On the best constant for Hardy's inequality in

Let be a domain in and . We consider the (generalized) Hardy inequality , where . The inequality is valid for a large family of domains, including all bounded domains with Lipschitz boundary. We here explore the connection between the value of the Hardy constant and the existence of a minimizer for this Rayleigh quotient. It is shown that for all smooth -dimensional domains, , where is the one-dimensional Hardy constant. Moreover it is shown that for all those domains not possessing a minimizer for the above Rayleigh quotient. Finally, for , it is proved that if and only if the Rayleigh quotient possesses a minimizer. Examples show that strict inequality may occur even for bounded smooth domains, but for convex domains.

     

On the localization of binding for Schrödinger operators and its extension to elliptic operators

In this paper we study the asymptotic behavior of the ground state energyE(R) of the Schrödinger operatorP _R=?Δ+V ₁(x)+V ₂(x-R),x,R ∈?ⁿ, where the potentialsV _i are small perturbations of the Laplacian in ?ⁿ,n≥3. The methods presented here apply also in the investigation of the ground state energyE(g) of the operatorPg=P+V ₁(x)+V ₂(gx), x ∈X,g ∈G, whereP _g is an elliptic operator which is defined on a noncompact manifoldX, G is a discrete group acting onX by diffeomorphismsG×X∈(g, x)→gx∈X, andP is aG-invariant elliptic operator which is subcritical inX.     

Large time behavior of the heat kernel

In this paper we study the large time behavior of the (minimal) heat kernel k_P^M(x,y,t) of a general time-independent parabolic operator Lu=u_t+P(x,∂_x)u which is defined on a noncompact manifold M. More precisely, we prove that

     

Invariant measures for algebraic actions, Zariski dense subgroups and Kazhdan's property

Let be any locally compact non-discrete field. We show that finite invariant measures for -algebraic actions are obtained only via actions of compact groups. This extends both Borel's density and fixed point theorems over local fields (for semisimple/solvable groups, resp.). We then prove that for -algebraic actions, finitely additive finite invariant measures are obtained only via actions of amenable groups. This gives a new criterion for Zariski density of subgroups and is shown to have representation theoretic applications. The main one is to Kazhdan's property for algebraic groups, which we investigate and strengthen.

     

A film model for the prediction of flooding and flow reversal for gas-liquid flow in vertical tubes

A model is presented which demonstrates that the process of flooding and flow reversal can be explained on the basis of a film mechanism. The model predicts well the gas flow rate at which flooding and flow reversal begins and ends for a given liquid flow rate and the presence of a hysteresis loop between flooding and flow reversal. The predictions of the theory are in satisfactory agreement with experimental flooding data.     

Determination of lysine in protein hydrolyzates using lysine decarboxylase from salmonella hadar

Lysine may be determined in protein hydrolyzates with the aid of lysine decarboxylase contained in cell-free extracts of Salmonella hadar grown under suitable conditions.     

Flow pattern characterization in two phase flow by electrical conductance probe

An improved system of conductance probes is used to identify the flow patterns in two phase horizontal, near horizontal and upward flows. The results show that this system is very well suited to distinguish among flow patterns consistent with visual observations.     

Numerical analysis of large elastic-plastic deformation of beams due to dynamic loading

Numerical calculations were performed for two examples of the response of elastic-plastic beams subjected to dynamic loads. These were a simply supported, axially restrained beam under suddenly applied uniform pressure, and an axially restrained, clamped beam with a central mass that is impacted by a projectile. Large elastic-plastic deflections were considered, and the method of finite differences was used. Two different constitutive equations were assumed: the elástic-perfectly plastic relation, and a special elastic-viscoplastic, strain hardening model. Analysis of the results included examining the interaction between the bending moment and the axial force, the variation of the axial force, bending moment and deflection with time, and the propagation velocities of the various phenomena during motion. Experiments were carried out in which a rifle projectile hit a central mass which had been fastened to a clamped beam. Comparison between the theoretical and experimental dynamic deflections shows good agreement for relatively short response times.     

Blue fluorescent dye-protein complexes based on fluorogenic cyanine dyes and single chain antibody fragments

Fluoromodules are complexes formed upon the noncovalent binding of a fluorogenic dye to its cognate biomolecular partner, which significantly enhances the fluorescence quantum yield of the dye. Previously, several single-chain, variable fragment (scFv) antibodies were selected from a yeast cell surface-displayed library that activated fluorescence from a family of unsymmetrical cyanine dyes covering much of the visible and near-IR spectrum. The current work expands our repertoire of genetically encodable scFv-dye pairs by selecting and characterizing a group of scFvs that activate fluorogenic violet-absorbing, blue-fluorescing cyanine dyes, based on oxazole and thiazole heterocycles. The dye binds to both yeast cell surface-displayed and soluble scFvs with low nanomolar K(d) values. These dye-protein fluoromodules exhibit high quantum yields, approaching unity for the brightest system. The promiscuity of these scFvs with other fluorogenic cyanine dyes was also examined. Fluorescence microscopy demonstrates that the yeast cell surface-displayed scFvs can be used for multicolor imaging. The prevalence of 405 nm lasers on confocal imaging and flow cytometry systems make these new reagents potentially valuable for cell biological studies.