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31.
The following conjecture may have never been explicitly stated, but seems to have been floating around: if the vertex set
of a graph with maximal degree Δ is partitioned into sets V
i
of size 2Δ, then there exists a coloring of the graph by 2Δ colors, where each color class meets each V
i
at precisely one vertex. We shall name it the strong 2Δ-colorability conjecture. We prove a fractional version of this conjecture. For this purpose, we prove a weighted generalization of a theorem of Haxell,
on independent systems of representatives (ISR’s). En route, we give a survey of some recent developments in the theory of
ISR’s.
The research of the first author was supported by grant no 780/04 from the Israel Science Foundation, and grants from the
M. & M. L. Bank Mathematics Research Fund and the fund for the promotion of research at the Technion.
The research of the third author was supported by the Sacta-Rashi Foundation. 相似文献
32.
Ron Aharoni Eli Berger Agelos Georgakopoulos Amitai Perlstein 《Journal of Combinatorial Theory, Series B》2011,101(1):1-17
We prove a strong version of the Max-Flow Min-Cut theorem for countable networks, namely that in every such network there exist a flow and a cut that are “orthogonal” to each other, in the sense that the flow saturates the cut and is zero on the reverse cut. If the network does not contain infinite trails then this flow can be chosen to be mundane, i.e. to be a sum of flows along finite paths. We show that in the presence of infinite trails there may be no orthogonal pair of a cut and a mundane flow. We finally show that for locally finite networks there is an orthogonal pair of a cut and a flow that satisfies Kirchhoff's first law also for ends. 相似文献
33.
The potent Diels-Alder diene, phencyclone, 1, reacts with N-pentafluorophenylmaleimide, 2, to form an adduct, 3, characterized by 1H, 13C, and 19F NMR at 300, 75 and 282 MHz, respectively. The one-dimensional (1D) and two-dimensional (2D) 1H and 13C NMR spectra of 3 at ambient temperatures imply a slow exchange limit (SEL) regime with respect to rotation of the unsubstituted bridgehead phenyl groups about severely hindered C(sp2)-C(sp3) bonds. Major non-bonded interactions are expected between the ortho protons of the C6H5 groups and H-1, 8 of the phenanthrenoid moiety of 3. 19F 1D and 2D (COSY) NMR spectra show that the SEL regime also obtains for rotation about the N-C6F5 bond of 3, with five separate fluorine signals seen, consistent with a preferred conformation in which the C6F5 may lie roughly perpendicular to the plane of the pyrrolidinedione moiety, and may be in the mirror symmetry plane of 3. The results are considered relevant to hindered aryl rotations in numerous Pharmaceuticals. Selected spectral data for 2 and precursors are also presented. 相似文献
34.
Building on the earlier analysis by Berlin (1991) , this paper reviews various studies on integrating mathematics and science in the 1990s and provides some implications for further research. The areas identified for further exploration include comparison of the nature of mathematics and science, epistemological debates in mathematics and in science education, the bases used to emphasize science over mathematics or vice versa, empirical evidence of effectiveness of integration, connections between teacher education programs for integration and teachers' subsequent classroom teaching practices, perceptions of integration on the part of teacher educators, contextual difficulties in implementing integrated approaches and possible solutions, and rationales of integrating mathematics and science through technology. In order to help all students become scientifically literate, which most reform documents call for, more focused attention on integration of curriculum and instruction is necessary. 相似文献
35.
Ron M. Roth 《Designs, Codes and Cryptography》1996,9(2):177-191
Codes
of length 2
m
over {1, -1} are defined as null spaces of certain submatrices of Hadamard matrices. It is shown that the codewords of
all have an rth order spectral null at zero frequency. Establishing the connection between
and the parity-check matrix of Reed-Muller codes, the minimum distance of
is obtained along with upper bounds on the redundancy of
. An efficient algorithm is presented for encoding unconstrained binary sequences into
. 相似文献
36.
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.
37.
Molecular mass distribution of sodium alginate by high-performance size-exclusion chromatography 总被引:8,自引:0,他引:8
Ci SX Huynh TH Louie LW Yang A Beals BJ Ron N Tsang WG Soon-Shiong P Desai NP 《Journal of chromatography. A》1999,864(2):199-210
A sensitive high-performance size-exclusion chromatography (HPSEC) method with simple UV detection was developed for the molecular mass analysis of sodium alginate. It was used to evaluate alginates of varying molecular mass and the results were compared with the viscosity measurements. This HPSEC method was sensitive to serve as the stability indicating method for alginate after storage under different conditions. The information of relative molecular mass distribution of alginate was provided with reference to pullulan molecular mass standards. The comparison of the HPSEC chromatograms of alginate, pullulan and dextran revealed the effect of chemical composition of a polysaccharide and its effect on apparent molecular mass distribution. 相似文献
38.
