Indifference pricing for CRRA utilities

We study utility indifference pricing of claim streams with intertemporal consumption and constant relative risk aversion utilities. We derive explicit formulas for the derivatives of the utility indifference price with respect to claims and wealth. The elegant structure of these formulas is a reflection of surprising algebraic identities for the derivatives of the optimal consumption stream. Namely, the partial derivative of the optimal consumption stream with respect to the endowment is always a projection. Furthermore, it is an orthogonal projection with respect to a natural “economic inner product”. These algebraic identities generate cancellations between the terms entering derivatives of the indifference price and allow us to prove sharp global bounds for the indifference price that become exact when the claims to wealth ratio is large and risk aversion is between one and two. For general risk aversion, we show that, in the large claims to wealth ratio limit, the asymptotic expansion of the indifference price is given in terms of fractional powers of the wealth, depending on risk aversion. When risk aversion is equal to one, the fractional power depends on the underlying claim.     

Intermediates and transport phenomena in two‐temperature synthesis of ZnGeP2

High quality semiconducting ternary compound ZnGeP₂ was synthesized by a modified two‐temperature technique using high purity elemental zinc, germanium and phosphorus as the starting materials. Transport phenomena of zinc and phosphorus vapors and the major reaction intermediates, taking place in ZnGeP₂ formation, were studied by interrupting the synthesis process using quenching technique as well as by adjusting the temperatures of cold and hot zones. The powder X‐ray diffraction analysis showed that the major reaction intermediates were ZnP₂, Zn₃P₂, and GeP, which proportions were changed at the different temperature stages. ZnP₂ was formed in the temperature gradient region and ZnGeP₂ was formed in the hot zone when the temperature of the hot zone was higher than 900 °C. The 520‐1040 °C temperature profile was chosen for the ZnGeP₂ synthesis and charge amount per run reached 200 g. The powder X‐ray diffraction pattern of the synthesized ZnGeP₂ compound was in agreement with the standard pattern of ZnGeP₂. These results demonstrated that the synthesized ZnGeP₂ compound was a single phase. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Expression, High Cell Density Culture and Purification of Recombinant EC-SOD in Escherichia coli

Superoxide dismutase (SOD) catalyzes the dismutation of the biologically toxic superoxide anion into oxygen and hydrogen peroxide and is deployed by the immune system to kill invading microorganisms. Extracellular SOD (EC-SOD) is a copper- and zinc-containing glycoprotein found predominantly in the soluble extracellular compartment that consists of ～30-kDa subunits. Here, we purified recombinant EC-SOD3 (rEC-SOD) from Escherichia coli BL21(DE3) expressing a pET-SOD3-1 construct. Cells were cultured by high-density fed-batch fermentation to a final OD₆₀₀ of 51.8, yielding a final dry cell weight of 17.6 g/L. rEC-SOD, which was expressed as an inclusion body, comprised 48.7% of total protein. rEC-SOD was refolded by a simple dilution refolding method and purified by cation-exchange and reverse-phase chromatography. The highly purified rEC-SOD thus obtained was a mixture of monomers and dimers, both of which were active. The molecular weights of monomeric and dimeric rEC-SOD were 25,255 and 50,514 Da, respectively. The purified rEC-SOD had 4.3 EU/mg of endotoxin and the solubility of rEC-SOD was more than 80% between pH 7 and 10. In 2 L of fed-batch fermentation, 60 mg of EC-SOD (99.9% purity) could be produced and total activity was 330.24 U. The process established in this report, involving high-cell-density fermentation, simple dilution refolding, and purification with ion-exchange and reverse-phase chromatography, represents a commercially viable process for producing rEC-SOD.     

New fluorescent sensor for antimony and transition metal cations based on rhodamine amide-arm homotrioxacalix[3]arene

A new fluorescent sensor 1 based on the rhodamine amide-armed homotrioxacalix[3]arene was synthesized, and its sensing behavior toward metal ions was investigated by UV–vis and fluorescence spectroscopies. Upon the addition of metal cations (Sb³⁺, Fe³⁺, Ni²⁺), a significant fluorescent enhancement in the range of 500–600 nm and colorimetric change was observed.     

Comparison of particle-in-cell simulations with experimentally observed frequency shifts between ions of the same mass-to-charge in fourier transform ion cyclotron resonance mass spectrometry

It has been previously observed that the measured frequency of ions in a Fourier transform mass spectrometry experiment depend upon the number of trapped ions, even for populations consisting exclusively of a single mass-to-charge. Since ions of the same mass-to-charge are thought not to exert a space-charge effect among themselves, the experimental observation of such frequency shifts raises questions about their origin. To determine the source of such experimentally observed frequency shifts, multiparticle ion trajectory simulations have been conducted on monoisotopic populations of Cs⁺ ranging from 10² ions to 10⁶ ions. A close match to experimental behavior is observed. By probing the effect of ion number and orbital radius on the shift in the cyclotron frequency, it is shown that for a monoisotopic population of ions, the frequency shift is caused by the interaction of ions with their image-charge. The addition of ions of a second mass-to-charge to the simulation allows the comparison of the magnitude of the frequency shift resulting from space-charge (ion-ion) effects versus ion interactions with their image charge.     

