The Character of Pure Spinors

The character of holomorphic functions on the space of pure spinors in ten, eleven and twelve dimensions is calculated. From this character formula, we derive in a manifestly covariant way various central charges which appear in the pure spinor formalism for the superstring. We also derive in a simple way the zero momentum cohomology of the pure spinor BRST operator for the D=10 and D=11 superparticle.Comment: 42 pages, 2 picture

Обґрунтування параметрів зберігання напою кисломолочного дитячого харчування "Біолакт"

Changes in the quality indicators of sour-milk infant drink «Biolakt» characterized by high probiotic and immunomodulatory properties and low allergic effect that were made according to the improved technology and stored in sealed-off containers at temperature (4±2) ºС during 28 days have been studied: organoleptic properties of taste and odour, consistency and appearance; physical and chemical properties – titrated acidity, ºТ; active acidity, pH units; moisture retention property, %; microbiological properties – number of living cells of mixed cultures B. bifidum 1 + B. longum Ya3 + B. infantis 512, CFU/cm³; the most probable number of living cells of monocultures L. acidophilus La-5, CFU/cm³; presence of coli form bacteria in 0.3 cm³; presence of Salmonella in 50 cm3; biochemical properties – antioxidant activity, activity units; and maximum possible content of malondialdehyde at complete oxidation of the product ingredients, mg/100 g. It is proved that under indicated conditions in the course of 24 days the studied samples of target products possess high organoleptic and standardized for sour-milk infant drinks physical, chemical, biochemical and microbiological indicators and are, also, characterized by high content of probiotics: (0.43 – 8.60)∙109 and (0.25 – 1.10)∙109 CFU/cm3 of living cells of bifidus bacteria and lactobacilli, accordingly. It has been established that the limit storage period of sour-milk infant drink «Biolakt» produced according to the improved technology and stored at temperature (4±2) ºС should not exceed 12 days with due account of the safety margin for sour-milk infant drinks (provided they are kept in sealed-off containers). It has been proved that the target product formulas should include lactulose, polyunsaturated fatty acids omega-3 FT EU of «Fortitech» company (Denmark), vitamin complex FT 041081EU of «Fortitech» company (Denmark) and/or complex of mineral substances FT 042836EU of «Fortitech» company (Denmark).Досліджено зміну показників якості напоїв кисломолочних дитячого харчування «Біолакт» з підвищеними пробіотичними й імуномодулюючими властивостями та зниженим алергенним ефектом, вироблених за удосконаленою технологією, при зберіганні у герметичній тарі за температури (4±2) ºС протягом 28 діб: органолептичних – смаку та запаху, кольору, консистенції та зовнішнього вигляду; фізико-хімічних – титрованої кислотності, ºТ; активної кислотності, од. рН; вологоутримуючої здатності, %; мікробіологічних – кількості життєздатних клітин змішаних культур B. bifidum 1 + B. longum Я3 + B. infantis 512, КУО/см³; найбільш вірогідне число життєздатних клітин монокультур L. acidophilus La-5, КУО/см3; наявності бактерій групи кишкових паличок у 0,3 см³; наявності Salmonella у 50 см³; біохімічних – антиоксидантної активності, од. акт.; максимально можливого вмісту малонового діальдегіду при повному окисненні інгредієнтів продукту, мг/100 г. Показано, що при зазначених умовах протягом 24 діб досліджені зразки цільових продуктів мають високі органолептичні, нормовані для кисломолочних напоїв дитячого харчування фізико-хімічні, біохімічні та мікробіологічні, показники, а також характеризуються високим вмістом пробіотиків: (0,43 – 8,60)∙109 та (0,25 –1,10)∙109 КУО/см3 життєздатних клітин біфідобактерій та лактобацил, відповідно. Встановлено, що граничний термін зберігання напоїв кисломолочних дитячого харчування «Біолакт», вироблених за удосконаленою технологією, за температури (4±2) °С не повинен перевищувати 12 діб із врахуванням коефіцієнту запасу для кисломолочних продуктів дитячого харчування (за умови зберігання у герметичній тарі). Доведено, що рецептури цільових продуктів повинні включати лактулозу, поліненасичені жирні кислоти омега-3 FT EU фірми «Fortitech» (Данія), комплекс вітамінів FT 041081EU фірми «Fortitech» (Данія) та/або комплекс мінеральних речовин FT 042836EU фірми «Fortitech» (Данія)

On the numerical closeness of the effective phenomenological electroweak mixing angle θ\theta and the \MS parameter θ^\hat\theta

It happens that $s^2$ and $\hat s^2$ are equal with 0.1% accuracy, though they are split by radiative corrections and a natural estimate for their difference is 1%. This degeneracy occurs only for $m_t$ value close to 170\GeV, so no deep physical reason can be attributed to it. However, another puzzle of the Standard Model, the degeneracy of s_\Eff^2 and $s^2$, is not independent of the previous one since a good physical reason exists for s_\Eff^2 and $\hat s^2$ degeneracy. We present explicit formulas which relate these three angles.Comment: 10 pages, latex, 3 figures included; published on MPLA. A few numerical estimates are improved; journal-ref is adde

Chronopotentiometry at platinum electrode in KF-NaF-AlF3-Al2O3 melt

Some features of the mechanism of the anode process on platinum in KF–NaF–AlF3–Al2O3 melt at 750–780 °C depending on the of anodic current density (0.5 mA/cm2 to 2.0 A/cm2) and anodic pulse duration have been studied using chronopotentiometry method. In curves of change in the platinum anode potential a small peak at current densities of 10–30 mA/cm2 and a clear peak at current densities of 0.5–2.0 A/cm2 are recorded when the current is cut on. Analysis of dependencies of the transition time on the current density indicates that the first peak in curve is associated with the formation of an oxide compound on the platinum surface, and the second one is related to hindering the diffusion for delivery of electroactive particles to its surface.The study was supported by the Russian Foundation for Basic Research (grant № 13–03–00829 A)

