Computational complexity of inner and outerj-radii of polytopes in finite-dimensional normed spaces

This paper studies the complexity of computing (or approximating, or bounding) the various inner and outer radii of ann-dimensional convex polytope in the space ⁿ equipped with an _p norm or a polytopal norm. The polytopeP is assumed to be presented as the convex hull of finitely many points with rational coordinates (V-presented) or as the intersection of finitely many closed halfspaces defined by linear inequalities with rational coefficients (-presented). The innerj-radius ofP is the radius of a largestj-ball contained inP; it isP's inradius whenj = n and half ofP's diameter whenj = 1. The outerj-radius measures how wellP can be approximated, in a minimax sense, by an (n — j)-flat; it isP's circumradius whenj = n and half ofP's width whenj = 1. The binary (Turing machine) model of computation is employed. The primary concern is not with finding optimal algorithms, but with establishing polynomial-time computability or NP-hardness. Special attention is paid to the case in whichP is centrally symmetric. When the dimensionn is permitted to vary, the situation is roughly as follows: (a) for general -presented polytopes in _p spaces with 1相似文献   

Cp*Me5P6C5: Ein neues Carbaphosphan mit einem Strukturelement aus dem Hittorfschen Phosphor

Cp*Me₅P₆C₅: A New Carbaphosphane with a Structure Unit of Hittorf-Phosphorus The thermolysis of 1,2,3-tris(pentamethylcyclopentadienyl)cyclotriphosphane [(Cp*P)₃, 1 ] or 2,3,4,6-Tetrakis(pentamethylcyclopentadienyl)bicyclo[3.1.0]hexaphosphane [Cp*₄P₆, 2 ] leads in addition to the known 3,4-bis(pentamethylcyclopentadienyl)tricyclo[3.1.0.0^{2, 6}]hexaphosphane [Cp*₂P₆, 3 ] to the pentacyclic carbaphosphanes 3,4,5,6,11-pentamethyl-endo-9-pentamethylcyclopentadienyl- 3,4,5,6,11-pentacarba-pentacyclo [6.1.1^1,8.1^3,6.0^2,70^10,11]-4-en-undecaphosphane and 3,4,5,6,11-pentamethyl-exo-9-pentamethylcyclopentadienyl-3,4,5,6,11-pentacarba-pentacyclo [6.1.1^1,8.1^3,6.0^2,70^10,11]-4-en-undecaphosphane [Cp*Me₅P₆C₅, 4a, 4b ]. Furthermore, other polyphosphanes are formed, like 1,2,3,4-tetrakis(pentamethylcyclopentadienyl)cyclotetraphosphane [(Cp*P)₄, 5 ] and 2,4-bis(pentamethylcyclopentadienyl)-tetraphosphabicyclo[1.1.0]butane [(Cp*P)₂P₂, 6 ]. The structure of 4a and 4b is determined by NMR-spectroscopy. The molecule contains a P₅C₃-cunean-unit, to which a C₂Me₂-brigde and a PCp*-brigde is bonded.     

茄黄斑螟性信息素化学的结构签定(英文)

本文采用TLC、GC、微量臭氧化和GC-MS等分析方法,从茄黄斑螟雌蛾性腺体提取物中,分离和鉴定出性信息素反-11-十六碳烯醇乙酸酯(1a)。触角电位和田间试验证明,天然提取物和合成样品均有强烈的生物活性。     

Synthesis,molecular structures,and thermal decomposition of heterometallic (π-cyclooctadiene)platinum-bis(tricarbonyliron-μ3-chalcogenides)[Fe—Fe], (π-C8H12)Pt(μ3-X)2Fe2(CO)6, where X = S,Se, or Te

Transmetallation of the Fe₃(₃-X)₂(CO)₉ clusters (X = S, Se, or Te) under the action of (-C₈H₁₂)PtCl₂ afforded new heterometallic clusters (-C₈H₁₂)Pt(₃-X)₂Fe₂(CO)₆ (2—4, respectively), which were characterized by X-ray diffraction analysis. The (-C₈H₁₂)Pt fragment in these clusters is bound to two ₃-bridging chalcogen atoms X. The iron atoms are linked to each other. The coordination environment about the Pt atom is planar-square; the Pt...Fe distance is larger than 3.2 . In the synthesis of cluster 4, a new Pt complex was also obtained for which the structure (CO)₂Pt(-Te)₂Pt(CO)₂ (5) was proposed. According to the results of differential scanning calorimetry, thermal decomposition of complex 5 gave rise only to PtTe, whereas complexes 1—4 gave products with the empirical formula Fe₂PtX₂C₂O₂. The influence of the steric effects on the geometry of the clusters is discussed.     

