An improved approximation algorithm for requirement cut

This note presents improved approximation guarantees for the requirement cut problem: given an n-vertex edge-weighted graph G=(V,E), and g groups of vertices X₁,…,X_g⊆V with each group X_i having a requirement r_i between 0 and |X_i|, the goal is to find a minimum cost set of edges whose removal separates each group X_i into at least r_i disconnected components. We give a tight Θ(logg) approximation ratio for this problem when the underlying graph is a tree, and show how this implies an O(logk⋅logg) approximation ratio for general graphs, where .     

A Fourier transform speckle method to determine the change in angle of illumination

It is analytically shown that the position of the Fourier transform of the speckle pattern produced by a coherently illuminated, diffusely reflecting surface depends upon its angle of illumination. A method is proposed to measure small changes in this angle by doubly exposing the photographic plate with the original and laterally displaced Fourier transforms of the object speckle. The method is well suited for accurate measurements of the wedge angle and tilt of optical surfaces and to determine variations in refractive index or temperature of axially symmetric phase objects.     

A new approach to irreversibility from maximum entropy estimation

This paper deals with the study of some irreversible processes like slow heating of a thermodynamic system or of inhomogeneity, i.e. spatially local equilibrium in it, based on the principle of maximum entropy estimation, in a stochastic model.     

Probing chromosome structure with dynamic force relaxation

We report measurements of the dynamics of force relaxation in single mitotic chromosomes, following step strains applied with micropipettes of force constant approximately 1 nN/microm. The force relaxes exponentially after an elongation (l/l(0)) to less than 3x native length, with a relaxation time approximately 2 sec. This relaxation time corresponds to an effective viscosity approximately 10(5) times that of water. We experimentally rule out solvent flow into the chromosome as the mechanism for the relaxation time. Instead, the relaxation can be explained in terms of the disentanglement dynamics of approximately 80 kb chromatin loop domains.     

Angular forces in the lattice dynamics of b.c.c. metals

The lattice dynamics of the b.c.c. lattice has been investigated using the central and the angular forces which are in general rotationally invariant. It has been observed that the four force constants are related to three elastic constants only. Dispersion curves for sodium were calculated and were found to be in excellent agreement with experiment.     

Dynamics of laser hole drilling with nanosecond periodically pulsed laser

Results are presented on the dynamics of the laser drilling process for a single hole using a periodically pulsed nanosecond laser with a repetition rate up to 60 kHz. The intensity dependence of drilling velocity was determined by measuring the delay time between the beginning of exposure and the moment when the hole opens. The hole collapse phenomenon was observed in our experiments. The competition process between material ejection and the flow of the liquid phase into the ejected area is supposed to be responsible for the hole collapse.     

Interactions of Nile Blue with Micelles, Reverse Micelles and a Genomic DNA

In this contribution we report studies on the nature of binding of a small ligand/drug Nile blue (NB) with sodium dodecyl sulfate (SDS) micelles, bis-(2-ethylehexyl) sulfosuccinate (AOT)/isooctane reverse micelles (RM) and a genomic DNA extracted from Salmon sperm. With detailed steady state and picosecond resolved optical spectroscopic techniques, we examined the fluorescence quenching of the ligand upon complexation with the SDS monomers and DNA. Polarization analyzed picosecond-resolved fluorescence measurements reveal geometrical restriction on the probe in SDS micelles, AOT-RM and DNA. Steady state and time resolved studies on the probe in nanocages of AOT RM with various degrees of hydration (w₀) reveal the existence of NB as two distinct species namely, neutral and cationic. This study confirms that the emission of NB in aqueous micelles and DNA solution is due to the cationic form of the drug. Our experiments clearly identified non-specific electrostatic and intercalative modes of interaction of the probe with the DNA at lower and higher DNA concentrations respectively. The nature of binding of NB in presence of the DNA and SDS micelles reveals that the binding affinity of the probe is higher with the micelles than with the DNA. The complex rigidity of NB with DNA and its fluorescence quenching with DNA elucidate a strong recognition mechanism between NB and DNA.     

Fine-structure energy levels, oscillator strengths and lifetimes in Co XV

Excitation energies from ground state for 97 fine-structure levels as well as oscillator strengths and radiative decay rates for all electric-dipole-allowed and intercombination transitions among the fine-structure levels of the terms belonging to the (1s ²2s ²2p ⁶)3s ²3p, 3s ³ p ², 3s ²3d, 3p ³, 3s3p3d, 3p ²3d, 3s3d ², 3s ²4s, 3s ²4p, 3s ²4d, 3s ²4f, and 3s3p4s configurations of Co XV are calculated, using extensive configuration-interaction (CI) wave functions, obtained with the CIV3 computer code of Hibbert. The important relativistic effects in intermediate coupling are included through the Breit-Pauli approximation via spin-orbit, spin-other-orbit, spin-spin, Darwin and mass correction terms. Small adjustments to the diagonal elements of the Hamiltonian matrices have been made. Our calculated excitation energies, including their ordering, are in excellent agreement with the experimental results and the experimentally compiled energy values of the National Institute for Standards and Technology (NIST) wherever available. The mixing among several fine-structure levels is found to be very strong, with most of the strongly mixed levels belonging to the (1s ²2s ²2p ⁶)3p ²3d and 3s3d ² configurations. The strong mixing among several fine-structure levels makes it very difficult to identify them uniquely. Perhaps, that may be the reason for the lack of both experimental and theoretical results for these levels. We believe that our extensive calculated values can guide experimentalists in identifying the fine-structure levels in their future work. From our radiative decay rates we have also calculated radiative lifetimes of some fine-structure levels. In this calculation we also predict new data for several fine-structure levels where no other theoretical and/or experimental results are available.     

Dispersion analysis and improved F-expansion method for space–time fractional differential equations

Nonlinear Dynamics - In this article, an improved F-expansion method with the Riccati equation is suggested for space–time fractional differential equations for exact solutions. The...