A new multi-linear universal hash family

A new universal hash family is described which generalises a previously known multi-linear hash family. Messages are sequences over a finite field ${\mathbb{F}_q}$ while keys are sequences over an extension field ${\mathbb{F}_{q^n}}$ . A linear map ${\psi}$ from ${\mathbb{F}_{q^n}}$ to itself is used to compute the output digest. Of special interest is the case q = 2. For this case, we show that there is an efficient way to implement ${\psi}$ using a tower field representation of ${\mathbb{F}_{q^n}}$ . From a practical point of view, the focus of our constructions is small hardware and other resource constrained applications. For such platforms, our constructions compare favourably to previous work.     

When Min(A)−1 is Hausdorff

For a commutative ring with identity, say A, its collection of minimal prime ideals is denoted by Min(A). The hull-kernel topology on Min(A) is a well-studied structure. For example, it is known that the hull-kernel topology on Min(A) has a base of clopen subsets, and classifications of when Min(A) is compact abound. Recently, a program of studying the inverse topology on Min(A) has begun. This article adds to the growing literature. In particular, we characterize when Min(A)^?1 is Hausdorff. In the final section, we consider rings of continuous functions and supply examples.     

Patterns in Ge cluster growth on clean and oxidized Si(111)-(7 × 7) surfaces

Ge atoms have been deposited on domain-patterned clean Si(111)-(7 × 7) and oxidized Si(111)-(7 × 7) surfaces. Clustering of Ge from the deposited Ge adatoms on these two kinds of surfaces shows contrasting patterns. On the clean Si surface, clustering predominantly occurs on domain boundaries, which include step edges on two sides. This leaves small domains denuded. Ge diffusion length has been estimated from the size of these denuded domains. For large domains, additional clustering is observed within the domains. For the oxidized Si surface, the pattern formation is in sharp contrast with that for the clean Si surface. In this case the domain boundaries remain relatively empty and there is strong clustering within the domains leading to the formation of dense Ge nanoislands within the domains. This contrasting pattern formation has been explained via a reaction diffusion model.     

Synthesis,Characterization and Biological Activity Studies on 6-<Emphasis Type="Italic">p</Emphasis>-Dimethylaminophenyl-5,6-dihydrobenzoimidazo[1,2-<Emphasis Type="Italic">c</Emphasis>]quinazoline: Crystal Structure of the Title Compound and Comparative Study with Related Derivatives

Abstract  

Reaction of o-aminophenylbenzimidazole with p-dimethylaminobenzaldehyde yielded 6-p-dimethylaminophenyl-5,6-dihydrobenzoimidazo[1,2-c]quinazoline, which was characterized by elemental analysis, IR, UV–Vis, ¹H NMR, ¹³C NMR, mass spectral studies and X-ray crystal structure analysis. Studies on the antimicrobial activity of the compound revealed that it is active against fungus Yeast but not Bacillus subtilis. The compound crystallized in the space group P2₁/n with the unit cell parameters a = 10.652(2) ?, b = 11.002(2) ?, c = 15.753(2) ?, β = 109.29(2)° and the structure was refined to an R-factor of 0.0479. The hydropyrimidine ring in the quinazoline moiety is in skew-boat conformation. The dimethylamino group attached to phenyl ring is in conjugation with it. The structure was stabilized by intermolecular C–H–N interactions. A few of the related quinazolines (6-p-hydroxyphenyl-5,6-dihydrobenzoimidazo[1,2-c]quinazoline; 6-phenyl-5,6-dihydrobenzoimidazo[1,2-c]quinazoline; 6-pyridyl-5,6-dihydrobenzoimidazo[1,2-c]quinazoline; 6-furyl-5,6-dihydrobenzoimidazo[1,2-c]quinazoline) were also examined for their biological activity, in addition to their characterization by IR, UV–Vis, ¹H and ¹³C NMR spectral studies along with structural comparison.     

