Primitive polynomials,singer cycles and word-oriented linear feedback shift registers

Using the structure of Singer cycles in general linear groups, we prove that a conjecture of Zeng et al. (Word-Oriented Feedback Shift Register: σ-LFSR, 2007) holds in the affirmative in a special case, and outline a plausible approach to prove it in the general case. This conjecture is about the number of primitive σ-LFSRs of a given order over a finite field, and it generalizes a known formula for the number of primitive LFSRs, which, in turn, is the number of primitive polynomials of a given degree over a finite field. Moreover, this conjecture is intimately related to an open question of Niederreiter (Finite Fields Appl 1:3–30, 1995) on the enumeration of splitting subspaces of a given dimension.     

Chemically modified oximato complexes of titanium(IV) isopropoxide as new precursors for the sol-gel preparation of nano-sized titania: Crystal and molecular structure of [Ti{ONC10H16}4·2CH2Cl2]

Reactions of [Ti(OPrⁱ)₄] with various oximes, in anhydrous refluxing benzene yielded complexes of the type [Ti{OPrⁱ}_4−n{L}_n], where, n = 1-4 and LH = (CH₃)₂CNOH (1-4), C₉H₁₆CNOH (5-8) and C₉H₁₈CNOH (9-12). The compounds were characterized by elemental analyses, molecular weight measurements, FAB-mass, FT-IR and NMR (¹H, ¹³C{¹H}) spectral studies. The FAB-mass spectra of mono- (1), and di- (2), (6), (10) substituted products indicate their dimeric nature and that of tri- (3) and tetra- (4), (8) substituted derivatives suggest their monomeric nature. Crystal and molecular structure of [Ti{ONC₁₀H₁₆}₄·2CH₂Cl₂] (8A) suggests that the oximato ligands bind the metal in a dihapto η²-(N, O) manner, leading to the formation of an eight coordinated species. Thermogravimetric curves of (3), (6) and (10) exhibit multi-step decomposition with the formation of TiO₂ as the final product in each case, at 900 °C. Low temperature (∼600 °C) sol-gel transformations of (2), (3), (4), (6), (7) and (8) yielded nano-sized titania (a), (b), (c), (d), (e) and (f), respectively. Formation of anatase phase in all the titania samples was confirmed by powder XRD patterns, FT-IR and Raman spectroscopy. SEM images of (a), (b), (c), (d), (e) and (f) exhibit formation of nano-grains with agglomer like surface morphologies. Compositions of all the titania samples were investigated by EDX analyses. The absorption spectra of the two representative samples, (a) and (f) indicate an energy band gap of 3.17 eV and 3.75 eV, respectively.     

Group Algebras Satisfying a Certain Lie Identity

ABSTRACT

Let K be a field of characteristic p ≠ 2 and let G be any group. A characterization of group algebras KG satisfying the Lie identity [[x,y],[u,v],[z,t]] = 0 for all x,y,u,v,z,t ? KG is obtained.     

A Rationally Designed Bimetallic Platinum (II)-Ferrocene Antitumor Agent Induces Non-Apoptotic Cell Death and Exerts in Vivo Efficacy

Despite phenomenal clinical success, the efficacy of platinum anticancer drugs is often compromised due to inherent and acquired drug resistant phenotypes in cancers. To circumvent this issue, we designed two heterobimetallic platinum (II)-ferrocene hybrids that display multi-pronged anticancer action. In cancer cells, our best compound, 2 , platinates DNA, produces reactive oxygen species, and has nucleus, mitochondria, and endoplasmic reticulum as potential targets. The multi-modal mechanism of action of these hybrid agents lead to non-apoptotic cell death induction which enables circumventing apoptosis resistance and significant improvement in platinum cross resistance profile. Finally, in addition to describing detail mechanistic insights, we also assessed its stability in plasma and demonstrate anticancer efficacy in an in vivo A2780 xenograft model. Strikingly, compared to oxaliplatin, our compound displays better tolerability, safety profile and efficacy in vivo.     

Molecular Interactions of Non-Steroid Anti-Inflammatory Drug Dolonex in Aqueous Solutions of L-Alanine/L-Valine at Different Temperatures: Viscometric Approach

Russian Journal of Physical Chemistry A - The viscosities of aqueous solutions of L-alanine and L-valine with non-steroid anti-inflammatory drug dolonex (0.020, 0.040, 0.060 mol kg–1) have...     

Dyson’s partition ranks and their multiplicative extensions

We study the Dyson rank function N(r, 3; n), the number of partitions of n with rank \(\equiv r \pmod 3\). We investigate the convexity of these functions. We extend N(r, 3; n) multiplicatively to the set of partitions, and we determine the maximum value when taken over all partitions of size n.     

Nonsimilar incompressible laminar boundary layers with magnetic field

The solution of the steady laminar incompressible nonsimilar magneto-hydrodynamic boundary layer flow and heat transfer problem with viscous dissipation for electrically conducting fluids over two-dimensional and axisymmetric bodies with pressure gradient and magnetic field has been presented. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The computations have been carried out for flow over a cylinder and a sphere. The results indicate that the magnetic field tends to delay or prevent separation. The heat transfer strongly depends on the viscous dissipation parameter. When the dissipation parameter is positive (i.e. when the temperature of the wall is greater than the freestream temperature) and exceeds a certain value, the hot wall ceases to be cooled by the stream of cooler air because the ‘heat cushion’ provided by the frictional heat prevents cooling whereas the effect of the magnetic field is to remove the ‘heat cushion’ so that the wall continues to be cooled. The results are found to be in good agreement with those of the local similarity and local nonsimilarity methods except near the point of separation, but they are in excellent agreement with those of the difference-differential technique even near the point of separation.     

2',3'-Dideoxy-3'-thionucleoside triphosphates: syntheses and polymerase substrate activities

All four 2',3'-dideoxy-3'-thio-nucleosides (ddtNTPs) function as substrates for the Y410F mutant of Deep Vent (exo-) DNA polymerase. Not only are the ddtNTPs incorporated to form the N + 1 product, but further elongations are observed in which the key step is attack of the 3'-thiol on the 5'-triphosphate. Although other polymerases are likely to differ in their use of the ddtNTPs, there does not appear to be a fundamental prohibition against using a thiol nucleophile on a phosphate anhydride electrophile. The syntheses of four ddtNTPs (C, T, A, G) are described. [structure: see text]