is based on the space OM endowed with is natural topology in contrary to previous constructions. Thus, this construction fits perfectly in the general scheme of construction of Colombeau type algebras and reveals better properties of G?. This is illustrated by the natural introduction of a regularity theory in G?, of the Fourier transform, with the definition of GO'C, the space of rapidly generalized distributions which is the Fourier image of G?.

scholarly journals A New Approach to Diffeomorphism Invariant Algebras of Generalized Functions

2015 ◽  
Vol 58 (3) ◽  
pp. 717-738
Author(s):  
E. A. Nigsch
Keyword(s):  
Generalized Functions ◽  
New Approach ◽  
Local Setting ◽  
Algebras Of Generalized Functions ◽  
Nonlinear Generalized Functions

AbstractWe develop the diffeomorphism invariant Colombeau-type algebra of nonlinear generalized functions in a modern and compact way. Using a unifying formalism for the local setting and on manifolds, the construction becomes simpler and more accessible than before.

scholarly journals MICROLOCAL ANALYSIS OF GENERALIZED FUNCTIONS: PSEUDODIFFERENTIAL TECHNIQUES AND PROPAGATION OF SINGULARITIES

2005 ◽  
Vol 48 (3) ◽  
pp. 603-629 ◽  
Author(s):  
Claudia Garetto ◽  
Günther Hörmann
Keyword(s):  
Pseudodifferential Operators ◽  
Hyperbolic Equations ◽  
Regularity Theory ◽  
Regularity Result ◽  
Generalized Functions ◽  
Generalized Solutions ◽  
Original Definition ◽  
Characteristic Sets ◽  
Propagation Of Singularities ◽  
Definition Of

AbstractWe characterize microlocal regularity, in the $\mathcal{G}^{\infty}$-sense, of Colombeau generalized functions by an appropriate extension of the classical notion of micro-ellipticity to pseudodifferential operators with slow-scale generalized symbols. Thus we obtain an alternative, yet equivalent, way of determining generalized wavefront sets that is analogous to the original definition of the wavefront set of distributions via intersections over characteristic sets. The new methods are then applied to regularity theory of generalized solutions of (pseudo)differential equations, where we extend the general non-characteristic regularity result for distributional solutions and consider propagation of $\mathcal{G}^{\infty}$-singularities for homogeneous first-order hyperbolic equations.

Seeing, imagined, and lived

2020 ◽  
Vol 3 (2) ◽  
Author(s):  
Anandi Silva Knuppel
Keyword(s):  
Sensory Experience ◽  
Religious Practices ◽  
Daily Lives ◽  
New Approach ◽  
Theories Of Practice ◽  
Sources Of Authority ◽  
Definition Of

Scholarship on Hindu traditions and practices proposes the practice of darshan as fundamental to Hindu traditions, particularly in temple worship, observing that devotees seek out images of deities primarily to see them and “receive” their darshan. These works typically gloss the definition of darshan with a sentence or two about seeing, exchanging glances, and/or receiving blessings. In this paper, I focus on the ways in which darshan is ideally imagined in conjunction with other bodily sensory practices through sources of authority, such as texts and senior devotees, to create a specific sensory experience and expectation in the transnational Gaudiya Vaishnava community. I then look to the lived realitiesof darshan in this tradition, specifically how devotees negotiate the structures created through sources of authority in their daily lives. Through this juxtaposition of idealized and lived darshan, I argue that we need a new approach towards theories of practice to take into account the complexities of darshanic moments in this and other religious practices.

scholarly journals Certain fundamental properties of generalized natural transform in generalized spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shrideh Khalaf Al-Omari ◽  
Serkan Araci
Keyword(s):  
Inversion Formula ◽  
Acta Math ◽  
Generalized Functions ◽  
General Nature ◽  
Qualitative Behavior ◽  
Fundamental Properties ◽  
Integrable Functions ◽  
Extended Operator ◽  
Definition Of ◽  
Space Of Integrable Functions

AbstractThis paper considers the definition and the properties of the generalized natural transform on sets of generalized functions. Convolution products, convolution theorems, and spaces of Boehmians are described in a form of auxiliary results. The constructed spaces of Boehmians are achieved and fulfilled by pursuing a deep analysis on a set of delta sequences and axioms which have mitigated the construction of the generalized spaces. Such results are exploited in emphasizing the virtual definition of the generalized natural transform on the addressed sets of Boehmians. The constructed spaces, inspired from their general nature, generalize the space of integrable functions of Srivastava et al. (Acta Math. Sci. 35B:1386–1400, 2015) and, subsequently, the extended operator with its good qualitative behavior generalizes the classical natural transform. Various continuous embeddings of potential interests are introduced and discussed between the space of integrable functions and the space of integrable Boehmians. On another aspect as well, several characteristics of the extended operator and its inversion formula are discussed.

scholarly journals A generalized inversion formula for the continuous Jacobi transform

1987 ◽  
Vol 10 (4) ◽  
pp. 671-692 ◽  
Author(s):  
Ahmed I. Zayed
Keyword(s):  
Analytic Function ◽  
Inversion Formula ◽  
Generalized Functions ◽  
Generalized Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generalized Inversion ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Jacobi Transform

In this paper we extend the definition of the continuous Jacobi transform to a class of generalized functions and obtain a generalized inversion formula for it. As a by-product of our technique we obtain a necessary and sufficient condition for an analytic functionF(λ)inReλ>0to be the continuous Jacobi transform of a generalized function.

