Binary functions,degeneracy, and alternating dimaps

This paper continues the study of combinatorial properties of binary functions — that is, functions $f:2^E\to ?$ such that $f(0?)=1$, where $E$ is a finite set. Binary functions have previously been shown to admit families of transforms that generalise duality, including a trinity transform, and families of associated minor operations that generalise deletion and contraction, with both these families parameterised by the complex numbers. Binary function representations exist for graphs (via the indicator functions of their cutset spaces) and indeed arbitrary matroids (as shown by the author previously). In this paper, we characterise degenerate elements – analogues of loops and coloops – in binary functions, with respect to any set of minor operations from our complex-parameterised family. We then apply this to study the relationship between binary functions and Tutte’s alternating dimaps, which also support a trinity transform and three associated minor operations. It is shown that only the simplest alternating dimaps have binary representations of the form we consider, which seems to be the most direct type of representation. The question of whether there exist other, more sophisticated types of binary function representations for alternating dimaps is left open.     

Photooptical Properties of Polymethacrylates Having Cyanoazobenzene‐Containing Side Groups with Lateral Methyl Substituents and Different Spacer Length

New photochromic polymethacrylates with different spacer length having azobenzene side groups and lateral methyl substituents were synthesized. The phase behavior of polymethacrylates and their photooptical properties were studied and compared with unsubstituted analogues. It is shown that an introduction of lateral methyl substituents results in almost complete suppression of liquid crystalline (LC) phase formation and strong decrease of photoinduced dichroism values. It is found that rates of the photoinduced E‐Z isomerization and back thermal Z‐E isomerization are almost independent on spacer lengths. Due to the presence of lateral substituents, the photoinduced azobenzene Z‐form shows remarkable long lifetime, and back thermal conversion at room temperature takes more than 10 days. Specific peculiarities of the photoorientation process in polymer films under the polarized UV and visible light action were studied and their mechanism is suggested. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1337–1342     

On an Entropy of Z_+~k-Actions

In this paper,a definition of entropy for Z+k(k≥2)-actions due to Friedland is studied.Unlike the traditional definition,it may take a nonzero value for actions whose generators have finite(even zero) entropy as single transformations.Some basic properties are investigated and its value for the Z+k-actions on circles generated by expanding endomorphisms is given.Moreover,an upper bound of this entropy for the Z+k-actions on tori generated by expanding endomorphisms is obtained via the preimage entropies,which are entropy-like invariants depending on the "inverse orbits" structure of the system.     

基于虚拟相位平面的相位展开方法

在基于相位分析的三维测量系统中,为了准确地得到物体的高度,相位展开扮演着很重要的角色。传统的相位展开方法常常需要额外的投影图,而傅里叶变换轮廓术只需要采集一幅或两幅变形条纹图就可以实现对物体轮廓的测量,其方法速度快,易于实现。针对傅里叶变换轮廓术方法计算得到的截断相位分布,本文提出了一种利用截断相位与参考平面相位差值2π的整数倍数获得截断相位的正确级次,辅助相位展开的方法。当被测物体较复杂,或者相位截断次数较多时,该方法在已有参考平面相位的基础上虚拟新的相位平面,依次比较截断相位和虚拟相位,进行多次分级相位展开,结合多个展开相位结果,最终得到正确的展开相位。该方法展开速度快,展开错误不会蔓延传递。仿真和实物实验结果证明了该方法的可行性,说明该方法可用于傅里叶变换轮廓术中进行截断相位的快速展开。     

A Stereoselective Total Synthesis of Xyolide,a Natural Bioactive Nonenolide

A stereoselective total synthesis of xyolide, a naturally occurring bioactive nonenolide, has been accomplished. The acid fragment of the molecule has been prepared from D ‐mannitol and the alcohol fragment from (2Z)‐but‐2‐ene‐1,4‐diol. The synthesis involves the coupling of these two fragments using the Yamaguchi esterification protocol, followed by intramolecular ring‐closing methathesis. The diastereoisomeric alcohol fragment has also been utilized in this synthesis by employing the Mitsunobu esterification.     

