Binary functions,degeneracy, and alternating dimaps

This paper continues the study of combinatorial properties of binary functions — that is, functions $f:2^E\to ?$ such that $f(0?)=1$, where $E$ is a finite set. Binary functions have previously been shown to admit families of transforms that generalise duality, including a trinity transform, and families of associated minor operations that generalise deletion and contraction, with both these families parameterised by the complex numbers. Binary function representations exist for graphs (via the indicator functions of their cutset spaces) and indeed arbitrary matroids (as shown by the author previously). In this paper, we characterise degenerate elements – analogues of loops and coloops – in binary functions, with respect to any set of minor operations from our complex-parameterised family. We then apply this to study the relationship between binary functions and Tutte’s alternating dimaps, which also support a trinity transform and three associated minor operations. It is shown that only the simplest alternating dimaps have binary representations of the form we consider, which seems to be the most direct type of representation. The question of whether there exist other, more sophisticated types of binary function representations for alternating dimaps is left open.     

The Möbius Transformation and Smirnov’s Inequality for Polynomials

Differential inequalities for polynomials generalizing the well-known Smirnov, Rahman, Schmeisser, and Bernstein inequalities are obtained.

     

Total Electron Content Measurements in the Ionosphere Disturbed by High-Power High-Frequency Waves by the Methods of Incoherent Scattering of Radio Waves and Radio Sounding by Glonass Satellite Signal

Radiophysics and Quantum Electronics - We present the results of comparing the total electron content measurements based on GLONASS satellite signals and the EISCAT UHF incoherent scatter radar...     

Stereochemistry of the citrate anion in compounds containing guanidinium and citrate ions

Journal of Structural Chemistry - An analysis is presented for the results obtained in the studies initiated by A. E. Shvelashivili, Corresponding Member, Academy of Sciences of Georgia, and...     

Et2Zn-mediated stoichiometric C(sp)-H silylation of 1-alkynes and chlorosilanes

A first example of an Et₂Zn mediated silylation of 1-aklynes is reported. A series of functional groups are tolerated in this reaction. Mechanistic studies support Zn alkynilides as intermediates in the reaction. This reaction protocol provides a practical method for the preparation of alkynylsilanes and expands the application of organometallic zinc in organic synthesis.     

<Emphasis Type="Italic">FCC/BCC</Emphasis> competition and enhancement of saturation magnetization in nanocrystalline Co-Ni-Fe films

The structure, chemical composition, and magnetic properties of electrochemically deposited nanocrystalline Co-Ni-Fe films were investigated using a number of techniques. A high saturation magnetic induction up to B _s = 21 kG was attained. An enhancement of the saturation magnetization compared to the ideal anticipated one was revealed, which correlated with the nonlinear behavior of the structural phase composition and lattice parameters with the change of the composition. The text was submitted by the authors in English.     

Phase state stabilization of ammonium nitrate for creating an oxidizing agent for smokeless gas-generating formulations yielding no toxic combustion products

Methods for phase stabilization of ammonium nitrate were sought for in order to considerably expand the application area of this oxidizing agent in various-purpose self-combustible formulations, including that in a new generation of gas-generating formulations for automobile air bags. New methods for stabilization of ammonium nitrate were studied and, in particular, a search was made for organic compounds that can stabilize ammonium nitrate even at their low content. The mechanism of phase state stabilization of ammonium nitrate by compounds of this kind was examined.     

Carbon adsorbents for the sorpting and concentrating nobel metals

Kinetic, sorption and selectivity properties of commercial adsorbents are improved by adding petroleum residues (tar asphaltene concentrates) 13% of whole mass. Obtained adsorbents can be used for selective extraction of nobel metals from multicomponent polymetallic solutions of heavy metals and fro sewages purification for removing arsenic.     

Diffraction by a Corrugated Interface. Complete Transformation of an Incident Wave to the Diffraction Lobe

Using the simplest (sinusoidal) corrugation profile in the approximation of absence of losses in the material as an example, we study the regimes of complete transformation of an incident wave to the diffraction lobe by a corrugated metal surface or a corrugated interface of two dielectric media. A numerical-intuitive pattern of appearance and evolution of such regimes with increasing corrugation amplitude is revealed. It is shown that the regimes of complete transformation of an incident wave to the diffraction lobe are possible in both the case of autocollimation and the case of a considerable deviation from it. The examination is based on a numerical method of solving the integral equation by means of a specially created interactive processing system in Visual Fortran.