Pub Date : 2021-12-01DOI: 10.1088/978-0-7503-3655-0ch11
Jeffrey H. Williams
{"title":"Dimensions involving molecules and fields","authors":"Jeffrey H. Williams","doi":"10.1088/978-0-7503-3655-0ch11","DOIUrl":"https://doi.org/10.1088/978-0-7503-3655-0ch11","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":"35 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86952343","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}
Pub Date : 2021-12-01DOI: 10.1088/978-0-7503-3655-0ch10
Jeffrey H. Williams
{"title":"The equilibrium between matter and energy","authors":"Jeffrey H. Williams","doi":"10.1088/978-0-7503-3655-0ch10","DOIUrl":"https://doi.org/10.1088/978-0-7503-3655-0ch10","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":"2 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87346293","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}
Pub Date : 2021-12-01DOI: 10.1088/978-0-7503-3655-0ch2
Jeffrey H. Williams
{"title":"A brief history of dimensional analysis: a holistic approach to physics","authors":"Jeffrey H. Williams","doi":"10.1088/978-0-7503-3655-0ch2","DOIUrl":"https://doi.org/10.1088/978-0-7503-3655-0ch2","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":"11 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81860993","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}
Pub Date : 2021-12-01DOI: 10.1088/978-0-7503-3655-0ch14
Jeffrey H. Williams
{"title":"The great principle of similitude in biology and sport","authors":"Jeffrey H. Williams","doi":"10.1088/978-0-7503-3655-0ch14","DOIUrl":"https://doi.org/10.1088/978-0-7503-3655-0ch14","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":"90 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82264724","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}
Pub Date : 2021-12-01DOI: 10.1088/978-0-7503-3655-0ch8
Jeffrey H. Williams
{"title":"Continuum forces","authors":"Jeffrey H. Williams","doi":"10.1088/978-0-7503-3655-0ch8","DOIUrl":"https://doi.org/10.1088/978-0-7503-3655-0ch8","url":null,"abstract":"","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":"30 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83086785","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}
Pub Date : 2021-11-09DOI: 10.1142/s0219025723500224
Ramiro Scorolli
In a recent article Lanconelli and Scorolli (2021) extended to the multidimensional case a Wong-Zakai-type approximation for It^o stochastic differential equations proposed by Oksendal and Hu (1996). The aim of the current paper is to extend the latter result to system of stochastic differential equations of It^o type driven by fractional Brownian motion (fBm) like those considered by Hu (2018). The covariance structure of the fBm precludes us from using the same approach as that used by Lanconelli and Scorolli and instead we employ a truncated Cameron-Martin expansion as the approximation for the fBm. We are naturally led to the investigation of a semilinear hyperbolic system of evolution equations in several space variables that we utilize for constructing a solution of the Wong-Zakai approximated systems. We show that the law of each element of the approximating sequence solves in the sense of distribution a Fokker-Planck equation and that the sequence converges to the solution of the Ito^o equation, as the number of terms in the expansion goes to infinite.
{"title":"Wong-Zakai approximations for quasilinear systems of Ito's type stochastic differential equations driven by fBm with H > 1 2","authors":"Ramiro Scorolli","doi":"10.1142/s0219025723500224","DOIUrl":"https://doi.org/10.1142/s0219025723500224","url":null,"abstract":"In a recent article Lanconelli and Scorolli (2021) extended to the multidimensional case a Wong-Zakai-type approximation for It^o stochastic differential equations proposed by Oksendal and Hu (1996). The aim of the current paper is to extend the latter result to system of stochastic differential equations of It^o type driven by fractional Brownian motion (fBm) like those considered by Hu (2018). The covariance structure of the fBm precludes us from using the same approach as that used by Lanconelli and Scorolli and instead we employ a truncated Cameron-Martin expansion as the approximation for the fBm. We are naturally led to the investigation of a semilinear hyperbolic system of evolution equations in several space variables that we utilize for constructing a solution of the Wong-Zakai approximated systems. We show that the law of each element of the approximating sequence solves in the sense of distribution a Fokker-Planck equation and that the sequence converges to the solution of the Ito^o equation, as the number of terms in the expansion goes to infinite.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":"75 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89170033","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}
Pub Date : 2021-11-06DOI: 10.1142/s0219025723500091
Haesung Lee
We show the $L^r(mathbb{R}^d, mu)$-uniqueness for any $r in (1, 2]$ and the essential self-adjointness of a Dirichlet operator $Lf = Delta f +langle frac{1}{rho}nabla rho , nabla f rangle$, $f in C_0^{infty}(mathbb{R}^d)$ with $d geq 3$ and $mu=rho dx$. In particular, $nabla rho$ is allowed to be in $L^d_{loc}(mathbb{R}^d, mathbb{R}^d)$ or in $L^{2+varepsilon}_{loc}(mathbb{R}^d, mathbb{R}^d)$ for some $varepsilon>0$, while $rho$ is required to be locally bounded below and above by strictly positive constants. The main tools in this paper are elliptic regularity results for divergence and non-divergence type operators and basic properties of Dirichlet forms and their resolvents.
