Approximation of some classes of set-valued periodic functions by generalized trigonometric polynomials

Generalizations of some known results on the best, best linear and best one-sided approxima- tions by trigonometric polynomials of the classes of 2\pi - periodic functions presented in the form of convolutions to the case of set-valued functions are obtaine

Features of the second-order visual filters sensitive to the spatial frequency modulations

We investigated selectivity of 2nd order visual filters sensitive to the spatial frequency (SF) modulations to orientation and to SF of modulation. We carried out psychophysical experiment using masking paradigm. It was found that 2nd order filters are selective to SF of modulation (with bandwidth +1.5 octaves), and do not show any selectivity to orientation of modulation. We suppose receptive fields of 2nd order mechanisms have concentric form.Comment: 3 pages, 4 figure

Organizational properties of second-order visual filters sensitive to the orientation modulations

Here we show psychophysical study of second-order visual mechanisms sensitive to the orientation modulations. Selectivity to orientation, phase and spatial frequency of modulation is measured. Bandwidths for phase (0,5{\pi}) and orientation (33,75 deg) are defined, but there is no evidence for spatial frequency selectivity.Comment: 4 pages, 3 figures; this is the English version of paper; it's published in Russia

Determination of Low-Energy Parameters of Neutron--Proton Scattering on the Basis of Modern Experimental Data from Partial-Wave Analyses

The triplet and singlet low-energy parameters in the effective-range expansion for neutron--proton scattering are determined by using the latest experimental data on respective phase shifts from the SAID nucleon--nucleon database. The results differ markedly from the analogous parameters obtained on the basis of the phase shifts of the Nijmegen group and contradict the parameter values that are presently used as experimental ones. The values found with the aid of the phase shifts from the SAID nucleon--nucleon database for the total cross section for the scattering of zero-energy neutrons by protons, $\sigma_{0}=20.426$b, and the neutron--proton coherent scattering length, $f=-3.755$fm, agree perfectly with the experimental cross-section values obtained by Houk, $\sigma_{0}=20.436\pm 0.023$b, and experimental scattering-length values obtained by Houk and Wilson, $f=-3.756\pm 0.009$fm, but they contradict cross-section values of $\sigma_{0}=20.491\pm 0.014$b according to Dilg and coherent-scattering-length values of $f=-3.7409\pm 0.0011$fm according to Koester and Nistler.Comment: 17 pages, to be published in Physics of Atomic Nucle

Free multiflows in bidirected and skew-symmetric graphs

A graph (digraph) $G=(V,E)$ with a set $T\subseteq V$ of terminals is called inner Eulerian if each nonterminal node $v$ has even degree (resp. the numbers of edges entering and leaving $v$ are equal). Cherkassky and Lov\'asz showed that the maximum number of pairwise edge-disjoint $T$-paths in an inner Eulerian graph $G$ is equal to $\frac12\sum_{s\in T} \lambda(s)$, where $\lambda(s)$ is the minimum number of edges whose removal disconnects $s$ and $T-\{s\}$. A similar relation for inner Eulerian digraphs was established by Lomonosov. Considering undirected and directed networks with ``inner Eulerian'' edge capacities, Ibaraki, Karzanov, and Nagamochi showed that the problem of finding a maximum integer multiflow (where partial flows connect arbitrary pairs of distinct terminals) is reduced to $O(\log T)$ maximum flow computations and to a number of flow decompositions. In this paper we extend the above max-min relation to inner Eulerian bidirected and skew-symmetric graphs and develop an algorithm of complexity $O(VE\log T\log(2+V^2/E))$ for the corresponding capacitated cases. In particular, this improves the known bound for digraphs. Our algorithm uses a fast procedure for decomposing a flow with O(1) sources and sinks in a digraph into the sum of one-source-one-sink flows.Comment: 21 pages, 4 figures Submitted to a special issue of DA

Study of the Low-Energy Characteristics of Neutron-Neutron Scattering in the Effective-Range Approximation

