The problem of the expected utility maximization in a reinsurance market for a single period model is well understood under a general setting.This paper studies the problem in a continuous time model.For reciprocal type of reinsurance strategies and exponential utility functions,with the concept of the Pareto optimality in game theory,we obtain the characterization of the core of cooperative reinsurance games and show that the core,which contains all of the Pareto optimal cooperative reinsurance strategies,is non-empty.Examples are provided to illustrate that the core is non-empty under the given situations and the Pareto optimal cooperative reinsurance strategy is shown to be a proportional reinsurance strategy when there are only two insurance companies considered.
> The influence of stochastic dispersion on an optical soliton communication system is investigated, and the method of reducing this influence is also given. The analysis shows that the existence-of stochastic dispersion results in the arrival time jitter, which is in proportion to the mean square fluctuation of the imaginary component of stochastic dispersion and is related to soliton amplitude and velocity. The influence of stochastic dispersion can be reduced by using filtering method in frequency domain.
A novel quasi-optical resonance system - modified axisymmetrical quasi-optical cavity of oblique rotation (MAQCOR) - is proposed. Using the Laplace integral transformation, the kinetic theory of the high relativistic electron cyclotron maser with MAQCOR is carried out within the framework of the linearized Vlasov-Maxwell equations. The formulas of beam-wave interaction power, starting current and frequency shift have been derived. Some important problem, such as high-order harmonic, modes competition, influence of the rotating angle and space-charge effect are analyzed and discussed in detail, and a series of new conclusions are obtained. A theoretical basis is laid for the design of this novel quasi-optical gyrotron.
> A double embedding model of inletting reinforcement grain and hollow matrix ball into the effective media of the particulate-reinforced composite is advanced. And with this model the distributions of thermal stress in different phases of the composite during cooling are studied. Various expressions for predicting elastic and elastoplastic thermal stresses are derived. It is found that the reinforcement suffers compressive hydrostatic stress and the hydrostatic stress in matrix zone is a tensile one when temperature decreases; when temperature further decreases, yield area in matrix forms; when the volume fraction of reinforcement is enlarged, compressive stress on grain and tensile hydrostatic stress in matrix zone decrease; the initial temperature difference of the interface of reinforcement and matrix yielding rises, while that for the matrix yielding overall decreases.
The solution of kinetic Alfven wave wider action of anomalous resistance has two branches: the slow wave, V-PV-A cos theta will be in a wave-broken state. Such traveling surge structure is a typical self-organization phenomenon and its wave form is determined by parameter beta which represents the magnitude of resistance. High beta leads to shock-like structure and low beta to the appearance of some solitary waves in front of the shock. According to the study on solitary wave, shock wave and traveling surge in conjunction with self-organization of nonlinear dynamics, a general definition of wave can be given.
> The area stability of CNN system is instigated and the existence of its periodic solution is given.
> A new fast ray tracing algorithm based on adaptive space subdivision is presented. Unlike the conventional octree and 3DDDA algorithms, the new algorithm subdivides the object space nonuniformly with the division planes coplanar with the boundary planes of bounding volumes of objects. At each recursive step, the concerned rectangular space is divided into two subcells. The partitioning direction and division plane is dynamically selected so that it has the least possibility to intersect the objects within and the difference of the number of objects enclosed in each subcell is small. An efficient traversal algorithm to search for the next node that the ray will enter is also designed. Theoretical analysis and experimental results show that the new algorithm is potential.
> Hayman’s conjecture has been completely proved: if f(z) is a transcendental meromorphic function in the plane, then ff’ assumes every finite non-zero complex value infinitely often. Furthermore, some related criteria have been deduced for normality of a family of meromorphic functions and results on the angular distribution have been given.
A generalized Aboronov-Bohm plus oscillator (ABO) system is worked out. The normalized wave functions and energy eigenvalues for the ABO system are obtained with the path integral method.
The concept of para-product operators over locally compact Vilenkin groups is established and the applications to the para-linearization in nonlinear problems are studied. This kind of operators plays a special role in dealing with those functions which do not have the classical derivatives.
