Structure and magnetic properties of the nanocomposites γ-Fe<Subscript>2</Subscript>O<Subscript>3</Subscript>-SiO<Subscript>2</Subscript>

The structural features and magnetic properties of composite materials Fe₂O₃-SiO₂ consisting of γ-Fe₂O₃ nanoparticles in an amorphous porous matrix of SiO₂ were considered. The studied samples were synthesized by the sol-gel method. The structure of γ-Fe₂O₃-SiO₂ depending on the heating temperature was studied by electron microscopy, X-ray diffraction analysis, ESR and IR spectroscopy. Magnetic measurements were performed on a SQUID magnetometer in the range 2–350 K.     

The property of maximal transcendentality: Calculation of anomalous dimensions in the N = 4 SYM and master integrals

We review results for the universal anomalous dimension γ _uni (j) of Wilson twist-2 operators in the N = 4 Supersymmetric Yang-Mills theory having the property of maximal transcendentality. It is shown that the similar property is ibserved in the results for master integrals.     

Small-x behavior of the structure function and its slope for “frozen” and analytic strong-coupling constants

Using the leading-twist approximation of the Wilson operator product expansion with “frozen” and analytic versions of the strong-coupling constant, we show that the Bessel-inspired behavior of the structure function F₂ and its slope ∂lnF₂/∂ln(1/x) at small values of x, obtained for a flat initial condition in the DGLAP evolution equations, leads to good agreement with experimental data of deep-inelastic scattering at DESY HERA.     

Landau–Khalatnikov–Fradkin Transformation and Even $$\zeta$$ Functions

Physics of Atomic Nuclei - An exact formula that relates standard $$\zeta$$ functions and so-called hatted $$\zeta$$ ( $$\hat{\zeta}$$ ) functions in all orders of perturbation theory is presented....     

Gas-sensitivity properties of nanoscale Au-In<Subscript>2</Subscript>O<Subscript>3</Subscript> materials

A possibility was demonstrated of producing the chemical sensors based on Au-In₂O₃ obtained using a sol-gel technology. The sensors exhibit high sensitivity and selectivity toward CO. The differences in gas-sensitivity properties of In₂O₃ sensor with respect to CO and CH₄ at different ways of doping with Au(III) was examined. The effect of the gold nanoparticles size and the state of the indium oxide surface on the characteristics of Au-In₂O₃ and Au/In₂O₃ sensors at the detection of CO and CH₄ was examined.     

Anomalous dimensions of the Wilson operators in $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory

We present results for the universal anomalous dimension γ _uni(j) of Wilson twist-2 operators in the = 4 supersymmetric Yang-Mills theory in the first four orders of perturbation theory. The text was submitted by the authors in English.     

About Derivatives in Analytic QCD

JETP Letters - The importance of (fractional) derivatives is demonstrated in the case of analytic QCD. As an example, the Bjorken sum rule is considered.     

Analytic solution of the multiloop Baxter equation

The asymptotic spectrum of anomalous dimensions of gauge-invariant operators in maximally supersymmetric Yang–Mills theory is believed to be described by a long-range integrable spin chain model. We focus in this study on its sl(2)$sl(2)$ subsector spanned by the twist-two single-trace Wilson operators, which are shared by all gauge theories, supersymmetric or not. We develop a formalism for the solution of the perturbative multiloop Baxter equation encoding their asymptotic anomalous dimensions, using Wilson polynomials as basis functions and Mellin transform technique. These considerations yield compact results which allow analytical calculations of multiloop anomalous dimensions bypassing the use of the principle of maximal transcendentality. As an application of our method we analytically confirm the known four-loop result. We also determine the dressing part of the five-loop anomalous dimensions.     

The property of maximal transcendentality: Calculation of Feynman integrals

We consider examples of two-loop two- and three-point Feynman integrals for which the calculation results have the property of maximal transcendentality.