A refined Poisson summation formula for certain Braverman-Kazhdan spaces

Braverman and Kazhdan(2000) introduced influential conjectures aimed at generalizing the Fourier transform and the Poisson summation formula. Their conjectures should imply that quite general Langlands L-functions have meromorphic continuations and functional equations as predicted by Langlands' functoriality conjecture. As an evidence for their conjectures, Braverman and Kazhdan(2002) considered a setting related to the so-called doubling method in a later paper and proved the corresponding Poisson summation formula under restrictive assumptions on the functions involved. The connection between the two papers is made explicit in the work of Li(2018). In this paper, we consider a special case of the setting in Braverman and Kazhdan's later paper and prove a refined Poisson summation formula that eliminates the restrictive assumptions of that paper. Along the way we provide analytic control on the Schwartz space we construct; this analytic control was conjectured to hold(in a slightly different setting) in the work of Braverman and Kazhdan(2002).     

Evaluation of Electrospun PCL-PLGA for Sustained Delivery of Kartogenin

In this study, kartogenin was incorporated into an electrospun blend of polycaprolactone and poly(lactic-co-glycolic acid) (1:1) to determine the feasibility of this system for sustained drug delivery. Kartogenin is a small-molecule drug that could enhance the outcome of microfracture, a cartilage restoration procedure, by selectively stimulating chondrogenic differentiation of endogenous bone marrow mesenchymal stem cells. Experimental results showed that kartogenin did not affect the electrospinnability of the polymer blend, and it had negligible effects on fiber morphology and scaffold mechanical properties. The loading efficiency of kartogenin into electrospun membranes was nearly 100%, and no evidence of chemical reaction between kartogenin and the polymers was detected by Fourier transform infrared spectroscopy. Analysis of the released drug using high-performance liquid chromatography–photodiode array detection indicated an abundance of kartogenin and only a small amount of its major hydrolysis product. Kartogenin displayed a typical biphasic release profile, with approximately 30% being released within 24 h followed by a much slower, constant rate of release up to 28 days. Although additional development is needed to tune the release kinetics and address issues common to electrospun scaffolds (e.g., high fiber density), the results of this study demonstrated that a scaffold electrospun from biodegradable synthetic polymers is a suitable kartogenin delivery vehicle.     

Strengthening the Connection between Science,Society and Environment to Develop Future French and European Bioeconomies: Cutting-Edge Research of VAALBIO Team at UCCS

The development of the future French and European bioeconomies will involve developing new green chemical processes in which catalytic transformations are key. The VAALBIO team (valorization of alkanes and biomass) of the UCCS laboratory (Unité de Catalyse et Chimie du Solide) are working on various catalytic processes, either developing new catalysts and/or designing the whole catalytic processes. Our research is focused on both the fundamental and applied aspects of the processes. Through this review paper, we demonstrate the main topics developed by our team focusing mostly on oxygen- and hydrogen-related processes as well as on green hydrogen production and hybrid catalysis. The social impacts of the bioeconomy are also discussed applying the concept of the institutional compass.     

On the dimension of the solution set to the homogeneous linear functional differential equation of the first order

Consider the homogeneous equation $$u'(t) = l(u)(t){\rm{ for a}}{\rm{.e}}{\rm{. }}t \in [a,b]$$ where ?: C([a, b];?) → L([a, b];?) is a linear bounded operator. The efficient conditions guaranteeing that the solution set to the equation considered is one-dimensional, generated by a positive monotone function, are established. The results obtained are applied to get new efficient conditions sufficient for the solvability of a class of boundary value problems for first order linear functional differential equations.     

Extensions of the Levine-Nahikian method for constructing involutory matrices

Various characterizations for sums of matrices over arbitrary fields to be involutions are established. Applications of these results in constructing involutions of matrices with elements from finite fields are considered.     

