Antiferromagnetic spin-wave states in a linear chain with nearest- and next-nearest-neighbour interactions

The spectrum of short-closed chains up to N=12 are studied by exact diagonalization to obtain the spin-wave spectrum of the Hamiltonian H=2J Sigma i=1Nsi.si+1+2J alpha Sigma i=1Nsi.si+2, -1.0formula obtained by the Anderson approximation (1952). The results of short chains indicate that S=0 bound magnon states lie partly below the spin-wave states with S=1 only for alpha >or=0.3 and alpha

Orbit perturbation theory of beam-plasma instability

The nonlinear theory of the instability caused by an electron beam-plasma interaction is studied. A nonlinear analysis has been carried out using many-body methods. A general formula for a neutral collisionless plasma, without external fields, is derived. This could be used for calculating the saturation levels of other instabilities. The effect of orbit perturbation theory on the beam-plasma instability is briefly reviewed.

Matrices of finite Lorentz transformations in a noncompact basis. III. Completeness relation for O(2, 1)

A parametrization of the elements of the three-dimensional Lorentz group O(2, 1), suited to the use of a noncompact O(1, 1) basis in its unitary representations, is derived and used to set up the representation matrices for the entire group. The Plancherel formula for O(2, 1) is then expressed in this basis.

X-ray crystal structure of a ternary copper(II) vitamin B6 complex, hydroxo(2,2'-bipyridyl)(pyridoxinato) copper(II) monohydrate. A rare example of monodentate coordination of copper(II) by the hydroxyl ion

A ternary metal complex involving Vitamin B6 with the formula [Cu(bipy)(pn) (OH)]H2O (bipy = 2,2'²-bipyridine, PN = anionic pyridoxine) has been synthesized and studied in the solid state by means of spectroscopy and X-ray crystallography. The geometry around copper(II) is distorted square pyramidal, two oxygens from phenolic and 4-(hydroxymethyl) groups of pn, two nitrogens from bipy and an axial OH- ion forming the coordination sphere. In this structure pn exists in a new anionic form with deprotonation of the phenolic group. The structure also provides a rare example of monodentate hydroxyl coordination to copper.

Simplified theory of optical nonlinearities in spin-polarized semiconductors

The spin degree of freedom is largely disregarded in existing theories of the density-dependent optical properties of an interacting electron-hole plasma in quasiequilibrium. Here, we extended the pair equation, which is applicable to a bulk semiconductor at elevated temperatures, to calculate optical nonlinearities due to a spin-polarized plasma. We obtained agreement with recent circular dichroism data in laser-excited GaAs by using the plasma density alone as the fitting parameter. The simplicity of our theory, based on the analytical pair-equation formula, makes it ideal for conveniently modelling absorption in a carrier spin-polarized semiconductor.

Kafka on the Shore

Kafka On The Shore consists of three simple concrete letterforms floating on a gallery wall. Reminiscent of minimalist sculpture, the mathematical expression of the letterforms states that ‘r’ is greater than ‘g’. Despite this material simplicity, the solemn presentation of the formula suggests a sense of foreboding, a quiet menace. The work was created as a response to the economic theories of Thomas Piketty presented in his book Capital in the Twenty-First Century. The primary finding of Piketty’s data-driven research is the formula presented by the work; that historically, wealth and inequity both flourish when the rate of return on capital (r) is greater than the rate of economic growth (g). With this simple mathematical summary the book acts as a sobering indictment on the present state of economic inequality.

Nd2O3 : Eu3+ nanocrystalline phosphor - a new potential thermoluminescing material for dosimetry

Nanoparticles of trivalent Eu3+-doped Nd2O3 phosphors have been prepared using a low-temperature solution combustion method with metal nitrate as precursor and oxalyldihydrazide as a fuel at a fairly low temperature (<500 degrees C) and in a very short time (<5 min). A powder X-ray diffraction pattern reveals that cubic Nd2O3 : Eu3+ crystallites are directly obtained without the requirement of further calcinations. The crystallite size, evaluated from Scherer's formula, was found to be in the range of 20-30 nm. The microstructure and morphology were studied by scanning electron microscopy, which showed the phosphor to be foamy and fluffy in nature. Thermoluminescence characteristics of the Nd2O3 : Eu3+ have been studied using gamma irradiation. These demonstrate that the phosphor is suitable for use as a dosimeter.

