Construction of a Self-assembling Intertwined Spiral Solvent Channel Based on Interactions between Macrocycles and CH_2Cl_2

The construction of an unprecedented intertwined spiral solvent channel is driven by weak C–Cl…O and C–H…N interactions based on extraordinary parallel spirals which were structured from supramolecular synthon macrocycle 1（C44H44N4O4） with a propargylamine backbone. The product is characterized by ^1H NMR, ^13C NMR, IR and HRMS, and further confirmed by single-crystal X-ray diffraction. It crystallizes in the monoclinic system, space group C2/c, with a = 28.922（3）, b = 8.5069（9）, c = 21.687（2）A^°, β = 130.6320（10）°, V = 4049.4（7） A^°3 and Z = 8. A total of 11874 reflections were collected, of which 4942 were independent（Rint = 0.0590） and 2937 were observed with I 〉 2σ（I）. The final full-matrix least-squares refinement gave R（I 〉 2s（I）） = 0.069 and w R = 0.167, S = 1.05,（Δρ）max = 0.20 and（Δρ）min =-0.22 e·A^1-3. The fluorescence of the product is discussed.

基于混沌系统和动态DNA编码与运算的彩色图像加密算法

现有结合混沌系统和DNA计算的图像加密算法因DNA编码规则和运算规则单一、加密结构安全性低,导致算法易被破解。为此,提出一种结合Intertwining Logistic映射和动态DNA编码与运算的彩色图像加密算法。该算法包括置乱阶段和扩散阶段,在置乱阶段,利用模拟退火算法构造的置乱序列分别对彩色图像信道进行行和列置乱,得到置乱信道。在扩散阶段,先根据随机序列值动态选择各置乱信道每个像素点的DNA编码规则及运算规则,然后结合密文反馈机制进行DNA加密计算。实验结果表明,该算法具有良好的抗攻击能力及加密效果。

The Geometry of the Mappings by General Dirichlet Series

We dealt in a series of previous publications with some geometric aspects of the mappings by functions obtained as analytic continuations to the whole complex plane of general Dirichlet series. Pictures illustrating those aspects contain a lot of other information which has been waiting for a rigorous proof. Such a task is partially fulfilled in this paper, where we succeeded among other things, to prove a theorem about general Dirichlet series having as corollary the Speiser’s theorem. We have also proved that those functions do not possess multiple zeros of order higher than 2 and the double zeros have very particular locations. Moreover, their derivatives have only simple zeros. With these results at hand, we revisited GRH for a simplified proof.

A self-cited pixel summation based image encryption algorithm

In this paper, a novel image encryption algorithm is presented based on self-cited pixel summation. With the classical mechanism of permutation plus diffusion, a pixel summation of the plain image is employed to make a gravity influence on the pixel positions in the permutation stage. Then, for each pixel in every step of the diffusion stage, the pixel summation calculated from the permuted image is updated. The values from a chaotic sequence generated by an intertwining logistic map are selected by this summation. Consequently, the keystreams generated in both stages are dependent on both the plain image and the permuted image. Because of the sensitivity of the chaotic map to its initial conditions and the plain-imagedependent keystreams, any tiny change in the secret key or the plain image would lead to a significantly different cipher image. As a result, the proposed encryption algorithm is immune to the known plaintext attack（KPA） and the chosen plaintext attack（CPA）. Moreover, experimental simulations and security analyses show that the proposed permutationdiffusion encryption scheme can achieve a satisfactory level of security.

The Determinacy of Lexical Selectional Restriction and Its Basis for Existence

In this paper, the determinacy of regular lexical selectional restrictions is examined from both the internal structures of the single selectional restrictions (i.e.semantic selectional restrictions) and relationship between the structures of several selectional restrictions. Hence, our analysis and description are shifted from casual and indeterminate strings and markers on case basis to determined rules and circumspect dynamic systems, from lexical precepts to knowledge precepts, from the state of memory to rational deduction and rhetorical devices. Further studies indicate that selectional restrictions are intertwined structures, a feature that makes it possible to be one of the bases for lexical selectional restrictions to come into existence. Its related theories are the grarantee for scientific observations of selectional restriction structures.

Higher Genus Characters for Vertex Operator Superalgebras on Sewn Riemann Surfaces

We review our recent results on computation of the higher genus characters for vertex operator superalgebras modules. The vertex operator formal parameters are associated to local parameters on Riemann surfaces formed in one of two schemes of (self- or tori- ) sewing of lower genus Riemann surfaces. For the free fermion vertex operator superalgebra we present a closed formula for the genus two continuous orbifold partition functions (in either sewings) in terms of an infinite dimensional determinant with entries arising from the original torus Szeg? kernel. This partition function is holomorphic in the sewing parameters on a given suitable domain and possesses natural modular properties. Several higher genus generalizations of classical (including Fay’s and Jacobi triple product) identities show up in a natural way in the vertex operator algebra approach.

