Renewed Looks at the Distribution of a Sum of Independent or Dependent Discrete Random Variables and Related Problems

Methodology and Computing in Applied Probability - Butler and Stephens (2017) have investigated the exact and approximate distributions of a sum S of independent binomial random variables with...     

Identities for minors of the Laplacian, resistance and distance matrices

It is shown that if L and D are the Laplacian and the distance matrix of a tree respectively, then any minor of the Laplacian equals the sum of the cofactors of the complementary submatrix of D, up to sign and a power of 2. An analogous, more general result is proved for the Laplacian and the resistance matrix of any graph. A similar identity is proved for graphs in which each block is a complete graph on r vertices, and for q-analogues of such matrices of a tree. Our main tool is an identity for the minors of a matrix and its inverse.     

Inverses of -distance matrices of a tree

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.     

Optical Emission Spectroscopy of Carbon Clusters Produced in a Hollow Cathode Sputter Source

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.     

A generalization of a theorem of Ky Fan on simplicial maps

A combinatorial result is proved which generalizes a theorem of Ky Fan on simplicial maps from a pseudomanifold. A version of the Kronecker Theorem in Topology is also derived as a special case.     

Electrical and electrochemical properties of pretreated thermally and γ-irradiated TiO2

Electrical conductivity and Seebeck voltage developed in thermally pretreated and -irradiated TiO₂ was measured as a function of temperature. The conversion of n-type TiO₂ into p-type and vice versa observed after irradiation was explained in terms of ionization of Ti³⁺ donors and lattice O⁼ species, subsequent trapping of carriers in adsorbed oxygen and further formation of p-type inversion layer on the oxide surface during irradiation. The sign of the EMF of the electrochemical Ag/Ag⁺ concentration cell by the addition of heated and -irradiated TiO₂ in one of the compartment of the cell was found to be opposite to that due to the addition of the corresponding heated but non-irradiated oxide sample.     

The near ultraviolet absorption spectra ofortho- andmeta-thiocresols

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.     

Stable periodic vibroimpacts of an oscillator

The asymptotically stable vibrations of a loaded oscillator colliding periodically with a rigid mass are described. Comparison of the numerical results with the few existing examples is encouraging but inconclusive. Better overall agreement is demonstrated with fairly comprehensive measurements from a specially built experimental rig. Impact motions are shown to be very sensitive to small fluctuations in the clearance between masses and the stiffness and loading of the oscillator near its linear, or collisionless, resonant frequency. The rigid mass is quite an effective damper at or just above this frequency condition.