Medial axis transform (MAT) is a basic tool for shape analysis. But, in spite of its usefulness, it has some drawbacks, one of which is its instability under the boundary perturbation. To handle this problem in practical situations, various “pruning” methods have been proposed, which are usually heuristic in their nature and without sufficient error analyses. In this paper, we show that, althou...

1. Relative rates of enzyme inactivation were measured in liver slices, homogenates and cytosol fractions as well as in the presence of trypsin and at acid pH. The enzymes chosen are all present in the cytosol fraction of rat liver, and have widely different degradation rate constants in vivo. 2. The inactivation rates of lactate dehydrogenase, fructose bisphosphate aldolase, glucose 6-phosphat...

Abstract. In this paper, we discuss the relative K-stability and the modified K-energy associated to the Calabi’s extremal metric on toric manifolds. We give a sufficient condition in the sense of convex polytopes associated to toric manifolds for both the relative Kstability and the properness of modified K-energy. In particular, our results hold for toric Fano manifolds with vanishing Futaki-...

and Applied Analysis 3 Moreover, using the condition (iii), we obtain z (t) ≤ h (t) h −1 (τ 0 ) ( 󵄩󵄩󵄩󵄩y0 − x0 󵄩󵄩󵄩󵄩 + 󵄨󵄨󵄨󵄨η 󵄨󵄨󵄨󵄨) . (12) Then from (12), we get 󵄩󵄩󵄩󵄩x (t, τ0, y0) − x (t − η, t0, x0) 󵄩󵄩󵄩󵄩 ≤ [ 󵄩󵄩󵄩󵄩y0 − x0 󵄩󵄩󵄩󵄩 + 󵄨󵄨󵄨󵄨τ0 − t0 󵄨󵄨󵄨󵄨] h (t) h −1 (τ 0 ) . (13) So by Definition 1 with c = 1, the solution x(t, τ 0 , y 0 ) of (2) is ITDhS with respect to the solution x(t − η, t 0 , x 0 ). T...

In this paper we analyze the dynamics of N point vortices moving on a sphere from the point of view of geometric mechanics. The formalism is developed for the general case of N vortices, and the details are worked out for the ~integrable! case of three vortices. The system under consideration is SO~3! invariant; the associated momentum map generated by this SO~3! symmetry is equivariant and cor...

Surface energies of Si(001), (110), (111), and (113) surfaces with different reconstructions are calculated systematically using first-principles total-energy method. In order to quantitatively compare their relative stability, the surface energies of different surface orientations and their respective theoretical bulk atom energies are determined simultaneously by linear fitting slab supercell...

Treatment-related decreases in Dysfunctional Attitudes Scale (DAS; Weissman & Beck, 1978) scores have been interpreted as evidence that dysfunctional attitudes are state-dependent concomitants of depression. Data from the National Institute of Mental Health Treatment of Depression Collaborative Research Program were used to reexamine the stability of dysfunctional attitudes. Mean scores for Per...

The aim of this paper is to improve a theorem of János Kollár by a different method. For a given smooth Complex projective threefold X of general type, suppose the plurigenus Pk(X) ≥ 2, Kollár proved that the (11k + 5)-canonical map is birational. Here we show that either the (7k+3)-canonical map or the (7k+5)-canonical map is birational and the (13k+6)-canonical map is stably birational onto i...

In the present paper we apply geometric methods, and in particular the reduced energy–momentum (REM) method, to the analysis of stability of planar rotationally invariant relative equilibria of three-point-mass systems. We analyse two examples in detail: equilateral relative equilibria for the three-body problem, and isosceles triatomic molecules. We discuss some open problems to which the meth...

in this work, we investigated the stability of molybdate-phosphonic acid (mpa) complex by density functionaltheory (dft) computations in six solvents with the dielectric constant ranging from 1.92 to 10.36. the methodsare used for calculations are b3lyp and b3pw9 i that have been studied in two series of basis sets: d95nand6-31+g (d,p) for hydrogen and oxygen atoms; lanl2dz for mo and phosphoru...