Cohomology Groups of Deformations of Line Bundles on Complex Tori

The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative deformations of complex tori. Our analysis interpolates between two extreme cases. The first case is a calculation of the space of (cohomological) theta functions for line bundles over constant, commutative deformations. The second case is a calculation of the cohomologies of non-commutative deformations of degree-zero line bundles.Comment: 24 pages, exposition improved, typos fixe

Connexin-Mediated Signaling in Nonsensory Cells Is Crucial for the Development of Sensory Inner Hair Cells in the Mouse Cochlea

Mutations in the genes encoding for gap junction proteins connexin 26 (Cx26) and connexin 30 (Cx30) have been linked to syndromic and nonsyndromic hearing loss in mice and humans. The release of ATP from connexin hemichannels in cochlear nonsensory cells has been proposed to be the main trigger for action potential activity in immature sensory inner hair cells (IHCs), which is crucial for the refinement of the developing auditory circuitry. Using connexin knock-out mice, we show that IHCs fire spontaneous action potentials even in the absence of ATP-dependent intercellular Ca(2+) signaling in the nonsensory cells. However, this signaling from nonsensory cells was able to increase the intrinsic IHC firing frequency. We also found that connexin expression is key to IHC functional maturation. In Cx26 conditional knock-out mice (Cx26(Sox10-Cre)), the maturation of IHCs, which normally occurs at approximately postnatal day 12, was partially prevented. Although Cx30 has been shown not to be required for hearing in young adult mice, IHCs from Cx30 knock-out mice exhibited a comprehensive brake in their development, such that their basolateral membrane currents and synaptic machinery retain a prehearing phenotype. We propose that IHC functional differentiation into mature sensory receptors is initiated in the prehearing cochlea provided that the expression of either connexin reaches a threshold level. As such, connexins regulate one of the most crucial functional refinements in the mammalian cochlea, the disruption of which contributes to the deafness phenotype observed in mice and DFNB1 patients. SIGNIFICANCE STATEMENT: The correct development and function of the mammalian cochlea relies not only on the sensory hair cells, but also on the surrounding nonsensory cells. Although the nonsensory cells have been largely implicated in the general homeostasis in the mature cochlea, their involvement in the initial functional differentiation of the sensory inner hair cells is less clear. Using mutant mouse models for the most common form of congenital deafness in humans, which are knock-outs for the gap-junction channels connexin 26 and connexin 30 genes, we show that defects in nonsensory cells prevented the functional maturation of inner hair cells. In connexin knock-outs, inner hair cells remained stuck at a prehearing stage of development and, as such, are unable to process sound information

On the theory of resonant susceptibility of dielectric glasses in magnetic field

The anomalous magnetic field dependence of dielectric properties of insulating glasses in the temperature interval $10mK<T<50mK$ is considered. In this temperature range, the dielectric permittivity is defined by the resonant contribution of tunneling systems. The external magnetic field regulates nuclear spins of tunneling atoms. This regulation suppresses a nuclear quadrupole interaction of these spins with lattice and, thus, affects the dielectric response of tunneling systems. It is demonstrated that in the absence of an external magnetic field the nuclear quadrupole interaction $b$ results in the correction to the permittivity $\delta\chi\sim| b| /T$ in the temperature range of interest. An application of a magnetic field results in a sharp increase of this correction approximately by a factor of two when the Zeeman splitting $m$ approaches the order of $| b|$. Further increase of the magnetic field results in a relatively smooth decrease in the correction until the Zeeman splitting approaches the temperature. This smooth dependence results from tunneling accompanied by a change of the nuclear spin projection. As the magnetic field surpasses the temperature, the correction vanishes. The results obtained in this paper are compared with experiment. A new mechanism of the low temperature nuclear spin-lattice relaxation in glasses is considered.Comment: 9 Pages, 5 Figures, To be submitted to the Physical Review B, please send comment

