Approximation to Complex numbers by certain biquadratic numbers

A result of Davenport and Schmidt related to Wirsing's problem is generalized so that complex numbers are approximated using the algebraic integers T from the field, $\text{Q((?D)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$, together with numbers of degree two over T. Here D is a square free positive integer.     

Early iNOS impairment and late eNOS enhancement during reperfusion following 2.49 MHz continuous ultrasound exposure after ischemia

ObjectiveIschemia reperfusion (IR) injury, occurring during heart attacks, hemorrhagic shock, and bypass and transplant surgeries, impairs microcirculatory function and nitric oxide (NO) synthesis. We report the regulation of endothelial and inducible NO synthase (eNOS and iNOS) proteins as a consequence of the application of continuous mode diagnostic frequency ultrasound application following IR injury.MethodsAnimals were assigned to one of five groups for microcirculatory assessment or Western blot analysis (WB) as follows: (1) IR+iNOS inhibition (1400W); and (2) IR+1400W+ultrasound for microcirculatory assessment, (3) Control; (4) IR; and (5) IR+ultrasound for WB. Functional capillary density and microvascular diameter, flow velocity, and flow were monitored for microcirculatory assessment. Skin tissue samples were harvested for WB. 2.49 MHz continuous ultrasound was used for application.ResultsBoth the inhibition of iNOS alone and iNOS inhibition with ultrasound irradiation positively influenced the microcirculation of observed animals relative to baseline values. Ultrasound exposure resulted in a significant production of eNOS protein in skin tissue harvested 24 h into reperfusion (p < 0.01). iNOS levels from the same tissue of ultrasound exposed animals were found to be significantly decreased 0.5 h into reperfusion (p < 0.05).ConclusionProtection from lasting IR injury effects in the microcirculation, with continuous mode diagnostic frequency ultrasound, results from augmented eNOS protein levels during late reperfusion. Ultrasound inhibited iNOS protein production during early reperfusion may also confer protection from IR injury.     

Lower bounds for the axial three-index assignment problem

This paper describes new bounding methods for the axial three-index assignment problem (3AP). For calculating 3AP lower bounds, we use a projection method followed by a Hungarian algorithm, based on a new Lagrangian relaxation. We also use a cost transformation scheme, which iteratively transforms 3AP costs in a series of equivalent 3APs, which provides the possibility of improving the 3AP lower bound. These methods produce efficiently computed relatively tight lower bound.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

The Role of Calcium in UVB-lnduced Damage in Irradiated Ocular Lenses

Abstract— The purpose of this study was to evaluate the role of altered calcium homeostasis in the development of irreversible membrane damage in the UVB-irradiated ocular lens. In particular, experiments were designed to determine whether restricting calcium influx could prevent membrane damage that typically leads to ion imbalances and lens opacification following short-term exposure to ultraviolet light (UVB). The influx of calcium was reduced by culturing lenses in a low-calcium culture medium containing 0.3 mM Ca²+ rather than physiological concentrations of 1.6 mM. This low-calcium protocol retarded calcium accumulation in UVB-irradiated lenses for 2 days of culture, and opacification was delayed by 24 h. Loss of transparency did occur during the second day of culture, but more slowly than in irradiated lenses cultured in normal-calcium medium. Membrane damage was assessed by evaluating loss in cation transport activity, assessed by measuring ⁸⁶Rb uptake into cultured lenses. Uptake was markedly inhibited in UVB-irradiated lenses and low-calcium culture did not prevent this inhibition of cation transport, a finding that explains why low-calcium protocol did not help maintain sodium homeostasis in irradiated lenses. Inhibition of cation transport and sodium accumulation eventually caused lens hydration and light scattering during extended culture in the absence of significant calcium elevation. Additional experiments were done to establish whether initial damage sustained by membranes could be repaired through the biosynthesis of new membrane proteins. Incorporation of ¹⁴C-histidine in membranes of the UVB-exposed lens was measured to assess membrane synthesis essential for repairing membrane damage. The rate of membrane protein synthesis, assessed by measuring incorporation of labeled amino acids, declined in UVB cataract, despite the prevention of calcium accumulation. These results suggest that one explanation for irreversible gain in sodium and calcium content accompanying opacification is the inability of lenses to replenish damaged membrane proteins comprising ion channels or transporters.