Oscillatory criteria for nonlinearnth-order differential equations with quasiderivatives

Sufficient conditions are given for the existence of oscillatory proper solutions of a differential equation with quasiderivativesL _n y=f(t,L ₀ y, ..., L _n–1 y) under the validity of the sign conditionf(t,x ₁ ,...,x _n )x ₁0,f(t,0,x ₂ ,...,x _n )=0 on ₊ x ⁿ .     

Separately harmonic and subharmonic functions

Let u(x, y) be defined in B ₁×B ₂ where B ₁ ^m and B ₂ ⁿ , and assume that u(x, ·) harmonic for every fixed x and u(·, y) is subharmonic for every fixed y. We show that if u(·, y) is, in addition, C ² for each y then u is subharmonic in B ₁×B ₂ in both variables jointly.     

Combination of three analytical techniques for speciation of Al in environmental samples

An analytical scheme is proposed which combines three speciation techniques for determination of particular Al species in soil extracts and percolating waters. A cation-exchange fast protein liquid chromatography — inductively coupled plasma atomic emission spectrometry (FPLC-ICP-AES) procedure, a microcolumn chelating ion-exchange chromatography- atomic absorption spectrometry (MCC-ETAAS) technique and the 8-hydroxyquinoline spectrophotometric method (8HQ-spectrophotometry) were employed. The FPLC-ICP-AES procedure offers determination of Al³⁺ (retention time 4.5 min) and Al(OH)²⁺ species (retention time 4.0 min) which are separated from Al(OH)⁺ ₂ (retention time 1.5min). AlF²⁺ coelutes with Al(OH)²⁺ species, while Al(SO₄)⁺, AlF⁺ ₂ and negatively charged Al organic complexes coelute with Al(OH)⁺ ₂ species. The MCC-ETAAS technique enables determination of the sum of positively charged monomeric aqua- and hydroxy-Al species plus sulphate- and fluoro-Al complexes. Employing the 8HQ-spectrophotometry the sum of positively charged monomeric aqua- and hydroxy-Al species plus sulphato- and most of the labile organic Al species are determined. The sensitivities of these selected techniques were adequate for speciation of Al in the samples analyzed. On the basis of the specific selectivity of a particular technique various groups of Al species may be determined. Thus, the comparison of analytical data from complementary procedures provides more comprehensive information on Al species present in soil extracts and percolating waters.     

Heterogeneous catalyst: Amberlyst-15 catalyzes the synthesis of 14-substituted-14H-dibenzo[a,j]xanthenes under solvent-free conditions

A one-pot condensation of β-naphthol with aldehydes in the presence of Amberlyst-15 to give 14-substituted-14H-dibenzo[a,j]xanthenes under solvent-free condition is described.     

On the accuracy of molecular properties by coupled-cluster methods for some difficult examples: Oxygen atom,iron atom,and cyano radical

Coupled-cluster (CC ) methods at the level of CCSD , CCSD +T (CCSD ), CCSD (T ), CCSDT -1, and CCSDT -3 are applied to calculations of the dipole moment and polarizability of the CN molecule, ionization potentials and electron affinities of the oxygen and iron atoms and CN molecule, and the energy splitting of the ⁵D and ⁵F states of the iron atom. Both UHF and ROHF references are applied. Extended basis sets are used in some comparison of CC data to experiment. All calculated atomic and molecular properties are known as challenging problems, suitable for a careful analysis of the performance of sophisticated versions of the CC approach. Attention is paid to energy terms distinguishing CCSD (T ) from CCSD +T (CCSD ). We exploit results from various iterative and noniterative high-level CC methods in the assessment of error bars in calculations of atomic and molecular properties. © 1994 John Wiley & Sons, Inc.     

Fourth-order diagrammatic MB-RSPT calculations of the interaction energy between two helium atoms

The efficiency of the MB-RSPT in the calculations of the correlation contributions to the interaction energies was investigated, using He₂ as a model Van der Waals system. The attention has been focused on the convergency of the perturbation expansion in the calculations of the interaction energy and on the analysis of the fourth-order terms of MB-RSPT. The rôle of the renormalization term in the correct long-range behaviour of the interaction potential has been emphasized.     

Propagating transverse electric and transverse magnetic modes in liquid crystal-clad planar waveguides

ABSTRACT

In a planar dielectric waveguide, weak confinement of a propagating mode in a high index core leads to a measurable evanescent interaction with the cladding. In this work, we study the effect of a reorientable anisotropic cladding on the behaviour of Transverse Electric (TE) and Transverse Magnetic (TM) mode polarisations using a liquid crystal (LC)-clad waveguide architecture. The polarised evanescent field of a guided mode interacts with a voltage-tunable birefringent LC cladding to deflect an out-coupled beam. Experimental measurements are coupled with a theoretical framework and show good consistency with simulation results. We isolate the effect of mode confinement by changing the thickness of the high index core. Interactions between the LC index ellipsoid and the mode polarisation are probed by changing the initial alignment of the LC. Finally, we examine the difference in deflection between TE and TM modes, which incorporates both a change in mode confinement and a difference in LC index components.