Article
Physics, Multidisciplinary
Ryan M. McMullen, Michael C. Krygier, John R. Torczynski, Michael A. Gallis
Summary: This study compares the Navier-Stokes equations with molecular-gas-dynamics simulations and finds that the equations fail to describe the dissipation range of turbulent gas flows due to the neglect of thermal fluctuations. The research also reveals that the spectra in molecular-gas-dynamics simulations exhibit quadratic growth with wave number in the dissipation range, in contrast to the exponential decay in the Navier-Stokes spectra. Furthermore, the transition to quadratic growth occurs at length scales larger than the gas molecular mean free path.
PHYSICAL REVIEW LETTERS
(2022)
Article
Physics, Multidisciplinary
Naveed Merchant, Jeffrey D. Hart
Summary: A new nonparametric test of equality of two densities is proposed in this study. The test statistic is an average of log-Bayes factors constructed from kernel density estimates. The study demonstrates how to choose prior densities for the bandwidths of the kernel estimates to accurately calculate the log-Bayes factors. Critical values of the test statistic are determined through a permutation distribution based on the data. An attractive feature of the test is that when the critical value is set to 0, both type I and type II error probabilities tend to 0 as sample sizes increase.
Article
Mathematics
Oscar Dominguez, Sergey Tikhonov
Summary: In this paper, we study sharp pointwise inequalities for maximal operators, specifically strengthening DeVore's inequality for smoothness moduli and a logarithmic variant of Bennett-DeVore-Sharpley's inequality for rearrangements. As a consequence, we improve the classical Stein-Zygmund embedding and establish new inequalities and estimates. Our approach is based on limiting interpolation techniques.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics, Applied
Abhishek Ghosh, Vivek Tewary
Summary: In this article, we present Hessian estimates for Kolmogorov-Fokker-Planck operators in non-divergence form in several Banach function spaces. Our approach relies on a representation formula and recently developed sparse domination techniques in harmonic analysis. When applied to weighted Lebesgue spaces, our result provides sharp quantitative Hessian estimates for the Kolmogorov-Fokker-Planck operators.
ANNALI DI MATEMATICA PURA ED APPLICATA
(2023)
Article
Mathematics, Applied
Mohammad Reza Haddadi, Vahid Parvaneh, Monica Bota
Summary: In this study, we provide an iterative algorithm for fixed point issues in vector spaces. We demonstrate that the presented algorithm performs better under weaker conditions compared to the Ishikawa technique in Banach spaces. By comparing the convergence behavior of iterations and considering several offered cases, we support the major findings.
Article
Physics, Fluids & Plasmas
Nandita Pan, Supratik Banerjee
Summary: In the study of inertial range energy transfer in three-dimensional fully developed binary fluid turbulence under the assumption of statistical homogeneity, exact relations corresponding to the energy cascade were derived using two-point statistics. The study found that the exact relation in binary fluid turbulence differs from that of incompressible magnetohydrodynamic turbulence, and speculated an inverse cascade of energy under certain conditions. An alternative form of the exact relation was also proposed, predicting a k-3/2 law for the turbulent energy spectrum.
Article
Mathematics, Applied
Eminjan Sabir, Jixiang Meng
Summary: This paper discusses the concepts of Hamiltonian connection and spanning k-connectedness in graph theory, as well as the generalization of some theorems and new results related to them.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Astronomy & Astrophysics
P. Simon, F. Sahraoui
Summary: This study presents a more general method for deriving laws governing turbulent isentropic flow, demonstrating that known MHD exact laws are specific cases of this general law. The difference between different forms of MHD exact laws lies in certain source terms and the explicit form of the flux term dependent on internal energy.
ASTROPHYSICAL JOURNAL
(2021)
Article
Astronomy & Astrophysics
Merced Montesinos, Diego Gonzalez
Summary: The article introduces new topological invariants in four dimensions, which are generalizations of the Nieh-Yan topological invariant, obtained through a systematic method. The explicit expressions of the new 4-forms for particular choices of 1-forms are provided, showing that the Nieh-Yan form arises as a particular case.
Article
Mathematics
Mohamed Abd El-Hady Kassem, Huda M. Alshanbari
Summary: In this study, we introduce new concepts of higher-order type-I functions and higher-order pseudo-convexity type-I functions. The application of sublinear functionals to these concepts is crucial to our main findings. Furthermore, we establish and study six new types of higher-order duality models and programs for multiple objective nonlinear programming problems under these concepts. Additionally, we use these concepts to formulate and prove the theorems of weak duality, strong duality, and strict converse duality for these new six types of higher-order model programs.
Article
Mathematics, Applied
Jian-Feng Zhu, Antti Rasila
Summary: This paper studies the spaces of Holder continuous functions and differentiable functions on the unit disk, investigating their norm estimates and properties for different values of p. By utilizing the Sobolev embedding theorem, the properties of functions in different spaces are derived.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Biochemical Research Methods
Joao Paulo Pereira Zanetti, Lucas Peres Oliveira, Leonid Chindelevitch, Joao Meidanis
Summary: This study aims to generalize the rank distance model by using a matrix representation of genomes, in order to accommodate genomes with different gene content. The rank distance is extended by adding insertions, deletions, and substitutions, as well as using the rank-indel distance which only includes insertions and deletions of entire chromosomes. The results show that rank distances are more robust for comparing distantly related species.
Article
Mechanics
Francesco Coscarella, Giuseppe Curulli, Nadia Penna, Roberto Gaudio
Summary: In the last two decades, numerous studies have focused on using predictive formulas to assess the maximum scour depth produced by propeller jets. However, most of the existing formulas are based on empirical arguments and may have scale issues and inconsistencies with the physics of the scouring problem. Recent studies have applied the phenomenological theory of turbulence and sediment incipient-motion theory to derive predictive formulas for different scour cases. In this study, a new physically based model is proposed that incorporates all relevant parameters controlling the scouring process induced by propeller rotation. The model is validated against laboratory-scale experimental data, showing good agreement with literature predictions and lower scattering levels compared to empirical formulas.
Article
Mathematics, Applied
Sergio Polidoro, Annalaura Rebucci, Bianca Stroffolini
Summary: In this study, we investigate the regularity properties of a second order linear operator with constant coefficients, including Hormander's hypoellipticity condition and the continuity of second order derivatives for Dini continuous functions. We also consider the case of coefficients being Dini continuous functions and establish a Taylor formula for solutions under minimal regularity assumptions.
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
(2022)
Article
Mathematics, Applied
Dimiter Prodanov
Summary: This study investigates the general properties of local generalizations of derivatives under the usual topology of the real line, introducing the concept of modular derivatives and establishing conditions for their existence and continuity. Additionally, a generalized Taylor-Lagrange property is proven, highlighting the unique continuous property of derivatives under the Lipschitz condition.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2021)
