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We consider the question whether, given a countable family of lattices in a locally compact abelian group G, there exist functions such that the resulting generalized shift-invariant system is a tight frame of . This paper develops a new approach to the study of generalized shift-invariant system via almost periodic functions, based on a novel unconditional convergence property. From this theory, we derive characterizing relations for tight and dual frame generators, we introduce the system bandwidth as a measure of the total bandwidth a generalized shift-invariant system can carry, and we show that the so-called Calderón sum is uniformly bounded from below for generalized shift-invariant frames. Without the unconditional convergence property, we show, counter intuitively, that even orthonormal bases can have arbitrary small system bandwidth. Our results show that the question of existence of frame generators for a general lattice system is rather subtle and depends on analytical and algebraic properties of the lattice system. 相似文献
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Carotenoids are an essential component of cashew and can be used in pharmaceuticals, cosmetics, natural pigment, food additives, among other applications. The present work focuses on optimizing and comparing conventional and ultrasound-assisted extraction methods. Every optimization step took place with a 1:1 (w:w) mixture of yellow and red cashew apples lyophilized and ground in a cryogenic mill. A Simplex-centroid design was applied for both methods, and the solvents acetone, methanol, ethanol, and petroleum ether were evaluated. After choosing the extractor solvent, a central composite design was applied to optimize the sample mass (59–201 mg) and extraction time (6–34 min). The optimum conditions for the extractor solvent were 38% acetone, 30% ethanol, and 32% petroleum ether for CE and a mixture of 44% acetone and 56% methanol for UAE. The best experimental conditions for UAE were a sonication time of 19 min and a sample mass of 153 mg, while the CE was 23 min and 136 mg. Comparing red and yellow cashews, red cashews showed a higher carotenoid content in both methodologies. The UAE methodology was ca. 21% faster, presented a more straightforward composition of extracting solution, showed an average yield of superior carotenoid content in all samples compared to CE. Therefore, UAE has demonstrated a simple, efficient, fast, low-cost adjustment methodology and a reliable alternative for other applications involving these bioactive compounds in the studied or similar matrix. 相似文献
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设n为自然数,σ(n)表示n的所有正因子和函数.令d是n的真因子,若n满足σ(n)=2n-d,则称n为亏因子为d的亏完全数.本文给出了具有四个素因子的奇亏完全数的一些性质的刻画. 相似文献
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Mauduit与Sárkzy在一系列论文中研究了κ元序列的伪随机性.本文通过对模pq剩余类环Z_(pq)进行分割,进而结合离散对数的方法,构造了一大族长度为pq的伪随机κ元序列,并证明其具有很好的伪随机性. 相似文献
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The modular software MOLSIM for all‐atom molecular and coarse‐grained simulations is presented with focus on the underlying concepts used. The software possesses four unique features: (1) it is an integrated software for molecular dynamic, Monte Carlo, and Brownian dynamics simulations; (2) simulated objects are constructed in a hierarchical fashion representing atoms, rigid molecules and colloids, flexible chains, hierarchical polymers, and cross‐linked networks; (3) long‐range interactions involving charges, dipoles and/or anisotropic dipole polarizabilities are handled either with the standard Ewald sum, the smooth particle mesh Ewald sum, or the reaction‐field technique; (4) statistical uncertainties are provided for all calculated observables. In addition, MOLSIM supports various statistical ensembles, and several types of simulation cells and boundary conditions are available. Intermolecular interactions comprise tabulated pairwise potentials for speed and uniformity and many‐body interactions involve anisotropic polarizabilities. Intramolecular interactions include bond, angle, and crosslink potentials. A very large set of analyses of static and dynamic properties is provided. The capability of MOLSIM can be extended by user‐providing routines controlling, for example, start conditions, intermolecular potentials, and analyses. An extensive set of case studies in the field of soft matter is presented covering colloids, polymers, and crosslinked networks. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc. 相似文献
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Consider a simple graph and its proper edge coloring c with the elements of the set . We say that c is neighbor set distinguishing (or adjacent strong) if for every edge , the set of colors incident with u is distinct from the set of colors incident with v. Let us then consider a stronger requirement and suppose we wish to distinguishing adjacent vertices by sums of their incident colors. In both problems the challenging conjectures presume that such colorings exist for any graph G containing no isolated edges if only . We prove that in both problems is sufficient. The proof is based on the Combinatorial Nullstellensatz, applied in the “sum environment.” In fact the identical bound also holds if we use any set of k real numbers instead of as edge colors, and the same is true in list versions of the both concepts. In particular, we therefore obtain that lists of length ( in fact) are sufficient for planar graphs. 相似文献