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1.
Asaf Levin 《Operations Research Letters》2004,32(6):530-534
Consider the following problem: given a ground set and two minimization objectives of the same type find a subset from a given subset-class that minimizes the first objective subject to a budget constraint on the second objective. Using Megiddo's parametric method we improve an earlier weakly polynomial time algorithm. 相似文献
2.
High-performance liquid chromatography separated successively and quantitatively the food flavoring agents pyrimidines, purines and nucleosides, followed by nucleotides, then by polyphenols and finally by pyrazines with a reversed-phase octadecylsilica (μBondapak C18) column and various proportions of methanol, water, acetic acid and tetrabutylammonium phosphate (PIC A). The polar solvent (solvent A) was water—acetic acid—PIC A (97.5:1.5:1.0) and the relatively non-polar solvent (solvent B) was methanol—acetic acid—PIC A (97.5:1.5:1.0). Purines, pyrimidines, and nucleosides were eluted with solvent A. Nucleotides were eluted with a mixture of solvents A and B (9:1). Polyphenols were separated with a gradient starting at 10% solvent B and finishing at 25% solvent B, and finally the pyrazines were removed successively from the column with a gradient starting at 25% solvent B and finishing at 45% solvent B. The resolution and reproducibility were excellent for more than 50 compounds. By this method beverages could be analyzed directly, without solvent extraction, for flavoring compounds. 相似文献
3.
Asaf Kleopas Sugih 《European Polymer Journal》2009,45(1):155-164
The ring opening polymerization (ROP) of p-dioxanone using a protected monosaccharide (1,2;3,4-di-O-isopropylidene-α-d-galactopyranose)/Al(OiPr)3 initiator system to yield polydioxanone with a protected monosaccharide end-group is described. The products were synthesized at 60-100 °C and characterized by 1H and 13C NMR, and MALDI-TOF mass spectrometry. Besides the desired polydioxanone functionalised with a monosaccharide end-group, also polydioxanone with an OiPr end-group was formed (20-30%). Systematic studies showed that the polymer yield is a function of the reaction temperature and the reaction time, with higher temperatures (100 °C) leading to lower yields. The average chain length of the polymers is between 7 and 58 repeating units and may be tuned by the monomer to monosaccharide ratio (at constant Al(OiPr)3 intake). A statistical model has been developed that successfully describes the experimentally observed relation between the average chain length of the functionalized polymer and reaction parameters. 相似文献
4.
Salant A Amitay-Sadovsky E Banin U 《Journal of the American Chemical Society》2006,128(31):10006-10007
Gold-tipped CdSe rods (nanodumbbells) were solubilized in an aqueous phase and self-assembled in a head-to-tail manner using biotin disulfide and avidin. The disulfide end of the biotin molecule attaches to the gold tip of the nanodumbbell, and the biotin end of the molecule is able to conjugate to an avidin protein. The avidin can strongly conjugate up to four biotin molecules. Changing the ratios of biotin to nanodumbbells leads to the formation of dimers, trimers, and flowerlike structures. To further improve the distribution of chain lengths, a separation method based upon weight was applied using a concentration gradient. The gold tips provide effective anchor points for constructing complex nanorod structures by self-assembly. 相似文献
5.
A milestone in probability theory is the law of the iterated logarithm (LIL), proved by Khinchin and independently by Kolmogorov in the 1920s, which asserts that for iid random variables with mean 0 and variance 1 In this paper we prove that LIL holds for various functionals of random graphs and hypergraphs models. We first prove LIL for the number of copies of a fixed subgraph H. Two harder results concern the number of global objects: perfect matchings and Hamiltonian cycles. The main new ingredient in these results is a large deviation bound, which may be of independent interest. For random k‐uniform hypergraphs, we obtain the Central Limit Theorem and LIL for the number of Hamilton cycles. 相似文献
6.
Reut Levi Guy Moshkovitz Dana Ron Ronitt Rubinfeld Asaf Shapira 《Random Structures and Algorithms》2017,50(2):183-200
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded‐degree graph. Given an edge e in G we would like to decide whether e belongs to a connected subgraph consisting of edges (for a prespecified constant ), where the decision for different edges should be consistent with the same subgraph . Can this task be performed by inspecting only a constant number of edges in G ? Our main results are:
- We show that if every t‐vertex subgraph of G has expansion then one can (deterministically) construct a sparse spanning subgraph of G using few inspections. To this end we analyze a “local” version of a famous minimum‐weight spanning tree algorithm.
- We show that the above expansion requirement is sharp even when allowing randomization. To this end we construct a family of 3‐regular graphs of high girth, in which every t‐vertex subgraph has expansion . We prove that for this family of graphs, any local algorithm for the sparse spanning graph problem requires inspecting a number of edges which is proportional to the girth.
7.
A 1‐factorization of a graph G is a collection of edge‐disjoint perfect matchings whose union is E(G). In this paper, we prove that for any ?>0, an (n,d,λ)‐graph G admits a 1‐factorization provided that n is even, C0 ≤ d ≤ n?1 (where C0=C0(?) is a constant depending only on ?), and λ ≤ d1??. In particular, since (as is well known) a typical random d‐regular graph Gn,d is such a graph, we obtain the existence of a 1‐factorization in a typical Gn,d for all C0 ≤ d ≤ n?1, thereby extending to all possible values of d results obtained by Janson, and independently by Molloy, Robalewska, Robinson, and Wormald for fixed d. Moreover, we also obtain a lower bound for the number of distinct 1‐factorizations of such graphs G, which is better by a factor of 2nd/2 than the previously best known lower bounds, even in the simplest case where G is the complete graph. 相似文献
8.
A celebrated result of Gowers states that for every ?>0 there is a graph G such that every ?-regular partition of G (in the sense of Szemerédi’s regularity lemma) has order given by a tower of exponents of height polynomial in 1/?. In this note we give a new proof of this result that uses a construction and proof of correctness that are significantly simpler and shorter. 相似文献
9.
10.
We study a new kind of online bin packing with conflicts, motivated by a problem arising when scheduling jobs on the Grid. In this bin packing problem, the set of items is given at the beginning, together with a set of conflicts on pairs of items. A conflict on a pair of items implies that they cannot be assigned to a common bin. The online scenario is realized as follows. Variable-sized bins arrive one by one, and items need to be assigned to each bin before the next bin arrives. We analyze the online problem as well as semi-online versions of it, which are the variant where the sizes of the arriving bins are monotonically non-increasing as well as the variant where they are monotonically non-decreasing. 相似文献