Squeezed states, metaplectic group, and operator möbius transformations

We present an analysis, based on the metaplectic group Mp(2), of the recently introduced single-mode inverse creation and annihilation operators and of the associated eigenstates of different two-photon annihilation operators. We motivate and obtain a quantum operator form of the classical Mobius or fractional linear transformation. The subtle relation to the two unitary irreducible representations of Mp(2) is brought out. For problems involving inverse operators the usefulness of the Bargmann analytic function representation of quantum mechanics is demonstrated. Squeezing, bunching, and photon-number distributions of the four families of states that arise in this context are studied both analytically and numerically

Squeezed vacuum as an eigenstate of two-photon annihilation operator

We introduce the inverse annihilation and creation operators a-1 and a(dagger-1) by their actions on the number states. We show that the squeezed vacuum exp(1/2xia(dagger2)]\0] and squeezed first number state exp[1.2xia(dagger2)]\n = 1] are respectively the eigenstates of the operators (a(dagger-1)a) and (aa(dagger-1)) with the eigenvalue xi.

Photocytotoxicity and DNA photocleavage activity of La(III) and Gd(III) complexes of phenanthroline bases

Lanthanide(II) complexes La(B)(acac)(3)] (1-3) and Gd(B)(acac)(3)] (4-6), where B is a N,N-donor phenanthroline base, viz., 1,10-phenanthroline (phen in 1, 4), dipyrido3,2-d:2',3'-f]quinoxaline (dpq in 2, 5) and dipyrido3,2-a:2',3'-c]phenazine (dppz in 3, 6), have been prepared and characterized. The Gd(111) complexes 4 6 are structurally characterized by single crystal X-ray crystallography. The complexes display GdO6N2 coordination with the ligands showing bidentate chelating mode of bonding. The complexes are non-electrolytic in aqueous DMF and exhibit ligand-centered absorption bands in the UV region. The dppz complexes show a band at 380 nm in DMF. The La(111) complexes are diamagnetic. The Gd(III) complexes are paramagnetic with magnetic moment that corresponds to seven unpaired electrons. The Complexes are avid binders to calf thymus DNA giving K-b values in the range of 4.7 x 10(4) 6.1 x 10(5) M-1 with a relative binding order: 3, 6 (dppz) > 2, 5 (dpq) > 1, 4 (phen). The binding data suggest DNA surface and/or groove binding nature of the complexes. The dpq and dppz complexes efficiently cleave SC DNA to its nicked circular form in UV-A light of 365 nm via formation of both singlet oxygen (O-1(2)) and hydroxyl radical (HO center dot) species. The dppz complexes 3 and 6 exhibit significant PDT effect in He La cervical cancer cells giving respective IC50 value of 460(+/- 50) and 530(+/- 30) nM in UV-A light of 365 rim, and are essentially non-toxic in dark with an IC50 value of >100 mu M. The dppz ligand alone is cytotoxic in dark and UV-A light. A significant decrease in the dark toxicity of the dppz base is observed on binding to the Ln(III) ion while retaining its photocytotoxicity.

Schiff base oxovanadium(IV) complexes of phenanthroline bases showing DNA photocleavage activity at near-IR light and photocytotoxicity

Oxovanadium(IV) complexes VO(L)(B)](ClO4) (1-3) of N-2-pyridylmethylidine-2-hydroxyphenylamine (HL) Schiff base and phenanthroline bases (B), viz. 1,10-phenanthroline (phen in 1), dipyrido3,2-d: 2',3'-f] quinoxaline (dpq in 2) or dipyrido3,2-a: 2',3'-c] phenazine (dppz in 3), were prepared, characterized and their DNA binding property, photo-induced DNA cleavage activity and photocytotoxicity in HeLa cells studied. The crystal structure of 1 shows the presence of a VO2+ moiety in VO2N4 coordination geometry. The complexes show a d-d band at similar to 830 nm in DMF. The complexes display an oxidative V(V)-V(IV) response near 0.5 V versus SCE and a reductive V(IV)/V(III) response near -0.65 V in DMF -0.1 M TBAP. The complexes that are avid binders to CT DNA giving K-b values within 7.1 x 10(4) to 3.2 x 10(5) M-1, do not show any significant chemical nuclease activity in presence of 3-mercaptopropionic acid or glutathione. The dpq and dppz complexes are photocleavers of pUC19 DNA in UV-A light of 365 nm forming both O-1(2) and (OH)-O-center dot radicals and in near-IR light of 785 nm forming (OH)-O-center dot radicals. The dppz complex exhibits photocytotoxicity in visible light in HeLa cells (IC50 = 6.8 mu M). Flow-cytometric study on this complex shows a high sub-G1 phase in light compared to dark indicating PDT effect. (C) 2011 Elsevier B. V. All rights reserved.

