RUIN PROBABILITY IN A SEMI-MARKOV RISK MODEL WITH CONSTANT INTEREST FORCE AND HEAVY-TAILED CLAIMS

In the present paper, we consider a kind of semi-Markov risk model （SMRM） with constant interest force and heavy-tailed claims~ in which the claim rates and sizes are conditionally independent, both fluctuating according to the state of the risk business. First, we derive a matrix integro-differential equation satisfied by the survival probabilities. Second, we analyze the asymptotic behaviors of ruin probabilities in a two-state SMRM with special claim amounts. It is shown that the asymptotic behaviors of ruin probabilities depend only on the state 2 with heavy-tailed claim amounts, not on the state 1 with exponential claim sizes.

Geometrical structures, vibrational frequencies, force constants and dissociation energies of isotopic water molecules (H_2O, HDO, D_2O, HTO, DTO, and T_2O) under dipole electric field

The dissociation limits of isotopic water molecules are derived for the ground state. The equilibrium geometries, the vibrational frequencies, the force constants and the dissociation energies for the ground states of all isotopic water molecules under the dipole electric fields from -0.05 a.u. to 0.05 a.u. are calculated using B3P86/6-311＋＋G（3df,3pf）. The results show that when the dipole electric fields change from -0.05 a.u. to 0.05 a.u., the bond length of H-O increases whereas the bond angle of H-O H decreases because of the charge transfer induced by the applied dipole electric field. The vibrational frequencies and the force constants of isotopic water molecules change under the influence of the strong external torque. The dissociation energies increase when the dipole electric fields change from -0.05 a.u. to 0.05 a.u. and the increased dissociation energies are in the order of H2O, HDO, HTO, D2O, DTO, and T2O under the same external electric fields.

Skeleton Vibrations and Force Constants of ［Fe_2Cr（μ_3－O）（glycine）_6（H_2O）_3］（NO_3）_7．3H_2O

The iR and Raman spectra were rrieasured for[Fe_2Cr(μ_3-O)-(glycine)_6 (H_2O)_3] (NO_3)_7. 3H2O in the range of 2000～90 cm￣-1. The assignment of the main skeleton vibrations was made in comparison with related compounds. A simplified model as well as a simplified general valence force field was used in the normal coordinate analysis of the skeleton and a set of force constants has been obtained. The calculated frequencies agree well with the observed ones, with a mean deviation of 1.8% which confirms the assignn: ient of their vibrational spectra. On the basis of the data obtained some discussions were made.

A Simple Approach to Compute Interatomic Force Constant for Mono and Diatomic Semiconductors

In this paper, a mathematical relation was found between interatomic Hooke’s force constant and both the bulk modulus and interatomic distance in solid crystals, considering that the forces which have effect on an atom are only those resulted from the neighboring atoms, and the forces are subject to Hooke’s law as the deflections of atoms from their equilibrium positions are very small. This work has been applied on some solid semiconducting crystals of diatomic primitive cell, including crystals of mono-atomic primitive cell automatically, by using linear statistical fitting with computer programming and, then, using mathematical analysis, proceeding from the vibrational dispersion relation of solid linear lattice, these two methods have been used in the process in order to support each other and for the result to be satisfying and reasonable. This is a contribution to the process of using computer programming in physics to facilitate mathematical analyses and obtain the required relations and functions by designing and developing appropriate computer programs in line with the macro and micro natures of materials. The importance of this is in enhancing our understanding of the interatomic actions in cells and of the crystal structure of materials in general and semiconductors in particular, as it is a step of the initial steps to facilitate the process of calculating energies and extracting mathematical relations between correlation energy and temperature as well as between sub-fusion and fusion energies with temperature.

Tribological Characteristic of Diamond-like Carbon Films Investigated by Lateral Force Microscope

Tribological characteristic of different thick diamond-like carbon (DLC) films was studied. A geometrical method was applied to calibrate the cantilever spring constant and to calculate the normal and lateral forces, respectively. Experimental results show that the lateral force under different applied loads is proportional to the normal force for the DLC films with the thickness of 153.4nm and 64.9nm. However, for the thickness of 4.48nm and 2.78nm DLC films, lateral force is nonlinear to normal force, which is opposed to the Amonton's law.The single asperity regime and the DMT model were put forward to predict the possible nanotribological mechanism between the probe and DLC film.

On the Definition of Propellant Force

Comments are given on the various physical definitions of the force constant of propellant. As there are more or less defects in these definitions, two new definitions are presented to reflect the physical essence of propellant force more perfectly and could well compatible with the mathematical expression.

