St Petersburg Mathematical Journal最新文献

{"title":"Three dimensions of metric-measure spaces, Sobolev embeddings and optimal sign transport","authors":"N. Nikolski","doi":"10.1090/spmj/1752","DOIUrl":"https://doi.org/10.1090/spmj/1752","url":null,"abstract":"<p>A sign interlacing phenomenon for Bessel sequences, frames, and Riesz bases <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis u Subscript k Baseline right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>k</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(u_{k})</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> in <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L squared\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">L^2</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> spaces over the spaces of homogeneous type <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Omega equals left-parenthesis normal upper Omega comma rho comma mu right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi mathvariant=\"normal\">Ω<!-- Ω --></mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi mathvariant=\"normal\">Ω<!-- Ω --></mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>ρ<!-- ρ --></mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>μ<!-- μ --></mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Omega =(Omega ,rho ,mu )</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> satisfying the doubling/halving conditions is studied. Under some relations among three basic metric-measure parameters of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper Omega\">\u0000 <mml:semantics>\u0000 <mml:mi mathvariant=\"normal\">Ω<!-- Ω --></mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">Omega</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, asymptotics is obtained for the mass moving norms <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-vertical-bar u Subscript k Baseline double-vertical-bar Subscript upper K upper R\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">‖<!-- ‖ --></mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mi>k</mml:mi>\u0000 </mml:msub>\u0000 <mml:msub>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">‖<!-- ‖ --></mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>K</mml:mi>\u0000 <mml:mi>R</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">|u_k|_{KR}</mml:annotation>\u0000 </","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45377022","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 the local finite separability of finitely generated associative rings","authors":"S. Kublanovskiĭ","doi":"10.1090/spmj/1751","DOIUrl":"https://doi.org/10.1090/spmj/1751","url":null,"abstract":"It is proved that analogs of the theorems of M. Hall and N. S. Romanovskii are not true in the class of commutative rings. Necessary and sufficient conditions for the local finite separability of monogenic rings are established. As a corollary, it is proved that a finitely generated torsion-free PI-ring is locally finitely separable if and only if its additive group is finitely generated.","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41659194","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 the least common multiple of several consecutive values of a polynomial","authors":"A. Dubickas","doi":"10.1090/spmj/1755","DOIUrl":"https://doi.org/10.1090/spmj/1755","url":null,"abstract":"<p>The periodicity is proved for the arithmetic function defined as the quotient of the product of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k plus 1\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">k+1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> values (where <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k greater-than-or-equal-to 1\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:mo>≥<!-- ≥ --></mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">k geq 1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>) of a polynomial <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f element-of double-struck upper Z left-bracket x right-bracket\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mo>∈<!-- ∈ --></mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">Z</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mi>x</mml:mi>\u0000 <mml:mo stretchy=\"false\">]</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">fin {mathbb Z}[x]</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> at <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"k plus 1\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">k + 1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> consecutive integers <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f left-parenthesis n right-parenthesis f left-parenthesis n plus 1 right-parenthesis midline-horizontal-ellipsis f left-parenthesis n plus k right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>⋯<!-- ⋯ --></mml:mo>\u0000 <mml:mi>f</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mi>k</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">{f(n) f(n + 1) cdots f(n + k)}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</i","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49298082","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":"Automorphisms of algebraic varieties and infinite transitivity","authors":"I. Arzhantsev","doi":"10.1090/spmj/1749","DOIUrl":"https://doi.org/10.1090/spmj/1749","url":null,"abstract":"This is a survey of recent results on multiple transitivity for automorphism groups of affine algebraic varieties. The property of infinite transitivity of the special automorphism group is treated, which is equivalent to the flexibility of the corresponding affine variety. These properties have important algebraic and geometric consequences. At the same time they are fulfilled for wide classes of varieties. Also, the situations are studied where infinite transitivity occurs for