On Saint Venant’s Principle: Elastic Shells and Plates

1960 ◽  
Vol 27 (3) ◽  
pp. 417-422 ◽  
Author(s):  
P. M. Naghdi
Keyword(s):  
Fixed Point ◽  
Integral Formula ◽  
Middle Surface ◽  
The Other ◽  
Elastic Shells ◽  
Partial Derivatives ◽  
Other Hand ◽  
Derivatives Of ◽  
Surface Loads

This investigation is concerned with an examination of the validity of Saint Venant’s principle in the theory of thin elastic shells and plates. With the aid of an integral formula derived for the displacements and their relevant partial derivatives of all orders at a fixed point of the shell middle surface, the conclusions reached may be roughly stated as follows: If the loads acting on the shell maintained in equilibrium are purely edge loads, then the orders of magnitude of the displacements and stresses are in accord with the traditional statement of Saint Venant’s principle. On the other hand, if the loads on the shell are purely surface loads, then the conclusions concerning the orders of magnitude of the displacements and stresses are the same as those of the modified Saint Venant principle.

scholarly journals Well-definedness and observational equivalence for inductive–coinductive programs

2019 ◽  
Vol 29 (4) ◽  
pp. 419-468
Author(s):  
Henning Basold ◽  
Helle Hvid Hansen
Keyword(s):  
Fixed Point ◽  
Modal Logic ◽  
The Other ◽  
Observational Equivalence ◽  
Other Hand ◽  
Inductive Types ◽  
Point Types ◽  
Usual Topology

Abstract We define notions of well-definedness and observational equivalence for programs of mixed inductive and coinductive types. These notions are defined by means of tests formulas which combine structural congruence for inductive types and modal logic for coinductive types. Tests also correspond to certain evaluation contexts. We define a program to be well-defined if it is strongly normalizing under all tests, and two programs are observationally equivalent if they satisfy the same tests. We show that observational equivalence is sufficiently coarse to ensure that least and greatest fixed point types are initial algebras and final coalgebras, respectively. This yields inductive and coinductive proof principles for reasoning about program behaviour. On the other hand, we argue that observational equivalence does not identify too many terms, by showing that tests induce a topology that, on streams, coincides with usual topology induced by the prefix metric. As one would expect, observational equivalence is, in general, undecidable, but in order to develop some practically useful heuristics we provide coinductive techniques for establishing observational normalization and observational equivalence, along with up-to techniques for enhancing these methods.

scholarly journals II. Compounds isomeric with the sulphocyanic ethers.—I. On the mustard oil of the ethyl series

1868 ◽  
Vol 16 ◽  
pp. 254-258
Keyword(s):  
Royal Society ◽  
The Other ◽  
Mustard Oil ◽  
Other Hand ◽  
Derivatives Of

The results of my researches on the chloroform-derivatives of the primary monamines, which, as I have shown, are isomeric with the nitriles, could not fail to direct my attention to allied groups of bodies, with the view of discovering similar isomerisms. In a note communicated to the Royal Society some months ago, I expressed the expectations which even then appeared to be justified in the following manner:—“In conclusion, I may be permitted to announce as everv probable the existence of a series of bodies isomeric with the sulphocyanides. Already M. Cloëz has shown that the action of chloride of cyanogen on ethylate of potassium gives rise to the formation of an ethylic cyanate possessing properties absolutely different from those belonging to the cyanate discovered by M. Wurtz. On comparing, on the other hand the properties of the methylic and ethylic sulphocyamdes with those of the sulphocyanides of allyl and phenyl, it can scarcely be doubted that we have here the representatives of two groups entirely different, and that the terms of the methyl- and ethyl-series which correspond to oil of mustard, and to the sulphocyanide of phenyl, still remain to be discovered. Experiments with which I am now engaged will show whether these bodies cannot be obtained by the action of the iodides of methyl and ethyl on sulphocyanide of silver."

Application of Maple on Solving the Differential Problem of Rational Functions

2013 ◽  
Vol 479-480 ◽  
pp. 855-860
Author(s):  
Chii Huei Yu
Keyword(s):  
Problem Solving ◽  
Research Methods ◽  
Research Method ◽  
Rational Functions ◽  
The Other ◽  
Mathematical Software ◽  
Differential Problem ◽  
Binomial Theorem ◽  
Other Hand ◽  
Derivatives Of

This paper uses the mathematical software Maple as the auxiliary tool to study the differential problem of four types of rational functions. We can obtain the closed forms of any order derivatives of these rational functions by using binomial theorem. On the other hand, we propose four examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. For this reason, Maple provides insights and guidance regarding problem-solving methods.

