[10] **viXra:1704.0320 [pdf]**
*submitted on 2017-04-24 08:43:53*

**Authors:** Yakov A. Iosilevskii

**Comments:** 72 pages

This exposition has the following main objects in view. (1) All main depth-integrated time-dependent and time-averaged characteristics, – as the velocity potential, velocity, pressure, momentum flux density tensor, volumetric kinetic, potential, and total energies, Poynting (energy flux density) vector, radiation (wave) stress tensor, etc, – of the ideal (inviscid, incompressible, and irrotational) fluid flow in an imaginary wave-perturbed infinite water layer with an arbitrary shaped bed and with a free upper boundary surface, and also the pertinent depth-integrated time-dependent and time-averaged differential continuity equations, – as those of the mass density, energy density, and momentum flux density (Euler’s and Bernoulli’s equations), etc, – are rigorously deduced from the respective basic local (bulk and surface) characteristics and from the respective bulk continuity equations, with allowance for the corresponding exact kinematic boundary conditions at the upper (free) and bottom surfaces and also with allowance for the corresponding exact dynamic boundary condition at the free surface, which follows from the basic Bernoulli equation. (2) The recursive asymptotic perturbation method with respect to powers of ka that has been developed recently by the present author for the local characteristics and bulk continuity equations of the ideal fluid flow in the presence of a priming (seeding) progressive, or standing, monochromatic gravity water wave (PPPMGWW or PSPMGWW) of a wave number k>0 and of wave amplitude a>0 in an imaginary infinite water layer of a uniform depth d>0 is extended to flow’s momentary and time-averaged (TA), depth-integrated (DI) characteristics and to their continuity equations, particularly to the 3x3 radiation, or wave, stress tensor (RST). (3) The extended recursive method is applied to PPPMGWW’s and PSPMGWW’s with the purpose to obtain their main TADI characteristics in terms of elementary functions. (4) The first non-vanishing asymptotic approximation of a characteristic, particularly that of the 3x3-TADIRST, of a PPPMGWW or PSPMGWW is generalized to a priming progressive, or standing, quasi-pane (PPQP or PSQP) MGWW. (5) The longshore wave–induced sediment transport rate, expressed by the so-called CERC (Coastal Engineering Research Council) formula, is briefly discussed in its relation to the (x,y)-component of the 3x3-TADIRST of the pertinent PPQPMGWW. (6) The presently common 2x2-TADIRST’s of progressive and standing water waves, which have been deduced by various writers from intuitive considerations and have been canonized about 55 years ago, are revised in accordance with the 3x3 ones of the recursive asymptotic theory.

**Category:** Mathematical Physics

[9] **viXra:1704.0264 [pdf]**
*submitted on 2017-04-20 18:59:25*

**Authors:** Paul J. Werbos

**Comments:** 15 pages, 36 equations, 34 references

Today’s standard model of physics treats the physical masses of elementary particles as given, and assumes that they have a bare radius of zero, as in the older classical physics of Lorentz. Many physicists have studied the properties of the Yang-Mills-Higgs model of continuous fields in hopes that it might help to explain where elementary particles (and their masses) come from in the first place. This paper reviews some of the important prior work on Yang-Mills-Higgs and solitons in general, but it also shows that stable particles in that model cannot have intrinsic angular momentum (spin). It specifies four extensions of Yang-Mills Higgs, the Lagrangians L1 through L4, which are closer to the standard model of physics, and shows that one of the four (L3) does predict/explain spin from a purely neoclassical theory. The paper begins by summarizing the larger framework which has inspired this work, and ends by discussing two possibilities for further refinement.

**Category:** Mathematical Physics

[8] **viXra:1704.0223 [pdf]**
*submitted on 2017-04-17 17:50:17*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 2 Pages.

Define and explain Incalculability.

**Category:** Mathematical Physics

[7] **viXra:1704.0199 [pdf]**
*replaced on 2017-04-17 09:28:29*

**Authors:** J. Akande, D.K.K. Adjaï, L.H. Koudahoun, Y.J.F. Kpomahou, M.D. Monsia

**Comments:** 16 pages

The problem of finding exact trigonometric periodic solutions to non-linear differential equations is still an open mathematical research field. In this paper it is shown that the Painlevé-Gambier XVIII equation and its inverted version may exhibit exact trigonometric periodic solutions as well as other quadratic Liénard type equations but with amplitude-dependent frequency. Other inverted Painlevé-Gambier equations are also shown to admit exact periodic solutions.

**Category:** Mathematical Physics

[6] **viXra:1704.0157 [pdf]**
*submitted on 2017-04-12 08:50:23*

**Authors:** Valery B. Smolensky

**Comments:** 3 Pages.

The article, according to the author, sheds new light on the nature of PI. The original output of PI as a function of States of nature.

