Pub Date : 2018-01-01DOI: 10.4310/MAA.2018.V25.N1.A2
Tujin Kim, F. Huang
. In this paper we are concerned with the non-steady Navier-Stokes and Stokes prob- lems with mixed boundary conditions involving Tresca slip condition, leak condition, one-sided leak conditions, velocity, pressure, rotation, stress and normal derivative of velocity together. We get variational inequalities with one unknown which are equivalent to the original PDE problems for the smooth solutions. Then, we study existence and uniqueness of solutions to the corresponding variational inequalities. Special attention is given to a case that through boundary there is leak, and for such a case under a compatibility condition at the initial instance it is proved that for the small data there exists a unique solution on the given interval of time. Relying the results, we get existence, uniqueness and estimates of solutions to the Navier-Stokes and Stokes problems with the boundary conditions.
{"title":"The non-steady Navier–Stokes systems with mixed boundary conditions including friction conditions","authors":"Tujin Kim, F. Huang","doi":"10.4310/MAA.2018.V25.N1.A2","DOIUrl":"https://doi.org/10.4310/MAA.2018.V25.N1.A2","url":null,"abstract":". In this paper we are concerned with the non-steady Navier-Stokes and Stokes prob- lems with mixed boundary conditions involving Tresca slip condition, leak condition, one-sided leak conditions, velocity, pressure, rotation, stress and normal derivative of velocity together. We get variational inequalities with one unknown which are equivalent to the original PDE problems for the smooth solutions. Then, we study existence and uniqueness of solutions to the corresponding variational inequalities. Special attention is given to a case that through boundary there is leak, and for such a case under a compatibility condition at the initial instance it is proved that for the small data there exists a unique solution on the given interval of time. Relying the results, we get existence, uniqueness and estimates of solutions to the Navier-Stokes and Stokes problems with the boundary conditions.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488529","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}
Pub Date : 2017-10-19DOI: 10.4310/maa.2019.v26.n2.a4
Ryan M. Evans, Arvind K. Balijepalli, Anthony J. Kearsley
A partial differential equation (PDE) was developed to describe time-dependent ligand-receptor interactions for applications in biosensing using field effect transistors (FET). The model describes biochemical interactions at the sensor surface (or biochemical gate) located at the bottom of a solution-well, which result in a time-dependent change in the FET conductance. It was shown that one can exploit the disparate length scales of the solution-well and biochemical gate to reduce the coupled PDE model to a single nonlinear integrodifferential equation (IDE) that describes the concentration of reacting species. Although this equation has a convolution integral with a singular kernel, a numerical approximation was constructed by applying the method of lines. The need for specialized quadrature techniques was obviated and numerical evidence strongly suggests that this method achieves first-order accuracy. Results reveal a depletion region on the biochemical gate, which non-uniformly alters the surface potential of the semiconductor.
{"title":"Diffusion-limited reactions in nanoscale electronics","authors":"Ryan M. Evans, Arvind K. Balijepalli, Anthony J. Kearsley","doi":"10.4310/maa.2019.v26.n2.a4","DOIUrl":"https://doi.org/10.4310/maa.2019.v26.n2.a4","url":null,"abstract":"A partial differential equation (PDE) was developed to describe time-dependent ligand-receptor interactions for applications in biosensing using field effect transistors (FET). The model describes biochemical interactions at the sensor surface (or biochemical gate) located at the bottom of a solution-well, which result in a time-dependent change in the FET conductance. It was shown that one can exploit the disparate length scales of the solution-well and biochemical gate to reduce the coupled PDE model to a single nonlinear integrodifferential equation (IDE) that describes the concentration of reacting species. Although this equation has a convolution integral with a singular kernel, a numerical approximation was constructed by applying the method of lines. The need for specialized quadrature techniques was obviated and numerical evidence strongly suggests that this method achieves first-order accuracy. Results reveal a depletion region on the biochemical gate, which non-uniformly alters the surface potential of the semiconductor.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2017-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44119724","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}
Pub Date : 2017-06-29DOI: 10.4310/maa.2019.v26.n1.a2
M. Pflaum, Graeme Wilkin
In this article we study Whitney (B) regular stratified spaces with the action of a compact Lie group $G$ which preserves the strata. We prove an equivariant submersion theorem and use it to show that such a $G$-stratified space carries a system of $G$-equivariant control data. As an application, we show that if $A subset X$ is a closed $G$-stratified subspace which is a union of strata of $X$, then the inclusion $i : A hookrightarrow X$ is a $G$-equivariant cofibration. In particular, this theorem applies whenever $X$ is a $G$-invariant analytic subspace of an analytic $G$-manifold $M$ and $A hookrightarrow X$ is a closed $G$-invariant analytic subspace of $X$.
