The Hoop Conjecture in Spherically Symmetric Spacetimes

We give general sufficient conditions for the existence of trapped surfaces due to concentration of matter in spherically symmetric initial data sets satisfying the dominant energy condition. These results are novel in that they apply and are meaningful for arbitrary spacelike slices, that is they do not require any auxiliary assumptions such as maximality, time-symmetry, or special extrinsic foliations, and most importantly they can easily be generalized to the nonspherical case once an existence theory for a modified version of the Jang equation is developed. Moreover, our methods also yield positivity and monotonicity properties of the Misner-Sharp energy

Elevated temperature crack growth

Critical gas turbine engine hot section components such as blades, vanes, and combustor liners tend to develop minute cracks during early stages of operations. The ability of currently available path-independent (P-I) integrals to correlate fatigue crack propagation under conditions that simulate the turbojet engine combustor liner environment was determined. To date, an appropriate specimen design and a crack displacement measurement method were determined. Alloy 718 was selected as the analog material based on its ability to simulate high temperature behavior at lower temperatures in order to facilitate experimental measurements. Available P-I integrals were reviewed and the best approaches are being programmed into a finite element post processor for eventual comparison with experimental data. The experimental data will include cyclic crack growth tests under thermomechanical conditions, and, additionally, thermal gradients

Geometric Aspects of the Moduli Space of Riemann Surfaces

This is a survey of our recent results on the geometry of moduli spaces and Teichmuller spaces of Riemann surfaces appeared in math.DG/0403068 and math.DG/0409220. We introduce new metrics on the moduli and the Teichmuller spaces of Riemann surfaces with very good properties, study their curvatures and boundary behaviors in great detail. Based on the careful analysis of these new metrics, we have a good understanding of the Kahler-Einstein metric from which we prove that the logarithmic cotangent bundle of the moduli space is stable. Another corolary is a proof of the equivalences of all of the known classical complete metrics to the new metrics, in particular Yau's conjectures in the early 80s on the equivalences of the Kahler-Einstein metric to the Teichmuller and the Bergman metric.Comment: Survey article of our recent results on the subject. Typoes corrrecte

Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras

We present a procedure to construct (n+1)-Hom-Nambu-Lie algebras from n-Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n+k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions

Elevated temperature crack growth

The objective of the Elevated Temperature Crack Growth Project is to evaluate proposed nonlinear fracture mechanics methods for application to combustor liners of aircraft gas turbine engines. During the first year of this program, proposed path-independent (P-I) integrals were reviewed for such applications. Several P-I integrals were implemented into a finite-element postprocessor which was developed and verified as part of the work. Alloy 718 was selected as the analog material for use in the forthcoming experimental work. A buttonhead, single-edge notch specimen was designed and verified for use in elevated-temperature strain control testing with significant inelastic strains. A crack mouth opening displacement measurement device was developed for further use

Hom-quantum groups I: quasi-triangular Hom-bialgebras

We introduce a Hom-type generalization of quantum groups, called quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative analogues of Drinfel'd's quasi-triangular bialgebras, in which the non-(co)associativity is controlled by a twisting map. A family of quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular bialgebra, such as Drinfel'd's quantum enveloping algebras. Each quasi-triangular Hom-bialgebra comes with a solution of the quantum Hom-Yang-Baxter equation, which is a non-associative version of the quantum Yang-Baxter equation. Solutions of the Hom-Yang-Baxter equation can be obtained from modules of suitable quasi-triangular Hom-bialgebras.Comment: 21 page

Structural Characteristics Of Sr1-xLaxTi 3+δ As A Function Of Oxygen Partial Pressure At 1400°C

