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961.
Let Id,n?k[x0,?,xn] be a minimal monomial Togliatti system of forms of degree d. In [4], Mezzetti and Miró-Roig proved that the minimal number of generators μ(Id,n) of Id,n lies in the interval [2n+1,(n+d?1n?1)]. In this paper, we prove that for n4 and d3, the integer values in [2n+3,3n?1] cannot be realized as the number of minimal generators of a minimal monomial Togliatti system. We classify minimal monomial Togliatti systems Id,n?k[x0,?,xn] of forms of degree d with μ(Id,n)=2n+2 or 3n (i.e. with the minimal number of generators reaching the border of the non-existence interval). Finally, we prove that for n=4, d3 and μ[9,(d+33)]?{11} there exists a minimal monomial Togliatti system Id,n?k[x0,?,xn] of forms of degree d with μ(In,d)=μ.  相似文献   
962.
Recently Lipschitz equivalence of self‐similar sets on has been studied extensively in the literature. However for self‐affine sets the problem is more awkward and there are very few results. In this paper, we introduce a w‐Lipschitz equivalence by repacing the Euclidean norm with a pseudo‐norm w. Under the open set condition, we prove that any two totally disconnected integral self‐affine sets with a common matrix are w‐Lipschitz equivalent if and only if their digit sets have equal cardinality. The main methods used are the technique of pseudo‐norm and Gromov hyperbolic graph theory on iterated function systems.  相似文献   
963.
For wide classes of locally convex spaces, in particular, for the space C p ( X ) of continuous real‐valued functions on a Tychonoff space X equipped with the pointwise topology, we characterize the existence of a fundamental bounded resolution (i.e., an increasing family of bounded sets indexed by the irrationals which swallows the bounded sets). These facts together with some results from Grothendieck's theory of ( D F ) ‐spaces have led us to introduce quasi‐ ( D F ) ‐spaces, a class of locally convex spaces containing ( D F ) ‐spaces that preserves subspaces, countable direct sums and countable products. Regular ( L M ) ‐spaces as well as their strong duals are quasi‐ ( D F ) ‐spaces. Hence the space of distributions D ( Ω ) provides a concrete example of a quasi‐ ( D F ) ‐space not being a ( D F ) ‐space. We show that C p ( X ) has a fundamental bounded resolution if and only if C p ( X ) is a quasi‐ ( D F ) ‐space if and only if the strong dual of C p ( X ) is a quasi‐ ( D F ) ‐space if and only if X is countable. If X is metrizable, then C k ( X ) is a quasi‐ ( D F ) ‐space if and only if X is a σ‐compact Polish space.  相似文献   
964.
The paper concerns a particular example of the Gibbs sampler and its mixing efficiency. Coordinates of a point are rerandomized in the unit square [0,1]2 to approach a stationary distribution with density proportional to exp(?A2(u?v)2) for (u,v)[0,1]2 with some large parameter A.Diaconis conjectured the mixing time of this process to be O(A2) which we confirm in this paper. This improves on the currently known O(exp(A2)) estimate.  相似文献   
965.
We extend Feichtinger's minimality property on the smallest non-trivial time-frequency shift invariant Banach space, to the quasi-Banach case. Analogous properties are deduced for certain matrix spaces.We use these results to prove that the pseudo-differential operator Op(a) is a Schatten-q operator from M to Mp and r-nuclear operator from M to Mr when aMr for suitable p, q and r in (0,].  相似文献   
966.
Withaferin A (WA) is one of the major bioactive steroidal lactones with extensive pharmacological activities present in the plant Withania somnifera. The absolute oral bioavailability of WA remains unknown and human‐related in vitro data are not available. Therefore, in the present study, the absolute oral bioavailability of WA in male rats and the in vitro screening of absorption factors by Q‐trap and LC–MS/MS analysis were conducted to explore possible clinical properties of WA. The developed and validated analytical methods were successfully applied to the pharmacokinetic studies and in vitro measurement of WA. The oral bioavailability was determined to be 32.4 ± 4.8% based on intravenous (5 mg/kg) and oral (10 mg/kg) administrations of WA in male rats. The in vitro results showed that WA could be easily transported across Caco‐2 cells and WA did not show as a substrate for P‐glycoprotein. Moreover, the stability of WA was similar between male rat and human in simulated gastric fluid (stable), in intestinal microflora solution (slow decrease) and in liver microsomes (rapid depletion, with a half‐life of 5.6 min). As such, the first‐pass metabolism of WA was further verified by rat intestine‐liver in situ perfusion, revealing that WA rapidly decreased and 27.1% remained within 1 h, while the content of three major metabolites (M1, M4, M5) identified by Q‐trap increased. This perfusion result is consistent with the oral bioavailability results in vivo. The first‐pass metabolism of WA might be the main barrier in achieving good oral bioavailability in male rats and it is predicted to be similar in humans. This study may hold clinical significance.  相似文献   
967.
An efficient, economic and high yielding method was described for the synthesis of baclofen (BAC) pharmacopoeial impurities (impurity A and impurity B) which can be used for gram‐scale synthesis. Furthermore, a novel ecofriendly thin‐layer chromatographic TLC–densitometric method was established and validated for the determination of BAC and its synthesized impurities. The developed TLC–densitometric method is based on the chromatographic separation using TLC plates (60 F254) using a green mobile phase of ethyl acetate–methanol–ammonia solution, 33% (8:2:0.1, by volume) with UV scanning at 220 nm. The proposed method was validated with respect to International Conference on Harmonization guidelines. The validated method was successfully applied for determination of BAC in pure form and in its commercial dosage form. Additionally, the greenness profile of the developed method was evaluated and compared with those of the reported chromatographic methods. The developed method was found to be superior to the published methods, being environmentally benign.  相似文献   
968.
General Lp dual curvature measures have recently been introduced by Lutwak, Yang and Zhang [24]. These new measures unify several other geometric measures of the Brunn–Minkowski theory and the dual Brunn–Minkowski theory. Lp dual curvature measures arise from qth dual intrinsic volumes by means of Alexandrov-type variational formulas. Lutwak, Yang and Zhang [24] formulated the Lp dual Minkowski problem, which concerns the characterization of Lp dual curvature measures. In this paper, we solve the existence part of the Lp dual Minkowski problem for p>1 and q>0, and we also discuss the regularity of the solution.  相似文献   
969.
The Adimurthi–Druet [1] inequality is an improvement of the standard Moser–Trudinger inequality by adding a L2-type perturbation, quantified by α[0,λ1), where λ1 is the first Dirichlet eigenvalue of Δ on a smooth bounded domain. It is known [3], [10], [14], [19] that this inequality admits extremal functions, when the perturbation parameter α is small. By contrast, we prove here that the Adimurthi–Druet inequality does not admit any extremal, when the perturbation parameter α approaches λ1. Our result is based on sharp expansions of the Dirichlet energy for blowing sequences of solutions of the corresponding Euler–Lagrange equation, which take into account the fact that the problem becomes singular as αλ1.  相似文献   
970.
This work presents sufficient conditions for the existence of homoclinic solutions for second order coupled discontinuous systems of differential equations on the real line without the usual growth condition in the literature.The arguments apply the fixed point theory, Green's functions technique, L1-Carathéodory functions, lower and upper solutions and Schauder's fixed point theorem.  相似文献   
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