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Methods and applications of analysis最新文献

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Certain normal surface singularities of general type 一般型法线表面的奇异性
IF 0.3
Methods and applications of analysis Pub Date : 2017-01-01 DOI: 10.4310/MAA.2017.V24.N1.A6
K. Konno
{"title":"Certain normal surface singularities of general type","authors":"K. Konno","doi":"10.4310/MAA.2017.V24.N1.A6","DOIUrl":"https://doi.org/10.4310/MAA.2017.V24.N1.A6","url":null,"abstract":"Koyama’s inequality for normal surface singularities gives the upper bound on the self-intersection number of the canonical cycle in terms of the arithmetic genus. For those singularities of fundamental genus two attaining the bound, a formula for computing the geometric genus is shown and the resolution dual graphs are roughly classified. In Gorenstein case, the multiplicity and the embedding dimension are also computed.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"24 1","pages":"71-97"},"PeriodicalIF":0.3,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
An intrinsic approach to stable embedding of normal surface deformations 法向曲面变形稳定嵌入的内在方法
IF 0.3
Methods and applications of analysis Pub Date : 2017-01-01 DOI: 10.4310/MAA.2017.v24.n2.a4
A. Harris
{"title":"An intrinsic approach to stable embedding of normal surface deformations","authors":"A. Harris","doi":"10.4310/MAA.2017.v24.n2.a4","DOIUrl":"https://doi.org/10.4310/MAA.2017.v24.n2.a4","url":null,"abstract":"We introduce the notion of involutive Kodaira-Spencer deformations of the regular part X0 of a normal surface singularity, which form a subspace of the analytic cohomology H(X0, T X0). Examples of involutive deformations for which the Stein completion does not embed in a complex Euclidean space of stable dimension are in fact well-known. Under the assumption that X0 admits a Kähler metric with L-curvature, we show that unstable deformations are avoided if the holomorphic functions which determine an embedding of the central fibre are correspondingly deformed into functions which can be uniformly bounded on compact subsets.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"24 1","pages":"277-292"},"PeriodicalIF":0.3,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Residual algebraic restrictions of differential forms 微分形式的残差代数限制
IF 0.3
Methods and applications of analysis Pub Date : 2017-01-01 DOI: 10.4310/MAA.2017.V24.N1.A4
G. Ishikawa, S. Janeczko
{"title":"Residual algebraic restrictions of differential forms","authors":"G. Ishikawa, S. Janeczko","doi":"10.4310/MAA.2017.V24.N1.A4","DOIUrl":"https://doi.org/10.4310/MAA.2017.V24.N1.A4","url":null,"abstract":"We study germs of differential forms over singular varieties. The geometric restriction of differential forms to singular varieties is introduced and algebraic restrictions of differential forms with vanishing geometric restrictions, called residual algebraic restrictions, are investigated. Residues of plane curves-germs, hypersurfaces, Lagrangian varieties as well as the geometric and algebraic restriction via a mapping were calculated.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"24 1","pages":"45-61"},"PeriodicalIF":0.3,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Sextic curves with six double points on a conic 圆锥曲线上有六个双点的六次曲线
IF 0.3
Methods and applications of analysis Pub Date : 2017-01-01 DOI: 10.4310/MAA.2017.V24.N2.A6
K. Konno, Ezio Stagnaro
{"title":"Sextic curves with six double points on a conic","authors":"K. Konno, Ezio Stagnaro","doi":"10.4310/MAA.2017.V24.N2.A6","DOIUrl":"https://doi.org/10.4310/MAA.2017.V24.N2.A6","url":null,"abstract":"Let C6 be a plane sextic curve with 6 double points that are not nodes. It is shown that if they are on a conic C2, then the unique possible case is that all of them are ordinary cusps. From this it follows that C6 is irreducible. Moreover, there is a plane cubic curve C3 such that C6 = C 3 2 + C 3 . Such curves are closely related to both the branch curve of the projection to a plane of the general cubic surface from a point outside it and canonical surfaces in P or P whose desingularizations have birational invariants q > 0, pg = 4 or pg = 5, P2 ≤ 23.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"24 1","pages":"295-302"},"PeriodicalIF":0.3,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Zero-dimensional gradient singularities 零维梯度奇点
IF 0.3
Methods and applications of analysis Pub Date : 2017-01-01 DOI: 10.4310/MAA.2017.V24.N2.A1
A. Aleksandrov, Hui-Qin Zuo, Henry Laufer
{"title":"Zero-dimensional gradient singularities","authors":"A. Aleksandrov, Hui-Qin Zuo, Henry Laufer","doi":"10.4310/MAA.2017.V24.N2.A1","DOIUrl":"https://doi.org/10.4310/MAA.2017.V24.N2.A1","url":null,"abstract":". We discuss an approach to the problem of classifying zero-dimensional gradient quasihomogeneous singularities using simple properties of deformation theory. As an example, we enumerate all such singularities with modularity ℘ = 0 and with Milnor number not greater than 12. We also compute normal forms and monomial vector-bases of the first cotangent homology and cohomology modules, the corresponding Poincar´e polynomials, inner modality, inner modularity, primitive ideals, etc.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"10 1","pages":"169-184"},"PeriodicalIF":0.3,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Minimizers for open-shell, spin-polarised Kohn–Sham equations for non-relativistic and quasi-relativistic molecular systems 非相对论和准相对论分子系统的开壳、自旋极化Kohn-Sham方程的最小解
IF 0.3
Methods and applications of analysis Pub Date : 2016-11-29 DOI: 10.4310/MAA.2016.V23.N3.A4
