Using Schr\"{o}dinger's formalism, we investigate the quantum eigenstates of heavy mesons trapped by a point-like defect and Cornell's potential. One implements this to model considering spherical metric profile coupled it. Furthermore, Nikiforov-Uvarov method is applied theory study mesons. To calculate information entropy (QIE), one considers wave functions that describe charmonium bottomoniu...

We prove several results about three families of graphs. For queen graphs, defined from the usual moves of a chess queen, we find the edge-chromatic number in almost all cases. In the unproved case, we have a conjecture supported by a vast amount of computation, which involved the development of a new edge-coloring algorithm. The conjecture is that the edge-chromatic number is the maximum degre...

We show a property of strings is expressible in the two-variable fragment of rst-order logic if and only if it is expressible by both a 2 and a 2 sentence. We thereby establish: where UTL stands for the string properties expressible in the temporal logic withèventually in the future' andèventually in the past' as the only temporal operators and UL stands for the class of unambiguous languages. ...

This paper is a continuation of [8]. Let A and B be two first order structures of the same vocabulary L. We denote the domains of A and B by A and B respectively. All vocabularies are assumed to be relational. The Ehrenfeucht-Fräıssé-game of length γ of A and B denoted by EFGγ(A,B) is defined as follows: There are two players called ∀ and ∃. First ∀ plays x0 and then ∃ plays y0. After this ∀ pl...

This paper is a continuation of [8]. Let A and B be two first order structures of the same vocabulary L. We denote the domains of A and B by A and B respectively. All vocabularies are assumed to be relational. The Ehrenfeucht-Fräıssé-game of length γ of A and B denoted by EFGγ(A,B) is defined as follows: There are two players called ∀ and ∃. First ∀ plays x0 and then ∃ plays y0. After this ∀ pl...

We describe the work and underlying ideas of the Helsinki Logic Group in infinitary logic. The central idea is to use trees and Ehrenfeucht-Fräıssé games to measure differences between uncountable models. These differences can be expressed by sentences of so-called infinitely deep languages. This study has ramified to purely set-theoretical problems related to properties of trees, descriptive s...

The first-order logical theory Th(N, x + 1, F (x)) is proved to be complete for the class ATIME-ALT(2O(n), O(n)) when F (x) = 2x, and the same result holds for F (x) = cx, xc (c ∈ N, c ≥ 2), and F (x) = tower of x powers of two. The difficult part is the upper bound, which is obtained by using a bounded Ehrenfeucht-Fräıssé game.

Any primitive binary word contains at least two unbordered conjugates. We characterize binary words that have exactly two unbordered conjugates and show that they can be expressed as a product of two palindromes. In this paper we relate two elementary properties of finite words: being a palin-drome and being unbordered. These two concepts are in a sense complementary. Unbordered words have maxi...

‎let $d_{n,m}=big[frac{2n+1-sqrt{17+8(m-n)}}{2}big]$ and‎ ‎$e_{n,m}$ be the graph obtained from a path‎ ‎$p_{d_{n,m}+1}=v_0v_1 cdots v_{d_{n,m}}$ by joining each vertex of‎ ‎$k_{n-d_{n,m}-1}$ to $v_{d_{n,m}}$ and $v_{d_{n,m}-1}$‎, ‎and by‎ ‎joining $m-n+1-{n-d_{n,m}choose 2}$ vertices of $k_{n-d_{n,m}-1}$‎ ‎to $v_{d_{n,m}-2}$‎. ‎zhang‎, ‎liu and zhou [on the maximal eccentric‎ ‎connectivity ind...