PS-b-P (DMS-stat-VMS)嵌段聚合物的制备及性能

采用活性阴离子聚合方法,以仲丁基锂为引发剂,以苯乙烯、六甲基环三硅氧烷（D3）和2,4,6-三乙烯基-2,4,6-三甲基环三硅氧烷（V3）为反应单体,分步聚合制备了聚苯乙烯-b-聚（二甲基硅氧烷-stat-乙烯基甲基硅氧烷）[PS-b-P（DMS-stat-VMS）]嵌段聚合物.采用傅里叶变换红外光谱、氢核磁共振谱及凝胶渗透色谱对共聚物的化学结构、分子量及分子量分布进行了表征,并通过扫描电子显微镜、原子力显微镜及接触角等测试方法研究了共聚物各链段组分对共聚物形貌及表面亲疏水/油性的影响.结果表明,所制备的共聚物分子量分布较窄,由于各组分性能的差异而呈现出微相分离结构,同时该共聚物保留了PS-b-PDMS原有的表面性质,为设计结构多样性及性能优异的聚硅氧烷共聚物提供了新思路.     

基于聚乙烯的无规和嵌段接枝共聚物的制备

采用乙烯配位聚合和巯基-烯点击化学相结合的方法制备了羟基封端的线性聚乙烯,末端羟基含量接近100%;利用酰氯与羟基的高效反应,将羟基封端的聚乙烯转化为降冰片烯封端的聚乙烯大单体(PE-NB).使用Grubbs II代催化剂,将大分子单体与降冰片烯(NB)单体进行开环易位共聚,通过调整单体的投料比和加料方式制备了分子量和组成可控的聚降冰片烯-g-聚乙烯(PNB-g-PE)接枝共聚物.其中,无规共聚时,大单体的转化率接近100%,所得无规接枝共聚物的重均分子量为1.79×10~4~3.14×10~4,分子量分布指数为2.09~2.60,聚乙烯链段的质量分数为4.6%~16.8%;而嵌段共聚时,由于空间位阻原因,大单体的转化率约为80%.热分析研究发现,由于空间位阻,接枝共聚物的结晶度较聚乙烯前驱体略有下降,且接枝度越大,结晶能力下降得越多.     

Precision Graphene Nanoribbon Heterojunctions by Chain-Growth Polymerization

Graphene nanoribbons (GNRs) are considered promising candidates for next-generation nanoelectronics. In particular, GNR heterojunctions have received considerable attention due to their exotic topological electronic phases at the heterointerface. However, strategies for their precision synthesis remain at a nascent stage. Here, we report a novel chain-growth polymerization strategy that allows for constructing GNR heterojunction with N=9 armchair and chevron GNRs segments ( 9-AGNR/cGNR ). The synthesis involves a controlled Suzuki–Miyaura catalyst-transfer polymerization (SCTP) between 2-(6′-bromo-4,4′′-ditetradecyl-[1,1′:2′,1′′-terphenyl]-3′-yl) boronic ester ( M1 ) and 2-(7-bromo-9,12-diphenyl-10,11-bis(4-tetradecylphenyl)-triphenylene-2-yl) boronic ester ( M2 ), followed by the Scholl reaction of the obtained block copolymer ( poly-M1/M2 ) with controlled M_n (18 kDa) and narrow Đ (1.45). NMR and SEC analysis of poly-M1/M2 confirm the successful block copolymerization. The solution-mediated cyclodehydrogenation of poly-M1/M2 toward 9-AGNR/cGNR is unambiguously validated by FT-IR, Raman, and UV/Vis spectroscopies. Moreover, we also demonstrate the on-surface formation of pristine 9-AGNR/cGNR from the unsubstituted copolymer precursor, which is unambiguously characterized by scanning tunneling microscopy (STM).     