ІНФОРМАЦІЙНО-ПРАВОВІ АСПЕКТИ ОБЛІКОВОГО ВІДОБРАЖЕННЯ ЗЕМЕЛЬНИХ РЕСУРСІВ СІЛЬСЬКОГОСПОДАРСЬКОГО ПРИЗНАЧЕННЯ

Analysis of recent research and also the accounting practices of entities of the agricultural sector showed that the questions of accounting ensuring of land resources of agricultural purpose in Ukraine is insufficiently developed, especially in terms of the reflection of transactions with land shares, which are the objects of the lease agreements. The purpose of the article is to to develop methodological approaches to the accounting of transactions with land for agricultural purposes, the basis of which will be based on the reliability of the accounting procedures and compliance with applicable legislation. Results. This article describes regulations regarding the calculation of land shares. A number of synthetic and analytical accounts for the balance sheet and off-balance sheet accounting of rights to land shares in the use of agricultural enterprise has been suggested. Conclusions. The method of registration of land shares in a state or municipal agricultural enterprises due to privatization has been developed.В статье охарактеризованы нормативно-правовые акты по учету земельных долей (паев). Предложен ряд синтетических и аналитических счетов для балансового та внебалансового учета права на земельные доли (паи) в пользовании сельскохозяйственного предприятия. Разработана методика учета земельных долей (паев) в государственных или коммунальных сельскохозяйственных предприятиях в результате их приватизации.У статті охарактеризовано нормативно-правові акти щодо обліку земельних часток (паїв). Запропоновано ряд синтетичних та аналітичних рахунків для балансового та позабалансового обліку права на земельні частки (паї) в користуванні сільськогосподарського підприємства. Розроблено методику обліку земельних часток (паїв) у державних чи комунальних сільськогосподарських підприємствах внаслідок їх приватизації

Cladoceran birth and death rates estimates

I. Birth and death rates of natural cladoceran populations cannot be measured directly. Estimates of these population parameters must be calculated using methods that make assumptions about the form of population growth. These methods generally assume that the population has a stable age distribution. 2. To assess the effect of variable age distributions, we tested six egg ratio methods for estimating birth and death rates with data from thirty-seven laboratory populations of Daphnia pulicaria. The populations were grown under constant conditions, but the initial age distributions and egg ratios of the populations varied. Actual death rates were virtually zero, so the difference between the estimated and actual death rates measured the error in both birth and death rate estimates. 3. The results demonstrate that unstable population structures may produce large errors in the birth and death rates estimated by any of these methods. Among the methods tested, Taylor and Slatkin's formula and Paloheimo's formula were most reliable for the experimental data. 4. Further analyses of three of the methods were made using computer simulations of growth of age-structured populations with initially unstable age distributions. These analyses show that the time interval between sampling strongly influences the reliability of birth and death rate estimates. At a sampling interval of 2.5 days (equal to the duration of the egg stage), Paloheimo's formula was most accurate. At longer intervals (7.5–10 days), Taylor and Slatkin's formula which includes information on population structure was most accurate

Study of the functional product’s protein compounds digestion features

The aim of the study was to investigate the transformation of meat product’s proteins from pig hearts and aortas during enzymatic hydrolysis in an in vitro model of the gastrointestinal tract. The model consisted of three phases simulating digestion processes: “oral cavity” phase (a-amylase, pH 7.0; 2 min), “stomach” phase (pork pepsin, pH 3.0; 120 min), “intestine” phase (pork pancreatin, pH 7.0; 130 min). The product was sequentially subjected to hydrolysis, at the end of each phase, samples were taken to determine the protein concentration (biuret method) and visualize the protein fractions (one-dimensional electrophoresis). A significant increase in protein concentration at the “stomach” phase was revealed by 3.2 times, and the absolute content by 4.6 times. At the “intestine” phase, a decrease in the number of peptide complexes with copper ions by 1.8 times, the absolute protein content by 8.5% was re‑ vealed. The noted tendency was confirmed by electrophoretic studies — at the stage, simulating digestion in the stomach, the prod‑ ucts of meat product’s proteins hydrolysis were visualized; at the “intestine” phase, a low expression of protein fractions in the range of more than 10 kDa is shown. The maximum hydrolysis of protein compounds at the “stomach” phase to poly- and oligopeptides was confirmed, continuing at the “intestine” stage with the accumulation of free amino acids. This methodology makes it possible to visualize the products of hydrolysis of proteins in a meat product at all stages of the model and to monitor changes in protein concentration in the system

Split structures in general relativity and the Kaluza-Klein theories

We construct a general approach to decomposition of the tangent bundle of pseudo-Riemannian manifolds into direct sums of subbundles, and the associated decomposition of geometric objects. An invariant structure {\cal H}^r defined as a set of r projection operators is used to induce decomposition of the geometric objects into those of the corresponding subbundles. We define the main geometric objects characterizing decomposition. Invariant non-holonomic generalizations of the Gauss-Codazzi-Ricci's relations have been obtained. All the known types of decomposition (used in the theory of frames of reference, in the Hamiltonian formulation for gravity, in the Cauchy problem, in the theory of stationary spaces, and so on) follow from the present work as special cases when fixing a basis and dimensions of subbundles, and parameterization of a basis of decomposition. Various methods of decomposition have been applied here for the Unified Multidimensional Kaluza-Klein Theory and for relativistic configurations of a perfect fluid. Discussing an invariant form of the equations of motion we have found the invariant equilibrium conditions and their 3+1 decomposed form. The formulation of the conservation law for the curl has been obtained in the invariant form.Comment: 30 pages, RevTeX, aps.sty, some additions and corrections, new references adde