The spin density distribution in some phenyl substituted imidazyl and pyrryl radicals

ENDOR spectroscopy has been used to interpret the E.S.R. spectra of the 2,4,5-triphenylimidazyl, tetraphenylpyrryl, tetrakis (p-tolyl) pyrryl, tetrakis (p-anisyl) pyrryl radicals. Using the hyperfine coupling constants thus obtained in conjunction with a McLachlan-type HMO calculation the spin density distribution in these radicals is calculated. The configuration of the phenyl rings and the deviation of their bond lengths from hexagonal symmetry is inferred from the MO parameters required to fit the experimental couplings.     

Simulation of the inherent turbulence and wake interaction inside an infinitely long row of wind turbines

The turbulence in the interior of a wind farm is simulated using large eddy simulation and the actuator line technique implemented in the Navier–Stokes equations. The simulations are carried out for an infinitely long row of turbines simulated by applying cyclic boundary conditions at the inlet and outlet. The simulations investigate the turbulence inherent to the wind turbines as no ambient turbulence or shear is added to this idealised case. The simulated data give insight into the performance of the wind turbines operating in the wake of others as well as details on key turbulent quantities. One of the key features of wakes behind wind turbines is the dynamic wake meandering, which is shown to be related to the wind turbine spacing and the vortex shedding from the turbine as a bluff body. The flow is analysed and reconstructed by applying proper orthogonal decomposition.     

Sintering of a bcc structure of spherical particles of equal and different sizes

Solid-state sintering of a bcc structure of spherical particles has been studied numerically by use of simple shape parameters to describe the state of the unit cell. Both free and pressure-assisted sintering of particles of equal and different sizes for various ratios of boundary and surface diffusion have been considered. At low relative densities, the evolution of particle radius, interparticle junction radius and shrinkage predicted by the bcc model are rather similar to sintering of a simple row of particles. At higher densities, the porosity closes up; that is, the junctions start to interact, or the next-nearest neighbours in the particle structure attain contact. Quantative measures of the density at the transition from open pore space between the particles to closed porosity as well as the density at which the next-nearest neighbours start to touch are derived. Furthermore, different dihedral angles and the evolution of relative density and sintering stresses are studied.     

Self-adjoint algebras of unbounded operators

Unbounded *-representations of *-algebras are studied. Representations called self-adjoint representations are defined in analogy to the definition of a self-adjoint operator. It is shown that for self-adjoint representations certain pathologies associated with commutant and reducing subspaces are avoided. A class of well behaved self-adjoint representations, called standard representations, are defined for commutative *-algebras. It is shown that a strongly cyclic self-adjoint representation of a commutative *-algebra is standard if and only if the representation is strongly positive, i.e., the representations preserves a certain order relation. Similar results are obtained for *-representations of the canonical commutation relations for a finite number of degrees of freedom.Work supported in part by U.S. Atomic Energy Commission under Contract AT(30-1)-2171 and by the National Science Foundation.Alfred P. Sloan Foundation Fellow.     

Linewidths of HCl broadened by CO2 and N2 and CO broadened by CO2

High resolution measurement of the linewidths of HCl broadened by CO₂ and N₂ and CO broadened by CO₂ have been performed in both the 1-0 and 2-0 bands of HCl and the 2-0 band of CO. The data were analyzed by the direct and the peak absorption methods. Values of the linewidths obtained by the two methods are in good agreement. For |m| ≤ 3, for the case of HCl + CO₂, the agreement is good for the values obtained in both bands of HCl. However for |m| > 3, the HCl + CO₂ linewidths in the 1-0 band are smaller than the corresponding lines in the 2-0 band by as much as 11% for |m| = 9. Lines (|m| ≤ 3) of the 1-0 and 2-0 bands of HCl broadened by CO₂ were also analyzed in terms of the super-Lorentzian line profile proposed by Varanasi, S. K. Sarangi, and G. D. T. Tejwani (J. Quan. Spectr. Radiative Transfer12, 857 (1972)) and the Lorentzian profile. The results indicate that near the line center (within 3γ), the shape of HCl + CO₂ lines are Lorentzian.