Graphene Saturable Absorber Mirror for Mode-Locked Orange Pulse Laser

Journal of Russian Laser Research - We demonstrate a passively-mode-locked Pr3+: LuLiF4 laser operated at the 604 nm orange wave-length, using monolayer graphene as a saturable absorber. The...     

Positive solutions of singular boundary value problem of negative exponent Emden—Fowler equation

This paper investigates the existence of positive solutions of a singular boundary value problem with negative exponent similar to standard Emden-Fowler equation. A necessary and sufficient condition for the existence of C[0, 1] positive solutions as well as C¹[0, 1] positive solutions is given by means of the method of lower and upper solutions with the Schauder fixed point theorem.     

Computations of critical groups and applications to asymptotically linear wave equation and beam equation

In this paper, by using the Morse index theory for strongly indefinite functionals developed in [Nonlinear Anal. TMA, in press], we compute precisely the critical groups at the origin and at infinity, respectively. The abstract theorems are used to study the existence (multiplicity) of nontrivial periodical solutions for asymptotically wave equation and beam equation with resonance both at infinity and at zero.     

Nondegeneracy and uniqueness of positive solutions for Robin problem of second order ordinary differential equations and its applications

This article studies positive solutions of Robin problem for semi-linear second order ordinary differential equations. Nondegeneracy and uniqueness results are proven for homogeneous differential equations. Necessary and sufficient conditions for the existence of one or two positive solutions for inhomogeneous differential equations or differential equations with concave-convex nonlinearities are obtained by making use of the nondegeneracy and uniqueness results for positive solutions of homogeneous differential equations.     

Fluorimetric determination of ascorbic acid with o-phenylenediamine

A simple and sensitive fluorimetric method for the determination of ascorbic acid (AA) is described. The method is based on the condensation reaction between AA and o-phenylenediamine (OPDA) in the absence of the oxidant. The fluorescence intensity is measured at excitation and emission wavelengths of 360 and 430 nm, respectively. Under optimum condition, a linear relationship is obtained between the fluorescence intensity and the concentration of AA in the range of 0.05-40 μg ml⁻¹. The detection limit is 0.006 μg ml⁻¹, which is obviously lower than that of other fluorimetric methods reported.     

Upper bound of Kähler angles on the β-symplectic critical surfaces

Let (M,g) be a Kähler surface and \mathrm{\Sigma } be a \beta-symplectic critical surface in M. If L_q\left(\mathrm{\Sigma }\right) is bounded for some q>3, then we give a uniform upper bound for the Kähler angle on \mathrm{\Sigma }. This bound only depends on M,q,\beta and the L_q functional of \mathrm{\Sigma }. For q>4, this estimate is known and we extend the scope of q.     

Pentacoordinate spirosilicate anion, bis(2,2′-biphenyldiyl)methylsilicate, synthesized by the lithium cleavage of dimethoxyethane

The reaction of spirobisilafluorene (1) with lithium in dimethoxyethane produces lithium 1-methyl-spirobisilafluorenide (2), a stable pentacoordinate silicon compound with five carbon ligands, and lithium 2-methoxyethoxide, which was identified by trapping with Ph₃SiCl to give Ph₃Si-OCH2CH2OCH3 (4). The X-ray crystal structure of 2 shows that the geometry at silicon is an idealized trigonal bipyramid, slightly distorted toward a square pyramid. Methanolysis of 2 cleaves a Si-aryl bond producing a methyl biphenylsilafluorene, 3. Crystal structures are reported for 3 and 4.     

Unusual frequency dispersion effects of the nonlinear optical response in highly conjugated (polypyridyl)metal-(porphinato)zinc(II) chromophores

The syntheses and electrooptic properties of a new family of nonlinear optical chromophores are reported. These species feature an ethyne-elaborated, highly polarizable porphyrinic component and metal polypyridyl complexes that serve as integral donor and acceptor elements. Examples of this structural motif include ruthenium(II) [5-(4'-ethynyl-(2,2';6',2' '-terpyridinyl))-10,20-bis(2',6'-bis(3,3-dimethyl-1-butyloxy)phenyl)porphinato]zinc(II)-(2,2';6',2' '-terpyridine)(2+) bis-hexafluorophosphate (Ru-PZn); osmium(II) [5-(4'-ethynyl-(2,2';6',2'-terpyridinyl))-10,20-bis(2',6'-bis(3,3-dimethyl-1-butyloxy)phenyl)porphinato]zinc(II)-(2,2';6',2'-terpyridine)(2+) bis-hexafluorophosphate (Os-PZn); ruthenium(II) [5-(4'-ethynyl-(2,2';6',2'-terpyridinyl))-15-(4'-nitrophenyl)ethynyl-10,20-bis(2',6'-bis(3,3-dimethyl-1-butyloxy)phen-yl)porphinato]zinc(II)-(2,2';6',2' '-terpyridine)(2+) bis-hexafluorophosphate (Ru-PZn-A); osmium(II) [5-(4'-ethynyl-(2,2';6',2' '-terpyridinyl))-15-(4'-nitrophenyl)ethynyl-10,20-bis(2',6'-bis(3,3-dimethyl-1-butyloxy)phenyl)porphinato]zinc(II)-(2,2';6',2' '-terpyridine)(2+) bis-hexafluorophosphate (Os-PZn-A); and ruthenium(II) [5-(4'-ethynyl-(2,2';6',2' '-terpyridinyl))osmium(II)-15-(4'-ethynyl-(2,2';6',2'-terpyridinyl))-10,20-bis (2',6'-bis(3,3-dimethyl-1-butyloxy)phenyl)porphinato]zinc(II)-bis(2,2';6',2'-terpyridine)(4+) tetrakis-hexafluorophosphate (Ru-PZn-Os). The frequency dependence of the dynamic hyperpolarizability of these compounds was determined from hyperRayleigh light scattering (HRS) measurements carried out at fundamental incident irradiation wavelengths (lambda(inc)) of 800, 1064, and 1300 nm. These data show that (i) coupled oscillator photophysics and metal-mediated cross-coupling can be exploited to elaborate high beta(0) supermolecules that exhibit significant excited-state electronic communication between their respective pigment building blocks; (ii) high-stability metal polypyridyl compounds constitute an attractive alternative to electron releasing dialkyl- and diarylamino groups, the most commonly used donor moieties in a wide range of established nonlinear optical dyes; (iii) this design strategy enables ready elaboration of chromophores having extraordinarily large dynamic hyperpolarizabilities (beta(lambda) values) at telecommunication relevant wavelengths; and (iv) porphyrin B- and Q-state-derived static hyperpolarizabilities (beta(0) values) can be designed to have the same or opposite sign in these species, thus providing a new means to regulate the magnitude of lambda(inc)-specific dynamic hyperpolarizabilities.     

Copper-Catalyzed Amination of Aryl Halides with Aqueous Ammonia under Mild Conditions

A Cu(I) generated in situ from CuSO₄·5H₂O/sodium ascorbate catalyzed cross‐coupling reaction of aryl halides with aqueous ammonia for the synthesis of primary aromatic amines has been developed. Key to the success included the application of aqueous ammonia under a homogeneous condition.