In this paper, the complexity of recognizing the critical configurations of the two-dimensional Abelian sandpile model is studied, some known facts are reviewed, and a simplified proof of the burning test is presented. Then, the existence of sublinear time algorithms solving the aforementioned problem is studied, with a lower bound for the monotone complexity of the problem established by emplo...

this paper, deals with some equivalence relations in fuzzy subgroups. further the probability of commuting two fuzzy subgroups of some finite abelian groups is defined.

We present a weak-coupling Yang–Mills model supporting non-Abelian magnetic flux tubes and non-Abelian confined magnetic monopoles. In the dual description the magnetic flux tubes are prototypes of the QCD strings. Dualizing the confined magnetic monopoles we get gluelumps which convert a “QCD string” in the excited state to that in the ground state. Introducing a mass parameter m we discover a...

Abelian pattern matching is a new class of pattern matching problems. In abelian patterns, the order of the characters in the substrings does not matter, e.g. the strings abbc and babc represent the same abelian pattern a+2b+c. Therefore, unlike classical pattern matching, we do not look for an exact (ordered) occurrence of a substring, rather the aim here is to find any permutation of a given ...

We discuss abelian variety and use it to generalize the concept of elliptic curve we discussed in the class. We state some of the basic properties of abelian variety and in particular 1-dimensional abelian variety. The main result of this report is to show that elliptic curve is that the only 1-dimensional abelian variety.

In one-component Abelian sandpile models, the toppling probabilities are independent quantities. This is not the case in multicomponent models. The condition of associativity of the underlying Abelian algebras imposes nonlinear relations among the toppling probabilities. These relations are derived for the case of two-component quadratic Abelian algebras. We show that Abelian sandpile models wi...

Given an א1-free abelian group G we characterize the class CG of all torsion abelian groups T satisfying Ext(G, T ) = 0 assuming the special continuum hypothesis CH. Moreover, in Gödel’s constructable universe we prove that this characterizes CG for arbitrary torsion-free abelian G. It follows that there exist some ugly א1-free abelian groups.

The theory of protomodular categories provides a simple and general context in which the basic theorems needed in homological algebra of groups, rings, Lie algebras and other non-abelian structures can be proved [2] [3] [4] [5] [6] [7] [9] [20]. An interesting aspect of the theory comes from the fact that there is a natural intrinsic notion of normal monomorphism [4]. Since any internal reflexi...

We used a renormalisation group based smoothing to address two questions related to Abelian dominance. Smoothing enabled us to extract the Abelian heavy-quark potential from time-like Wilson loops on Polyakov gauge projected configurations. We obtained a very small string tension which is inconsistent with the string tension extracted from Polyakov loop correlators. This shows that the Polyakov...

We used a renormalisation group based smoothing to address two questions related to Abelian dominance. Smoothing enabled us to extract the Abelian heavy-quark potential from time-like Wilson loops on Polyakov gauge projected configurations. We obtained a very small string tension which is inconsistent with the string tension extracted from Polyakov loop correlators. This shows that the Polyakov...