Low loss and frequency (1 kHz-1 MHz) independent dielectric characteristics of 3BaO-3TiO(2)-B2O3 glasses

X-ray powder diffraction along with differential thermal analysis carried out on the as-quenched samples in the 3BaO-3TiO(2)-B2O3 system confirmed their amorphous and glassy nature, respectively. The dielectric constants in the 1 kHz-1 MHz frequency range were measured as a function of temperature (323-748 K). The dielectric constant and loss were found to be frequency independent in the 323-473 K temperature range. The temperature coefficient of dielectric constant was estimated using Havinga's formula and found to be 16 ppm K-1. The electrical relaxation was rationalized using the electric modulus formalism. The dielectric constant and loss were 17 +/- 0.5 and 0.005 +/- 0.001, respectively at 323 K in the 1 kHz-1 MHz frequency range which may be of considerable interest to capacitor industry.

Delamination of Surfactant-Intercalated Brucite-Like Hydroxy Salts of Cobalt and Copper and Solvothermal Decomposition of the Resultant Colloidal Dispersions

Surfactant anion intercalated hydroxy salts of copper and cobalt of the formula M(OH)(2-x)(surf)(x)center dot mH(2)O [M = Cu, Co; surf = dodecyl sulfate. dodecyl benzene sulfonate. and x = 0.5 for Cu and 0.67 for Co] delaminate readily in 1-butanol to give translucent colloidal dispersions that are stable for months. The extent of delamination and the colloidal dispersion observed in these solids is higher than what had been observed for layered double hydroxides. The dispersions yield the corresponding nanoparticulate oxides on solvothermal decomposition. While the copper hydroxy salt forms similar to 300 nm dendrimer-like CuO nanostructures comprising nanorods of similar to 10 nm diameter, the cobalt analogue forms similar to 20 nm superparamagnetic particles of Co3O4.

Boson-fermion duality in SU(m vertical bar n) supersymmetric Haldane-Shastry spin chain

By using the Y(gl(m|n)) super Yangian symmetry of the SU(m|n) supersymmetric Haldane-Shastry spin chain, we show that the partition function of this model satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom. As a byproduct of this study of the duality relation, we find a novel combinatorial formula for the super Schur polynomials associated with some irreducible representations of the Y(gl(m|n)) Yangian algebra. Finally, we reveal an intimate connection between the global SU(m|n) symmetry of a spin chain and the boson-fermion duality relation. (C) 2007 Elsevier B.V. All rights reserved.

Spherical means with centers on a hyperplane in even dimensions

Given a real-valued function on R-n we study the problem of recovering the function from its spherical means over spheres centered on a hyperplane. An old paper of Bukhgeim and Kardakov derived an inversion formula for the odd n case with great simplicity and economy. We apply their method to derive an inversion formula for the even n case. A feature of our inversion formula, for the even n case, is that it does not require the Fourier transform of the mean values or the use of the Hilbert transform, unlike the previously known inversion formulas for the even n case. Along the way, we extend the isometry identity of Bukhgeim and Kardakov for odd n, for solutions of the wave equation, to the even n case.

1-[5-Acetyl-4-(4-bromophenyl)-2,6-dimethyl-1,4-dihydropyridin-3-yl]eth anone monohydrate

The 1,4-dihydropyridine ring in the title hydrate, C17H18BrNO2 center dot H2O, has a flattened-boat conformation, and the benzene ring is occupies a position orthogonal to this [dihedral angle: 82.19 (16)degrees]. In the crystal packing, supramolecular arrays mediated by N-H center dot center dot center dot O-water and O-water-H center dot center dot center dot O-carbonyl hydrogen bonding are formed in the bc plane. A highly disordered solvent molecule is present within a molecular cavity defined by the organic and water molecules. Its contribution to the electron density was removed from the observed data in the final cycles of refinement and the formula, molecular weight and density are given without taking into account the contribution of the solvent molecule.

