A two-dimensional ruin problem on the positive quadrant

In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance company). Modeling the risk processes of the insurance companies by Cramér-Lundberg processes we obtain the Laplace transform in space of the probability that either of the insurance companies is ruined in finite time. Subsequently, for exponentially distributed claims, we derive an explicit analytical expression for this joint ruin probability by explicitly inverting this Laplace transform. We also provide a characterization of the Laplace transform of the joint ruin time.     

On the spacel P(β)

Let\(\{ \beta (n)\} _{n = 0}^\infty \) be a sequence of positive numbers and 1 ≤p < ∞. We consider the spacel ^P(β) of all power series\(f(z) = \sum\limits_{n = 0}^\infty {\hat f(n)z^n } \) such that\(\sum\limits_{n = 0}^\infty {|\hat f(n)|^p |\beta (n)|^p } \). We give a necessary and sufficient condition for a polynomial to be cyclic inl ^P(β) and a point to be bounded point evaluation onl ^P(β).     

New construction of special Lagrangian submanifolds in T^＊R^n equipped with the standard metric

A class of twisted special Lagrangian submanifolds in T~*R~n and a kind of austere submanifold from conormal bundle of minimal surface of R~3 are constructed.     

Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings

In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.     

四元Goethals码的对偶码

Abstract. The trace representation of the dual of quaternary Goethals code δ(m) is given . It isproved that the shortened code of δ(m) is cyclic and its generators are shown.     

加细函数正交性的一个判别准则

In this note, a criterion for orthonormality of refinable functions via characteristicpolynomial of a matrix is given.     

STABILITY OF A KIND OF COMPOUND BOUNDARY VALUE PROBLEM WITH RESPECT TO THE PERTURBATION OF BOUNDARY CURVE

In this paper, we discuss the stability of general compound boundary value prob-lems combining Riemann boundary value problem for an open arc and Hilbert bound-ary value problem for a unit circle with respect to the perturbation of boundary curve.     

ON SOLUTIONS TO SEMILINEAR INTEGRODIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper, using the theory of resolvent operators, Banach,s contraction prin-ciple and Schauder,s fixed point theorem, we study the existence of integral solutions to semilinear integrodifferential equations under nonlocal conditions in Banach space. An example is provided to illustrate the results obtained.     

THE POINCAR BIFURCATION IN CUBIC HAMILTONIAN SYSTEMS WITH HETEROCLINIC LOOP

In this paper, we investigate the Poincar bifurcation in cubic Hamiltonian systems with heteroclinic loop, under small general cubic perturbations. We prove that the system has at most two limit cycles and has at least two limit cycles, respectively.