Mutagenic significance of proton acidities in methylated guanine and thymine bases and deoxynucleosides: A theoretical study

Proton changes have been advanced as being the key molecular basis for the mutagenecity of alkylated DNA bases and nucleosides, leading to questions as to which protons are involved and whether the protic changes are tautomeric shifts or abstractions. This semiempirical molecular orbital study seeks to clarify the issue by examining the various possibilities open for these protic changes in a number of methylated guanines and thymines and their deoxynucleosides. Proton shifts leading to tautomer formation are not predicted as being thermodynamically favourable in most cases. The most feasible proton abstractions are predicted to involve the Watson-Crick protons in all cases, which corroborates Watson-Crick proton loss as providing the key molecular basis for the induction of point mutations. The calculated proton acidities correlate well with experimental data. The gas-phase deprotonation enthalpies for a number of alkylated nucleosides are found to correlate linearly with the solvent-phase pK(a) values. The theoretically calculated enthalpies in a simulated aqueous solvent phase of the deprotonation reactions of various nucleic acid bases are also found to have good linear correlations with experimental pK(a) values. The consensus of these calculations is that O-6-alkyldeoxyguanosines, and O-2- and O-4-alkyldeoxythymidines would be mutagenic while N-7-alkyldeoxyguanosines would not be mutagenic (as experiment indicates). The untested N-3-methyldeoxyguanosine is predicted to be mutagenic. (C) 1997 Elsevier Science B.V.

Synthesis, spectral characterization and in vitro microbiological evaluation of novel glyoxal, biacetyl and benzil bis-hydrazone macrocyclic Schiff bases and their Co(II), Ni(II) and Cu(II) complexes

A series of binuclear Co(II), Ni(II) and Cu(II) complexes were synthesized by the template condensation of glyoxal, biacetyl or benzil bis-hydrazide, 2,6-diformyl-4-methylphenol and Co(11), Ni(II) or Cu(II) chloride in a 2:2:2 M ratio in ethanol. These 22-membered macrocyclic complexes were characterized by elemental analyses, magnetic, molar conductance, spectral, thermal and fluorescence studies. Elemental analyses suggest the complexes have a 2:1 stoichiometry of the type (M2LX2]center dot nH(2)O and Ni(2)LX(2)2H(2)O]center dot nH(2)O (where M = Co(II) and Cu(II); L = H2L1, H2L2 and H2L3; X = Cl; n = 2). From the spectroscopic and magnetic studies, it has been concluded that the Co(11) and Cu(11) complexes display a five coordinated square pyramidal geometry and the Ni(II) complexes have a six coordinated octahedral geometry. The Schiff bases and their metal complexes have also been screened for their antibacterial and antifungal activities by the MIC method. (C) 2011 Elsevier Ltd. All rights reserved.

The extended Enskog operator for simple fluids with continuous potentials: single particle and collective properties

We generalized the Enskog theory originally developed for the hard-sphere fluid to fluids with continuous potentials, such as the Lennard–Jones. We derived the expression for the k and ω dependent transport coefficient matrix which enables us to calculate the transport coefficients for arbitrary length and time scales. Our results reduce to the conventional Chapman–Enskog expression in the low density limit and to the conventional k dependent Enskog theory in the hard-sphere limit. As examples, the self-diffusion of a single atom, the vibrational energy relaxation, and the activated barrier crossing dynamics problem are discussed.

Ternary copper(II) complexes of thiosemicarbazones and heterocyclic bases showing N3OS coordination as models for the type-2 centers of copper monooxygenases

