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Properties of Boolean Functions with Extremal Number of Prime Implicants

Journal of Applied and Industrial Mathematics 2022年第1期16卷 8-21页

作者： Chukhrov, I.P. Institute of Computer Aided Design Russian Academy of Sciences Moscow123056 Russia

Abstract: The known lower bound for the maximum number of prime implicants (maximal faces) ofa Boolean function differs from the upper bound by a factor of (Formula presented.) and is asymptotically attained on a symmetric belt function. To study theproperties of extremal functions, we define subsets of functions that have the minimum andmaximum vertices of the maximal faces in the belts (Formula presented.), respectively. Here the fraction of the number of vertices in each layer is atleast (Formula presented.), and for any such vertex the ratio of the number of maximal faces to themaximum possible number is at least (Formula presented.). Conditions on the parameters (Formula presented.) and (Formula presented.) are obtained under which the number of prime implicants of a Booleanfunction in such a subset is equal to the maximum value asymptotically or in the order of growth. © 2022, Pleiades Publishing, Ltd.

关键词： Boolean functions

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About the Formation of Polygonal Structures over the Rotating Disk

About the Formation of Polygonal Structures over the Rotatin...

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2023 Applied Mathematics, Computational Science and Mechanics: Current Problems, AMCSM 2023

作者： Maksimov, Fedor A. Institute of Computer Aided Design of the Russian Academy of Sciences Moscow Russia

ISBN: (纸本)9798350348576

The problem of viscous gas flow over a rotating disk is investigated using numerical simulation. The conditions in which axisymmetric flow is destroyed with the formation of almost regular polygonal structures are considered. With a fixed size of a disk rotating at the same speed, the viscosity and the thickness of the layer above the disk determine the flow. The flow maps with a sequential change from an octagon to a quadrilateral were obtained as a result of numerical experiments. © 2023 IEEE.

关键词： Navier Stokes equations

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Implementing the Peano and WKB Approaches to Find Vibrational Modes and Frequencies of a Thin Rod with Variable Parameters

Implementing the Peano and WKB Approaches to Find Vibrationa...

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2024 International Conference Days on Diffraction, DD 2024

作者： Zakharov, Dmitrii D. Nikitin, Ilya S. Institute of Computer Aided Design Russian Academy of Sciences Moscow123056 Russia Moscow127994 Russia

ISBN: (纸本)9798331511722

The free-bending oscillations of a thin rod under var-ious conditions at its ends are considered. The parameters of stiffness and inertia depend on the longi-Tudinal coordinate. The respective solutions to the Bernoulli-Euler equation are obtained using Peano and WKB methods. Dispersion equations are inves-Tigated. As shown, the rarely used Peano method is an efficient tool for this problem and allows one to find modes and frequencies. The comparison demonstrates that the WKB method predicts frequencies satisfactorily even by the leading order term, but it is inaccurate in calculating modes. The Peano approach can be used to calculate rod made of functionally graded material with variable Young's mod-ulus and mass density, and also with variable pro-files. Numerical examples are presented in the context of practical assessment of the strength loss in an experimental study of alloys subjected to cyclic point loading at the resonance of bending vibrations. © 2024 IEEE.

关键词： Euler equations

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Mathematical modeling of the vortices couple dynamics in a stratified fluid 16

Mathematical modeling of the vortices couple dynamics in a s...

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16th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2024

作者： Gushchin, V.A. Smirnova, I.A. Institute for Computer Aided Design RAS 84/32-14 Profsoyuznaya str. Moscow Russia

The problem of the dynamics of the vortex couple in stratified fluid is considered. The couple is two vortexes, arranged symmetrically relative to the vertical axis, but with the opposite direction of rotation, so that it begins to rise upwards. The mathematical model of a couple of vortices in a viscous stratified medium was studied. Salinity is chosen as a stratifying component, just as it can be implemented in the laboratory. The task is described by the Navier-Stokes equations in the Boussinesq approximation. To solve the problem, the SMIF method is used, of course, the finite different scheme of which has such properties as the second order of approximation on spatial variables, minimal scheme dissipation and dispersion, performance in wide range of Reynolds and Froude numbers and, most importantly, when solving wave processes are a property of monotony. The dynamics of such a couple are studied depending on its geometric sizes, the intensity of the vortexes and the depth of their initial immersion. © 2024 institute of Physics Publishing. All rights reserved.