Characterization of cryoinjury-induced infarction with manganese-and gadolinium-enhanced MRI and optical spectroscopy in pig hearts

Purpose

To investigate progression of cryoinjury in pigs using contrast-enhanced magnetic resonance imaging (MRI) as well as optical spectroscopy and imaging.

Methods

Cryoinjury was produced in 16 pigs in vivo and investigated using Gd-and Mn-enhanced MRI, optical imaging/spectroscopy and histology in acute and chronic setting up to 4 weeks after the injury.

Results

(1) Acute cryoinjury resulted in formation of a lesion with a severely reduced rate of sub-epicardial indocyanine green (intravascular optical flow tracer) passage. In vivo late Gd-enhanced MRI showed a ∼10 mm deep hypointense area that was surrounded by a hyperintense rim while ex vivo Mn-enhanced MRI (MEMRI) detected a homogenous hypointense zone. Histological and spectroscopic examination revealed embolic erythrocytes blockages within the cryolesion with a thin necrotic rim neighboring the normal myocardium. (2) Chronic 4-week cryoinjury was characterized by uniform Gd-enhancement, whereas MEMRI revealed reduced Mn²⁺enhancement. Histological examination showed replacement of the cryoinjured myocardium by scar tissue.

Conclusions

Acute cryoinjury resulted in formation of a no-reflow core embolized by erythrocytes and surrounded by a rim of necrotic tissue. Upon injury progression, the no-reflow zone shrunk and was completely replaced with scar tissue by 4 weeks after injury.     

Switching Phenomena in a System with No Switches

It is widely believed that switching phenomena require switches, but this is actually not true. For an intriguing variety of switching phenomena in nature, the underlying complex system abruptly changes from one state to another in a highly discontinuous fashion. For example, financial market fluctuations are characterized by many abrupt switchings creating increasing trends (“bubble formation”) and decreasing trends (“financial collapse”). Such switching occurs on time scales ranging from macroscopic bubbles persisting for hundreds of days to microscopic bubbles persisting only for a few seconds. We analyze a database containing 13,991,275 German DAX Future transactions recorded with a time resolution of 10 msec. For comparison, a database providing 2,592,531 of all S&P500 daily closing prices is used. We ask whether these ubiquitous switching phenomena have quantifiable features independent of the time horizon studied. We find striking scale-free behavior of the volatility after each switching occurs. We interpret our findings as being consistent with time-dependent collective behavior of financial market participants. We test the possible universality of our result by performing a parallel analysis of fluctuations in transaction volume and time intervals between trades. We show that these financial market switching processes have properties similar to those of phase transitions. We suggest that the well-known catastrophic bubbles that occur on large time scales—such as the most recent financial crisis—are no outliers but single dramatic representatives caused by the switching between upward and downward trends on time scales varying over nine orders of magnitude from very large (≈10² days) down to very small (≈10 ms).     

Rapid discrimination of archaeal tetraether lipid cores by liquid chromatography-tandem mass spectrometry

Atmospheric pressure chemical ionization liquid chromatography-tandem mass spectrometry (APCI LC-MS/MS) of tetraether lipid cores of archaeal origin reveals distinct dissociation pathways for three classes of core lipid extracted from Methanobacter thermautotrophicus. Within these classes, two isobaric tetraether lipids, one a scarcely reported lipid constituent of M. thermautotrophicus and the other an artefact formed during extraction from cultured cells, were identified and distinguished via their MS(2) spectra. APCI LC-MS/MS discriminates different tetraether core lipid types and isobaric species and reveals the mass of the constituent biphytanyl chains within the tetraether cores, albeit without full elucidation of their structures. Furthermore, the method allows direct estimation of the relative proportions of tetraether core lipids from chromatographic peak area measurement, allowing rapid profiling of these compounds in microbiological and environmental extracts.     

Existence of solutions for variational inequalities on Riemannian manifolds

We establish the existence and uniqueness results for variational inequality problems on Riemannian manifolds and solve completely the open problem proposed in [S.Z. Németh, Variational inequalities on Hadamard manifolds, Nonlinear Anal. 52 (2003) 1491–1498]. Also the relationships between the constrained optimization problem and the variational inequality problems as well as the projections on Riemannian manifolds are studied.