A new regularization method for feynman diagrams

In an analytic regularization method a new technique, in which the spins of the particles are used as regulating parameters, has been developed.     

Search for possible anapole and electric dipole moments of the proton on the basis of the pp ⇌ e+ e− annihilation reaction

Differential and total cross sections are found for the formation of an electron-positron pair during the annihilation of longitudinally polarized protons and antiprotons (pp e⁺ e^–) and for the inverse reaction (e⁺ e^- pp) in the single-photon approximation, account is taken of the anapole and electric dipole moments of the proton, which violate C, P, and T parity. Possible ways to determine the square moduli of the form factors for the anapole [G₁(q²)] and electric dipole [G₂(q²)] moments and to determine the relative phase of the form factors F_e(q²) and G₂(q²) [F_m(q²) and G₁(q²)] are pointed out. Estimates are found for ¦(G₁q²)¦² and ¦G₂(q²) ¦² with q² = –6.8 (GeV/c)².Translated from Izvestiya VUZ. Fizika, No. 8, pp. 59–65, August, 1970.The authors thank Professor A. A. Sokolov, Professor I. M. Ternov, and Yu. M. Loskutov for discussions of these results.     

Bremsstrahlung emission of photons in the case of scattering of neutrons by nuclei with arbitrary spins

In the Born approximation, expressions are obtained for the angular and energy distribution of bremsstrahlung photons emitted by relativistic neutrons in the field of a nucleus that has an electric quadrupole moment, and magnetic dipole and octupole moments. The expression obtained for the cross section (d=d_E+d_M) describes the total electromagnetic bremsstrahlung of the neutrons due to the interaction of the magnetic moment of the neutron with the electric (Ze, Q) and magnetic ( _I, ) multiple moments of the target nucleus. It is shown that in contrast to the bremsstrahlung of electrons the bremsstrahlung cross section of neutrons does not contain an infrared divergence. The application of the formulas to⁹Be and²⁷Al nuclei is considered. The results are used to investigate the electromagnetic emission of neutral Fermi particles with spin 1/2 and can be used to obtain additional information about the interaction of their magnetic moment with the multiple moments of a nucleus of arbitrary spin.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 60–69, December, 1974.We thank Professor D. D. Ivanenko for discussing the work.     

Sharp estimates for the convergence rate of Fourier series of complex variable functions in <Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript>(D, <Emphasis Type="Italic">p</Emphasis>(<Emphasis Type="Italic">z</Emphasis>))

Sharp estimates are derived for the convergence rate of Fourier series in terms of orthogonal systems of functions for certain classes of complex variable functions, and the Kolmogorov N-widths of these classes are determined. These issues find applications in numerical analysis methods.     

On a problem for operator-differential second-order equations with nonlocal boundary condition

An operator-differential second-order equation with nonlocal boundary condition at zero is considered on the semiaxis. Here we give sufficient conditions on the operator coefficients for the regular solvability of the boundary-value problem. Moreover, we obtain conditions for the completeness andminimality of the derivative of the chain of eigen- and associated vectors generated by the boundary-value problem under study and establish the completeness and minimality of the decreasing elementary solutions of the operator-differential equation under consideration.     

Some new estimates of the Fourier-Bessel transform in the space \mathbb{L}_2 \left( {\mathbb{R}_ + } \right)

The Fourier-Bessel integral transform $$g\left( x \right) = F\left[ f \right]\left( x \right) = \frac{1} {{2^p \Gamma \left( {p + 1} \right)}}\int\limits_0^{ + \infty } {t^{2p + 1} f\left( x \right)j_p \left( {xt} \right)dt}$$ is considered in the space $\mathbb{L}_2 \left( {\mathbb{R}_ + } \right)$ . Here, j _p (u) = ((2 ^p Γ(p+1))/(u ^p ))J _p (u) and J _p (u) is a Bessel function of the first kind. New estimates are proved for the integral $$\delta _N^2 \left( f \right) = \int\limits_N^{ + \infty } {x^{2p + 1} g^2 \left( x \right)dx, N > 0,}$$ in $\mathbb{L}_2 \left( {\mathbb{R}_ + } \right)$ for some classes of functions characterized by a generalized modulus of continuity.     

Some issues concerning approximations of functions by Fourier-Bessel sums

Some issues concerning the approximation of one-variable functions from the class $\mathbb{L}_2 $ by nth-order partial sums of Fourier-Bessel series are studied. Several theorems are proved that estimate the best approximation of a function characterized by the generalized modulus of continuity.     

Convergence rate estimates for “spherical” partial sums of double Fourier series

The convergence of Fourier double series of 2π-periodic functions from the space $\mathbb{L}_2$ is analyzed. The convergence rate of spherical partial sums of a double Fourier series is estimated for some classes of functions characterized by a generalized modulus of continuity.     

Studies on the zeros of Bessel functions and methods for their computation: 3. Some new works on monotonicity,convexity, and other properties

This paper continues the study of real zeros of Bessel functions begun in the previous parts of this work (see M. K. Kerimov, Comput. Math. Math. Phys. 54 (9), 1337–1388 (2014); 56 (7), 1175–1208 (2016)). Some new results regarding the monotonicity, convexity, concavity, and other properties of zeros are described. Additionally, the zeros of q-Bessel functions are investigated.