979 resultados para Signless Laplacian spectrum of a graph


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The Raman spectrum of C-deuterated γ-glycine (NH3+CD2COO-) in the crystal powder form was taken using λ 2536·5 excitation. 26 Raman lines were recorded. Of these, eight lines are attributed to the external oscillations and eighteen Raman lines to the internal oscillations. Proper assignments are given to the observed frequencies.

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The Raman spectrum of a single crystal of triglycine selenate G3Se which is ferroelectric below 22° C. has been photographed using λ 2537 excitation. 42 Raman lines have been recorded of which 6 belong to the lattice spectrum, 3 are due to NH...O oscillations and the remaining 33 are due to internal oscillations of the ions of glycine and SeO4--. There is a close similarity between the spectrum of triglycine selenate and the spectrum of its isomorph, triglycine sulphate, the frequency shifts due to the SO4-- ion being replaced by the frequency shifts due to the SeO4-- ion. The existence of glycine in the zwitterion form in the structure of G3Se is substantiated by the appearance in the Raman spectrum of lines which are attributable to NH3+ groups and COO- groups. The appearance of the additional C-H line at 2982 cm.-1 in the spectrum of triglycine selenate which is absent in the spectrum of α-glycine indicates the existence of planar monoprotonated glycine also in the structure, as indicated by X-ray studies.

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Raman spectrum of a single crystal of sodium iodide has been recorded for the first time using lambda 2537 excitation. The general features of the spectrum are discussed in the light of the existing theories on the dynamics of the alkali halides. The authors wish to thank Professor D.Y.Phadke of the Tata Institute of Fundamental Research, Bombay, for presenting the crystal of Nal used in the present investigation.

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Raman spectrum of a single crystal of lanthanum ethyl sulphate has been recorded for the first time using the λ 2537 radiation Forty-one lines have been identified out of which eight belong to the lattice oscillations, seven to the internal vibrations of the water molecule and the remaining twenty-six to the internal vibrations of the ethyl sulphate group. The Raman spectrum of ethyl sulphate (liquid) has also been recorded using the λ 4358 excitation and is compared with the spectrum of lanthanum ethyl sulphate. Thirty Raman lines could be identified in the spectrum of ethyl sulphate, of which fourteen are recorded for the first time. Probable assignments of the observed frequencies are also given. The sulphate group is found to have O-SO3 structure in lanthanum ethyl sulphate, while it has a co-ordination {Mathematical expression} in ethyl sulphate.

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The Raman spectrum of cyclohexanol has been studied in detail in the liquid state at 30° C. and at about 68° C. and in the solid state at about 13° C. The O-H stretching frequency of cyclohexanol has been found to extend from 3106-3571 cm.-1 in the liquid state at 30° C. and from 3204-3652 cm.-1 at 68° C. The 38 lines recorded in the present investigation have been following frequency shifts: 342, 408, 458, 478, 555, 653, 789, 834, 843, 863, 887, 920, 966, 978, 1024, 1047, 1070, 1139, 1173, 1184, 1210, 1235, 1252, 1301, 1329, 1346, 1362, 1438, 1448, 1464, 2660, 2684, 2710, 2854, 2896, 2925, 2940, 3106 to 3511 (band). Those lines which are italicized are the additional lines observed for the first time. The Raman lines at 966 cm.-1 and 1070 cm.-1 have been assigned to C-OH stretching vibrations of the axial and equatorial isomers. The ratio of the integrated intensity of the 1070 cm.-1 line to the 966 cm.-1 gave the equilibrium constant K as 2·896 at 30° C. and as 2·66 at 68° C. Knowing K, the free energy different Δ F was calculated and it was found to be 0·64 Kcal./mole at 30° C. and 0·66 Kcal./mole at about 68° C. Reasonable assignment has been made for most of the observed Raman lines.

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The Raman spectrum of crystalline boric acid is recorded using mercuryλ2537 excitation. Fifteen Raman lines, three of them belonging to the lattice spectrum, are reported. Satisfactory assignments of all the observed Raman frequencies are made using the available X-ray crystal structure data. From the presence of a new high frequency Raman band at about 3420 cm.−1 it is suggested that there might be a small number of long, weak O-H....O hydrogen bonds in the crystal, in addition to the hydrogen bonds of moderate strength reported from X-ray diffraction data.

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The emission spectrum of bismuth monobromide has been investigated and a vibrational analysis of the A→X system has been made. About 286 bands were recorded in the region λλ 4595–6063 and the isotope effect due to Br79 and Br81 was observed in about 87 bands. A value of 2·74 ev. for the dissociation energy of the excited state has been obtained and arguments have been given to show that the dissociation products in the excited state are Bi(4S3/2) and Br(2P3/2) and that those of the ground state are most probably Bi (4S3/2) and Br (2P1/2) atoms.

