Probability Thermodynamics and Probability Quantum Field

In this paper, we introduce probability thermodynamics and probability quantum fields. By probability we mean that there is an unknown operator, physical or nonphysical, whose eigenvalues obey a certain statistical distribution. Eigenvalue spectra define spectral functions. Various thermodynamic quantities in thermodynamics and effective actions in quantum field theory are all spectral functions. In the scheme, eigenvalues obey a probability distribution, so a probability distribution determines a family of spectral functions in thermodynamics and in quantum field theory. This leads to probability thermodynamics and probability quantum fields determined by a probability distribution. There are two types of spectra: lower bounded spectra, corresponding to the probability distribution with nonnegative random variables, and the lower unbounded spectra, corresponding to probability distributions with negative random variables. For lower unbounded spectra, we use the generalized definition of spectral functions. In some cases, we encounter divergences. We remove the divergence by a renormalization procedure. Moreover, in virtue of spectral theory in physics, we generalize some concepts in probability theory. For example, the moment generating function in probability theory does not always exist. We redefine the moment generating function as the generalized heat kernel, which makes the concept definable when the definition in probability theory fails. As examples, we construct examples corresponding to some probability distributions. Thermodynamic quantities, vacuum amplitudes, one-loop effective actions, and vacuum energies for various probability distributions are presented

KINEMATIC CHARACTERISTICS OF THE STEINEMANNSTEMME MOVE ON THE UNEVEN BAR: A CASE STUDY

The purpose of this paper is to present a biomechanical analysis of an innovative technique on the uneven bar in international gymnastic competitions. Based on the motion trajectory of body’s center of gravity, the angle variation diagram of shoulder and hip joints and the principle of Coriolis, the study has probed into some key techniques used in this routine. They are as follows: The first technique is from ordinary grip to back somersault and arm extension. Secondly, the technique of downswing to low vertical plane of the bar is examined, followed by that of the releasing grip in order; then the turn with bend and extension adjustment in flight and finally the balance of handstand on the lower bar. The proper technical method and its main points are provided here for reference of elite gymnasts, coaches and researchers

Stability and convergence of the two parameter cubic spline collocation method for delay differential equations

AbstractIn this paper, we propose the cubic spline collocation method with two parameters for solving delay differential equations (DDEs). Some results of the local truncation error and the convergence of the spline collocation method are given. We also obtain some results of the linear stability and the nonlinear stability of the method for DDEs. In particular, we design an algorithm to obtain the ranges of the two parameters α,β which are necessary for the P-stability of the collocation method. Some illustrative examples successfully verify our theoretical results

Indenter Shape Dependent Dislocation Actives and Stress Distributions of Single Crystal Nickel during Nanoindentation: A Molecular Dynamics Simulation

The influences of indenter shape on dislocation actives and stress distributions during nanoindentation were studied by using molecular dynamics (MD) simulation. The load-displacement curves, indentation-induced stress fields, and dislocation activities were analyzed by using rectangular, spherical, and Berkovich indenters on single crystal nickel. For the rectangular and spherical indenters, the load-displacement curves have a linear dependence, but the elastic stage produced by the spherical indenter does not last longer than that produced by the rectangular indenter. For a Berkovich indenter, there is almost no linear elastic regime, and an amorphous region appears directly below the indenter tip, which is related to the extremely singular stress field around the indenter tip. In three indenters cases, the prismatic dislocation loops are observed on the {111} planes, and there is a sudden increase in stress near the indenter for the Berkovich indenter. The stress distributions are smooth with no sudden irregularities at low-indentation depths; and the stress increases and a sudden irregularity appears with the increasing indentation depths for the rectangular and spherical indenters. Moreover, the rectangular indenter has the most complex dislocation activities and the spherical indenter is next, while very few dislocations occur in the Berkovich indenter case

Significant Comparative Characteristics between Orphan and Nonorphan Genes in the Rice (Oryza sativa L.) Genome

Microsatellites are short tandem repeats of one to six bases in genomic DNA. As microsatellites are highly polymorphic and play a vital role in gene function and recombination, they are an attractive subject for research in evolution and in the genetics and breeding of animals and plants. Orphan genes have no known homologs in existing databases. Using bioinformatic computation and statistical analysis, we identified 19,26 orphan genes in the rice (Oryza sativa ssp. Japanica cv. Nipponbare) proteome. We found that a larger proportion of orphan genes are expressed after sexual maturation and under environmental pressure than nonorphan genes. Orphan genes generally have shorter protein lengths and intron size, and are faster evolving. Additionally, orphan genes have fewer PROSITE patterns with larger pattern sizes than those in nonorphan genes. The average microsatellite content and the percentage of trinucleotide repeats in orphan genes are also significantly higher than in nonorphan genes. Microsatellites are found less often in PROSITE patterns in orphan genes. Taken together, these orphan gene characteristics suggest that microsatellites play an important role in orphan gene evolution and expression

Statistical delay distribution analysis on high-speed railway trains

Published by SpringerOpen, Heidelber