Secants of Lagrangian Grassmannians

We study the dimensions of secant varieties of Grassmannian of Lagrangian subspaces in a symplectic vector space. We calculate these dimensions for third and fourth secant varieties. Our result is obtained by providing a normal form for four general points on such a Grassmannian and by explicitly calculating the tangent spaces at these four points.     

Frustration signatures in the anisotropic model of a nine-spin <Emphasis Type="Italic">s</Emphasis> = 3/2 ring with bond defect

Effects of magnetic frustration in the model of nine-membered antiferromagnetic s = 3/2 molecular spin ring are investigated. We use a Heisenberg spin model with nearest-neighbor interactions, single-ion anisotropy and with tunable bond defect leading to continuously varying topology: from closed to open ring. In order to identify a frustrated phase we calculate the full energy spectrum of the model and a number of thermodynamic quantities at low temperature. The calculations are performed by means of numerically exact methods: quantum transfer matrix and exact diagonalization. It is shown that total and local magnetizations, nearest-neighbor spin correlations and spin fluctuations can serve as consistent frustration signatures. Magnetizations and spin-spin correlations are reduced in the frustrated phase whereas fluctuations and correlations of fluctuations increase. The ground state in a frustrated phase is a m = 1/2 doublet and in the non-frustrated phase a m = 3/2 doublet. In the system studied bipartiteness is not opposite to frustration as there are regions in the parameter space for which the system is neither bipartite nor frustrated.     

The Six-Nucleon Yakubovsky Equations for <Superscript>6</Superscript><Emphasis Type="Italic">He</Emphasis>

The six-nucleon problem for the bound state is formulated in the Yakubovsky scheme. Hints for a numerical implementation are provided.     

Pulse generation at 1.5-μm wavelength in new EAT14 glasses doped with Er<Superscript>3+</Superscript> and Yb<Superscript>3+</Superscript> ions

The paper describes investigation of pulse laser generation in newly developed EAT14 glasses with the use of MALO saturable absorber. Different initial transmission of the saturable absorbers and different transmission of the output coupler were investigated. The laser generation was carried out using 976-nm pump wavelength. Comparison of peak powers, slop efficiencies and thresholds was made with a view to choose the best set of glass and saturable absorber for “eye-safe” microchip laser range-finder. The generated wavelengths by each sample were measured.     

Solid phase synthesis of two muramyl pentapeptide derivatives

Solid phase peptide synthesis (SPPS) of two selected muramyl pentapeptide derivatives is described. The simplicity of removing the protecting groups via one-step deprotection and cleavage from the resin is the biggest advantage of SPPS. Using this method, two muramyl pentapeptide derivatives, D-MurN₃-L-Ala-D-iGlu-L-Lys-D-Ala-D-Ser (5) and D-MurN₃-L-Ala-D-iGlu-L-Lys-D-Ala-D-Ala (6), were obtained. Their chemical structures were confirmed by high-resolution mass spectrometry (HRMS) and nuclear magnetic resonance (NMR) spectroscopy. To determine the absolute configuration of the carbon atom in the side chain of the muramic acid derivative, single-crystal X-ray diffraction measurements were recorded.     

Biphenyl-type sensing system in proton-rich environment by fluorescence and quantum-chemical calculations

Biphenyl derivative N-allyl-N′-(4′-nitro[1,1′-biphenyl]-4-yl)thiourea (BP1) was synthesized as a functional fluorescent sensor for protons and their photophysical properties were studied. The influence of environment protonation on photophysical properties of the biphenyls in solutions was investigated using UV absorption, steady-state and time-resolved fluorescence spectroscopy. Semi-empirical and DFT calculations and optimization of the molecular structure of the biphenyl derivatives in vacuum, in polar solvents and in a proton-rich environment were conducted using the HyperChem, Amsol and Gaussian3 software package. Fluorescence quenching with addition of acidic acid was observed and the Stern-Volmer quenching rate constant was about 3.0×10⁹ M⁻¹ s⁻¹. Intermolecular hydrogen bonds formations by the protons with the sulphur being substituted to the biphenyls generate charge movement and strong increase (×5) of the dipole moment of the fluorophore.     

Photoacoustic spectra of Zn<Subscript>1-x</Subscript>Be<Subscript>x</Subscript>Te near the energy gap

The results of experimental studies of optical and structural properties in bulk crystals of Zn_1-xBe_xTe (x = 0.02, 0.06 and 0.12) were presented. The amplitude and phase photoacoustic (PA) spectra were measured and analyzed in dependence on the wavelength of the excitation optical beam, at different frequencies of modulation, using the PA microphone (PAmic) and PA piezoelectric (PApze) spectroscopy methods. The differences in PA spectra of as grown and annealed in zinc vapor samples were observed.