Arylhydrazonothiazolidinones: Ring Cleavage and Alkylation of the 5-Arylhydrazono Derivatives of Rhodanine and Isorhodanine

1979 ◽  
Vol 34 (3) ◽  
pp. 507-510 ◽  
Author(s):  
Nazmi A. Kassab ◽  
Sanaa O. Abd Allah ◽  
Said A. Elbahaii
Keyword(s):  
Hydrazine Hydrate ◽  
The Other ◽  
Ring Cleavage ◽  
Ethyl Bromoacetate ◽  
Other Hand ◽  
Alkyl Derivatives ◽  
Derivatives Of

Abstract The 5-arylhydrazono derivatives of rhodanine and isorhodanine were subjected to the action of hydrazine hydrate to afford the arylhydrazonomercaptomethyl-triazolinones (3) and -triazolinthiones (3) respectively. Treatment of 1 with benzylamine afforded thioxalic acid dibenzylamide (5). On the other hand treatment of 2 with the same reagent afforded the corresponding benzylimino derivatives (6).Alkylation of 1 and 2 with ethyl bromoacetate and chloroacetamide yielded the corresponding S-alkyl derivatives (7) and (8), respectively.

Using Maple to Study the Partial Differential Problems

2013 ◽  
Vol 479-480 ◽  
pp. 800-804 ◽  
Author(s):  
Chii Huei Yu
Keyword(s):  
Infinite Series ◽  
Partial Derivative ◽  
Higher Order ◽  
The Other ◽  
Mathematical Software ◽  
Partial Differential ◽  
Differential Problem ◽  
Partial Derivatives ◽  
Order Partial Derivative ◽  
Derivatives Of

This paper uses the mathematical software Maple for the auxiliary tool to study the partial differential problem of two types of multivariable functions. We can obtain the infinite series forms of any order partial derivatives of these two types of multivariable functions by using differentiation term by term theorem, and hence greatly reduce the difficulty of calculating their higher order partial derivative values. On the other hand, we propose two examples of multivariable functions to evaluate their any order partial derivatives, and some of their higher order partial derivative values practically. At the same time, we employ Maple to calculate the approximations of these higher order partial derivative values and their infinite series forms for verifying our answers.

Polyhedral boron derivatives of porphyrins and phthalocyanines

2001 ◽  
Vol 05 (11) ◽  
pp. 767-781 ◽  
Author(s):  
VLADIMIR I. BREGADZE ◽  
IGOR B. SIVAEV ◽  
DETLEF GABEL ◽  
DIETER WÖHRLE
Keyword(s):  
Neutron Capture ◽  
Tumor Therapy ◽  
The Other ◽  
Medical Applications ◽  
Neutron Capture Therapy ◽  
Current Interest ◽  
Boron Compounds ◽  
Other Hand ◽  
The One ◽  
Derivatives Of

The synthesis of compounds containing polyhedral boron cages and porphyrin or phthalocyanine units connected covalently in one molecule is reviewed. The importance of these compounds arises, on the one hand, from the use of polyhedral boron derivatives in neutron capture therapy for cancer; on the other hand, porphyrins and phthalocyanines are known as photosensitizers in photodynamic tumor therapy. Current interest in the binding of polyhedral boron compounds to porphyrins and phthalocyanines is due to the observation that porphyrins and phthalocyanines show improved uptake and good persistence in tissues. Medical applications of compounds containing polyhedral boron cages and porphyrin or phthalocyanine units in one molecule are briefly discussed.

scholarly journals Charge transfer control by substituents: Donor pyrroles and fluoro-anilines

2005 ◽  
Vol 7 (3) ◽  
pp. 121-124 ◽  
Author(s):  
Antje Neubauer ◽  
Sukumaran Murali ◽  
Wolfgang Rettig
Keyword(s):  
Charge Transfer ◽  
Benzene Ring ◽  
The Other ◽  
Substituted Benzenes ◽  
Other Hand ◽  
Alkane Solvents ◽  
New Compounds ◽  
Derivatives Of ◽  
Acceptor Moiety ◽  
Donor Substituent

