Averaging Oscillations with Small Fractional Damping and Delayed Terms

We demonstrate the method of averaging for conservative oscillators which may be strongly nonlinear, under small perturbations including delayed and/or fractional derivative terms. The unperturbed systems studied here include a harmonic oscillator, a strongly nonlinear oscillator with a cubic nonlinearity, as well as one with a nonanalytic nonlinearity. For the latter two cases, we use an approximate realization of the asymptotic method of averaging, based on harmonic balance. The averaged dynamics closely match the full numerical solutions in all cases, verifying the validity of the averaging procedure as well as the harmonic balance approximations therein. Moreover, interesting dynamics is uncovered in the strongly nonlinear case with small delayed terms, where arbitrarily many stable and unstable limit cycles can coexist, and infinitely many simultaneous saddle-node bifurcations can occur.     

Selection in Monotone Matrices and Computingkth Nearest Neighbors

Anm×nmatrix =(a_{i, j}), 1≤i≤mand 1≤j≤n, is called atotally monotonematrix if for alli₁, i₂, j₁, j₂, satisfying 1≤i₁<i₂≤m, 1≤j₁<j₂≤n.[formula]We present an[formula]time algorithm to select thekth smallest item from anm×ntotally monotone matrix for anyk≤mn. This is the first subquadratic algorithm for selecting an item from a totally monotone matrix. Our method also yields an algorithm of the same time complexity for ageneralized row-selection problemin monotone matrices. Given a setS={p₁,…, p_n} ofnpoints in convex position and a vectork={k₁,…, k_n}, we also present anO(n^4/3log^c n) algorithm to compute thek_ith nearest neighbor ofp_ifor everyi≤n; herecis an appropriate constant. This algorithm is considerably faster than the one based on a row-selection algorithm for monotone matrices. If the points ofSare arbitrary, then thek_ith nearest neighbor ofp_i, for alli≤n, can be computed in timeO(n^7/5 log^c n), which also improves upon the previously best-known result.     

Microstructure and topography of vapor deposited,sputtered and annealed (111) palladium films

The microstructural effects of argon ion bombardment and thermal annealing on vapor deposited (111) Pd films on mica substrates have been studied. Sputtering resulted in surface roughening as well as in the formation of an amorphous phase and double positioned twins. In the higher fluence zones, relatively large blisters were formed. Moderate annealing of the sputtered film did not restore the original smoothness of the surface. The hillocks became larger while their density decreased.     

Rotational spectra and structure of the Ar2-H2S complex: pulsed nozzle Fourier transform microwave spectroscopic and ab initio studies

This paper reports the rotational spectrum and structure of the Ar2-H2S complex and its HDS and D2S isotopomers. The ground state structure has heavy-atom C2v symmetry with the two Ar atoms indistinguishable and H2S freely rotating as evinced by the fact that asymmetric top energy levels with Kp=odd levels are missing. The rotational constants for the parent isotopomer are: A=1733.115(1) MHz, B=1617.6160(5) MHz and C=830.2951(2) MHz. Unlike the Ar-H2S complex, the Ar2-H2S does not show an anomalous isotopic shift in rotational constants on deuterium substitution. However, the intermolecular potential is still quite floppy, leading to very different centrifugal distortion constants for the three isotopomers. The Ar-Ar and Ar-c.m.(H2S) distances are determined to be 3.820 A and 4.105 A, respectively. The A rotational constants for Ar2-H2S/HDS/D2S isotopomers are very close to each other and to the B constant of free Ar2, indicating that H2S does not contribute to the moment of inertia about the a-axis. Ab initio calculations at MP2 level with aug-cc-pVQZ basis set lead to an equilibrium C2v minimum structure with the Ar-Ar line perpendicular to the H-H line and the S away from Ar2. The centrifugal distortion constants, calculated using the ab initio force field, are in reasonable agreement with the experimental values. However, they do not show the variation observed for different isotopmers. The binding energy of Ar2-H2S has been determined to be 507 cm-1(6.0 kJ mol-1) by CBS extrapolation after correcting for basis set superposition error. Potential energy scans point out that the barrier for internal rotation of H2S about its b axis is only 10 cm-1 and it is below the zero point energy (13.5 cm-1) in this torsional degree of freedom. Internal rotation of H2S about its a- and c-axes also have small barriers of about 50 cm-1 only, suggesting that H2S is extremely floppy within the complex.     

Electronic structure of mercury oligomers and exciplexes: models for long-range/multicenter bonding in phosphorescent transition-metal compounds

Spectroscopic and bonding properties of Hg(n) oligomers and *Hg(n) exciplexes are determined by rigorous theoretical treatments. Reliable values that agree well with experimental data have been computed for the luminescence energies and other molecular spectroscopic parameters by making a careful selection of theoretical methods and basis sets. The calculations clarified the assignments for several phosphorescence bands in the mercury vapor based on calculated energies and other parameters that quantify the large excited-state distortion in the emitting states. Both the weak ground-state mercurophilic bonding and the stronger covalent bonding in the triplet and quintet excited states studied are found to be cooperative, which is important for fundamental and applied research for luminescent and magnetic materials that have spectral behavior similar to that of Hg(n) systems.     

