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Subject. This article deals with the control and management aspects of regional development on the basis of Leontief’s balance model. Objectives. The article aims to develop schemes for stable estimation of aggregate parameters of region balance models based on a shortened sample of input-output statistical data and rules for their subsequent regularization. Methods. For the study, we used multiple forms of regional economic balance model transformation based on the aggregation of data of the selected regional subsystems. Results. The primary estimates of aggregate input-output matrix for the southern regions of the Tyumen Oblast were obtained from the statistical input-output data for 2014–2018. To comply with the productivity conditions, additional information was introduced into the estimation algorithm reflecting the balance dependence for the reference input-output matrix for the Russian Federation and for the southern regions of the Tyumen Oblast in retrospective (2004–2013). Conclusions. The result of regularization of aggregate input-output matrix for the southern regions of the Tyumen Oblast obtained from the statistical input-output data on the basis of the least squares method indicates that the backward estimation technique cannot act as a basic tool for the primary construction of balance models of regional economies. However, backward estimation algorithms with subsequent regularization are effective in correcting the reference input-output matrix using actual data of the region’s socio-economic development.

The article proposes one of the tools for effective forest management a methodology for assessing forest biodiversity based on the Shannon index or the evenness of biomes formed by dominant edificator trees. The concept is given and the formula for determining the Shannon biodiversity index for communities (biomes) is provided, depending on the probability distribution of edificator trees. Moreover, the biome index is determined on the basis of the occurrence, and the probability distribution of edificators is determined by the dominant species: larch, pine, cedar, spruce and birch on the territory of their continuous and mosaic growth in the taiga and forest-tundra zones of forestry enterprises in the north of Western Siberia. This makes it possible to give a preliminary estimate of the possible values of the biodiversity index of a vast area occupied by forest using satellite observations. Using the descriptions of biomes of the noted edificator trees given by B.N. Norin, V.I. Valutskiy and E.I. Lapshina, the authors of the article obtained indices of the Shannon biodiversity and uniformity for a number of biomes similar in terms of growing conditions to the forest zone of the Yamalo-Nenets Autonomous Area. The probability distribution of edificator trees was obtained on the basis of data on the growing area of these species on the interactive map Forests of Russia as of 01.01.2018. As a result, an assessment of the biodiversity of the forest area in each forestry enterprise was obtained and a map of the Yamalo-Nenets Autonomous Area forestry enterprises with the digital values of this index is provided.

Intelligent information systems are at present actively incorporated in almost all industry fields. Out of many approaches to construction of such systems, the following two methods are worthy of noting: a method involving the use of expert knowledge, which include, in particular, fuzzy modeling), and a method of supervised machine learning, which estimate this knowledge from the available data marked depending on the objectresponse pairs. Each of these methods has its essential advantages and drawbacks. A combined use of both the approaches for solving the classification case is given. The proposed method for training a fuzzy classifier includes fuzzification of the input features of objects, shaping of logical rule conditions for the fuzzy model rule base, and selection of the most typical rule conclusions for filling the relational matrix. The terms of input features and their membership functions behave as the fuzzy model hyperparameters. As an example, the case of binary classification in a two-dimensional coordinate space with a nonlinear distribution of classes is considered. The sets of terms and membership functions ensuring high-quality classification on the training and test data have been found for each of the coordinates. The fuzzy classifier trained using the proposed method is able to solve a number of binary and multi-class classification cases. It can be applied in a situation involving difficulties in specifying an a priori rule base, and supervised learning is allowed to be used as a solution. Since the approach has logical rules at its heart, transparency of the model is ensured, and explanations to the results yielded by the model can be done.

