On presentations of integer polynomial points of simple groups over number fields

Let K be a number field and let A be its ring of integers. Let G be a connected, noncommutative, absolutely almost simple algebraic K-group. If the K-rank of G equals 2, then G(A[t]) is not finitely presented.     

Finiteness properties of arithmetic groups over function fields

We determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FP _∞ by comparing its large-scale geometry to the large-scale geometry of lattices in real semisimple Lie groups.     

Analysis of the ground configuration of Tm3+ in YVO4

An analysis has been made of the optical spectrum of Tm³⁺ in YVO₄ reported by K. D. Knoll. The approach taken was to describe the Tm³⁺ free ion as completely as possible and then to describe the effects of the crystal field on these levels. Parameters were obtained that gave an r.m.s. deviatioa of 10.6 cm^?1 in a least squares fit. In Knolls' earlier analysis, which did not describe the free ion adequately, several sets of parameters were given that are consistent with different portions of the spectrum. The results computed with our parameters gave a new interpretation of the ³F₄ and ³H₅ multiplets and gave g_∥ factors in good agreement with the measurements. The efiects of the hyperfine interaction and the spin-crystal field interaction on the energy levels resulted in displacements of smaller than 0.1 cm^?1.     

Aryl Sulfonium Salts for Site‐Selective Late‐Stage Trifluoromethylation

Incorporation of the CF₃ group into arenes has found increasing importance in drug discovery. Herein, we report the first photoredox‐catalyzed cross‐coupling of aryl thianthrenium salts with a copper‐based trifluoromethyl reagent, which enables a site‐selective late‐stage trifluoromethylation of arenes. The reaction proceeds with broad functional group tolerance, even for complex small molecules on gram scale. The method was further extended to produce pentafluoroethylated derivatives.     

On Numerical Solution of the Markov Renewal Equation: Tight Upper and Lower Kernel Bounds

We develop tight bounds and a fast parallel algorithm to compute the Markov renewal kernel. Knowledge of the kernel allows us to solve Markov renewal equations numerically to study non-steady state behavior in a finite state Markov renewal process. Computational error and numerical stability for computing the bounds in parallel are discussed using well-known results from numerical analysis. We use our algorithm and computed bounds to study the expected number of departures as a function of time for a two node overflow queueing network.     

Workload in queues having priorities assigned according to service time

System designers often implement priority queueing disciplines in order to improve overall system performance; however, improvement is often gained at the expense of lower priority cystomers. Shortest Processing Time is an example of a priority discipline wherein lower priority customers may suffer very long waiting times when compared to their waiting times under a democratic service discipline. In what follows, we shall investigate a queueing system where customers are divided into a finitie number of priority classes according to their service times.We develop the multivariate generating function characterizing the joint workload among the priority classes. First moments obtained from the generating function yield traffic intensities for each priority class. Second moments address expected workloads, in particular, we obtain simple Pollaczek-Khinchine type formulae for the classes. Higher moments address variance and covariance among the workloads of the priority classes.This work was supported in part by National Science Foundation Grant DDM-8913658.     

Recent progress in the development of type II interband cascade lasers

Type-II interband cascade lasers combine the advantage of an interband optical transition with interband tunneling to enable the cascading of type-II quantum well active regions as is done in type-I quantum cascade laser. The relatively high radiative efficiency resulting from interband optical transitions translates into very low-threshold current densities, and when combined with the high quantum efficiency of cascade lasers, this diode laser design has the potential to operate under cw conditions at room temperature with high output power. Experimental results have already demonstrated some of this potential including high differential external quantum efficiency (>600%), high peak output power (6 W/facet at 80 K), high cw power conversion efficiency (>17% at 80 K), and operation at 300 K under pulsed conditions. Recent work aimed at reducing device thermal resistance and increasing cw operating temperature is reviewed including the demonstration of significant reductions in thermal resistance (averaging 25 K/W or 40% for 1-mm-long devices), 80 K cw operation at 3.4 μm with high-power conversion efficiency (23%) and high differential external quantum efficiency (532%), and cw operation up to 214 K.     

Exponential higher dimensional isoperimetric inequalities for some arithmetic groups

We show that arithmetic subgroups of semisimple groups of relative \mathbb Q{{\mathbb Q}}-type A _n , B _n , C _n , D _n , E ₆, or E ₇ have an exponential lower bound to their isoperimetric inequality in the dimension that is 1 less than the real rank of the semisimple group.     

Bonding of fluorine-implanted and annealed silicon

The effects of low temperature annealing on crystalline silicon samples, made amorphous by the ion-implantation of fluorine ions, has been studied using infrared spectroscopy. The implantation process is shown to result in a metastable state which, upon subsequent thermal annealing, converts to the well-characterized stretching and bending modes found in deposited silicon-fluorine films. Using arguments based on molecular orbital theory and model calculations, the metastable state is identified as a silicon-fluorine-silicon bridge.     

Connectivity properties of horospheres in Euclidean buildings and applications to finiteness properties of discrete groups

Let G(O_S)\mathbf{G}(\mathcal{O}_{S}) be an S-arithmetic subgroup of a connected, absolutely almost simple linear algebraic group G over a global function field K. We show that the sum of local ranks of G determines the homological finiteness properties of G(O_S)\mathbf{G}(\mathcal{O}_{S}) provided the K-rank of G is 1. This shows that the general upper bound for the finiteness length of G(O_S)\mathbf{G}(\mathcal{O}_{S}) established in an earlier paper is sharp in this case.