The structural characteristics of Sr1-x Lax TiO3+δ (0≤x≤0.4) at 1400°C have been investigated as a function of ambient oxygen partial pressure. A modified Rietveld pattern-fitting structure-refinement program [H. M. Rietveld, J. Appl. Crystallogr. 2, 65 (1969)] was used to determine the nature of the distortions of the fundamental perovskite unit cell, the degree of lattice perfection, and the cation vacancy concentrations. Specimens equilibrated in forming gas displayed a linear relation between x, the lattice parameters, and the degree of lattice perfection while those samples annealed in air and oxygen deviated significantly from linearity. A monoclinic distortion of the perovskite structure was seen in the samples at low oxygen partial pressures while a second phase or layer type of distortion appeared in samples with x\u3e0.2 under oxidizing conditions

Ternary q-Virasoro-Witt Hom-Nambu-Lie algebras

In this paper we construct ternary $q$-Virasoro-Witt algebras which $q$-deform the ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos using $su(1,1)$ enveloping algebra techniques. The ternary Virasoro-Witt algebras constructed by Curtright, Fairlie and Zachos depend on a parameter and are not Nambu-Lie algebras for all but finitely many values of this parameter. For the parameter values for which the ternary Virasoro-Witt algebras are Nambu-Lie, the corresponding ternary $q$-Virasoro-Witt algebras constructed in this article are also Hom-Nambu-Lie because they are obtained from the ternary Nambu-Lie algebras using the composition method. For other parameter values this composition method does not yield Hom-Nambu Lie algebra structure for $q$-Virasoro-Witt algebras. We show however, using a different construction, that the ternary Virasoro-Witt algebras of Curtright, Fairlie and Zachos, as well as the general ternary $q$-Virasoro-Witt algebras we construct, carry a structure of ternary Hom-Nambu-Lie algebra for all values of the involved parameters

Covalent Binding and other Mechanisms of Primaquine Toxicity

A dose-dependent covalent binding of primaquine to mouse liver microsomal protein was found in both in vitro and in vivo studies. The binding in vitro was linear during the first 90 minutes of incubation and dependent on the concentration of mouse liver microsomal protein. The in vitro covalent binding was markedly enhanced by cofactors. Pretreatment of mice with phenobarbital, a cytochrome P450 inducer, increased the microsomal cytochrome P450 content and the in vitro covalent binding significantly. Binding was markedly inhibited when microsomal metabolism inhibitors (SK&F-525A, metyrapone and piperonyl butoxide), and sulfhydryl-contai ni ng compounds were added to the incubation system. Conversely, the inhibitory effect of inhibitors was not shown on in vivo binding; also induction with phenobarbital decreased the extent of covalent bindi ng in vivo. These findings pointed to the possibility that the extent of in vivo formation of metabolites which can bind covalently may be limited. However, injection of PQ (80 mg/Kg) into mice decreased the glutathione content of liver and erythrocytes, possibly through the formation of reactive metabolites. The NADPH-induced peroxidation of lipid of mouse mi crosomes and human erythrocyte membranes were markedly inhibited by PQ and 5H6DPQ (a PQ derivative), respectively. In contrast, PQ and its derivatives enhanced the NADPH-i nduced peroxidation of the lipids of intact erythrocytes. A significant amount of PQ metabolite(s) (formed by the mouse liver microsomal cofactor system) was bound covalently to the total protein of both normal and G6PD-deficient erythrocytes.. The net binding to the protein of G6PD-defi ci ent red cells was significantly greater than that to normal cells. A measurable amount of covalent binding of PQ metabolite(s) to human hemoglobin was also demonstrated. A small but significant amount of PQ metabolite(s) was also bound to human erythrocyte membrane protein. PQ and its derivatives decreased the amount of measurable sulfhydryl groups of G6PD-defi ci ent human erythrocyte membranes significantly but had no effect on the -SH groups of normal cell membranes. These results suggest that covalent binding of PQ metabolite(s) to human erythrocyte total protein and membrane protein as well as to hemoglobin may play an important role in hemolysis, particularly after cellular GSH and membrane sulfhydryl groups are depleted