Russian Journal of Mathematical Physics最新文献

{"title":"On the Lagrangian Embedding of ({rm U}(n)) in the Grassmannian ({rm Gr} (n -1, 2 n -1))","authors":"N. Tyurin","doi":"10.1134/S1061920824601770","DOIUrl":"10.1134/S1061920824601770","url":null,"abstract":"<p> In the present paper we combine our previous results in the studies of Lagrangian geometry of the Grassmannian <span>({rm Gr} (k, n))</span> with the example of Lagrangian embedding of the full flag variety in the direct product of projective spaces, found by D. Bykov. As the result, we construct a Langrangian immersion of the group <span>({rm U}(n))</span>, as a submanifold, into the complex Grassmanian <span>({rm Gr} (n-1, 2 n-1))</span> equipped with the symplectic form, by the Plücker embedding. </p><p> <b> DOI</b> 10.1134/S1061920824601770 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"210 - 218"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Short-Wave Solutions of the Wave Equation with Localized Velocity Perturbations Whose Wavelength Is Not Comparable to the Scale of Localized Inhomogeneity. One-Dimensional Case","authors":"A.I. Allilueva,&nbsp;A.I. Shafarevich","doi":"10.1134/S1061920825600400","DOIUrl":"10.1134/S1061920825600400","url":null,"abstract":"<p> The paper studies a wave equation whose velocity has a localized perturbation at some point <span>(x_0)</span>. The initial condition has the form of a rapidly oscillating wave packet whose wavelength is not comparable with the scale of the inhomogeneity. In this case, the length of the initial wave is of the order of <span>(varepsilon,)</span> and the width of the localized inhomogeneity is of the order of <span>(sqrt{varepsilon},)</span> where <span>(varepsilon)</span> is a small parameter that tends to 0. </p><p> <b> DOI</b> 10.1134/S1061920825600400 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"1 - 10"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908683","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Thom Isomorphism in Gauge-Equivariant (K)-Theory of (C^*)-Bundles","authors":"D. Fufaev,&nbsp;E. Troitsky","doi":"10.1134/S106192082460168X","DOIUrl":"10.1134/S106192082460168X","url":null,"abstract":"<p> For a bundle of compact Lie groups <span>(pcolon {cal G} to B)</span> over a compactum <span>(B)</span> (with the structure group of automorphisms of the corresponding group), we introduce the gauge-equivariant <span>(K)</span>-theory group <span>(K_{{cal G}}^{0}(X; {mathcal A} ))</span> of a bundle <span>(pi_{X}colon X to B)</span> endowed with a continuous action of <span>({cal G})</span> constructed using bundles <span>(Eto X)</span> with the typical fiber being a projective finitely generated module over a unital <span>(C^*)</span>-algebra <span>( {mathcal A} )</span>. The index of a family of gauge-invariant (= <span>({cal G})</span>-equivariant) Fredholm operators naturally takes values in these groups. We introduce and study products and use them to define the Thom homomorphism in gauge-equivariant <span>(K)</span>-theory and prove that this homomorphism is an isomorphism. </p><p> <b> DOI</b> 10.1134/S106192082460168X </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"44 - 64"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Restricting/Extending Operators to/from Thick Hilbert (C^*)-Submodules","authors":"V.M. Manuilov","doi":"10.1134/S1061920824601782","DOIUrl":"10.1134/S1061920824601782","url":null,"abstract":"<p> Given an essential ideal <span>(Jsubset A)</span> of a <span>(C^*)</span>-algebra <span>(A)</span> and a Hilbert <span>(C^*)</span>-module <span>(M)</span> over <span>(A)</span>, we place <span>(M)</span> between two other Hilbert <span>(C^*)</span>-modules over <span>(A)</span>, <span>(M_Jsubset Msubset M^J)</span>, in such a way that every submodule here is thick, i.e., its orthogonal complement in the greater module is trivial. We introduce the class <span>(mathbb B_J(M))</span> of <span>(J)</span>-adjointable operators on a Hilbert <span>(C^*)</span>-module <span>(M)</span> over <span>(A)</span> and prove that this class isometrically embeds in the <span>(C^*)</span>-algebras of all adjointable operators both of <span>(M_J)</span> and of <span>(M^J)</span>. </p><p> <b> DOI</b> 10.1134/S1061920824601782 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"123 - 128"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Action of Reduced Powers on the Homology of Products of Complex Projective Spaces and Products of Lens Spaces","authors":"Th.Yu. Popelensky","doi":"10.1134/S1061920825600230","DOIUrl":"10.1134/S1061920825600230","url":null,"abstract":"<p> The so-called ‘hit problem’ initiated by Peterson in [1] as an attempt at better understanding the <span>(E_2)</span>-page of the Adams spectral sequence <span>(operatorname{mod} 2)</span> (that is the cohomology of the Steenrod algebra <span>( {mathcal{A}_2} )</span>) turned out to be very difficult. The hit problem is to determine a minimal generating set for the cohomology of products of infinite projective spaces <span>({mathbb R} P^infty)</span> as a module over the Steenrod algebra <span>( {mathcal{A}_2} )</span> at the prime 2. The dual problem is to determine the set of <span>( {mathcal{A}_2} )</span>-annihilated elements in the homology of the same spaces. Anick showed that the set of <span>( {mathcal{A}_2} )</span>-annihilated elements in the products of infinite projective spaces <span>({mathbb R} P^infty)</span> forms a free associative algebra [6]. Ault and Singer proved that, for every <span>(k ge 0)</span>, the set of <span>(k)</span>-partially <span>( {mathcal{A}_2} )</span>-annihilated elements in homology of products of <span>({mathbb R} P^infty)</span> (that is a set of elements that are annihilated by <span>(Sq^{2^i})</span> for all <span>(i le k)</span>) also