Derivatives of N-phenyl pyrrole with a para-donor substituent on the acceptor benzene ring are compared. It is shown that by a suitable increase of the donor strength of the pyrrolo group, CT fluorescence can be achieved even for donor-donor substituted benzenes. On the other hand, introducing fluoro substituents into the acceptor moiety strongly enhances the CT formation tendency, and several new compounds with CT fluorescence even in alkane solvents are presented.

scholarly journals Theory of the Icon of Christos Yannaras

2021 ◽  
Vol 4 ◽  
pp. 64-69
Author(s):  
Tina Mosiakina
Keyword(s):  
The Other ◽  
Surrounding World ◽  
Other Hand ◽  
The Aesthetic ◽  
Theological Thought ◽  
Derivatives Of ◽  
The Erotic

The article regards the phenomenon of the icon in the interpretation of Greek theologian and philosopher Christos Yannaras. His work Personality and Eros is taken as a basis, where the author describes this phenomenon, based on a thorough body of works of Orthodox thought.The icon is primarily considered not only as a model of reality, reflection or image of events and objects, or allegory-allegory; attention is focused on the icon as a category of cognition. The study traces the conditions of functioning of the iconological language, as well as its connection with apophatic and cataphatic theological thought. The specifics of the poetics of the iconological language are also revealed, aiming at both concealment and elucidation of the truth.An attempt is also made to transfer the theory of the icon to the anthropological plane, in accordance with the erotic gesture of self-denial. The focus is on the aesthetic component of the iconic perception not only of icons but also of other phenomena of art or the surrounding world. Thus, owing to the derivatives of the theory of the icon, the analysis of art in the anthropological plane is carried out.Possible types of reduction of the iconological language according to the function of the icon as a means of cognition are also revealed. In this regard, the significance of the so-called ‘theology of assimilation’ and its possible connection with the moralistic reduction in the interpretation of Ch. Yannaras are analyzed. On the other hand, aesthetic reduction is also described, which, in turn, has the ability to provoke iconoclastic resistance.Thus, the aim of the work is to study the phenomenon of the icon as a category of knowledge in the works of Ch. Yannaras, as well as to consider the icon and the iconological language in their connection with issues of the aesthetic and anthropological nature.

scholarly journals Consolidation via Tacit Culpability Measures: Between Explicit and Implicit Degrees of Culpability

2021 ◽  
Author(s):  
Jandson S. Ribeiro ◽  
Matthias Thimm
Keyword(s):  
Fixed Point ◽  
Knowledge Base ◽  
Special Class ◽  
Belief Change ◽  
Minimal Change ◽  
The Other ◽  
Preference Relations ◽  
Other Hand ◽  
The One ◽  
Rationality Postulates

Restoring consistency of a knowledge base, known as consolidation, should preserve as much information as possible of the original knowledge base. On the one hand, the field of belief change captures this principle of minimal change via rationality postulates. On the other hand, within the field of inconsistency measurement, culpability measures have been developed to assess how much a formula participates in making a knowledge base inconsistent. We look at culpability measures as a tool to disclose epistemic preference relations and build rational consolidation functions. We introduce tacit culpability measures that consider semantic counterparts between conflicting formulae, and we define a special class of these culpability measures based on a fixed-point characterisation: the stable tacit culpability measures. We show that the stable tacit culpability measures yield rational consolidation functions and that these are also the only culpability measures that yield rational consolidation functions.

scholarly journals Bottom-Up derivatives of tree expressions

2021 ◽  
Vol 55 ◽  
pp. 4
Author(s):  
Samira Attou ◽  
Ludovic Mignot ◽  
Djelloul Ziadi
Keyword(s):  
Fixed Point ◽  
Tree Automaton ◽  
Bottom Up ◽  
Regular Tree ◽  
Partial Derivatives ◽  
New Family ◽  
Derivatives Of

In this paper, we extend the notion of (word) derivatives and partial derivatives due to (respectively) Brzozowski and Antimirov to tree derivatives using already known inductive formulae of quotients. We define a new family of extended regular tree expressions (using negation or intersection operators), and we show how to compute a Brzozowski-like inductive tree automaton; the fixed point of this construction, when it exists, is the derivative tree automaton. Such a deterministic tree automaton can be used to solve the membership test efficiently: the whole structure is not necessarily computed, and the derivative computations can be performed in parallel. We also show how to solve the membership test using our (Bottom-Up) partial derivatives, without computing an automaton.

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