A novel synthesis route for brookite rich titanium dioxide photocatalyst involving organic intermediate

Journal of Sol-Gel Science and Technology - High temperature stable brookite rich titanium dioxide of average crystallite size 20&;nbsp;nm has been prepared by a novel aqueous sol–gel...     

Path integral quantization corresponding to the deformed Heisenberg algebra

In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.     

Inner derivations and norm equality

We characterize when the norm of the sum of two bounded operators on a Hilbert space is equal to the sum of their norms.

     

Synthèse de nouveaux dérivés tétrahydroquinoléines et quinoléines via la réaction d'aza-Diels-Alder suivie d'aromatisation

The Aza-Diels-Alder reaction of aldimines with isoeugenol is described. New 1,2,3,4-tetrahydroquinoline and quinoline structures are reported. The stereo- and regioselectivities of the [4+2] cycloaddition are discussed.     

Selective double Suzuki cross-coupling reactions. Synthesis of unsymmetrical diaryl (or heteroaryl) methanes

Using a double Suzuki cross-coupling reaction ortho- or para-bromobenzyl bromides are easily transformed into unsymmetrical diaryl (or heteroaryl) methanes     

Studies on heterocyclic enamines: New syntheses of 4H-pyranes,pyranopyrazoles and pyranopyrimidines

The behaviour of several 2-amino-3-cyano-4H-pyran derivatives toward a variety of nucleophilic reagents is reported.     

An improved max-flow-based lower bound for minimizing maximum lateness on identical parallel machines

In this paper, we introduce a new concept of semi-preemptive scheduling and we show how it can be used to derive a maximum-flow-based lower bound for the P|r_j|L_max which dominates the well-known preemptive lower bound. We show that, in some cases, the proposed bound strictly dominates the preemptive one while having the same complexity.     

Convergence analysis of perturbed hemivariational inequalities

We consider the rate of convergence for a class of perturbed hemivariational inequalities in reflexive Banach Spaces. Our results can be viewed as an extension and refinement of some previous known results in this area.     

Existence and boundary behavior for singular nonlinear differential equations with arbitrary boundary conditions

Existence theory is developed for the equation ?(u)=F(u), where ? is a formally self-adjoint singular second-order differential expression and F is nonlinear. The problem is treated in a Hilbert space and we do not require the operators induced by ? to have completely continuous resolvents. Nonlinear boundary conditions are allowed. Also, F is assumed to be weakly continuous and monotone at one point. Boundary behavior of functions associated with the domains of definitions of the operators associated with ? in the singular case is investigated. A special class of self-adjoint operators associated with ? is obtained.