关键词： Navier Stokes equations

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Numerical Modeling of Fatigue Fracture Based on the Nonlocal Theory of Cyclic Damage

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Mathematical Models and computer Simulations 2024年第5期16卷 655-666页

作者： Burago, N.G. Nikitin, I.S. Nikitin, A.D. Stratula, B.A. Institute for Computer Aided Design Russian Academy of Sciences Moscow Russian Federation Ishlinsky Institute of Problems in Mechanics Russian Academy of Sciences Moscow Russian Federation

Based on a multimode model of fatigue failure, a numerical method for calculating the kinetics of fracture, nucleation, and development of fatigue quasi-cracks is proposed. For specimens with notches having different curvature radii, processes of high-frequency cyclic tension-compression with different cycle stress ratios are considered. The convergence of numerical solutions for the processes of nucleation and development of quasi-cracks, as well as for durability, is ensured by the use of a nonlocal damage function near the fracture zones. The effectiveness of the developed numerical procedure is demonstrated by the computational experiments. The results of calculations of fatigue failure are presented for various modes of cyclic loading with different cycle stress ratios, taking into account artificially inserted defects. © Pleiades Publishing, Ltd. 2024.

关键词： convergence of numerical solution cyclic damage model high-cycle fatigue high-frequency tensile-compression tests mesh refinement nonlocal damage criterion notched specimens very high cycle fatigue

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computer System for Forming Compositions and Modeling the Properties of Secondary Polymer Materials 5

Computer System for Forming Compositions and Modeling the Pr...

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5th International Conference on Control Systems, Mathematical Modeling, Automation and Energy Efficiency, SUMMA 2023

作者： Chistyakova, Tamara Balabekovna Novozhilova, Inna Vasilievna Razygraev, Aleksandr Sergeevich Goncharova, Tatyana Sergeevna Saint-Petersburg State Institute of Technology Department of Computer-Aided Design and Control Systems Saint Petersburg Russia

ISBN: (纸本)9798350309126

The computer system for forming compositions and modeling the secondary polymer materials properties is described in the article. The polymer compositions are formed using a customizable dataware, which includes a polymer wastes database and a knowledge base for recycling polymers into useful polymer products The knowledge base is developed using a product-frame model for representing knowledge about polymers and their compatibility. Modeling and research of the secondary polymers properties (strength, elasticity and density) is carried out based on the mathematical models. The result of the modeling system is a technological map for the composite polymer mixture synthesis and the production of a useful polymer product. The map includes data on the recipe, physicochemical and technological properties of polymers as secondary raw materials, polymer composition, hardware and technological design of the process, values of technological controlled variables of individual stages of processing. The use of a modeling system in production makes it possible to reduce the time required to solve the problem of selecting compositions, as well as reconfiguring production for a new task, improve the consumer characteristics of polymer products and reduce defects. © 2023 IEEE.

关键词： Materials properties

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On the Influence of Spatial Distribution of Reflectors on the Initiation of Gas Detonation

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Lobachevskii Journal of Mathematics 2025年第1期46卷 273-282页

作者： Lopato, A.I. Institute for Computer Aided Design of the Russian Academy of Sciences Moscow 123056 Russian Federation Moscow Institute of Physics and Technology Moscow oblast Dolgoprudny 141701 Russian Federation Institute of Computer Sciences and Mathematical Modeling Sechenov First Moscow State Medical University Moscow 119991 Russian Federation

Abstract: The work is devoted to the mathematical modeling of the initiation of gas detonation in a channel with a profiled end wall. The two-dimensional geometry of the channel filled with a model hydrogen-oxygen mixture is considered. The mathematical model is based on the system of Euler equations supplemented by Arrhenius kinetics. Numerical experiments are carried out using triangular computational grids and the finite volume method. The formation of detonation waves occurs as a result of reflection of the incident plane shock wave with a Mach number of 2.45 from the end of the channel consisting of two elliptical fragments and sections of the flat wall. The distance between the elliptical sections varied widely to study the influence of this parameter on the processes of ignition of the mixture and formation of detonation waves. A nonlinear dependence of the detonation initiation time on this parameter was obtained. The nonlinear dependence is associated with different degrees of influence of factors affecting the intensity of the process of mixture combustion and the formation of detonation waves. © Pleiades Publishing, Ltd. 2025.

关键词： compression waves detonation initiation mixture combustion shock wave reflection unstructured triangular grids

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Intelligent Technologies for designing Information Systems for Controlling the Polymer Waste Processing into Useful Technical Products

Intelligent Technologies for Designing Information Systems f...