In this work, method of preparation FDM 3D printed PLLA/HAp composite scaffolds of three compositions (12.5, 25, and 50 wt.% of HAp) was proposed. Influence of hydroxyapatite weight fraction on morphological and mechanical properties of PLLA/HAp composite scaffolds was studied. Morphological and mechanical properties of 3D-pinted scaffolds were investigated by scanning electron microscopy and nanoindentation. Results of scanning electron microscopy analysis showed that proposed method of composite mixing allows obtaining highly filled composites with homogeneous distribution of HAp powder in the PLLA-matrix. Results of nanoindentation showed growth of Young’s modulus with an increasing of HAp weight fraction. The maximum value of 8111 ± 714 MPa Young’s modulus was reached for the composite with 50 wt.% of HAp

The process of obtaining of lactic acid oligomer as by-product for synthesis of biodegradable polylactide was investigated. Synthesis of oligomer was carried out by azeotropic distillation of water. Aromatic hydrocarbons such as toluene, chlorobenzene, bromobenzene and o-dichlorobenzene were used. They form heteroazeotropes. This allowed to control the volume of distilled water. The time of obtaining of oligomer of lactic acid in presence aromatic hydrocarbons and without them was compare in the article. The reaction of obtaining of oligomer was carried out in a rotary vacuum evaporator and in laboratory distillation installation in presence of catalyst (ZnO in the amount of 1.5% by weight) for reaction assessment. It was shown that the using of azeotropic distillation of water from reaction mass allow to reduce the time of oligomer synthesis compared to standard distillation of water from the lactic acid solution. It implements by reducing of viscosity of reaction mass that improves heat and mass transfer in the reactor. These factors contribute to increase rate of distillation of solution water and water which release in the process of polycondensation of lactic acid. The oligomer yield also increases. The actual control of concentrating of the aqueous solution of lactic acid and the oligomer obtaining reaction carried out according to the rate of distillation of the water from the reactor. Also the control was carried out by changing the molecular weight of the oligomer. The molecular weight of the oligomers obtained was determined by gel permeation chromatography. It reached 1600 g/mol. Lactic acid oligomer of a linear structure was obtained under these conditions. IR spectra of the oligomer of lactic acid indicate the simultaneous process of concentration of the lactic acid solution and polycondensation of lactic acid.

Thanks to the modification of the force spectroscopy method, when a neutrophil is fixed on the tip, and an endotheliocyte culture is grown on the substrate, the exact indicators of the adhesion force and adhesion work between cells have been investigated. The high variability of adhesion contacts in different donors associated with different expression profiles of neutrophils. It was found by flow cytometry that the EA.hy926 cell line actively expresses VCAM-1, as well as P- and E-selectin under the Staphylococcus aureus influence after 60 min of co-incubation. At the same time, the integral indicators of the adhesion force and adhesion work in the “neutrophil – endothelial cell” interaction were significantly inhibited by S. aureus in all studied donors. Since the VCAM-1 receptor is not involved in the adhesion bonds between neutrophils and endothelial cells, the suppression of the interaction is associated with the inhibition of P- and E-selectins, but direct receptors removal from the endothelial cells surface of the EA.hy926 cell line does not occur. Escherichia coli causes multidirectional effects in the system of interaction “neutrophil – endothelial cell”, depending on the expression profile of the donor's neutrophils. However, the cumulative effect of interaction from all donors shows that in general, under the influence of E. coli, there is an increase in adhesion force and a suppression of adhesion work.

Ultraperipheral collisions of high energy protons are a source of approximately real photons colliding with each other. Photon fusion can result in production of yet unknown charged particles in very clean events. The cleanliness of such an event is due to the requirement that the protons survive during the collision. Finite sizes of the protons reduce the probability of such outcome compared to point-like particles. We calculate the survival factors and cross sections for the production of heavy charged particles at the Large Hadron Collider., Comment: 15 pages, 7 figures; version accepted by JHEP

Binding of native bacterial protein SlyD to metal affinity matrices remains a major problem in affinity purification of His-tagged recombinant proteins from Escherichia coli cells. In this study, four novel E. coli strains that lack the expression of SlyD/SlyX, were engineered using λ-red mediated chromosomal deletion. The resultant mutant E. coli strains allow us to obtain SlyD-free proteins immediately after metal affinity chromatography, and eliminate additional purification processes. As a model protein, bispecific antibodies composed of anti-F4/80 VHH module and anti-TNF VHH module (MYSTI-2) were used. Using this protein we have shown that the SlyD/SlyX-deficient E. coli strains allow us to obtain a fully functional protein.

