St Petersburg Mathematical Journal最新文献

{"title":"On the number of faces of the Gelfand–Zetlin polytope","authors":"E. Melikhova","doi":"10.1090/spmj/1714","DOIUrl":"https://doi.org/10.1090/spmj/1714","url":null,"abstract":"The combinatorics of the Gelfand–Zetlin polytope is studied. Geometric properties of a linear projection of this polytope onto a cube are employed to derive a recurrence relation for the \u0000\u0000 \u0000 f\u0000 f\u0000 \u0000\u0000-polynomial of the polytope. This recurrence relation is applied to finding the \u0000\u0000 \u0000 f\u0000 f\u0000 \u0000\u0000-polynomials and \u0000\u0000 \u0000 h\u0000 h\u0000 \u0000\u0000-polynomials for one-parameter families of Gelfand–Zetlin polytopes of simplest types.","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49633345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Diagonal complexes for surfaces of finite type and surfaces with involution","authors":"G. Panina, J. Gordon","doi":"10.1090/spmj/1709","DOIUrl":"https://doi.org/10.1090/spmj/1709","url":null,"abstract":"<p>Two constructions are studied that are inspired by the ideas of a recent paper by the authors.</p>\u0000\u0000<p>— The <italic> diagonal complex</italic> <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper D\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">D</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal {D}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and its barycentric subdivision <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper B script upper D\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">B</mml:mi>\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">D</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal {BD}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> related to an oriented surface of finite type <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F\">\u0000 <mml:semantics>\u0000 <mml:mi>F</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">F</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> equipped with a number of labeled marked points. This time, unlike the paper mentioned above, boundary components without marked points are allowed, called <italic>holes</italic>.</p>\u0000\u0000<p>— The <italic>symmetric diagonal complex</italic> <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper D Superscript i n v\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">D</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>inv</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal {D}^{operatorname {inv}}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and its barycentric subdivision <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper B script upper D Superscript i n v\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">B</mml:mi>\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">D</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>inv</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">mathcal {BD}^{operatorname {inv}}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> related to a <italic>symmetric</italic> (=with an involution) oriented surface <inline-formula content-type=\"math","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41261484","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The order of growth of an exponential series near the boundary of the convergence domain","authors":"G. Gaisina","doi":"10.1090/spmj/1708","DOIUrl":"https://doi.org/10.1090/spmj/1708","url":null,"abstract":"<p>For a class of analytic functions in a bounded convex domain <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> that admit an exponential series expansion in <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper D\">\u0000 <mml:semantics>\u0000 <mml:mi>D</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">D</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, the behavior of the coefficients of this expansion is studied in terms of the growth order near the boundary <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"partial-differential upper G\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi mathvariant=\"normal\">∂<!-- ∂ --></mml:mi>\u0000 <mml:mi>G</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">partial G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. In the case where <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> has a smooth boundary, unimprovable two-sided estimates are established for the order via characteristics depending only on the exponents of the exponential series and the support function of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. As a consequence, a formula is obtained for the growth of the exponential series via the coefficients and the support function of the convergence domain <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\">\u0000 <mml:semantics>\u0000 <mml:mi>G</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">G</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41505606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Elliptic solitons and “freak waves”","authors":"V. Matveev, A. Smirnov","doi":"10.1090/spmj/1713","DOIUrl":"https://doi.org/10.1090/spmj/1713","url":null,"abstract":"It is shown that elliptic solutions to the AKNS hierarchy equations can be obtained by exploring spectral curves that correspond to elliptic solutions of the KdV hierarchy. This also allows one to get the quasirational and trigonometric solutions for AKNS hierarchy equations as a limit case of the elliptic solutions mentioned above.","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42432684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Joint weighted universality of the Hurwitz zeta-functions","authors":"A. Laurinčikas, G. Vadeikis","doi":"10.1090/spmj/1712","DOIUrl":"https://doi.org/10.1090/spmj/1712","url":null,"abstract":"<p>Joint weighted universality theorems are proved concerning simultaneous approximation of a collection of analytic functions by a collection of shifts of Hurwitz zeta-functions with parameters <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"alpha 1 comma ellipsis comma alpha Subscript r Baseline\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:msub>\u0000 <mml:mi>α<!-- α --></mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mo>…<!-- … --></mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>α<!-- α --></mml:mi>\u0000 <mml:mi>r</mml:mi>\u0000 </mml:msub>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">alpha _1,dots ,alpha _r</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. For this, linear independence is required over the field of rational numbers for the set <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-brace log left-parenthesis m plus alpha Subscript j Baseline right-parenthesis colon m element-of double-struck upper N 0 equals double-struck upper N union StartSet 0 EndSet comma j equals 1 comma ellipsis comma r right-brace\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo>\u0000 <mml:mi>log</mml:mi>\u0000 <mml:mo>⁡<!-- ⁡ --></mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>m</mml:mi>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>α<!