By using magnetic sweeping method, the temperature and magnetic field dependencies of the experimental current density and the normalized relaxation rate have been obtained. The true critical current density corresponding to the zero activation energy has been carried out based on the collective-pinning and the thermally-activated flux motion models, and therefore the influences of the quantum tunneling effect and the thermal activation effect on the experimental critical current density are distinguished. It is found that, with temperature lower than 10 K, the relaxation rate will not drop to zero when T approaches zero K because of the occurrence of the flux quantum tunneling. This additional flux motion further reduces the experimental critical current density j making it saturated with lowering temperature.
The constraints arising from the quantum mechanical symmetry on wavefunctions, and the effect of the constraints on the structures and internal notions of quantum states are studied.
If the matrix measure of connection weight of Hopfield-type continuous feedback neural network is less than the reciprocal of maximal product of resistance and gain constants, then the network system is globally and exponentially stable. The above reciprocal is a sharp upper bound of matrix measure of connection weight which guarantees that the above conclusion holds. The above result answers partially the open problem proposed by Vidyasagar recently, i.e. whether neural network with ''nearly'' symmetric connection weight can exhibit limit cycles. The relation between the network time constant and the global exponential convergence rate is pointed out, and application to optimization computation of our results is also given.
> A statistical mechanics framework of fuzzy random polymer networks is established based on the theories of fuzzy systems. The entanglement effect is manifested quantitatively by introducing an entanglement tensor and membership function and the amorphous structure is treated as the fuzzy random network made up of macromolecular coils entangled randomly. A random tetrahedral entangled-crosslinked cell is chosen as an average representative unit of the fuzzy random polymer network structure. By making use of the theory of fuzzy probability and statistical mechanics, the expression for the free energy of deformation is given, which fits well with the experimental data on rubber elasticity under various deformation modes. Both classical statistical theory and Mooney-Rivlin equation can be taken as its special cases.
> The mechanism for bifurcation of elastic-plastic buckling of the semi-infinite cylindrical shell under impacting axial loads is proposed based on the theory of stress wave. Numerical results on three kinds of end supports and step and impulse loads are given.
> The final value problem for the classical coupled Klein-Gordon-Schrodinger equations is studied in . This leads to the construction of the modified wave operator Ω, for certain scattered data. When initial functions belong to (Ω) which denotes the range domain of Ω, the global existence and asymptotic behavior of solutions of Cauchy problem tor the coupled Klein-Gordon-Schrodinger equations are proved.
A trust region algorithm for equality constrained optimization is proposed, which is a nonmonotone one in a certain sense. The augmented Lagrangian function is used as a merit function. Under certain conditions, the global convergence theorems of the algorithm are proved.
Two forms of basic equations and 5 basic matrices in the matrix analysis of networks from nonlinear networks to linear networks are obtained and their origins in physics are correctly explained. Furthermore, the whole 12 general characteristic formulae of the 4 fundamental network elements as well as some important new results, which were not in the conventional theory, have;also been obtained during inference for both nonlinear and linear networks.
A new magnetopause model is proposed based on observation results, in which the magnetic field includes one constant component and one monotonically increasing component, so that magnetic field shear exists during the intervals when the interplanetary magnetic field has a northward component. Under this model, a completely analytical self-consistent equilibrium distribution function is derived based on the Vlasov-Maxwell equations. Through the analysis of this distribution function and its moments, the following on be concluded: (i) The equilibrium distribution function consists of a homogeneous Maxwellian distribution and two inhomogeneous shifted-Maxwellian distributions. There are ''hole'' and ''bump'' structures which have different cross-field drift velocities in the velocity distribution. (ii) The density decreases monotonously from the outside of the magnetopause to the inside. (iii) The electrical current distribution is a typical current sheet structure. (iv) Under a certain condition of temperature parameters, the thickness of the magnetopause may be larger than the ion gyroradius. These results are applicable to the region of the low-latitude magnetopause during the intervals when the interplanetary magnetic field has a northward component.
> A method of fabricating pure germanium dioxide hollow-core fibers has been introduced for the first time. The output power of the fabricated fiber can come to 18 W, with the transmission loss of 1.23 dB/m at 10.6 μm. The mechanism of transmitting CO2 laser by the fiber is analyzed, the transmitting loss is further discussed and its application fields are envisaged.
