A BSDE approach to risk-based asset allocation of pension funds with regime switching

An asset allocation problem of a member of a defined contribution (DC) pension fund is discussed in a hidden, Markov regime-switching, economy using backward stochastic differential equations, (BSDEs). A risk-based approach is considered, where the member selects an optimal asset mix with a view to minimizing the risk described by a convex risk measure of his/her terminal wealth. Firstly, filtering theory is adopted to transform the hidden, Markov regime-switching, economy into one with complete observations and to develop, (robust), filters for the hidden Markov chain. Then the optimal asset allocation problem of the member is formulated as a two-person, zero-sum stochastic differential game between the member and the market in the economy with complete observations. The BSDE approach is then used to solve the game problem and to characterize the saddle point of the game problem. An explicit expression for the optimal asset mix is obtained in the case of a convex risk measure with quadratic penalty and it can be considered a generalized version of the Merton ratio. An explicit expression for the optimal strategy of the market is also obtained, which leads to a risk-neutral wealth dynamic and may provide some insights into asset pricing in the economy with inflation risk and regime-switching risk. Numerical examples are provided to illustrate financial implications of the BSDE solution.     

Applications of ICP-MS in marine analytical chemistry

Summary The versatility of ICP-MS in marine analytical chemistry is illustrated with applications to the multielement trace analysis of two recently released marine reference materials, the coastal seawater CASS-2 and the non-defatted lobster hepatopancreas tissue LUTS-1, and to the determination of tributyltin and dibutyltin in the harbour sediment reference material PACS-1 by HPLC-ICP-MS. Seawater analyses were performed after separation of the trace elements either by adsorption on immobilized 8-hydroxy-quinoline or by reductive coprecipitation with iron and palladium. Simultaneous determination of seven trace elements in LUTS-1, including mercury, by isotope dilution ICP-MS, was achieved after dissolution by microwave digestion with nitric acid and hydrogen peroxide. Butyltin species in PACS-1 were separated by cation exchange HPLC of an extract of the sediment; method detection limits for tributyltin and dibutyltin in sediment samples are estimated to be 5 ng Sn/g and 12 ng Sn/g, respectively.Summer assistant 1988Summer assistant 1989     

Synthesis of PbSeTe single ternary alloy and core/shell heterostructured nanocubes

We report a robust method for synthesis of monodisperse PbSeTe single ternary alloy and core/shell heterostructured nanocubes, respectively. The key synthetic strategy to produce such different classes of nanocubes is to precisely control the time of reaction and successive growth. The crystallinity, shape/size distributions, structural characteristics, and compositions of as-prepared nanocubes, both ternary alloy and core/shell, were carefully studied. A plausible growth mechanism for developing each type of lead chalcogenide nanocubes is proposed. These delicately designed PbSeTe nanoscale architectures offer tunable compositions in PbSeTe ternary alloy and nano-interfaces in core/shell nanocubes, which are the critical factors in controlling thermal conductivity for applications in thermoelectrics.     

Evaluation of extraction methods for quantification of aqueous fullerenes in urine

There is a growing concern about the human and environmental health effects of fullerenes (e.g., C(60)) due to their increasing application in research, medicine, and industry. Toxicological and pharmacokinetic research requires standard methods for extraction and detection of fullerenes from biological matrices such as urine. The present study validates the use of liquid-liquid extraction (LLE) and solid-phase extraction (SPE) methods in conjunction with liquid chromatography-mass spectrometry (LC-MS) for the quantitative determination of C(60) in human and synthetic urine as compared with ultrapure water. Glacial acetic acid, which is necessary to prevent emulsions during LLE, inhibited C(60) detection by LC-MS, but this could be mitigated with evaporation. Aqueous C(60) aggregates (nC(60)) were spiked at 180 μg/L into the components of a synthetic urine recipe to determine their individual impacts on extraction and detection. Urea, creatinine, and a complex protein (i.e., gelatin) were found to impair SPE, leading to a low recovery rate of 43 ± 4% for C(60) spiked into human urine. In contrast, C(60) was consistently recovered from synthetic matrices using LLE, and recovery in human urine was 80 ± 6%. These results suggest that LLE combined with LC-MS is suitable for studying the clearance of fullerenes from the body. LLE is a robust technique that holds promise for extracting C(60) from other complex biological matrices (e.g., blood, sweat, amniotic fluid) in toxicological studies, enabling a better understanding of the behavior of fullerenes in human and animal systems and facilitating a more comprehensive risk evaluation of fullerenes.     

A conjecture of Erd?s on graph Ramsey numbers

The Ramsey number r(G) of a graph G is the minimum N such that every red–blue coloring of the edges of the complete graph on N vertices contains a monochromatic copy of G. Determining or estimating these numbers is one of the central problems in combinatorics.One of the oldest results in Ramsey Theory, proved by Erd?s and Szekeres in 1935, asserts that the Ramsey number of the complete graph with m edges is at most . Motivated by this estimate Erd?s conjectured, more than a quarter century ago, that there is an absolute constant c such that for any graph G with m edges and no isolated vertices. In this short note we prove this conjecture.     

New procedure to generate multipliers in complex Neumann problem and effective Kohn algorithm

The purpose of this paper is threefold. (i) To explain the effective Kohn algorithm for multipliers in the complex Neumann problem and its difference with the full-real-radical Kohn algorithm, especially in the context of an example of Catlin-D’Angelo concerning the ineffectiveness of the latter. (ii) To extend the techniques of multiplier ideal sheaves for the complex Neumann problem to general systems of partial differential equations. (iii) To present a new procedure of generation of multipliers in the complex Neumann problem as a special case of the multiplier ideal sheaves techniques for general systems of partial differential equations.     

Infrared Spectroscopy of Size-Selected Hydrated Carbon Dioxide Radical Anions CO2.−(H2O)n (n=2–61) in the C−O Stretch Region

Understanding the intrinsic properties of the hydrated carbon dioxide radical anions CO₂^.−(H₂O)_n is relevant for electrochemical carbon dioxide functionalization. CO₂^.−(H₂O)_n (n=2–61) is investigated by using infrared action spectroscopy in the 1150–2220 cm⁻¹ region in an ICR (ion cyclotron resonance) cell cooled to T=80 K. The spectra show an absorption band around 1280 cm⁻¹, which is assigned to the symmetric C−O stretching vibration ν_s. It blueshifts with increasing cluster size, reaching the bulk value, within the experimental linewidth, for n=20. The antisymmetric C−O vibration ν_as is strongly coupled with the water bending mode ν₂, causing a broad feature at approximately 1650 cm⁻¹. For larger clusters, an additional broad and weak band appears above 1900 cm⁻¹ similar to bulk water, which is assigned to a combination band of water bending and libration modes. Quantum chemical calculations provide insight into the interaction of CO₂^.− with the hydrogen-bonding network.