Structure of 2-Methyl-5,6,7-triphenyl-6,7-dihydropyrazolo[2,3-\u3cem\u3ea\u3c/em\u3e]pyrimidine

C25H21N3, Mr = 363.46, monoclinic, P21/n, a = 9.245 (2), b = 23.502 (5), c = 9.340 (2) Å, β= 103.50(3)°, V=1973.3(2) Å3, Z=4, Dx= 1.220 (2) g cm-3, λ (Mo Kα )= 0.71069 Å, μ = 0.068 cm-1, F(000) = 768, T= 292 K, R = 0.091 for 1442 unique observed reflections. The dihydropyrimidine ring adopts a distorted sofa conformation. The aryl substituents on the saturated C atoms have an axial orientation

Bound, virtual and resonance SS-matrix poles from the Schr\"odinger equation

A general method, which we call the potential $S$-matrix pole method, is developed for obtaining the $S$-matrix pole parameters for bound, virtual and resonant states based on numerical solutions of the Schr\"odinger equation. This method is well-known for bound states. In this work we generalize it for resonant and virtual states, although the corresponding solutions increase exponentially when $r\to\infty$. Concrete calculations are performed for the $1^+$ ground and the $0^+$ first excited states of $^{14}\rm{N}$, the resonance $^{15}\rm{F}$ states ($1/2^+$, $5/2^+$), low-lying states of $^{11}\rm{Be}$ and $^{11}\rm{N}$, and the subthreshold resonances in the proton-proton system. We also demonstrate that in the case the broad resonances their energy and width can be found from the fitting of the experimental phase shifts using the analytical expression for the elastic scattering $S$-matrix. We compare the $S$-matrix pole and the $R$-matrix for broad $s_{1/2}$ resonance in ${}^{15}{\rm F}$Comment: 14 pages, 5 figures (figures 3 and 4 consist of two figures each) and 4 table

Semiorthogonal decompositions of derived categories of equivariant coherent sheaves

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of bounded derived category of G-equivariant coherent sheaves on X into components, equivalent to derived categories of twisted representations of the group. If the group is finite or reductive over the algebraically closed field of zero characteristic, this gives a full exceptional collection in the derived equivariant category. We apply our results to particular varieties such as projective spaces, quadrics, Grassmanians and Del Pezzo surfaces.Comment: 28 pages, uses XY-pi

An annotated list of cartilaginous fishes (Chondrichthyes: Elasmobranchii, Holocephali) of the coastal waters of Sakhalin Island and the adjacent southern part of the Sea of Okhotsk

An annotated list of cartilaginous fish (Chondrichthyes: Elasmobranchii, Holocephali) is given for the first time in the 200-year history of studying the ichthyofauna of Sakhalin Island and adjacent waters of the southern part of the Sea of Okhotsk (including the coast of Hokkaido Island) and the northern Sea of Japan. The list includes 43 species in two classes, eight orders, 16 families, and 25 genera. Information on nature conservation status, English and Latin names, depths of habitat, and distribution within the coastal waters of Sakhalin are presented. For a number of species caught off the coast of Sakhalin and in the adjacent waters, information is provided on collection specimens confirming their presence in the region under study. For a number of species of the Rajiformes order (Arctoraja parmifera, A. smirnovi, A. simoterus), the modern ranges and taxonomic status are being refined in the light of new data. The taxonomic status of the so-called “disputed” taxa is discussed as well as the validity of the species considered in the Bathyraja matsubarai complex. Based on the study of the collections, Arctoraja simoterus, previously unknown in the waters of Russia, as well as Myliobatis tobijei, caught in the Bering Sea, has been discovered, which significantly expands the range of this species to the north

Assembling nanostructures from DNA using a composite nanotweezers with a shape memory effect

The article demonstrates a technique for fabricating a structure with the inclusion of suspended DNA threads and manipulating them using composite nanotweezers with shape memory effect. This technique could be suitable for stretching of nanothin DNA-like conductive threads and for measuring their electrical conductivity, including the I-V characteristic directly in the electron microscope chamber, where the nanotweezers provide a two-sided clamping of the DNA tip, giving a stable nanocontact to the DNA bundle. Such contact, as a part of 1D nanostructure, is more reliable during manipulations with nanothreads than traditional measurements when a nanothread is touched by a thin needle, for example, in a scanning tunnel microscope.Comment: To be presented on IEEE 3M-NANO 201

Fermionic construction of partition functions for two-matrix models and perturbative Schur function expansions

A new representation of the 2N fold integrals appearing in various two-matrix models that admit reductions to integrals over their eigenvalues is given in terms of vacuum state expectation values of operator products formed from two-component free fermions. This is used to derive the perturbation series for these integrals under deformations induced by exponential weight factors in the measure, expressed as double and quadruple Schur function expansions, generalizing results obtained earlier for certain two-matrix models. Links with the coupled two-component KP hierarchy and the two-component Toda lattice hierarchy are also derived.Comment: Submitted to: "Random Matrices, Random Processes and Integrable Systems", Special Issue of J. Phys. A, based on the Centre de recherches mathematiques short program, Montreal, June 20-July 8, 200

Negative high-frequency differential conductivity in semiconductor superlattices

We examine the high-frequency differential conductivity response properties of semiconductor superlattices having various miniband dispersion laws. Our analysis shows that the anharmonicity of Bloch oscillations (beyond tight-binding approximation) leads to the occurrence of negative high-frequency differential conductivity at frequency multiples of the Bloch frequency. This effect can arise even in regions of positive static differential conductivity. The influence of strong electron scattering by optic phonons is analyzed. We propose an optimal superlattice miniband dispersion law to achieve high-frequency field amplification

Fermionic construction of partition function for multi-matrix models and multi-component TL hierarchy

We use $p$-component fermions $(p=2,3,...)$ to present $(2p-2)N$-fold integrals as a fermionic expectation value. This yields fermionic representation for various $(2p-2)$-matrix models. Links with the $p$-component KP hierarchy and also with the $p$-component TL hierarchy are discussed. We show that the set of all (but two) flows of $p$-component TL changes standard matrix models to new ones.Comment: 16 pages, submitted to a special issue of Theoretical and Mathematical Physic