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21.
22.
R. N. Bapat 《Proceedings Mathematical Sciences》1959,50(3):183-191
The absorption spectra ofortho- andmeta-thiocresols have been studied in the present investigation. The ortho-thiocresol spectrum consists of about forty-five bands of rather a diffuse nature and in general low intensity in the region from 2873 Å to 2600 Å. The maximum number of bands is obtained by using a path length of 330 cm. for absorption, the temperature of the bulb being maintained at 14°C. Several of these bands are assigned as due tov-v-transitions. The (0, 0) band is chosen at 35386 cm.?1 which is the strongest band on the longer wavelength side. Vibrational frequencies in the excited state have values 729, 957 and 1159 and combinations and overtones of these are present. Themeta-thiocresol spectrum consists of about forty bands of rather a diffuse nature and very weak intensities in the region from 2900 Å to 2590 Å. The maximum number of bands is obtained by using a path length 200 cm. for absorption and by keeping the temperature of the bulb at 20° C. The (0, 0) band is chosen to be that at 34793 cm.?1 which is the strongest band on the longer wavelength side. Vibrational frequencies in the excited state have values 492, 611, 720, 845, 965, 1016 and 1155 cm.?1 and combinations and overtones of these are present. 相似文献
23.
A threshold graph on n vertices is coded by a binary string of length n−1. We obtain a formula for the inertia of (the adjacency matrix of) a threshold graph in terms of the code of the graph. It is shown that the number of negative eigenvalues of the adjacency matrix of a threshold graph is the number of ones in the code, whereas the nullity is given by the number of zeros in the code that are preceded by either a zero or a blank. A formula for the determinant of the adjacency matrix of a generalized threshold graph and the inverse, when it exists, of the adjacency matrix of a threshold graph are obtained. Results for antiregular graphs follow as special cases. 相似文献
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25.
R. B. Bapat 《Linear and Multilinear Algebra》2013,61(3):219-242
For a graph G, we define its perturbed Laplacian matrix as D?A(G) where A(G) is the adjacency matrix of G and D is an arbitrary diagonal matrix. Both the Laplacian matrix and the negative of the adjacency matrix are special instances of the perturbed Laplacian. Several well-known results, contained in the classical work of Fiedler and in more recent contributions of other authors are shown to be true, with suitable modifications, for the perturbed Laplacian. An appropriate generalization of the monotonicity property of a Fiedler vector for a tree is obtained. Some of the results are applied to interval graphs. 相似文献
26.
DC Muddiman AP Null JC Hannis 《Rapid communications in mass spectrometry : RCM》1999,13(12):1201-1204
Electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICRMS) has been used to determine the mass of a double-stranded 500 base-pair (bp) polymerase chain reaction (PCR) product with an average theoretical mass of the blunt-ended (i.e. unadenylated) species of 308 859.35 Da. The PCR product was generated from the linearized bacteriophage Lambda genome which is a double-stranded template. Utilization of ethanol precipitation in tandem with a rapid microdialysis step to purify and desalt the PCR product was crucial to obtain a precise mass measurement. The PCR product (0.8 pmol/μL) was electrosprayed from a solution containing 75% acetonitrile, 25 mM piperidine, and 25 mM imidazole and was infused at a rate of 200 nL/min. The average molecular mass and the corresponding precision were determined using the charge-states ranging from 172 to 235 net negative charges. The experimental mass and corresponding precision (reported as the 95% confidence interval of the mean) was 309 406 +/- 27 Da (87 ppm). The mass accuracy was compromised due to the fact that the PCR generates multiple products when using Taq polymerase due to the non-template directed 3'-adenylation. This results in a mixture of three PCR products with nearly identical mass (i.e. blunt-ended, mono-adenylated and di-adenylated) with unknown relative abundances that were not resolved in the spectrum. Thus, the experimental mass will be a weighted average of the three species which, under our experimental conditions, reflects a nearly equal concentration of the mono- and di-adenylated species. This report demonstrates that precise mass measurements of PCR products up to 309 kDa (500 bp) can be routinely obtained by ESI-FTICR requiring low femtomole amounts. Copyright 1999 John Wiley & Sons, Ltd. 相似文献
27.
V. Rajnikant V.K. Gupta V.D. Rangari S.R. Bapat R.B. Agarwal R. Gupta 《Crystal Research and Technology》2001,36(1):93-100
The crystal structure of the title compound (3 α ‐acetoxy‐urs‐12‐en‐24‐oic acid, C32H50O4) has been determined by X‐ray crystallographic techniques. The compound crystallizes into orthorhombic space group P212121 with unit cell parameters : a = 12.773(2), b=16.381(4), c=27.929(7)Å. The structure has been solved by direct methods and refined to R = 0.054 for 4930 observed reflections. The structure contains two crystallographically independent molecules in the asymmetric unit which are almost identical in geometry. Rings A, B, D and E have chair conformations while ring C assumes a sofa conformation in both the molecules. The molecules in the structure are linked together by intra‐ and intermolecular O‐H…= and C‐H…O hydrogen bonds. 相似文献
28.
The determinant and the inverse of the distance matrix of a tree have been investigated in the literature, following the classical formulas due to Graham and Pollak for the determinant, and due to Graham and Lovász for the inverse. We consider two q-analogs of the distance matrix of a tree and obtain formulas for the inverses of the two distance matrices. Yan and Yeh have previously obtained expressions for the determinants of the two distance matrices. Some related results are proved. 相似文献
29.
Arvind Saxena Prashant Kumar Swaroop Banerjee K. P. Subramanian Bhas Bapat 《光谱学快报》2014,47(2):114-118
A hollow cathode sputter source is developed to trace the production of carbon clusters and study the influence of discharge current and argon gas pressure on cluster production using an optical emission spectroscopic technique. Optical emission spectra from the hollow cathode source reveal the production of the C2 Swan band. The sputter source is optimized for the maximum carbon cluster yield. The vibrational temperature analysis of the C2 cluster is carried out using the Boltzmann plot method. The dependence of vibrational temperature on argon gas pressure is discussed and the dominant method for C-C association in the glow discharge is suggested. 相似文献
30.
The study of a mixed graph and its Laplacian matrix have gained quite a bit of interest among the researchers. Mixed graphs are very important for the study of graph theory as they provide a setup where one can have directed and undirected edges in the graph. In this article we present a more general structure, namely the weighted directed graphs and supply appropriate generalizations of several existing results for mixed graphs related to singularity of the corresponding Laplacian matrix. We also prove many new combinatorial results relating the Laplacian matrix and the graph structure. 相似文献