Решение квантильных дифференциальных уравнений Пфаффа при отсутствии полной интегрируемости

?

Решение квантильных дифференциальных уравнений Пфаффа при отсутствии полной интегрируемости

Вестник Самарского государственного университета. Естественнонаучная серия. 2012. Т. 94. № 3/1. С. 20–39.

Мелкумова Л. Э., Шатских С. Я.

The present work deals with quantile Pfaffian differential equations which are constructed using two-dimensional conditional quantiles of multidimensional probability distributions. As it was shown in [3] in case when the initial probability distributions have reproducible conditional quantiles this kind of Pfaffian equations is completely integrable and the integral manifold is the conditional quantile of maximum dimension. In this paper we discuss properties of integral manifolds of maximum possible dimension for quantile Pfaffian equations which are not completely integrable. Manifolds of this type are described in terms of conditional quantiles of intermediate dimensions.

Priority areas: mathematics

Language: Russian

Text on another site

Pairings on the algebra of Laurent series over a ring

Levashev V., / Series arXiv "math". 2026. No. 2609.06010.

We prove that continuous A-bilinear pairings on the ring of Laurent series that are invariant under continuous automorphisms coincide, up to a constant, with the pairing given by the residue of a differential form over any commutative associative ring with identity. ...

Added: September 24, 2026

From non-polynomial invariants to non-Liouvillian first integrals

Demina M.V., Nechitailo V., Analysis and Mathematical Physics 2026 Vol. 16 No. 5 P. 1–25

We present a method of finding non-Liouvillian first integrals of rational two-dimensional differential systems. The method is based on the existence of two independent invariants that satisfy a linear second-order ordinary differential equation with respect to one of the variables. We call systems with this property R-integrable. These invariants are not necessarily polynomial; they can ...

Added: September 24, 2026

Iterative construction of the R-matrices in arbitrary dimensions

Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.

We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter. By analyzing the ...

Added: September 24, 2026

On static manifolds with boundary admitting a nowhere-vanishing static potential

Medvedev V., / Series arXiv "math". 2026.

We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...

Added: September 19, 2026

Vague stimulating ideas, images and metaphors in scientific thinking: researchers' work with horizons of unclear knowledge

Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.

Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...

Added: September 15, 2026

On phase-lock area parquet in a special slow-fast limit of model of Josephson junction.

Glutsyuk A., / Series arXiv "math". 2026.

B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...

Added: September 8, 2026

Infinitely many graph manifolds with unique geometrical piece that admit arbitrarily many Anosov flows

Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.

Anosov flows have a long and rich history, firstly motivated by the study of geodesic flows in negative curvature surface by Anosov and Sinai. Not every closed manifold admits an Anosov flow for well-known reasons: the fundamental group of a 3-manifold M admitting an Anosov flow must have exponential growth, and M must be universally covered by R3. Nevertheless, there ...

Added: August 31, 2026

New bound on S1× S2-setting Bell locality of a nonseparable Werner state

Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.

In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...

Added: July 21, 2026

On functional equations for Chow polylogarithms

Bolbachan V., / Series math "arxiv.org". 2024.

Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity. To prove this, we study ...

Added: July 16, 2026

On Goncharov’s conjecture in next to Milnor degree

Bolbachan V., / Series math "arxiv.org". 2024.

Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...

Added: July 16, 2026

Statistical inference based on band-limited kernels: Rational-infinitely divisible distributions and beyond

Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.

This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...

Added: July 9, 2026

Strong Approximations for Markov Chains Weakly Converging to Diffusions

Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.

In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...

Added: June 11, 2026

Bifurcations and Structural Stability of Generic PC-HC Families

Dorovskiy A., / Series arXiv "math". 2026.

In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...

Added: May 14, 2026

On the minimum number of maximal distance-k independent sets in trees

Taletskii D., / Series arXiv "math". 2026.

A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...

Added: May 1, 2026

On Arithmetic Mirror Symmetry for smooth Fano fourfolds

Ovcharenko M., / Series arXiv "math". 2026.

We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...

Added: April 30, 2026

On weak solutions to the 1d compressible Navier-Stokes equations: a Lipschitz continuous dependence on data in weaker norms and an error of their homogenization

Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.

We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...

