On derivatives of fuzzy multi-dimensional mappings and applications under generalized differentiability

2021 ◽  
pp. 1-19
Author(s):  
M. Miri Karbasaki ◽  
M. R. Balooch Shahriari ◽  
O. Sedaghatfar
Keyword(s):  
Linear Function ◽  
Level Set ◽  
Fuzzy Numbers ◽  
Sufficient Condition ◽  
Continuous Linear ◽  
Generalized Differentiability ◽  
Relationship Of ◽  
The Relationship ◽  
Derivatives Of ◽  
Dimensional Mapping

This article identifies and presents the generalized difference (g-difference) of fuzzy numbers, Fréchet and Gâteaux generalized differentiability (g-differentiability) for fuzzy multi-dimensional mapping which consists of a new concept, fuzzy g-(continuous linear) function; Moreover, the relationship between Fréchet and Gâteaux g-differentiability is studied and shown. The concepts of directional and partial g-differentiability are further framed and the relationship of which will the aforementioned concepts are also explored. Furthermore, characterization is pointed out for Fréchet and Gâteaux g-differentiability; based on level-set and through differentiability of endpoints real-valued functions a characterization is also offered and explored for directional and partial g-differentiability. The sufficient condition for Fréchet and Gâteaux g-differentiability, directional and partial g-differentiability based on level-set and through employing level-wise gH-differentiability (LgH-differentiability) is expressed. Finally, to illustrate the ability and reliability of the aforementioned concepts we have solved some application examples.

scholarly journals EXACT NONNULL WAVELIKE SOLUTIONS TO GRAVITY WITH QUADRATIC LAGRANGIANS

1994 ◽  
Vol 09 (02) ◽  
pp. 167-179 ◽  
Author(s):  
M.D. ROBERTS
Keyword(s):  
Gravitational Radiation ◽  
Riemann Tensor ◽  
Gravitational Energy ◽  
Cross Terms ◽  
Linearized Theory ◽  
Relationship Of ◽  
The Relationship ◽  
Poynting Vectors ◽  
Derivatives Of

Solutions to gravity with quadratic Lagrangians are found for the simple case where the only nonconstant metric component is the lapse N and the Riemann tensor takes the form [Formula: see text] thus these solutions depend on cross terms in the Riemann tensor and therefore complement linearized theory where it is the derivatives of the Riemann tensor that matter. The relationship of this metric to the null gravitational radiation metric of Peres is given. Gravitational energy Poynting vectors are constructed for the solutions and one of these, based on the Lanczos tensor, supports the indication in the linearized theory that nonnull gravitational radiation can occur.

XIV.—Forerunners, Congeners, and Derivatives of the Eustace Legend

PMLA ◽  
1904 ◽  
Vol 19 (3) ◽  
pp. 335-448 ◽  
Author(s):  
Gordon Hall Gerould
Keyword(s):  
Comparative Literature ◽  
And Control ◽  
Relationship Of ◽  
The Relationship ◽  
Derivatives Of

In any study which involves the consideration of a network of stories, it is chiefly necessary to regard the skeleton upon which the tales in question are built up. Although it is impossible to decide upon the relationship of the various members of a cycle without some consideration of individual incidents and even turns of thought or phrase, it is constantly necessary to check and control the information thus gained by the larger matters of motive and purpose. Individual incidents and all the flesh and blood of a narrative are so easily changed that the skeleton appears stable in comparison. With due regard to the kaleidoscopic changes which are familiar to every student of this field of comparative literature, it furnishes the clue by which the labyrinth of plots must be threaded, if at all.

