Characterization of Lyapunov pairs in the nonlinear case and applications

The paper presents a characterization of the Lyapunov pairs for a general initial value problem with a possibly multivalued m$m$-accretive operator on an arbitrary Banach space by means of the contingent derivative related to the operator. The proof is based on tangency and flow-invariance arguments combined with a priori estimates and approximation. The abstract results are applied to obtain precise a priori estimates for the mild solutions. They readily lead to the existence of global solutions and various controllability properties. Important Lyapunov pairs are pointed out in connection with specific problems.     

The Poisson equation on complete manifolds with positive spectrum and applications

In this paper we investigate the existence of a solution to the Poisson equation on complete manifolds with positive spectrum and Ricci curvature bounded from below. We show that if a function f has decay f=O(r−1−ε) for some ε>0, where r is the distance function to a fixed point, then the Poisson equation Δu=f has a solution u with at most exponential growth.We apply this result on the Poisson equation to study the existence of harmonic maps between complete manifolds and also existence of Hermitian-Einstein metrics on holomorphic vector bundles over complete manifolds, thus extending some results of Li-Tam and Ni.Assuming moreover that the manifold is simply connected and of Ricci curvature between two negative constants, we can prove that in fact the Poisson equation has a bounded solution and we apply this result to the Ricci flow on complete surfaces.     

NORM CALCULATIONS OF A CLASS OF INTEGRAL OPERATORS

In this paper we calculate the norm of a special class of integral operators acting on LP （C^n, dvs）, where dvs is the Gaussian measure on C^n.     

Unifying local–global type properties in vector optimization

It is well-known that all local minimum points of a semistrictly quasiconvex real-valued function are global minimum points. Also, any local maximum point of an explicitly quasiconvex real-valued function is a global minimum point, provided that it belongs to the intrinsic core of the function’s domain. The aim of this paper is to show that these “local min–global min” and “local max–global min” type properties can be extended and unified by a single general local–global extremality principle for certain generalized convex vector-valued functions with respect to two proper subsets of the outcome space. For particular choices of these two sets, we recover and refine several local–global properties known in the literature, concerning unified vector optimization (where optimality is defined with respect to an arbitrary set, not necessarily a convex cone) and, in particular, classical vector/multicriteria optimization.     

The NADH Electrochemical Detection Performed at Carbon Nanofibers Modified Glassy Carbon Electrode

In this work, the capability of carbon nanofibers to be used for the design of catalytic electrochemical biosensors is demonstrated. The direct electrochemistry of NADH was studied at a glassy carbon electrode modified using carbon nanofibers. A decrease of the oxidation potential of NADH by more than 300 mV is observed in the case of the assembled carbon nanofiber‐glassy carbon electrode comparing with a bare glassy carbon electrode. The carbon nanofiber‐modified electrode exhibited a wide linear response range of 3×10^?5 to 2.1×10^?3 mol L^?1 with a correlation coefficient of 0.997 for the detection of NADH, a high specific sensitivity of 3637.65 (μA/M cm²), a low detection of limit (LOD=3σ) of 11 μM, and a fast response time (3 s). These results have confirmed the fact that the carbon nanofibers represent a promising material to assemble electrochemical sensors and biosensors.     

Proximity problems on line segments spanned by points

Finding the closest or farthest line segment (line) from a point are fundamental proximity problems. Given a set S of n points in the plane and another point q, we present optimal O(nlogn) time, O(n) space algorithms for finding the closest and farthest line segments (lines) from q among those spanned by the points in S. We further show how to apply our techniques to find the minimum (maximum) area triangle with a vertex at q and the other two vertices in S{q} in optimal O(nlogn) time and O(n) space. Finally, we give an O(nlogn) time, O(n) space algorithm to find the kth closest line from q and show how to find the k closest lines from q in O(nlogn+k) time and O(n+k) space.     

Diffractionless flow of light in all-optical microchips

We introduce the concept of a hybrid 2D-3D photonic band gap (PBG) heterostructure which enables both complete control of spontaneous emission of light from atoms and planar light-wave propagation in engineered wavelength-scale microcircuits. Using three-dimensional (3D) light localization, this heterostructure enables flow of light without diffraction through micron-scale air waveguide networks. Achieved by intercalating two-dimensional photonic crystal layers containing engineered defects into a 3D PBG material, this provides a general and versatile solution to the problem of "leaky modes" and diffractive losses in integrated optics.     

Acrolein detection based on alcohol dehydrogenase inhibition

This paper presents the effect of acrolein on three dehydrogenases and proposes a fast spectrometric method for acrolein analysis. We have found that alcohol dehydrogenase (ADH) and aldehyde dehydrogenase (AlDH) are inhibited by low acrolein concentrations (0.2?mM) while inhibition of glutamate dehydrogenase (GDH) is not observed even at higher acrolein concentrations (1?mM). Acrolein is a suicide substrate for AlDH and ADH inhibition by acrolein is competitive. Cysteine (L-Cys) and glutathione (GSH) react with acrolein and thus reduce its expected inhibitory effect. ADH was chosen to develop a spectrophotometric method for acrolein analysis based on enzyme inhibition. The calibration curve is linear between 0.2 and 1.0?mM acrolein.