Fixed point results for generalized quasicontraction mappings in abstract metric spaces

In this paper, we introduce the concept of generalized quasicontraction mappings in an abstract metric space. By using this concept, we construct an iterative process which converges to a unique fixed point of these mappings. The result presented in this paper generalizes the Banach contraction principle in the setting of metric space and a recent result of Huang-Zhang for contractions. We also validate our main result by an example.     

Near‐exact supersymmetric partner potentials: Construction and exploitation

Precise supersymmetric (SUSY) partner potentials can be generated only for exactly solvable problems of the stationary Schrödinger equation. This is a severe restriction, as most problems are not amenable to exact solutions. We employ here a linear variational strategy to explicitly construct approximate SUSY partners of a few common, not exactly solvable potentials and subsequently examine their properties to explore the advantages in practical implementation. The efficacy of our proposed scheme is commendable. We demonstrate that, for symmetric potentials, the constructed partners may be so good that the overall recipe has the nicety of generating the whole eigenspectrum by employing only half of the full Hilbert space functions. A similar strategy is shown to work for the odd states too, with proper boundary conditions. Pilot calculations involve a number of low‐lying states of some mixed oscillator and double‐well potentials. Analysis of the results reveals a few interesting features of the problem of construction of approximate SUSY partners and their practical use. Particularly, we identify places where the operator‐level approximations are involved and how far they affect the bounding properties of energies that are obtained as eigenvalues of a matrix diagonalization problem associated with linear variations. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Synthesis of mesoporous γ-alumina by sol–gel process and its characterization and application for sorption of Pu(IV)

Mesoporous γ-alumina samples were prepared by the sol–gel process from the boehmite sol having different template solutions. Copper doped material was also prepared from sol containing template solution along with copper nitrate. Studies were performed to understand the influence of templates on the morphology of the synthesized samples particularly with respect to specific surface area and porosity. Synthesized samples were used to study sorption of Pu(IV) from nitric acid–oxalic acid solutions. Distribution ratios (D) for Pu(IV) were determined using the γ-alumina samples with an objective to employ these for the recovery of Pu.     

Global Minimum‐Energy Structure and Spectroscopic Properties of I2.−⋅n H2O Clusters: A Monte Carlo Simulated Annealing Study

The vibrational (IR and Raman) and photoelectron spectral properties of hydrated iodine‐dimer radical‐anion clusters, I₂^.? ? n H₂O (n=1–10), are presented. Several initial guess structures are considered for each size of cluster to locate the global minimum‐energy structure by applying a Monte Carlo simulated annealing procedure including spin–orbit interaction. In the Raman spectrum, hydration reduces the intensity of the I? I stretching band but enhances the intensity of the O? H stretching band of water. Raman spectra of more highly hydrated clusters appear to be simpler than the corresponding IR spectra. Vibrational bands due to simultaneous stretching vibrations of O? H bonds in a cyclic water network are observed for I₂^.? ? n H₂O clusters with n≥3. The vertical detachment energy (VDE) profile shows stepwise saturation that indicates closing of the geometrical shell in the hydrated clusters on addition of every four water molecules. The calculated VDE of finite‐size small hydrated clusters is extrapolated to evaluate the bulk VDE value of I₂^.? in aqueous solution as 7.6 eV at the CCSD(T) level of theory. Structure and spectroscopic properties of these hydrated clusters are compared with those of hydrated clusters of Cl₂^.? and Br₂^.?.     

Investigation of carrier scattering mechanisms in molybdenum diselenide single crystals by hall effect measurements

Molybdenum diselenide (MoSe₂) belong to the large family of layered transition metal dichalcogenides. It consists of weakly coupled sandwiched layers i.e. Se – Mo – Se in which a Mo atom layer is enclosed within two Se layers. This structure makes MoSe₂ extremely anisotropic in character and leads to unusual structural properties. In addition, MoSe₂ possess flexible nature along with good carrier mobility to make them potential candidate for fabricating flexible high mobility electronic devices such as Schottky barrier devices, FETs, solar cell etc. In context of this authors made an effort to study the low temperature (12 < T < 300 K) electronic transport properties of Molybdenum diselenide (MoSe₂). Through the investigation the temperature dependent Hall mobility study revealed that the grown crystals of MoSe₂possess a mixed scattering mechanism. It has been found that observed temperature dependant mobility has at least two transitions from lattice to impurity scatterings showing an imprint of multicarrier nature of this semiconductor originating from its complex band structure. It has been observed that the studied crystals have at least two group of carriers of differing origins in which transition between dominant scattering mechanisms occur at different temperatures. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some problems and conjectures in number theory

In this article, we shall discuss some interesting, viable, meaningful, applicable and productive conjectures and methods to deal with some fundamental results in the theory of numbers.     

Geometrical solution of some cubic equations with non-real roots

A general cubic equation ax ³ + bx ² + cx + d = 0 where a, b, c, d ∈R, a ≠ 0 has three roots with two possibilities—either all three roots are real or one root is real and the remaining two roots are imaginary. Dealing with the second possibility this paper attempts to give the geometrical locations of the imaginary roots of the equation under three different sets of conditions. These sets of conditions include: (i) the real root of the given cubic equation is given, (ii) the real part of an imaginary root is given, and (iii) the imaginary part of an imaginary root is given.     

Effect of Analyte Concentration on the Laser-Induced Plasma Temperature and Electron Density in Liquid Matrix

In the present work, we report spectroscopic studies of laser-induced plasmas produced by focusing the second harmonic (532 nm) of a Nd:YAG laser onto the laminar flow of a liquid containing chromium. The plasma temperature is determined from the coupled Saha–Boltzmann plot and the electron density is evaluated from the Stark broadening of an ionic line of chromium [Cr(II)] at 267.7 nm. Our results reveal a decrease in plasma temperature with an increase in Cr concentration up to a certain concentration level; after that, it becomes approximately constant, while the electron density increases with an increase in analyte (Cr) concentration in liquid matrix.     

Recent developments in the study of higher order nonclassical states

Our recent observations ort higher order nonclassicality are described. Recently we have shown that a generalized notion of higher order nonclassicality (in terms of higher order moments) can be introduced. Under this generalized framework of higher order nonclassicality, conditions of higher order squeezing and higher order subpoissonian photon statistics are derived. Further, with the help of simple density matrices, it is shown that the higher order antibunching (HOA) and higher order subpoissonian photon statistics (HOSPS) are not the manifestation of the same phenomenon and consequently it is incorrect to use the condition of HOA as a test of HOSPS. It is established that the HOA and HOSPS may exist even in absence of the corresponding lower order phenomenon. It is also shown that the potential sources of Single photon must satisfy the condition of HOA. Most of the intermediate states are shown to satisfy the criteria of HOA. A protocol for comparison of potential Single photon sources (SPS) is reported here and the protocol is used to compare some of the existing proposals of SPS. Further, it is shown that it is possible to derive an arbitrarily large number of criterion for higher order nonclassicality but all of them does not yield new and interesting information.