Movement and Deformation Rules of Gauss Coordinates Based on Ellipsoid Expanded Modal

2011 ◽  
Vol 368-373 ◽  
pp. 2211-2215
Author(s):  
Li Xin Jin ◽  
Lian Jun Wang ◽  
Song Lin Yang
Keyword(s):  
Theoretical Foundation ◽  
Geodetic Coordinates ◽  
Geodetic Height ◽  
Longitudinal Coordinate ◽  
Movement And Deformation ◽  
Major Radius ◽  
Straight Lines ◽  
Relationship Of ◽  
The Relationship ◽  
Derivatives Of

This paper studies on deducing the analytic formulae on Gauss coordinates displacement before or after the increase of major radius of ellipsoid expanded modals, which is based on the partial derivatives of geodetic coordinates in Gauss coordinates deducing from direct solution formulae of the Gauss projection coordinates in conjunction with differential coefficient formulae and variable of geodetic coordinates. On this theoretical foundation, analyzing the relationships between Gauss coordinates displacement and other mathematical parameter . The relationship of graphics between point displacement components of latitudinal coordinate dy and longitudes is similar to the straight lines. The relationship of graphics between point displacement components of longitudinal coordinate dx and latitudinal coordinate dy, and the geodetic height is similar to the straight lines.

Discotische Flüssigkristalle: Beziehung zwischen Molekülstruktur und discogenen Eigenschaften scheibenförmiger Verbindungen, nicht-flüssigkristalline Ester des myo-Inosits und des Mytilits [1,2]

1985 ◽  
Vol 40 (7) ◽  
pp. 981-986 ◽  
Author(s):  
Bernd Kohne ◽  
Klaus Praefcke ◽  
Werner Stephan ◽  
Peter Nürnberg
Keyword(s):  
Chemical Structure ◽  
Liquid Crystalline ◽  
Methyl Group ◽  
Molecular Core ◽  
Relationship Of ◽  
The Relationship ◽  
Derivatives Of

Abstract A modified synthesis of mytilitol and the synthesis of various esters of the cyclitols myo-inositol (la) and mytilitol (2a) is described. Because of steric reasons all these derivatives of the two naturally occuring compounds exhibit no discotic mesophases. For instance, in comparison to mesomorphous scyllitol hexaesters already the methyl group perpendicular to the molecular core in the analogous hexaesters 2b-d of mytilitol suppresses discotic liquid crystalline character totally. This effect is discussed in connection to the relationship of mesomorphism with chemical structure of disc-shaped molecules.

Displace Regulation of Gauss Coordinates Based on Ellipsoid Expanded Modal

2011 ◽  
Vol 105-107 ◽  
pp. 1333-1337
Author(s):  
Li Xin Jin ◽  
Lian Jun Wang ◽  
Song Lin Yang
Keyword(s):  
Theoretical Foundation ◽  
Geodetic Coordinates ◽  
Differential Coefficient ◽  
Geodetic Height ◽  
Longitudinal Coordinate ◽  
Major Radius ◽  
Straight Lines ◽  
Relationship Of ◽  
The Relationship ◽  
Derivatives Of

This paper studies on deducing the analytic formulae on Gauss coordinates displacement before or after the increase of major radius of ellipsoid expanded modals, which is based on the partial derivatives of geodetic coordinates in Gauss coordinates deducing from direct solution formulae of the Gauss projection coordinates in conjunction with differential coefficient formulae and variable of geodetic coordinates. On this theoretical foundation, analyzing the relationships between Gauss coordinates displacement and other mathematical parameter . The relationship of graphics between point displacement components of latitudinal coordinate dy and longitudes is similar to the straight lines. The relationship of graphics between point displacement components of longitudinal coordinate dx and latitudinal coordinate dy, and the geodetic height is similar to the straight lines.

