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1.
In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers
to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge
bounds equal one, stable multi-sets are equivalent to stable sets.
For the stable multi-set problem, we derive reduction rules and study the associated polytope. We state necessary and sufficient
conditions for the extreme points of the linear relaxation to be integer. These conditions generalize the conditions for the
stable set polytope. Moreover, the classes of odd cycle and clique inequalities for stable sets are generalized to stable
multi-sets and conditions for them to be facet defining are determined.
The study of stable multi-sets is initiated by optimization problems in the field of telecommunication networks. Stable multi-sets
emerge as an important substructure in the design of optical networks.
Received: February 14, 2001/Revised version: September 7, 2001 相似文献
2.
This paper presents a few novel results, and collects together what is known and conjectured about the branching graph of a polyhex. 相似文献
3.
4.
Haim Gvirtzman Mordeckai Magaritz Eugenia Klein Arie Nadler 《Transport in Porous Media》1987,2(1):83-93
Cold stage Scanning Electron Microscopy (SEM) with a rapid cooling technique makes it possible to investigate the water phase within unsaturated porous media. It is thought that this technique preserves the main features of the micromorphology of the water menisci as it exists in the liquid phase in soils. Saddle-shaped elements, as well as pendular rings of water, were observed with concave and convex curvatures of the water-air interface. The hydraulic conductivity of an unsaturated soil may be inferred from SEM photographs. Observations of isolated water menisci indicate the existence of an immobile water domain. The surface geometry of the water menisci was analyzed quantitatively and surface tension and capillary pressure were determined. 相似文献
5.
Ivan Gutman Sabina Gojak Niko Radulovi? Boris Furtula 《Monatshefte für Chemie / Chemical Monthly》2006,46(2):277-284
In a recent work it was demonstrated that in linear hexagonal chains the distribution of π-electrons into rings (as computed
by means of the Randić–Balaban method) is uniform, irrespective of the nature of the terminal fragments. We now establish that an analogous, yet somewhat
more complex, uniformity in the π-electron distribution exists also in double linear hexagonal chains, as well as in some
other benzenoid systems. 相似文献
6.
Extremal hexagonal chains 总被引:6,自引:0,他引:6
Ivan Gutman 《Journal of mathematical chemistry》1993,12(1):197-210
Some extremal properties of the linear chainL
h ofh hexagons are pointed out. In the class of all hexagonal chains withh hexagons,L
h has minimumK,Z andx
1 values, as well as maximum W and values;K = number of perfect matchings,Z = number of independent edge sets (Hosoya index),x
1 = largest graph eigenvalue,W = Wiener index, = number of independent vertex sets (Merrifield-Simmons index). The extremality ofL
h with respect toZ, andx
1 is demonstrated here for the first time.Dedicated to Frank Harary, teacher, inspirer and friend, pioneer, champion and proprietor of graph theory, on the occasion of his 70th birthday. 相似文献
7.
Arie L. Gutman Marina Etinger Gennady Nisnevich Felix Polyak 《Tetrahedron: Asymmetry》1998,9(24):1022
The enantiomerically pure chiral benzocyclic amines 6–8 were obtained by asymmetric transamination of the corresponding prochiral ketones 9a–c. The method involves: (a) formation of chiral imines 10a–c from the prochiral ketones 9a–c and the inexpensive chiral auxiliary (R)- or (S)-phenylethylamine (PEA); (b) asymmetrically induced reduction of these imines to the diastereomeric amines 11a–c and 12a–c; (c) catalytic hydrogenation to remove the benzylic fragment of the chiral PEA auxiliary. The stereoselectivity of the imine reduction, as well as the regioselectivity of the catalytic hydrogenation, are strongly dependent on the size of the saturated ring condensed with the benzene ring. This approach was used to develop a convenient, high yielding, and stereoselective route to several practically important optically active α-amino substituted benzocyclic compounds. 相似文献
8.
The thermal expansion properties of crystalline organic compounds are investigated by data mining of the Cambridge Structural Database (CSD). The mean volumetric thermal expansion coefficient is 168.8 × 10−6 K−1 and the mean uniaxial thermal expansion coefficient is 71.4 × 10−6 K−1, based on 745 and 1129 different observations, respectively. Normal and anomalous coefficients can be identified using these values and the associated standard deviations. The anisotropy of the thermal expansion is also evaluated and found to have a very broad distribution. 4719 different structures, comprising 4093 different molecular compounds and 626 additional polymorphs have been analyzed on their thermal expansion properties. Approximately 34% of these structures may have at least one orthogonal axis with negative thermal expansion, much more than generally believed. Moreover 127 structures have been identified which could have negative volumetric thermal expansion. Experimental validation using a robust protocol with data collected at more than 2 different temperatures is required to validate these cases.The thermal expansion properties of crystalline organic compounds are investigated by data mining of the Cambridge Structural Database (CSD). Negative uniaxial thermal expansion is much more common than generally believed. 相似文献
9.
Wavelength-dependent properties of photodynamic therapy using hypericin in vitro and in an animal model 总被引:2,自引:0,他引:2
Blank M Kostenich G Lavie G Kimel S Keisari Y Orenstein A 《Photochemistry and photobiology》2002,76(3):335-340
Wavelength effects in photodynamic therapy (PDT) with hypericin (HY) were examined in a C26 colon carcinoma model both in vitro and in vivo. Irradiation of HY-sensitized cells in vitro with either 550 or 590 nm caused the loss of cell viability in a drug- and light-dose-dependent manner. The calculated ratio of HY-based PDT (HY-PDT) efficiencies at these two wavelengths was found to correlate with the numerical ratio of absorbed photons at each wavelength. In vivo irradiation of C26-derived tumors, 6 h after intraperitoneal administration of HY (5 mg/kg), caused extensive vascular damage and tumor necrosis. The depth of tumor necrosis (d) was more pronounced at 590 than at 550 nm and increased when the light dose was raised from 60 to 120 J/cm2. The maximal depths of tumor necrosis (at 120 J/cm2) were 7.5+/-1.5 mm at 550 nm and 9.9+/-0.8 mm at 590 nm. Both values are rather high in view of the limited penetration of green-yellow light into the tissue. Moreover, the depth ratio, d590/d550 = 1.3 (P < 0.001), is smaller than expected considering the 2.2-fold lower HY absorbance and the 1.7-fold lower tissue penetration of radiation at 550 than at 590 nm. This finding indicates that in vivo the depth at which HY-PDT elicits tumor necrosis is not only determined by photophysical considerations (light penetration, number of absorbed photons) but is also influenced significantly by other mechanisms such as vascular effects. Therefore, despite the relatively short-wavelength peaks of absorption, our observations suggest that HY is an effective photodynamic agent that can be useful in the treatment of tumors with depths in the range of 1 cm. 相似文献
10.
Graph theory is applied to the study of the dependence of total π-electron energy, π-electron charge distribution and free valency indices of conjugated hydrocarbons on molecular topology. It is shown that the number of loops in the molecular graph determines these quantities. 相似文献