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# Journal of Generalized Lie Theory and Applications

ISSN: 1736-4337

Open Access

## Articles in press and Articles in process

Commentary Pages: 1 - 1

### Methods for Solving a System of Linear Equations

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.

Commentary Pages: 1 - 1

### Fock Space of Level infinity and Characters of Vertex Operators

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.

Editorial Pages: 319 - 319

### Vertex Operation Formula

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∞.

Editorial Pages: 317 - 317

### Towards General Theory of Access

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.

Commentary Pages: 320 - 320

### Differential Years Topology

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.

Commentary Pages: 321 - 321

### Regular and Irregular Isotheory of Lie Santilli

Rudolf Grigard

One of us (Santilli) has directed methodical investigations on the abovementioned recorded inheritances over various many years and papers cited in that proposing that the demonstrated limits start from the math hidden quantum mechanics, rather than on its essential aphorisms. All the more especially, the restrictions started from the nearby differential person of twentieth century arithmetic on the grounds that such a analytics is exclusively relevant to dynamical frameworks of point-like particles moving in vacuum under Hamiltonian communications, which frameworks are known as outside dynamical frameworks. His Lie hypothesis is exclusively appropriate to dynamical frameworks comprising of point-like particles moving in vacuum under direct and Hamiltonian associations (frameworks known as outside dynamical frameworks
Short Communication Pages: 322 - 322

### Budworm Spruce Model

Jennifer Gray

Mathematical modeling is the art of translating problems from an application area into tractable mathematical formulations whose theoretical and numerical analysis provides insight, answers, and guidance useful for the originating application. Mathematical modeling is indispensable in many applications, gives direction for the problem solutions, and prepares the way for better designing or control system. Physiological environment manages connections between individual creatures furthermore outside ecological powers, like temperature, with an emphasis on how individual physiology and conduct changes across various climate: Populace environment manages the elements and design (age, size, sex, and so forth) of gatherings of living beings of similar species. Local area nature bargains with the natural connections (hunter prey, contest, mutualism, and so forth), which happen between species. Numerical methodologies incorporate differential conditions (both conventional what's more halfway), necessary conditions, and lattice hypothesis. Models for networks are regularly outlined as frameworks of normal differential conditions, with independent conditions for every one of the cooperating populaces

Mini Thesis Pages: 1 - 6

### Construction of Right Cheban Loops of Small Order

In this study, we give constructions of right cheban loops of order 4t, using a multiplication defined on cartesian product of (C2t X C2) where C2t is a cyclic group of order 2t, t is a positive integer: 3,4 and 6 and C2 is a cyclic group of order 2, each gives a right cheban loop of orders 12, 16 and 24. It was found that smallest non-associative right cheban loop is of order 12 and finite examples of right cheban loops of orders 12,16 and 24 are generated as shown in the cayley tables.

Research Article Pages: 1 - 4

### The topological features of the Valent integrable case on the Lie algebra e(3)

This paper aims at studying a new integrable Hamiltonian system due to valent. This is a Hamiltonian system with two degrees of freedom where the additional integral is polynomial of degree 3. The critical points and the bifurcation diagram of the Hamiltonian are obtained and the non-degeneracy conditions are verified. Thereafter the topology of iso-energy surfaces is found. Also for zero value of one of the parameters, the type of non-degenerate critical points of rank zero is calculated, the bifurcation diagram of the momentum map is constructed and finally the molecules (fomenko invariants) are found.

Barcelona, Spain

### International Conference and Expo on Mechatronics, Electronics and Automotive Engineering

San Francisco, USA

#### Journal Highlights

###### Citations: 1926

Journal of Generalized Lie Theory and Applications received 1926 citations as per Google Scholar report

Barcelona, Spain

### International Conference and Expo on Mechatronics, Electronics and Automotive Engineering

San Francisco, USA

Barcelona, Spain

### International Conference and Expo on Mechatronics, Electronics and Automotive Engineering

San Francisco, USA

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