Singular solutions for second-order non-divergence type elliptic inequalities in punctured balls

We study the existence and non-existence of positive singular solutions of second-order non-divergence type elliptic inequalities of the form $\sum\limits_{i,j = 1}^N {a_{ij} (x)\frac{{\partial ^2 u}} {{\partial x_i \partial x_j }}} + \sum\limits_{i = 1}^N {b_i (x)\frac{{\partial u}} {{\partial x_i }} \geqslant K(x)u^p ,} - \infty < p - \infty , $ with measurable coefficients in a punctured ball B _R \{0} of ? ^N , N ≥ 1. We prove the existence of a critical value p* which separates the existence region from the non-existence region. We show that in the critical case p = p*, the existence of a singular solution depends on the rate at which the coefficients (a _{i j} ) and (b _i ) stabilize at zero, and we provide some optimal conditions in this setting.     

A relaxation approach to hencky’s plasticity

Givenμ, κ, c>0, we consider the functional

Polynomial bounds for Large Bernoulli sections of ℓ 1 N

We present a quantitative form of the result of Bai and Yin from [2], and use to show that the section of ℓ ₁ ^(1+δ)n spanned byn random independent sign vectors is with high probability isomorphic to euclidean with isomorphism constant polynomial in δ⁻¹. Partially supported by BSF grant 2002-006. Supported by the National Science Foundation under agreement No. DMS-0111298. Supported in part by the Israel Science Academy.     

A characterization of duality through section/projection correspondence in the finite dimensional setting

In this paper, we show that the well-known duality operation in the context of convex bodies in Rn is completely characterized by its property of interchanging sections with projections. Our results are compared to results by Böröczky-Schneider and Artstein-Milman, who showed that in many cases, the property of order reversing is sufficient to determine a duality operation, up to obvious linear modifications. In fact, we provide another result that recovers a known characterization of duality by the property of order reversing, and up to a mild condition, also a characterization of duality by interchanging sections by projections.     

Affinity capillary electrophoresis study of the linkage existing between proton and zinc ion binding to bacitracin A1

Measurements by capillary electrophoresis (CE) of bacitracin A(1) effective mobility at different pH values permitted to estimate the five acidic dissociation constants and the Stokes radii at different protonation stages of the macrocyclic dodecapeptide. The pK(a) values were 3.6 and 4.4 for the two carboxylic groups of the lateral chains of D-Asp-11 and D-Glu-4, respectively, 6.4 for the aza-atom of the imidazole ring of His-10, 7.6 for the amino group of N-terminal Ile-1 and 9.7 for the delta-amino group of D-Orn-7, very close to the values obtained by other researchers by titration experiments. In agreement with a rigid macrocyclic structure the Stokes radii of different protonated forms ranged only between 14.3 and 14.8 A. Best fitting procedures performed on experimental mobility measured at two different pH values (5.50 and 6.72) in the presence of increasing Zn(+2) concentration allowed confirming the model that assumes the binding of Zn(+2) to P(0) peptide form with a 1.5 x 10(3) M(-1) intrinsic association constant. Following to Zn(+2) binding, the pK(a) of the amino group of N-terminal Ile-1 is shifted from 7.6 to 5.9 and the Stokes radius is reduced of about 3 A. The mean charge of the bacitracin A(1)-Zn(+2) complex resulted +1.67 and +1.12 at pH 5.50 and 6.72, respectively. These results suggest that the amino group of N-terminal Ile-1 is not essential for Zn(+2) binding.