热处理对Nylon—11结构的影响

对不同温度热处理过的Nylon－11样品，采用广角X射线衍射（WAXD），根据X射线衍射强度理论，用多重峰图解分峰方法研究了Nylon－11结构的变化，并导出了计算Nylon－11结晶度的公式．所得结果与密度法、DSC法进行了比较．同时也给出了Nylon－11的有关热力学参数，     

A SAPO-11 Silicoaluminophosphate Molecular Sieve with Stable Crystal Structure

A SAPO-11 silicoaluminophosphate molecular sieve with stable crystal structure was synthesized for the first time. After removing template by calcination, its crystal space group still retains Icm2 which the as-synthesized has. The catalyst deriving from the present SAPO-I 1 materials shows higher isomerization selectivity and higher paraffin hydroisomerization yield than those reported elsewhere.     

中甘11号结球甘蓝高产喷肥模式化初探

依据系统工程理论的原理和方法，研究了Ｓｒ、Ｂ、Ｚｎ、Ｍｏ、Ｃｕ五种微显元素对中甘１１号结球甘蓝产量、品质的影响及各因子间的复合效应。试验结果表明，各因子对中甘１１号产量的作用是：Ｓｒ＞Ｂ＞Ｚｎ＞Ｃｕ＞Ｍｏ。获得了中甘１１号亩产在６０００ｋｇ以上的优化组合方案是：Ｓｒ０．０５４％～０．０６１％，Ｂ０．０３５％～０．０４２％，Ｚｎ０．０４７％～０．０５７％，Ｍｏ０．０３２％～０．０３８％，Ｃｕ０．０５０％～０．０５６％，为微量元素在蔬菜上的应用提供了科学依据．     

Potentiometric and antimicrobial studies on the asymmetric Schiff bases and their binuclear Ni(II) and Fe(III) complexes; synthesis and characterization of the complexes

The protonation constants of two nitro-Schiff bases SB¹, SB² and three asymmetric tetradentate diimines H₂L¹, H₂L² and H₂L³ and the stability constants of their ML type binuclear Ni(II) and Fe(III) complexes have been determined potentiometrically. The asymmetric diimines are (2OH) RCHNC₆H₄CHNR′ (2OH) type compounds [where R = R′ = phenyl for H₂L¹; R = naphthyl, R′ = phenyl for H₂L² and R = R′ = naphthyl for H₂L³]. The effect of tautomeric forms on the acid-base properties of the diimines has been investigated and discussed. In addition, dimeric and binuclear Ni(II) and Fe(III) complexes of the diimines have been synthesized and characterized by physical and spectroscopic techniques. Also, in vitro antimicrobial activities of the diimines and the complexes have been evaluated against three bacteria: Micrococcus luteus (NRLL B-4375), Bacillus cereus (RSKK 863), Escherichia coli (ATCC 11230) and the fungus: Candida albicans (ATCC 10239).     

Photochromic dihetarylethenes. 11. Synthesis and photochromic properties of diarylethenes containing furan or furopyrimidine bridges

Procedures were developed for the synthesis of substituted bis(2,5-dimethyl-3-thienyl)furans based on 1,2-bis(2,5-dimethyl-3-thienyl)-2-hydroxyethanone. Dithienylethene structures in which the ethene fragment is involved in the furan or furopyrimidine system possess photochromic properties and their open forms exhibit fluorescence.     

Titania-supported mixed HPMoV polyoxometallates as precursors of hydrodesulfurization catalysts

HDS catalysts were prepared by loading H₃PMo₁₂O₄₀ or H₄PMo₁₁V₁O₄₀ polyoxometallates on TiO₂ (0.5 and 1.0 mmol (Mo+V)). Activity of the catalysts was tested in the HDS of thiophene. The activity of catalysts of low concentration was 2–3 times higher than the activity of those of high concentration. Temperature programmed reduction (TPR) and IR spectroscopy were used to determine the properties of the catalyst. TPR measurements proved that vanadium promotes and stabilizes HDS activity due to an increase in the Mo⁵⁺/Mo⁴⁺ ratio.