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Toufik Hadjersi 《Applied Surface Science》2007,253(9):4156-4160
The mechanism of metal-assisted electroless etching of silicon in HF-oxidizing agent-H2O etching system as a function of oxidizing agent concentration was studied. Three types of oxidizing agent were experimented namely Na2S2O8, K2Cr2O7 and KMnO4. Their concentrations were varied from 0.05 M to 0.3 M. The layers formed on silicon were investigated by scanning electron microscopy (SEM), X-ray diffraction (XRD) and energy-dispersive X-ray (EDX). It is shown that an insoluble solid-phase film (K2SiF6) form on silicon surface when concentration of K2Cr2O7 or KMnO4 increases in chemical solutions. On other hand, when Na2S2O8 concentration increases, the surface roughness decreases without any chemical complex formation. 相似文献
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We count derangements, involutions and unimodal elements in the wreath product C
r
≀ S
n
by the numbers of excedances, fixed points and 2-cycles. Properties of the generating functions, including combinatorial
formulas, recurrence relations and real-rootedness are studied. The results obtained specialize to those on the symmetric
group S
n
and on the hyperoctahedral group B
n
when r = 1, 2, respectively. 相似文献
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Toufik Zaimi 《Archiv der Mathematik》2006,87(2):124-128
Let N be a positive rational integer and let P be the set of powers of a Salem number of degree d. We prove that for any α∈P the fractional parts of the numbers
, when n runs through the set of positive rational integers, are dense in the unit interval if and only if N≦ 2d − 4. We also show that for any α∈P the integer parts of the numbers αn are divisible by N for infinitely many n if and only if N≦ 2d − 3.
Received: 27 April 2005 相似文献
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Let x and y be two variables satisfying the commutation relation xy=qyx+hf(y), where f(y) is a polynomial. In this paper, using Young diagrams and generating functions techniques, we study the binomial formula
(x+y)
n
and we present an identity for x
m
y. The connection to Operator Calculus is discussed and several special cases are treated explicitly. 相似文献
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In this paper, the approximate controllability of neutral stochastic fractional differential equations involving nonlocal initial conditions is studied. By using Sadovskii’s fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of semilinear fractional stochastic differential equations with nonlocal conditions under the assumption that the corresponding linear system is approximately controllable. Finally, an application to a fractional partial stochastic differential equation with nonlocal initial condition is provided to illustrate the obtained theory. 相似文献
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Johannes Hatzl Toufik Mansour Mark Shattuck 《Journal of Mathematical Modelling and Algorithms》2011,10(2):193-203
Consider the set S of points in the plane consisting of the ordered pairs (i, j ), where
1 \leqslant i \leqslant m1 \leqslant i \leqslant m and
1 \leqslant j \leqslant n1 \leqslant j \leqslant n. A problem related to the study of segmentation evaluation of visual images concerns finding a permutation σ of the points of S for which the sum
?s ? Sd(s, s(s)) \sum\limits_{s \in S}d(s, \sigma(s)) 相似文献 |