Six ternary copper(II) complexes of general formulation [CuLB] (1-6), where L is dianionic ONS-donor thiosemicarbazones derived from the condensation of salicylaldehyde with thiosemicarbazides and B is NN-donor heterocyclic bases like 2,2'-bipyridine, 1,10-phenanthroline and 2,9-dimethyl-1,10-phenanthroline, are prepared from a reaction of copper(II) acetate hydrate with the heterocyclic base (B) and the thiosemicarbazone (H2L) in MeOH, and structurally characterized by X-ray diffraction technique. Crystal structures of the complexes display a distorted square-pyramidal (4 + 1) coordination geometry having the ONS-donor thiosemicarbazone bonded at the basal plane. The chelating heterocyclic bases exhibit axial-equatorial mode of bonding. The complexes are one-electron paramagnetic and they show axial X-band EPR spectra in DMF-toluene glass at 77 K giving g(parallel to)(A(parallel to)) and g(perpendicular to) values of similar to2.2 (175 x 10(-4) cm(-1)) and similar to2.0 indicating a {d(x2-y2)}(1) ground state. The complexes show a d-d band near 570 nm and a charge transfer band near 400 nm in DMF. The complexes are redox active and exhibit a quasireversible Cu(II)-Cu(I) couple in DMF-0.1 M tetrabutylammonium perchlorate near 0.1 V vs. SCE. They are catalytically active in the oxidation of ascorbic acid in presence of dioxygen. The complexes with a CuN3OS coordination model the ascorbate oxidation property of dopamine beta-hydroxylase and peptidylglycine a-hydroxylating monooxygeanase. (C) 2003 Elsevier Science B.V. All rights reserved.

Ferrocene-Conjugated L-Tryptophan Copper(II) Complexes of Phenanthroline Bases Showing DNA Photocleavage Activity and Cytotoxicity

Ferrocene-conjugated L-tryptophan (L-Trp) reduced Schiff base (Fc-TrpH) copper(II) complexes [Cu(Fc-Trp)(L)](ClO(4)) of phenanthroline bases (L), viz. 2,2'-bipyridine (bpy in 1), 1,10-phenanthroline (phen in 2), dipyrido[3,2-d:2',3'-f]quinoxaline (dpq in 3), and dipyrido[3,2-a:2',3'-c]phenazine (dppz in 4), were prepared and characterized and their photocytotoxicity studied. Cationic reduced Schiff base (Ph-TrpH) complexes [Cu(Ph-Trp)(L)(H(2)O)] (ClO(4)) (L = phen in 5; dppz in 6) having the ferrocenyl moiety replaced by a phenyl group and the Zn(II) analogue (7) of complex 4 were prepared and used as control species. The crystal structures of 1 and 5 with respective square-planar CuN(3)O and square-pyramidal CuN(3)O(2) coordination geometry show significantly different core structures. Complexes 1-4 exhibit a Cu(II)-Cu(I) redox couple near -0.1 V and the Fc(+)-Fc couple at similar to 0.5 V vs SCE in DMF-0.1 M [Bu(4)(n)N] (ClO(4)) (Fc = ferrocenyl moiety). The complexes display a copper(II)-based d-d band near 600 nm and a Fc-centered band at similar to 450 nm in DMF-Tris-HCl buffer. The complexes are efficient binders to calf thymus DNA. They are synthetic chemical nucleases in the presence of thiol or H(2)O(2), forming hydroxyl radicals. The photoactive complexes are cleavers of pUC19 DNA in visible light, forming hydroxyl radicals. Complexes 2-6 show photocytotoxicity in HeLa cancer cells, giving IC(50) values of 4.7, 10.2, 1.3, 4.8, and 4.3 mu M, respectively, in visible light with the appearance of apoptotic bodies. The complexes also show photocytotoxicity in MCF-7 cancer cells. Nuclear chromatin cleavage has been observed with acridine orange/ethidium bromide (AO/EB) dual staining with complex 4 in visible light. The complexes induce caspase-independent apoptosis in the HeLa cells.

An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space and internal property variables. In addition, the operator splitting allows to decouple the equations for temperature, solute partial density and particle size distribution. Further, a nodal point based parallel finite element algorithm for multi-dimensional population balance systems is presented. The method is applied to study a crystallization process assuming, for simplicity, a size independent growth rate and neglecting agglomeration and breakage of particles. Simulations for different wall temperatures are performed to show the effect of cooling on the crystal growth. Although the method is described in detail only for the case of d=2 space and s=1 internal property variables it has the potential to be extendable to d+s variables, d=2, 3 and s >= 1. (C) 2011 Elsevier Ltd. All rights reserved.

Bases and Ideal Generators for Projective Monomial Curves

In this article we study bases for projective monomial curves and the relationship between the basis and the set of generators for the defining ideal of the curve. We understand this relationship best for curves in P-3 and for curves defined by an arithmetic progression. We are able to prove that the latter are set theoretic complete intersections.