Cow's milk allergy and the development of tolerance

Aims: To gain insight on the immunological processes behind cow’s milk allergy (CMA) and the development of oral tolerance. To furthermore investigate the associations of HLA II and filaggrin genotypes with humoral responses to early oral antigens. Methods: The study population was from a cohort of 6209 healthy, full-term infants who in a double-blind randomized trial received supplementary feeding at maternity hospitals (mean duration 4 days): cow’s milk (CM) formula, extensively hydrolyzed whey formula or donor breast milk. Infants who developed CM associated symptoms that subsided during elimination diet (n=223) underwent an open oral CM challenge (at mean age 7 months). The challenge was negative in 112, and in 111 it confirmed CMA, which was IgE-mediated in 83. Patients with CMA were followed until recovery, and 94 of them participated in a follow-up study at age 8-9 years. We investigated serum samples at diagnosis (mean age 7 months, n=111), one year later (19 months, n=101) and at follow-up (8.6 years, n=85). At follow-up, also 76 children randomly selected from the original cohort and without CM associated symptoms were included. We measured CM specific IgE levels with UniCAP (Phadia, Uppsala, Sweden), and β-lactoglobulin, α-casein and ovalbumin specific IgA, IgG1, IgG4 and IgG levels with enzyme-linked immunosorbent assay in sera. We applied a microarray based immunoassay to measure the binding of IgE, IgG4 and IgA serum antibodies to sequential epitopes derived from five major CM proteins at the three time points in 11 patients with active IgE-mediated CMA at age 8-9 years and in 12 patients who had recovered from IgE-mediated CMA by age 3 years. We used bioinformatic methods to analyze the microarray data. We studied T cell expression profile in peripheral blood mononuclear cell (PBMC) samples from 57 children aged 5-12 years (median 8.3): 16 with active CMA, 20 who had recovered from CMA by age 3 years, 21 non-atopic control subjects. Following in vitro β-lactoglobulin stimulation, we measured the mRNA expression in PBMCs of 12 T-cell markers (T-bet, GATA-3, IFN-γ, CTLA4, IL-10, IL-16, TGF-β, FOXP3, Nfat-C2, TIM3, TIM4, STIM-1) with quantitative real time polymerase chain reaction, and the protein expression of CD4, CD25, CD127, FoxP3 with flow cytometry. To optimally distinguish the three study groups, we performed artificial neural networks with exhaustive search for all marker combinations. For genetic associations with specific humoral responses, we analyzed 14 HLA class II haplotypes, the PTPN22 1858 SNP (R620W allele) and 5 known filaggrin null mutations from blood samples of 87 patients with CMA and 76 control subjects (age 8.0-9.3 years). Results: High IgG and IgG4 levels to β-lactoglobulin and α-casein were associated with the HLA (DR15)-DQB1*0602 haplotype in patients with CMA, but not in control subjects. Conversely, (DR1/10)-DQB1*0501 was associated with lower IgG and IgG4 levels to these CM antigens, and to ovalbumin, most significantly among control subjects. Infants with IgE-mediated CMA had lower β -lactoglobulin and α-casein specific IgG1, IgG4 and IgG levels (p<0.05) at diagnosis than infants with non-IgE-mediated CMA or control subjects. When CMA persisted beyond age 8 years, CM specific IgE levels were higher at all three time points investigated and IgE epitope binding pattern remained stable (p<0.001) compared with recovery from CMA by age 3 years. Patients with persisting CMA at 8-9 years had lower serum IgA levels to β-lactoglobulin at diagnosis (p=0.01), and lower IgG4 levels to β-lactoglobulin (p=0.04) and α-casein (p=0.05) at follow-up compared with patients who recovered by age 3 years. In early recovery, signal of IgG4 epitope binding increased while that of IgE decreased over time, and binding patterns of IgE and IgG4 overlapped. In T cell expression profile in response to β –lactoglobulin, the combination of markers FoxP3, Nfat-C2, IL-16, GATA-3 distinguished patients with persisting CMA most accurately from patients who had become tolerant and from non-atopic subjects. FoxP3 expression at both RNA and protein level was higher in children with CMA compared with non-atopic children. Conclusions: Genetic factors (the HLA II genotype) are associated with humoral responses to early food allergens. High CM specific IgE levels predict persistence of CMA. Development of tolerance is associated with higher specific IgA and IgG4 levels and lower specific IgE levels, with decreased CM epitope binding by IgE and concurrent increase in corresponding epitope binding by IgG4. Both Th2 and Treg pathways are activated upon CM antigen stimulation in patients with CMA. In the clinical management of CMA, HLA II or filaggrin genotyping are not applicable, whereas the measurement of CM specific antibodies may assist in estimating the prognosis.

