Portfolio optimization in stochastic markets

We consider a multiperiod mean-variance model where the model parameters change according to a stochastic market. The mean vector and covariance matrix of the random returns of risky assets all depend on the state of the market during any period where the market process is assumed to follow a Markov chain. Dynamic programming is used to solve an auxiliary problem which, in turn, gives the efficient frontier of the mean-variance formulation. An explicit expression is obtained for the efficient frontier and an illustrative example is given to demonstrate the application of the procedure.     

Instability analysis of semiconductor injection lasers with saturable absorption and self-sustained pulsations on the centre manifold

The small-signal analysis of a simple model of three rate equations is performed rigorously by means of both the Routh-Hurwitz theorem and Descartes' sign rule, and the relationship between bistable behaviour and self-sustained pulsations (SSPs) is investigated. Because one eigenvalue of the Jacobian of the model system is always negative, small-amplitude, sinusoidal SSPs can be described in terms of Haken's dressed-mode variables on a two-dimensional centre manifold. Possible simplifications for the switching modelling are also mentioned.     

Exact and approximate results for the Anderson impurity model

This paper provides exact and rigorous upper and lower bounds to the ground state energy of the Single Impurity Anderson Model in the limit of infiniteU. The upper bound approximates the ground state energy very well and the corresponding state may be used as a starting point for further investigations. The energy spectrum of the Single Impurity Anderson Model is calculated exactly for a special non-trivial model density of states describing the bare band electrons. All approaches introduced here are compared to this exact result and to other ground state energy calculations.     

Empirical minimization

We investigate the behavior of the empirical minimization algorithm using various methods. We first analyze it by comparing the empirical, random, structure and the original one on the class, either in an additive sense, via the uniform law of large numbers, or in a multiplicative sense, using isomorphic coordinate projections. We then show that a direct analysis of the empirical minimization algorithm yields a significantly better bound, and that the estimates we obtain are essentially sharp. The method of proof we use is based on Talagrand's concentration inequality for empirical processes. Research partially supported by NSF under award DMS-0434393. Research partially supported by the Australian Research Council Discovery Porject DP0343616.     

On the Erlang Loss Model with Time Dependent Input

We consider the M(t)/M(t)/m/m queue, where the arrival rate λ(t) and service rate μ(t) are arbitrary (smooth) functions of time. Letting p_n(t) be the probability that n servers are occupied at time t (0≤ n≤ m, t > 0), we study this distribution asymptotically, for m→∞ with a comparably large arrival rate λ(t) = O(m) (with μ(t) = O(1)). We use singular perturbation techniques to solve the forward equation for p_n(t) asymptotically. Particular attention is paid to computing the mean number of occupied servers and the blocking probability p_m(t). The analysis involves several different space-time ranges, as well as different initial conditions (we assume that at t = 0 exactly n₀ servers are occupied, 0≤ n₀≤ m). Numerical studies back up the asymptotic analysis. AMS subject classification: 60K25,34E10 Supported in part by NSF grants DMS-99-71656 and DMS-02-02815     

Determination of the rate of nonradiative relaxation,processes on excitation of electronic states in YAG:Nd3+

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 2, pp. 229–233, February, 1991.     

Long-Term Changes in a Heat Exchanger Steel

The steel ASTM A213 P22 is used for superheater outlet header in power plants. During duty cycles lasting over tens of years the temperature is of the order of 545°C and the pressure 125 atm. The microscopic changes in these steels are hard to analyze under working conditions, but they are believed to be responsible for the appearance of creeps in such devices. Investigation of the microscopic modifications will help to predict future failures due to creeps, increasing the reliability and saving a lot of money.We report the investigation of such changes in ASTM A213 P22 steel in use for 30 years as a Superheater header at Haifa power station. The analysis has been carried out using Mössbauer Spectroscopy, X-ray diffraction and optical microscopy. As a result it seems that the morphology and phase change of the carbide phases M₃C/M₇C₃ and M₂₃C₆ are the most prominent changes leading to the material failures.