Graphs whose vertices are graphs with bounded degree: Distance problems

By an f-graph we mean a graph having no vertex of degree greater than f. Let U(n,f) denote the graph whose vertex set is the set of unlabeled f-graphs of order n and such that the vertex corresponding to the graph G is adjacent to the vertex corresponding to the graph H if and only if H is obtainable from G by either the insertion or the deletion of a single edge. The distance between two graphs G and H of order n is defined as the least number of insertions and deletions of edges in G needed to obtain H. This is also the distance between two vertices in U(n,f). For simplicity, we also refer to the vertices in U(n,f) as the graphs in U(n,f). The graphs in U(n,f) are naturally grouped and ordered in levels by their number of edges. The distance nf/2 from the empty graph to an f-graph having a maximum number of edges is called the height of U(n,f). For f =2 and for f≥(n-1)/2, the diameter of U(n,f) is equal to the height. However, there are values of the parameters where the diameter exceeds the height. We present what is known about the following two problems: (1) What is the diameter of U(n,f) when 3≥f<(n-1)/2? (2) For fixed f, what is the least value of n such that the diameter of U(n,f) exceeds the height of U(n,f)?     

Heterodyne measurement of Wigner distributions for classical optical fields

We demonstrate a two-window heterodyne method for measuring the x-p cross correlation, ??(*)(x)? (p)?, of an optical field ? for transverse position x and transverse momentum p. This scheme permits independent control of the x and p resolution. A simple linear transform of the x-p correlation function yields the Wigner phase-space distribution. This technique is useful for both coherent and low-coherence light sources and may permit new biological imaging techniques based on transverse coherence measurement with time gating. We point out an interesting analogy between x-p correlation measurements for classical-wave and quantum fields.     

Bianchi Type-V Bulk Viscous Barotropic Fluid Cosmological Model with Variable G and Λ

We investigate the Bianchi type-V bulk viscous barotropic fluid cosmological model with variable gravitational constant G and the cosmological constant A, assuming the condition on metric A/A=B/B=C/C=m/tn potential aswhere A, B, and C are functions of time t, while m and n are constants. To obtain the deterministic mo del, we also assume the relations P = p - 3η H, p = 7P, η = ηop^s, where p is the isotropic pressure, η the bulk viscosity,0≤r≤1 H the Hubble constant, ηo and s are constants. Various physical aspects of the model are discussed.The case of n = 1 is also discussed to compare the results with the actual universe.     

Bulk viscous L.R.S. Bianchi type V tilted stiff fluid cosmological model in general relativity

Locally rotationally symmetric (L.R.S.) Bianchi type V bulk viscous tilted stiff fluid cosmological model is investigated. To get the deterministic model of the universe, we have also assumed a condition A=Bⁿ between metric potentials A, B where n is the constant. The behaviour of the model in presence and absence of bulk viscosity and singularities in the model are also discussed. In general, the models represent accelerating, shearing, tilted and non-rotating universe. The models have point type singularity in presence and absence of bulk viscosity both.     

Bulk Viscous Bianchi Type I Cosmological Models with Time-Dependent Cosmological Term Λ

Bianchi type I cosmological models with time-varying cosmological constant Λ and bulk viscous fluid are investigated. Cosmic matter is chosen to obey a barotropic equation of state. Exact solutions of Einstein’s field equations are obtained assuming the volume expansion θ proportional to the eigen values of shear tensor σ _ij . Physical and kinematical properties of the models are discussed considering bulk viscosity to be a power function of matter density.     

Magnetized Stiff Fluid Cylindrically Symmetric Universe with Two Degrees of Freedom in General Relativity

A magnetized stiff fluid cylindrically symmetric universe with two degrees of freedom for perfect fluid distribution, is investigated. The magnetic field is due to an electric current produced along x-axis. The distribution consists of an electrically neutral perfect fluid with an infinite electrical conductivity. The behaviour of the model in presence and absence of magnetic field is discussed. The other physical aspects of the model related to the observations are also discussed.     

Bianchi Type I String Dust Magnetized Cosmological Models in Lyra Geometry

Bianchi type I string dust cosmological models in the presence and absence of magnetic field in the frame work of Lyra geometry are investigated. To get the deterministic model of the universe, we assume that the eigenvalue (σ₁¹ ) of shear tensor (σ_i ^j ) is proportional to expansion (θ ). This leads to A =(BC)ⁿ, where A, B, C are metric potentials and n is a constant. To discuss the results in terms of cosmic time t, we have considered n = 1. The physical and geometrical aspects of the models and singularities in the models are also discussed.     

4‐Acetonyl­idene‐1‐ethyl‐2,3,4,5‐tetra­hydro‐1H‐1,5‐benzodiazepin‐2‐one

The title compound, C₁₄H₁₆N₂O₂, contains a diazepine ring, which appears in a boat conformation. An intramolecular hydrogen bond is formed between the NH group of the diazepine ring and a carbonyl O atom of one of the side chains.     

Derivative Spectrophotometric Methods for Determination of Gefitinib in Bulk and in Formulation

Journal of Applied Spectroscopy - A rapid, sensitive, cost effective and reproducible first-order derivative spectrophotometric method was developed for the estimation of gefitinib in bulk and in...     

Spectrofluorimetric Method for Determination of Solifenacin Succinate in Bulk and in Tablet Formulation

Journal of Applied Spectroscopy - A sensitive, reproducible, and cost-effective spectrofluorimetric method was developed for the quantification of solifenacin succinate in bulk and its tablet...