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НОВЫЕ ФОРМУЛЫ, СВЯЗАННЫЕ С АНАЛИТИЧЕСКОЙ ТЕОРИЕЙ ЧИСЕЛ, И ИХ ПРИЛОЖЕНИЕ К СТАТИСТИЧЕСКОЙ ФИЗИКЕ
Теоретическая и математическая физика. 2018. Т. 196. № 1. С. 161–166.
Since the deep paper by Bohr and Kalckar in 1938, it has been known that the Ramanujan formula in
number theory is related to statistical physics and nuclear theory. From the early 1970s, there have been
attempts to generalize number theory from the space of integers to the space of rational numbers, i.e., to
construct a so-called analytic number theory. In statistical physics, we consider parameters such as the
volume V , temperature T, and chemical potential μ, which are not integers and are consequently related
to analytic number theory. This relation to physical concepts leads us to seek new relations in analytic
number theory, and these relations turn out to be useful in statistical physics.
Priority areas:
mathematics
Language:
Russian
Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407
In this paper, we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that, in some cases, this boundary is sharp. ...
Added: May 19, 2026
Malinovsky A. M., Пилипенко С. В., Mikhalchenko A. O. et al., Astronomy Reports 2026 Vol. 70 P. 1–6
Radiation from rotational transitions of CO molecules in distant galaxies creates a chaotic background with an intensity reaching 1000 Jy/sr at a wavelength of approximately 1 mm. This background will pose a serious problem, when measuring spectral distortions of the cosmic microwave background, in particular, the mu-distortion, which presumably has an intensity of less than ...
Added: May 19, 2026
Kaveev A. K., Fedorov V. V., Pavlov A. V. et al., Journal of Materials Chemistry C 2026 Vol. 14 No. 7 P. 2697–2705
Bismuth nanostructures represent a promising material platform for semiconductor nanooptoelectronics and colorimetry owing to the multi-colored light reflection and quantum confinement. In this work, we study the photoluminescent properties of bismuth nanostructures grown using molecular beam epitaxy on the planar CaF2/Si(111) surface. We demonstrate the different surface morphologies of Bi, ranging from planar films obtained ...
Added: May 19, 2026
Pavlova T., V.M. Shevlyuga (Шевлюга В. М., Applied Surface Science 2026 Vol. 736 P. 166813–166813
The objective of miniaturizing doped areas in silicon, with the ultimate goal of achieving atomic-precision doping, requires a fundamental understanding of the dopant incorporation process at the atomic level. We present a combined scanning tunneling microscopy (STM) and density functional theory (DFT) investigation of single phosphorus atom incorporation into the Si(100) surface. Phosphorus was supplied ...
Added: May 19, 2026
Pasternak D., Romshin A., Khmelnitsky Р. et al., Carbon 2026 Vol. 256 Article 121655
A single-photon source (SPS) is a key component required for quantum communication devices. We report the
discovery of bright diamond-based SPS created by nature. It is shown that narrow (≤2 nm) lines observed in the
500-800 nm range in photoluminescence (PL) spectra of the surface layer of untreated Yakut diamonds rich in
nitrogen and hydrogen are linked to ...
Added: May 19, 2026
Жакупов О. Б., European Journal of Mathematics 2025 Vol. 11 Article 84
We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute ...
Added: May 18, 2026
Smirnov A., Kurtina D. A., Saitov S. R. et al., Optical Materials: X 2026 Vol. 30 Article 100441
Chiral semiconductor nanostructures and nanoparticles are promising materials for applications in biological sensing, enantioselective separation, photonics, and spin-polarized devices. Here we performed a detailed analysis of optical properties of chiral CdSe nanoplatelets with thickness of 2 and 3 monolayers (ML) with Nacetyl-L-cysteine ligands. We studied the absorption spectra peculiarities, analyzed time-resolved photoluminescence and investigated circular ...
Added: May 18, 2026
Smirnov A., Mantsevich V. N., Saitov S. R. et al., Journal of Applied Physics 2026 Vol. 139 Article 185702
This work presents a comprehensive investigation into the temperature-dependent thermally stimulated conductivity and photoconductivity of vacuum-annealed thin films based on core–shell CdSe/CdS nanoplatelets passivated with oleic acid ligands. Controlled thermal annealing under vacuum conditions leads to a substantial increase in both dark and photoinduced conductivity, which is primarily attributed to partial desorption of the ligands. ...
