Asymptotic behavior of solutions of forced nonlinear neutral difference equations

In this paper, we consider the asymptotic behavior of solutions of the forced nonlinear neutral difference equation $$\Delta \left[ {x(n) - \sum\limits_{i - 1}^m {p_i (n)x(n - k_i )} } \right] + \sum\limits_{j = 1}^s {q_j (n)f(x(n - l_j )) = r(n)} $$ with sign changing coefficients. Some sufficient conditions for every solution of (*) to tend to zero are established. The results extend and improve some known theorems in literature.     

A counterexample to Sorenson’s conjecture: The finitely generated case

It is shown that there exists a finitely generated, left amenable semigroup which is right cancellative but not left cancellative. This resolves negatively a question raised by M. Klawe.     

Asymptotic behavior of certain delay differential equations with forcing term

We study the asymptotic behavior of solutions of the following forced delay differential equation:

Some sufficient conditions that guarantee every solution of the equation to converge to zero are obtained. The results obtained are applied to some well-known delay differential ecological equations with forcing term.     

Alignment-free optical modules using solder-bump-bonding technique for free-space optical interconnections

We propose alignment-free optical modules using a solder-bump-bonding technique for constructing free-space optical interconnection systems without a special alignment procedure. Bonding pads for mounting an optoelectronic device chip are fabricated by exposing a photosensitive resin film to light traveling through the optical system of the module so that the image positions of the bonding pads on both image planes of the optical interconnection system are aligned with each other. A device chip is mounted by solder-bump bonding and is set at a proper position by the surface tension of molten solder. The effectiveness of the technique is verified by constructing alignment-free optical modules.     

Morita Invariant Properties of Twisted Poisson Manifolds

In this letter, we study some invariants of integrable twisted Poisson manifolds under Morita equivalence. We show that two twisted symplectic manifolds are Morita equivalent if and only if their fundamental groups are isomorphic. Moreover, the first cohomology group of twisted Poisson manifolds is invariant under Morita equivalence. Finally, we prove that if two twisted Poisson manifolds are Morita equivalent, then their representation categories are equivalent.      

The fluorescent reaction product in the determination of aromatic aldehydes with 2,2''-dithiobis(1-amino-naphthalene)

The fluorescent product formed from benzaldehyde or p-hydroxybenzaldehyde with the reagent in the presence of tri-n-butylphosphine, phosphite and sulphite has been characterized by elemental and structural analysis as the corresponding 2-arylnaphtho [1,2-d ] thiazole.     

Total synthesis of nagilactone F,biologically active nor-diterpenoid dilactone isolated from podocarpus nagi

Nagilactone F was synthesized from (+)-podocarpic acid of the established structure. This work constitutes the first total synthesis of the biologically active norditerpenoid dilactones in $\text{Podocarpus}$ plants.     

A short and stereoselective synthesis of the (±) Prelog-Djerassi lactonic acid

Reaction of meso-4-carbomethoxy-2-methylpentanal ($\text{1}$) with crotyltri-n-butyltin at ?78°C in the presence of 1 eq BF₃·OEt₂, followed by the lactonization with BF₃·OEt₂, gave 6-(1-methylallyl)-3,4,5,6-tetrahydro-3,5-dimethyl-2-pyranone ($\text{2a}$) with the correct stereochemistry (erythro, anti-Cram) in 92% yield, which was converted to the title compound ($\text{3}$) in 85% yield upon the ozonolytic cleavage of the double bond.     

Effects of additional Higgses in supersymmetric grand unified theories

We consider modifications of the minimal supersymmetric SU(5) grand unified model. With the additional Higgses 10 +$\text{10}$, the theory may be modified so that the proton decays dominantly via the conventional mode p→e⁺π with the lifetime π_p=(0.04-710)×10³⁰yr, and sin²θ_W=0.222±0.003.     

Rational design of an L-histidine-derived minimal artificial acylase for the kinetic resolution of racemic alcohols

This communication describes the rational design of an l-histidine-derived minimal artificial acylase. Our new artificial acylase, tert-butyldiphenylsilyl ether of N-(2,4,6-triisopropylbenzenesulfonyl)-pi(Me)-l-histidinol, is a simple and small molecule (molecular weight = 660) that contains only one chiral carbon center that originates from natural l-histidine. The kinetic acylation of racemic secondary alcohols induced by this compound showed an S (kfast/kslow) value of up to 93. A reusable polystyrene-bound artificial acylase was also developed to examine its practical usability.