Wasserman V Kizelsztein P Garbuzenko O Kohen R Ovadia H Tabakman R Barenholz Y 《Langmuir : the ACS journal of surfaces and colloids》2007,23(4):1937-1947
The piperidine nitroxide tempamine (TMN) is a cell-permeable, stable radical having antioxidant, anticancer, and proapoptotic and/or pronecrotic activities, as was demonstrated by us in cell cultures. We also demonstrated synergism between TMN and doxorubicin in doxorubicin-sensitive and doxorubicin-resistant cell lines. Treatment of the C26 mouse colon carcinoma model in vivo also demonstrated synergism between TMN and doxorubicin in sterically stabilized liposomes (SSLs) containing TMN (SSL-TMN) and those containing doxorubicin. The above effects of TMN and SSL-TMN motivated us to develop and optimize the SSL-TMN formulation so that it will be able to reach the disease site with a sufficiently high TMN level and a release rate needed to achieve a therapeutic effect. Because TMN is an amphipathic weak base, it was remote loaded by an intraliposome high/extraliposome low transmembrane ammonium sulfate gradient. The kinetics and level of TMN loading were monitored by cyclic voltammetry (CV) and electron paramagnetic resonance (EPR); the latter also indicates TMN precipitation in the intraliposomal aqueous phase. The regeneration of the original CV and EPR signals by the ionophore nigericin indicates that TMN remained fully intact during loading and release. The cardinal role of the transmembrane ammonium ion gradient in the loading process was proven by the use of the selective ionophores nonactin (for NH4+) and nigericin (for H+). The anion of the ammonium salts affects loading stability and the rate of TMN release, both mediated through the TMN state of aggregation in the intraliposomal aqueous phase. The greater the TMN salt precipitation, the slower the TMN release rate. This was supported by measurement of osmolality, which is inversely related to TMN salt precipitate. Precipitation is in the order SO4(-2)>Cl-1>glucuronate-1. Liposome lipid composition, magnitude of the transmembrane ammonium ion gradient, and type of anion of the ammonium salt determine the amount of TMN loaded and its release rate. 相似文献
39.
Ron S. Dickson Gary S. Evans Gary D. Fallon 《Journal of organometallic chemistry》1982,236(2):C49-C52
The complexes (η-C5Me5)2Rh2(μ-CO) {μ-η2,η2-C(O)CRCR} are obtained from reactions between (η-C5Me5)2Rh2(CO)2 and the alkynes RCCR (R CF3, CO2Me, or Ph) at 25°C. The molecular geometry of the complex with R CF3 has been established by X-ray diffraction; the bridging 'ene-one' unit adopts a μ-η2,η2 conformation. Other complexes isolated from these reactions include (η-C5Me5)Rh(C6R6) (R CF3, CO2Me), (η-C5Me)2Rh2(C4R4) (R CO2Me) and (η-C5Me5)2Rh2(CO2C2R2) (R Ph). The reaction between (η-C5Me5)2Rh2(CO)2 and C6F5CCC6F5 gives (η-C5Me5)2Rh2(CO)2(C6F5C2C6F5). Mononuclear complexes such as (η-C5Me5)Co(C4R4CO) are the major products isolated from reactions between (η-C5Me5)2CO2(CO)2 and alkynes at 25°C. 相似文献
40.
Udo Feldkamp Ron Wacker Hendrik Schroeder Wolfgang Banzhaf Christof M Niemeyer 《Chemphyschem》2004,5(3):367-372
We report on the microarray-based in vitro evaluation of two libraries of DNA oligonucleotide sequences, designed in silico for applications in supramolecular self-assembly, such as DNA computing and DNA-based nanosciences. In this first study which is devoted to the comparison of sequence motif properties theoretically predicted with their performance in real-life, the DNA-directed immobilization (DDI) of proteins was used as an example of DNA-based self-assembly. Since DDI technologies, DNA computing, and DNA nanoconstruction essentially depend on similar prereguisites, in particular, large and uniform hybridization efficiencies combined with low nonspecific cross-reactivity between individual sequences, we anticipate that the microarray approach demonstrated here will enable rapid evaluation of other DNA sequence libraries. 相似文献