Weak beam control of multiple quadratic soliton generation

Theoretical predictions and experimental observations show that a weak harmonic seed beam can control the process of generating multiple quadratic solitons in periodically poled KTiOPO4 by inputting only a fundamental beam. This all-optical switching does not depend on the relative phase of the input beams, an unusual property for such coherent solitons.     

Impact Oscillator with Hertz's Model of Contact

Dynamic properties of simple mechanical 1 DOF system containing soft stop is described and analyzed. The proposed general dynamical impact model respects the nonlinearity of the restoring contact force between solid bodies as function of deformation and velocity. It describes the real behavior of impacting system more exact than the piecewise linear model or the Kelvin–Voigt model and even model based on application of constant coefficient of restitution. Free and forced vibrations of system with Hertz's contact are investigated and domains of various types of impact motion, response curves and phase-plane trajectories are presented.     

Stimulated Raman scattering in natural crystals of fluorapatite,Ca5(PO4)3F

Hexagonal Ca₅(PO₄)₃F, known as natural crystal fluorapatite and oldest host‐crystal for Ln³⁺‐lasant ions, is presented as a Raman‐active material. High‐order Raman‐induced χ⁽³⁾‐nonlinear processes are discovered in natural crystals of fluorapatite under picosecond pumping at 1.064 μm and 0.532 μm wavelength. A multitude of Stokes and anti‐Stokes components is generated in the ultraviolet, visible and near‐infrared spectral region by stimulated Raman scattering (SRS) and Raman four‐wave mixing (FWHM), resulting in a frequency comb with a width of 520 THz. The spectral lines are identified and attributed to the ν₁(A_g) vibration mode of the tetrahedral [PO₄] units which is related to a Raman shift of ω_SRS ≈ 965 cm⁻¹. The first Stokes steady‐state Raman gain coefficient in the near‐infrared spectral range is estimated to be >0.38 cm·GW⁻¹. Finally, a short review of SRS‐promoting vibration modes and observed χ⁽³⁾‐ nonlinear interactions in all known SRS‐active natural crystals (minerals) is given.

     

New upper bounds for the chromatic number of a graph*

We show that for any graph G, the chromatic number χ(G) ≤ Δ₂(G) + 1, where Δ₂(G) is the largest degree that a vertex ν can have subject to the condition that ν is adjacent to a vertex whose degree is at least as big as its own. Moreover, we show that the upper bound is best possible in the the following sense: If Δ₂(G) ≥ 3, then to determine whether χ(G) ≤ Δ₂(G) is an NP‐complete problem. © 2001 John Wiley & Sons, Inc. J Graph Theory 36: 117–120, 2001     

Pyrimido[5,4-b]quinolines. II. Reactions at the heterocyclic ring-carbon and nitrogen atoms

10-Chloro-7,8-dimethylpyrimido[5,4-b]quinolin-2,4(1H,3H)dione (I) was unreactive toward ammonia but it reacted with 2 molecules of n-butylamine, presumably via Dimroth-type ring-opening and closure, to give the N₃-butyl, N₁₀-butylamino derivative (IV). In similar reactions of 10-chloro-2,4-dimethoxy-7,8-dimethylpyrimido[5,4-b]quinoline (II) only the 4-meth-oxyl was displaced by either ammonia or n-butylamine. Alkyllithium reagents also displaced the 4-methoxyl as well as added to the 3,4 double bond of II to yield the corresponding gem-dialkyl substituted (C₄) derivatives; the C₁₀ chlorine remained unreactive. 2,4-Dimethoxy-7,8-di-methylpyrimido[5,4-b]quinoline-10-one (III) could be alkylated only in the form of the thallium salt. Treatment of the benzyl derivative of III with methylmagnesium bromide led only to the displacement of the 4-methoxyl by a methyl group.     