We propose a model-independent approach for the search of charged long-lived particles produced in ultraperipheral collisions at the LHC. The main idea is to improve event reconstruction at ATLAS and CMS with the help of their forward detectors. Detection of both scattered protons in forward detectors allows complete recovery of event kinematics. Though this requirement reduces the number of events, it greatly suppresses the background, including the large background from the pile-up., Comment: 23 pages, 12 figures. This is the version published in JHEP

Nanoparticles are increasingly being used for treatment and diagnostic purposes, but their effects on cells is not fully understood. Here, the interaction of fluorescent up-conversion nanoparticles (UpC-NPs) with neutrophils was investigated by imaging and measurement of membrane-cytosceletal elasticity by atomic force microscopy. It was found that UpC-NPs induce the death of neutrophils mainly by necrosis, and to a smaller extent by a novel process called 'mummification'. Necrosis occurs by gradual loss of intracellular contents and nuclei, 45-110min after exposure to UpC-NPs. Mummification is apparent as an increase in the rigidity of the neutrophils' membrane and acquisition of a characteristic bumpy shape with numerous protrusions; this structure does not change during atomic force microscopy scanning. Coating UpC-NPs with protein by incubation with serum leads to (1) formation of nanoparticle aggregates in the nm and μm size range, (2) a reduction in toxicity, (3) reduced mummification of neutrophils, and (4) no significant reduction of the elasticity of the membrane-cytoskeletal complex of neutrophils 30min after exposure to coated UpC-NPs. The study shows that serum proteins greatly curb the toxicity of nanoparticles and reveals mummification as a novel mechanism of UpC-NP-induced cell death.

An approach to the properties of the [Formula: see text] system developed to solve the famous [Formula: see text] problem is used to calculate the partial widths ratios to [Formula: see text] and [Formula: see text] in the [Formula: see text] and [Formula: see text] decays. We obtain the results in agreement with the experimental data.

We discuss if the resonance recently observed by CMS can be responsible for the deviation of the experimentally measured muon anomalous magnetic moment from the theoretical prediction., 11 pages, 2 figures, 2 tables

The vacuum effect on the yield and purity of lactide obtained by catalytic lactic acid oligomer depolymerization was investigated. As raw material for the lactic acid oligomer synthesis the L-lactic acid aqueous solution was used. It was shown that the highest yield of raw-lactide takes place via distillation under a vacuum. The raw-lactide in all fractions was purified by recrystallization from dry ethyl acetate. The highest yield of raw-lactide is observed at a vacuum of 10 ... 15 mbar. The distillation process of raw-lactide is complicated with chemical reactions. Control of the reaction, raw materials and products was performed using DTA, gel permeation chromatography, infrared spectroscopy and high performance liquid chromatography.

A method of oxidative mineralization of the salicylic acid and its derivatives as well as medicinal products containing salicylic acid as the active ingredient was investigated. Destruction of the organic compounds is possible both in the electrolyte under the oxidant, electrochemically formed in situ in the sulphuric acid solutions, and at the anode so. Simultaneously, at the cathode, reduction of the zinc ions, contained in a number of medicinal products, is possible. Final products of the oxidation are simple non-toxic organic compounds, carbon dioxide, and water. This process is the most effective in the 40% sulphuric acid at the current density of 0.5–0.8 A/cm2 and the temperature of 30–50 °C.

The objective following of the present study was to investigate the effect of different storage time and conditions on the stability of lactide. In this study the samples of lactide with different purities were stored under three various storage conditions and the compound integration was monitored for a period of 2 weeks. The storage conditions selected were (1) in the desiccator, (2) in the glove box under argon and (3) under ambient atmosphere. The purity of samples was performed on HPLC and Karl Fischer titration during all period of storage. It was shown that the initial purity of the lactide has a significant bearing on the lactide degradation.