Investigation of the Relationship of Muscle Mechanical Characteristics with Biosignal Energy

2006 ◽  
Vol 113 ◽  
pp. 151-156
Author(s):  
Mečislovas Mariūnas ◽  
Kristina Kojelyte
Keyword(s):  
Mechanical Characteristics ◽  
Extreme Points ◽  
Shift Function ◽  
Energy Equality ◽  
Second Derivatives ◽  
Digital Methods ◽  
Relationship Of ◽  
The Relationship ◽  
Analytical Expressions ◽  
Derivatives Of

Based on biosignal energy equality to the work performed by a muscle, in the estimation of energy dissipation within a biolotronic system, analytical expressions have been derived that have helped to calculate major mechanical characteristics of the muscle including elongation of the muscle, speed and acceleration of such elongation. The paper presents the analysis of relevant digital methods alongside with the formulae for the calculation of major mechanical characteristics when the relationship of a muscle biosignal that is presented in a graphical way. As shown, fatigue of the muscle is characterized by one of extreme points of the phase shift function. The values of the first and the second derivatives of the elongation function may be used for the evaluation of functional capacity of the muscle.

scholarly journals Biologically active derivatives of fullerene C60. Current state and development prospects

2020 ◽  
Vol 99 (3) ◽  
pp. 11-20
Author(s):  
S.D. Fazylov ◽  
◽  
О.А. Nurkenov ◽  
Z.M. Muldakhmetov ◽  
A.M. Gazaliev ◽  
...  
Keyword(s):  
Water Solubility ◽  
Biological Properties ◽  
Fullerene C60 ◽  
Biologically Active ◽  
Current State ◽  
Amino Derivatives ◽  
Relationship Of ◽  
The Relationship ◽  
Active Effects ◽  
Derivatives Of

The article presents literature review on the physicochemical and biological properties of fullerene C60, as well as the authors' own experimental data on the synthesis of fullerene derivatives of amines and natural alkaloids. It is shown that the presence of a fullerene fragment in the structure of the compound provides a significant improvement or the appearance of qualitatively new mechanical, chemical, physical, biological and other properties associated with the manifestation of nanoscale factors. The issues of the relationship of the structure, water solubility and biological activity of fullerene С60 derivatives are considered. Many biologically active effects of various modified derivatives of fullerene C60 are described, which have membrane-active, antibacterial, antiviral, immunomodulating, HIV inhibitory enzymes and other properties. It was noted that preparations containing a fullerene fragment are effective against hepatitis C virus, and are also able to efficiently trap free radicals. Derivatives of fullerenes can also be used as antioxidant, neuroprotective and other agents. Particular attention is paid to the authors' own results on the synthesis of amino derivatives of fullerenes.

scholarly journals Chapman-Kolmogorov Equations for a Complete Set of Distinct Reliability States of an Object

2018 ◽  
Vol 9 (4) ◽  
pp. 49-70
Author(s):  
Paweł SZCZEPAŃSKI ◽  
Józef ŻUREK
Keyword(s):  
Graph Theory ◽  
Research Work ◽  
Technical Diagnostics ◽  
Transition Rates ◽  
Kolmogorov Equations ◽  
Reliability Characteristics ◽  
Complete Set ◽  
Relationship Of ◽  
The Relationship ◽  
Derivatives Of

The Chapman-Kolmogorov equations indicated in the title are a pretext to demonstrate a mathematically unrecognised truth about the effect of the reliability states of elements (which are generally understood as “subjects”) on the reliability states of a complete set of the same elements, which is called an object. Of importance here are not just the reliability characteristics of individual elements, but the independencies, dependencies and interdependencies between the elements. The relations were described in the language of graph theory. The availability matrix of the language of graph theory was translated to determine the size and probabilities of distinct reliability states of the object, the derivatives of their similarities, and the transition rates adequate to those derivatives. This article continues the research work which identifies the relationship of the properties of a complete set of distinct reliability states of an object with a widely understood theory of systems. The previous papers referred, among others, to: risk, safety, structure entropy, the reliability of the results of checks, and – most of all – technical diagnostics, both in the area of its algorithms and of its optimisation. The object’s serial reliability structure was not assumed in any of those papers, recognising that it would be a serious abuse. The research results were referred to all possible structures of a three-element object. It is believed that by virtue of the block diagrams appropriate to those structures, the readers hereof are provided with a realistic opportunity to practically (and inexpensively) verify the ideas presented here.

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