CONVERGENCE RATES IN THE STRONG LAWS OF NONSTATIONARYρ~*-MIXING RANDOM FIELDS

By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.

CONVERGENCERATESIN THESTRONG LAWSOFASYMPTOTICALLY NEGATIVELY ASSOCIATEDRANDOM FIELDS

In this paper, a notion of negative side ρ \|mixing ( ρ\+- \|mixing) which can be regarded as asymptotic negative association is defined, and some Rosenthal type inequalities for ρ\+- \|mixing random fields are established. The complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are also discussed for ρ\+-\| mixing random fields. The results obtained extend those for negatively associated sequences and ρ\+*\| mixing random fields.

STRONG LAW OF LARGE NUMBERS AND SHANNON-MCMILLAN THEOREM FOR MARKOV CHAINS FIELD ON CAYLEY TREE

This paper studies the strong law of large numbers and the Shannom-McMillan theorem for Markov chains field on Cayley tree. The authors first prove the strong law of large number on the frequencies of states and orderd couples of states for Markov chains field on Cayley tree. Then they prove the Shannon-McMillan theorem with a.e. convergence for Markov chains field on Cayley tree. In the proof, a new technique in the study the strong limit theorem in probability theory is applied.

Precise asymptotics in the law of the logarithm for random fields in Hilbert space

Consider the positive d-dimensional lattice Z^d（d≥2） with partial ordering ≤, let {XK; K∈Z＋^d} be i.i.d, random variables taking values in a real separable Hilbert space （H, ｜｜·｜｜） with mean zero and covariance operator ∑ and set partial sums SN =∑K≤nXK,K,N∈Z＋^d. Under some moment conditions, we obtain the precise asymptotics of a kind of weighted infinite series for partial sums SN as ε↓ by using the truncation and approximation methods. The results are related to the convergence rates of the law of the logarithm in Hilbert space, and they also extend the results of （Gut and Spataru, 2003）.

New approach for obtaining the time-evolution law of a chaotic light field in a damping gaining-process

A new approach for studying the time-evolution law of a chaotic light field in a damping-gaining coexisting process is presented. The new differential equation for determining the parameter of the density operator p（t） is derived and the solution of f for the damping and gaining processes are studied separately. Our approach is direct and the result is concise since it is not necessary for us to know the Kraus operators in advance.

Positions Open in the Field of Plasma and Fusion

Institute of Plasma Physics, Chinese Academy of Sciences (ASIPP), one of the most important Laboratories on magnetically confined fusion in China and the Nuclear Fusion Research Center of the World Laboratory, is searching for 5 senior and 10 junior scientists of plasma and fusion in the following superconducting tokamak research areas: theory and simulation, diverter and edge physics, plasma diagnostics, electron cyclotron resonant heating, ion cyclotron resonant heating, lower hybrid wave, neutral beam injection, reactor design, fusion material, superconducting engineering.

Positions Open in the Field of Plasma and Fusion

Institute of Plasma Physics, Chinese Academy of Sciences (ASIPP), one of the most important laboratories on magnetically confined fusion in China and the Nuclear Fusion Research Center of the World Laboratory, is searching for 5 senior and 10 junior scientists of plasma and fusion in the following superconducting tokamak research areas: theory and simulation, diverter and edge physics, plasma diagnostics, electron cyclotron resonant heating, ion cyclotron resonant heating, lower hybrid wave, neutral beam injection, reactor design, fusion material, superconducting engineering.

Positions Open in the Field of Plasma and Fusion

Institute of Plasma Physics, Chinese Academy of Sciences (ASIPP), one of the most important laboratories on magnetically confined fusion in China and the Nuclear Fusion Research Center of the World Laboratory, is searching for 5 senior and 10 junior scientists of plasma and fusion in the following superconducting tokamak research areas: theory and simulation, diverter and edge physics, plasma diagnostics, electron cyclotron resonant heating, ion cyclotron resonant heating, lower hybrid wave, neutral beam injection, reactor design, fusion material, superconducting engineering.

