Stereo- and regioselective synthesis of β-amino-β-tetrazolylvinylphosphonates

Addition of 5-substituted tetrazoles to dimethyl [(N,N-diisopropylamino)ethynyl]phosphonate proceeds regio- and stereoselectively to yield (Z)-[2-diisopropylamino-2-(tetrazolyl)vinyl]phosphonic acid dimethyl esters. The Z-configuration of the products was confirmed by ¹Н NMR spectroscopy and single-crystal X-ray diffraction. The reactions occur via nucleophilic attack of tetrazole involving predominantly the N-1 atom of the tetrazole ring.     

Inverse compton scattering on laser beam and monochromatic isotropic radiation

Most of the known literature on inverse compton scattering (ICS) is based on earliest theoretical attempts and later approximations led by F.C. Jones and J.B. Blumenthal. We found an independent and more general analytical procedure which provide both relativistic and ultrarelativistic limits for ICS. These new analytical expressions can be derived in a straightforward way and they contain the previously reminded Jones’ results. Our detailed solutions may be probed by already existing as well future ICS experiments.     

Structure of commutative cancellative integral residuated lattices on (0, 1]

ΠMTL-algebras were introduced as an algebraic counterpart of the cancellative extension of monoidal t-norm based logic. It was shown that they form a variety generated by ΠMTL-chains on the real interval [0, 1]. In this paper the structure of these generators is investigated. The results illuminate the structure of cancellative integral commutative residuated chains, because every such algebra belongs to the quasivariety generated by the zero-free subreducts on (0, 1] of all ΠMTL-chains on [0, 1]. The work of the author was partly supported by the grant No. A100300503 of the Grant Agency of the Academy of Sciences of the Czech Republic and partly by the Institutional Research Plan AV0Z10300504.     

Observation of 99% pump depletion in single-pass second-harmonic generation in a periodically poled lithium niobate waveguide

We report 99% pump depletion in single-pass second-harmonic generation. Quasi-cw pulses at 1550 nm were frequency doubled in an annealed proton-exchanged waveguide formed in periodically poled lithium niobate. Measurements of pump depletion and second-harmonic generation agree with results from numerical integration of the coupled-mode equations that describe the process.     

Highly efficient second-harmonic generation in buried waveguides formed by annealed and reverse proton exchange in periodically poled lithium niobate

Efficient three-wave mixing devices have numerous applications, including wavelength conversion, dispersion compensation, and all-optical switching. Second-harmonic generation (SHG) is a useful diagnostic for near-degenerate operation of these devices. With buried waveguides formed in periodically poled lithium niobate by annealed and reverse proton exchange, we demonstrate what is believed to be the highest normalized conversion efficiency (150%/W cm(2)) for SHG in the 1550-nm communications band reported to date.     

Low-threshold spatial solitons in reverse-proton-exchanged periodically poled lithium niobate waveguides

Combining reverse proton exchange and uniform periodic poling in LiNbO3 planar waveguides, we demonstrate low-energy spatial optical solitons by second-harmonic generation at room temperature, with a threshold as low as 23 pJ/microm at 1.5 microm.     

Behaviour of weak solutions of compressible Navier-Stokes equations for isothermal fluids with a nonlinear stress tensor

The aim of this paper is to study the behaviour of a weak solution to Navier-Stokes equations for isothermal fluids with a nonlinear stress tensor for time going to infinity. In an analogous way as in [18], we construct a suitable function which approximates the density for time going to infinity. Using properties of this function, we can prove the strong convergence of the density to its limit state. The behaviour of the velocity field and kinetic energy is mentioned as well.     

Product Ł ukasiewicz Logic

u logic plays a fundamental role among many-valued logics. However, the expressive power of this logic is restricted to piecewise linear functions. In this paper we enrich the language of u logic by adding a new connective which expresses multiplication. The resulting logic, P, is defined, developed, and put into the context of other well-known many-valued logics. We also deal with several extensions of this propositional logic. A predicate version of P logic is introduced and developed too.The work of the first author was supported by the Grant Agency of the Czech Republic under project GACR 201/02/1540, by the Grant Agency of the Czech Technical University in Prague under project CTU 0208613, and by Net CEEPUS SK-042.The work of the second author was supported by grant IAA1030004 of the Grant Agency of the Academy of Sciences of the Czech Republic.