Explicit Calculations of Tensor Product Coefficients for E7

We propose a new method to calculate coupling coefficients of E7 tensor products. Our method is based on explicit use of E7 characters in the definition of a tensor product. When applying Weyl character formula for E7 Lie algebra, one needs to make sums over 2903040 elements of E7 Weyl group. To implement such enormous sums, we show we have a way which makes their calculations possible. This will be accomplished by decomposing an E7 character into 72 participating A7 characters.

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Lateral Transshipment as an effective approach to cut costs in the multi item small business sector

Consumer behavior is unpredictable that retailers often face the challenge of meeting their demands. Those retailers that are in the close proximity with the original manufacturers would generally be able to meet their demands and could provide customer satisfaction. Retailers need to stay in constant touch with the producer for supplies and this coordination is called as lateral transshipment.  Lateral transshipment is the best approach to cut costs and plays an important role in the inventory management.  This approach is more effective in multi item small business sector.

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Notes on the Chern-Character

The aim of this note is to give an axiomatic and elementary treatment of Chern-characters of vector bundles with values in a class of cohomology-theories arising in topology and algebra. Given a theory of Chern-classes for complex vector bundles with values in singular cohomology one gets in a natural way a Chern-character from complex K-theory to singular cohomology using the projective bundle theorem and the Newton polynomials. The Chern-classes of a complex vector bundle may be defined using the notion of an Euler class and one may prove that a theory of Chern-classes with values in singular cohomology is unique. In this note it is shown one may relax the conditions on the theory for Chern-classes and still get a Chern character. Hence the Chern-character depends on some choices.

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New Square Method

The “new square method” is an improved approach based on the “least square method”. It calculates not only the constants and coefficients but also the variables’ power values in a model in the course of data regression calculations, thus bringing about a simpler and more accurate calculation for non-linear data regression processes.

In non-linear data regression calculations, the “least square method” is applied for mathematical substitutions and transformations in a model, but the regression results may not always be correct, for which we have made improvement on the method adopted and named the improved one as “new square method”.

A New Method for Analysis of Biomolecules Using the BSM-SG Atomic Models

Biomolecules and particularly proteins and DNA exhibit some mysterious features that cannot find satisfactory explanation by quantum mechanical modes of atoms. One of them, known as a Levinthal’s paradox, is the ability to preserve their complex three-dimensional structure in appropriate environments. Another one is that they possess some unknown energy mechanism.

The Basic Structures of Matter Super gravitation Unified Theory (BSM-SG) allows uncovering the real physical structures of the elementary particles and their spatial arrangement in atomic nuclei. The resulting physical models of the atoms are characterized by the same interaction energies as the quantum mechanical models, while the structure of the elementary particles influence their spatial arrangement in the nuclei. The resulting atomic models with fully identifiable parameters and angular positions of the quantum orbits permit studying the physical conditions behind the structural and bonding restrictions of the atoms connected in molecules.

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Riccati-Bernoulli Sub-ODE as a new technique to find solutions to the nonlinear equations

Riccati-Bernoulli Sub-ODE is a new method to construct the exact traveling wave solutions of the nonlinear modified Korteweg-de Vries (mKdV) equation. This method can be used to solve the nonlinear, random modified Korteweg-de Vries (mKdV) equation. It serves as effective tool to solve many mathematical and physics problems. The travelling wave solutions of these equations can be expressed by hyperbolic functions, trigonometric functions and rational functions. Although several methods are in existence to find out the solution analytical solutions for the linear and nonlinear equations, Jacobi elliptic function method could find the exact solution to the non-linear equations as these equations can be converted into a set of algebraic equations.

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Solitary Waves for the Modified Korteweg-De Vries Equation in Deterministic Case and Random Case

In this paper, we present a new method, the so called Riccati-Bernoulli Sub-ODE method to construct exact traveling wave solutions of the nonlinear modified Korteweg-de Vries (mKdV) equation and also,we use this method in order to solve the nonlinear random modified Korteweg-de Vries (mKdV) equation. It has been shown that the proposed method is effective tools to in order to solve many mathematical physics problems. The travelling wave solutions of these equations are expressed by hyperbolic functions, trigonometric functions and rational functions. The impression of the random coefficient in our problem is studied, by using some distributions through some cases studies.

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Invariant Tensor Product

Various forms of invariant tensor products appeared in the literature implicitly, for example, in Schur’s orthogonality for finite groups. In many cases, they are employed to study the space HomG(π1, π2) where one of the representations π1 and π2 is irreducible. In this paper, we formulate the concept of invariant tensor product uniformly. We also study the invariant tensor functor associated with discrete series representations for classical groups. For motivations and applications.

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