我们证明了任意$r in (1, 2]$的$L^r(mathbb{R}^d, mu)$ -唯一性和Dirichlet算子$Lf = Delta f +langle frac{1}{rho}nabla rho , nabla f rangle$, $f in C_0^{infty}(mathbb{R}^d)$与$d geq 3$和$mu=rho dx$的本质自伴随性。特别地，$nabla rho$可以在$L^d_{loc}(mathbb{R}^d, mathbb{R}^d)$中，对于某些$varepsilon>0$，也可以在$L^{2+varepsilon}_{loc}(mathbb{R}^d, mathbb{R}^d)$中，而$rho$则需要由严格的正常量在上下局部限定。本文的主要工具是发散型和非发散型算子的椭圆正则性结果和狄利克雷形式的基本性质及其解。
{"title":"Strong uniqueness of finite dimensional Dirichlet operators with singular drifts","authors":"Haesung Lee","doi":"10.1142/s0219025723500091","DOIUrl":"https://doi.org/10.1142/s0219025723500091","url":null,"abstract":"We show the $L^r(mathbb{R}^d, mu)$-uniqueness for any $r in (1, 2]$ and the essential self-adjointness of a Dirichlet operator $Lf = Delta f +langle frac{1}{rho}nabla rho , nabla f rangle$, $f in C_0^{infty}(mathbb{R}^d)$ with $d geq 3$ and $mu=rho dx$. In particular, $nabla rho$ is allowed to be in $L^d_{loc}(mathbb{R}^d, mathbb{R}^d)$ or in $L^{2+varepsilon}_{loc}(mathbb{R}^d, mathbb{R}^d)$ for some $varepsilon>0$, while $rho$ is required to be locally bounded below and above by strictly positive constants. The main tools in this paper are elliptic regularity results for divergence and non-divergence type operators and basic properties of Dirichlet forms and their resolvents.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":"120 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72529332","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}
Pub Date : 2021-11-03DOI: 10.1142/s0219025722500266
M. Voit
We study criteria which ensure that Gibbs states (often also called generalized vacuum states) on distance-regular graphs are positive. Our main criterion assumes that the graph can be embedded into a growing family of distance-regular graphs. For the proof of the positivity we then use polynomial hypergroup theory and translate this positivity into the problem whether for x ∈ [−1, 1] the function n 7→ xn has a positive integral representation w.r.t. the orthogonal polynomials associated with the graph. We apply our criteria to several examples. For Hamming graphs and the infinite distance-transitive graphs we obtain a complete description of the positive Gibbs states.