We derive the multipole expansion of the magnetostatic field due to a localized current distribution, including contact terms up to the octopole term. Because of the contact fields, new multipole moments arise compared to the multipole expansion of just the external field. For the quadrupolar contact field, the new multipole moment is the anapole moment. For the octopolar contact field two new multipole moments arise, only one of which has been discussed previously. We discuss the dipolar, quadrupolar, and octopolar contact fields and the corresponding new multipole moments and give some applications to an extension of Jackson’s theorems for mean magnetic fields, parity violation and the anapole moment, lunar magnetism, and hyperfine interactions.

This article describes a method for the determination of residual solvents in lactide after its recrystallization using gas chromatography-mass spectrometry. The developed method is simple and linear. Study of specificity, accuracy, repeatability and reproducibility showed that the method is suitable for solving presumed problems. It allows identifying and quantifying the sufficiently small content (from 72 µg/ml) of solvents in lactide.

Contact terms for the electric dipole and magnetic dipole fields are well known. We give a simple derivation of the contact term of the electric quadrupole field. We then consider applications to the surface potential across a vapor/liquid interface of a nonpolar fluid, an extension of Jackson’s theorems for the mean electric fields for spherical regions of space with and without a fixed system of charges, and hyperfine interactions due to the electric quadrupole-monopole and quadrupole-quadrupole interactions of two bound particles of spin one or greater.

Hyperoxia and alkalemia, as a result of pulmonary hyperventilation and elevation of plasma DNA (pDNA), are seen during the first 24 h after ischemic stroke. In this study we have examined the correlation between pDNA and these blood parameters in health and stroke. Acid-base equilibrium, oxygen status, hemoglobin affinity to oxygen and concentration of pDNA in arterial blood were measured after the intravenous injection of homologous long-chain DNA to healthy rats and rats subjected to common carotid arterial occlusion. In addition the effect of adding homologous DNA to human and rat venous blood samples was studied in vitro. Hyperoxia, alkalemia, and an increase in hemoglobin affinity to oxygen were seen in rats with artificial stroke. A marked decrease in pulmonary hyperventilation and hemoglobin affinity to oxygen was observed after injection of homologous genomic DNA (10(-6) g/mL of blood). After the DNA injection, blood gas measurement and concentration of pDNA were correlated. Addition of DNA at a concentration of 10(-7) g/mL to venous blood samples in vitro increased oxygen saturation that disappeared when the dose of the DNA increased 10-fold. Thus, a change of pDNA concentration or size can alter acid-base equilibrium, oxygen status, and oxygen transport. These results may be important for a better understanding of the mechanisms of stroke and other diseases associated with the elevation of pDNA concentration, and they open the possibility of new therapeutic approaches.

Nonperturbative phenomena in quantum chromodynamics (QCD) and, in particular, confinement are reviewed. As an example of the treatment, an exact solution of the =2 supersymmetric Yang–Mills gauge theory is presented. Prospects for application of the duality idea in QCD are discussed.

The dependence of the Z-resonance shape on the location of the threshold of the N\bar{N} production (N is the 4th generation neutrino) is analyzed. The bounds on the existence of 4th generation are derived from the comparison of the theoretical expression for the Z-lineshape with the experimental data. The 4th generation is excluded at 95% C. L. for m_N

Russian Abstract: В статье анализируются особенности интеллектуализации труда в России в период восстановительного экономического роста, проблемы, связанные с реализацией данной закономерности.English Abstract: The article analyzes the features of intellectualization of labor in Russia during the recovery of economic growth, the problems associated with the implementation of this pattern.

Russian Abstract: В статье рассматривается понятие "качество жизни" и обосновывается целесообразность исследования качества жизни с позиций воспроизводственного подхода.English Abstract: In article the concept "quality of life" is considered and expediency of research of quality of life from positions of reproduction approach locates.

Russian Abstract: Авторы приводят дополнительную аргументацию для повышения роли образования в повышении качества жизни.English Abstract: The authors provide an additional argument for increasing the role of education in improving the quality of life.

