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Gallium oxide (Ga2O3) is a new semiconductor material which has the advantage of ultrawide bandgap, high breakdown electric field, and large Baliga’s figure of merit (BFOM), so it is a promising candidate for the next-generation high-power devices including Schottky barrier diode (SBD). In this paper, the basic physical properties of Ga2O3 semiconductor have been analyzed. And the recent investigations on the Ga2O3-based SBD have been reviewed. Meanwhile, various methods for improving the performances including breakdown voltage and on-resistance have been summarized and compared. Finally, the prospect of Ga2O3-based SBD for power electronics application has been analyzed.

Photoelectron spectroscopy measurements and density functional theory calculations are combined to determine structures of Nb 2 n (n 3 8) clusters. A detailed comparison between observed and calculated electronic binding energies shows that the clusters have low-symmetry compact 3D structures and the lowest possible total spin, except for the three-and five-ato clusters which are in triplet states. We fin evidence for the coexistence of two isomers of Nb 2 8 under some experimental conditions. This approach shows great promise for structural characterization of small clusters.

The new main-chain benzoxazine copolymer oligomers with bulky hydrocarbon end groups are first designed and synthesized. In particular, the aliphatic diamine based copolymers owning low dielectric constants (<3) and ultralow dielectric losses (<0.005) under high frequencies, is suitable for applications in the field of high-frequency communications. Therefore, this work not only provides a facile and effective protocol to simultaneously obtain excellent high-frequency dielectric properties, and improved processing and thermal properties of benzoxazine resins, but also widens the scope of the design and synthesis of functional and high-performance thermosetting polymers.

We consider a portfolio optimization problem which is formulated as a stochastic control problem. Risky asset prices obey a logarithmic Brownian motion, and interest rates vary according to an ergodic Markov diffusion process. The goal is to choose optimal investment and consumption policies to maximize the infinite horizon expected discounted hyperbolic absolute risk aversion (HARA) utility of consumption. A dynamic programming principle is used to derive the dynamic programming equation (DPE). The subsolution-supersolution method is used to obtain existence of solutions of the DPE. The solutions are then used to derive the optimal investment and consumption policies. Introduction.In the classical Merton portfolio optimization problem, an investor dynamically allocates wealth between a risky and a riskless asset and chooses a consumption rate, with the goal of maximizing total expected discounted utility of consumption. For a hyperbolic absolute risk aversion (HARA) utility function the Merton problem has a simple explicit solution. See, for example, Fleming and Soner [16, Example 5.2]. In the Merton model, the interest rate r of the riskless asset is a constant and the risky asset price fluctuates randomly according to a logarithmic Brownian motion. However, in our real world, even for money in the bank, the interest rate may fluctuate from time to time. Therefore, in the present paper we assume that the "riskless" interest rate r t is an ergodic Markov diffusion process on the real line −∞ < r < ∞. A typical example is the Vasicek model, in which r t is of OrnsteinUhlenbeck type. In addition, the change of interest rate could be correlated with price fluctuation of the risky asset. A recent example is that the U.S. Federal Reserve has lowered the interest rate several times since 2000, due to the poor performance of the U.S. stock market. We also take this into account in this paper; see section 2. For the case where the change of interest rate is independent of the price change of the risky asset, similar problems were considered in [27,28].Another motivation for our work comes from models for optimal investment, production, and consumption, of a kind considered by Fleming and Stein [18]. This interpretation of our model will be explained at the end of section 2. See also Fleming and Pang [12].We use the dynamic programming method. The stochastic control problem we consider has state variables x t , r t , where x t is wealth. The controls are the fraction u t of wealth in the risky asset and c t = Ct xt , where C t is the consumption rate. The state

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Thoroughly revised for its second edition, this advanced textbook provides an introduction to the basic methods of computational physics, and an overview of progress in several areas of scientific computing by relying on free software available from CERN. The book begins by dealing with basic computational tools and routines, covering approximating functions, differential equations, spectral analysis, and matrix operations. Important concepts are illustrated by relevant examples at each stage. The author also discusses more advanced topics, such as molecular dynamics, modeling continuous systems, Monte Carlo methods, genetic algorithm and programming, and numerical renormalization. It includes many more exercises. This can be used as a textbook for either undergraduate or first-year graduate courses on computational physics or scientific computation. It will also be a useful reference for anyone involved in computational research.

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