Integrable systems with quadratic nonlinearity in Fourier space

The Lax pair representation in Fourier space is used to obtain a list of integrable scalar evolutionary equations with quadratic nonlinearity. The famous systems of this type such as KdV, intermediate long-wave equation (ILW), Camassa-Holm and A. Degasperis systems are represented in this list. Some new systems are obtained as well. The generalizations on two-dimensional and discrete systems are discussed.Comment: 6 page

Generalized Drinfeld-Sokolov Reductions and KdV Type Hierarchies

Generalized Drinfeld-Sokolov (DS) hierarchies are constructed through local reductions of Hamiltonian flows generated by monodromy invariants on the dual of a loop algebra. Following earlier work of De Groot et al, reductions based upon graded regular elements of arbitrary Heisenberg subalgebras are considered. We show that, in the case of the nontwisted loop algebra $\ell(gl_n)$, graded regular elements exist only in those Heisenberg subalgebras which correspond either to the partitions of $n$ into the sum of equal numbers $n=pr$ or to equal numbers plus one $n=pr+1$. We prove that the reduction belonging to the grade $1$ regular elements in the case $n=pr$ yields the $p\times p$ matrix version of the Gelfand-Dickey $r$-KdV hierarchy, generalizing the scalar case $p=1$ considered by DS. The methods of DS are utilized throughout the analysis, but formulating the reduction entirely within the Hamiltonian framework provided by the classical r-matrix approach leads to some simplifications even for $p=1$.Comment: 43 page

On Asymptotic Expansion in the Random Allocation of Particles by Sets

We consider a scheme of equiprobable allocation of particles into cells by sets. The Edgeworth type asymptotic expansion in the local central limit theorem for a number of empty cells left after allocation of all sets of particles is derived.Comment: 15 page

HgCdTe quantum wells grown by molecular beam epitaxy

CdxHg₁₋xTe-based (x = 0 – 0.25) quantum wells (QWs) of 8 – 22 nm in thickness were grown on (013) CdTe/ZnTe/GaAs substrates by molecular beam epitaxy. The composition and thickness (d) of wide-gap layers (spacers) were x ∼ 0.7 mol.frac. and d ∼ 35 nm, respectively, at both sides of the quantum well. The thickness and composition of epilayers during the growth were controlled by ellipsometry in situ. It was shown that the accuracy of thickness and composition were ∆x = ± 0.002, ∆d = ± 0.5 nm. The central part of spacers (10 nm thick) was doped by indium up to a carrier concentration of ∼10¹⁵ cm⁻³ . A CdTe cap layer 40 nm in thickness was grown to protect QW. The compositions of the spacer and QWs were determined by measuring the Е₁ and Е₁+∆₁ peaks in reflection spectra using layer-by-layer chemical etching. The galvanomagnetic investigations (the range of magnetic fields was 0 – 13 T) of the grown QW showed the presence of a 2D electron gas in all the samples. The 2D electron mobility µe = (2.4 – 3.5)×10⁵ cm² /(V·s) for the concentrations N = (1.5 – 3)×10¹¹ cm⁻² (x < 0.11) that confirms a high quality of the grown QWs

Atomic structure at 2.5 Å resolution of uridine phosphorylase from E. coli as refined in the monoclinic crystal lattice

AbstractUridine phosphorylase from E. coli (Upase) has been crystallized using vapor diffusion technique in a new monoclinic crystal form. The structure was determined by the molecular replacement method at 2.5 Å resolution. The coordinates of the trigonal crystal form were used as a starting model and the refinement by the program XPLOR led to the R-factor of 18.6%. The amino acid fold of the protein was found to be the same as that in the trigonal crystals. The positions of flexible regions were refined. The conclusion about the involvement in the active site is in good agreement with the results of the biochemical experiments