Added: May 18, 2026
Масютин Д. А., Moiseev E., Komarov S. et al., Письма в Журнал технической физики 2026 Т. 52 № 7 С. 27–30
Исследованы инжекционные полупроводниковые микролазеры с кольцевым резонатором радиусом 15 мкм с несимметричным расположением внутреннего отверстия резонатора. Показано, что асимметрия обеспечивает формирование в диаграмме направленности двух лепестков излучения, разориентированных на 50° относительно оси смещения внутреннего отверстия. Измеренная добротность резонаторов сопоставима с добротностью дисковых резонаторов и находится на уровне ∼ 10^6. ...
Added: May 18, 2026
The Journal of Physical Chemistry Letters 2026 Vol. 17 No. 18 P. 5386–5394
We demonstrate and rationalize the effect of Au nanoparticles (NPs) on the hierarchical g-C3N4/CeO2 heterojunction. g-C3N4/CeO2 decorated with monodispersed plasmonic Au NPs was synthesized. Detailed analyses showed that CeO2 nanocubes and monodispersed Au NPs were evenly distributed over the 2D g-C3N4 surface, forming a robust interface enriched with abundant active sites. The structure enabled efficient separation of photogenerated charge ...
Added: May 16, 2026
Das A., Paul R., Sharma N. et al., Colloids and Surfaces A: Physicochemical and Engineering Aspects 2026 Vol. 728 P. 138830
Niobium-doped TiO2 (Nb-TiO2), demonstrates dual functionality as an efficient photocatalyst for dye degradation and a promising photoelectrocatalyst for water oxidation. Nb incorporation via a facile hydrothermal method was confirmed by XRD (Rietveld refinement), XPS, TEM, FT-IR, Raman, and BET analyses, indicating successful lattice doping and structural modification. Photocatalytic dye degradation experiments were conducted using a model ...
Added: May 16, 2026
Lerman L. M., Turaev D. V., Regular and Chaotic Dynamics 2026 Vol. 31 No. 3 P. 349–369
We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic H´enonlike map and study bifurcations of the ...
Added: May 15, 2026
Aleskerov F. T., Yakuba V. I., Khutorskaya O. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
Added: May 15, 2026
Kuptsov P., Panyushev A., Stankevich N., Chaos 2026 Vol. 36 No. 5 Article 053138
We develop a machine-learning approach to reproduce the behavior of two versions of the van der Pol oscillator exhibiting a subcritical Andronov–Hopf bifurcation, with or without a codimension-2 Bautin point. We construct a neural-network model that functions as a recur rent map and train it on short segments of oscillator trajectories. The results show that, ...
Added: May 15, 2026
Kolokolov I., Lebedev V., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2026 Vol. 113 Article 054117
We theoretically investigate the correlation functions of the phase of a light wave propagating through a
turbulent medium. We use an equation for the logarithm of a wave packet envelope, which includes a secondorder
nonlinear term. Based on this equation, we develop a diagrammatic technique to calculate corrections
to the correlation function obtained in the linear approximation. We ...
Added: May 15, 2026
Гущина В. А., / Series chemrxiv-2023-vpzhz-v2 "ChemRxiv". 2023.
All-inorganic perovskite CsPbBr3 and Cs4PbBr6 nanoparticles are being intensively studied due to their unique properties and wide range of applications; however, however, the nature of their optical properties is not yet fully understood due to the difficulty of synthesis of singlephase nanoparticles. In this article we describe the features of the synthesis of single-phase particles ...
Added: May 14, 2026
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
Гущина В. А., Mendeleev Communications 2025 Vol. 35 No. 2 P. 193–195
All-inorganic perovskite CsPbBr3 and Cs4PbBr6 nanoparticles are intensively studied for their unique optical properties, though synthesizing single-phase nanoparticles has posed challenges. Detailed synthesis method of CsPbBr3 and Cs4PbBr6 single-phase nanoparticles and their chemical and phase analysis are described. Distinctive optical characteristics, such as photoluminescence, optical band gap and the Urbach tail region, are revealed and explained within the current ...
Added: May 14, 2026
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
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
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
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 2026