Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Towards a green synthesis of isoquinoline: Beckmann rearrangement of E,-cinnamaldoxime over H-zeolites

Isoquinoline was prepared through the Beckmann rearrangement of cinnamaldoxime over different H-zeolites, K-10 montmorillonite clay, amorphous SiO2–Al2O3 and γ-alumina under well-optimized conditions of temperature, weight hourly space velocity and catalyst loading. Cinnamaldoxime under ambient reaction conditions over the catalysts underwent migration of the anti-styryl moiety to electron deficient nitrogen (Beckmann rearrangement) followed by an intramolecular cyclization to yield isoquinoline. Cinnamo-nitrile (dehydration product) and cinnamaldehyde were formed as by-products. Isoquinoline formation was high on zeolite catalysts (ca. >86.5%) and mordenite (ca. 92.3%) was the most efficient in the series. Catalysts were susceptible for deactivation and the decrease in the percentage conversion of oxime with time is associated with a corresponding increase in the acid hydrolysis producing salicylaldehyde at later stages of the reaction. However, these catalysts retain activity considerably and can be recycled without loss of activity and change of product distribution.

Prevention of photooxidation in blue-green emitting Cu doped ZnSe nanocrystals

This communication highlights unstable blue-green emitting Cu doped ZnSe nanocrystals stabilized by diluting the surface Se with a calculated amount of S.

Metal Nanoparticles via the Atom-Economy Green Approach

Metal nanoparticles (NPs) of Cu(air-stable),Ag,and Au have been prepared using an atom-economy green approach Simple mechanical stirring of solid mixtures (no solvent) of a metal salt and ammonia borane at 60 degrees C resulted in the formation of metal NPs. In this reaction, ammonia borane is transformed into a BNHx polymer, which protects the NPs formed and halts their growth. This results in the formation of the BNHx polymer protected monodisperse NPs Thus, ammonia borane used in these reactions plays a dual role (reducing agent andprecursor for the stabilizing agent).

Dolezal's theorem revisited

This paper presents an improved version of Dolezal's theorem, in the area of linear algebra with continuously parametrized elements. An extension of the theorem is also presented, and applications of these results to system theory are indicated.

Towards a green synthesis of LAB's: Effect of rare earth metal ions on the benzene alkylation with 1-dodecene over NaFAU-Y zeolites

Chemically modified microporous materials can be prepared as robust catalysts suitable for application in vapor phase processes such as Friedel-Crafts alkylation. In the present paper we have investigated the use of rare earth metal (Ce3+, La3+, RE3+, and Sm3+) exchanged Na-Y zeolites as catalysts for the alkylation of benzene with long chain linear 1-olefin; 1-dodecene. Thermodesorption studies of 2,6-dimethylpyridine adsorbed catalysts (in the temperature range 573 to 873 K) show that the rare earth zeolites are highly Bronsted acidic in nature. A perfect correlation between catalyst selectivity towards the desired product (2-phenyldodecane) and Bronsted acid sites amount has been observed. (c) 2006 Springer Science + Business Media, Inc.

Synthesis and enhanced green photoluminescence emission from BCT ZnS nanocrystals

Body-centered-tetragonal (BCT) ZnS nanocrystals have been synthesized, for the first time to the best of our knowledge, by using the chemical coprecipitation method at higher synthesis temperatures of 65 and 95 degrees C. It is confirmed from X-ray diffraction (XRD) studies that in the high-temperature-synthesized samples, cubic and BCT phases coexist, in contrast to the room-temperature-synthesized sample, which consists of only cubic phase with sizes of the particles lying between 2 and 3 nm. The sizes of BCT phase nanocrystals are bigger than those of cubic phase of ZnS. The presence of BCT phase of ZnS in the samples is increased from 40 to 90% when the temperature of synthesis is increased from 65 to 95 degrees C. The nanocrystalline nature and UV-Vis absorption characteristics of the prepared samples have been studied with a transmission electron microscope (TEM) and a UV-Visible pectrophotometer, respectively. The room-temperature-synthesized ZnS sample shows photoluminescence (PL) emission in the blue region with multiple peaks, whereas the high-temperature-synthesized samples show PL emissions in the visible region. The Gaussian fittings of the measured PL spectra shows that three PL peaks at 429, 477, and 525 nm are appeared in the 65 degrees C sample and two peaks at 491 and 540 nm appear in the 95 degrees C sample with the enhanced PL intensity of the green peak at 540 nm. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

A multiplier theorem for the sublaplacian on the Heisenberg group

A multiplier theorem for the sublaplacian on the Heisenberg group is proved using Littlewood-Paley-Stein theory of g-functions.

A Circuit-Based Proof of Toda′s Theorem

We present a simple proof of Toda′s result (Toda (1989), in "Proceedings, 30th Annual IEEE Symposium on Foundations of Computer Science," pp. 514-519), which states that circled plus P is hard for the Polynomial Hierarchy under randomized reductions. Our approach is circuit-based in the sense that we start with uniform circuit definitions of the Polynomial Hierarchy and apply the Valiant-Vazirani lemma on these circuits (Valiant and Vazirani (1986), Thoeret. Comput. Sci.47, 85-93).

Experimental Test of the Quantum No-Hiding Theorem

The no-hiding theorem says that if any physical process leads to bleaching of quantum information from the original system, then it must reside in the rest of the Universe with no information being hidden in the correlation between these two subsystems. Here, we report an experimental test of the no-hiding theorem with the technique of nuclear magnetic resonance. We use the quantum state randomization of a qubit as one example of the bleaching process and show that the missing information can be fully recovered up to local unitary transformations in the ancilla qubits.

Central Limit Theorem for truncated heavy tailed Banach valued random vectors

In this paper the question of the extent to which truncated heavy tailed random vectors, taking values in a Banach space, retain the characteristic features of heavy tailed random vectors, is answered from the point of view of the central limit theorem.

Kinetic evolution studies of silver nanoparticles in a bio-based green synthesis process

Silver nanoparticles are being extensively studied due to their widespread applications and unique properties. In the present study, the growth kinetics of silver nanoparticles as synthesized on reduction of silver nitrate solution by aqueous extract of Azadirachta indica leaves was investigated. The formation of silver nanoparticles was preliminarily monitored by measuring the absorption maxima at different time intervals after adding the reducing agent to the silver salt solution (0.5, 1, 1.5, 2, 2.5, 3, 3.5 and 4 h). At different time points characterization studies were conducted using X-ray diffraction studies, FT-IR techniques, zeta potential studies and transmission electron microscopy. The total available silver in the reaction medium was determined at different durations using ICP-OES. The changes in reduction potential in the medium were also monitored using potentiometric analysis. The results confirm a definite change in the medium pertaining to formation of the stable nanoparticles after 2 h, and a significant increase in the agglomeration tendency after 4 h of interaction. The growth kinetic data of the nanoparticles till 3.5 h was found to fit the LSW model confirming diffusion limited growth. (C) 2011 Elsevier B.V. All rights reserved.

A compact proof of Fisher�s Fundamental Theorem for multiple loci

A systematic method is formulated to carry out theoretical analysis in a multilocus multiallele genetic system. As a special application, the Fundamental Theorem of Natural Selection is proved (in the continuous time model) for a multilocus multiallele system if all pairwise linkage disequilibria are zero.