A calculation of the cross section for the reaction νγ → νμ+μ− which is induced by the neutrino magnetic moment, is described in detail. The expression obtained for this cross section is used to determine the asymptotic behavior of the cross section for the reaction νN → νNμ+μ− by the Weiszacker-Williams method. It is shown that, upon going over from the nucleus involved to a structureless particle (for example, an electron), the resulting expression is doubled owing to integration with respect to the virtual-photon momentum over the region mμ≪Q≪Eν, where the Weiszacker-Williams approximation is not applicable. The method developed here makes it possible to obtain straightforwardly the known asymptotic expressions for the cross sections describing the reactions eN → eNμ+μ− and e+e− → W+W−e+e−.

Some aspects of local order in the amorphous state of a glassy polymer are discussed. The physical principles behind a cluster model involving the new concept of a structural defect are presented. A comparative analysis of three major approaches to describing the amorphous state of a polymer is given. It is shown that the cluster model is in reality a unified model which presents a new explanation for many qualitative results produced in the past on polymer structure and processes involved and which, unlike previous approaches, has the advantage of being quantitative. Possible future directions in polymer structure studies are outlined.

The review considers various manifestations of fractality in the description of the synthesis of macromolecules and the formation of the quasi-equilibrium state in polymers, fluctuation free volume, macromolecular frameworks, order parameters, and dissipative structures, acting as centres of shear stress in clusters. The possibility of numerical modelling of the properties of network polymers within the framework of fractal formalism is demonstrated. The methods for determination of the fractal dimension are described. The bibliography includes 248 references.

Data on the fractal forms of macromolecules, the existence of which is predetermined by thermodynamic nonequlibrium and by the presence of deterministic order, are considered. The limitations of the concept of polymer fractal (macromolecular coil), of the Vilgis concept, and of the possibility of modelling in terms of the percolation theory and diffusion-limited irreversible aggregation are discussed. It is noted that not only macromolecular coils but also the segments of macromolecules between topological fixing points (cross-links, entanglements) are stochastic fractals; this is confirmed by the model of structure formation in a network polymer. The bibliography includes 141 references.

We suggest returning to a different presentation of the e+e- \to \bar{f} f data off the Z peak, with the hope of using zeroes of specific amplitudes to enhance the sensitivity to new physics.

The Hamilton least action principle, a reformulated Maupertuis least action principle, and their reciprocals, are shown to be useful as direct methods for approximate solutions of dynamics problems. We discuss applications to trajectories of all types, i.e., periodic, quasiperiodic, chaotic, scattering, and arbitrary segments of arbitrary trajectories. The analogy with the standard technique used in quantum mechanics is very striking, especially in one of the reformulations (extremization of the mean energy), and in the calculational procedure (Rayleigh–Ritz type).

This lecture is based on a number of papers published during last three years by V. A. Novikov, M. I. Vysotsky and myself (several of them were coauthored also by N. A. Nekrasov, A. N. Rozanov and V. P. Yurov). The list of this papers will be given at the end of the lecture. Further references may be found in them.

The analysis of the newest data on the leptonic $Z$-decays and $m_W$ appears to reveal the first manifestations of electroweak radiative corrections. In fact, these data differ, at the level of $2\sigma$, from their electroweak Born values, while they agree, to within $1\sigma$, with the theoretical values which take the electroweak radiative corrections into account. Previous data were within $1\sigma$ in agreement with both sets of values., Comment: 10 pages, 2 figures, preprint CERN-TH.7217/94

