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21.
Abstract We performed numerical simulations to demonstrate localization phenomena of Bose–Fermi mixture systems on incommensurate optical lattices by changing Bose–Bose and Bose–Fermi interactions. Visibility patterns of the bosons were measured to observe bosonic coherence in various selections of the interaction parameters. We found that the coherence was enhanced with repulsive Bose–Fermi interactions. It was also enhanced with attractive Bose–Fermi interactions but only in certain conditions. The enhancement by repulsive interactions and that by attractive interactions occurred with different mechanisms. 相似文献
22.
K. Vijay Reddy 《Philosophical Magazine Letters》2013,93(7):253-260
Stacking fault tetrahedra (SFTs) are known to form during the rolling process of face-centered cubic metals and to deteriorate their structural properties. However, the atomistic mechanism of formation and destruction of SFTs during such material processing is still unclear. We have performed molecular dynamics simulations of the nanoscale cryo-rolling process for single-crystal nickel and here report the mechanism behind the formation and collapse of SFTs. It is found that SFTs are formed through dissociation of Shockley partial dislocation loops in the specimen. On the other hand, destruction of SFTs occurs under compressive stress and follows an inverse Silcox-Hirsch mechanism. 相似文献
23.
The goal of this two-part series of papers is to show that constructive logic with strong negation N is definitionally equivalent to a certain axiomatic extension NFL
ew
of the substructural logic FL
ew
. In this paper, it is shown that the equivalent variety semantics of N (namely, the variety of Nelson algebras) and the equivalent variety semantics of NFL
ew
(namely, a certain variety of FL
ew
-algebras) are term equivalent. This answers a longstanding question of Nelson [30]. Extensive use is made of the automated
theorem-prover Prover9 in order to establish the result.
The main result of this paper is exploited in Part II of this series [40] to show that the deductive systems N and NFL
ew
are definitionally equivalent, and hence that constructive logic with strong negation is a substructural logic over FL
ew
.
Presented by Heinrich Wansing 相似文献
24.
Elia Zardini 《Studia Logica》2008,90(3):337-368
According to the naive theory of vagueness, the vagueness of an expression consists in the existence of both positive and
negative cases of application of the expression and in the non-existence of a sharp cut-off point between them. The sorites
paradox shows the naive theory to be inconsistent in most logics proposed for a vague language. The paper explores the prospects
of saving the naive theory by revising the logic in a novel way, placing principled restrictions on the transitivity of the
consequence relation. A lattice-theoretical framework for a whole family of (zeroth-order) “tolerant logics” is proposed and
developed. Particular care is devoted to the relation between the salient features of the formal apparatus and the informal
logical and semantic notions they are supposed to model. A suitable non-transitive counterpart to classical logic is defined.
Some of its properties are studied, and it is eventually shown how an appropriate regimentation of the naive theory of vagueness
is consistent in such a logic. 相似文献
25.
Algebraic Aspects of Cut Elimination 总被引:2,自引:2,他引:0
We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with cut, by using the quasi-completion of these Gentzen structures. It is shown that the quasi-completion is a generalization of the MacNeille completion. Moreover, the finite model property is obtained for many cases, by modifying our completeness proof. This is an algebraic presentation of the proof of the finite model property discussed by Lafont [12] and Okada-Terui [17]. 相似文献
26.
Sergei P. Odintsov 《Studia Logica》2005,80(2-3):291-320
The article is devoted to the systematic study of the lattice εN4⊥ consisting of logics extending N4⊥. The logic N4⊥ is obtained from paraconsistent Nelson logic N4 by adding the new constant ⊥ and axioms ⊥ → p, p → ∼ ⊥. We study interrelations between εN4⊥ and the lattice of superintuitionistic logics. Distinguish in εN4⊥ basic subclasses of explosive logics, normal logics, logics of general form and study how they are relate.
The author acknowledges support by the Alexander von Humboldt-Stiftung and by Counsil for Grants under RF President, project
NSh - 2112.2003.1. 相似文献
27.
Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss
the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and
establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain
interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices.
Dedicated to the memory of Willem Johannes Blok 相似文献
28.
Minimal Varieties of Involutive Residuated Lattices 总被引:1,自引:0,他引:1
We establish the existence uncountably many atoms in the subvariety lattice of the variety of involutive residuated lattices.
The proof utilizes a construction used in the proof of the corresponding result for residuated lattices and is based on the
fact that every residuated lattice with greatest element can be associated in a canonical way with an involutive residuated
lattice.
Dedicated to the memory of Willem Johannes Blok 相似文献
29.
The equivalence connective in ukasiewicz logic has its algebraic counterpart which is the distance function d(x,y) =|x–y| of a positive cone of a commutative -group. We make some observations on logically motivated algebraic structures involving the distance function. 相似文献
30.
The least element 0 of a finite meet semi-distributive lattice is a meet of meet-prime elements. We investigate conditions
under which the least element of an algebraic, meet semi-distributive lattice is a (complete) meet of meet-prime elements.
For example, this is true if the lattice has only countably many compact elements, or if |L| < 2ℵ0, or if L is in the variety generated by a finite meet semi-distributive lattice. We give an example of an algebraic, meet semi-distributive
lattice that has no meet-prime element or join-prime element. This lattice L has |L| = |LC| = 2ℵ0 where Lc is the set of compact elements of L.
Dedicated to the memory of Willem Johannes Blok
AMS subject classification: 06B05
While working on this paper, the first author was supported by the INTAS grant no. 03-51-4110, the second author was partially
supported by the Hungarian National Foundation for Scientific Research (OTKA) grant no. T37877, and the third author was supported
by the US National Science Foundation grant no. DMS0245622. 相似文献