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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From Monge-Ampere-Boltzman to Euler Equations

In Hsiao study the convergence of the VPB system to the Incompressible Euler Equations. Bernier and Grégoire show that weak solution of Vlasov-Monge-Ampère converge to a solution of the incompressible Euler equations when the parameter goes to 0, Brenier and Loeper for details. So, is a ligitim question to look for the convergence of a weak solution of BMA (of course if such solution exists) to a solution of the incompressible Euler equations when the parameter goes to 0.
The study of the existence and uniqueness of solution to the BMA system seems a difficult matter. Here we assume the existence and uniqueness of smooth solution to the BMA and we just look to the asymptotic analysis of this system.

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On Finding the Upper Confidence Limit for a Binomial Proportion when Zero Successes are Observed

We consider confidence interval estimation for a binomial proportion when the data have already been observed and x, the observed number of successes in a sample of size n, is zero. In this case, the main objective of the investigator is usually to obtain a reasonable upper bound for the true probability of success, i.e., the upper limit of a one-sided confidence interval. In this article, we use observed interval length and p-confidence to evaluate eight methods for finding the upper limit of a confidence interval for a binomial proportion when x is known to be zero. Long-run properties such as expected interval length and coverage probability are not applicable because the sample data have already been observed. We show that many popular approximate methods that are known to have good long-run properties in the general setting perform poorly when x=0 and recommend that the Clopper-Pearson exact method be used instead.

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Important Discovery of Preferred Velocity of 30000 ∓ 425 M/S of the Solar Motion of the Earth

With the recent relative advancement of Technology, particularly with the digital storage oscilloscopes, we analyze precursor signals. They became known in the literature, precursor signals. However they are usually attributed to a symmetrical Fourier analysis of square pulses with dual time components, one unnatural time prior the pulse event and second a natural time after the pulse event.

However, every arbitrary mathematical analysis may not be suitable for a particular physical case, as the complex solutions of an equation of a physical problem are usually rejected, as complex numbers solutions. Also, a particular mathematical number may be analyzed as the limit of an infinite number of numerical sequences. This does not mean that every term of each such sequence, plays a real role in a physical situation.

Studies of the Regular and Irregular Iso representations of the Lie-Santilli Isotheory

As it is well known, the Lie theory is solely applicable to dynamical systems consisting of point-like particles moving in vacuum under linear and Hamiltonian interactions (systems known as exterior dynamical systems). One of the authors (R.M. Santilli) has proposed an axiom-preserving broadening of the Lie theory, known as the Lie-Santilli iso theory, that is applicable to dynamical; systems of extended, nonspherical and deformable particles moving within a physical medium under Hamiltonian as well as non-linear and non-Hamiltonian interactions (broader systems known as interior dynamical systems).

In this paper, we study apparently for the first time regular and irregular iso representations of Lie-Santilli iso algebras occurring when the structure quantities are constants or functions, respectively. A number of applications to particle and nuclear physics are indicated. It should be indicated that this paper is specifically devoted to the study of iso representations under the assumption of a knowledge of the Lie-Santilli iso theory, as well as of the isotopies of the various branches of 20th century applied mathematics, collectively known as iso mathematics, which is crucial for the consistent formulation and elaboration of iso theories.