Stereoselective Synthesis of the Non‐Lactonic Portion of (Z)‐Cryptofolione and Approaches towards Its Conversion to (Z)‐Cryptofolione

The stereoselective synthesis of the non‐lactonic part of the natural G₂ checkpoint inhibitor, (Z)‐cryptofolione, has been accomplished. Butane‐1,4‐diol was used as the starting material, and the stereogenic centers were generated through L ‐proline‐catalyzed α‐aminoxylation and Maruoka asymmetric allylation. We attempted to convert this non‐lactonic moiety to (Z)‐cryptofolione via olefin cross‐metathesis reaction, but by this approach another naturally occurring lactonic compound, goniothalamin, was obtained.     

Z‐Selective Cross Metathesis with Ruthenium Catalysts: Synthetic Applications and Mechanistic Implications

Olefin cross metathesis is a particularly powerful transformation that has been exploited extensively for the formation of complex products. Until recently, however, constructing Z‐olefins using this methodology was not possible. With the discovery and development of three families of ruthenium‐based Z‐selective catalysts, the formation of Z‐olefins using metathesis is now not only possible but becoming increasingly prevalent in the literature. In particular, ruthenium complexes containing cyclometalated NHC architectures developed in our group have been shown to catalyze various cross metathesis reactions with high activity and, in most cases, near perfect selectivity for the Z‐isomer. The types of cross metathesis reactions investigated thus far are presented here and explored in depth.     

Application of ‘Operational Quadrature Methods’ in Time Domain Boundary Element Methods

The usual time domain Boundary Element Method (BEM) contains fundamentalsolutions which are convoluted with time-dependent boundary data andintegrated over the boundary surface. Here, a new approach for theevaluation of the convolution integrals, the so-called OperationalQuadrature Methods developed by Lubich, is presented. In thisformulation, the convolution integral is numerically approximated by aquadrature formula whose weights are determined using the Laplacetransform of the fundamental solution and a linear multisep method. Tostudy the behaviour of the method, the numerical convolution of afundamental solution with a unit step function is compared with theanalytical result. Then, a time domain Boundary Element formulationapplying the Operational Quadrature Methods is derived. For thisformulation only the fundamental solutions in Laplace domain arenecessary. The properties of the new formulation are studied with anumerical example.     

Fourier Transform in Bounded Domains

The functional analysis, the concept of distributionsu in the sense of Schwartz [7] andtheir extension given by Gelfand and Shilov [5]to ultradistributions u ,enables us to find by the means of the Fourier transform a secondlanguage to characterize physical behaviour. Almost any expressionwith physical meaning can be transformed, even if it isformulated in domains with complicated boundaries and evenif it is not integrable.Numerical procedures in the transformed space can bedeveloped in analogy to those well known in engineeringmechanics like the methods of Finite or BoundaryElements (FEM or BEM). Basis of the approaches presentedhere is the analytical representation of characteristicdistribution of a domain and the theorem of Parseval whichstates the invariance of energy in respect to thetransformation. In addition, the concept of thecharacteristic distribution leads to a very simplederivation of the Green-Gauss formulas fundamental for theBoundary or Finite Elements (e.g. [6]).     

傅里叶变换红外光谱仪中动镜系统的设计

为提升傅里叶变换红外光谱仪的整体性能,基于立体角镜与平面镜组合的光学结构,设计了一种柔性支撑机构的摆动型动镜机构.建立和分析该机构控制模型,设计了相适应的反馈控制算法.结果表明:该结构具有无摩擦、抗震性好等优点;光学结构能够很好地补偿动镜摆动造成的倾斜与横移误差,保证仪器的重复性与稳定性;通过对控制算法参量的调整,动镜机构的扫描准确度优于98.4%.在4cm-1的光谱分辨率条件下,使用该动镜机构所测得的红外光谱信噪比优于80000:1,能够满足高准确度定量分析的要求.