First synthesis and structural report on selenophen-2-yl containing pnictogens: Biological activities of tris(selenophen-2-yl)stibine

A new tertiary stibine and bismuthine containing C-heterocyclic selenophene ring have been synthesized. Tris(2-selenophenyl)stibine (1) and tris(2-selenophenyl) bismuthine (2) and characterized by IR, MS, ¹H, ¹³C, COSY, HETCOR NMR spectroscopy. Crystal structures of stibine and bismuthine have been determined. In an attempted synthesis of tris(2-selenophenyl) phosphine, an oxidative product tris(2-selenophenyl) phosphine oxide (3) was isolated under the experimental conditions used, whose X-ray crystal structure was also determined. To best of our knowledge C-heterocyclic selenophene-2-yl pnictogens are first of their kind, as not many examples are known even with other p-block metal/metalloids.The biological activity of compound (1) was determined. The compound (1) shows a significant selectivity (>85%) for carcinogenic cell K and U growth inhibition. The toxicity of tris(selenophen-2-yl) stibine (1) on larvae of Artemia Salina was studied and the LC₅₀ value was 589.6 μM.     

Zinc(II)-selective sensors based on dibenzo-24-crown-8 in PVC matrix

Membranes of dibenzo-24-crown-8 (I) as an ion active material in poly(vinylchloride) (PVC) based matrix have been tried for zinc(II)-selective sensors. The effect of anion excluder, sodium tetraphenylborate (NaTPB) and plasticizers, tris(2-ethylhexyl)phosphate (TEP), tributylphosphate (TBP), dibutylphthalate (DBP), dibutyl(butyl)phosphonate (DBBP), 1-chloronaphthalene (CN) and dioctylphthalate (DOP) on the performance of the membrane electrodes has also been studied. It was observed that the membrane having the composition (I): PVC:NaTPB:DOP in the ratio 10:200:2:100 gave the best results with a wide working concentration range of 9.2 × 10⁻⁵ to 1.0 × 10⁻¹ M, Nernstian slope of 29.0 ± 0. 5 mV/decade of activity, fast response time of 12 s and good selectivity over a number of mono-, bi-, and trivalent cations. The sensor works well in a pH range 4.8-6.2 and can be employed for the estimation of zinc ions in partially non-aqueous medium having up to 10% (v/v) methanol, ethanol or acetone content. The practical utility of the sensor has been demonstrated by using it successfully as an indicator electrode in the potentiometric titration of Zn²⁺ with EDTA and also for the determination of Zn²⁺ in a real sample analysis of wastewater.     

An improved synthesis of Fmoc-N-methyl serine and threonine

An improved method for the synthesis of Fmoc-N-methyl serine and threonine has been developed, which involves formation and subsequent reduction of the corresponding oxazolidinone with a Lewis acid under mild conditions, with improved yields and shorter reaction times.     

New oxo-bridged dinuclear peroxotungsten(VI) complexes: Synthesis, stability and activity in bromoperoxidation

Two new dinuclear oxo-bridged peroxo complexes of tungsten with coordinated dipeptides of the type, Na₂[W₂O₃(O₂)₄(glycyl-glycine)₂] · 3H₂O (1) and Na₂[W₂O₃(O₂)₄(glycyl-leucine)₂] · 3H₂O (2) have been synthesized from the reaction of H₂WO₄, 30% H₂O₂ and the respective dipeptide at pH ca. 2.5. Synthesis of the compounds, in addition to pH, is sensitive to reaction temperature and concentrations of the components. The compounds were characterized by elemental analysis, spectral and physico-chemical methods including thermal analysis. In the dimeric complexes the two W(VI) centres with edge bound peroxo groups are bridged by an oxo group. The dipeptides occurring as zwitterions bind the metal centers through O (carboxylate) atoms leading to hepta co-ordination around each W(VI). Thermal stability of the compounds as well as their stability in solution were determined. The compounds are highly stable toward decomposition in solutions of acidic as well as physiological pH. These compounds, besides another similar dimeric compound Na₂[W₂O₃(O₂)₄(cystine)] · 4H₂O (3) efficiently oxidized bromide to a bromination competent intermediate in phosphate buffer at physiological pH, a reaction in which only two of the peroxide groups of the complex species were found to be active. The complexes could also mediate bromination of organic substrate in aqueous-organic media.     

Ring expansive routes to quinolizidine alkaloids: formal synthesis of (-)-lasubine II

The application of two nitrogen ring expansion reactions to lasubine alkaloid synthesis is reported. The approach involves a conjugate reduction/alkylation sequence carried out on triisopropylsilyl-protected (S)-4-(-)-hydroxycyclopentenone, the formation of the quinolizidone ring system through nitrogen ring expansion, and the addition of an arylmetallic species to the resulting lactam. This work resulted in the preparation of 2-epi-lasubine II and a formal synthesis of lasubine II. [reaction: see text]