REGULARITY OF VIBRATION RESPONSE OF MECHANICAL SYSTEM UNDER AFFECT OF VARI-FREQUENCY EXCITING FORCE

The vibration response formulas of the mechanical system under the affect of thevari-frequency exciting force are deduced. It is proved by the theoretical analysis and experimentalresults that the vibration response amplitude of the mechanical system under the affect of thevari-frequency exciting force is far smaller than that under the affect of the constant frequency exciting force on condition that the exciting force amplitudes are just the same;while the vari-fre-quency rate a increases to 5 Hz per second the vibration amplitude will decrease to 10% only as lowas that under the affect of the constant frequency exciting force. All these conclusions will be of significance for revealing the mechanism of suppressing chatter in van-speed cutting and analyzing theexperimental results of sine-wave scanning exciting test.

Research on Suspension Gravity Compensation System of Lunar Rover with Magnetic Levitation Servo

In order to overcome the shortcomings of the traditional sling suspension method,such as complex structure of suspension truss,large running resistance,and low precision of position servo system,a gravity compensation method of lunar rover based on the combination of active suspension and active position following of magnetic levitation is proposed,and the overall design is carried out.The dynamic model of the suspension module of microgravity compensation system was established,and the decoupling control between the constant force component and the position servo component was analyzed and verified.The constant tension control was achieved by using hybrid force/position control.The position following control was realized by using fuzzy adaptive PID(proportional⁃integral⁃differential)control.The stable suspension control was realized based on the principle of force balance.The simulation results show that the compensation accuracy of constant tension could reach more than 95%,the position deviation was less than 5 mm,the position deviation angle was less than 0.025°,and the air gap recovered stability within 0.1 s.The gravity compensation system has excellent dynamic performance and can meet the requirements of microgravity simulation experiment of lunar rover.

Proportion Integration Differentiation(PID)Control Strategy of Belt Sander Based on Fuzzy Algorithm

Aiming at solving the problems of response lag and lack of precision and stability in constant grinding force control of industrial robot belts,a constant force control strategy combining fuzzy control and proportion integration differentiation(PID)was proposed by analyzing the signal transmission process and the dynamic characteristics of the grinding mechanism.The simulation results showed that compared with the classical PID control strategy,the system adjustment time was shortened by 98.7%,the overshoot was reduced by 5.1%,and the control error was 0.2%-0.5%when the system was stabilized.The optimized fuzzy control system had fast adjustment speeds,precise force control and stability.The experimental analysis of the surface morphology of the machined blade was carried out by the industrial robot abrasive grinding mechanism,and the correctness of the theoretical analysis and the effectiveness of the control strategy were verified.

A UNIVERSAL ANALYTIC POTENTIAL-ENERGY FUNCTION BASED ON A PHASE FACTOR

Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.

The Finite-time Ruin Probability for the Jump-Diffusion Model with Constant Interest Force

In this paper, we consider the finite time ruin probability for the jump-diffusion Poisson process. Under the assurnptions that the claimsizes are subexponentially distributed and that the interest force is constant, we obtain an asymptotic formula for the finite-time ruin probability. The results we obtain extends the corresponding results of Kliippelberg and Stadtmüller and Tang.

New Method on Constructing Analytic Potential Function of Diatomic Molecules

A new method on constructing analytical potential energy functions is presented, and then a relatively universal analytical potential energy function for precisely calculating the spectra of ＇iatomic molecules and ions is derived. Furthermore, six kinds of common potential energy curves containing three main potential curves i,e. steady state, metastable state and repulsive state are obtained from this potential energy function. Finally, spectroscopic parameters of thirteen diatomic molecules and ions including BeD-X^2∑＋, BeT-X^2∑^＋ and Na2-X^1∑g^＋ etc are calculated by using the potential function, as a consequence, all calculation results are in good agreement with experimental data.

Statistical mechanics of a nonequilibrium steady-state classical particle system driven by a constant external force

A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time.In this work,the statistical mechanics of such a system is derived solely based on the equiprobability and ergodicity principles,free from any conclusions drawn on equilibrium statistical mechanics or local equilibrium hypothesis.The momentum space distribution is determined by a random walk argument,and the position space distribution is determined by employing the equiprobability and ergodicity principles.The expressions for energy,entropy,free energy,and pressures are then deduced,and the relation among external force,drift velocity,and temperature is also established.Moreover,the relaxation towards its equilibrium is found to be an exponentially decaying process obeying the minimum entropy production theorem.

