Uniform estimates for order statistics and Orlicz functions

We establish uniform estimates for order statistics: Given a sequence of independent identically distributed random variables ξ ₁, … , ξ _n and a vector of scalars x = (x ₁, … , x _n ), and 1 ≤ k ≤ n, we provide estimates for \mathbb E   k-min_{1 ￡ i ￡ n} |x_ix_i|{\mathbb E \, \, k-{\rm min}_{1\leq i\leq n} |x_{i}\xi _{i}|} and \mathbb E k-max_{1 ￡ i ￡ n}|x_ix_i|{\mathbb E\,k-{\rm max}_{1\leq i\leq n}|x_{i}\xi_{i}|} in terms of the values k and the Orlicz norm ||y_x||_M{\|y_x\|_M} of the vector y _x  = (1/x ₁, … , 1/x _n ). Here M(t) is the appropriate Orlicz function associated with the distribution function of the random variable |ξ ₁|, G(t) = \mathbb P ({ |x₁| ￡ t}){G(t) =\mathbb P \left(\left\{ |\xi_1| \leq t\right\}\right)}. For example, if ξ ₁ is the standard N(0, 1) Gaussian random variable, then G(t) = ?{\tfrac2p}ò₀^t e^-\fracs22ds {G(t)= \sqrt{\tfrac{2}{\pi}}\int_{0}^t e^{-\frac{s^{2}}{2}}ds }  and M(s)=?{\tfrac2p}ò₀^se^-\frac12t2dt{M(s)=\sqrt{\tfrac{2}{\pi}}\int_{0}^{s}e^{-\frac{1}{2t^{2}}}dt}. We would like to emphasize that our estimates do not depend on the length n of the sequence.     

Homogenization of First Order Equations with (u/ε)-Periodic Hamiltonians Part II: Application to Dislocations Dynamics

This paper is concerned with a result of homogenization of a non-local first order Hamilton–Jacobi equation describing the dislocations dynamics. Our model for the interaction between dislocations involves both an integro-differential operator and a (local) Hamiltonian depending periodicly on u/ε. The first two authors studied in a previous work homogenization problems involving such local Hamiltonians. Two main ideas of this previous work are used: on the one hand, we prove an ergodicity property of this equation by constructing approximate correctors which are necessarily non periodic in space in general; on the other hand, the proof of the convergence of the solution uses here a twisted perturbed test function for a higher dimensional problem. The limit equation is a nonlinear diffusion equation involving a first order Lévy operator; the nonlinearity keeps memory of the short range interaction, while the Lévy operator keeps memory of long ones. The homogenized equation is a kind of effective plastic law for densities of dislocations moving in a single slip plane.     

Image Space Analysis for Constrained Inverse Vector Variational Inequalities via Multiobjective Optimization

In this paper, we employ the image space analysis to study constrained inverse vector variational inequalities. First, sufficient and necessary optimality conditions for constrained inverse vector variational inequalities are established by using multiobjective optimization. A continuous nonlinear function is also introduced based on the oriented distance function and projection operator. This function is proven to be a weak separation function and a regular weak separation function under different parameter sets. Then, two alternative theorems are established, which lead directly to sufficient and necessary optimality conditions of the inverse vector variational inequalities. This provides a partial answer to an open question posed in Chen et al. (J Optim Theory Appl 166:460–479, 2015).     

Anti-depressant and anxiolytic like behaviors in PKCI/HINT1 knockout mice associated with elevated plasma corticosterone level

Background  

Protein kinase C interacting protein (PKCI/HINT1) is a small protein belonging to the histidine triad (HIT) family proteins. Its brain immunoreactivity is located in neurons and neuronal processes. PKCI/HINT1 gene knockout (KO) mice display hyper-locomotion in response to D-amphetamine which is considered a positive symptom of schizophrenia in animal models. Postmortem studies identified PKCI/HINT1 as a candidate molecule for schizophrenia and bipolar disorder. We investigated the hypothesis that the PKCI/HINT1 gene may play an important role in regulating mood function in the CNS. We submitted PKCI/HINT1 KO mice and their wild type (WT) littermates to behavioral tests used to study anti-depressant, anxiety like behaviors, and goal-oriented behavior. Additionally, as many mood disorders coincide with modifications of hypothalamic-pituitary-adrenal (HPA) axis function, we assessed the HPA activity through measurement of plasma corticosterone levels.     

Surface bodies and p-affine surface area

The surface body is a generalization of the floating body. Its relation to p-affine surface area is studied.     

Alternating π‐conjugated block copolymers with precise block length

A Sonogashira polycondensation reaction has been used to synthesize copolymers consisting of alternating oligo(p‐phenyleneethynylene) with a precise block length as an electron‐rich component and 1,4‐bis(2‐phenylene‐2‐cyanovinylene)benzene or 2,6‐bis(2‐pyridinylene‐ethynylene)pyridine as an electron‐poor component. The copolymers differ in the length of the phenyleneethynylene block (trimer or pentamer) and the content of the electron‐poor component. The length of the phenyleneethynylene block has no influence on the maximum wavelength. The electron‐poor cyano‐block component lowers the optical band‐gap energy of the copolymers. The value is equivalent to that of poly(cyano‐phenylenevinylene) (CN‐PPV) (2.3–2.4 eV). © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3574–3587, 2005     

Symmetry and nodal properties in the global bifurcation analysis of quasi-linear elliptic equations

Communicated by J. B. McLeod     

Isothermal titration calorimetry of Ni(II) binding to histidine and to N-2-aminoethylglycine

Isothermal titration calorimetry (ITC) is used to study the complexation thermodynamics of Ni(II) with histidine (His) and with N-2-aminoethylglycine (EDMA). The titrations were performed in HEPES and Tris buffers at various ionic strengths and pH values around 8. The results show the influence of the experimental conditions on the shape and fitting parameters of the calorimetric curves. For the studied systems, the main reaction is concomitant with a number of side reactions which contribute to the global energy measured. From the calorimetric data measured, the formation constants for the species NiHEPES⁺, Tris⁺His⁻, TrisNiHis⁺ and [Ni(EDMA)₂OH]⁻ have been evaluated for the first time and the values obtained properly validated.