The influence of the mass difference between the charged and neutral pions on the low-energy characteristics of nucleon-nucleon interaction in the $^{1}S_{0}$ spin-singlet state is studied within the framework of the effective-range approximation. By making use of the experimental singlet neutron-proton scattering parameters and the experimental value of neutron-neutron virtual-state energy, the following values were obtained for the neutron-neutron scattering length and effective range: $a_{nn}=-16.59(117)$fm, $r_{nn}=2.83(11)$fm. The calculated neutron-neutron scattering length $a_{nn}$ is in good agreement with one of the two well known and differing experimental values of this quantity, and the calculated effective range $r_{nn}$ is also in good agreement with present-day experimental results.Comment: 12 pages, 1 table. Slightly modified version of the article published in Physics of Atomic Nucle

Description of the Low-Energy Doublet Neutron-Deuteron Scattering on the Basis of the Triton Bound and Virtual State Parameters

Low-energy doublet neutron-deuteron scattering is described on the basis of the triton bound and virtual state parameters - the energies and the nuclear vertex constants of these states. The van Oers-Seagrave formula is derived from the Bargmann representation of the S matrix for a system having two states. The presence of a pole in this formula is shown to be a direct corollary of the existence of a low-energy triton virtual state. Simple explicit expressions for the nd scattering length and for the pole of the function $k\cot \delta$ are obtained in terms of the triton bound and virtual state parameters. Numerical calculations of the nd low-energy scattering parameters show their high sensitivity to variations in the asymptotic normalization constant of the virtual state $C_{v}^{2}$. The $C_{v}^{2}$ value fitted in our model to the experimental result for the nd scattering length is $C_{v}^{2}=0.0592$.Comment: 15 pages, 1 figur

P-matrix Description of Interaction of Two Charged Hadrons And Low-energy Nuclear-Coulomb Scattering Parameters

The scattering of two charged strongly interacting particles is described on the basis of the P-matrix approach. In the P matrix, it is proposed to isolate explicitly the background term corresponding to purely Coulomb interaction, whereby it becomes possible to improve convergence of the expansions used and to obtain a correct asymptotic behavior of observables at high energies. The expressions for the purely Coulomb background P matrix, its poles and residues, and purely Coulomb eigenfunctions of the P-matrix approach are obtained. The nuclear-Coulomb low-energy scattering parameters of two charged hadrons are investigated on the basis of this approach combined with the method of isolating the background P matrix. Simple explicit expressions for the nuclear-Coulomb scattering length and effective range in terms of the residual P matrix are derived. These expressions give a general form of the nuclear-Coulomb low-energy scattering parameters for models of finite-range strong interaction. Specific applications of the general expressions derived in this study are exemplified by considering some exactly solvable models of strong interaction containing hard core repulsion, and, for these models, the nuclear-Coulomb low-energy scattering parameters for arbitrary values of the orbital angular momentum are found explicitly. In particular, the nuclear-Coulomb scattering length and effective range are obtained explicitly for the boundary-condition model, the model of a hard-core delta-shell potential, the Margenau model, and the model of hard-core square-well potential.Comment: 23 page

On the Connection Between the Charged and Neutral Pion-Nucleon Coupling Constants in the Yukawa Model

In the Yukawa model for nuclear forces, a simple relation between the charged and neutral pion-nucleon coupling constants is derived. The relation implies that the charged pion-nucleon coupling constant is larger than the neutral one since the np interaction is stronger than the pp interaction. The derived value of the charged pion-nucleon constant shows a very good agreement with one of the recent experimental values. The relative splitting between the charged and neutral pion-nucleon coupling constants is predicted to be practically the same as that between the charged and neutral pion masses. The charge dependence of the NN scattering length arising from the mass difference between the charged and neutral pions is also analyzed.Comment: 19 pages. Slightly modified and typos corrected version of the article published in PEPAN Letter

Optimal recovery of convolutions of nn functions according to linear information

We found the optimal linear information and the optimal method of its use to recovery of the convolution of n functions on some classes of $2\pi$ - periodic functions