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131.
B. Krishna Das Jaydeb Sarkar Santanu Sarkar 《Complex Analysis and Operator Theory》2014,8(6):1325-1339
Maximality of a contractive tuple of operators is considered. A characterization for a contractive tuple to be maximal is obtained. The notion of maximality for a submodule of the Drury–Arveson module on the \(d\) -dimensional unit ball \({\mathbb {B}}_d\) is defined. For \(d=1\) , it is shown that every submodule of the Hardy module over the unit disc is maximal. But for \(d\ge 2\) we prove that any homogeneous submodule or submodule generated by polynomials is not maximal. A characterization of maximal submodules is obtained. 相似文献
132.
Let N ≥ 5 and \({{\mathcal{D}}^{2,2} (\mathbb{R}^N)}\) denote the closure of \({C_0^\infty (\mathbb{R}^N)}\) in the norm \({\|u\|_{{\mathcal{D}}^{2,2} (\mathbb{R}^N)}^2 := \int\nolimits_{\mathbb{R}^N} |\Delta u|^2.}\) Let \({K \in C^2 (\mathbb{R}^N).}\) We consider the following problem for ? ≥ 0: $$(P_\varepsilon) \left\{\begin{array}{llll}{\rm Find} \, u \in {\mathcal{D}}^{2, 2} (\mathbb{R}^N) \, \, {\rm solving} :\\ \left.\begin{array}{lll}\Delta^2 u = (1+ \varepsilon K (x)) u^{\frac{N+4}{N-4}}\\ u > 0 \end{array}\right\}{\rm in} \, \mathbb{R}^N.\end{array}\right.$$ We show an exact multiplicity result for (P ? ) for all small ? > 0. 相似文献
133.
Santanu Sarkar 《Designs, Codes and Cryptography》2014,73(2):383-392
We consider an RSA variant with Modulus \(N=p^rq\) . This variant is known as Prime Power RSA. In PKC 2004, May proved when decryption exponent \(d<N^{ \frac{r}{(r+1)^2}}\) or \(d< N^{\left( \frac{r-1}{r+1}\right) ^2}\) , one can factor \(N\) in polynomial time. In this paper, we improve this bound when \(r \le 5\) . We provide detailed experimental results to justify our claim. 相似文献
134.
Time evolution of volume fraction of the minor phase is studied in an alumina-doped sodium borosilicate glass inside the immiscible region. It is shown that such a study permits a distinction between the two mechanisms of phase separation; namely spinodal decomposition and nucleation and growth. For spinodal decomposition, the volume fraction decreases initially, whereas for nucleation and growth, it increases with heat-treatment time. 相似文献
135.
Goutam Mukhopadhyay Jasmina Khanam Arunabha Nanda Arindam Basu Sarkar 《Chromatographia》2010,71(7-8):699-702
A simple, sensitive and precise reverse phase liquid chromatographic method has been developed and validated for quantification of bovine serum albumin (BSA), α-lactalbumin (α-La) and β–lactoglobulin (β-Lg) that are removed from whey waste by foam fractionation method. The data is reproducible over a wide concentration range. This optimized method allowed analysis of BSA, α-La, β-Lg in a mixture within 5 min and could be applied to the analysis of a variety of commercial and laboratory whey products within a short time. 相似文献
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The neutron diffraction data analysis of deuterated liquid 2-propanol at room temperature to define its molecular conformation
is presented. 2-Propanol being a large molecule with twelve atomic sites, the conformation analysis is tricky and an improved
method of data analysis is given. The intermolecular structural correlations, i.e., hydrogen-bonded liquid structure, can
be modelled accurately to extract the nature of the average hydrogen-bonded molecular association in liquid state at room
temperature. Like other alcohols these are mostly hexamer ring chain (HRC) clusters. The cluster analysis of recent X-ray
data available in the literature also support the same liquid structure. 相似文献
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