Added: April 18, 2026

Bifurcation Analysis and Dynamical Phenomena in the Problem of the Rolling Motion of a Dynamically Symmetric Spherical Top with One Nonholonomic Constraint

Kilin A. A., Ivanova T. B., Lobachevskii Journal of Mathematics 2025 No. 46 P. 1113–1138

In this paper, we address the problem of the rolling motion of a sphere with axisymmetric mass distribution on a horizontal plane. It is assumed that the sphere does not slip as it rolls in the direction of the projection of the symmetry axis onto the supporting plane. The system under consideration admits a redundant ...

Added: December 10, 2025

Региональный и субрегиональный аспекты доходного неравенства населения России

Sirotin V., Arkhipova M., Кириллова О. А., Финансы и бизнес 2025 Т. 21 № 4 С. 3–13

The article presents a model of the evolution of the latent regional structure of income inequality based on a two-component model of a mixture of probability distributions, which makes it possible to identify trends in changes in this area. The process of stratification of the regional structure of income inequality is analyzed, accompanied by an ...

Added: April 17, 2025

Reducing the sample size when estimating conditional quantiles

Shatskikh S. Y., Мелкумова Л. Э., , in: CEUR Workshop ProceedingsVol. 1638: ITNT 2016, Information Technology and Nanotechnology.: CEUR-WS.org, 2016. P. 769–781.

In this paper we propose an idea to use a certain property of multivariate probability distributions, that we call the conditional quan- tile reproducibility, to decrease the amount of observations required to construct a statistical estimate of a n-dimensional conditional quantile of the distribution. For the class of probability distributions, satisfying to this property, we ...

Added: June 8, 2021

Построение многомерных распределений вероятностей с вполне воспроизводимыми условными квантилями

Мелкумова Л. Э., Известия высших учебных заведений. Математика 2020 № 11 С. 29–45

It is known that when a multivariate probability distribution has a “big” conditional quantile that is fully reproducible when narrowed to uni-variate quantiles, then the respective quantile differential equation is completely integrable. Yet the converse is not true in general. In this paper, we show that, provided that certain conditions are satisfied, from the given ...

Added: June 8, 2021

Воспроизводимость условных квантилей многомерных распределений и упрощенная конструкция из парных копул

Мелкумова Л. Э., Шатских С. Я., Теория вероятностей и ее применения 2021 Т. 66 № 1 С. 196–208

We give an equivalent definition of the conditional quantile reproducibility property for multivariate probability distributions using the concept of copula. Based on this definition, we establish a connection between the conditional quantile reproducibility property and the simplifying assumption from the simplified pair copula construction. Additionally, we show that the conditional quantile reproducibility is preserved when ...

Added: June 8, 2021

On linearizability via nonlocal transformations and first integrals for second-order ordinary differential equations

Sinelshchikov D., Chaos, Solitons and Fractals 2020 Vol. 141 Article 110318

Nonlinear second-order ordinary differential equations are common in various fields of science, such as physics, mechanics and biology. Here we provide a new family of integrable second-order ordinary differential equations by considering the general case of a linearization problem via certain nonlocal transformations. In addition, we show that each equation from the linearizable family admits ...

Added: September 30, 2020

Пары Лакса для линейных гамильтоновых систем

Жеглов А. Б., Osipov D., Сибирский математический журнал 2019 Т. 60 № 4 С. 760–776

In the paper, Lax pairs for linear Hamiltonian systems of differential equations are constructed. In particular, Groebner bases are used for the computations. It is proved that the maps which appear in the construction of Lax pairs are Poisson. Various properties of first integrals of the system which are obtained from the Lax pairs are ...

Added: October 8, 2019

Lax representation and quadratic first integrals for a family of non-autonomous second-order differential equations

Sinelshchikov D., Гаюр И. Ю., Кудряшов Н. А., Journal of Mathematical Analysis and Applications 2019 Vol. 480 No. 1 P. 123375-1–123375-14

We consider a family of non-autonomous second-order differential equations, which generalizes the Liénard equation. We explicitly find the necessary and sufficient conditions for members of this family of equations to admit quadratic, with the respect to the first derivative, first integrals. We show that these conditions are equivalent to the conditions for equations in the ...

Added: September 8, 2019