Orders on Braid Groups

It is shown that the braid group IE1.gif" alt=" $$B\left( n \right)\left( {n \geqslant 3} \right)$$ " align="middle" border="0"> defies lattice ordering.     

Sheaves on Involutive Quantaloids

We extend the well-known notions of a singleton, complete IE1.gif" alt=" $$Q$$ " align="middle" border="0"> -set, presheaf and sheaf over a complete Heyting algebra or a right-sided idempotent quantale to arbitrary involutive quantaloids. We show that sheaves on IE2.gif" alt=" $$Q$$ " align="middle" border="0"> and complete IE3.gif" alt=" $$Q$$ " align="middle" border="0"> -sets come to the same thing. This paper can be considered as a symmetric version of an earlier work of the author.     

Optimal Ternary Linear Rate 1/2 Codes

In this paper, we classify all optimal linear[n, n/2] codes up to length 12. We show that thereis a unique optimal [10, 5, 5] code up to equivalence.     

On reinsurance and investment for large insurance portfolios

We consider a problem of optimal reinsurance and investment for an insurance company whose surplus is governed by a linear diffusion. The company’s risk (and simultaneously its potential profit) is reduced through reinsurance, while in addition the company invests its surplus in a financial market. Our main goal is to find an optimal reinsurance-investment policy which minimizes the probability of ruin. More specifically, in this paper we consider the case of proportional reinsurance, and investment in a Black-Scholes market with one risk-free asset (bond, or bank account) and one risky asset (stock). We apply stochastic control theory to solve this problem. It transpires that the qualitative nature of the solution depends significantly on the interplay between the exogenous parameters and the constraints that we impose on the investment, such as the presence or absence of shortselling and/or borrowing. In each case we solve the corresponding Hamilton-Jacobi-Bellman equation and find a closed-form expression for the minimal ruin probability as well as the optimal reinsurance-investment policy.     

Tail Dependence Comparison of Survival Marshall–Olkin Copulas

The multivariate tail dependence describes the amount of dependence in the upper-orthant tail or lower-orthant tail of a multivariate distribution and can be used in the study of dependence among extreme values. We derive an explicit expression of tail dependence of multivariate survival Marshall–Olkin copulas, and obtain a sufficient condition under which tail dependencies of two survival Marshall–Olkin copulas can be compared. Some examples are also presented to illustrate our results.      

内部激励源二自由度结构扬声器振动特性分析

有别于多数基于简单振子结构的扬声器,针对一类内部激励源二自由度(IE2DOF)结构的扬声器,用类比线路图法建立集总参数模型,计算分析了这种结构的频率响应,同时计算了其固有共振频率和固有反共振频率。使用叠加法分析内部激励源对频响的影响。最后实际测量和理论计算吻合,进一步支持了理论模型,揭示了IE2DOF结构扬声器的振动特性。     

Risk management of a bond portfolio using options

In this paper, we elaborate a formula for determining the optimal strike price for a bond put option, used to hedge a position in a bond. This strike price is optimal in the sense that it minimizes, for a given budget, either Value-at-Risk or Tail Value-at-Risk. Formulas are derived for both zero-coupon and coupon bonds, which can also be understood as a portfolio of bonds. These formulas are valid for any short rate model that implies an affine term structure model and in particular that implies a lognormal distribution of future zero-coupon bond prices. As an application, we focus on the Hull-White one-factor model, which is calibrated to a set of cap prices. We illustrate our procedure by hedging a Belgian government bond, and take into account the possibility of divergence between theoretical option prices and real option prices. This paper can be seen as an extension of the work of Ahn and co-workers [Ahn, D., Boudoukh, J., Richardson, M., Whitelaw, R., 1999. Optimal risk management using options. J. Financ. 54, 359-375], who consider the same problem for an investment in a share.     

On the riemann zeta-function and the divisor problem II

Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of IE1.gif" alt=" $$\left| {\zeta \left( {\frac{1}{2} + it} \right)} \right|$$ " align="middle" border="0"> . If E ^*(t)=E(t)-2πΔ^*(t/2π) with IE2.gif" alt=" $$\Delta *\left( x \right) + 2\Delta \left( {2x} \right) - \frac{1}{2}\Delta \left( {4x} \right)$$ " align="middle" border="0"> , then we obtain

Recent developments in synchrotron vacuum ultraviolet photoionization coupled to mass spectrometry

In recent years, increasing attention has been paid to “soft” photoionization (PI), which will potentially become a standard, universal ionization method. Tunable synchrotron vacuum ultraviolet (SVUV) light, a quasi-continuous light with good energy resolution and high photon flux, has proved an ideal source for “soft” PI in various research fields (e.g., combustion chemistry and molecular imaging).This review focuses on combinations of SVUV light with commonly used techniques (e.g., molecular-beam sampling, laser desorption, ion desorption, and thermal vaporization). These couplings have successful applications in flame chemistry, organic analysis, chemical imaging and aerosol mass spectrometry.     

Kubilius-Type Sequences of Additive Functions

We consider conditions under which the distributions of sequences of integer-valued nonnegative strongly additive functions can be approximated by the distributions of sums of independent random variables.__________Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 2, pp. 270–281, April–June, 2005.