Next-to-leading power two-loop soft functions for the Drell-Yan process at threshold

We calculate the generalized soft functions at $$ \mathcal{O} $$ O ($$ {\alpha}_s^2 $$ α s 2 ) at next-to-leading power accuracy for the Drell-Yan process at threshold. The operator definitions of these objects contain explicit insertions of soft gauge and matter fields, giving rise to a dependence on additional convolution variables with respect to the leading power result. These soft functions constitute the last missing ingredient for the validation of the bare factorization theorem to NNLO accuracy. We carry out the calculations by reducing the soft squared amplitudes into a set of canonical master integrals and we employ the method of differential equations to evaluate them. We retain the exact d-dimensional dependence of the convolution variables at the integration boundaries in order to regulate the fixed-order convolution integrals. After combining the soft functions with the relevant collinear functions, we perform checks of the results at the cross-section level against the literature and expansion-by-regions calculations, at NNLO and partly at N3LO, finding agreement.

FECOCRNIMOTIW HIGH-ENTROPIC COATINGS AND THEIR PROPERTIES

The objects of study were high-entropy coatings of the composition FeCoCrNiMoTiW made by mechanical alloying. It is shown that the hardness of most stainless steels is 1.5-2 times less than high-entropy coatings, and the dry friction coefficients are in the range of 0.08-0.16. Such a difference in the coefficients of friction for high-entropy coatings is due to their nanostructural feature and the manifestation of the dimensional dependence of their properties. Theoretically, we consider the question of the response of the electron subsystem in high-entropy alloys to an external action during friction from the standpoint of nonequilibrium statistical thermodynamics. As a result, it was shown that the coefficient of friction of the coating decreases with the use of a high-entropy alloy and with a decrease in the surface energy of the coating.

Forecast of mechanical properties of metal products

Introduction. The mechanical properties of the metal depend primarily on their chemical composition and structure. The structure of metal materials is formed under the influence of different temperature modes of manufacture and cooling. Models for predicting the mechanical properties of steels and cast irons are based on the influence of chemical composition and structure. The paper considers an approach that allows to evaluate the mechanical properties of rolling (C) cast iron rolls with a pearlitic (P) matrix depending on the complex influence of the elements of their chemical composition. Materials and methods. The working area of СПХН roll cast iron samples from the surface up to 50 mm doped with chromium (X) and nickel (H) was investigated. The carbide content varied from 10 to 15 %; and lamellar graphite did not exceed 2 %. The results of the experiment. In the work for modeling the mechanical characteristics of cast iron rolls used the method of planning experiments. The choice of this technique is due to the multi-parameter technology of production of solid metal casting. The application of this technique allowed to obtain models for predicting the mechanical characteristics of roll cast iron SPHN depending on the influence of the elements of the chemical composition of the rolls (C, Si, Mn, P, S, Cr, Ni). The error in predicting the tensile strength sВ, bending strength sзгин bending and hardness according to the Shore HSD method did not exceed 5,89 %. When checking the models for convergence of results by Fisher's criterion at a critical value of Fcrit = 2,400 for sВ, this coefficient was 1,249; for sзгин fold was 1,289 and for HSD - 1,012. To analyze the effect of carbon on mechanical characteristics, two-dimensional dependence plots are constructed. Conclusions. Within the operating values of the parameters of the chemical composition of cast iron rolling mills СПХН-45 in accordance with existing regulations, a forecast of their mechanical characteristics within the allowable limits of error of experimental data. The results of the work allow to obtain mathematical models in the process of production of rolls of the СПХН brand to quickly establish their chemical composition within the standard technology in accordance with the customer's requirements for these mechanical characteristics. In addition, the obtained models can predict these characteristics of the manufactured rolls with minimal material and time costs. Keywords: rolling mills; elements of chemical composition; mechanical characteristics; multiparameter technology

Modeling of Stochastic Wind Based on Operational Flight Data Using Karhunen–Loève Expansion Method

Wind has a significant influence on the operational flight safety. To quantify the influence of the wind characteristics, a wind series generator is required in simulations. This paper presents a method to model the stochastic wind based on operational flight data using the Karhunen–Loève expansion. The proposed wind model allows us to generate new realizations of wind series, which follow the original statistical characteristics. To improve the accuracy of this wind model, a vine copula is used in this paper to capture the high dimensional dependence among the random variables in the expansions. Besides, the proposed stochastic model based on the Karhunen–Loève expansion is compared with the well-known von Karman turbulence model based on the spectral representation in this paper. Modeling results of turbulence data validate that the Karhunen–Loève expansion and the spectral representation coincide in the stationary process. Furthermore, construction results of the non-stationary wind process from operational flights show that the generated wind series have a good match in the statistical characteristics with the raw data. The proposed stochastic wind model allows us to integrate the new wind series into the Monte Carlo Simulation for quantitative assessments.

Learning Vine Copula Models for Synthetic Data Generation

A vine copula model is a flexible high-dimensional dependence model which uses only bivariate building blocks. However, the number of possible configurations of a vine copula grows exponentially as the number of variables increases, making model selection a major challenge in development. In this work, we formulate a vine structure learning problem with both vector and reinforcement learning representation. We use neural network to find the embeddings for the best possible vine model and generate a structure. Throughout experiments on synthetic and real-world datasets, we show that our proposed approach fits the data better in terms of loglikelihood. Moreover, we demonstrate that the model is able to generate high-quality samples in a variety of applications, making it a good candidate for synthetic data generation.

Dimension-Free Error Bounds from Random Projections

Learning from high dimensional data is challenging in general – however, often the data is not truly high dimensional in the sense that it may have some hidden low complexity geometry. We give new, user-friendly PAC-bounds that are able to take advantage of such benign geometry to reduce dimensional-dependence of error-guarantees in settings where such dependence is known to be essential in general. This is achieved by employing random projection as an analytic tool, and exploiting its structure-preserving compression ability. We introduce an auxiliary function class that operates on reduced dimensional inputs, and a new complexity term, as the distortion of the loss under random projections. The latter is a hypothesis-dependent data-complexity, whose analytic estimates turn out to recover various regularisation schemes in parametric models, and a notion of intrinsic dimension, as quantified by the Gaussian width of the input support in the case of the nearest neighbour rule. If there is benign geometry present, then the bounds become tighter, otherwise they recover the original dimension-dependent bounds.