Physical Mathematics

The Lorentz-Transformation (LT) is the basis of the Theories of Relativity, which are capable of describing the experimentally manifold confirmed relativistic phenomena that deviate from classical physics. Here I present a proof that results in an alternative interpretation of the LT. In particular, the LT cannot be applied to high relative velocities and related space-time modeling – one of the most important tools in physics and astronomy – and will lead to a dead end. Two experiments are proposed to test this idea.

Purpose: Transarterial 90Y microspheres radioembolization is emerging as a multidisciplinary promising therapeutic modality for primary and metastatic cancer in the liver. Actually two different type of microspheres are used, whose main characteristic is the different density of activity (activity per microsphere). In this paper the effect due to the possible different distribution of the microspheres in a target is presented and discussed from a macrodosimetric point of view. Material and methods: A 100 g virtual soft-tissue target region has been builded. The administered activity was chosen to have a target average absorbed dose of 100 Gy and the number of 90Y microspheres needed was calculated for two different activity-per-microsphere values (2500) Bq/microsphere and 50 Bq/microsphere, respectively). The spheres were randomly distributed in the target and the Dose Volume Histograms were obtained for both. The cells surviving fractions (SF) for four different values of the radiobiological parameter α were calculated from the Linear - Quadratic model. Results: The DVH obtained are very similar and the SF is almost equal for both the activity-per- microsphere values. Conclusions: This macrodosimetric approach shows no radiobiological difference between the glass and resin microspheres. Thus the different number of microspheres seems to have no effect when the number of spheres is big enough that the distance between the spheres in the target can be considered small compared to the range of the β-particles of 90Y.

This paper shows that there are deeper symmetries within physics than are currently recognised. The use of SI units in their existing form hides that gravity is not the weakest force. The paper shows through symmetry arguments that Planck’s constant h and the Gravitational constant G are both dimensionless ratios when dimensional analysis is used at property levels deeper than mass, length and time. The resultant adjustments shown to be needed for SI units produce much simpler sets of units which also solve the issue of why magnetic field H and magnetic inductance B have not previously had the same units. The result shows that gravitational and charge fields have the same strengths when considered in fractional adjusted-Planck values. By showing that h and G are dimensionless, they can be understood to be unit-dependent ratios which can be eliminated from all equations by merging them within new adjusted SI units. The implications are that mass and charge sizes, and distance, are not the properties which separate quantum and classical gravitational systems. The equivalence of gravitational and inertial mass is also shown. The new type of dimensional analysis shows how to uncover any law of nature or universal constant and that the current set of properties of nature is missing two from the set, whose dimensions and units can be inferred.

The paper is devoted to the hierarchy of a symmetr y breaking in the Non symmetric Kaluza–Klein (Jordan–Thiry) Theory. The basic idea consists in a deformation of a vacuum states manifold to the cartesian product of vacuum states manifolds of every stage of a symmetry breaking .In the paper we consider a pattern of a spontaneous symmetry breaking including a hierarchy in the Non symmetr ic Kaluza–Klein (Jordan–Thiry) Theory.

Establishment of an LC equation and of a local fields equation describing permanently localized photons from the analysis of kinetic energy circulation within the energy structure of the double-particle photon that Louis de Broglie hypothesized in the early 1930's. Among other interesting features, these equations provide a mechanical explanation to the localized photon properties of self-propelling at the speed of light and of self-guiding in straight line when no external interaction tends to deflect its trajectory. This paper summarizes the seminal considerations that led to the development of the 3-spaces model.

The profound effects of chemotherapy on the combined dynamics of the hematological stem cells and their differentiated neutrophils is examined. G-CSF is often used to deal with this neutropenia and the response is highly variable. To shape the neutrophil response to chemotherapy and G-CSF, periodic parametric resonance is discussed. Periodic oscillation in neutrophil levels and the subharmonic 1:2 resonance phenomena are observed with the assumption of periodic chemotherapy is given. The work is aim to stimulate further investigations and the practical applications

This paper is concerned with finding linear representations for seven-dimensional real, indecomposable nilpotent Lie algebras. We consider the first 39 algebras presented in Gong’s classification which was based on the upper central series dimensions. For each algebra, we give a corresponding matrix Lie group, a representation of the Lie algebra in terms of left-invariant vector field and left-invariant one forms.

In this manuscript we have studied the laminar convective heat and mass transfer flow of an incompressible, viscous, electrically conducting fluid over a fluid over an impulsively started vertical plate with conduction-radiation embedded in a porous medium in the occurrence of transverse magnetic field. An exact solution is derived by solving the dimensionless main coupled partial differential equations using Laplace transform technique. The properties of important physical parameters on the velocity, temperature, concentration, Skin friction, Sherwood number and Nusselt number have been studied through graphs.

In this paper we propose an algorithm for the calculation of the exact values of compactly-supported Daubechies wavelet functions. The algorithm is iterative, performing a single convolution operation at each step. It requires solving, at the first step only, a linear system of a relatively small size. The novelty of the algorithm is that once the values at dyadic points at a certain level j are calculated they do not need to be updated at the next step. We find that this algorithm is superior to the well-known cascade algorithm proposed by Ingrid Daubechies. This algorithm can serve well in wavelet based methods for the numerical solutions of differential equations. The algorithm is tested on Daubechies scaling functions as well as Daubechies coiflets. Comparison with the values obtained using the cascade algorithm is made. We found that the cascade algorithm results converge to ours

Merits, attributes and challenges associated with the application of analytical (mathematical) predictive modeling in electronics materials science and engineering are addressed, based mostly on the author’s research during his tenure with Basic Research, Bell Laboratories and then – with UC-Santa Cruz and Portland State University, Portland, OR, USA. The emphasis is on some practically important, yet paradoxical (i.e., intuitively non-obvious), materials reliability-related situations/phenomena in electronics and optics. It is concluded that all the three basic approaches in Microelectronics and Photonics Materials Science and Engineering - analytical (mathematical) modeling, numerical modeling (simulation) and experimental investigations - are equally important in understanding the physics of the materials behavior and in designing, on this basis, viable and reliable electronic devices and products. As they say, if your only tool is a hammer, all the problems look like nails to you, do they not?