On semiring complexity of Schur polynomials

Semiring complexity is the version of arithmetic circuit complexity that allows only two operations: addition and multiplication. We show that semiring complexity of a Schur polynomial {s_\lambda(x_1,\dots,x_k)} labeled by a partition {\lambda=(\lambda_1\ge\lambda_2\ge\cdots)} is bounded by {O(\log(\lambda_1))} provided the number of variables $k$ is fixed

Multiple Factorizations of Bivariate Linear Partial Differential Operators

We study the case when a bivariate Linear Partial Differential Operator (LPDO) of orders three or four has several different factorizations. We prove that a third-order bivariate LPDO has a first-order left and right factors such that their symbols are co-prime if and only if the operator has a factorization into three factors, the left one of which is exactly the initial left factor and the right one is exactly the initial right factor. We show that the condition that the symbols of the initial left and right factors are co-prime is essential, and that the analogous statement "as it is" is not true for LPDOs of order four. Then we consider completely reducible LPDOs, which are defined as an intersection of principal ideals. Such operators may also be required to have several different factorizations. Considering all possible cases, we ruled out some of them from the consideration due to the first result of the paper. The explicit formulae for the sufficient conditions for the complete reducibility of an LPDO were found also

DBT degradation enhancement by decorating Rhodococcus erythropolis IGST8 with magnetic Fe3O4 nanoparticles

Biodesulfurization (BDS) of dibenzothiophene (DBT) was carried out by Rhodococcus erythropolis IGST8 decorated with magnetic Fe3O4 nanoparticles, synthesized in-house by a chemical method, with an average size of 45-50 nm, in order to facilitate the post-reaction separation of the bacteria from the reaction mixture. Scanning electron microscopy (SEM) showed that the magnetic nanoparticles substantially coated the surfaces of the bacteria. It was found that the decorated cells had a 56% higher DBT desulfurization activity in basic salt medium (BSM) compared to the nondecorated cells. We propose that this is due to permeabilization of the bacterial membrane, facilitating the entry and exit of reactant and product, respectively. Model experiments with black lipid membranes (BLM) demonstrated that the nanoparticles indeed enhance membrane permeability

Morpholinium perchlorate

In the title salt, C4H10NO+·ClO4 −, which has three independent formula units, the cations are linked into chains along [100] by N—H⋯O hydrogen bonds. Each cation acts both as a donor and as an acceptor, and every cation makes one N—H⋯O hydrogen bond with a ClO4 − anion. The crystal studied was an inversion twin

Complex Chiral Modulations in FeGe close to Magnetic Ordering

We report on detailed polarized small-angle neutron scattering on cubic FeGe in magnetic fields applied either along (transverse) the scattering vector or parallel (longitudinal)to the neutron beam. The ($H,T$) phase diagrams for all principal axes contain a segmented $A$-phase region just below the onset of magnetic order. Hexagonal Bragg-spot patterns were observed across the entire $A$-phase region for the longitudinal geometry. Scattering intensity was observed in parts of the A phase for both scattering configurations. Only in a distinct pocket ($A_1$) vanishing scattering intensity was found in the transverse geometry.Comment: This paper has been withdrawn by the author due to misunderstanding with some of the co-author

Hidden quantum phase transition in Mn1−x_{1-x}Fex_{x}Ge: evidence brought by small-angle neutron scattering

The magnetic system of the Mn$_{1-x}$Fe$_{x}$Ge solid solution is ordered in a spiral spin structure in the whole concentration range of $x \in [0 \div 1]$. The close inspection of the small-angle neutron scattering data reveals the quantum phase transition from the long-range ordered (LRO) to short range ordered (SRO) helical structure upon increase of Fe-concentration at $x \in [0.25 \div 0.4]$. The SRO of the helical structure is identified as a Lorentzian contribution, while LRO is associated with the Gaussian contribution into the scattering profile function. The scenario of the quantum phase transition with $x$ as a driving parameter is similar to the thermal phase transition in pure MnGe. The quantum nature of the SRO is proved by the temperature independent correlation length of the helical structure at low and intermediate temperature ranges with remarkable decrease above certain temperature $T_Q$. We suggest the $x$-dependent modification of the effective Ruderman-Kittel-Kasuya-Yosida exchange interaction within the Heisenberg model of magnetism to explain the quantum critical regime in Mn$_{1-x}$Fe$_{x}$Ge.Comment: 6 pages, 4 figure

The HVEDC Method for the Production of Tungsten Based Alloys

The purpose of this study is to investigate HVEDC method for the production of tungsten-based alloys. It is established that the method of high-voltage electro-discharge compaction, in addition to some economic and time benefits, contributes to a minimal change in the microstructure and does not lead to grain growth, therebyimproving mechanical characteristics. Keywords: powder metallurgy, tungsten heavy alloys, high-voltage electro-discharge consolidation

Constructive factorization of LPDO in two variables

We study conditions under which a partial differential operator of arbitrary order $n$ in two variables or ordinary linear differential operator admits a factorization with a first-order factor on the left. The factorization process consists of solving, recursively, systems of linear equations, subject to certain differential compatibility conditions. In the generic case of partial differential operators one does not have to solve a differential equation. In special degenerate cases, such as ordinary differential, the problem is finally reduced to the solution of some Riccati equation(s). The conditions of factorization are given explicitly for second- and, and an outline is given for the higher-order case.Comment: 16 pages, to be published in Journal "Theor. Math. Phys." (2005

An algorithm for calculating the Lorentz angle in silicon detectors

Future experiments will use silicon sensors in the harsh radiation environment of the LHC (Large Hadron Collider) and high magnetic fields. The drift direction of the charge carriers is affected by the Lorentz force due to the high magnetic field. Also the resulting radiation damage changes the properties of the drift. In this paper measurements of the Lorentz angle of electrons and holes before and after irradiation are reviewed and compared with a simple algorithm to compute the Lorentz angle.Comment: 13 pages, 7 figures, final version accepted by NIMA. Mainly clarifications included and slightly shortene