Trace formulas for relative Schatten class perturbations

We derive trace formulas for a pair of self-adjoint operators $H+V$ and H under the assumption that ${(H?\mathrm{i})}^{?1}V$ is in a Schatten class. This extends the trace formulas of [8], where V alone is assumed to be in a Schatten class. Our trace formulas apply, in particular, in the setting of differential operators and are based on Taylor-like approximations of operator functions. This significantly improves non-Taylor based trace formulas of [10].     

Enhanced reducibility of Ce1-xTixO2 compared to that of CeO2 and higher redox catalytic activity of Ce1-x-yTixPtyO2-delta compared to that of Ce1-xPtxO2-delta

Nanocrystalline Ce(1)(-)(x)Ti(x)O(2) (0 < or = x < or = 0.4) and Ce(1-)(x)(-)(y)Ti(x)Pt(y)O(2)(-)(delta) (x = 0.15, y = 0.01, 0.02) solid solutions crystallizing in fluorite structure have been prepared by a single step solution combustion method. Temperature programmed reduction and XPS study of Ce(1)(-)(x)Ti(x)O(2) (x = 0.0-04) show complete reduction of Ti(4+) to Ti(3+) and reduction of approximately 20% Ce(4+) to Ce(3+) state compared to 8% Ce(4+) to Ce(3+) in the case of pure CeO(2) below 675 degrees C. The substitution of Ti ions in CeO(2) enhances the reducibility of CeO(2). Ce(0.84)Ti(0.15)Pt(0.01)O(2)(-)(delta) crystallizes in fluorite structure and Pt is ionically substituted with 2+ and 4+ oxidation states. The H/Pt atomic ratio at 30 degrees C over Ce(0.84)Ti(0.15)Pt(0.01)O(2)(-)(delta) is 5 and that over Ce(0.99)Pt(0.01)O(2)(-)(delta) is 4 against just 0.078 for 8 nm Pt metal particles. Carbon monoxide and hydrocarbon oxidation activity are much higher over Ce(1-)(x)(-)(y)Ti(x)Pt(y)O(2) (x = 0.15, y = 0.01, 0.02) compared to Ce(1)(-)(x)Pt(x)O(2) (x = 0.01, 0.02). Synergistic involvement of Pt(2+)/Pt degrees and Ti(4+)/Ti(3+) redox couples in addition to Ce(4+)/Ce(3+) due to the overlap of Pt(5d), Ti(3d), and Ce(4f) bands near E(F) is shown to be responsible for improved redox property and higher catalytic activity.     

Determination of signs of hyperfine coupling constants for an S = ½ system through E.P.R., ENDOR and double ENDOR

A systematic method of obtaining relative signs of hyperfine coupling constants is described. It applies to systems consisting of (a) a set of one or more nuclei coupled fairly strongly to the electron spin, and possessing a two-fold (or higher) axis of symmetry, together with (b) a set of weakly coupled nuclei defining superhyperfine transitions. ENDOR measurements for several E.P.R. hyperfine transitions, with the field oriented along the symmetry axis, give relative signs of hyperfine components for this direction. Signs for the other directions can then be obtained through ENDOR measurements on a single hyperfine transition at various field orientations. Additional double ENDOR measurements may be necessary for very weakly coupled nuclei. This method can complement double ENDOR studies in favourable cases. It is illustrated by the determination of signs of coupling constants of protons and of ⁷⁵As in the AsO₄ ^4- radical in KH₂AsO₄.     

Finite Diagonal Random Matrices

The goal of this article is to extend some results of Popescu (Probab. Theory Relat. Fields 144:179, 2009) in several directions. We establish the limiting spectral distribution (LSD) for r-diagonal matrices under reduced moment conditions compared to those required by Popescu. We also deal with the joint convergence of several sequences of such matrices. In particular, we show that there is a large class of such matrices where the joint limit is not free while the marginals are semicircular. We also consider matrices of the form $X_{n}X_{n}^{T}$ where X _n is a sequence of nonsymmetric r-diagonal random matrices and establish their limiting spectral distribution.     

Organocatalytic Green Approach Towards the Fabrication of Fused Benzo N,N‐containing Heterocycles Facilitated by Ultrasonic Irradiation

The development of a metal‐free protocol for transformations in organic synthesis offers a significant potential environmental benefit. This article reports the exploration of meglumine, a nontoxic and biodegradable amino sugar, as an organocatalyst for the synthesis of biologically active 1H‐dibenzo[b,e][1,4]diazepin‐1‐ones, highly regioselective benzimidazole derivatives and derivatives of quinoxalines. Operational simplicity, mild reaction conditions, shorter reaction times, and use of green solvents are the highlights of this protocol. The advantage of ultrasonic irradiation has been significantly explored for the synthesis of the aforesaid compounds. Furthermore, the multifaceted use of o‐phenylenediamine has also been accentuated in the study.     

CsF promoted rapid synthesis of spirooxindole-pyran annulated heterocycles at room temperature in ethanol

A newer, versatile, and straightforward synthetic strategy for the construction of functionalized spirooxindole-pyran annulated heterocycles is described. The procedure is based on CsF-promoted rapid tandem Knoevenagel-Michael-Cyclocondensation reaction of isatin, malononitrile, and 4-hydroxycoumarin/barbituric acids/pyrazolone at room temperature in ethanol. This methodology has various advantages like easy operational, excellent yields within short reaction time (3-25 min), and simple isolation of products. The CsF has a dual role as a base and carbonyl activator.     

Exploration of structural and physicochemical properties of small molecules to inhibit NMDA functionality

Structural Chemistry - The N-methyl-D-aspartate (NMDA) is the family of glutamate receptor, which is involved in controlling synaptic plasticity and memory function; but overactivation of this...     

Degree constrained subgraphs

In this paper, we present new structural results about the existence of a subgraph where the degrees of the vertices are pre-specified. Further, we use these results to prove a 16-edge-weighting version of a conjecture by Karoński, ?uczak and Thomason, an asymptotic 2-edge-weighting version of the same conjecture, and a version of Louigi's Conjecture.     

Spectroscopic studies of catanionic reverse microemulsion: correlation with the superactivity of horseradish peroxidase enzyme in a restricted environment

Catanionic microemulsions formed by dodecyltrimethylammonium bromide (DTAB), sodium dodecyl sulfate (SDS), n-hexanol, dodecane, and citrate buffer have been characterized by using dynamic light scattering (DLS) and spectroscopic studies. While the DLS measurements provide information about the hydrodynamic diameters of the microemulsion droplets formed upon variation of the constituents, steady-state and time-resolved fluorescence emission experiments probe the polarity and the dynamics of the trapped solvent pool inside of the microemulsion droplets of nanometer dimension. In addition, time-resolved fluorescence anisotropy shows the rigidity of the confined solvent pool as well as the coupling between the motion of a solute and those of the solvent molecules. The results obtained from the DLS and those from the steady-state and time-resolved fluorescence emission studies have been found to correlate well with the superactivity of horseradish peroxidase enzyme in the catanionic microemulsions. Subsequently, the time-zero estimate for the dynamic Stokes shift in these microemulsions reveals that approximately 50% of the total solvent dynamical response is missed due to the limited time resolution employed in our experiments. The amplitude of the missing portion is similar to what has been observed recently for nanoscopic water by Fayer and co-workers (Piletic, I. R.; Tan, H.-S.; Fayer, M. D. J. Phys. Chem. B 2005, 109, 21273).