{"title":"POSITIVITY OF GIBBS STATES ON DISTANCE-REGULAR GRAPHS","authors":"M. Voit","doi":"10.1142/s0219025722500266","DOIUrl":"https://doi.org/10.1142/s0219025722500266","url":null,"abstract":"We study criteria which ensure that Gibbs states (often also called generalized vacuum states) on distance-regular graphs are positive. Our main criterion assumes that the graph can be embedded into a growing family of distance-regular graphs. For the proof of the positivity we then use polynomial hypergroup theory and translate this positivity into the problem whether for x ∈ [−1, 1] the function n 7→ xn has a positive integral representation w.r.t. the orthogonal polynomials associated with the graph. We apply our criteria to several examples. For Hamming graphs and the infinite distance-transitive graphs we obtain a complete description of the positive Gibbs states.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":"4 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89841570","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}
Pub Date : 2021-10-14DOI: 10.1142/s0219025723500054
M. Popa
A recent work by A. Mandarino, T. Linowski and K. .{Z}yczkowski left open the following question. If $ mu_N $ is a certain permutation of entries of a $ N^2 times N^2 $ matrix ("mixing map") and $ U_N $ is a $ N^2 times N^2 $ Haar unitary random matrix, then is the family $ U_N, U_N^{mu_N}, ( U_N^2 )^{mu_N}, dots , ( U_N^m)^{mu_N} $ asymptotically free? (here by $A^{ mu}$ we understand the matrix resulted by permuting the entries of $ A $ according to the permutation $ mu $). This paper presents some techniques for approaching such problems. In particular, one easy consequence of the main result is that the question above has an affirmative answer.
A. Mandarino, T. Linowski和K. Życzkowski最近的一项研究留下了以下问题。如果$ mu_N $是一个$ N^2 times N^2 $矩阵(“混合映射”)的某个元素的排列，$ U_N $是一个$ N^2 times N^2 $ Haar酉随机矩阵，那么族$ U_N, U_N^{mu_N}, ( U_N^2 )^{mu_N}, dots , ( U_N^m)^{mu_N} $是渐近自由的吗?(这里通过$A^{ mu}$我们理解根据$ mu $的排列对$ A $的条目进行排列所得到的矩阵)。本文提出了解决这类问题的一些技术。特别是，主要结果的一个简单结果是，上面的问题有一个肯定的答案。
{"title":"Answer to a question by A. Mandarino, T. Linowski and K. Zyczkowski","authors":"M. Popa","doi":"10.1142/s0219025723500054","DOIUrl":"https://doi.org/10.1142/s0219025723500054","url":null,"abstract":"A recent work by A. Mandarino, T. Linowski and K. .{Z}yczkowski left open the following question. If $ mu_N $ is a certain permutation of entries of a $ N^2 times N^2 $ matrix (\"mixing map\") and $ U_N $ is a $ N^2 times N^2 $ Haar unitary random matrix, then is the family $ U_N, U_N^{mu_N}, ( U_N^2 )^{mu_N}, dots , ( U_N^m)^{mu_N} $ asymptotically free? (here by $A^{ mu}$ we understand the matrix resulted by permuting the entries of $ A $ according to the permutation $ mu $). This paper presents some techniques for approaching such problems. In particular, one easy consequence of the main result is that the question above has an affirmative answer.","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":"57 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85663891","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}
Pub Date : 2021-10-08DOI: 10.1142/s021902572150017x
Ali Reza Neisi, M. Asgari
The concept of Riesz-duals of a frame is a recently introduced concept with broad implications to frame theory in general, as well as to the special cases of Gabor and wavelet analysis. In this paper, we introduce various alternative Riesz-duals, with a focus on what we call Riesz-duals of type I and II. Next, we provide some characterizations of Riesz-dual sequences in Banach spaces. A basic problem of interest in connection with the study of Riesz-duals in Banach spaces is that of characterizing those Riesz-duals which can essentially be regarded as M-basis. We give some conditions under which an Riesz-dual sequence to be an M-basis for [Formula: see text].
{"title":"A characterization of Riesz-dual sequences which are near-Markushevich bases","authors":"Ali Reza Neisi, M. Asgari","doi":"10.1142/s021902572150017x","DOIUrl":"https://doi.org/10.1142/s021902572150017x","url":null,"abstract":"The concept of Riesz-duals of a frame is a recently introduced concept with broad implications to frame theory in general, as well as to the special cases of Gabor and wavelet analysis. In this paper, we introduce various alternative Riesz-duals, with a focus on what we call Riesz-duals of type I and II. Next, we provide some characterizations of Riesz-dual sequences in Banach spaces. A basic problem of interest in connection with the study of Riesz-duals in Banach spaces is that of characterizing those Riesz-duals which can essentially be regarded as M-basis. We give some conditions under which an Riesz-dual sequence to be an M-basis for [Formula: see text].","PeriodicalId":50366,"journal":{"name":"Infinite Dimensional Analysis Quantum Probability and Related Topics","volume":"14 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84912170","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}
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