arXiv subjects

Alexander Karpov

Publications and source records attributed to Alexander Karpov.

7 recordsLinked to original sources

arXiv2026

Improved lower bounds for the maximum size of Condorcet domains

Condorcet domains are sets of linear orders with the property that, whenever voters' preferences are restricted to the domain, the pairwise majority relation (for an odd number of voters) is transitive and hence a linear order. Determining the maximum size of a Condorcet domain, sometimes under additional constraints, has been a longstanding problem in the mathematical theory of majority voting. The exact maximum is only known for $n\leq 8$ alternatives. In this paper we use a structural analysis of the largest domains for small $n$ to design a new inductive search method. Using an implementation of this method on a supercomputer, together with existing algorithms, we improve the size of the largest known domains for all $9 \leq n \leq 20$. These domains are then used in a separate construction to obtain the currently largest known domains for $21 \leq n \leq 25$, and to improve the best asymptotic lower bound for the maximum size of a Condorcet domain to $\Omega(2.198139^n)$. Finally, we discuss properties of the domains found and state several open problems and conjectures.

cs.DM↗

arXiv2024

Local Diversity of Condorcet Domains

Several of the classical results in social choice theory demonstrate that in order for many voting systems to be well-behaved the set domain of individual preferences must satisfy some kind of restriction, such as being single-peaked on a political axis. As a consequence it becomes interesting to measure how diverse the preferences in a well-behaved domain can be. In this paper we introduce an egalitarian approach to measuring preference diversity, focusing on the abundance of distinct suborders one subsets of the alternative. We provide a common generalisation of the frequently used concepts of ampleness and copiousness. We give a detailed investigation of the abundance for Condorcet domains. Our theorems imply a ceiling for the local diversity in domains on large sets of alternatives, which show that in this measure Black's single-peaked domain is in fact optimal. We also demonstrate that for some numbers of alternatives, there are Condorcet domains which have largest local diversity without having maximum order.

econ.TH↗

arXiv2023

Parameters of nucleon densities and the Coulomb barrier in heavy-ion collisions

When modeling nuclear processes which occur in heavy-ion reactions, it is necessary to calculate the potential energy of interaction between two nuclei. One of the main features determining the dynamics of the nucleus-nucleus collision is the Coulomb barrier, the knowledge of which is especially important when low- and intermediate-energy reactions are being studied. Our goal is to establish a parameterization of nucleon density distributions for calculation of the nucleus-nucleus double-folding potential in nuclear reactions. Special attention is paid to the description of the Coulomb barrier. The study analyzes experimental data on charge radii, diffuseness, and neutron skin thickness of atomic nuclei. The nucleus-nucleus potential is calculated in the framework of the double-folding method with the effective nucleon-nucleon interaction taken in the form of the zero-range Migdal potential. Based on this analysis and comparison with the Bass potential, parameters of nucleon density distributions are fitted to reproduce the Coulomb barrier. A method for correcting the parameters of nucleon densities to reproduce the Coulomb barrier with the double-folding potential is proposed. The presented way to correct nucleon densities allows obtaining a satisfactory description of the Coulomb barrier that is important for modeling near-barrier collisions of heavy ions.

nucl-th↗

arXiv2023

Bipartite peak-pit domains

In this paper, we introduce the class of bipartite peak-pit domains. This is a class of Condorcet domains which include both the classical single-peaked and single-dipped domains. Our class of domains can be used to model situations where some alternatives are ranked based on a most preferred location on a societal axis, and some are ranked based on a least preferred location. This makes it possible to model situations where agents have different rationales for their ranking depending on which of two subclasses of the alternatives one is considering belong to. The class of bipartite peak-pit domains includes most peak-pit domains for $n\leq 7$ alternatives, and the largest Condorcet domains for each $n\leq 8$. In order to study the maximum possible size of a bipartite peak-pit domain we introduce set-alternating schemes. This is a method for constructing well-structured peak-pit domains which are copious and connected. We show that domains based on these schemes always have size at least $2^{n-1}$ and some of them have sizes larger than the domains of Fishburn's alternating scheme. We show that the maximum domain size for sufficiently high $n$ exceeds $2.1973^n$. This improves the previous lower bound for peak-pit domains $2.1890^n$ from \cite{karpov2023constructing}, which was also the highest asymptotic lower bound for the size of the largest Condorcet domains.

cs.DM↗

arXiv2019

Role of charge equilibration in multinucleon transfer in damped collisions of heavy ions

In this work, the charge equilibration process has been analyzed within the Langevin-type dynamical approach. Its duration and energy dependence are discussed. We have analyzed the isotopic distributions of final products obtained in the isospin-asymmetric 58Ni,40Ca + 208Pb reactions. Comparison of 58Ni,64Ni + 208Pb systems have been done in order to analyze the final yields of neutron-rich heavy nuclides.

nucl-th↗

arXiv2018

Analysis of multinucleon transfer reactions involving spherical and statically deformed nuclei using a Langevin-type approach

An increasing interest in multinucleon transfer processes in low-energy deep inelastic (damped) collisions of heavy ions appeared in recent years is due, in part, to by the possibility of using them as a method of production of heavy neutron-enriched nuclei. Possible promising projectile-target combinations include nuclei deformed in the ground state (e.g., actinides). Mutual orientations of such the nuclei in the entrance channel of the reaction may significantly influence the reaction dynamics. Available experimental data on multinucleon transfer reactions with statically deformed as well as spherical heavy nuclei 144Sm + 144Sm, 154Sm + 154Sm, 160Gd + 186W, and 208Pb + 208Pb/238U have been analyzed within the developed model. A good agreement of the calculated quantities with the corresponding experimental data is reached. Special attention in the paper is paid to analysis of production possibility of the neutron-enriched isotopes of heavy and superheavy elements in multinucleon transfer processes in the 238U + 238U/248Cm/254Es collisions.

nucl-th↗

arXiv2012

Future of superheavy element research: Which nuclei could be synthesized within the next few years?

Low values of the fusion cross sections and very short half-lives of nuclei with Z$>$120 put obstacles in synthesis of new elements. Different nuclear reactions (fusion of stable and radioactive nuclei, multi-nucleon transfers and neutron capture), which could be used for the production of new isotopes of superheavy (SH) elements, are discussed in the paper. The gap of unknown SH nuclei, located between the isotopes which were produced earlier in the cold and hot fusion reactions, can be filled in fusion reactions of $^{48}$Ca with available lighter isotopes of Pu, Am, and Cm. Cross sections for the production of these nuclei are predicted to be rather large, and the corresponding experiments can be easily performed at existing facilities. For the first time, a narrow pathway is found to the middle of the island of stability owing to possible $β^+$-decay of SH isotopes which can be formed in ordinary fusion reactions of stable nuclei. Multi-nucleon transfer processes at near barrier collisions of heavy (and very heavy, U-like) ions are shown to be quite realistic reaction mechanism allowing us to produce new neutron enriched heavy nuclei located in the unexplored upper part of the nuclear map. Neutron capture reactions can be also used for the production of the long-living neutron rich SH nuclei. Strong neutron fluxes might be provided by pulsed nuclear reactors and by nuclear explosions in laboratory conditions and by supernova explosions in nature. All these possibilities are discussed in the paper.

nucl-th↗