A set of equations representing the $W/Z$ mass ratio and various observables of $Z$ decays in terms of $\bar\alpha \equiv\alpha (m_Z)$, $G_{\mu}$, $m_Z$, $m_t$, $m_H$, $\bar\alpha_{s} \equiv\alpha_{s} (m_Z)$, $m_b$ and $m_\tau$ (all other fermion masses being neglected) are compared with the latest data of the four LEP detectors, which at the level of one standard deviation coincide with their Born values. Our global fit gives: $m_t = 161^{+ 15 +16}_{-16 -22} \bar\alpha_{s} = 0.119 \pm 0.006 \pm 0.002$, where the central values correspond to $m_H = 300$ GeV, the first errors are statistical and the second ones represent shifts of the central values corresponding to $m_H = 1000$ GeV($+$) and 60 GeV($-$). The predicted mass of the top is smaller than in the recent fits by 4 GeV. The {\it predicted} values of $m_W/m_Z$ and the LEP observables, based on the fitted values of $m_t$ and $\bar{\alpha}_s$, show a weak dependence on $m_H$ and differ by several {\it predicted} standard deviations from the corresponding Born values. The uncertainties of the predicted values and their deviations from the corresponding Born values determine the experimental accuracy required to observe electroweak radiative corrections.

In his first paper on wave mechanics, Schrodinger presented a heuristic argument which led from the Hamilton–Jacobi equation through the quantum variational principle to his famous wave equation. In his second paper, Schrodinger withdrew this heuristic argument as “incomprehensible.” We show by using a recently generalized form of Maupertuis’ principle that Schrodinger’s original heuristic argument can be made more logical. Aside from pedagogical interest, this path is useful as a method of quantization of general mechanical systems.

We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler-Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's principle. Reciprocal principles are also derived for both the generalized Maupertuis and the Hamilton principles. The Reciprocal Maupertuis Principle is the classical limit of Schr\"{o}dinger's variational principle of wave mechanics, and is also very useful to solve practical problems in both classical and semiclassical mechanics, in complete analogy with the quantum Rayleigh-Ritz method. Classical, semiclassical and quantum variational calculations are carried out for a number of systems, and the results are compared. Pedagogical as well as research problems are used as examples, which include nonconservative as well as relativistic systems.

Strong immunosuppression occurs after severe traumatic brain injury (TBI) and most likely contributes substantially to the patient morbidity and mortality. However, the mechanisms of this immunosuppression are unknown. For the lowering of stressful factors, severe TBI was induced in anaesthetized rats. The lymphocyte subsets from 60 rats with severe TBI were analyzed using monoclonal antibody by the indirect immunofluorescence method. The blood of 30 rats without TBI was used as a control. When compared to the control group, the rats with TBI showed a remarkable reduction in the relative number of CD4(+), RT-Ia(+), Thy-1(+) and ICO-111(+) lymphocytes during the first 2 h after injury. Further reduction in the number of CD4(+) cells was determined in the rats during all the period of the experimental observation. The number of lymphocytes expressing membrane Thy-1 and ICO-111 antigens was significantly decreased 7 days after the trauma. The relative number of RT-Ia(+) lymphocytes was significantly reduced in rats with TBI during 14 days following the trauma. A significant decrease in the luminescence intensity of all the analyzed antigen-positive cells was also observed in rats with TBI. Between the 7th and the 14th days after the trauma a positive correlation between the number of Thy-1(+) PBLs and the number of RT-Ia(+) lymphocytes was determined. Similar results on lymphocyte immunophenotype were seen in patients with TBI. Thus, the cellular immune response is identical in patients and in animals with TBI. Severe brain traumatic injury leads to a reduced expression of cell surface antigens and causes a decrease in the number of antigen-positive lymphocytes and in the intensity of their luminescence.

Severe immunosuppression occurs after large thermal burns and probably contributes substantially to patient morbidity and mortality. The mechanism of immunosuppression is much unknown. T lymphocyte subsets from 45 severely patients with burns and 35 healthy donors were analyzed using monoclonal antibodies by indirect immunofluorescence method. Compared to healthy donors, patients with burns have shown a profound reduction in relative number of CD3(+) lymphocytes during the 24-h period following injury, which was accompanied by a decrease in CD4 but not CD8 subsets. Activated lymphocytes, while determined by the expression of CD25, CD26 and CD71, were insignificantly increased in patients with burns. The expression HLA DR was insignificantly decreased on peripheral blood lymphocytes from thermally injured patients. Additionally, the significant decrease of CD95 antigen expression was observed in all patients with burns. Also, significant decrease of the luminescence intensity in all analyzed antigens was observed in patients with burns. Numerous positive correlations between CD3(+), CD8(+), CD25(+), CD26(+) and CD71(+) cells were revealed, especially during the first week after thermal trauma. We conclude that the thermal injury produces a profound relative CD3(+) and CD4(+) cell lymphopenia with signs of moderate lymphocyte activation.

