The definition of the environment factor of Weibull series system is given. The point and interval estimations of the environment factor are derived when the lifetimes of units are exponential or Weibull distributions. The precision of the proposed confidence interval is studied by simulation. The simulation results show that the proposed procedure is satisfactory.

In this paper, the pricing problems of Bala options are studied under the nonlinear Black-Scholes model. Firstly, the partial differential equations for the Bala options are transformed into a series of parabolic equations with constant coefficients by the perturbation method of doubleparameter. Secondly, the approximate pricing formulae of the Bala options are given by solving those parabolic equations with constant coefficients. Finally, the error estimates of the approximate solutions are given by using Green function.

Several European options pricing of domestic currency, with the stochastic differential equations of the stock price of foreign currency which is jump-diffusion process and of the foreign exchange, are obtained by martingale pricing method. Under the risk-neutral hypothesis, the factors affecting the foreign exchange rate and the price of the stocks are correlative.

The paper introduces and solves the hedging problems of non-tradable assets. Based on financial market practice, the non-tradable assets hedging model is constructed. Three meanvariance and quadratic hedging objectives are introduced on jump-diffusion model. The optimal hedging strategies, which are formulated by observable variables in backward form are given by an auxiliary process and Hilbert projection theorem. Finally the effectivity of the hedging strategies is tested via Monte Carlo.

In this paper, the pricing problems of geometric average Asian options are studied under the nonlinear Black-Scholes model. Firstly, the partial differential equations for the Asian options are transformed into a series of parabolic equations with constant coefficients by the perturbation method of single-parameter. Secondly, the approximate pricing formulae of the geometric average Asian options are given by solving those parabolic equations with constant coefficients. Finally, the error estimates of the approximate solutions are given by using Green function.

A new approach to model the M/M/1 queue with multiple working vacations is provided. By the GI/M/1 type Markov process and matrix analytic method, the explicit expression for the stationary queue length distribution is given firstly. Furthermore, the probability of the exact number of vacations that the sever has taken is also obtained. The more accurate descriptions for the status of the server are new results for the queue model.

This paper is concerned with the stochastic generalized Nash equilibrium problem. A variational inequality form reformulation for SGNEP is proposed. Then by employing the expected residual minimization method, a new model is obtained to solve this problem. Finally, by using quasiMonte Carlo method, this model can be solved.

In this paper, a class of nonsmooth multi-objective programming problems is studied. By using generalized Farkas lemma and scalarization of multi-objective function, the optimality conditions of cone weakly efficient solution are given for the problem of minimizing a multi-objective function, where the multi-objective function is the sum of a differentiable multi-objective function and a cone convex multi-objective function, subject to a set of differentiable nonlinear functions with a controlled cone on a convex subset of a finite dimensional Euclidean space, under the conditions similar to the Abadie constraint qualification.

Let $G=(V(G), E(G))$ be a simple connected graph with vertex $V(G)$ and edge set $E(G)$. Two graphs are said to be Laplacian cospectral if they have the same Laplacian spectrum. In this paper, two kinds of bicyclic graphs $Q(n; n_{1}, n_2, \cdots , n_t)$ and $B(n; n_{1}, n_{2})$ are defined. It is proved that graphs $Q(n; n_{1})$, $Q(n; n_{1}, n_{2})$, $Q(n; n_{1}, n_{2}, n_{3})$, and $B(n; n_{1}, n_{2})$ are determined by their Laplacian spectra.

A class of graphs constructed by $H$ and $K_s$ was studied, where $H$ is a bipartite graph of order $n$ and $K_s$ is the complete graph of order $s$. It was shown that a sharp upper bound of the least signless Laplacian eigenvalue (the least $Q$-eigenvalue) is $s$. Based on this, for any given positive integer $s$ and positive even number $n$, a class of graphs of order $n+s$ was constructed which have eigenvalue $s$ as their least $Q$-eigenvalue. Also, for any given smallest degree $\delta$ and order $n$ such that $2\leq\delta\leq\frac{n-1}{2}$, a class of graphs of order $n$ was constructed which have eigenvalue $\delta-1$ as their least $Q$-eigenvalue.

This paper defines chain and $\mathbf{R}$-circle on quaternionic hyperbolic space, and gives the property of chains under the vertical projection. The uniqueness of chain passing through two distinct points and qc-horizontality of $\mathbf{R}$-circles are proved, and the relationship between $\mathbf{R}$-circle and pure imaginary $\mathbf{R}$-circle is given.

A class of fractional nonlinear disturbed thermal wave equation is considered. Firstly, the solution of typical fractional disturbed thermal wave equation is obtained. Then the arbitrary order approximate analytic solutions for fractional generalized nonlinear disturbed thermal wave equation initial boundary value problem are constructed by using the method of functional analysis mapping. The physical sense of solution is stated simply. The approximate analysis solution makes up for the deficiency of the simple numerical simulation solution.

Inspired by the ideas of Hoffmann-Ostenhof and Laptev, a class of Hardy-type inequalities with homogeneous weight are given. Using the one-dimensional Hardy-type inequality which has been obtained by Avkhadiev and Wirths, a class of weighted Hardy-type inequalities with remainder term are proved. The results obtained generalize the results of Hoffmann-Ostenhof and Laptev to the weighted and with the remainder term case.

The paper mainly studies the complementary basic matrices in $\mathbb{S}$. It first introduces the concepts of the intrinsic products and proves the Laplace's Theorem in $\mathbb{S}$. Accordingly, the determinants of CB-matrices are the same and for any nonzero term in the determinant of one CB-matrix, there exists an equal term in the determinant of the other CB-matrix and vice versa. By the same time, for a given permutation which determines the nonzero term of the determinant of one CB-matrix, a method is given to find a permutation who determines the same nonzero term in the determinant of the other CB-matrix.