A rigorous definition of semi-Markov dependent risk model is given. This model is a generalization of the Markov dependent risk model. A criterion and necessary conditions of semi- Markov dependent risk model are obtained. The results clarify relations between elements among semi-Markov dependent risk model more clear and are applicable for Markov dependent risk model.
The electronic structures,chemical bonding,elastic and optical properties of the ternary stannide phase Na2MgSn were investigated by using density-fimctional theory（DFT） within generalized gradient approximation（GGA）.The calculated energy band structures show that Na2MgSn is an indirect semiconductor material with a narrow band gap 0.126 eV.The density of state（DOS）and the partial density of state（PDOS） calculations show that the DOS near the Fermi level is mainly from the Na 2p,Mg 3p and Sn5 p states.Population analysis suggests that there are strongly bonded Mg-Sn honeycomb layers in Na2MgSn.Basic physical properties,such as lattice constant,bulk modulus,shear modulus,elastic constants c（ij） were calculated.The elastic modulus E and Poisson ratio v were also predicted.The results show that Na2MgSn is mechanically stable soft material and behaves in a brittle manner.Detailed analysis of all optical functions reveals that Na2MgSn is a better dielectric material,and reflectivity spectra show that Na2MgSn promise as good coating materials in the energy regions 6.24-10.49 eV.
Given a new Double-Markov risk model DM = （μ, Q, v, H; Y, Z） and Double-Markov risk process U = {U（t）, t 〉 0}. The ruin or survival problem is addressed. Equations which the survival probability satisfied and the formulas of calculating survival probability are obtained. Recursion formulas of calculating the survival probability and analytic expression of recursion items are obtained. The conclusions are expressed by Q matrix for a Markov chain and transition probabilities for another Markov Chain.
The electronic structures, chemical bonding and elastic properties of the Co2P-type structure phase ultra-incompressible Re2P （orthorhombic phase） were investigated by density-functional theory （DFT） within generalized gradient approximation （GGA）. The calculated energy band structures show that the orthorhombic structure phase Re2P is metallic material. The density of state （DOS） and the partial density of state （PDOS） calculations show that the DOS near the Fermi level is mainly from the Re-5d state. Population analysis suggests that the chemical bonding in Re2P has predominantly covalent character with mixed covalent-ionic character. Basic physical properties, such as lattice constant, bulk modulus, shear modulus, and elastic constants Cij, were calculated. The elastic modulus and Poisson ratio were also predicted. The results show that the Co2P-type structure phase Re2P is mechanically stable and behaves in a brittle manner.
Periodic dividend problem is a meaningful issue. Based on a compound binomial model with periodic dividend, we use a homogeneous, ergodic and irreducible discrete-time Markov chain to express the evolution from one period to the subsequent of the economic or the environmental and climatic conditions. We derive some properties about the model. A system of integral equations for the expectation and the r-th moment of discounted dividends until ruin time are obtained respectively. Moreover, by using of Contraction Mapping Principle, we solve the equation system and obtain the explicit expression.
The electronic structures,chemical bonding,elastic and optical properties of the novel hP24 phase WB3 were investigated by using density-functional theory(DFT) within generalized gradient approximation(GGA).The calculated energy band structures show that the hP24 phase WB3 is metallic material.The density of state(DOS) and the partial density of state(PDOS) calculations show that the DOS near the Fermi level is mainly from the W 5d and B 2p states.Population analysis suggests that the chemical bonding in hP24-WB3 has predominantly covalent characteristics with mixed covalent-ionic characteristics.Basic physical properties,such as lattice constant,bulk modulus,shear modulus and elastic constants Cij were calculated.The elastic modulus E and Poisson ratio υ were also predicted.The results show that hP24-WB3 phase is mechanically stable and behaves in a brittle manner.Detailed analysis of all optical functions reveals that WB3 is a better dielectric material,and reflectivity spectra show that WB3 can be promised as good coating material in the energy regions of 8.5-11.4 eV and 14.5-15.5 eV.