Phonon dispersion relations of crystalline solids based on LAMMPS package

The phonon dispersion relations of crystalline solids play an important role in determining the mechanical and thermal properties of materials.The phonon dispersion relation,as well as the vibrational density of states,is also often used as an indicator of variation of lattice thermal conductivity with the external stress,defects,etc.In this study,a simple and fast tool is proposed to acquire the phonon dispersion relation of crystalline solids based on the LAMMPS package.The theoretical details for the calculation of the phonon dispersion relation are derived mathematically and the computational flow chart is present.The tool is first used to calculate the phonon dispersion relation of graphene with two atoms in the unit cell.Then,the phonon dispersions corresponding to several potentials or force fields,which are commonly used in the LAMMPS package to modeling the graphene,are obtained to compare with that from the DFT calculation.They are further extended to evaluate the accuracy of the used potentials before the molecular dynamics simulation.The tool is also used to calculate the phonon dispersion relation of superlattice structures that contains more than one hundred of atoms in the unit cell,which predicts the phonon band gaps along the cross-plane direction.Since the phonon dispersion relation plays an important role in the physical properties of condensed matter,the proposed tool for the calculation of the phonon dispersion relation is of great significance for predicting and explaining the mechanical and thermal properties of crystalline solids.

Precise calculations on spectroscopic parameters of diatomic molecules using a novel potential energy function

A novel scheme for potential energy functions of diatomic molecules is derived using a function with phase factors. Six kinds of potential curves of common shapes are obtained by adjusting the phase factors. Spectroscopic parameters of the ground states for ten kinds of molecules are calculated using the potential energy functions. The results agree well with experimental data.

A universal potential energy function and precise calculations on the molecular spectra

By using a function with a phase factor,a universal analytic potential energy function applied to the interactions between diatoms or molecules is derived and six kinds of potential curves of common shapes are obtained by adjusting the phase factor.The spectroscopic parameters of ten diatomic molecules are calculated by using the potential energy function;as a consequence,all calculation results are in good agreement with experimental data.

A new method to evaluate force constants from experimental spectral data

An iterative procedure is proposed to facilitate the determination of molecular vi-brational force constants from the experimental fundamental frequencies. Proper restrictions are introduced to the force constants based on physical considerations for getting reasonable results. The experimental data of Coriolis coupling coefficients and isotopic frequency shifts are utilized to reduce the uncertainty of the calculated force constants when they are available. A series of various kinds of molecules have been calculated by this method and the results are satisfactory.

Study on Infrared Spectra and Chemical Bonding of the Cluster Anion[Cl_2FeS_2MoS_2Cu(PPh_3)_2]￣-

The Fourier transform infrared spectra of the cluster anion[Cl2Fe2S2MoS2Cu(PPh3)2]- are measured between 550 and 90 cm(-1).The empirical assignments have been made for the vibration bands of main valence bonds.In order to verify the assignments of the bands and obtain the force constants the approximate normal coordinate analysis for the title anion has been carried out.It is found that the calculated frequencies are in good agreement with the observed ones.While Quantum-Chemical calculation is used to elucidate the chemical bonding characteristics for the title anion.

Why Static O-H Bond Parameters Cannot Characterize the Free Radical Scavenging Activity of Phenolic Antioxidants: ab initio Study

The static O-H bond parameters including O-H bond length, O-H charge difference, O-H Mulliken population and O-H bond stretching force constant (k) for 17 phenols were calculated by ab initio method HF/6-31G**. In combination with the O-H bond dissociation enthalpies (BDE) of the phenols determined by experiment, it was found that there were poor correlationships between the static O-H bond parameters and O-H BDE. Considering the good correlationship bt tween O-H BDE and logarithm of free radical scavenging rate constant for phenolic antioxidant, it is reasonable to believe that the ineffectiveness of static O-H bond parameters in characterizing antioxidant activity arises from the fact that they cannot measure the O-H BDE.

Elaborating strengthen mechanism of Pt-Ir solid solution superalloy at finite temperature

Pt-Ir alloy is potential superalloys used above 1300℃because of their high strength and creep resistance.However,the ductility of Pt-Ir alloy has rapidly deteriorated with the increase of Ir,resulting in poor machinability.This work quantitatively evaluated the solid solution strengthening(SSS)and grain refinement strengthening(GRS)of Pt-Ir alloy using first-principles calculations combined with experimental characterization.Here,the stretching force constants in the second nearest neighbor region(SFC^(2nd))of pure Ir(193.7 eV·nm^(-2))are 3.40 times that of pure Pt(57.0 eV·nm^(-2)),i.e.,the interatomic interaction is greatly enhanced with the increase of Ir content,which leads to the decrease of ductility,and modulus misfit plays a dominant role in SSS.Then,the physical mechanisms responsible for the hardness(H_(V))of Pt-Ir alloy,using the power-law-scaled function of electron work function coupled SSS and GRS,are attributed to the electron redistribution caused by different Ir content.Furthermore,a thorough assessment of the thermodynamic characteristics of Pt-Ir binary alloy was conducted,culminating in development of a mapping model that effectively relates enmposition,temperature and strength.The results revealed that the compressive strength incrcases with the Ir content,and the highest strength was observed in Pt_(0.25)Ir_(0.75).This study provides valuable insights into the Pt-Ir alloy system.