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2023 Seminar on Information Systems Theory and Practice, ISTP 2023

作者： Chistyakova, Tamara B. Paukin, Oleg A. Novozhilova, Inna V. Razygraev, Aleksandr S. Goncharova, Tatyana S. Department of Computer-Aided Design and Control Systems St. Petersburg State Institute of Technology Saint Petersburg Russia

ISBN: (纸本)9798350345193

The article describes intelligent technologies used in the design of an information system for controlling the polymer waste processing into useful technical products. The basis of the system is a configurable information model that includes a database of characteristics of polymer waste and a knowledge base of the processes of their recycling into technical products (containers, packing materials, etc.). The knowledge base is built using a production-frame model for the representation of unformalized knowledge about the polymers compatibility, the quantitative ratio of the components of a composite mixture, waste processing methods to obtain a homogeneous mixture with specified properties (strength, resistance to aggressive substance, etc.). The result of the functioning of the system is the formation of a technological map of the production of a technical product, including information about the formulation and synthesis process of the polymer composition, specifications of the hardware design and the values of the technological modes of the production stages. Testing of the system according to the LLC "Plastic processing plant named after "Komsomolskaya Pravda" on the basis of the Polymer Ecology Training Center of SPSIT confirmed its operability and the possibility of use at polymer industry enterprises. The use of the system allows you to reduce the time spent on solving the problem of reconfiguration of production and selection of compositions, reduce defects and improve the consumer characteristics of products. ©2023 IEEE.

关键词： Intelligent systems

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design and Simulation of Compact Array Antenna for mm Wave Wireless Biomedical Systems

Biomedical Materials & Devices

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Biomedical Materials & Devices 2025年 1-15页

作者： Raj, Arun Mandal, Durbadal Computer Aided Electromagnetic Design Laboratory ECE-Department National Institute of Technology Durgapur India

The contemporary communication landscape necessitates antennas with broad bandwidth, high gain, and reduced dimensions for optimal performance across diverse frequency ranges. An innovative fractal array antenna is designed with a hybrid three-way power divider; the antenna achieves a broad, long-range directional beam within a compact 100 mm2 area using a 1.6 mm Roger substrate. Moreover, the proposed antenna exhibits a wide bandwidth notch around 80 GHz, boasting a 37.61 GHz bandwidth and 48.87% fractional coverage across the 24–100 GHz spectrum. The Proposed antenna design comprises two symmetry and ten-element fractal antennae resonating at 80 GHz, spanning a frequency range from 58.14 to 95.75 GHz. With a compact size, it attains a peak gain of 8.83 dBi and a nearly matched impedance of about 50 Ohm, indicated by a voltage standing wave ratio of approximately 1.027, respectively. In mm-wave applications, the antenna demonstrates enhanced radiation characteristics concerning phi = 0°, 90°, and theta 90° orientations. The proposed antenna, with a minimum reflection coefficient of − 37.94 dB and isotropic sensitivity of − 2.15 dB, demonstrates exceptional impedance matching and signal reception, essential for wireless biomedical systems. Operating efficiently in the 80 GHz band supports high data rate transmission and low-latency communication, which are vital for real-time health monitoring, implantable devices, and body area networks. The high front-to-back ratio of 22 dB ensures minimized interference and enhanced directional performance, crucial in densely populated environments like hospitals with diverse communication needs ranging from short-range diagnostics to long-range telemetry. At the same time, its compact structure makes it suitable for integration into wearable or implantable platforms. The robust radiation characteristics across multiple orientations support mobility and adaptability

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Live Feedback for Training Through Real-Time Data Visualizations: A Study with League of Legends

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Proceedings of the ACM on Human-computer Interaction 2022年第CHIPLAY期6卷 1–23页

作者： Rijnders, Frans Wallner, Günter Bernhaupt, Regina Department of Industrial Design Eindhoven University of Technology Eindhoven Netherlands Institute of Computer Graphics Johannes Kepler University Linz Linz Austria

With competitive gaming on the rise, players have developed an increased interest in data-driven feedback of their in-game performance. In many cases, this feedback is presented visually post-play but live companions that provide real-time analytics are gaining more and more attention. However, the design of such systems poses different requirements which have been little explored from a scholarly point of view. In this paper, we report on a study of two visualizations - a physical and digital one - providing live feedback to League of Legends players designed based on a community survey (N= 175) and expert input. We further discuss results of a qualitative evaluation with 13 players and an expert, touch upon potential benefits and drawbacks of physical and digital implementations, and present derived design considerations and challenges for such real-time data visualizations, revolving around issues of information density, contextualization, representation, and a diverse range of user needs. © 2022 ACM.

关键词： Visualization

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