The Commutants of the Dunkl Operators on <i>ε</i>(R^d)

We consider the harmonic analysis associated with the Dunkl operators on Rd. We study the Dunkl mean-periodic functions on the space ε(Rd) (the space of C∞-functions). We characterize also the continuous linear mappings from ε(Rd) into itself which commute with the Dunkl operators.

Bimodule and twisted representation of vertex operator algebras

In this paper, for a vertex operator algebra V with an automorphism g of order T, an admissible V-module M and a fixed nonnegative rational number n ∈1/T Z_+, we construct an A_(g,n)(V)-bimodule Ag,n(M) and study its properties, discuss the connections between bimodule A_(g,n)(M) and intertwining operators. Especially, bimodule A _(g,n)-1T(M) is a natural quotient of A_(g,n)(M) and there is a linear isomorphism between the space IM^k M Mjof intertwining operators and the space of homomorphisms HomA_(g,n)(V)(A_(g,n)(M) A_(g,n)(V)M^j(s), M^k(t)) for s, t ≤ n, M^j, M^k are g-twisted V modules, if V is g-rational.

C*-Algebraic Intertwiners for Degenerate Principal Series of Special Linear Groups

The author constructs unitary intertwiners for degenerate C*-algebraic universal principal series of SL(n + 1) over a local field by explicitely normalizing standard intertwining integrals at the level of Hilbert modules.

Toward a Multi-Layered Chiasme-Focused Topology: A Reading of Merleau-Ponty's Later Writings

This paper traces the genealogy of reversibility,chiasma,and chiasme in Merleau-Ponty's writings and offers a new characterisation of his later ontology in terms of a multi-layered chiasme-focused topology informed by subtle differences and interconnections among these notions.We need to grasp the significance of reversibility not only in terms of constant recoil and impossible overlap but also of its situatedness in the crisscrossing between Dasein and things,and between the inside/invisible and the outside/visible."Chiasma" was initially introduced as a reference to the intersection of perspectives.Merleau-Ponty deploys it to articulate macroscopic insights concerning the nature of philosophy and the interweaving connections between self,other,and the world.In comparison,"reversibility" is primarily used to describe the microscopic bond between touching-touched and perceiving-perceived.I argue that,as Merleau-Ponty's ultimate choice of wording,"chiasme" incorporated the significance of both "reversibility" and "chiasma." A chiasme-focused topology that retains the significance of all three of the terms would serve to better convey the import of Merleau-Ponty's later ontology,which aims to dissolve and to re-configure our conceptions about being,body,self,and the other from within and from below.

Harmonic Analysis Associated with the Heckman-Opdam-Jacobi Operator on R^(d+1)

In this paper we consider the Heckman-Opdam-Jacobi operatorΔ_(H J)on R^(d+1).We define the Heckman-Opdam-Jacobi intertwining operator V_(H J),which turns out to be the transmutation operator betweenΔ_(H J)and the LaplacianΔ_(d+1).Next we construct^(t)V_(H J)the dual of this intertwining operator.We exploit these operators to develop a new harmonic analysis corresponding toΔ_(H J).

The Controversies and Challenges in the Management of Twin Pregnancy: From the Perspective of International Federation of Gynecology and Obstetrics Guidelines

The rate of multiple pregnancy is increasing, mainly because of the widespread use of assisted reproduction techniques and families’ desire for twins. Twin pregnancy accounts for a higher risk of chromosomal abnormalities, structural malformations, and neonatal adverse events than singleton pregnancy. The presence of artery-vein anastomoses, unbalanced placenta sharing, and abnormal cord insertion in monochorionic twins is associated with twin complications such as twin-to-twin transfusion syndrome, selective intrauterine growth restriction, and twin anemia polycythemia sequence. Although many guidelines and studies have established and improved the processes about the antenatal surveillance and management of twin pregnancy, they also raise more controversies and challenges. This review aims to highlight the international consensus on the antenatal care of twin pregnancies and analyze the controversies and predicaments based on the published International Federation of Gynecology and Obstetrics guidelines and research.

Tensor products of complementary series of rank one Lie groups

We consider the tensor product π_α ? π_βof complementary series representations π_α and π_β of classical rank one groups SO_0(n, 1), SU(n, 1) and Sp(n, 1). We prove that there is a discrete component π_(α+β)for small parameters α and β(in our parametrization). We prove further that for SO_0(n, 1) there are finitely many complementary series of the form π_(α+β+2j,)j = 0, 1,..., k, appearing in the tensor product π_α ? π_βof two complementary series π_α and π_β, where k = k(α, β, n) depends on α, β and n.