C. Argáez, M. Melgaard
{"title":"Minimizers for open-shell, spin-polarised Kohn–Sham equations for non-relativistic and quasi-relativistic molecular systems","authors":"C. Argáez, M. Melgaard","doi":"10.4310/MAA.2016.V23.N3.A4","DOIUrl":"https://doi.org/10.4310/MAA.2016.V23.N3.A4","url":null,"abstract":"We study the open-shell, spin-polarized Kohn-Sham models for non-relativistic and quasi-relativistic N-electron Coulomb systems, that is, systems where the kinetic energy of the electrons is given by either the non-relativistic operator −Δxn or the quasi-relativistic operator √−α−²Δxn + α−4 − α−². For standard and extended Kohn-Sham models in the local density approximation, we prove existence of a ground state (or minimizer) provided that the total charge Ztot of K nuclei is greater than N − 1. For the quasi-relativistic setting we also need that Ztot is smaller than a critical charge Zc = 2α−¹π−¹.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"23 1","pages":"269-292"},"PeriodicalIF":0.3,"publicationDate":"2016-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488616","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bernstein polynomial of $2$-Puiseux pairs irreducible plane curve singularities 2 -Puiseux对不可约平面曲线奇点的Bernstein多项式
IF 0.3
Methods and applications of analysis Pub Date : 2016-11-03 DOI: 10.4310/MAA.2017.V24.N2.A2
Enrique Artal Bartolo, P. Cassou-Noguès, I. Luengo, A. Melle-Hern'andez
{"title":"Bernstein polynomial of $2$-Puiseux pairs irreducible plane curve singularities","authors":"Enrique Artal Bartolo, P. Cassou-Noguès, I. Luengo, A. Melle-Hern'andez","doi":"10.4310/MAA.2017.V24.N2.A2","DOIUrl":"https://doi.org/10.4310/MAA.2017.V24.N2.A2","url":null,"abstract":"In 1982, Tamaki Yano proposed a conjecture predicting the set of b-exponents of an irreducible plane curve singularity germ which is generic in its equisingularity class. In cite{ACLM-Yano2} we proved the conjecture for the case in which the germ has two Puiseux pairs and its algebraic monodromy has distinct eigenvalues. In this article we aim to study the Bernstein polynomial for any function with the hypotheses above. In particular the set of all common roots of those Bernstein polynomials is given. We provide also bounds for some analytic invariants of singularities and illustrate the computations in suitable examples.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"24 1","pages":"185-214"},"PeriodicalIF":0.3,"publicationDate":"2016-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Unwinding spirals I 展开螺旋I
IF 0.3
Methods and applications of analysis Pub Date : 2016-03-10 DOI: 10.4310/maa.2018.v25.n3.a3
A. Fish, L. Paunescu
{"title":"Unwinding spirals I","authors":"A. Fish, L. Paunescu","doi":"10.4310/maa.2018.v25.n3.a3","DOIUrl":"https://doi.org/10.4310/maa.2018.v25.n3.a3","url":null,"abstract":". Inspired by the previous works by Freedman and He [FH], and Katznelson, Subhashis Nag, and Sullivan [KNS], we study the spiraling behaviour around a singularity of bi-Lipschitz homeomorphisms in R 2 . In particular, we show that there is no bi-Lipschitz homeomorphism of R 2 that maps a spiral with a sub-exponential decay of winding radii to an unwound arc. This result is sharp as shows an example of a logarithmic spiral.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"25 1","pages":"225-232"},"PeriodicalIF":0.3,"publicationDate":"2016-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Asymptotic analysis of difference equations with quadratic coefficients 二次系数差分方程的渐近分析
IF 0.3
Methods and applications of analysis Pub Date : 2016-01-01 DOI: 10.4310/MAA.2016.V23.N2.A2
Xiang-Sheng Wang
{"title":"Asymptotic analysis of difference equations with quadratic coefficients","authors":"Xiang-Sheng Wang","doi":"10.4310/MAA.2016.V23.N2.A2","DOIUrl":"https://doi.org/10.4310/MAA.2016.V23.N2.A2","url":null,"abstract":"In this paper, we study asymptotic solutions of second-order difference equations with quadratic coefficients. According to the parameter values, we classify the difference equations into three cases and derive Plancherel-Rotach type asymptotic formulas of the solutions respectively. As direct applications of our main results, we also provide asymptotic formulas of associated Meixner-Pollaczek polynomials, associated Meixner polynomials, and associated Laguerre polynomials, respectively.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"23 1","pages":"155-172"},"PeriodicalIF":0.3,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A functional inequality and its applications to a class of nonlinear fourth-order parabolic equations 一类非线性四阶抛物型方程的泛函不等式及其应用
IF 0.3
Methods and applications of analysis Pub Date : 2016-01-01 DOI: 10.4310/MAA.2016.V23.N2.A3
Xiangsheng Xu
{"title":"A functional inequality and its applications to a class of nonlinear fourth-order parabolic equations","authors":"Xiangsheng Xu","doi":"10.4310/MAA.2016.V23.N2.A3","DOIUrl":"https://doi.org/10.4310/MAA.2016.V23.N2.A3","url":null,"abstract":"In this article we study the initial-boundary value problem for a family of nonlinear fourth order parabolic equations. The classical quantum drift-diffusion model is a member of the family. Two new existence theorems are established. Our approach is based upon a semi-discretization scheme, which generates a sequence of positive approximate solutions, and a functional inequality of the type","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":"55 1","pages":"173-204"},"PeriodicalIF":0.3,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
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