Estimates of covering numbers of convex sets with slowly decaying orthogonal subsets

Covering numbers of precompact symmetric convex subsets of Hilbert spaces are investigated. Lower bounds are derived for sets containing orthogonal subsets with norms of their elements converging to zero sufficiently slowly. When these sets are convex hulls of sets with power-type covering numbers, the bounds are tight. The arguments exploit properties of generalized Hadamard matrices. The results are illustrated by examples from machine learning, neurocomputing, and nonlinear approximation.     

Synthesis of ultrafine SiC from rice hulls (husks): A plasma process

Heat-treated rice hulls have been used as precursor material for synthesis of ultrafne SiC in a RF plasma reactor. Rice hulls containing finely distributed silica and active carbon act as a source for SiC formation. The plasma-synthesized powder contained ultrafnc -SiC with excess carbon and some unreacted silica. Post-treatment processes such as oxidation and acid (HF) treatment appear to be effective in removing the excess carbon and silica.     

Analysis of neem oils by LC–MS and degradation kinetics of azadirachtin-A in a controlled environment

Since it was first isolated, the oil extracted from seeds of neem (Azadirachtin indica A juss) has been extensively studied in terms of its efficacy as an insecticide. Several industrial formulations are produced as emulsifiable solutions containing a stated titer of the active ingredient azadirachtin-A (AZ-A). The work reported here is the characterization of a formulation of this insecticide marketed under the name of Neem-azal T/S and kinetic studies of the major active ingredient of this formulation. We initially performed liquid–liquid extraction to isolate the neem oil from other ingredients in the commercial mixture. This was followed by a purification using flash chromatography and semi-preparative chromatography, leading to ¹³C NMR identification of structures such as azadirachtin-A, azadirachtin-B, and azadirachtin-H. The neem extract was also characterized by HPLC–MS using two ionization sources, APCI (atmospheric pressure chemical ionization) and ESI (electrospray ionization) in positive and negative ion modes of detection. This led to the identification of other compounds present in the extract—azadirachtin-D, azadirachtin-I, deacetylnimbin, deacetylsalannin, nimbin, and salannin. The comparative study of data gathered by use of the two ionization sources is discussed and shows that the ESI source enables the largest number of structures to be identified. In a second part, kinetic changes in the main product (AZ-A) were studied under precise conditions of pH (2, 4, 6, and 8), temperature (40 to 70 °C), and light (UV, dark room and in daylight). This enabled us to determine the degradation kinetics of the product (AZ-A) over time. The activation energy of the molecule (75±9 kJ mol^–1) was determined by examining thermal stability in the range 40 to 70 °C. The degradation products of this compound were identified by use of HPLC–MS and HPLC–MS–MS. The results enabled proposal of a chemical degradation reaction route for AZ-A under different conditions of pH and temperature. The data show that at room temperature and pH between 4 and 5 the product degrades into two preferential forms that are hydrolyzed to a single product over time and as a function of pH change.     

On a class of functions with equal infima over a domain and its boundary

In this paper, we present a class of functions:f:X such that inf _xX f(x)= , whereX is a nonempty, finitely compact and convex set in a vector space andB _x ={xX: y aff(X){x:[x, y]X={x}. Our main tool is a recent minimax theorem by Ricceri (Ref. 1).     

Neem Oil As Pesticide

Use of synthetic pesticides has resulted into health hazards, ecological imbalance, resistance in pests and environmental pollution.1 Singh, R. 1997. “Studies in formulation of pesticide emulsion”. India: UDCT, University of Mumbai. , Ph.D. Thesis [Google Scholar] Neem oil is natural pesticide and has excellent insecticidal properties. Hence, attempts are being made to develop neem oil emulsions to be used as pesticide. Surfactants like castor‐oil based, nonyl phenol‐based, sodium lauryl sulphate, and calcium alkyl benzene sulphonate were tried to develop stable emulsions. Neem extract based emulsifiable concentrates were prepared by using methanol. Stability of emulsion as a function of type of surfactants, hydrophile‐lipophile balance (HLB) of surfactants and hardness of water was studied. Larvasidal effects of emulsions and emulsifiable concentrates were examined. Laboratory experiments have shown effectiveness of these emulsions and emulsifiable concentrates as pesticide.     

Enveloppes convexes des processus gaussiens

Let X={X(t), t[0,1]} be a process on [0,1] and V_X=Conv{(t,x)t[0,1], x=X(t)} be the convex hull of its path.The structure of the set ext(V_X) of extreme points of V_X is studied. For a Gaussian process X with stationary increments it is proved that:

• The set ext(V_X) is negligible if X is non-differentiable.

• If X is absolutely continuous process and its derivative X′ is continuous but non-differentiable, then ext(V_X) is also negligible and moreover it is a Cantor set.

It is proved also that these properties are stable under the transformations of the type Y(t)=f(X(t)), if f is a sufficiently smooth function.     

On Tori Triangulations Associated with Two-Dimensional Continued Fractions of Cubic Irrationalities

The notion of equivalence of multidimensional continued fractions is introduced. We consider some properties and state some conjectures related to the structure of the family of equivalence classes of two-dimensional periodic continued fractions. Our approach to the study of the family of equivalence classes of two-dimensional periodic continued fractions leads to revealing special subfamilies of continued fractions for which the triangulations of the torus (i.e., the combinatorics of their fundamental domains) are subjected to clear rules. Some of these subfamilies are studied in detail; the way to construct other similar subfamilies is indicated.     

Adaptive Smoothing Method,Deterministically Computable Generalized Jacobians,and the Newton Method

In this note, we show that a well-known integral method, which was used by Mayne and Polak to compute an -subgradient, can be exploited to compute deterministically an element of the plenary hull of the Clarke generalized Jacobian of a locally Lipschitz mapping regardless of its structure. In particular, we show that, when a locally Lipschitz mapping is piecewise smooth, we are able to compute deterministically an element of the Clarke generalized Jacobian by the adaptive smoothing method. Consequently, we show that the Newton method based on the plenary hull of the Clarke generalized Jacobian can be implemented in a deterministic way for solving Lipschitz nonsmooth equations.     

RRF rings which are not LRF

Define a ringA to be RRF (respectively LRF) if every right (respectively left)A-module is residually finite. We determine the necessary and sufficient conditions for a formal triangular matrix ring to be RRF (respectively LRF). Using this we give examples of RRF rings which are not LRF.     

T拟内射模与TQI环

本文定义并刻划了Ｔ拟内射模与Ｔ拟内射包，证明了ＷＧ－ｃｏｃｒｉｔｉｃａｌＴ拟内射模的自同态环为正则非奇异右自内射环．最后讨论了Ｔ拟内射模与Ｔ内射模一致的环，即ＴＱＩ环．还给出了Ｇａｂｒｉｅｌ拓扑Ｇ中每个右理想Ｔ拟内射的几个等价条件