This article will introduce the general formula of multiple Patterson function(MPF), and deduce therefrom phase structure invariants in reciprocal space that Hauptman and Karle introduced in a different way. By expand...This article will introduce the general formula of multiple Patterson function(MPF), and deduce therefrom phase structure invariants in reciprocal space that Hauptman and Karle introduced in a different way. By expanding the concept of the structure invariant, it may be found that a connection exists between the structure invariants in positive and reciprocal spaces. The phase question of MPF can be merged into the estimation question of phase structure invariants in the probability direct method.This theme will show the general group of Σ relationship without extra magnitudes. It might be one of the methods used in calculating MPF, and it primarily discusses the property of MPF.展开更多
In this paper, we study exhaustions, referred to as p-restrictions, of arbitrary nonelementary Kleinian groups with at most finitely many bounded parabolic elements. Special emphasis is put on the geometrically infini...In this paper, we study exhaustions, referred to as p-restrictions, of arbitrary nonelementary Kleinian groups with at most finitely many bounded parabolic elements. Special emphasis is put on the geometrically infinite case, where we obtain that the limit set of each of these Kleinian groups contains an infinite family of closed subsets, referred to as p-restricted limit sets, such that there is a Poincaré series and hence an exponent of convergence δp, canonically associated with every element in this family. Generalizing concepts which are well known in the geometrically finite case, we then introduce the notion of p-restricted Patterson measure, and show that these measures are non-atomic, δp-harmonic, δp-subconformal on special sets and δp-conformal on very special sets. Furthermore, we obtain the results that each p-restriction of our Kleinian group is of δp-divergence type and that the Hausdorff dimension of the p-restricted limit set is equal to δp.展开更多
Basing upon the recent development of the Patterson–Sullivan measures with a H¨older continuous nonzero potential function,we use tools of both dynamics of geodesic flows and geometric properties of negatively c...Basing upon the recent development of the Patterson–Sullivan measures with a H¨older continuous nonzero potential function,we use tools of both dynamics of geodesic flows and geometric properties of negatively curved manifolds to present a new formula illustrating the relation between the exponential decay rate of Patterson–Sullivan measures with a H¨older continuous potential function and the corresponding critical exponent.展开更多
External Dose to Recovery Teams Following a Wide-area Nuclear or Radiological Release Event.Michael D.Kaminski 1,Keith Sanders 2,Katherine Hepler 1,Matthew Magnuson 3,Jeremy Slagley 2(1.Strategic Security Sciences Div...External Dose to Recovery Teams Following a Wide-area Nuclear or Radiological Release Event.Michael D.Kaminski 1,Keith Sanders 2,Katherine Hepler 1,Matthew Magnuson 3,Jeremy Slagley 2(1.Strategic Security Sciences Division,Argonne National Laboratory,9700 S.Cass Avenue,Lemont,IL 60439;2.Air Force Institute of Technology,Department of Systems Engineering and Management,2950 Hobson Way,Wright-Patterson Air Force Base,OH 45433;3.US Environmental Protection Agency,Office of Research and Development,Center for Environmental Solutions and Emergency Response,Homeland Security&Materials and Management Division,26 W.Martin Luther King Drive,Cincinnati,OH 45268)Abstract:The common radionuclide 137 Cs is a gamma-ray source term for nuclear reactor accidents,nuclear detonations,and potential radionuclide dispersal devices.For wide-area contamination events,one remediation option integrates water washing activities with on-site treatment of water for its immediate reuse.展开更多
The main purpose of this paper is to show that the Poincaré <em>q</em>-polynomials admit a representation in terms of the symmetric functions and the Patterson-Selberg (or Ruelle-type) spectral functi...The main purpose of this paper is to show that the Poincaré <em>q</em>-polynomials admit a representation in terms of the symmetric functions and the Patterson-Selberg (or Ruelle-type) spectral functions. We have shown that the <em>q</em>-series elliptic genera can be expressed in terms of <em>q</em>-analogs of the classical special functions, specially the equivalence between the spectral Patterson-Selberg and the Ruelle functions. The main result of this manuscript is to show that this representation can be used in theoretical physics and we analyze them in terms of the Patterson-Selberg spectral function R (<em>s</em>).展开更多
Michaels Shawn James Hickenbottom生于1965年7月22日,是家中四个孩子里最小的。从很小的时候开始,Shawn就成为了一名狂热的摔迷,在高中的时候还曾和朋友举办过摔角比赛。起初,Shawn的父母对于他们儿子对摔角的‘痴迷’感到担心,但当...Michaels Shawn James Hickenbottom生于1965年7月22日,是家中四个孩子里最小的。从很小的时候开始,Shawn就成为了一名狂热的摔迷,在高中的时候还曾和朋友举办过摔角比赛。起初,Shawn的父母对于他们儿子对摔角的‘痴迷’感到担心,但当时年少的Shawn明白,他想要的就是摔角。由于年龄原因他最后决定先去上大学,到19岁后才能考虑摔角这件事,但是Shawn认为自己的大学生涯"除了喝酒"外什么也没学到。在这之后Shawn再次请求他的父母允许他接受些摔角的训练。展开更多
2015年6月23日,普立万公司在上海为其全新的亚洲创新中心正式启用举行了盛大的庆祝活动。该创新中心的设立有助于公司整合优势资源,实现协同创新,加快产品应用的开发,从而以更快的速度将创新解决方案推向整个亚洲市场。普立万公司总裁...2015年6月23日,普立万公司在上海为其全新的亚洲创新中心正式启用举行了盛大的庆祝活动。该创新中心的设立有助于公司整合优势资源,实现协同创新,加快产品应用的开发,从而以更快的速度将创新解决方案推向整个亚洲市场。普立万公司总裁兼首席执行官Robert M Patterson表示：＂我们很高兴在亚洲建立这座创新中心。以此为基地,我们将为亚洲客户和普立万的员工提供更有力的支持。展开更多
文摘This article will introduce the general formula of multiple Patterson function(MPF), and deduce therefrom phase structure invariants in reciprocal space that Hauptman and Karle introduced in a different way. By expanding the concept of the structure invariant, it may be found that a connection exists between the structure invariants in positive and reciprocal spaces. The phase question of MPF can be merged into the estimation question of phase structure invariants in the probability direct method.This theme will show the general group of Σ relationship without extra magnitudes. It might be one of the methods used in calculating MPF, and it primarily discusses the property of MPF.
