Right Alternative Unital Bimodules over the Matrix Algebras of Order $ \geq 3 $

Siberian Mathematical Journal - We address the unital right alternative bimodules over the matrix algebras  $ {\mathrm{M}}_{n}(\Phi) $ of order $ n\geq 3 $ , prove that each of these...     

On constructing generally periodic solutions of a complicated structure of a non-autonomous system of differential equations

In this paper, a numerical scheme of constructing approximate generally periodical solutions of a complicated structure of a non-autonomous system of ordinary differential equations with periodical right-hand sides on the surface of a torus is considered. The existence of such solutions, as well as convergence of the method of successive approximations, is demonstrated. Results of a computational experiment are presented.     

Numerical and physical modeling of the dynamics of the Lorenz system

This paper describes a modification of the method of power series for the construction of approximate solutions of the Lorenz system. The results of a computer-aided simulation are presented. Also, physical modeling of the dynamics of the Lorenz system for processes occurring in an electric circuit is considered.     

Binary-(−1, 1)-nilalgebras

Translated from Matematicheskie Zametki, Vol. 48, No. 1, pp. 103–109, July, 1990.     

A novel procedure for rapid surface functionalisation and mediator loading of screen-printed carbon electrodes

We report a simple and rapid procedure that leads to incorporation of mediator and introduction of amine functionality onto the surface of screen-printed carbon electrodes (SPCE). The electrodes were doped with cobalt phthalocyanine (CoPc) by enhanced adsorption in a process that uses minimal amounts of this redox mediator as compared with CoPc loaded inks. The CoPc-doped SPCE showed a substantially increased sensitivity to hydrogen peroxide and thiocholine as compared to unmodified electrodes. This greatly facilitated their use as transducers for the construction of amperometric biosensors based on enzymes producing oxidizable products such as hydrogen peroxide or thiols. Immobilisation of enzymes including glucose oxidase, acetylcholinesterase and choline oxidase was achieved through their multi-contact electrostatic interaction with polyethyleneimine (PEI) which was electrodeposited on the surface of CoPc-doped electrodes in one step from ethanolic solution. The efficiency of enzyme immobilisation was shown to depend on the molecular weight of the PEI used, reaching a maximum for 25 kDa PEI. The biosensors shown sensitivity to glucose at 130 nA mM⁻¹ (LOD 0.15 mM) and to acetylcholine at 70 nA mM⁻¹ (LOD 0.10 mM) under +0.6 V. Detection of glucose has been demonstrated at +0.4 V with the sensitivity of 60 nA mM⁻¹ and LOD of 0.33 mM. Possibility of the inhibition analysis of pesticides has been shown for acetylcholinesterase-based sensors.     

Isotopes of the alternative monster and the Skosyrsky algebra

We prove that the isotopes of the alternative monster and the Skosyrsky algebra satisfy the identity П_i=1⁴ [x_i, y_i] = 0. Hence, the algebras themselves satisfy the identity П_i=1⁴ (c, x_i, y_i) = 0. We also show that none of the identities П_i=1ⁿ(c, x_i, y_i) = 0 holds in all commutative alternative nil-algebras of index 3. Thus, we refute the Grishkov–Shestakov hypothesis about the structure of the free finitely generated commutative alternative nil-algebras of index 3.     

Regularization Methods in the Analysis of a Series of Scintillation Fluorescence Microscopy Images

Computational Mathematics and Modeling - We consider the construction of high-resolution images from a time series of fluorescence microscopy images obtained using a scintillator. A regularization...