-- α --></mml:mi>\u0000 <mml:mi>j</mml:mi>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mspace width=\"thinmathspace\" />\u0000 <mml:mo>:</mml:mo>\u0000 <mml:mspace width=\"thinmathspace\" />\u0000 <mml:mi>m</mml:mi>\u0000 <mml:mo>∈<!-- ∈ --></mml:mo>\u0000 <mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">N</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mn>0</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">N</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo>∪<!-- ∪ --></mml:mo>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">{</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mspace width=\"thickmathspace\" />\u0000 <mml:mi>j</mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mo>…<!-- … --></mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>r</mml:mi>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">}</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">{log (m+alpha _j),:, min mathbb {N}_0=mathbb {N}cup {0},;j=1,dots ,r}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41419235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Compact Hankel operators on compact Abelian groups","authors":"A. Mirotin","doi":"10.1090/spmj/1715","DOIUrl":"https://doi.org/10.1090/spmj/1715","url":null,"abstract":"The classical theorems of Kronecker, Hartman, Peller, and Adamyan–Arov–Krein are extended to the context of a connected compact Abelian group \u0000\u0000 \u0000 G\u0000 G\u0000 \u0000\u0000 with linearly ordered group of characters, on the basis of a description of the structure of compact Hankel operators on \u0000\u0000 \u0000 G\u0000 G\u0000 \u0000\u0000. Beurling’s theorem on invariant subspaces is also generalized. Some applications to Hankel operators on discrete groups are given.","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46261293","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dihedral modules with ∞-simplicial faces and dihedral homology for involutive 𝐴_{∞}-algebras over rings","authors":"S. Lapin","doi":"10.1090/spmj/1711","DOIUrl":"https://doi.org/10.1090/spmj/1711","url":null,"abstract":"<p>On the basis of combinatorial techniques of dihedral modules with <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal infinity\">\u0000 <mml:semantics>\u0000 <mml:mi mathvariant=\"normal\">∞<!-- ∞ --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">infty</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-simplicial faces, dihedral homology is constructed for involutive <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A Subscript normal infinity\">\u0000 <mml:semantics>\u0000 <mml:msub>\u0000 <mml:mi>A</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"normal\">∞<!-- ∞ --></mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:annotation encoding=\"application/x-tex\">A_{infty }</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-algebras over arbitrary commutative unital rings.</p>","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42773224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On a Bellman function associated with the Chang–Wilson–Wolff theorem: a case study","authors":"F. Nazarov, V. Vasyunin, A. Volberg","doi":"10.1090/spmj/1719","DOIUrl":"https://doi.org/10.1090/spmj/1719","url":null,"abstract":"The tail of distribution (i.e., the measure of the set \u0000\u0000 \u0000 \u0000 {\u0000 f\u0000 ≥\u0000 x\u0000 }\u0000 \u0000 {fge x}\u0000 \u0000\u0000) is estimated for those functions \u0000\u0000 \u0000 f\u0000 f\u0000 \u0000\u0000 whose dyadic square function is bounded by a given constant. In particular, an estimate following from the Chang–Wilson–Wolf theorem is slightly improved. The study of the Bellman function corresponding to the problem reveals a curious structure of this function: it has jumps of the first derivative at a dense subset of the interval \u0000\u0000 \u0000 \u0000 [\u0000 0\u0000 ,\u0000 1\u0000 ]\u0000 \u0000 [0,1]\u0000 \u0000\u0000 (where it is calculated exactly), but it is of \u0000\u0000 \u0000 \u0000 C\u0000 ∞\u0000 \u0000 C^infty\u0000 \u0000\u0000-class for \u0000\u0000 \u0000 \u0000 x\u0000 >\u0000 \u0000 3\u0000 \u0000 \u0000 x>sqrt 3\u0000 \u0000\u0000 (where it is calculated up to a multiplicative constant).\u0000\u0000An unusual feature of the paper consists of the usage of computer calculations in the proof. Nevertheless, all the proofs are quite rigorous, since only the integer arithmetic was assigned to a computer.","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46830079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Threshold approximations for the resolvent of a polynomial nonnegative operator pencil","authors":"V. Sloushch, T. Suslina","doi":"10.1090/spmj/1704","DOIUrl":"https://doi.org/10.1090/spmj/1704","url":null,"abstract":"<p>In a Hilbert space <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"German upper H\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"fraktur\">H</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathfrak {H}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, a family of operators <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A left-parenthesis t right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>A</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">A(t)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"t element-of double-struck upper R\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo>∈<!-- ∈ --></mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">R</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">tin mathbb {R}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, is treated admitting a factorization of the form <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper A left-parenthesis t right-parenthesis equals upper X left-parenthesis t right-parenthesis Superscript asterisk Baseline upper X left-parenthesis t right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>A</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:msup>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>∗<!-- ∗ --></mml:mo>\u0000 </mml:msup>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">A(t) = X(t)^* X(t)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, where <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X left-parenthesis t right-parenthesis equals upper X 0 plus upper X 1 t plus midline-horizontal-ellipsis plus upper X Subscript p Baseline t Superscript p\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:mn>0</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:msu","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49483908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solution asymptotics for the system of Landau–Lifshitz equations under a saddle-node dynamical bifurcation","authors":"L. Kalyakin","doi":"10.1090/spmj/1698","DOIUrl":"https://doi.org/10.1090/spmj/1698","url":null,"abstract":"A system of two nonlinear differential equations with slowly varying coefficients is treated. The asymptotics in the small parameter for the solutions that have a narrow transition layer is studied. Such a layer occurs near the moment where the number of roots of the corresponding algebraic system of equations changes. To construct the asymptotics, the matching method involving three scales is used.","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47708952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}