automorphism groups generated by finitely many one-parameter subgroups. In the appendices to the paper, the results on infinitely transitive actions in complex analysis and in combinatorial group theory are discussed.","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44296557","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":"Two stars theorems for traces of the Zygmund space","authors":"A. Brudnyi","doi":"10.1090/spmj/1744","DOIUrl":"https://doi.org/10.1090/spmj/1744","url":null,"abstract":"<p>For a Banach space <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\u0000 <mml:semantics>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> defined in terms of a big-<inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper O\">\u0000 <mml:semantics>\u0000 <mml:mi>O</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">O</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> condition and its subspace <italic>x</italic> defined by the corresponding little-<inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"o\">\u0000 <mml:semantics>\u0000 <mml:mi>o</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">o</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> condition, the biduality property (generalizing the concept of reflexivity) asserts that the bidual of <italic>x</italic> is naturally isometrically isomorphic to <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\u0000 <mml:semantics>\u0000 <mml:mi>X</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. The property is known for pairs of many classical function spaces (such as <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis script l Subscript normal infinity Baseline comma c 0 right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>ℓ<!-- ℓ --></mml:mi>\u0000 <mml:mi mathvariant=\"normal\">∞<!-- ∞ --></mml:mi>\u0000 </mml:msub>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>c</mml:mi>\u0000 <mml:mn>0</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">(ell _infty , c_0)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, (BMO, VMO), (Lip, lip), etc.) and plays an important role in the study of their geometric structure. The present paper is devoted to the biduality property for traces to closed subsets <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S subset-of double-struck upper R Superscript n\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>S</mml:mi>\u0000 <mml:mo>⊂<!-- ⊂ --></mml:mo>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">R</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:msup>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">Ssubset mathbb {R}^n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of a generalized Zygmund space <in","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43598591","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 the rate of decay at infinity for solutions to the Schrödinger equation in a half-cylinder","authors":"S. Krymskii, N. Filonov","doi":"10.1090/spmj/1746","DOIUrl":"https://doi.org/10.1090/spmj/1746","url":null,"abstract":"<p>Consider the equation <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"minus normal upper Delta u plus upper V u equals 0\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mi mathvariant=\"normal\">Δ<!-- Δ --></mml:mi>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:mi>V</mml:mi>\u0000 <mml:mi>u</mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">-Delta u + Vu = 0</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> in the half-cylinder <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-bracket 0 comma normal infinity right-parenthesis times left-parenthesis 0 comma 2 pi right-parenthesis Superscript d\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo stretchy=\"false\">[</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi mathvariant=\"normal\">∞<!-- ∞ --></mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mo>×<!-- × --></mml:mo>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mn>0</mml:mn>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mn>2</mml:mn>\u0000 <mml:mi>π<!-- π --></mml:mi>\u0000 <mml:msup>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mi>d</mml:mi>\u0000 </mml:msup>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">[0, infty ) times (0,2pi )^d</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> with periodic boundary conditions. Assume that the potential <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper V\">\u0000 <mml:semantics>\u0000 <mml:mi>V</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">V</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is bounded. The possible rate of decay at infinity for a nontrivial solution is studied. It is shown that the fastest rate of decay is <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"e Superscript minus c x\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mi>e</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mi>c</mml:mi>\u0000 <mml:mi>x</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">e^{-cx}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> for <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"d equals 1\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>d</mml:mi>\u0000 <mml:mo>=</mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">d=1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> or <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2\">\u0000 <mml:semant","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49192155","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 the algebraic cobordism spectra 𝐌𝐒𝐋 and 𝐌𝐒𝐩","authors":"I. Panin, C. Walter","doi":"10.1090/spmj/1748","DOIUrl":"https://doi.org/10.1090/spmj/1748","url":null,"abstract":"<p>The algebraic cobordism spectra <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"bold upper M bold upper S bold upper L\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"bold\">M</mml:mi>\u0000 <mml:mi mathvariant=\"bold\">S</mml:mi>\u0000 <mml:mi mathvariant=\"bold\">L</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbf {MSL}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> and <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"bold upper M bold upper S bold p\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"bold\">M</mml:mi>\u0000 <mml:mi mathvariant=\"bold\">S</mml:mi>\u0000 <mml:mi mathvariant=\"bold\">p</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbf {MSp}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> are constructed. They are commutative monoids in the category of symmetric <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T Superscript logical-and 2\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mi>T</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>∧<!