Hypersurfaces of Prescribed Curvature Measure

We consider the corresponding Christoffel-Minkowski problem for curvature measures. The existence of star-shaped $(n-k)$-convex bodies with prescribed $k$-th curvature measures ($k>0$) has been a longstanding problem. This is settled in this paper through the establishment of a crucial $C^2$ a priori estimate for the corresponding curvature equation on $\mathbb S^n$

A geometric characterization of a sharp Hardy inequality

In this paper, we prove that the distance function of an open connected set in $\mathbb R^{n+1}$ with a $C^{2}$ boundary is superharmonic in the distribution sense if and only if the boundary is {\em weakly mean convex}. We then prove that Hardy inequalities with a sharp constant hold on {weakly mean convex} $C^{2}$ domains. Moreover, we show that the {weakly mean convexity} condition cannot be weakened. We also prove various improved Hardy inequalities on mean convex domains along the line of Brezis-Marcus \cite{BM}.Comment: The results were improved to $C^2$ domain

Machine -Cell Location Problems for Multiproduct Flowlines.

Jobs (parts) and machines are usually grouped into part-families and machine-cells in a flexible, cellular manufacturing system to minimize the flows of all work-in-processes (WIP). As a result of this grouping, some parts may need processing on some machines that are not in their own cells. The parts requiring machines in other cells are called \u27exceptional parts,\u27 and the corresponding machines are called \u27 bottleneck machines.\u27 Usually, there are two ways to deal with this inter-cell flow problem: using a material handling system to move the exceptional parts among the cells or duplicating the bottleneck machine(s) for the corresponding exceptional part(s). The objective of this research is to minimize the total costs of these inter-cell flows. A two-phase procedure, machine-cell location (MCL) and duplication of bottleneck machines (DBM), is presented in this research to achieve this goal. The MCL problem covers both one-dimensional layout and two-dimensional layout, especially dealing with one-dimensional equidistant (1DE), one-dimensional non-equidistant (1DNE) and two-dimensional non-equidistant (2DNE) machine-cell location problems. All versions of the MCL problem fall under the general class of quadratic assignment problem (QAP) which is NP-hard and it is difficult to solve a large problem optimally. The DBM problem, which arises as a natural extension to the MCL problem, may be classified as an integer linear programming (ILP) problem and a solution to it may provide an alternative way to reduce the total inter-cell flow costs. The 1DE problem is solved first by using a simple depth-first heuristic (SDH) which is later modified to a directional decomposition heuristic (DDH) for a better quality of solution. The directional decomposition of inter-cell flow, the core foundation of the DDH algorithm, is then extended to the one-dimensional non-equidistant (1DNE) and the two-dimensional non-equidistant (2DNE) problems. This leads to the development of the modified directional decomposition heuristic (MDDH) and the quadra-directional decomposition heuristic (QDDH), respectively. Based on the solutions to various facets of the MCL problem, a binary ILP model is proposed for solving the DBM problem optimally. Empirical tests show that heuristic DDH and its extensions, MDDH and QDDH, are more efficient than most other comparable heuristics

Cloning and Characterization of Phospholipases A2 and Hyaluronidase Genes from the Venom of the Honeybee Apis mellifera carnica (Hymenoptera: Apidae)

Bee venom contains the allergic enzymes phospholipases A2 (PLA2) and hyaluronidase. These enzymes have been extensively studied as therapeutic modalities because of their proven effects in pharmaceutical and clinical applications. The cDNA cloning of PLA2 and hyaluronidase was amplified by RT-PCR from the total RNA of the venom gland of a honeybee (Apis mellifera carnica). The lengths of the PLA2 and hyaluronidase of Apis mellifera ligustica were 504 and 1146bp, respectively. The genes of PLA2 and hyaluronidase shared 90.94% and 96.65% homologies with A. mellifera ligustica and Apis cerana cerana, respectively. Some similar PLA2 and hyaluronidase were also found in the venom of other bee species, We analyzed their sequences and compared them with those of other sources. A notable finding was that the two genes differed from those of A. mellifera ligustica and A. cerana cerana. The positions of the disulfide bonds of PLA2 and hyaluronidase were also completely different from those previously reported. We used the available sequences to construct a phylogenetic tree and discovered that these two genes of A. mellifera carnica belonged to the western honeybee, and was more closely related to that of A. mellifera ligustica than to any other insect