Stochastic evolution of innovation diffusion in heterogeneous groups: study of life cycle patterns

A theoretical framework has been proposed to study patternsof innovation diffusion in a heterogeneous population, withapplicability to a number of problem areas including marketing.The heterogeneity in the population is captured through randomlyvarying parameters, which have been modelled in terms of two-pointdistributions. The effect of heterogeneity leads to the generationof bi-modal life cycle patterns besides the conventional uni-modalpattern resulting from S-shaped curve. The stochastic evolutionof the mean and variance of the number of adopters is foundto depict a high level of relative fluctuation around the pointof inflexion. As a result of randomness in parameters, the resultingdifferential equation for the evolution of the mean of the adoptionprocess is characterized by a non-autonomous system having parameterswhich are no longer constant but become time dependent. Fordemonstrating the effectiveness of the proposed framework, areal data set which depicts a bi-modal life cycle curve is investigated.The fit is found to be extremely good while capturing appropriateproduct life cycle curve.     

Particle-rotor-model calculations in 125I

Recent experimental data on ¹²⁵I has revealed several interesting structural features. These include the observation of a three quasiparticle band, prolate and oblate deformed bands, signature inversion in the yrast positive-parity band and identification of the unfavoured πh _11/2 band showing very large signature splitting. In the present work, particle-rotor-model calculations have been performed for the πh _11/2 band, using an axially symmetric deformed Nilsson potential. The calculations reproduce the experimental results well and predict a moderate prolate quadrupole deformation of about 0.2 for the band.     

Crystallization kinetics of Li2O–Al2O3–GeO2–P2O5 glass–ceramics system

Journal of Thermal Analysis and Calorimetry - Lithium aluminum germanium phosphate glass–ceramics with NASICON structure find potential application in the field of energy storage...     

A New and Pragmatic Approach to the GIX/Geo/c/N Queues Using Roots

A simple and complete solution to determine the distributions of queue lengths at different observation epochs for the model GI^X/Geo/c/N is presented. In the past, various discrete-time queueing models, particularly the multi-server bulk-arrival queues with finite-buffer have been solved using complicated methods that lead to results in a non-explicit form. The purpose of this paper is to present a simple derivation for the model GI^X/Geo/c/N that leads to a complete solution in an explicit form. The same method can also be used to solve the GI^X/Geo/c/N queues with heavy-tailed inter-batch-arrival time distributions. The roots of the underlying characteristic equation form the basis for all distributions of queue lengths at different time epochs. All queue-length distributions are in the form of sums of geometric terms.

     

A Homomorphism Theorem and a Trotter Product Formula for Quantum Stochastic Flows with Unbounded Coefficients

We give a new method for proving the homomorphic property of a quantum stochastic flow satisfying a quantum stochastic differential equation with unbounded coefficients, under some further hypotheses. As an application, we prove a Trotter product formula for quantum stochastic flows and obtain quantum stochastic dilations of a class of quantum dynamical semigroups generalizing results of Goswami et al. (Inst H Poincare Probab Stat 41:505–522, 2005).     

N-benzoate-N′ salicylaldehyde ethynelediamine: A new fluorescent sensor for Zn2+ ion by “off-on” mode

Imbalance of zinc ion (Zn²⁺) in human body causes diseases like Alzheimer’s and Parkinson’s and therefore Zn²⁺ estimation in biological fluids has diagnostic values. Fluorescence “off-on” sensors have advantages of high sensitivity and in situ application over other sensors. A new fluorescent “off-on” Zn²⁺ sensor, N-benzoate-N′ salicylaldehyde ethynelediamine (L), has been synthesisied. In 1:1(v/v) CH₃OH:PBS (PBS?=?phosphate buffer solution), L shows ca. 20 times enhancement in fluorescence intensity on interaction with Zn²⁺, due to snapping of photoinduced electron transfer (PET) process, which is selective over metal ions - Na⁺, K⁺, Ca²⁺, Ni²⁺, Cu²⁺, Cd²⁺, Hg²⁺ and Pb²⁺. These metal ions either individually or all together does not interfere the sensing ability of L towards Zn²⁺. A 1:1 interaction between L and Zn²⁺ ion with binding constant 10^4.25 has been established from spectroscopic data.     

Some radii problems related to certain p-valent meromorphic functions

The purpose of the present paper is to introduce several new classes of p-valent meromorphic functions defined by Ruscheweyh derivative operator for meromorphic multivalent functions. Further, we investigate the radii problems of these analytic classes in the punctured unit disk.     

Efficient Synthesis of Structurally Novel Diaryl Ethers by Regioselective Functionalization

Synthesis of structurally novel and biologically useful 3′-substituted diaryl ethers employing Cu(0) as a catalyst, followed by regioselective either sulfonylation or carbonylation, is described.     

Single chemosensor for highly selective colorimetric and fluorometric dual sensing of Cu(II) as well as ‘NIRF’ to acetate ion

A novel fluorescent probe for the copper(II) ion in mixed aqueous media, based on fluorescence quenching mechanism with noticeable color change from light to dark yellow, was designed and synthesized. It also exhibited high selectivity for acetate in acetonitrile over other common anions in the near infrared region (NIR) accompanied with exciting color changes from light yellow to pink. Hence sensor 1 ascertains its dual chemosensing ability toward Cu(II) and acetate ions as evidenced by competitive experiments.