In this paper we give a survey about the Roper-Suffridge extension operator and the developments in the theory of univalent mappings in several variables to which it has led. We begin with the basic geometric properti...In this paper we give a survey about the Roper-Suffridge extension operator and the developments in the theory of univalent mappings in several variables to which it has led. We begin with the basic geometric properties (most of which now have a number of different proofs)and discuss relations with the theory of Loewner chains and generalizations and modifications of the operator, some of which are very recent.展开更多
Necessary and sufficient conditions are obtained for operator partial 2×2 matrices to have an idempotent completion, and all such completions are parametrically represented.
Given a principal value convolution on the Heisenberg group Hn = Cn × R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet k...Given a principal value convolution on the Heisenberg group Hn = Cn × R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.展开更多
We consider the topological entropy h(θ) of real unimodal maps as a function of the kneading parameter θ(equivalently, as a function of the external angle in the Mandelbrot set). We prove that this function is local...We consider the topological entropy h(θ) of real unimodal maps as a function of the kneading parameter θ(equivalently, as a function of the external angle in the Mandelbrot set). We prove that this function is locally Hlder continuous where h(θ) > 0, and more precisely for any θ which does not lie in a plateau the local Hlder exponent equals exactly, up to a factor log 2, the value of the function at that point.This confirms a conjecture of Isola and Politi(1990), and extends a similar result for the dimension of invariant subsets of the circle.展开更多
In this article, we review a construction in the complex geometry often known as the Penrose transform. We then present two new applications of this transform. One concerns the construction of symmetries of the massle...In this article, we review a construction in the complex geometry often known as the Penrose transform. We then present two new applications of this transform. One concerns the construction of symmetries of the massless field equations from mathematical physics. The otherconcerns obstructions to the embedding of CR structures on the three-sphere.展开更多
With the development of photovoltaic(PV) industry, installing small-scale PV systems which are integrated into the buildings becomes popular. Therefore, it is important to make optimal investment decisions for investo...With the development of photovoltaic(PV) industry, installing small-scale PV systems which are integrated into the buildings becomes popular. Therefore, it is important to make optimal investment decisions for investors and consumers. This paper proposes an improved group decision-making method which integrates the cumulative prospect theory and Choquet integral for the investment options of small-scale PV systems. From the perspective of sustainability, the alternatives are evaluated by four criteria, including economic benefits, solar energy condition, carbon emissions and social benefits. Since the performances of criteria are given by decision makers as linguistic variables, the proposed method measures the criteria values by intuitionistic trapezoidal fuzzy numbers. Then the alternatives are evaluated and ranked to determine the optimal option. Finally, the proposed method is implemented in a case study to illustrate its feasibility and effectiveness.展开更多
In this paper,we give a classification of real rank zero C^(*)-algebras that can be expressed as inductive limits of a sequence of a subclass of Elliott-Thomsen algebras C.
Hedge funds have recently become popular because of their low correlation with traditional investments and their ability to generate positive returns with a relatively low volatility.However,a close look at those high...Hedge funds have recently become popular because of their low correlation with traditional investments and their ability to generate positive returns with a relatively low volatility.However,a close look at those high-performing hedge funds raises the questions on whether their performance is truly superior and whether the high management fees are justified.Incurring no alpha costs,passive hedge fund replication strategies raise the question on whether they can similarly perform by improving efficiency at reduced costs.Therefore,this study investigates two different model approaches for the equity long/short strategy,where weighted segmented linear regression models are employed and combined with two-state Markov switching models.The main finding proves a short put option structure,i.e.,short equity market volatility,with the put structure present in all market states.We obtain an evidence that the hedge fund managers decrease their short-volatility profile during turbulent markets.展开更多
This paper proposes a scheme for password management by storing password encryptions on a server. The method involves having the encryption key split into a share for the user and one for the server. The user’s share...This paper proposes a scheme for password management by storing password encryptions on a server. The method involves having the encryption key split into a share for the user and one for the server. The user’s share shall be based solely on a selected passphrase. The server’s share shall be generated from the user’s share and the encryption key. The security and trust are achieved by performing both encryption and decryption on the client side. We also address the issue of countering dictionary attack by providing a further enhancement of the scheme.展开更多
In this work and its sister paper(Friedlander and Iwaniec(2023)),we give a new proof of the famous Linnik theorem bounding the least prime in an arithmetic progression.Using sieve machinery in both papers,we are able ...In this work and its sister paper(Friedlander and Iwaniec(2023)),we give a new proof of the famous Linnik theorem bounding the least prime in an arithmetic progression.Using sieve machinery in both papers,we are able to dispensh with the log-free zero density bounds and the repulsion property of exceptional zeros,two deep innovations begun by Linnik and relied on in earlier proofs.展开更多
