scholarly journals A New Abstract Domain for the Representation of Mathematically Equivalent Expressions

Author(s):  
Arnault Ioualalen ◽  
Matthieu Martel
1961 ◽  
Vol 3 (4) ◽  
pp. 443-451
Author(s):  
André Bareau

The Tibetan term which is pronounced jisa and written spyi signifies literally terra commune or, like spyi, the principal or capital piece of land. The fact it is not to be found in the classical dictionaries of the Tibetan language, such as those of Sarat Chandra Das and Jäschke, seems to show that it is fairly recent. In these works the terms closest to it are spyi-tor and, better still, spyi-thog, which refer to a common fund or a common piece of property. These terms, too, appear to be relatively recent or at least exclusively Tibetan, for the dictionaries give no Sanskrit equivalent and they suggest that the terms belong solely to the dialects of Western Tibet. The Sanskrit terms corresponding to spyi would be sāmanyabhūmi and sādharanabhūmi in the first and most satisfactory sense, of common land, and agrabhūmi, murdhabhūmi and sirobhūmi in the second sense. But these do not occur in the dictionaries of classic Sanskrit, nor of Buddhist Sanskrit (Edgerton), nor of Pali. Nor were any equivalent expressions either developed in Chinese Buddhism or preserved through Chinese translations of Sanskrit terms. If any Indian or Chinese terms corresponding to the Tibetan spyi-sa existed, they obviously formed no part of the canonical or even of the paracanonical literary language of Indian or ancient Chinese Buddhism. It follows that if Indian or Chinese Buddhism had an institution resembling the Tibetan jisa, the Buddhist monks must have considered it to be foreign to their activities and in some way unworthy.


Author(s):  
Kaiyuan Wang ◽  
Allison Sullivan ◽  
Manos Koukoutos ◽  
Darko Marinov ◽  
Sarfraz Khurshid

1973 ◽  
Vol 28 (3-4) ◽  
pp. 332-342
Author(s):  
Heinz Günter Becker

AbstractThe structure of the Bogoljubov -Valatin transformation and the HFB state is investigated by group-theoretical methods. A direct proof of the Bloch-Messiah factorization theorem shows that the second factor which contains the BCS part of the BV transformation can be chosen always real. An unitary representation of the Bogoljubov-Valatin group in the Fock space is constructed which allows to write down various equivalent expressions for the HFB state vector. The relation between the "unitary form" and the usual form of | HFB〉 is clarified using the "quasispin" concept in connection with a theorem about the factorization of the D(3) Lie group.


1992 ◽  
Vol 114 (3) ◽  
pp. 606-611 ◽  
Author(s):  
M. T. Hanson

This paper gives closed-form expressions in terms of elementary functions for the title problem of spherical Hertzian contact of elastic bodies possessing transverse isotropy. Traction in the contact region is also included in the form of Coulomb friction; thus the shear stress is proportional to the contact pressure. The present expressions derived here by integration of the point force Green’s functions are simpler and easier to apply than equivalent expressions which have previously been given.


1992 ◽  
Vol 15 (1) ◽  
pp. 103-106 ◽  
Author(s):  
A. Seth

In this paper aΓ-group congruence on a regularΓ-semigroup is defined, some equivalent expressions for anyΓ-group congruence on a regularΓ-semigroup and those for the leastΓ-group congruence in particular are given.


Author(s):  
Klaus-Uwe Panther ◽  
Linda L. Thornburg

In this article we investigate correlations between semantically equivalent expressions (organized in manner scales according to the formal properties of length, prosodic prominence, and grammaticalization) and their varying potential to trigger a certain metonymic interpretation. We focus on manner scales of past ability as well as semantically and logically similar expressions relating to human character traits/dispositions and external circumstances. Using the concepts of strength of metonymic link and coercion, we show that shorter, prosodically weaker and more grammaticalized members in these manner scales more strongly trigger the potentiality for actuality metonymy than their longer, prosodically stronger, and less grammaticalized counterparts.


2015 ◽  
Vol 23 (1) ◽  
pp. 67-73
Author(s):  
Kazuhisa Nakasho ◽  
Hiroyuki Okazaki ◽  
Hiroshi Yamazaki ◽  
Yasunari Shidama

Summary In this article, the equivalent expressions of the direct sum decomposition of groups are mainly discussed. In the first section, we formalize the fact that the internal direct sum decomposition can be defined as normal subgroups and some of their properties. In the second section, we formalize an equivalent form of internal direct sum of commutative groups. In the last section, we formalize that the external direct sum leads an internal direct sum. We referred to [19], [18] [8] and [14] in the formalization.


Author(s):  
Alex Friedlander

In this paper, I attempt to present several examples of tasks and some relevant findings that investigate the possibility of basing a part of the practice-oriented tasks on higher-level thinking skills, that are usually associated with processes of problem solving. The tasks presented and analysed here integrate problem solving-components – namely, reversed thinking, expressing and analysing patterns, and employing multiple solution methods, into the learning and practicing of algebraic procedures – such as creating equivalent expressions and solving equations.


Sign in / Sign up

Export Citation Format

Share Document