-- ∧ --></mml:mo>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">T^{wedge 2}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-spectra. The spectrum <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"bold upper M bold upper S bold p\">\u0000 <mml:semantics>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"bold\">M</mml:mi>\u0000 <mml:mi mathvariant=\"bold\">S</mml:mi>\u0000 <mml:mi mathvariant=\"bold\">p</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbf {MSp}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> comes with a natural symplectic orientation given either by a tautological Thom class <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"t h Superscript bold upper M bold upper S bold p element-of bold upper M bold upper S bold p Superscript 4 comma 2 Baseline left-parenthesis bold upper M bold upper S bold p Subscript 2 Baseline right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:msup>\u0000 <mml:mi>h</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"bold\">M</mml:mi>\u0000 <mml:mi mathvariant=\"bold\">S</mml:mi>\u0000 <mml:mi mathvariant=\"bold\">p</mml:mi>\u0000 </mml:mrow>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:mo>∈<!-- ∈ --></mml:mo>\u0000 <mml:msup>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"bold\">M</mml:mi>\u0000","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47168639","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":"Arrangements of a plane 𝑀-sextic with respect to a line","authors":"S. Orevkov","doi":"10.1090/spmj/1747","DOIUrl":"https://doi.org/10.1090/spmj/1747","url":null,"abstract":"The mutual arrangements of a real algebraic or real pseudoholomorphic plane projective \u0000\u0000 \u0000 M\u0000 M\u0000 \u0000\u0000-sextic and a line up to isotopy are studied. A complete list of pseudoholomorphic arrangements is obtained. Four of them are proved to be algebraically unrealizable. All the others with two exceptions are algebraically realized.","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45832975","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":"Jackson type inequalities for differentiable functions in weighted Orlicz spaces","authors":"R. Akgün","doi":"10.1090/spmj/1743","DOIUrl":"https://doi.org/10.1090/spmj/1743","url":null,"abstract":"In the present work some Jackson Stechkin type direct theorems of trigonometric approximation are proved in Orlicz spaces with weights satisfying some Muckenhoupt \u0000\u0000 \u0000 \u0000 A\u0000 p\u0000 \u0000 A_p\u0000 \u0000\u0000 condition. To obtain a refined version of the Jackson type inequality, an extrapolation theorem, Marcinkiewicz multiplier theorem, and Littlewood–Paley type results are proved. As a consequence, refined inverse Marchaud type inequalities are obtained. By means of a realization result, an equivalence is found between the fractional order weighted modulus of smoothness and Peetre’s classical weighted \u0000\u0000 \u0000 K\u0000 K\u0000 \u0000\u0000-functional.","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42305178","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":"Isomonodromic quantization of the second Painlevé equation by means of conservative Hamiltonian systems with two degrees of freedom","authors":"B. Suleimanov","doi":"10.1090/spmj/1739","DOIUrl":"https://doi.org/10.1090/spmj/1739","url":null,"abstract":"For the three nonstationary Schrödinger equations \u0000\u0000 \u0000 \u0000 i\u0000 ℏ\u0000 \u0000 Ψ\u0000 \u0000 τ\u0000 \u0000 \u0000 =\u0000 H\u0000 (\u0000 x\u0000 ,\u0000 y\u0000 ,\u0000 −\u0000 i\u0000 ℏ\u0000 \u0000 ∂\u0000 \u0000 ∂\u0000 x\u0000 \u0000 \u0000 ,\u0000 −\u0000 i\u0000 ℏ\u0000 \u0000 ∂\u0000 \u0000 ∂\u0000 y\u0000 \u0000 \u0000 )\u0000 Ψ\u0000 ,\u0000 \u0000 begin{equation*} ihbar Psi _{tau }=H(x,y,-ihbar frac {partial }{partial x},-ihbar frac {partial }{partial y})Psi , end{equation*}\u0000 \u0000\u0000\u0000 solutions are constructed that correspond to conservative Hamiltonian systems with two degrees of freedom whose general solutions can be represented by those of the second Painlevé equation. These solutions of the Schrödinger equations are expressed via fundamental solutions of systems of linear equations arising in the isomonodromic deformations method, the compatibility condition of which is the second Painlevé equation. The constructed solutions of two nonstationary Schrödinger equations are globally smooth. Some of the smooth solutions in question of one of these two equations exponentially tend to zero as \u0000\u0000 \u0000 \u0000 \u0000 x\u0000 2\u0000 \u0000 +\u0000 \u0000 y\u0000 2\u0000 \u0000 →\u0000 ∞\u0000 \u0000 x^2+y^2to infty\u0000 \u0000\u0000 if the corresponding solutions of linear systems that are used in the method of isomonodromic deformations are compatible on the so-called 1-tronquée solutions of the second Painlevé equation.","PeriodicalId":51162,"journal":{"name":"St Petersburg Mathematical Journal","volume":" ","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42734995","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}