In this paper we consider extreme points and support points for compact subclasses of normalized biholomorphic mappings of the Euclidean unit ball Bn in Cn. We consider the class S0(Bn) of biholomorphic mappings on Bn...In this paper we consider extreme points and support points for compact subclasses of normalized biholomorphic mappings of the Euclidean unit ball Bn in Cn. We consider the class S0(Bn) of biholomorphic mappings on Bn which have parametric representation, i.e., they are the initial elements f (·, 0) of a Loewner chain f (z, t) = etz + ··· such that {e-tf (·, t)}t 0 is a normal family on Bn. We show that if f (·, 0) is an extreme point (respectively a support point) of S0(Bn), then e-tf (·, t) is an extreme point of S0(Bn) for t 0 (respectively a support point of S0(Bn) for t ∈[0, t0] and some t0 > 0). This is a generalization to the n-dimensional case of work due to Pell. Also, we prove analogous results for mappings which belong to S0(Bn) and which are bounded in the norm by a fixed constant. We relate the study of this class to reachable sets in control theory generalizing work of Roth. Finally we consider extreme points and support points for biholomorphic mappings of Bn generated by using extension operators that preserve Loewner chains.展开更多
In the 1970’s,Folland and Stein studied a family of subelliptic scalar operators L_λwhich arise naturally in the(?)_b-complex.They introduced weighted Sobolev spaces as the natural spaces for this complex,and then o...In the 1970’s,Folland and Stein studied a family of subelliptic scalar operators L_λwhich arise naturally in the(?)_b-complex.They introduced weighted Sobolev spaces as the natural spaces for this complex,and then obtained sharp estimates for(?)b in these spaces using integral kernels and approximate inverses.In the 1990’s,Rumin introduced a differential complex for compact contact manifolds,showed that the Folland-Stein operators are central to the analysis for the corresponding Laplace operator,and derived the necessary estimates for the Laplacian from the Folland Stein analysis. In this paper,we give a self-contained derivation of sharp estimates in the anisotropic Folland-Stein spaces for the operators studied by Rumin using integration by parts and a modified approach to bootstrapping.展开更多
This paper gives explicit formulas for the Fourier expansion of general Eisenstein series and local Whittaker functions over SL2.They are used to compute both the value and derivatives of these functions at critical p...This paper gives explicit formulas for the Fourier expansion of general Eisenstein series and local Whittaker functions over SL2.They are used to compute both the value and derivatives of these functions at critical points.展开更多
The authors examine the quantization commutes with reduction phenomenon for Hamiltonian actions of compact Lie groups on closed symplectic manifolds from the point of view of topological K-theory and K-homology. They ...The authors examine the quantization commutes with reduction phenomenon for Hamiltonian actions of compact Lie groups on closed symplectic manifolds from the point of view of topological K-theory and K-homology. They develop the machinery of K-theory wrong-way maps in the context of orbifolds and use it to relate the quantization commutes with reduction phenomenon to Bott periodicity and the K-theory formulation of the Weyl character formula.展开更多
In this paper, we will present a CR-construction of the versal deformations of the singularities Vn (~- )C2/Zn, n ∈ {2, 3, 4,…} defined by the immersions of C2 into Cn+1Xn: (z,w) → (zn,zn-1w,…,zwn-1,wn).
文摘In this paper we give a survey about the Roper-Suffridge extension operator and the developments in the theory of univalent mappings in several variables to which it has led. We begin with the basic geometric properties (most of which now have a number of different proofs)and discuss relations with the theory of Loewner chains and generalizations and modifications of the operator, some of which are very recent.
基金Project supported by National Natural Science Foundation of China Provincial Natural Science Foundation of Shanxi
文摘Necessary and sufficient conditions are obtained for operator partial 2×2 matrices to have an idempotent completion, and all such completions are parametrically represented.
文摘Given a principal value convolution on the Heisenberg group Hn = Cn × R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.
文摘We consider the topological entropy h(θ) of real unimodal maps as a function of the kneading parameter θ(equivalently, as a function of the external angle in the Mandelbrot set). We prove that this function is locally Hlder continuous where h(θ) > 0, and more precisely for any θ which does not lie in a plateau the local Hlder exponent equals exactly, up to a factor log 2, the value of the function at that point.This confirms a conjecture of Isola and Politi(1990), and extends a similar result for the dimension of invariant subsets of the circle.
文摘In this article, we review a construction in the complex geometry often known as the Penrose transform. We then present two new applications of this transform. One concerns the construction of symmetries of the massless field equations from mathematical physics. The otherconcerns obstructions to the embedding of CR structures on the three-sphere.
基金Supported by the National Natural Science Foundation of China(71771085)
文摘With the development of photovoltaic(PV) industry, installing small-scale PV systems which are integrated into the buildings becomes popular. Therefore, it is important to make optimal investment decisions for investors and consumers. This paper proposes an improved group decision-making method which integrates the cumulative prospect theory and Choquet integral for the investment options of small-scale PV systems. From the perspective of sustainability, the alternatives are evaluated by four criteria, including economic benefits, solar energy condition, carbon emissions and social benefits. Since the performances of criteria are given by decision makers as linguistic variables, the proposed method measures the criteria values by intuitionistic trapezoidal fuzzy numbers. Then the alternatives are evaluated and ranked to determine the optimal option. Finally, the proposed method is implemented in a case study to illustrate its feasibility and effectiveness.