Production and hydrolysis of 3,4-dimethyl-2,5-diphenyl-1,3-oxazolidine

Summary Condensation of ephedrine with benzaldehyde, an acid catalyzed reversible reaction, producing 3,4-dimethyl-2,5-diphenyl-1,3-oxazolidine, was studied. If the starting reaction mixture contained acetic acid, it quantitatively reacted with ephedrine and produced a salt functioning as an acid catalyst. On the contrary, ephedrine hydrochloride had no catalytic effect.     

Microfluidic robotic device coupled with electrochemical sensor field for handling of paramagnetic micro-particles as a tool for determination of plant mRNA

The expression of genes responsible for the biosynthesis of stress proteins corresponds to the exposition of an organism to abiotic and/or biotic stress. We utilize two types of paramagnetic particles for isolation of total mRNA from early somatic embryos of Norway Spruce (Picea abies /L./ Karst.) and maize plants (Zea mays L.) treated with cadmium(II) ions. The paramagnetic particles were evaluated for analysis of real samples, and poly-adenine was used as a model mRNA. Various approaches (from non-automatic to fully automatic) were tested in terms of handling the particles.

Hydrogen‐Bond‐Based Magnetic Exchange Between μ‐Diethylnicotinamide(aqua)bis(X‐salicylato)copper(II) Polymeric Chains

Polymeric salicylatocopper(II) complexes of unusual composition [C u(X‐ sal)₂( μ‐denia)(H₂O)]_n [denia = diethylnicotinamide, and X‐sal = 5‐methylsalicylate ( 1 ), 3‐methylsalicylate ( 2 ), 4‐methoxysalicylate ( 3 ), 3,5‐dichlorosalicylate ( 4 ) and 3,5‐dibromosalicylate ( 5 )] were synthesized and characterized. Magnetic measurements were performed in the temperature range 1.8–300 K. The structural unit of all complexes consists of a Cu^II atom, which is monodentately coordinated by the pair of X‐salicylate anions in trans positions. Water and the diethylnicotinamide ligand occupy the other two basal plane positions of the tetragonal pyramid. The axial positions are occupied by a diethylnicotinamide oxygen atom of neighboring structural units, thus forming a spiral polymeric structure parallel to b axis. Magnetic measurements showed that all complexes 1 – 5 exhibit a susceptibility maximum at about 6–8 K. The obtained data fit to Bleaney–Bowers equation gave singlet‐triplet energy gaps 2J = –8.60 cm^–1 for 1 , 2J = –6.57 cm^–1 for 2 , 2J = –8.57 cm^–1 for 3 , 2J = –6.82 cm^–1 for 4 , and 2J = –6.45 cm^–1 for 5 . The supramolecular structure based on hydrogen bonds [described by supramolecular synthons R₂²(10) and R₂²(12)] is the pathway for antiferromagnetic interactions of the magnetically coupled pairs of copper atoms of neighboring chains within the 2D supramolecular layers. The results of the magnetic measurements suggest involvement of the COO groups in the magnetic interaction pathway for all five complexes.     

Formation of porous polymer morphology by microsyneresis during divinylbenzene polymerization

This article describes the investigation of the importance of various reaction conditions on microsyneretic pore formation during polymerization of divinylbenzene (DVB) under so‐called “solvothermal” conditions. To induce microsyneretic pore formation, the most important parameter is an unusually high dilution of monomers with a “good” porogen solvating the polymer chains. High dilution and solvation of the growing poly(DVB) chains promote the prolongation of the polymer chains rather than their interconnection by crosslinking. Consequently, when the polymer gel density reaches the point where syneresis starts, the polymer network is geometrically too extensive to be broken up into precipitating entities and, instead, porogen droplets are formed within the continuous polymer gel. The pore geometry created by microsyneresis offers high surface area in wide mesopores and hence, high capacity for supporting functional groups or reactions with much better accessibility than narrow pores between polymer microspheres produced by macrosyneresis in conventional styrenic polymer supports. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 774–781