Development and Validation of a Spectrofluorimetric Method for the Determination of Erlotinib in Spiked Human Plasma

A rapid and sensitive spectrofluorimetric method was developed and validated for the determination of erlotinib (ETB), a potent anticancer drug, in spiked human plasma without any derivatization. The described method was validated and the analytical parameters of linearity, accuracy, precision (intra- and inter-day), limit of detection (LOD), and limit of quantification (LOQ) were evaluated. The relation between the fluorescence intensity and concentration was found to be linear (r² 0.9998) over the range 125 to 1000?ng/mL with the detection limit of 15?ng/mL. A simple liquid-liquid extraction method was followed in order to extract the drug from spiked plasma. The mean absolute recoveries of ETB were 85.59?% (±0.57), 86.91?% (±1.77) and 89.31?% (±3.01) at spiked plasma ETB concentration of 5000, 3750 and 2500?ng/mL, respectively. The spectrofluorimetric method presented here is a rapid, simple, specific, and reproducible method and can be used to characterize the plasma pharmacokinetics of ETB.     

Transverse diffusion induced phase transition in asymmetric exclusion process on a surface

We extend one-dimensional asymmetric simple exclusion process (ASEP) to a surface and show that the effect of transverse diffusion is to induce a continuous phase transition from a constant density phase to a maximal current phase as the forward transition probability p is tuned. The signature of the non-equilibrium transition is evident in the finite size effects near the transition. The results are compared with similar couplings operative only at the boundary. It is argued that the nature of the phases can be interpreted in terms of the modifications of boundary layers.     

Universality in crossover function for convection in fluids with a free surface

We show that in the onset of convection in a thin fluid layer with a free surface, the passage from surface tension driven to buoyancy driven convection with changing thickness of the fluid layer follows a universal curve and can be calculated very accurately using a variational method. We have shown that the balance between surface tension traction to buoyancy force determines the crossover length scale of the fluid which is independent of viscosity or thermal diffusivity. We suggest a scenario near critical point of fluids in which this crossover can be observed.     

Momentum conservation leading to the generalized vectorial laws of reflection and refraction

This paper considers the newly discovered laws on reflection and refraction reported in 2005 by the author. A brief review of the said discovery has been made. To give the discovery a concrete foundation and to show the efficiency of the photon theory, theoretical proof of each of those discovered laws on reflection and refraction has been offered making use of the photon theory and on further application of the principle of conservation of momentum.     

Enhancement and quenching of single-molecule fluorescence

We present an experimental and theoretical study of the fluorescence rate of a single molecule as a function of its distance to a laser-irradiated gold nanoparticle. The local field enhancement leads to an increased excitation rate whereas nonradiative energy transfer to the particle leads to a decrease of the quantum yield (quenching). Because of these competing effects, previous experiments showed either fluorescence enhancement or fluorescence quenching. By varying the distance between molecule and particle we show the first experimental measurement demonstrating the continuous transition from fluorescence enhancement to fluorescence quenching. This transition cannot be explained by treating the particle as a polarizable sphere in the dipole approximation.     

Analysis of pseudo jahn–teller distortion based on natural bond orbital theory: Case study for silicene

Ground state (GS) instability of nondegenerate molecules in high symmetric structures is understood through Pseudo Jahn–Teller mixing of the electronic states through the vibronic coupling. The general approach involves setting up of a Pseudo Jahn–Teller (PJT) problem wherein one or more symmetry allowed excited states couple to the GS to create vibrational instability along a normal mode. This faces two major complications namely (1) estimating the adiabatic potential energy surfaces for the excited states which are often difficult to describe in case the excited states have charge-transfer or multi-excitonic (ME) character and (2) finding out how many such excited states (all satisfying the symmetry requirements for vibronic coupling) of increasing energies need to be coupled with the GS for a particular PJT problem. An analogous alternative approach presented here for the well-known case of symmetry breaking of planar (D_6h) hexasilabenzene (Si₆H₆) to the buckled (D_3d) structure involves identifying the second-order donor–acceptor, hyperconjugative interactions (E²_{i → j}) that stabilize the distorted structure. Following the recent work of Nori-Shargh and Weinhold, one observes that the orbitals involved in the vibronic coupling between the S₀/S_n states and those for the donor (filled)–acceptor (empty) interactions are identical. In fact, deletion of any particular pair of E²_{i → j} interaction creates vibrational instability in the buckled structure and as a corollary, deleting it for the planar structure removes its instability. The one-to-one correlation between the natural bond orbital theory and PJT theory assists in an intuitive identification of the relevant (few) excited states from a manifold of computed ones that cause symmetry breaking by vibronic coupling. © 2019 Wiley Periodicals, Inc.