scholarly journals A Possible Electro-Weak Model in SU(3) x U(1)

1979 ◽  
Author(s):  
Kwang -Chao Chou
Keyword(s):  
Weak Model

scholarly journals Convert a Strongly Connected Directed Graph to a Black-and-White 3-SAT Problem by the Balatonboglár Model

2020 ◽  
Author(s):  
Gábor Kusper ◽  
Csaba Biró
Keyword(s):  
Directed Graph ◽  
Directed Graphs ◽  
Deep Insight ◽  
Communication Graph ◽  
Sat Problem ◽  
Weak Model ◽  
Know How ◽  
Black And White ◽  
Communication Graphs ◽  
Strongly Connected

In a previous paper we defined the Black-and-White SAT problem which has exactly two solutions, where each variable is either true or false. We showed that Black-and-White $2$-SAT problems represent strongly connected directed graphs. We presented also the strong model of communication graphs. In this work we introduce two new models, the weak model, and the Balatonbogl\'{a}r model of communication graphs. A communication graph is a directed graph, where no self loops are allowed. In this work we show that the weak model of a strongly connected communication graph is a Black-and-White SAT problem. We prove a powerful theorem, the so called Transitions Theorem. This theorem states that for any model which is between the strong and the weak model, we have that this model represents strongly connected communication graphs as Blask-and-White SAT problems. We show that the Balatonbogl\'{a}r model is between the strong and the weak model, and it generates $3$-SAT problems, so the Balatonbogl\'{a}r model represents strongly connected communication graphs as Black-and-White $3$-SAT problems. Our motivation to study these models is the following: The strong model generates a $2$-SAT problem from the input directed graph, so it does not give us a deep insight how to convert a general SAT problem into a directed graph. The weak model generates huge models, because it represents all cycles, even non-simple cycles, of the input directed graph. We need something between them to gain more experience. From the Balatonbogl\'{a}r model we learned that it is enough to have a subset of a clause, which represents a cycle in the weak model, to make the Balatonbogl\'{a}r model more compact. We still do not know how to represent a SAT problem as a directed graph, but this work gives a strong link between two prominent fields of formal methods: SAT problem and directed graphs.

scholarly journals Periods and factors of weak model sets

2018 ◽  
Vol 229 (1) ◽  
pp. 85-132 ◽  
Author(s):  
Gerhard Keller ◽  
Christoph Richard
Keyword(s):  
Weak Model ◽  
Model Sets

An axiomatization of the logic with the rough quantifier

1991 ◽  
Vol 56 (2) ◽  
pp. 608-617 ◽  
Author(s):  
Michał Krynicki ◽  
Hans-Peter Tuschik
Keyword(s):  
Equivalence Relation ◽  
Equivalence Relations ◽  
Order Structure ◽  
Partition Model ◽  
Weak Model ◽  
First Order ◽  
Basic Properties ◽  
Generalized Quantifier ◽  
Order Language ◽  
The Right

We consider the language L(Q), where L is a countable first-order language and Q is an additional generalized quantifier. A weak model for L(Q) is a pair 〈, q〉 where is a first-order structure for L and q is a family of subsets of its universe. In case that q is the set of classes of some equivalence relation the weak model 〈, q〉 is called a partition model. The interpretation of Q in partition models was studied by Szczerba [3], who was inspired by Pawlak's paper [2]. The corresponding set of tautologies in L(Q) is called rough logic. In the following we will give a set of axioms of rough logic and prove its completeness. Rough logic is designed for creating partition models.The partition models are the weak models arising from equivalence relations. For the basic properties of the logic of weak models the reader is referred to Keisler's paper [1]. In a weak model 〈, q〉 the formulas of L(Q) are interpreted as usual with the additional clause for the quantifier Q: 〈, q〉 ⊨ Qx φ(x) iff there is some X ∊ q such that 〈, q〉 ⊨ φ(a) for all a ∊ X.In case X satisfies the right side of the above equivalence we say that X is contained in φ(x) or, equivalently, φ(x) contains X.

On H�ft's characterization of weak model classes

1995 ◽  
Vol 34 (2) ◽  
pp. 214-219
Author(s):  
P. Burmeister ◽  
F. Rossell� ◽  
L. Rudak
Keyword(s):  
Weak Model

ROUTING AND SORTING ON RECONFIGURABLE MESHES

1995 ◽  
Vol 05 (01) ◽  
pp. 81-95 ◽  
Author(s):  
MICHAEL KAUFMANN ◽  
HEIKO SCHRÖDER ◽  
JOP F. SIBEYN
Keyword(s):  
Linear Array ◽  
Alternative Scheme ◽  
Weak Model ◽  
Processor Arrays ◽  
Sorting Problems ◽  
Arbitrary Dimensions ◽  
Reconfigurable Meshes ◽  
Realistic Problem ◽  
Point To Point ◽  
Permutation Routing

We consider routing and sorting problems on mesh connected processor arrays under a very weak model of reconfiguration: we allow only uni-directional row or column buses, point-to-point communication, one-port-at-the-time serve by each processor. We present a scheme which is asymptoticly optimal for k-k sorting, for any arbitrary k > 0. It works optimally on meshes of arbitrary dimensions d, from the linear array to hypercubic networks with d < n1/3. The algorithm can also be used to perform k-k routing in the same time bound. We give an alternative scheme for permutation routing, which is asymptoticly slower, but has much better performance for realistic problem sizes.

A superstring inspired low-energy electro-weak model

1986 ◽  
Vol 175 (3) ◽  
pp. 304-308 ◽  
Author(s):  
Darwin Chang ◽  
Rabindra N. Mohapatra
Keyword(s):  
Low Energy ◽  
Weak Model
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