Coercive Persuasion As a Specific Type of Violence in Criminal Law

2020 ◽  
Vol 1 (1) ◽  
pp. 61-72
Author(s):  
Carlos Bardavío Antón
Keyword(s):  
Criminal Law ◽  
Comparative Law ◽  
Third Parties ◽  
Physical Injury ◽  
Comprehensive Understanding ◽  
Legal Doctrine ◽  
New Approach ◽  
Freedom Of Will ◽  
Definition Of ◽  
Regulatory Problems

The field of cults, and that of destructive or coercive cults in particular, has received little attention from the perspective of criminal law doctrine. Supporters of such groups often claim to be victims of a violation related to freedom of will. In this article, I consider various methodologies and manipulation techniques used by such groups and suggest that comparative law, criminal definitions, and regulatory problems provide the basis for a more comprehensive understanding of criminal phenomenology that includes these concerns: the loss of freedom through coercive persuasion, and thus being the victim of a crime, or through becoming an instrument for the commission of crimes ordered by third parties. Research shows that the conventional definition of crime against freedom of will and physical injury is inadequate. I posit that a new approach to legal doctrine and criminal classification is required to fight against new crime phenomenology. I propose a criminal classification aimed at considering coercive persuasion as a crime, and a definition for the criminalization of certain organizations that engage in willful misconduct or reckless conduct.

scholarly journals A Reconsideration on the Theory of Beauty: Previous Views and a New Approach Following Maslow's Theory (Part II)

2021 ◽  
Author(s):  
Iulia-Adina Lehene
Keyword(s):  
Nineteenth Century ◽  
Urban Planning ◽  
Civil Engineering ◽  
Philosophical Perspective ◽  
New Approach ◽  
Human Motivation ◽  
Definition Of ◽  
Concept Of Beauty

This paper is the second part of a work that aims to rethink the concept of beauty as close as possible to its essence and in a way that integrates the science of aesthetics with the field of construction. Within other theoretical and practical works, this study may be further used to physically reflect the definition of beauty in areas such as architecture, civil engineering or urban planning and support professionals in designing and building beautiful objects and constructions. However, it has to be added that the assumption that there must be a particular original aspect related to beauty that leads a human-made object to success, needs to be further identified. The approach to the concept of beauty is through a general philosophical perspective and partially through the areas mentioned above.The second part of the study includes the synthesised guidance provided by Monroe Beardsley through the theories on beauty from the nineteenth century until today. In addition, it comprises the scheme of concepts that characterised the beautiful in this time, including the lines that guided its study, previous ideas that support our later views on presented theory, and a brief exposition of Maslow's theory of human motivation followed by our theory on beauty and the conclusions.

scholarly journals Modern vision for critical flow in an egg-shaped section

2021 ◽  
Author(s):  
Hachemi Rachedi Lamia ◽  
Lakehal Moussa ◽  
Achour Bachir
Keyword(s):  
Froude Number ◽  
Critical Regime ◽  
Critical Flow ◽  
New Approach ◽  
Smooth Channel ◽  
Critical Flow Regime ◽  
Modern Vision ◽  
The One ◽  
Definition Of ◽  
Steep Slopes

Abstract The critical regime plays a primordial role in the study of gradually varying flows by classifying flow regimes and slopes. Through this work, a new approach is proposed to analyze critical flow regime in an egg-shaped channel. Based on both the definition of Froude number and Achour and Bedjaoui general discharge relationship, a relation between critical and normal depths is derived and then graphically represented for the particular case of a smooth channel characterized by a generating diameter equal to one meter. The results show the influence of the slope on the frequency of occurrence of the critical regime. At the same time and independently of the flow rate, a very advantageous approach for the calculation of the Froude number has been proposed. The study shows that there are six zones to differentiate the various flow states, namely: on the one hand for steep slopes two subcritical zones interspersed by a supercritical zone and on the other hand for mild slopes a zone corresponding to uniform flow, an area where the flow is probably gradually varied and finally an area where the flow is abruptly varied. Based on the specific energy equation, a validation process concluded that the proposed relationships were reliable.

scholarly journals Proposal of a composite indicator for measuring social media presence in the wine market

2020 ◽  
Author(s):  
Andrea Conchado Peiró ◽  
José Miguel Carot Sierra ◽  
Elena Vázquez Barrachina ◽  
Enrique Orduña Malea
Keyword(s):  
Social Media ◽  
Market Research ◽  
Initial Step ◽  
Composite Indicators ◽  
New Approach ◽  
Misleading Information ◽  
Social Media Networks ◽  
Wine Market ◽  
Definition Of ◽  
Research Analysis

Cybermetrics field is attracting considerable interest due to its utility as a data-oriented technique for research, though it may provide misleading information when used in complex systems. This paper outlines a new approach to market research analysis through the definition of composite indicators for cybermetrics, applied to the Spanish wine market. Our findings show that the majority of cellars were present in only one or two social media networks: Facebook, Twitter or both. Besides, the presence on the Web can be summarized into three principal components: website quality, presence on Facebook, and presence on Twitter. Three groups of cellars were identified according to their position in these components: cellars with a high number of errors in their website with complete absence of information in social media, cellars with strong presence in social media, and cellars in an intermediate position. Our results constitute an excellent initial step towards the definition of a methodology for building composite indicators in cybermetrics. From a practical approach, these indicators may encourage cellar managers to make better decisions towards their transition to the digital market.

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