本文研究了保留地层的紧李群$G$作用下的Whitney (B)正则分层空间。我们证明了一个等变淹没定理，并利用它证明了这样一个$G$-分层空间携带一个$G$-等变控制数据系统。作为一个应用，我们证明了如果$A 子集X$是$G$分层的封闭子空间，它是$X$的层的并，那么包含$i: A hookrightarrow X$是$G$-等变共轭。特别地，当$X$是解析$G$流形$M$的$G$不变解析子空间，$ a hookright row X$是$X$的$G$不变解析子空间时，这个定理适用。
{"title":"Equivariant control data and neighborhood deformation retractions","authors":"M. Pflaum, Graeme Wilkin","doi":"10.4310/maa.2019.v26.n1.a2","DOIUrl":"https://doi.org/10.4310/maa.2019.v26.n1.a2","url":null,"abstract":"In this article we study Whitney (B) regular stratified spaces with the action of a compact Lie group $G$ which preserves the strata. We prove an equivariant submersion theorem and use it to show that such a $G$-stratified space carries a system of $G$-equivariant control data. As an application, we show that if $A subset X$ is a closed $G$-stratified subspace which is a union of strata of $X$, then the inclusion $i : A hookrightarrow X$ is a $G$-equivariant cofibration. In particular, this theorem applies whenever $X$ is a $G$-invariant analytic subspace of an analytic $G$-manifold $M$ and $A hookrightarrow X$ is a closed $G$-invariant analytic subspace of $X$.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2017-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47535320","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}
{"title":"Singularities of low degree complete intersections","authors":"S. Kovács","doi":"10.14288/1.0043851","DOIUrl":"https://doi.org/10.14288/1.0043851","url":null,"abstract":"","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66895079","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}
Pub Date : 2017-01-01DOI: 10.4310/MAA.2017.V24.N1.A8
J. Seade
Introduction. There are several classical approaches to studying the geometry and topology of isolated singularities (V, 0) defined by a holomorphic map-germ (C, 0) f → (C, 0). One of these is by looking at resolutions of the singularity, π : Ṽ → V . Another is by considering the non-critical levels of the function f and the way how these degenerate to the special fiber V . Laufer’s formula for the Milnor number establishes a beautiful bridge between these two points of view. The formula says that if n = 3, then one has:
{"title":"Remarks on Laufer’s formula for the Milnor number, Rochlin’s signature theorem and the analytic Euler characteristic of compact complex manifolds","authors":"J. Seade","doi":"10.4310/MAA.2017.V24.N1.A8","DOIUrl":"https://doi.org/10.4310/MAA.2017.V24.N1.A8","url":null,"abstract":"Introduction. There are several classical approaches to studying the geometry and topology of isolated singularities (V, 0) defined by a holomorphic map-germ (C, 0) f → (C, 0). One of these is by looking at resolutions of the singularity, π : Ṽ → V . Another is by considering the non-critical levels of the function f and the way how these degenerate to the special fiber V . Laufer’s formula for the Milnor number establishes a beautiful bridge between these two points of view. The formula says that if n = 3, then one has:","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488292","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}
Pub Date : 2017-01-01DOI: 10.4310/MAA.2017.V24.N3.A2
Abraha Hailu
. We study the microlocal smoothness of C 2 solutions u of the first-order nonlinear partial differential equation x where f ( x,t,ζ 0 ,ζ ) is a complex-valued function which is C ∞ in all the variables ( x,t,ζ 0 ,ζ ) and holomorphic in the variables ( ζ 0 ,ζ ) . If the solution u is C 2 , σ ∈ Char( L u ) and 1 √− 1 σ ([ L u , ¯ L u ]) < 0 , then we show that σ / ∈ WF ( u ) . Here WF ( u ) denotes the C ∞ wave front set of u and Char( L u ) denotes the characteristic set of the linearized operator
{"title":"On Microlocal Smoothness of Solutions of First Order Nonlinear PDE","authors":"Abraha Hailu","doi":"10.4310/MAA.2017.V24.N3.A2","DOIUrl":"https://doi.org/10.4310/MAA.2017.V24.N3.A2","url":null,"abstract":". We study the microlocal smoothness of C 2 solutions u of the first-order nonlinear partial differential equation x where f ( x,t,ζ 0 ,ζ ) is a complex-valued function which is C ∞ in all the variables ( x,t,ζ 0 ,ζ ) and holomorphic in the variables ( ζ 0 ,ζ ) . If the solution u is C 2 , σ ∈ Char( L u ) and 1 √− 1 σ ([ L u , ¯ L u ]) < 0 , then we show that σ / ∈ WF ( u ) . Here WF ( u ) denotes the C ∞ wave front set of u and Char( L u ) denotes the characteristic set of the linearized operator","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488444","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}
Pub Date : 2017-01-01DOI: 10.4310/MAA.2017.v24.n1.a1
Henry B. Laufer
. We present the slides from a talk about Wall Street and about seasonality in United States home prices. Seasonality is approached via two non–standard paths: for prices we use initial listed prices, for seasonality we use easy Fourier analysis. Prices peak at the end of May. The amplitude of the seasonal change is large in recent years: 5.3%. There is a similar seasonality in the areas of listed homes. But the amplitude of the area change is much smaller: 1.9%. The price seasonality is uniform throughout most of the United States.