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The Raman spectrum of l-asparagine monohydrate in the form of a single crystal has been recorded for the first time. λ 2537 excitation has been used. Fifty-three Raman frequency shifts have been recorded. They are grouped as follows: Eight Raman lines coming under the lattice spectrum, three Raman lines arising from low-frequency vibrations of the hydrogen bonds and the remaining forty-two arising from the internal oscillations of the asparagine molecule. Appropriate assignments have been given for the observed Raman lines

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The Raman spectrum of strontium titanate has been recorded using λ 4358 of mercury as exciter. The observed spectrum consists of 7 Raman lines, one of which is of low frequency, as expected from the recent theory of Cochran. 6 of these Raman lines have been interpreted as the first order spectrum arising from a small deviation of the cubic strontium titanate from its idealized symmetry. It has been shown that one normal mode of SrTiO3 neglected by J.T. Last, will be really active in infrared absorption in the region of 440 cm-1 and that it has to be taken into account in the interpretation of the infrared spectra of titanates. The four vibrational modes of the unit cell of SrTiO3 correspond to frequencies of 90, 335, 441 and 620 cm-1 observed in Raman effect. The large width of the Raman lines and the additional lines at 256 cm-1 and 726 cm-1 have been attributed to a splitting of the longitudinal and transverse optical modes. With the observed frequencies it has been found possible to account for in a satisfactory manner the specific heat of SrTiO3 in the range 54·84° K to 1800° K.

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We study the properties of single red blood cells (RBCs) held in an optical-tweezers trap. We observe a change in the spectrum of Brownian fluctuations between RBCs from normal and malaria-infected samples. The change, caused by infection-induced structural changes in the cell, appears as a statistical increase in the mean (by 25%) and standard deviation (by 200%) of the corner frequency measured over similar to 100 cells. The increase is observed even though the ensemble of cells being measured consists mostly of cells that do not actually host the parasite, but are from an infected pool. This bystander effect appears to vindicate other observations that infected cells can affect the biomechanical properties of uninfected cells. The change is also observed to be independent of the stage of infection and its duration, highlighting its potential for disease detection. (C) 2010 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3427142].

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An expression for the spectrum and cross spectrum of an acoustic field measured at two vertically separated sensors in shallow water has been obtained for any correlated noise sources distributed over the surface. Numerical results are presented for the case where the noise sources, white noise and wind-induced colored noise, are contained within a circular disk centered over the sensors. The acoustic field is generally inhomogeneous except when the channel is deep. The coherence function becomes real for a large disk, for a radius greater than 25 times the depth of the channel, decreases with further increase of the size of the disk, and finally tapers off after certain limiting size, approximately given by 1/alpha, where alpha is the attenuation coefficient.

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A k-dimensional box is the Cartesian product R-1 X R-2 X ... X R-k where each R-i is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer k such that G can be represented as the intersection graph of a collection of k-dimensional boxes. A unit cube in k-dimensional space or a k-cube is defined as the Cartesian product R-1 X R-2 X ... X R-k where each R-i is a closed interval oil the real line of the form a(i), a(i) + 1]. The cubicity of G, denoted as cub(G), is the minimum integer k such that G can be represented as the intersection graph of a collection of k-cubes. The threshold dimension of a graph G(V, E) is the smallest integer k such that E can be covered by k threshold spanning subgraphs of G. In this paper we will show that there exists no polynomial-time algorithm for approximating the threshold dimension of a graph on n vertices with a factor of O(n(0.5-epsilon)) for any epsilon > 0 unless NP = ZPP. From this result we will show that there exists no polynomial-time algorithm for approximating the boxicity and the cubicity of a graph on n vertices with factor O(n(0.5-epsilon)) for any epsilon > 0 unless NP = ZPP. In fact all these hardness results hold even for a highly structured class of graphs, namely the split graphs. We will also show that it is NP-complete to determine whether a given split graph has boxicity at most 3. (C) 2010 Elsevier B.V. All rights reserved.

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A user friendly interactive computer program, CIRDIC, is developed which calculates the molar ellipticity and molar circular dichroic absorption coefficients from the CD spectrum. This, in combination with LOTUS 1-2-3 spread sheet, will give the spectra of above parameters vs wavelength. The code is implemented in MicroSoft FORTRAN 77 which runs on any IBM compatible PC under MSDOS environment.