The Roper-Suffridge extension operator and classes of biholomorphic mappings Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

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.

Idempotent Completions of Operator Partial Matrices

Necessary and sufficient conditions are obtained for operator partial 2×2 matrices to have an idempotent completion, and all such completions are parametrically represented.

Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on C^n Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

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.

The local Hlder exponent for the entropy of real unimodal maps In Memory of Lei Tan

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.

Some Penrose transforms in complex differential geometry Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

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.

An Improved Group Decision-Making Model for the Investment Options of Small-Scale Photovoltaic Systems Based on Cumulative Prospect Theory and Choquet Integral

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.

On the classification of certain real rank zero C^(*)-algebras

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.

Option-like properties in the distribution of hedge fund returns

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.

Passwords Management via Split-Key

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.

Sifting for small primes from an arithmetic progression

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.

Extreme points, support points and the Loewner variation in several complex variables

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.

Anisotropic estimates for sub-elliptic operators

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.

Eisenstein series for SL(2)

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.

射影几何学：第二版

本书作者是一位几何学名家，著有十多本几何学教材或专著，本书是其中一本广获好评的经典教材，它初版于1964年，修订版于1974年。这次由Springer出版公司首次按第二版推出平装本。

K-Theory and the Quantization Commutes with Reduction Problem

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.

CR deformations for rational homogeneous surface singularities

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).