Let $p$ be the smallest prime divisor of the order of a finite group $G$. We examine the structure of $G$ under the hypothesis that $p$-subgroups of $G$ of certain orders are complemented in $G$. In particular, we extend some recent results. 相似文献
Recent research shows that the class of rotation symmetric Boolean functions is potentially rich in functions of cryptographic significance. In this paper, based on the knowledge of compositions of an integer, we present two new kinds of construction of rotation symmetric Boolean functions having optimal algebraic immunity on either odd variables or even variables. Our new functions are of much better nonlinearity than all the existing theoretical constructions of rotation symmetric Boolean functions with optimal algebraic immunity. Further, the algebraic degree of our rotation symmetric Boolean functions are also high enough. 相似文献
In this paper, we establish some quotient calculus rules in terms of contingent derivatives for the two extended-real-valued functions defined on a Banach space and study a nonsmooth multiobjective fractional programming problem with set, generalized inequality and equality constraints. We define a new parametric problem associated with these problem and introduce some concepts for the (local) weak minimizers to such problems. Some primal and dual necessary optimality conditions in terms of contingent derivatives for the local weak minimizers are provided. Under suitable assumptions, sufficient optimality conditions for the local weak minimizers which are very close to necessary optimality conditions are obtained. An application of the result for establishing three parametric, Mond–Weir and Wolfe dual problems and several various duality theorems for the same is presented. Some examples are also given for our findings.
We have investigated the growth of magnesium-doped GaP (GaP:Mg) layers on GaN by metalorganic chemical vapor deposition. The hole carrier concentration increased linearly from 0.8×1018 to 4.2×1018 cm−3 as the Bis(cyclopentadienyl) magnesium (Cp2Mg) mole flow rate increased from 1.2×10−7 to 3.6×10−7 mol/min. However, the hole carrier concentration decreased when the CP2Mg mole flow rate was further increased. The double crystal X-ray diffraction (DCXRD) rocking curves showed that the GaP:Mg layers were single crystalline at low CP2Mg molar flow. However, the GaP:Mg layers became polycrystalline if the CP2Mg molar flow was too high. The decrease in hole carrier concentration at high CP2Mg molar flow was due to crystal quality deterioration of the GaP layer, which also resulted in the low hole mobility of the GaP:Mg layer. 相似文献
A micrometer-sized nanostructured, magnetic, ball-like FexOy-CeO2 composite was synthesized through an ethylene-glycol mediated process. The synthesized samples were characterized by scanning electron microscopy combined with energydisperse X-ray analysis, transmission electron microscopy and X-ray powder diffraction. In the synthesis system, polyethylene glycol (PEG) and urea were found to play significant roles in the formation of the micrometer-sized spherical architecture of the precursor. The details of morphology and particle size could be changed with the initial concentration of Fe(NO3)3·9H2O and Ce(NO3)3·6H2O as the reactants. The magnetic FexOy-CeO2 composite with a similar morphology was readily obtained by calcination from the precursor. The characterization of transmission electron microscopy showed the calcined ball-like architecture was a highly porous structure consisting of many nanoparticles. Because of the micrometer-sized nanostructure and the multi-components as well as the magnetism, the as-obtained FexOy-CeO2 composite showed better activity and potentially easy recovery for the harmless degradation of hexachlorobenzene (HCB). 相似文献