Probability Distributions of the Riemann Wave and an Integral of It

Doklady Physics - In this paper, we study the statistical characteristics of the Riemann wave and the integral of it. Such problems arise in the physics of fronts’ propagation, in particular,...     

Norbornene derivatives from a metal‐free,strain‐promoted cycloaddition reaction: New building blocks for ring‐opening metathesis polymerization reactions

The preparation of new ring opening metathesis polymerization (ROMP) monomers using a 1,3‐dipolar cycloaddition between aryl azides and norbornadiene is described. Various norbornenetriazolines, obtained through a solvent‐and catalyst‐free reaction, can subsequently be incorporated into polymer backbones through ROMP reactions. Furthermore, thermal decomposition of the triazoline moiety can allow for further polymer functionalization. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2357–2362     

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...     

Evolution of a Non-Uniform Deformed State in the Structure of Zinc-Chalcogenide Cubic Crystals Doped by 3 d Ions

The real structure of bulk Zn1 – хМхSe (S) crystals of diluted magnetic semiconductors with М = V, Cr, Fe, Co, Ni 3d impurities is characterized by neutron diffraction. These impurities are known to greatly destabilize even the initial lattices of pure zinc chalcogenides. Data on the resulting non-uniform microstrain field induced by atomic displacements are obtained from the structural peaks along the tangential and radial directions on the above crystals within a dopant concentration range of 0.01 ≤ х ≤ 0.10. Additional nodes with q = (1/3 1/3 1/3) 2π/a (q is the wave vector and a is the cubic unit cell) emerging in the reciprocal lattice of the cubic structure are considered as evidence for a pre-transition to the fcc (face-centered cubic)–hcp (hexagonal close-packed) phase state, which implies transitions from the fcc lattice along an 8-ray non-Lifshitz star with the wave vector k5 = μ(b1 + b2 + b3), where b1, b2, b3 are the reciprocal lattice vectors and μ ≈ 1/3.     

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.