Dilations of Gamma-contractions by solving operator equations

For a contraction P and a bounded commutant S of P. we seek a solution X of the operator equation S - S*P = (1 - P* P)(1/2) X (1 - P* P)(1/2) where X is a bounded operator on (Ran) over bar (1 - P* P)(1/2) with numerical radius of X being not greater than 1. A pair of bounded operators (S, P) which has the domain Gamma = {(z(1) + z(2), z(2)): vertical bar z(1)vertical bar < 1, vertical bar z(2)vertical bar <= 1} subset of C-2 as a spectral set, is called a P-contraction in the literature. We show the existence and uniqueness of solution to the operator equation above for a Gamma-contraction (S, P). This allows us to construct an explicit Gamma-isometric dilation of a Gamma-contraction (S, P). We prove the other way too, i.e., for a commuting pair (S, P) with parallel to P parallel to <= 1 and the spectral radius of S being not greater than 2, the existence of a solution to the above equation implies that (S, P) is a Gamma-contraction. We show that for a pure F-contraction (S, P), there is a bounded operator C with numerical radius not greater than 1, such that S = C + C* P. Any Gamma-isometry can be written in this form where P now is an isometry commuting with C and C. Any Gamma-unitary is of this form as well with P and C being commuting unitaries. Examples of Gamma-contractions on reproducing kernel Hilbert spaces and their Gamma-isometric dilations are discussed. (C) 2012 Elsevier Inc. All rights reserved.

Ferrocene-Conjugated Copper(II) Complexes of L-Methionine and Phenanthroline Bases: Synthesis, Structure, and Photocytotoxic Activity

Ferrocene-conjugated reduced Schiff base (Fc-metH) copper(II) complexes of L-methionine and phenanthroline bases, namely, Cu(Fc-met)(B)](NO3), where B is 1,10-phenanthroline (phen in 1), dipyrido3,2-d:2',3'-f]quinoxaline (dpq in 2), dipyrido3,2-a:2',3'-c]phenazine (dppz in 3), and 2-(naphthalen-1-yl)-1H-imidazo4,5-f]1,10]phenanthroline (nip in 4), were prepared and characterized and their photocytotoxicity studied (Fc = ferrocenyl moiety). Complexes Cu(Ph-met)(B)](NO3) of the reduced Schiff base from benzaldehyde and L-methionine (Ph-metH) and B (phen in 5, dppz in 6) were prepared and used as control species. Complexes 1 and 5 were structurally characterized by X-ray crystallography. Complex 1 as a discrete monomer has a CuN3OS core with the thiomethyl group as the axial ligand. Complex 5 has a polymeric structure with a CuN3O2 core in the solid state. Complexes 5 and 6 are formulated as Cu(Ph-met)(B)(H2O)] (NO3) in an aqueous phase based on the mass spectral data. Complexes 1-4 showed the Cu(II)-Cu(I) and Fc(+)-Fc redox couples at similar to 0.0 and similar to 0.5 V vs SCE, respectively, in DMF-0.1 M (Bu4N)-N-n](ClO4). A Cu(II)-based weak d-d band near 600 nm and a relatively strong ferrocenyl band at similar to 450 nm were observed in DMF-Tris-HCl buffer (1:4 v/v). The complexes bind to calf thymus DNA, exhibit moderate chemical nuclease activity forming (OH)-O-center dot radical species, and are efficient photocleavers of pUC19 DNA in visible light of 454, 568, and 647 rim, forming (OH)-O-center dot radical as the reactive oxygen species. They are cytotoxic in HeLa (human cervical cancer) and MCF-7 (human breast cancer) cells, showing an enhancement of cytotoxicity upon visible light irradiation. Significant change in the nuclear morphology of the HeLa cells was observed with 3 in visible light compared to the nonirradiated sample. Confocal imaging using 4 showed its nuclear localization within the HeLa cells.

An operator-splitting Galerkin/SUPG finite element method for population balance equations : stability and convergence

We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard finite elements, when the dimension of the equation is more than three, (ii) spurious oscillations in the solution induced by standard Galerkin approximation due to pure advection in the internal property coordinates. The key idea is to split the high-dimensional population balance equation into two low-dimensional equations, and discretize the low-dimensional equations separately. In the proposed splitting scheme, the shape of the physical domain can be arbitrary, and different discretizations can be applied to the low-dimensional equations. In particular, we discretize the physical and internal spaces with the standard Galerkin and Streamline Upwind Petrov Galerkin (SUPG) finite elements, respectively. The stability and error estimates of the Galerkin/SUPG finite element discretization of the population balance equation are derived. It is shown that a slightly more regularity, i.e. the mixed partial derivatives of the solution has to be bounded, is necessary for the optimal order of convergence. Numerical results are presented to support the analysis.