Optical Studies of the Antarctic Glacio-Oceanic System

The Antarctic system comprises of the continent itself, Antarctica, and the ocean surrounding it, the Southern Ocean. The system has an important part in the global climate due to its size, its high latitude location and the negative radiation balance of its large ice sheets. Antarctica has also been in focus for several decades due to increased ultraviolet (UV) levels caused by stratospheric ozone depletion, and the disintegration of its ice shelves. In this study, measurements were made during three Austral summers to study the optical properties of the Antarctic system and to produce radiation information for additional modeling studies. These are related to specific phenomena found in the system. During the summer of 1997-1998, measurements of beam absorption and beam attenuation coefficients, and downwelling and upwelling irradiance were made in the Southern Ocean along a S-N transect at 6°E. The attenuation of photosynthetically active radiation (PAR) was calculated and used together with hydrographic measurements to judge whether the phytoplankton in the investigated areas of the Southern Ocean are light limited. By using the Kirk formula the diffuse attenuation coefficient was linked to the absorption and scattering coefficients. The diffuse attenuation coefficients (Kpar) for PAR were found to vary between 0.03 and 0.09 1/m. Using the values for KPAR and the definition of the Sverdrup critical depth, the studied Southern Ocean plankton systems were found not to be light limited. Variabilities in the spectral and total albedo of snow were studied in the Queen Maud Land region of Antarctica during the summers of 1999-2000 and 2000-2001. The measurement areas were the vicinity of the South African Antarctic research station SANAE 4, and a traverse near the Finnish Antarctic research station Aboa. The midday mean total albedos for snow were between 0.83, for clear skies, and 0.86, for overcast skies, at Aboa and between 0.81 and 0.83 for SANAE 4. The mean spectral albedo levels at Aboa and SANAE 4 were very close to each other. The variations in the spectral albedos were due more to differences in ambient conditions than variations in snow properties. A Monte-Carlo model was developed to study the spectral albedo and to develop a novel nondestructive method to measure the diffuse attenuation coefficient of snow. The method was based on the decay of upwelling radiation moving horizontally away from a source of downwelling light. This was assumed to have a relation to the diffuse attenuation coefficient. In the model, the attenuation coefficient obtained from the upwelling irradiance was higher than that obtained using vertical profiles of downwelling irradiance. The model results were compared to field measurements made on dry snow in Finnish Lapland and they correlated reasonably well. Low-elevation (below 1000 m) blue-ice areas may experience substantial melt-freeze cycles due to absorbed solar radiation and the small heat conductivity in the ice. A two-dimensional (x-z) model has been developed to simulate the formation and water circulation in the subsurface ponds. The model results show that for a physically reasonable parameter set the formation of liquid water within the ice can be reproduced. The results however are sensitive to the chosen parameter values, and their exact values are not well known. Vertical convection and a weak overturning circulation is generated stratifying the fluid and transporting warmer water downward, thereby causing additional melting at the base of the pond. In a 50-year integration, a global warming scenario mimicked by a decadal scale increase of 3 degrees per 100 years in air temperature, leads to a general increase in subsurface water volume. The ice did not disintegrate due to the air temperature increase after the 50 year integration.

The mixed black hole partition function for the STU model

We evaluate the mixed partition function for dyonic BPS black holes using the recently proposed degeneracy formula for the STU model. The result factorizes into the OSV mixed partition function times a proportionality factor. The latter is in agreement with the measure factor that was recently conjectured for a class of N = 2 black holes that contains the STU model.