**Category:** Mathematical Physics

[5] **viXra:1704.0135 [pdf]**
*submitted on 2017-04-11 08:21:43*

**Authors:** Yakov A. Iosilevskii

**Comments:** 137 pages

It is shown with complete logical and mathematical rigor that under the appropriate hypotheses of analytical extension and of asymptotic matching, which are stated in the article, the nonlinear problem of irrotational and incompressible gravity waves on an infinite water layer of a constant depth d reduces to an infinite recursive sequence of linear two-plane boundary value problems for a harmonic velocity potential with respect to powers of a dimensionless real-valued scaling parameter ‘ka’, where k>0 is the wave number and a>0 the amplitude of a priming (seeding) progressive, or standing, plane monochromatic gravity water wave (briefly PPPMGWW or PSPMGWW respectively). The method, by which the given nonlinear water wave problem is treated in the exposition from scratch, can be regarded as a peculiar instance of the general perturbation method, which is known as the Liouville-Green (LG) method in mathematics and as the Wentzel-Kramers-Brillouin (WKB) method in physics. In the framework of the recursive theory developed, the velocity potential and any bulk or surface measurable characteristic of the wave motion is represented by an infinite asymptotic power series with respect to ‘ka’, whose all coefficients are expressed in quadratures in accordance with a well-established an algorithm for their successive calculation. The theory developed applies particularly in the case where the depth d is taken to infinity. Besides the priming velocity potential of the first, linear asymptotic approximation in ka, the partial velocity potential and all relevant characteristics of wave motion of the second order with respect to ka are calculated in terms of elementary functions both in the case of a PPPMGWW and in the case of a PSPMGWW. Accordingly, the recursive theory incorporates the conventional Airy (linear) theory of water waves linear as its first non-vanishing approximation with the following proviso. In the Airy theory, the boundary condition at the perturbed free (upper) surface of a water layer is paradoxically stated at the equilibrium plane z=0, in spite of the fact that at any instant of time some part of the plane is necessarily located in air or in vacuum, and not in water. This and also a similar paradox arising in computing the time averages of bulk characteristics at spatial points close to the perturbed free surface are solved in the article.

**Category:** Mathematical Physics

[4] **viXra:1704.0108 [pdf]**
*replaced on 2017-04-25 23:28:28*

**Authors:** Frederick Moxley

**Comments:** 15 Pages.

In the year 2017 it was formally conjectured that if the Bender-Brody-M\"uller (BBM) Hamiltonian can be shown to be self-adjoint, then the Riemann hypothesis holds true. Herein we discuss the domain and eigenvalues of the Bender-Brody-M\"uller conjecture. Moreover, a second quantization of the BBM Schr\"odinger equation is performed, and a closed-form solution for the nontrivial zeros of the Riemann zeta function is obtained. Finally, it is shown that all of the nontrivial zeros are located at $\Re(z)=1/2$.

**Category:** Mathematical Physics

[3] **viXra:1704.0080 [pdf]**
*submitted on 2017-04-06 17:43:13*

**Authors:** Gregory Natanson

**Comments:** 48 Pages.

The paper presents the uniform technique for constructing SUSY ladders of rational canonical Sturm-Liouville equations (RCSLEs) conditionally exactly quantized by Gauss-seed (GS) Heine polynomials. Each ladder starts from the RCSLE exactly quantized by classical Jacobi, generalized Laguerre or Romanovski-Routh polynomials. We then use its nodeless almost everywhere holomorphic (AEH) solutions formed by the appropriate set of non-orthogonal polynomials to construct multi-step rational SUSY partners of the given Liouville potential on the line. It was proven that eigenfunctions of each RCSLE in the ladder have an AEH form, namely, each eigenfunction can be represented as a weighted polynomial fraction (PFrs), with both numerator and denominator remaining finite at the common singular points of all the RCSLEs in the given ladder. As a result both polynomials satisfy the second-order differential equations of Heine type.

**Category:** Mathematical Physics

[2] **viXra:1704.0064 [pdf]**
*replaced on 2017-04-12 13:08:28*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 6 Pages.

A brief draft respect to a problem found in the equations of Euler and Navier-Stokes, whose adequate treatment solves a centennial problem about the solution of these equations and a most correct modeling of fluid movement.

**Category:** Mathematical Physics

[1] **viXra:1704.0018 [pdf]**
*submitted on 2017-04-03 04:36:13*

**Authors:** Andrej Liptaj

**Comments:** 7 Pages.

Results of perturbative calculations in quantum physics have the form of truncated power series in a coupling constant. In order to evaluate the uncertainty of such results, the power series of the inverse function are constructed. These are inverted and the difference between the outcome of this procedure and the initial power series is taken as uncertainty.

**Category:** Mathematical Physics