Inequivalent Quantization in the Field of a Ferromagnetic Wire

We argue that it is possible to bind neutral atom (NA) to the ferromagnetic wire (FW) by inequivalent quantization of the Hamiltonian. We follow the well known von Neumann’s method of self-adjoint extensions (SAE) to get this inequivalent quantization, which is characterized by a parameter Σ∈ℝ(mod2π). There exists a single bound state for the coupling constant η ²∈[0,1). Although this bound state should not occur due to the existence of classical scale symmetry in the problem. But since quantization procedure breaks this classical symmetry, bound state comes out as a scale in the problem leading to scaling anomaly. We also discuss the strong coupling region η ²<0, which supports bound state making the problem re-normalizable.     

Tandem RAFT Polymerization and Click Chemistry: An Efficient Approach to Surface Modification

PS grafted silica nanoparticles have been prepared by a tandem process that simultaneously employs RAFT polymerization and click chemistry. In a single pot procedure, azide‐modified silica, an alkyne functionalized RAFT agent and styrene are combined to produce the desired product. As deduced by thermal gravimetric and elemental analysis, the grafting density of PS on the silica in the tandem process is intermediate between analogous “grafting to” and “grafting from” techniques for preparing PS brushes on silica. Relative rates of RAFT polymerization and click reaction can be altered to control grafting density.

     

Rotating beams and non-rotating beams with shared eigenpair for pinned-free boundary condition

In this paper we look for a rotating beam, with pinned-free boundary conditions, whose eigenpair (frequency and mode-shape) is same as that of a uniform non-rotating beam for a particular mode. It is seen that for any given mode, there exists a flexural stiffness function (FSF) for which the ith mode eigenpair of a rotating beam with uniform mass distribution, is identical to that of a corresponding non-rotating beam with same length and mass distribution. Inserting these derived FSF’s in a finite element code for a rotating pinned-free beam, the frequencies and mode shapes of a non-rotating pinned-free beam are obtained. For the first mode, a physically realistic equivalent rotating beam is possible, but for higher modes, the FSF has internal singularities. Strategies for addressing these singularities in the FSF for finite element analysis are provided. The proposed functions can be used as test functions for rotating beam codes and also for targeted destiffening of rotating beams.     

Analytical test functions for free vibration analysis of rotating non-homogeneous Timoshenko beams

In this paper, the governing equations for free vibration of a non-homogeneous rotating Timoshenko beam, having uniform cross-section, is studied using an inverse problem approach, for both cantilever and pinned-free boundary conditions. The bending displacement and the rotation due to bending are assumed to be simple polynomials which satisfy all four boundary conditions. It is found that for certain polynomial variations of the material mass density, elastic modulus and shear modulus, along the length of the beam, the assumed polynomials serve as simple closed form solutions to the coupled second order governing differential equations with variable coefficients. It is found that there are an infinite number of analytical polynomial functions possible for material mass density, shear modulus and elastic modulus distributions, which share the same frequency and mode shape for a particular mode. The derived results are intended to serve as benchmark solutions for testing approximate or numerical methods used for the vibration analysis of rotating non-homogeneous Timoshenko beams.     

On vector variational-like inequalities and vector optimization problems with (<Emphasis Type="Italic">G</Emphasis>, <Emphasis Type="Italic">α</Emphasis>)-invexity

The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of (G, α)-invex functions. Examples are provided to elucidate our results.     

Ultrasonic velocity of binary systems at elevated pressures

Various empirical theories of ultrasonic velocity have been applied to three binary liquid mixtures, under pressures up to 200 MPa and their validity have been tested. A pressure dependent study of ultrasonic velocities has been made at 303.15 K. The agreement between theory and experiment is found to be quite satisfactory.     

Noise characteristics of a superlattice avalanche photodiode

The noise generated due to randomness of multiplication process in the avalanche region of an Al _x Ga_1–x As/GaAs quantum well p⁺-i-n⁺ structure has been studied. The paper presents a quantitative evaluation of the noise performance of the superlattice APD which has not been done so far. Further, useful design data for low noise structure is given.     

Synthesis of 2,2-dimethyl-5-hydroxy-3-(3-oxobutyl)-7-pentyl-4-chromone

Alkylation and deformylation of 2,2-dimethyl-3-hydroxymethylene-5-hydroxy-7-pentyl-4-chromone occurs in the same step to give the title compound.