The Natural Law of Transition of a Charged Particle into a Compound State under the Action of an Electroscalar Field

This article is the continuation of article [1] where the experimental facts of observation of the electroscalar radiation in the spectrum of the Sun have been presented [2]. This radiation comes into the world having a long wavelength, being longitudinal and extraordinarily penetrating. In accordance with the principle of least action, the Lagrangian of the electroscalar field and the tensor of energy-moment are determined using the variation the potential and coordinates. The equation of motion the charged particle in electroscalar field is determined and the energy of particle has the negative sign with respect to the mechanical energy of particle and the energy of electromagnetic field. So, this is decreasing the electrical potential of particle during the propagation. The electroscalar energy of charged particle and field’s force acting on the particle during their motion change the particle’s electrical status which, in its turn, may trigger the transition of the particle into a compound state during interaction with any object. Due to the continuity this process can lead the particle to the state which enters into a compound state with a negative energy for a different particle’s velocity. This state is the physical vacuum’s state. Analysis of the solar spectrum demonstrates that scattering and absorption of electroscalar wave go on the cavities of solids. The spreading out of electroscalar field obeys to the law of plane wave and the transfer the energy and information can occur in vacuum and any medium.

Energy states of the Hulthen plus Coulomb-like potential with position-dependent mass function in external magnetic fields

We need to solve a suitable exponential form of the position-dependent mass （PDM） Schr6dinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the actions of the external magnetic and Aharonov-Bohm （AB） flux fields. The bound state energies and their corresponding wave functions are calculated for the spatially-dependent mass distribution function of interest in physics. A few plots of some numerical results with respect to the energy are shown.

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES (X) -MASTER BALANCE LAW

Through a comparison between the expressions of master balance laws and the conservation laws derived by Noether＇s theorem, a unified master balance law and six physically possible balance equations for micropolar continuum mechanics are naturally deduced. Among them, by extending the well-known conventional concept of energymomentum tensor, the rather general conservation laws and balance equations named after energy-momentum, energy-angular momentum and energy-energy are obtained. It is clear that the forms of the physical field quantities in the master balance law for the last three cases could not be assumed directly by perceiving through the intuition. Finally, some existing results are reduced immediately as special cases.

Seepage field distribution and water inflow laws of tunnels in water-rich regions

Currently,the water inrush hazards during tunnel construction,the water leakage during tunnel operation,and the accompanying disturbances to the ecological environment have become the main problems that affect the structural safety of tunnels in water-rich regions.In this paper,a tunnel seepage model testing system was used to conduct experiments of the grouting circle and primary support with different permeability coefficients.The influences of the supporting structures on the water inflow laws and the distribution of the water pressure in the tunnel were analyzed.With the decrease in the permeability coefficient of the grouting circle or the primary support,the inflow rate of water into the tunnel showed a non-linear decreasing trend.In comparison,the water inflow reduction effect of grouting circle was much better than that of primary support.With the increase of the permeability coefficient of the grouting ring,the water pressure behind the primary lining increases gradually,while the water pressure behind the grouting ring decreases.Thus,the grouting of surrounding rock during the construction of water-rich tunnel can effectively weaken the hydraulic connection,reduce the influence range of seepage,and significantly reduce the decline of groundwater.Meanwhile,the seepage tests at different hydrostatic heads and hydrodynamic heads during tunnel operation period were also conducted.As the hydrostatic head decreased,the water pressure at each characteristic point decreased approximately linearly,and the water inflow rate also had a gradual downward trend.Under the action of hydrodynamic head,the water pressure had an obvious lagging effect,which was not conducive to the stability of the supporting structures,and it could be mitigated by actively regulating the drainage rate.Compared with the hydrostatic head,the hydrodynamic head could change the real-time rate of water inflow to the tunnel and broke the dynamic balance between the water pressure and water inflow rate,thereby affecting the stress state on the supporting structures.

STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Some strong laws of large numbers for the frequencies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields （NSMC） on Cayley trees are studied. In the proof, a new technique for the study of strong limit theorems of Markov chains is extended to the case of Markov chain fields, The asymptotic equipartition properties with almost everywhere （a,e.） convergence for NSMC on Cayley trees are obtained,

Unsteady temperature field of surrounding rock mass in high geothermal roadway during mechanical ventilation

To explore the spatial-temporal evolution law of rock mass temperature in high geothermal roadway during mechar^ical ventilation, a series of experiments were conducted based on the physical simulation test system of thermal and humid environment in high geothermal roadway, which is a method independently developed by China University of Mining and Technology. The results indicate that during ventilation, the disturbed region of the temperature extends gradually from shallow area to deep area in the surrounding rock mass of the roadway. Meanwhile, the temperature increases as the exponential function from shallow area to deep, with steady decrease of the temperature gradient and heat flux. As the ventilation proceeds, the relationship between dimensionless temperature and dimensionless time approximately meets Hill function.

Some Limit Theorems for Weighted Sums of Random Variable Fields

Let{Xn^-,n^-∈N^d}be a field of Banach space valued random variables, 0 〈r〈p≤2 and{an^-,k^-, （n^-,k^-） ∈ N^d × N^d ,k^-≤n^-} a triangular array of real numhers, where N^d is the d-dimensional lattice （d≥1 ）. Under the minimal condition that {｜｜Xn^-｜｜ r,n^- ∈N^d} is {｜an^-,k^-｜^r,（n^-,k^-）} ∈ N^d ×N^d,k^-≤n^-}-uniformly integrable, we show that ∑（k^-≤n^-）an^-,k^-,Xk^-^（L^r（or a,s,）→0 as ｜n^-｜→∞ In the above, if 0〈r〈1, the random variables are not needed to be independent. If 1≤r〈p≤2, and Banach space valued random variables are independent with mean zero we assume the Banaeh space is of type p. If 1≤r≤p≤2 and Banach space valued random variables are not independent we assume the Banach space is p-smoothable.

High-order field theory and a weak Euler–Lagrange–Barut equation for classical relativistic particle-field systems

In both quantum and classical field systems,conservation laws such as the conservation of energy and momentum are widely regarded as fundamental properties.A broadly accepted approach to deriving conservation laws is built using Noether's method.However,this procedure is still unclear for relativistic particle-field systems where particles are regarded as classical world lines.In the present study,we establish a general manifestly covariant or geometric field theory for classical relativistic particle-field systems.In contrast to quantum systems,where particles are viewed as quantum fields,classical relativistic particle-field systems present specific challenges.These challenges arise from two sides.The first comes from the mass-shell constraint.To deal with the mass-shell constraint,the Euler–Lagrange–Barut(ELB)equation is used to determine the particle's world lines in the four-dimensional(4D)Minkowski space.Besides,the infinitesimal criterion,which is a differential equation in formal field theory,is reconstructed by an integro-differential form.The other difficulty is that fields and particles depend on heterogeneous manifolds.To overcome this challenge,we propose using a weak version of the ELB equation that allows us to connect local conservation laws and continuous symmetries in classical relativistic particle-field systems.By applying a weak ELB equation to classical relativistic particle-field systems,we can systematically derive local conservation laws by examining the underlying symmetries of the system.Our proposed approach provides a new perspective on understanding conservation laws in classical relativistic particle-field systems.

A Unified Definition of Electrostatic and Magnetic Fields

This article originates from the observation that field lines are drawn using distinctive rules in magnetic field and electrostatic fields. It aims at reconciliating the definitions of these fields and thus reaching a consensus on the interpretation of field lines. Our unified field definition combines three orthogonal vectors and a unique scalar value. Field lines are then defined as isovalue lines of the scalar value, rendering it simpler to interpret in both field types. Specific to our field definition is the use of square root of vector’s cross product so that all vectors have the same physical unit. This enhanced field definition also enables a more efficient calculation of Biot-Savart law. This article is the first of a series allowing the drawing of isovalue contour lines.