forms a free associative algebra. </p><p> In this note, we investigate the dual problem at a prime <span>(p&gt;2)</span>. In this case, <span>({mathbb R} P^infty)</span> should be replaced by <span>({mathbb C} P^infty)</span> if one wants to ignore the action of the Bockstein operation <span>(beta)</span> or by the infinite <span>(p)</span>-lens space <span>(L^infty)</span> to take <span>(beta)</span> into consideration. We prove that, for any <span>(kge 0)</span>, a collection of elements in <span>({mathbb Z}/p)</span>-homology of products of <span>({mathbb C} P^infty)</span> (or <span>(L^infty)</span>) annihilated by all <span>(P^{p^i})</span>, <span>(ile k)</span>, forms a free algebra. The same holds for the collection of elements annihilated by <span>(beta)</span> and all <span>(P^{p^i})</span>, <span>(ile k)</span>. We also construct an explicit basis in the subspace <span>(barDelta(0)_{m,*}subset H_*(({mathbb C} P^infty)^{wedge m},{mathbb Z}/p))</span>, <span>(m=1, 2)</span>, annihilated by <span>(P^1)</span>. </p><p> <b> DOI</b> 10.1134/S1061920825600230 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"150 - 159"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908834","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonlocal de Sitter (sqrt{dS}) Gravity Model and Its Applications","authors":"I. Dimitrijevic,&nbsp;B. Dragovich,&nbsp;Z. Rakic,&nbsp;J. Stankovic","doi":"10.1134/S1061920824601824","DOIUrl":"10.1134/S1061920824601824","url":null,"abstract":"<p> A simple nonlocal de Sitter gravity model (<span>(sqrt{dS})</span>) shows good properties on cosmological and galactic scales. Its cosmological solution agrees very well with the experimental data. The rotation curves of spiral galaxies (Milky Way and M33) are also well described by the <span>(sqrt{dS})</span> model. This article contains a brief overview of earlier results, including a new result on finding an appropriate local description with a scalar field for cosmological solutions. </p><p> <b> DOI</b> 10.1134/S1061920824601824 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"11 - 27"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bifurcations of Magnetic Geodesic Flows on Surfaces of Revolution","authors":"I.F. Kobtsev,&nbsp;E.A. Kudryavtseva","doi":"10.1134/S1061920825600084","DOIUrl":"10.1134/S1061920825600084","url":null,"abstract":"<p> We study magnetic geodesic flows invariant under rotations on the 2-sphere. The dynamical system is given by a generic pair of functions <span>((f,Lambda))</span> in one variable. The topology of the Liouville fibration of the given integrable system near its singular orbits and singular fibers is described. The types of these singularities are computed. The topology of the Liouville fibration on regular 3-dimensional isoenergy manifolds is described by computing the Fomenko–Zieschang invariant. All possible bifurcation diagrams of the momentum mappings of such integrable systems are described. It is shown that the bifurcation diagram consists of two curves in the <span>((h,k))</span>-plane. One of these curves is a line segment <span>(h=0)</span>, and the other lies in the half-plane <span>(hge0)</span> and can be obtained from the curve <span>((a:-1:k) = (f:Lambda:1)^*)</span> projectively dual to the curve <span>((f:Lambda:1))</span> by the transformation <span>((a:-1:k)mapsto(a^2/2,k)=(h,k))</span>. </p><p> <b> DOI</b> 10.1134/S1061920825600084 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"65 - 96"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ky Fan Theorem for Sphere Bundles","authors":"G. Panina,&nbsp;R. Živaljević","doi":"10.1134/S1061920825600138","DOIUrl":"10.1134/S1061920825600138","url":null,"abstract":"<p> The classical Ky Fan theorem is a combinatorial equivalent of the Borsuk–Ulam theorem. It is a generalization and extension of Tucker’s lemma and, just like its predecessor, it pinpoints important properties of antipodal colorings of vertices of a triangulated sphere <span>(S^n)</span>. Here we describe generalizations of Ky Fan theorem for the case when the sphere is replaced by the total space of a triangulated sphere bundle. </p><p> <b> DOI</b> 10.1134/S1061920825600138 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"141 - 149"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908690","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Normal Subgroups Related to a One-Dimensional Pure Pseudorepresentation of a Group","authors":"A. I. Shtern","doi":"10.1134/S1061920825010133","DOIUrl":"10.1134/S1061920825010133","url":null,"abstract":"<p> By analogy with the normal subgroups related to pseudocharacters on groups, we introduce and study the properties of two normal subgroups of a group related to a one-dimensional pure pseudorepresentation on the group. </p><p> <b> DOI</b> 10.1134/S1061920825010133 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"185 - 188"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Fractional-Linear Integrals of Geodesics on Surfaces","authors":"B. Kruglikov","doi":"10.1134/S1061920824601836","DOIUrl":"10.1134/S1061920824601836","url":null,"abstract":"<p> In this note, we give a criterion for the existence of a fractional-linear integral for a geodesic flow on a Riemannian surface and explain that, modulo the Möbius transformations, the moduli space of such local integrals (if nonempty) is either the two-dimensional projective plane or a finite number of points. We also consider explicit examples and discuss a relation of such rational integrals to Killing vectors. </p><p> <b> DOI</b> 10.1134/S1061920824601836 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"32 1","pages":"97 - 104"},"PeriodicalIF":1.7,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143908648","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}