Electronic Structure of New Multiple Band Pt-Pnictide Superconductors APt3P

We report LDA calculated band structure, densities of states and Fermi surfaces for recently discovered Pt-pnictide superconductors APt3P (A=Ca,Sr,La), confirming their multiple band nature. Electronic structure is essentially three dimensional, in contrast to Fe pnictides and chalcogenides. LDA calculated Sommerfeld coefficient agrees rather well with experimental data, leaving little space for very strong coupling superconductivity, suggested by experimental data on specific heat of SrPt3P. Elementary estimates show, that the values of critical temperature can be explained by rather weak or moderately strong coupling, while the decrease of superconducting transition temperature Tc from Sr to La compound can be explained by corresponding decrease of total density of states at the Fermi level N(E_F). The shape of the density of states near the Fermi level suggests that in SrPt3P electron doping (such as replacement Sr by La) decreases N(E_F) and Tc, while hole doping (e.g. partial replacement of Sr with K, Rb or Cs, if possible) would increase N(E_F) and possibly Tc.Comment: 5 pages, 5 figure

Quantum Foam and Topological Strings

We find an interpretation of the recent connection found between topological strings on Calabi-Yau threefolds and crystal melting: Summing over statistical mechanical configuration of melting crystal is equivalent to a quantum gravitational path integral involving fluctuations of Kahler geometry and topology. We show how the limit shape of the melting crystal emerges as the average geometry and topology of the quantum foam at the string scale. The geometry is classical at large length scales, modified to a smooth limit shape dictated by mirror geometry at string scale and is a quantum foam at area scales g_s \alpha'.Comment: 55 page

Instantons on ALE spaces and orbifold partitions

We consider N=4 theories on ALE spaces of $A_{k-1}$ type. As is well known, their partition functions coincide with $A_{k-1}$ affine characters. We show that these partition functions are equal to the generating functions of some peculiar classes of partitions which we introduce under the name 'orbifold partitions'. These orbifold partitions turn out to be related to the generalized Frobenius partitions introduced by G. E. Andrews some years ago. We relate the orbifold partitions to the blended partitions and interpret explicitly in terms of a free fermion system.Comment: 28 pages, 10 figures; reference adde

Theoretical investigation of magnetic order in ReOFeAs, Re = Ce, Pr

Density functional theory (DFT) calculations are carried out on ReOFeAs, Re = Ce, Pr, the parent compounds of the high-T$_c$ superconductors ReO$_{1-x}$F$_{x}$FeAs, in order to determine the magnetic order of the ground state. It is found that the magnetic moments on the Fe sites adopt a collinear antiferromagnetic order, similar to the case of LaOFeAs. Within the generalized gradient approximation along with Coulomb onsite repulsion (GGA+U), we show that the Re magnetic moments also adopt an antiferromagnetic order for which, within the ReO layer, same spin Re sites lie along a zigzag line perpendicular to the Fe spin stripes. While within GGA the Re 4f band crosses the Fermi level, upon inclusion of onsite Coulomb interaction the 4f band splits and moves away from the Fermi level, making ReOFeAs a Mott insulator.Comment: 5 pages, 4 figure

Multicomponent theory of buoyancy instabilities in magnetized plasmas: The case of magnetic field parallel to gravity

We investigate electromagnetic buoyancy instabilities of the electron-ion plasma with the heat flux based on not the magnetohydrodynamic (MHD) equations, but using the multicomponent plasma approach when the momentum equations are solved for each species. We consider a geometry in which the background magnetic field, gravity, and stratification are directed along one axis. The nonzero background electron thermal flux is taken into account. Collisions between electrons and ions are included in the momentum equations. No simplifications usual for the one-fluid MHD-approach in studying these instabilities are used. We derive a simple dispersion relation, which shows that the thermal flux perturbation generally stabilizes an instability for the geometry under consideration. This result contradicts to conclusion obtained in the MHD-approach. We show that the reason of this contradiction is the simplified assumptions used in the MHD analysis of buoyancy instabilities and the role of the longitudinal electric field perturbation which is not captured by the ideal MHD equations. Our dispersion relation also shows that the medium with the electron thermal flux can be unstable, if the temperature gradients of ions and electrons have the opposite signs. The results obtained can be applied to the weakly collisional magnetized plasma objects in laboratory and astrophysics.Comment: Accepted for publication in Astrophysics & Space Scienc

Extended Seiberg-Witten Theory and Integrable Hierarchy

The prepotential of the effective N=2 super-Yang-Mills theory perturbed in the ultraviolet by the descendents of the single-trace chiral operators is shown to be a particular tau-function of the quasiclassical Toda hierarchy. In the case of noncommutative U(1) theory (or U(N) theory with 2N-2 fundamental hypermultiplets at the appropriate locus of the moduli space of vacua) or a theory on a single fractional D3 brane at the ADE singularity the hierarchy is the dispersionless Toda chain. We present its explicit solutions. Our results generalize the limit shape analysis of Logan-Schepp and Vershik-Kerov, support the prior work hep-th/0302191 which established the equivalence of these N=2 theories with the topological A string on CP^1 and clarify the origin of the Eguchi-Yang matrix integral. In the higher rank case we find an appropriate variant of the quasiclassical tau-function, show how the Seiberg-Witten curve is deformed by Toda flows, and fix the contact term ambiguity.Comment: 49 page