An Approximate Solution for a Class of Ill-Posed Nonhomogeneous Cauchy Problems

In this paper, we consider a nonhomogeneous differential operator equation of first order u ′ t + A u t = f t . The coefficient operator A is linear unbounded and self-adjoint in a Hilbert space. We assume that the operator does not have a fixed sign. We associate to this equation the initial or final conditions u 0 = Φ or u T = Φ . We note that the Cauchy problem is severely ill-posed in the sense that the solution if it exists does not depend continuously on the given data. Using a quasi-boundary value method, we obtain an approximate nonlocal problem depending on a small parameter. We show that regularized problem is well-posed and has a strongly solution. Finally, some convergence results are provided.

The plans of the town of Tobolsk in the second half of the eighteenth century as a historical resource

The authors attempt to identify and analyze the handwritten plans of Tobolsk created in the second half of the XVIII century. They are of both scientific and practical significance. The authors set the task to identify the city plans created during the specified period and analyze them as a historical source. These mapping materials enable identifying the changes in the architectural landscape of the city. State reforms, repeated fires, and di-lapidated buildings caused repeated rebuilding of the Siberian capital. There are changes in the creation of handwritten maps. The emotional component of cartographic materials is gradually lost, and the map as a picture is replaced by a drawing image of the space with a clearly fixed sign system. For the researcher, it is important to understand not only the graphic representation of the urban space, but also the text content, color scheme, artistic images and techniques, which makes it possible to get a better idea of the socio-cultural dominants of that time.

On Multivariate Bernstein Polynomials

In this paper, we first revisit and bring together as a sort of survey, properties of Bernstein polynomials of one variable. Secondly, we extend the results from one variable to several ones, namely—uniform convergence, uniform convergence of the derivatives, order of convergence, monotonicity, fixed sign for the p-th derivative, and deduction of the upper and lower bounds of Bernstein polynomials from those of the corresponding functions.

Novel attractive pairing interaction in strongly correlated superconductors

Conventional and unconventional superconductivity, respectively, arise from attractive (electron-phonon) and repulsive (many-body Coulomb) interactions with fixed-sign and sign-reversal pairing symmetries. Although heavy-fermions, cuprates, and pnictides are widely believed to be unconventional superconductors, recent evidence in one of the heavy fermion superconductor (CeCu_22Si_22) indicate the presence of a novel conventional type pairing symmetry beyond the electron-phonon coupling. We present a new mechanism of attractive potential between electrons, mediated by emergent boson fields (vacuum or holon) in the strongly correlated mixed valence compounds. In the strong coupling limit, localized electron sites are protected from double occupancy, which results in an emergent holon fields. The holon states can, however, attract conduction electrons through valence fluctuation channel, and the resulting doubly occupied states with local and conduction electrons condenseas Cooper pairs with onsite, fixed-sign, s-wave pairing symmetry. We develop the corresponding self-consistent theory of superconductivity, and compare the results with experiments. Our theory provides a new mechanism of superconductivity whose applicability extends to the wider class of intermetallic/mixed-valence materials and other flat-band metals.

Faktor-Faktor Yang Mempengaruhi Struktur Modal Dan Kebijakan Dividen Yang Terdaftar Di Jakarta Islamic Index (JII) Periode 2010-2014

The purpose of this research is to determine the direct effects of factors that caused capital structure and dividend policy. The approach research used are quantitative with analytical techniques PLS (Partial Least Square). The approach is a quantitative approach using analytical techniques PLS (Partial Least Square). Data collection using purposive sampling method and examines a sample of 12 company that that have fixed sign position in the JII during 2010-2014.The results of this research show that in profitability has positive significant effect on capital structure which is indicated with t-statistic is 2,409. Liquidity has negatif not significant on capital structure which is indicated with t-statistic 1,678. Capital structure has negatif significant effect on dividend policy which is indicated with t-statistic 3,568.

Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials

We study Schrödinger operators on L2(ℝd) and ℓ2(ℤd) with a random potential of alloy-type. The single-site potential is assumed to be exponentially decaying but not necessarily of fixed sign. In the continuum setting, we require a generalized step-function shape. Wegner estimates are bounds on the average number of eigenvalues in an energy interval of finite box restrictions of these types of operators. In the described situation, a Wegner estimate, which is polynomial in the volume of the box and linear in the size of the energy interval, holds. We apply the established Wegner estimate as an ingredient for a localization proof via multiscale analysis.