基金Research supported by the Schweizer Nationalfonds No. 20-61379.00 European Project TMR "Geometric Analysis" ACR-OFES No. UE 00.0349
文摘In this paper, we study exhaustions, referred to as p-restrictions, of arbitrary nonelementary Kleinian groups with at most finitely many bounded parabolic elements. Special emphasis is put on the geometrically infinite case, where we obtain that the limit set of each of these Kleinian groups contains an infinite family of closed subsets, referred to as p-restricted limit sets, such that there is a Poincaré series and hence an exponent of convergence δp, canonically associated with every element in this family. Generalizing concepts which are well known in the geometrically finite case, we then introduce the notion of p-restricted Patterson measure, and show that these measures are non-atomic, δp-harmonic, δp-subconformal on special sets and δp-conformal on very special sets. Furthermore, we obtain the results that each p-restriction of our Kleinian group is of δp-divergence type and that the Hausdorff dimension of the p-restricted limit set is equal to δp.
基金partially supported by NSFC(Grant Nos.11571207 and 11871045)the third author is partially supported by NSFC(Grant No.11871045)by the State Scholarship Fund from China Scholarship Council(CSC)
文摘Basing upon the recent development of the Patterson–Sullivan measures with a H¨older continuous nonzero potential function,we use tools of both dynamics of geodesic flows and geometric properties of negatively curved manifolds to present a new formula illustrating the relation between the exponential decay rate of Patterson–Sullivan measures with a H¨older continuous potential function and the corresponding critical exponent.
文摘External Dose to Recovery Teams Following a Wide-area Nuclear or Radiological Release Event.Michael D.Kaminski 1,Keith Sanders 2,Katherine Hepler 1,Matthew Magnuson 3,Jeremy Slagley 2(1.Strategic Security Sciences Division,Argonne National Laboratory,9700 S.Cass Avenue,Lemont,IL 60439;2.Air Force Institute of Technology,Department of Systems Engineering and Management,2950 Hobson Way,Wright-Patterson Air Force Base,OH 45433;3.US Environmental Protection Agency,Office of Research and Development,Center for Environmental Solutions and Emergency Response,Homeland Security&Materials and Management Division,26 W.Martin Luther King Drive,Cincinnati,OH 45268)Abstract:The common radionuclide 137 Cs is a gamma-ray source term for nuclear reactor accidents,nuclear detonations,and potential radionuclide dispersal devices.For wide-area contamination events,one remediation option integrates water washing activities with on-site treatment of water for its immediate reuse.
文摘The main purpose of this paper is to show that the Poincaré <em>q</em>-polynomials admit a representation in terms of the symmetric functions and the Patterson-Selberg (or Ruelle-type) spectral functions. We have shown that the <em>q</em>-series elliptic genera can be expressed in terms of <em>q</em>-analogs of the classical special functions, specially the equivalence between the spectral Patterson-Selberg and the Ruelle functions. The main result of this manuscript is to show that this representation can be used in theoretical physics and we analyze them in terms of the Patterson-Selberg spectral function R (<em>s</em>).
文摘Michaels Shawn James Hickenbottom生于1965年7月22日,是家中四个孩子里最小的。从很小的时候开始,Shawn就成为了一名狂热的摔迷,在高中的时候还曾和朋友举办过摔角比赛。起初,Shawn的父母对于他们儿子对摔角的‘痴迷’感到担心,但当时年少的Shawn明白,他想要的就是摔角。由于年龄原因他最后决定先去上大学,到19岁后才能考虑摔角这件事,但是Shawn认为自己的大学生涯"除了喝酒"外什么也没学到。在这之后Shawn再次请求他的父母允许他接受些摔角的训练。
文摘2015年6月23日,普立万公司在上海为其全新的亚洲创新中心正式启用举行了盛大的庆祝活动。该创新中心的设立有助于公司整合优势资源,实现协同创新,加快产品应用的开发,从而以更快的速度将创新解决方案推向整个亚洲市场。普立万公司总裁兼首席执行官Robert M Patterson表示：＂我们很高兴在亚洲建立这座创新中心。以此为基地,我们将为亚洲客户和普立万的员工提供更有力的支持。