基金supported by Northeast Normal University and National Natural Science Foundation of China(Grant No.11531003)supported by University of Toronto and National Natural Science Foundation of China(Grant No.11531003)+1 种基金supported by the Science and Technology Development Project of Jilin Province(Grant No.20190103028JH)National Natural Science Foundation of China(Grant Nos.11601104,11671167 and 11201171).
文摘In this paper,we give a classification of real rank zero C^(*)-algebras that can be expressed as inductive limits of a sequence of a subclass of Elliott-Thomsen algebras C.
文摘Hedge funds have recently become popular because of their low correlation with traditional investments and their ability to generate positive returns with a relatively low volatility.However,a close look at those high-performing hedge funds raises the questions on whether their performance is truly superior and whether the high management fees are justified.Incurring no alpha costs,passive hedge fund replication strategies raise the question on whether they can similarly perform by improving efficiency at reduced costs.Therefore,this study investigates two different model approaches for the equity long/short strategy,where weighted segmented linear regression models are employed and combined with two-state Markov switching models.The main finding proves a short put option structure,i.e.,short equity market volatility,with the put structure present in all market states.We obtain an evidence that the hedge fund managers decrease their short-volatility profile during turbulent markets.
文摘This paper proposes a scheme for password management by storing password encryptions on a server. The method involves having the encryption key split into a share for the user and one for the server. The user’s share shall be based solely on a selected passphrase. The server’s share shall be generated from the user’s share and the encryption key. The security and trust are achieved by performing both encryption and decryption on the client side. We also address the issue of countering dictionary attack by providing a further enhancement of the scheme.
基金supported by Natural Sciences and Engineering Research Council of Canada (NSERC) (Grant No. A5123)。
文摘In this work and its sister paper(Friedlander and Iwaniec(2023)),we give a new proof of the famous Linnik theorem bounding the least prime in an arithmetic progression.Using sieve machinery in both papers,we are able to dispensh with the log-free zero density bounds and the repulsion property of exceptional zeros,two deep innovations begun by Linnik and relied on in earlier proofs.
基金supported by the Natural Sciences and Engineering Research Council of Canada (Grant No. A9221)Grant-in-Aid for Scientific Research (C) from Japan Society for the Promotion of Science, 2011 (Grant No. 22540213)the Romanian Ministry of Education and Research, UEFISCSU-CNCSIS(Grants Nos. PN-II-ID 524/2007, 525/2007)
文摘In this paper we consider extreme points and support points for compact subclasses of normalized biholomorphic mappings of the Euclidean unit ball Bn in Cn. We consider the class S0(Bn) of biholomorphic mappings on Bn which have parametric representation, i.e., they are the initial elements f (·, 0) of a Loewner chain f (z, t) = etz + ··· such that {e-tf (·, t)}t 0 is a normal family on Bn. We show that if f (·, 0) is an extreme point (respectively a support point) of S0(Bn), then e-tf (·, t) is an extreme point of S0(Bn) for t 0 (respectively a support point of S0(Bn) for t ∈[0, t0] and some t0 > 0). This is a generalization to the n-dimensional case of work due to Pell. Also, we prove analogous results for mappings which belong to S0(Bn) and which are bounded in the norm by a fixed constant. We relate the study of this class to reachable sets in control theory generalizing work of Roth. Finally we consider extreme points and support points for biholomorphic mappings of Bn generated by using extension operators that preserve Loewner chains.
基金This work was supported by NSERC(Grant No.RGPIN/9319-2005)
文摘In the 1970’s,Folland and Stein studied a family of subelliptic scalar operators L_λwhich arise naturally in the(?)_b-complex.They introduced weighted Sobolev spaces as the natural spaces for this complex,and then obtained sharp estimates for(?)b in these spaces using integral kernels and approximate inverses.In the 1990’s,Rumin introduced a differential complex for compact contact manifolds,showed that the Folland-Stein operators are central to the analysis for the corresponding Laplace operator,and derived the necessary estimates for the Laplacian from the Folland Stein analysis. In this paper,we give a self-contained derivation of sharp estimates in the anisotropic Folland-Stein spaces for the operators studied by Rumin using integration by parts and a modified approach to bootstrapping.
基金supported by Natural Science Foundation of USA(Grant No.DMS-0855901)National Natural Science Foundation of China(Grant No.10628103)
文摘This paper gives explicit formulas for the Fourier expansion of general Eisenstein series and local Whittaker functions over SL2.They are used to compute both the value and derivatives of these functions at critical points.
文摘The authors examine the quantization commutes with reduction phenomenon for Hamiltonian actions of compact Lie groups on closed symplectic manifolds from the point of view of topological K-theory and K-homology. They develop the machinery of K-theory wrong-way maps in the context of orbifolds and use it to relate the quantization commutes with reduction phenomenon to Bott periodicity and the K-theory formulation of the Weyl character formula.
文摘In this paper, we will present a CR-construction of the versal deformations of the singularities Vn (~- )C2/Zn, n ∈ {2, 3, 4,…} defined by the immersions of C2 into Cn+1Xn: (z,w) → (zn,zn-1w,…,zwn-1,wn).