Phosphorous disulfide and its ions in the electronic ground state: a gas phase theoretical study

Ab initio molecular orbital theory and density functional theory calculations were performed on the electronic ground states of the open-shell PS₂ molecule and its singly charged ions. A comparison of the optimized molecular structures indicates as the stepwise one-electron reduction of the PS₂⁺ ion, to yield PS₂ and PS₂⁻, provokes a symmetric elongation of both PS bonds along with a bending of its linear equilibrium geometry. The ionization potential (IP), adiabatic electron affinity (EA_ad), and atomization energy (AE) of the open-shell PS₂ molecule were calculated at different levels of theory. The following values were obtained at the more realistic UMP4SDTQ/6-311+G(3df)//UHF/6-311+G(3df) level of theory: IP=8.32 eV, EA_ad=3.03 eV and AE=12.40 eV. At the same level of theory, the calculated vertical detachment energy (VDE) of the PS₂⁻ anion is 3.22 eV. The donor–acceptor complexes formed in the gas-phase upon interaction of either one or two ammonia molecules with PS₂⁺ were also investigated. The calculated gas-phase binding energies indicate that the formation of the bis-adduct is favored over that of the mono-adduct by a binding energy gain of about 20 kcal/mol.     

Shell correction in Bohr stopping theory

Second-harmonic cross-correlation operates a selection in time-phase among the randomly de-phased contributions to an optical field that propagated through a scattering medium. It can thus be used to selectively detect the weak contribution remaining coherent with the incident field. Received 7 May 1999     

Landau's theorem for biharmonic mappings

In this paper, we show the existence of Landau constant for biharmonic mappings of the form F(z)=²|z|G(z)+K(z), |z|<1, where G and K are harmonic.     

Noncooperative stochastic games under a n-stage local contraction assumption

We consider a class of noncooperative stochastic games with general state and action spaces and with a state dependent discount factor. The expected time duration between any two stages of the game is not bounded away from zero, so that the usual N-stage contraction assumption, uniform over all admissible strategies, does not hold. We propose milder sufficient regularity conditions, allowing strategies that give rise with probability one to any number of simultaneous stages. We give sufficient conditions for the existence of equilibrium and ∈-equilibrium stationary strategies in the sense of Nash. In the two-player zero-sum case, when an equilibrium strategy exists, the value of the game is the unique fixed point of a specific functional operator and can be computed by dynamic programming.     

Time-dependent harmonic oscillator in a magnetic field and an electric field on the non-commutative plane

In the non-commutative space, wave functions and geometric phases are derived for the time-dependent harmonic oscillator in external time-dependent magnetic and electric field. Explicit forms of the coherent states are also given, which are not the minimum uncertainty states for the coordinates and momenta.     

Common fixed point theorems for expansion mappings in various spaces

We prove expansion mappings theorems in various spaces i.e., metric spaces, generalized metric spaces, probabilistic metric spaces and fuzzy metric spaces, which generalize the results of various authors like Daffer and Kaneko [11], Ahmad, Ashraf and Rhoades [1], Vasuki [38], Rhoades [31] and Wang, Li, Gao and Iseki [40] etc. In the memory of 65^th birthday anniversary of his Father Late Sh. Ram Phool Sharma     

An intrinsic approach to Lichnerowicz conjecture

In this paper we give a proof of Lichnerowicz conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids thenice embeddings into eigenspaces of the Laplacian. Even if one wants to use these embeddings, this paper gives a more streamlined proof. As a byproduct, we get a simple criterion for a polynomial to be a Jacobi polynomial.     

Mapping problems, fundamental groups and defect measures

We study all the possible weak limits of a minimizing sequence, for p-energy functionals, consisting of continuous maps between Riemannian manifolds subject to a Dirichlet boundary condition or a homotopy condition. We show that if p is not an integer, then any such weak limit is a strong limit and, in particular, a stationary p-harmonic map which is C ^1,α continuous away from a closed subset of the Hausdorff dimension ≤ n − [p] − 1. If p is an integer, then any such weak limit is a weakly p-harmonic map along with a (n − p)-rectifiable Radon measure μ. Moreover, the limiting map is C ^1,α continuous away from a closed subset Σ=spt μ ∪ S with H ^{n − p} (S)=0. Finally, we discuss the possible varifolds type theory for Sobolev mappings. Partially supported by NSF Grant DMS 9626166     

Squeezing and sub-Poissonian effects up-to fourth order in fifth harmonic generation

The concept of squeezing of the electromagnetic field is investigated in fundamental mode in fifth harmonic generation with the approximation |gt|²?1, where g is coupling constant and t, the interaction time between waves during the process. It has been found that squeezing occurs in amplitude, amplitude-squared, amplitude-cubed and fourth-order amplitude states of the field for selective phase values of field amplitude of fundamental mode. The dependence of squeezing on the photon number has also been investigated and found to be sub-Poissonian in nature. The signal to noise ratio has been studied in different order. It is found that the signal to noise ratio is higher in lower order.