The Journey of SRS: An Initial Experience of Starting Sterotactic Radiosurgery Facility at Purbanchal Cancer Hospital—First in Nepal

Introduction: Radiotherapy (RT) is a vital cancer treatment modality for both curative and palliative purposes. Nepal is a developing country with a population of around 30 million people. Cancer affects 100 - 120 people out of every 100,000, and the figure is increasing. The number of radiation facility machines in the country is still countable in fingers. Purbanchal Cancer Hospital, Nepal is the first comprehensive cancer facility capable of performing stereotactic radiosurgery (SRS). Our facility has cutting-edge Varian Truebeam Linear Accelerators with millennium MLC, which makes SRS and SRT’S for intracranial lesions such as small benign and malignant tumors much easier. In addition to SRS, we are the pioneers of SBRT for lung using 4DCT, interstitial & intraluminal brachytherapy, RPM Gated & DIBH modalities in Nepal. Methods & Materials: The purpose of this study is to share our experience in establishing an SRS facility in the country, which includes training the RT team on the importance of process accuracy, patient selection, patient assessment, mould preparation, and describing image data acquisition, target, and organ at risk delineation on CT and MRI images, treatment planning process, and quality assurance. Results & Discussion: The plans for all SRS and SRT cases are based on target coverage, OAR sparing, hotspot inside the target, conformity index, heterogeneity index, and dose fall off. To select the final plan, we used strict passing criteria such as a conformity index Paddick (CIPaddick) more than 0.85, a falloff between 100% and 50% of less than 5.5 mm (maximum 6 mm in irregular targets), and a hotspot inside the target between 115 to 140 percent, as per clinical standards. In addition, we determined the CILomax and CIRTOG for each case. Passing criteria for verification plans are set as minimum of 95% for a 2% percentage dose difference (% DD) and a 2-mm distance to an agreement (DTA). We also gathered demographic data from patients treated in the first year, such as diagnosis, lesion size, dose fraction, heterogeneity index (HI), conformity index (CI) and gamma index. SRS/SRT treatment was successfully implemented, and over 40 patients were treated with positive clinical outcomes. Conclusion: SRS now has a wider range of alternatives, thanks to technology advancements in recent years. SRS’s dosimetric advantages have steadily been extended to extracranial locations. Purbanchal Cancer Hospital, Birtamode, Nepal established a comprehensive cancer facility with qualified workforce with the goal of providing high-quality treatment to the people of Nepal.

Stress field evolution law of mining environment reconstructing structure with change of filling height

For improving global stability of mining environment reconstructing structure,the stress field evolution law of the structure with the filling height change of low-grade backfill was studied by ADINA finite element analysis code.Three kinds of filling schemes were designed and calculated,in which the filling heights were 2,4,and 7 m,separately.The results show that there are some rules in the stress field with the increase of the filling height as follows:(1) the maximum value of tension stress of the roof decreases gradually,and stress conditions are improved gradually;(2) the tension stress status in the vertical pillar is transformed into the compressive stress status,and the carrying capacity is improved gradually;however,when the filling height is beyond 2.8 m,the carrying capacity of the vertical pillar grows very slowly,so,there is little significance to continue to fill the low-grade backfill;(3) the bottom pillar suffers the squeezing action from the vertical pillars at first and then the gravity action of the low-grade backfill,and the maximum value of tension stress of the bottom pillar firstly increases and then decreases.Considering the economic factor,security and other factors,the low-grade backfill has the most reasonable height(2.8 m) in the scope of all filling height.

A Self-Stabilized Field Theory of Neutrinos

In “A Self-linking Field Formalism” I establish a self-dual field structure with higher order self-induced symmetries that reinforce the first-order dynamics. The structure was derived from Gauss-linking integrals in R3 based on the Biot-Savart law and Ampere’s law applied to Heaviside’s equations, derived in strength-independent fashion in “Primordial Principle of Self-Interaction”. The derivation involves Geometric Calculus, topology, and field equations. My goal in this paper is to derive the simplest solution of a self-stabilized solitonic structure and discuss this model of a neutrino.