Dragan Obradovic , Lakshmi Narayan Mishra , Vishnu Narayan Mishra
The content of the system of linear equations makes it an interesting matter that can also be further expanded and deepened. The three methods most commonly used to solve systems of equations are substitution, elimination, and extended matrices. Replacement and elimination are simple methods that can efficiently solve most systems of two equations in a few direct steps. The extended matrix method requires several steps, but its application extends to a number of different systems. The elimination method is useful when the coefficient of one of the variables is equal (or its negative equivalent) in all equations.
Mohammad Reza Rahmati*
We present an extension of partition function of open Gromov Witten theory of CY 3-folds defined by the trace of an extended vertex operator and give a Representation theoretic interpretation of the trace of the vertex operator involved. Specifically, we consider a twist of the vertex operator with infinitely many Casimir operators. We extend the definition of the Fock space of level l, to let the level to be infinity. We prove a duality between gl∞ and a∞ = gl∞ of Howe type, which provides a decomposition of F∞ into irreducible representations obtained from joint highest weight vector for gl∞ and a∞. The decomposition of the Fock space F∞ into highest weight representations provide a method to calculate and interpret the extended trace. Alternatively, the trace can be interpreted as the character of a representation of gl(∞|∞) on the self-tensor product F ⊗ F of the ordinary Fock space. Thinking of the character as a super-trace we give another calculation as a result.
Andrew Cruz
The hint of a vertex administrator and clarify a representation theoretic translation of the follow. We think about a touch of the vertex administrator. The decomposition of the Fock space F∞ into highest weight representations provides a method to calculate and interpret the extended trace with limitlessly numerous Casimir administrators and process its follow as a person equation [1]. To do this, we characterize the Fock space of limitless level F∞.
Jennifer Stewart
Topological manifolds can't have any smooth structure can't be located as PL-manifolds). All the more unequivocally, if M4 is smooth and just associated with positive clear bilinear structure, the blend of Freedman's topological outcomes and Donaldson's scientific outcomes immediately drove to rather astounding outcomes. For instance, it followed that there are uncountable numerous non-isomorphic smooth or PL structures on R4. A good hypothesis of three-layered manifolds took longer.
Rudolf Grigard
Andrew Cruz
Paper incorporates and broadens a considerable lot of the ideas of availability getting from Hansen's (1959) fundamental paper, and fosters a hypothesis of access that sums up from the specific proportions of access that have become progressively normal. Access is currently estimated for a specific spot by a specific mode for a specific reason at a specific time in a specific year. The only reason to locate anywhere is to be near some people, places, and things, be far from others, and possess still others. Since being far from something is really just being near the absence of that thing, and possession is just the ability to have something (and legally prohibit someone else from having it), we can see that location is about proximity. we will perceive how far we can push admittance to everything. The terms access and availability are utilized reciprocally.
Sudarshan Kumaresan Muthuselvi*
DOI: 10.37421/2165-7920.2025.19.496
This paper introduces a new method for solving systems of equations of any order n with m variables by taking the help of row echelon form. Our approach generalizes the solution process by treating each variable as a constant relative to the others within the system. This method leverages the fact that in a given system, each variable has a unique value, allowing it to be considered fixed when solving for another variable. By systematically transforming the system into row echelon form, we can solve complex, high-order, and non-linear systems through a sequence of simplified, linear-like operations. The proposed framework is demonstrated to be effective for various types of equations, providing a versatile and efficient tool for solving intricate systems in mathematics.
DOI: 10.37421/1736-4337.2025.19.495
Hugo Lefevre
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