On the structure of the B\"acklund transformations for the relativistic lattices

The B\"acklund transformations for the relativistic lattices of the Toda type and their discrete analogues can be obtained as the composition of two duality transformations. The condition of invariance under this composition allows to distinguish effectively the integrable cases. Iterations of the B\"acklund transformations can be described in the terms of nonrelativistic lattices of the Toda type. Several multifield generalizations are presented

An Index for 4 dimensional Super Conformal Theories

We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on $S^3 \times$ time. Our index receives contributions from states invariant under at least one supercharge and captures all information -- that may be obtained purely from group theory -- about protected short representations in 4 dimensional superconformal field theories. In the case of the $\mathcal{N}=4$ theory our index is a function of four continuous variables. We compute it at weak coupling using gauge theory and at strong coupling by summing over the spectrum of free massless particles in $AdS_5\times S^5$ and find perfect agreement at large $N$ and small charges. Our index does not reproduce the entropy of supersymmetric black holes in $AdS_5$, but this is not a contradiction, as it differs qualitatively from the partition function over supersymmetric states of the ${\cal N}=4$ theory. We note that entropy for some small supersymmetric $AdS_5$ black holes may be reproduced via a D-brane counting involving giant gravitons. For big black holes we find a qualitative (but not exact) agreement with the naive counting of BPS states in the free Yang Mills theory. In this paper we also evaluate and study the partition function over the chiral ring in the $\mathcal{N}=4$ Yang Mills theory.Comment: harvmac 40+16 pages, v3: references and table of contents added, typos fixe

Holography of the N=1 Higher-Spin Theory on AdS4

We argue that the N=1 higher-spin theory on AdS4 is holographically dual to the N=1 supersymmetric critical O(N) vector model in three dimensions. This appears to be a special form of the AdS/CFT correspondence in which both regular and irregular bulk modes have similar roles and their interplay leads simultaneously to both the free and the interacting phases of the boundary theory. We study various boundary conditions that correspond to boundary deformations connecting, for large-N, the free and interacting boundary theories. We point out the importance of parity in this holography and elucidate the Higgs mechanism responsible for the breaking of higher-spin symmetry for subleading N.Comment: 19 page

The classical R-matrix of AdS/CFT and its Lie dialgebra structure

The classical integrable structure of Z_4-graded supercoset sigma-models, arising in the AdS/CFT correspondence, is formulated within the R-matrix approach. The central object in this construction is the standard R-matrix of the Z_4-twisted loop algebra. However, in order to correctly describe the Lax matrix within this formalism, the standard inner product on this twisted loop algebra requires a further twist induced by the Zhukovsky map, which also plays a key role in the AdS/CFT correspondence. The non-ultralocality of the sigma-model can be understood as stemming from this latter twist since it leads to a non skew-symmetric R-matrix.Comment: 22 pages, 2 figure

Launch of the Space experiment PAMELA

PAMELA is a satellite borne experiment designed to study with great accuracy cosmic rays of galactic, solar, and trapped nature in a wide energy range protons: 80 MeV-700 GeV, electrons 50 MeV-400 GeV). Main objective is the study of the antimatter component: antiprotons (80 MeV-190 GeV), positrons (50 MeV-270 GeV) and search for antimatter with a precision of the order of 10^-8). The experiment, housed on board the Russian Resurs-DK1 satellite, was launched on June, 15, 2006 in a 350*600 km orbit with an inclination of 70 degrees. The detector is composed of a series of scintillator counters arranged at the extremities of a permanent magnet spectrometer to provide charge, Time-of-Flight and rigidity information. Lepton/hadron identification is performed by a Silicon-Tungsten calorimeter and a Neutron detector placed at the bottom of the device. An Anticounter system is used offline to reject false triggers coming from the satellite. In self-trigger mode the Calorimeter, the neutron detector and a shower tail catcher are capable of an independent measure of the lepton component up to 2 TeV. In this work we describe the experiment, its scientific objectives and the performance in the first months after launch.Comment: Accepted for publication on Advances in Space Researc