Lobachevskii Journal of Mathematics

A numerical study was conducted in this article on the effect of the shape of the tip of the tube on the resonant oscillations of the gas. It was demonstrated that in tubes with flat, conical and spherical tips, the shape of the tip does not affect the resonant frequency when the radius of the cylindrical part of the tube and the height of the tip are equal, provided that the volumes of the resonators are equal too. For a tube with an reverse cone tip, there has been observed a downward shift in the resonant frequency in comparison to a closed uniform tube of equivalent length, as well as a decrease in the amplitude of gas pressure oscillations, which occurs due to an increase in the total length of the side wall of the reverse cone and, accordingly, an increase in near-wall losses. The reverse cone tip turns the tube into a less efficient resonator than the other above-mentioned tips.

For monotone mixed variational inequalities, a solution method is proposed that combines regularization and a descent technique over a gap (merit) function. The same uniformly convex auxiliary function is used to construct both regularized problems and gap functions. The regularized problems are solved by applying the method of descent over a gap function with inexact line search.

In this study, we explore the variables impacting the shape parameter changes in a Generalized Extreme Value (GEV) distribution and model the parameter to predict flood risk areas. Our dataset comprises satellite, meteorological, and hydrological data from the Mun River Basin collected over 13 years (2010–2022) from 17 stations of the Thai Meteorological Department and agricultural stations. The shape parameter is estimated via an Artificial Neural Network (ANN) approach for a non-stationary process and by Maximum Likelihood Estimation (MLE) for a stationary process. Using the Nash–Sutcliffe Coefficient (NSE) for comparison, we found that the non-stationary model was more suitable for the monthly maximum rainfall data from 10 stations, while the stationary model was applicable for the remaining 7 stations. Overall, all models had predictive accuracy with an average NSE greater than 0.80, indicating their suitability for monthly maximum rainfall data. The study culminates with the presentation of the return level of monthly maximum rainfall data for various return periods via a 2D map.

The paper deals with perturbations of the equation that have a number of conservation laws. When a small term is added to the equation its conserved quantities usually decay at individual rates, a phenomenon known as a selective decay. These rates are described by the simple law using the conservation laws’ generating functions and the added term. Yet some perturbation may retain a specific quantity(s), such as energy, momentum and other physically important characteristics of solutions. We introduce a procedure for finding such perturbations and demonstrate it by examples including the KdV–Burgers equation and a system from magnetodynamics. Some interesting properties of solutions of such perturbed equations are revealed and discussed.

We consider a Hamiltonian of a system of two fermions on a three-dimensional lattice $$\mathbb{Z}^{3}$$ with a finite spherically symmetric potential. It is proven that the corresponding Shrödinger operator $$H(\mathbf{k}),$$ where $$\mathbf{k}\in(-\pi,\pi]^{3}$$ is the total quasimomentum of the system, has four invariant subspaces $$L_{123}^{-},\,\,L_{1}^{-},\,\,L_{2}^{-},\,\,L_{3}^{-}$$ and it has no eigenfunctions in $$L_{123}^{-}$$ . We also show that the operator $$H(\mathbf{\Lambda}),\,\,\mathbf{\Lambda}=(\pi-2\lambda,\pi-2\lambda,\pi-2\lambda)$$ has four different threefold eigenvalues for small $$\lambda$$ .

In this paper, we consider the expressive Description Logic (DL) $$\mathcal{ALCQPI}_{R^{+}}$$ having concept constructors called part restrictions that realize rational grading. Part restrictions are able to convey statements about a rational part of a set of successors, and they essentially enrich the expressive capabilities of DLs. That is why it is important to evaluate the cost of their use with respect to the reasoning complexity. We modify the tableaux algorithm used for $$\mathcal{ALCNI}_{R^{+}}$$ (a DL with just number restrictions instead of qualified number ones), and augment it with a specific technique for dealing with part restrictions to prove that concept satisfiability and subsumption in the considered DL are still in PSPACE.

The paper is devoted to the study of the structures of idempotent and hyperassociative algebras. The goal is to explain new methodological developments in algebras, which will be of growing importance in the second order logic. Our results extend the corresponding results on semigroups too.

In this paper, we introduce the concept of a Semi Heyting Almost Distributive Lattice (SHADL) as a generalization of a Semi Heyting Algebra in the class of ADLs. We characterize an SHADL in terms of its principal ideals. We also give different sets of equations that define an SHADL.

In this note we consider several kind of partition functions of one-dimensional models with nearest — neighbor interactions I n , n ∈ Z and spin values ±1. We derive systems of recursive equations for each kind of such functions. These systems depend on parameters I n , n ∈ Z. Under some conditions on the parameters we describe solutions of the systems of recursive equations.

We get a new representation for the generating density of convex bodies in R 3 in terms of curvature radii of their projections, which is dual to the classical representation of W. Blaschke.