On the construction of general solution of the generalized sylvester equation

The problem of construction the general solution of the generalized matrix Sylvester equation is considered. Conditions of existence of solution of this equation are obtained and the algorithm for construction of this solution is given. For construction of the algorithm of this solution and the formulation of the condition of existence of this solution, the standard procedures of MATLAB package are used.Publisher's Versio

The Scientific and Social Activity of Professor N. N. Saltykov in Russia in 1894–1919

The scientific and social activity of Professor N. N. Saltykov in Russia in period 1894–1919 is presented

The order O(αˉ αˉs)O(\bar{\alpha}~\bar{\alpha}_s) and O(αˉ2)O(\bar{\alpha}^2) corrections to the decay width of the neutral Higgs boson to the bˉb\bar{b}b pair

We present the analytical expressions for the contributions of the order $O(\bar{\alpha}~\bar{\alpha}_s)$ and $O(\bar{\alpha}^2)$ corrections to the decay width of the Standard Model Higgs boson into the $\bar{b}b$-pair. The numerical value of the mixed QED and QCD correction of order $O(\bar{\alpha}~\bar{\alpha}_s)$ is comparable with the previously calculated terms in the perturbative series for $\Gamma(H^0\to\bar{b}b)$.Comment: LaTeX 5 pages, accepted for publication in Pisma Zh. Eksp. Teor. Fiz. v 66, N5 (1997

Relating Physical Observables in QCD without Scale-Scheme Ambiguity

We discuss the St\"uckelberg-Peterman extended renormalization group equations in perturbative QCD, which express the invariance of physical observables under renormalization-scale and scheme-parameter transformations. We introduce a universal coupling function that covers all possible choices of scale and scheme. Any perturbative series in QCD is shown to be equivalent to a particular point in this function. This function can be computed from a set of first-order differential equations involving the extended beta functions. We propose the use of these evolution equations instead of perturbative series for numerical evaluation of physical observables. This formalism is free of scale-scheme ambiguity and allows a reliable error analysis of higher-order corrections. It also provides a precise definition for $\Lambda_{\overline{\rm MS}}$ as the pole in the associated 't Hooft scheme. A concrete application to $R(e^+e^- \to {\rm hadrons})$ is presented.Comment: Plain TEX, 4 figures (available upon request), 22 pages, DOE/ER/40322-17

Calculating loops without loop calculations: NLO computation of pentaquark correlators

We compute next-to-leading order (NLO) perturbative QCD corrections to the correlators of interpolating pentaquark currents. We employ modular techniques in configuration space which saves us from the onus of having to do loop calculations. The modular technique is explained in some detail. We present explicit NLO results for several interpolating pentaquark currents that have been written down in the literature. Our modular approach is easily adapted to the case of NLO corrections to multiquark correlators with an arbitrary number of quarks/antiquarks.Comment: 23 pages, 1 figure, published version. arXiv admin note: text overlap with arXiv:hep-lat/031001

Compensation for Moral Damage Caused By a Crime

The modern development of social relations cannot be considered in isolation from the ethical component of human life. Questions of morality also concern many areas of state activity. One of them concerns investigation and trial. The implementation by the investigator, inquirer and court of the functions fixed in the Code of Criminal Procedure of the Russian Federation concerning many criminal cases involves the performance of activities related to compensation for moral damage caused by the crime. This issue is superficially regulated in the criminal procedure legislation. The conceptual complex considerably suggests taking into account the content of other branches of law. It is necessary to assess the content of the norms of civil legislation during the research of relations. Multiple influence on the nature of criminal procedural activity is shown. To solve this problem, issues related to the definition of the content of the concept of “moral harm” caused as a result of a crime are examined in the article. The features of establishing the amount of his monetary compensation to the victim, the civil plaintiff are reflected. The judicial practice of the considered sphere of legal regulation is analyzed. The analysis of the decisions of the Constitutional and Supreme Courts of the Russian Federation is also done in the present paper. The ratio of moral and other types of harm caused by the crime is carried out. Due to its ambiguity, the question of the relationship between moral and property damage is highlighted. Approaches to solving the problems identified by the Authors are formed taking into account the positions of other researchers in the legal literature. The analysis of peculiarities of assessment of moral harm is connected with the lack of clear normative criteria for its definition. The paper concludes that the high proportion of subjectivity in this area of legal regulation harms the solution of this issue. The increased attention in this area of relations to the content of a civil claim is determined. The necessity of substantiation of the amount of the relevant requirements on the part of interested parties in view of the implementation of the investigator, inquirer of security activity is reflected. A range of issues related to the definition of the procedural regime for the implementation of claims for material compensation for moral harm has been established. Proposals aimed at optimization of law enforcement activity on ensuring by the investigator, inquirer of the monetary compensation of the relevant moral and physical suffering and subsequent judicial activity are formulated

Recursive Graphical Construction of Feynman Diagrams in phi^4 Theory: Asymmetric Case and Effective Energy

The free energy of a multi-component scalar field theory is considered as a functional W[G,J] of the free correlation function G and an external current J. It obeys non-linear functional differential equations which are turned into recursion relations for the connected Greens functions in a loop expansion. These relations amount to a simple proof that W[G,J] generates only connected graphs and can be used to find all such graphs with their combinatoric weights. A Legendre transformation with respect to the external current converts the functional differential equations for the free energy into those for the effective energy Gamma[G,Phi], which is considered as a functional of the free correlation function G and the field expectation Phi. These equations are turned into recursion relations for the one-particle irreducible Greens functions. These relations amount to a simple proof that Gamma[G,J] generates only one-particle irreducible graphs and can be used to find all such graphs with their combinatoric weights. The techniques used also allow for a systematic investigation into resummations of classes of graphs. Examples are given for resumming one-loop and multi-loop tadpoles, both through all orders of perturbation theory. Since the functional differential equations derived are non-perturbative, they constitute also a convenient starting point for other expansions than those in numbers of loops or powers of coupling constants. We work with general interactions through four powers in the field.Comment: 34 pages; abstract expanded; section IV.E about absorption of tadpoles and one related reference added; eqs. (20) and (23) corrected; further references added; some minor beautifications; to be published by Phys.Rev.

Next-to-next-to-leading order fits to CCFR'97 xF3xF_3 data and infrared renormalons

We briefly summarize the outcomes of our recent improved fits to the experimental data of CCFR collaboration for $xF_3$ structure function of $\nu N$ deep-inelastic scattering at the next-to-next-to-leading order. Special attention is paid to the extraction of $\alpha_s(M_Z)$ and the parameter of the infrared renormalon model for $1/Q^2$-correction at different orders of perturbation theory. The results can be of interest for planning similar studies using possible future data of Neutrino Factories.Comment: 3 pages, presented at WG3 of 4th NuFact'02 Workshop, London 1-6 July, 200

Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme

We present in analytic form the matching conditions for the strong coupling constant alpha_s^(n_f)(mu) at the flavour thresholds to three loops in the modified minimal-subtraction scheme. Taking into account the recently calculated coefficient beta_3 of the Callan-Symanzik beta function of quantum chromodynamics, we thus derive a four-loop formula for alpha_s^(n_f)(mu) together with appropriate relationships between the asymptotic scale parameters Lambda^(n_f) for different numbers of flavours n_f.Comment: 10 pages (Latex), 3 figures (Postscript