Quartic double solids with icosahedral symmetry

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

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

Icosahedron in Birational Geometry

Yu. Prokhorov, Russian Journal of Mathematical Physics 2025 Vol. 32 P. 160–184

We study quotients of projective and affine spaces by various actions of the icosahedral group. Basically we concentrate on the rationality questions. ...

Added: November 28, 2025

Glass transition of aluminum melt. Molecular dynamics study

Kolotova L., Norman G., Pisarev V., Journal of Non-Crystalline Solids 2015 Vol. 429 P. 98–103

Molecular dynamics study of transition from liquid aluminum into an amorphous state is carried out. Different criteria for the glass transition are compared with each other: splitting of the second peak of the radial distribution function, increasing of the number of atoms with icosahedron-like environment, increase of the selfdiffusion activation energy, changes in the heat capacity. The discrepancy ...

Added: January 28, 2022

Стеклование переохлажденного расплава алюминия: молекулярно-динамическое исследование

Kolotova L., Norman G., Pisarev V., Журнал физической химии 2015 Т. 89 № 5 С. 796–800

С помощью метода молекулярной динамики исследовано стеклование переохлажденного расплава алюминия при изобарном и изохорном охлаждении. Для моделирования алюминия используется потенциал погруженного атома. Рассмотрены три критерия стеклования – расщепление второго пика парной корреляционной функции, увеличение числа искосаэдрических кластеров и измене ние энергии активации самодиффузии. Показано, что температуры стеклования, определенные по этим трем критериям, совпадают в пределах погрешностей. По результатам моделирования опреде лена ...

Added: January 28, 2022

On geometry of Fano threefold hypersurfaces

Cheltsov I., Park J., Ahmadinezhad H., / Series arXiv "math". 2020.

We prove that a quasi-smooth Fano threefold hypersurface is birationally rigid if and only if it has Fano index one. ...

Added: August 19, 2020

Kaehler-Einstein Fano threefolds of degree 22

Cheltsov I., Shramov K., / Series math "arxiv.org". 2018.

We study the problem of existence of K\"ahler--Einstein metrics on smooth Fano threefolds of Picard rank one and anticanonical degree 22 that admit a faithful action of the multiplicative group ℂ∗. We prove that, except possibly two explicitly described cases, all such smooth Fano threefolds are K\"ahler--Einstein. ...

Added: October 21, 2018

Small toric degenerations of Fano threefolds

Galkin S., / Series math "arxiv.org". 2018. No. 1809.02705.

We classify smooth Fano threefolds that admit degenerations to toric Fano threefolds with ordinary double points. ...

Added: September 25, 2018

Fano-Mathieu correspondence

Galkin S., / Series math "arxiv.org". 2018. No. 1809.02738.

We show that G-Fano threefolds are mirror-modular. 1. Mirror maps are inversed reversed Hauptmoduln for moonshine subgroups of SL2(ℝ). 2. Quantum periods, shifted by an integer constant (eigenvalue of quantum operator on primitive cohomology) are expansions of weight 2 modular forms (theta-functions) in terms of inversed Hauptmoduln. 3. Products of inversed Hauptmoduln with some fractional powers of shifted ...

Added: September 25, 2018

Prime Fano threefolds of genus 12 with a G_m-action

Prokhorov Y., Kuznetsov A., / Series arXiv "math". 2017.

We give an explicit construction of prime Fano threefolds of genus 12 with a G_m-action, describe their isomorphism classes and automorphism groups. ...

Added: November 29, 2017

Hilbert schemes of lines and conics and automorphism groups of Fano threefolds

Prokhorov Y., Kuznetsov A., Shramov K., Japanese Journal of Mathematics 2018 Vol. 13 No. 1 P. 109–185

We discuss various results on Hilbert schemes of lines and conics and automorphism groups of smooth Fano threefolds of Picard rank 1. Besides a general review of facts well known to experts, the paper contains some new results, for instance, we give a description of the Hilbert scheme of conics on any smooth Fano threefold ...

Added: November 22, 2017