A "toy model" of molecular evolution of sequences in copolymers is proposed and implemented using a molecular-dynamics-based algorithm. The model involves coupling of conformation-dependent and sequence-dependent properties. It is shown that this model allows the realization of two main possibilities: ascending and descending branches of evolution (in terms of information content of a sequence), depending on the interaction parameters shaping the conformation of a polymer globule. The problem of adequate description of information complexity of copolymer sequences is studied. It is shown that Shannon's entropy or compressibility of a sequence gives preference to random sequences and therefore cannot be applied for this purpose. On the other hand, the Jensen-Shannon divergence measure turns out to give the description of information complexity which corresponds to our intuitive expectations. In particular, this characteristic can adequately describe two branches of evolution mentioned above, exhibiting a singularity on the boundary of these regimes.

A simple graphical method is presented for extracting limits on the masses of the top quark and of the Higgs boson from precision electroweak data.

Data on the fractal forms of macromolecules, the existence of which is predetermined by thermodynamic nonequlibrium and by the presence of deterministic order, are considered. The limitations of the concept of polymer fractal (macromolecular coil), of the Vilgis concept, and of the possibility of modelling in terms of the percolation theory and diffusion-limited irreversible aggregation are discussed. It is noted that not only macromolecular coils but also the segments of macromolecules between topological fixing points (cross-links, entanglements) are stochastic fractals; this is confirmed by the model of structure formation in a network polymer. The bibliography includes 141 references.

Contribution to A.D.Sakharov memorial volume. A detailed review of the electroweak radiative corrections to the Z-boson decays in the framework of the Minimal Standard Modelm (MSM) is presented. After a short historical introduction we describe the optimal parametrization of the MSM, especially of the Born approximation, and derive expressions for the one-loop electroweak corrections. Finally a global fit of all relevant experimental data is performed, resulting in fitted values of the top-quark mass, m_t, and strong coupling constant /alpha_s. Allowed range for the value of the Higgs mass, m_H, is discussed. Various details of calculations are described in 16 appendices., 98 pages,21 EPS and PS figures,uses epsf.sty, separate file with the tared, compressed and uuencoded figures is awailable at http://wwwtheor.itep.ru/~vysotsky/figures.uu

The electroweak corrections to the Z -boson hadronic width are presented in a simple analytical form for the width itself, Λ h , for its ratio to the leptonic width, R l = Λ h Λ l , for the Λ b Λ h ratio, and for the total width Λ Z . The rational parametrization, advocated in our recent papers on leptonic decays, simplifies the analysis of the hadronic decays too. There are two main results of this analysis: (1) All electroweak precision measurements agree within 1 σ with the electroweak Born approximation if the gluon coupling constant α s = 0.12 . Thus the electroweak radiative corrections have not been observed experimentally. The unexpected smallness of electroweak radiative corrections is caused by the mutual cancellation of the large positive contribution of a heavy top quark and the large negative contribution of all other virtual particles. (2) With electroweak radiative corrections being taken into account, the value of α s extracted from the experimental value of Λ Z differs by ⩾ 3σ from that obtained from R l , if m t ⩾ 200 GeV; they agree within 1σ if m t ⩾ 150 GeV. Thus a low upper limit on m t can be obtained from hadronic decays of the Z -boson alone, even without data on its leptonic decays.

The data of the CHARM II and of the ALEPH, DELPHI, L3 and OPAL Collaborations are compared in the framework of (α(mZ), mZ, Gμ, mt, mH)-parametrization of the electroweak radiative corrections. The comparison shows that the physical meaning of the CHARM II results is more significant than was stated in the original publication of the CHARM Collaboration. In particular, CHARM II is very sensitive to the Z boson coupling to the muon neutrinos.