In 1967, Japanese physicist Morikazu Toda published the seminal papers [78] and [79], exhibiting soliton solutions to a chain of particles with nonlinear interactions between nearest neighbors. In the decades that followed, Toda’s system of particles has been generalized in different directions, each with its own analytic, geometric, and topological characteristics that sets it apart from the o...

If U and V are topologies on an abstract set X, then the triple (X, U, V) is a bitopological space. Using the theorem of Priestley on the representation of distributive lattices, results of Dilworth concerning the normal completion of the lattice of bounded, continuous, realvalued functions on a topological space are extended to include the lattice of bounded, semi-continuous, real-valued funct...

Lattice Gauge Theory in 4-dimensional Euclidean space-time is generalized to ribbon categories which replace the category of representations of the gauge group. This provides a framework in which the gauge group becomes a quantum group while space-time is still given by the ‘classical’ lattice. At the technical level, this construction generalizes the Spin Foam Model dual to Lattice Gauge Theor...

Following the point-set lattice-theoretic (poslat) approach to topology of S. E. Rodabaugh [11], we introduced a more general way to do categorical (fuzzy) topology under the name of categorically-algebraic (catalg) topology [12], which unified many lattice-valued topological settings, and provided the means of intercommunication between different such frameworks. Moreover, motivated by the res...

In this paper, the notion of generalized regular fuzzy irresolute, generalized regular fuzzy irresolute open  and generalized regular fuzzy irresolute closed maps in fuzzy  topological spaces are introduced and studied. Moreover, some separation axioms and $r$-GRF-separated sets are established. Also, the relations between generalized regular fuzzy continuous maps and generalized regular fuzzy ...

in this paper, the urysohn and completely hausdorff axioms in general topology are generalized to l-topological spaces so as to be compatible with pointwise metrics. some properties and characterizations are also derived

The paper is an attempt to represent a study of limit points, boundary points, exterior points, border, interior points and closure points in the common generalized topological space. This paper takes a look at the possibilities of an extended topological space and it also considers the new characterizations of dense set.

the relationship between the randic , wiener, hosoya , balaban, schultz indices, harary numbers anddistance matrix to enthalpies of formation (airf), heat capacity, (cp) , enthalpies of combustion (ah °c ),enthalpy of vaporization (ah °vap) and normal boiling points (bpk)of c2 c10 normal alkanes isrepresented

L-sets over a base set X are generalizations of classical sets where subsets are not specified by characteristic functions from X to {0, 1} but rather by functions from X to a lattice L. For an L-set a ∈ L and an element x ∈ X, a(x) is interpreted as the grade of membership of x in a. Stratified L-topological spaces are generalizations of topological spaces to the L-set case [1]. In [2], strati...

We study the non-trivial phase of two-dimensional breathing kagome lattice, displaying both edge and corner modes. The localized modes a flake were initially identified as signature higher-order topological but later shown to be trivial for perturbations that thought protect them. Using various theoretical simulation techniques, we confirm it does not display topology are nature. Nevertheless, ...