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51.
52.
In 1995, Voigt constructed a planar triangle-free graph that is not 3-list-colorable. It has 166 vertices. Gutner then constructed such a graph with 164 vertices. We present two more graphs with these properties. The first graph has 97 vertices and a failing list assignment using triples from a set of six colors, while the second has 109 vertices and a failing list assignment using triples from a set of five colors. 相似文献
53.
At present, the most successful approach for solving large-scale instances of the Symmetric Traveling Salesman Problem to optimality is branch-and-cut. The success of branch-and-cut is due in large part to the availability of effective separation procedures; that is, routines for identifying violated linear constraints.
For two particular classes of constraints, known as comb and domino-parity constraints, it has been shown that separation becomes easier when the underlying graph is planar. We continue this line of research by showing how to exploit planarity in the separation of three other classes of constraints: subtour elimination, 2-matching and simple domino-parity constraints. 相似文献
54.
Oleg Makarenkov Paolo Nistri 《Journal of Mathematical Analysis and Applications》2008,338(2):1401-1417
In this paper we consider a class of planar autonomous systems having an isolated limit cycle x0 of smallest period T>0 such that the associated linearized system around it has only one characteristic multiplier with absolute value 1. We consider two functions, defined by means of the eigenfunctions of the adjoint of the linearized system, and we formulate conditions in terms of them in order to have the existence of two geometrically distinct families of T-periodic solutions of the autonomous system when it is perturbed by nonsmooth T-periodic nonlinear terms of small amplitude. We also show the convergence of these periodic solutions to x0 as the perturbation disappears and we provide an estimation of the rate of convergence. The employed methods are mainly based on the theory of topological degree and its properties that allow less regularity on the data than that required by the approach, commonly employed in the existing literature on this subject, based on various versions of the implicit function theorem. 相似文献
55.
Counting labelled planar graphs, and typical properties of random labelled planar graphs, have received much attention recently. We start the process here of extending these investigations to graphs embeddable on any fixed surface S. In particular we show that the labelled graphs embeddable on S have the same growth constant as for planar graphs, and the same holds for unlabelled graphs. Also, if we pick a graph uniformly at random from the graphs embeddable on S which have vertex set {1,…,n}, then with probability tending to 1 as n→∞, this random graph either is connected or consists of one giant component together with a few nodes in small planar components. 相似文献
56.
We investigate solutions for a particular class of linear equations in dendriform algebras. Motivations as well as several applications are provided. The latter follow naturally from the intimate link between dendriform algebras and Rota–Baxter operators, e.g. the Riemann integral map or Jackson's q-integral. 相似文献
57.
L. G. M. Th. Tuinstra J. A. van Rhijn A. H. Roos W. A. Traag R. J. van Mazijk P. J. W. Kolkman 《Journal of separation science》1990,13(12):797-802
The occurrence of the highly toxic non-ortho substituted (planar) chlorobiphenyls (CBs) at low levels in wildlife, (human) fat, and fish generates the need for a routine analytical procedure. The use of a fully automated system for the separation of planar and non-planar CBs, consisting of a gel permeation chromatography system, a sample preparation system employing extraction columns, and a porous graphitic carbon HPLC column is described, and tested with horse fat. Gas chromatography on capillary columns, with electron-capture or high resolution mass spectrometric detection, is used for quantitation of the CBs. 相似文献
58.
Temporal sequences of planar laser-induced fluorescence (PLIF) images of several high-speed, transient flowfields created in a reflection-type shock tunnel facility were acquired. In each case, the test gas contained either nitric oxide or the hydroxyl radical, the fluorescent species. The processes of shock reflection from an endwall with a converging nozzle and of underexpanded free jet formation were examined. A comparison was also made between PLIF imaging and shadow photography. The investigation demonstrated some of the capabilities of PLIF imaging diagnostics in complex, transient, hypersonic flowfields, including those with combustion.Nomenclature
A
spontaneous emission rate
-
A
las
cross sectional area of laser sheet
-
B
laser absorption rate
-
C
opt
constant dependent on optical arrangement, collection efficiency, etc.
-
D
nozzle throat diameter
-
E
p
laser pulse energy
-
f
J
Boltzmann fraction of absorbing state
-
g
spectral convolution of laser and absorption lineshapes
-
k
Boltzmann constant
-
M
s
incident shock Mach number
-
N
noise, root-mean-square signal fluctuation
-
P
static pressure
-
P
1
initial pressure of test gas in shock tube
-
P
a
free jet ambient pressure
-
P
s
stagnation pressure
-
Q
electronic quenching rate of excited state
-
S
PLIF signal
-
t
time between shock reflection and image acquisition
-
T
static temperature
-
T
s
stagnation temperature
-
a
mole fraction of absorbing species 相似文献
59.
<正>The conformations ofγ-butyrolactone ring in solution were deduced on the basis of ~1H NMR spectra of geminal protons of the butyrolactone ring.A series of optically pure(Z)-(-)-4-(1'-alkoxyl-1'-carbalkoxy-methylene)-5(R)[(1R)-menthyloxy]-γ-butyr-olactones with a stable planar conformation of γ-butyrolactone ring were found. 相似文献
60.
Chun-Ting Lin 《Optics Communications》2011,284(1):195-200
An athermal metal-free planar waveguide concave grating demultiplexer is proposed. We designed the dielectric mirror at the grating facet instead of coating with the metal on the back wall of the grating facet. The transfer-matrix method is introduced to design the dielectric mirror and the reflectance spectral responses of the 2D waveguide structure are simulated using the FDTD software (RSoft, Inc.). To reduce the temperature sensitivity of the device, the three-focal-point method is introduced. We use the design example to show the high-reflectance bandwidth of the dielectric mirror. The fabrication errors are also taken into consideration. By using the numerical model of the scalar diffraction theory, the flat-top spectral responses of the channels are simulated. 相似文献