Syntheses and Studies of PEG-b-PNIPA Block Polymers

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Inheritance of hyper-duality in imprimitive Bose–Mesner algebras

We prove the following result concerning the inheritance of hyper-duality by block and quotient Bose–Mesner algebras associated with a hyper-dual pair of imprimitive Bose–Mesner algebras. Let and denote Bose–Mesner algebras. Suppose there is a hyper-duality ψ from the subconstituent algebra of with respect to p to the subconstituent algebra of with respect to . Also suppose that is imprimitive with respect to a subset of Hadamard idempotents, so is dual imprimitive with respect to the subset of primitive idempotents, where is the formal duality associated with ψ. Let denote the block Bose–Mesner algebra of on the block containing p, and let denote the quotient Bose–Mesner algebra of with respect to . Then there is a hyper-duality from the subconstituent algebra of with respect to p to the subconstituent algebra of with respect to .     

Uniformly Conditioned Bases of Spectral Subspaces

A condition number of an ordered basis of a finite-dimensional normed space is defined in an intrinsic manner. This concept is extended to a sequence of bases of finite-dimensional normed spaces, and is used to determine uniform conditioning of such a sequence. We address the problem of finding a sequence of uniformly conditioned bases of spectral subspaces of operators of the form T _n  = S _n  + U _n , where S _n is a finite-rank operator on a Banach space and U _n is an operator which satisfies an invariance condition with respect to S _n . This problem is reduced to constructing a sequence of uniformly conditioned bases of spectral subspaces of operators on ? ^n×1. The applicability of these considerations in practical as well as theoretical aspects of spectral approximation is pointed out.     

GENERALIZED BRAUER ALGEBRAS

ABSTRACT

Using some ideas of Brauer, we introduce what we call generalized Brauer algebras and, as a special case, Brauer orders. We show that many well-known classes of so-called crossed product algebras, and in particular, the well-known crossed product orders, can be obtained as special instances of our construction. We prove several results showing when Brauer orders are Azumaya, maximal, hereditary or Gorenstein.     

On complexity of round transformations

A modern block cipher consists of round transformations, which are obtained by alternatively applying permutations (P-boxes) and substitutions (S-boxes). Clearly, the most important attribute of a block cipher is its security. However, with respect to the hardware implementation, a good block cipher has to have a reasonable complexity as well. In this paper, we study complexity of round transformations satisfying some basic security criteria. There are several ways to define the complexity of a round transformation, and to choose “necessary” security criteria. It turns out, that for our purpose, it is suitable to view a round transformation as a single Boolean function, not separating it into S-boxes and P-boxes. We require that the Boolean function F possesses some fundamental properties imposed on each block cipher for security reasons; namely, we require that the function is a strictly non-linear bijection and that it has a good diffusion. The total number of variables in the normal algebraic form of the component functions of F is taken as its complexity. We find the minimum complexity of such functions, and this way we establish a lower bound on complexity of all round transformations. To show that the lower bound is the best possible, we construct a round transformation F^′ attaining the bound. We stress that it is not an aspiration of this paper to construct a round transformation which would be of practical use; F^′ is useful only from the theoretical point of view.     

Spectral inclusion for unbounded block operator matrices

In this paper we establish a new analytic enclosure for the spectrum of unbounded linear operators A admitting a block operator matrix representation. For diagonally dominant and off-diagonally dominant block operator matrices, we show that the recently introduced quadratic numerical range W²(A) contains the eigenvalues of A and that the approximate point spectrum of A is contained in the closure of W²(A). This provides a new method to enclose the spectrum of unbounded block operator matrices by means of the non-convex set W²(A). Several examples illustrate that this spectral inclusion may be considerably tighter than the one by the usual numerical range or by perturbation theorems, both in the non-self-adjoint case and in the self-adjoint case. Applications to Dirac operators and to two-channel Hamiltonians are given.     

A Flaw in the Use of Minimal Defining Sets for Secret Sharing Schemes

It is shown that in some cases it is possible to reconstruct a block design uniquely from incomplete knowledge of a minimal defining set for . This surprising result has implications for the use of minimal defining sets in secret sharing schemes.