{"title":"Seasonality in United States home prices","authors":"Henry B. Laufer","doi":"10.4310/MAA.2017.v24.n1.a1","DOIUrl":"https://doi.org/10.4310/MAA.2017.v24.n1.a1","url":null,"abstract":". We present the slides from a talk about Wall Street and about seasonality in United States home prices. Seasonality is approached via two non–standard paths: for prices we use initial listed prices, for seasonality we use easy Fourier analysis. Prices peak at the end of May. The amplitude of the seasonal change is large in recent years: 5.3%. There is a similar seasonality in the areas of listed homes. But the amplitude of the area change is much smaller: 1.9%. The price seasonality is uniform throughout most of the United States.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488179","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}
Pub Date : 2017-01-01DOI: 10.4310/MAA.2017.v24.n2.a9
T. Tomaru
. In this paper, we explain several results on the relations between the maximal ideal cycles for normal surface singularities and pencil of curves. Also we report recent results by the author on maximal ideal types for normal surface singularities of some type.
{"title":"Maximal ideal cycles and maximal ideal types for normal surface singularities","authors":"T. Tomaru","doi":"10.4310/MAA.2017.v24.n2.a9","DOIUrl":"https://doi.org/10.4310/MAA.2017.v24.n2.a9","url":null,"abstract":". In this paper, we explain several results on the relations between the maximal ideal cycles for normal surface singularities and pencil of curves. Also we report recent results by the author on maximal ideal types for normal surface singularities of some type.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488401","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}
Pub Date : 2017-01-01DOI: 10.4310/MAA.2017.V24.N1.A2
A. Aleksandrov
. The purpose of the paper is to introduce a notion of logarithmic differential forms on singular varieties. We also compute the Poincar´e series and generators of the corresponding modules in a few particular cases, including quasihomogeneous complete intersections, normal varieties, determinantal varieties, and others.
{"title":"Logarithmic differential forms on Cohen–Macaulay varieties","authors":"A. Aleksandrov","doi":"10.4310/MAA.2017.V24.N1.A2","DOIUrl":"https://doi.org/10.4310/MAA.2017.V24.N1.A2","url":null,"abstract":". The purpose of the paper is to introduce a notion of logarithmic differential forms on singular varieties. We also compute the Poincar´e series and generators of the corresponding modules in a few particular cases, including quasihomogeneous complete intersections, normal varieties, determinantal varieties, and others.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488223","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}
Pub Date : 2017-01-01DOI: 10.4310/MAA.2017.V24.N1.A10
S. Yau, Huaiqing Zuo
This survey paper discusses many different ways of characterizations of weighted homogeneous (quasi-homogeneity) isolated hypersurface singularities.
本文讨论了加权齐次(拟齐次)孤立超曲面奇点的许多不同的表征方法。
{"title":"Nine characterizations of weighted homogeneous isolated hypersurface singularities","authors":"S. Yau, Huaiqing Zuo","doi":"10.4310/MAA.2017.V24.N1.A10","DOIUrl":"https://doi.org/10.4310/MAA.2017.V24.N1.A10","url":null,"abstract":"This survey paper discusses many different ways of characterizations of weighted homogeneous (quasi-homogeneity) isolated hypersurface singularities.","PeriodicalId":18467,"journal":{"name":"Methods and applications of analysis","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70488187","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}
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