A pair of orthogonal frames

We start with a characterization of a pair of frames to be orthogonal in a shift-invariant space and then give a simple construction of a pair of orthogonal shift-invariant frames. This is applied to obtain a construction of a pair of Gabor orthogonal frames as an example. This is also developed further to obtain constructions of a pair of orthogonal wavelet frames.     

Synthesis and structural characterization of mono- and bisfunctional o-carboranes

Functionalized o-carboranes are interesting ligands for transition metals. Reaction of LiC2B10H11 with Me2NCH2CH2Cl in toluene afforded 1-Me2NCH2CH2-1,2-C2B10H11 (1). Treatment of 1 with 1 equiv. of n-BuLi gave [(Me2NCH2CH2)C2B10H10]Li ([1]Li), which was a very useful synthon for the production of bisfunctional o-carboranes. Reaction of [1]Li with RCH2CH2Cl afforded 1-Me2NCH2CH2-2-RCH2CH2-1,2-C2B10H10 (R = Me2N (2), MeO (3)). 1 and 2 were also prepared from the reaction of Li2C2B10H10 with excess Me2NCH2CH2Cl. Treatment of [1]Li with excess MeI or allyl bromide gave the ionic salts, [1-Me3NCH2CH2-2-Me-1,2-C2B10H10][I] (4) and [1-Me2N(CH2=CHCH2)CH2CH2-2-(CH2=CHCH2)-1,2-C2B10H10][Br] (6), respectively. Interaction of [1]Li with 1 equiv. of allyl bromide afforded 1-Me2NCH2CH2-2-(CH2=CHCH2)-1,2-C2B10H10 (5). Treatment of [1]Li with excess dimethylfulvene afforded 1-Me2NCH2CH2-2-C5H5CMe2-1,2-C2B10H10 (7). Interaction of [1]Li with excess ethylene oxide afforded an unexpected product 1-HOCH2CH2-2-(CH2=CH)-1,2-C2B10H10 (8). 1 and 3 were conveniently converted into the corresponding deborated compounds, 7-Me2NHCH2CH2-7,8-C2B9H11 (9) and 7-Me2NHCH2CH2-8-MeOCH2CH2-7,8-C2B9H10 (10), respectively, in MeOH-MeOK solution. All of these compounds were characterized by various spectroscopic techniques and elemental analyses. The solid-state structures of 4 and 6-10 were confirmed by single-crystal X-ray analyses.     

Organometallic Compounds of the Lanthanoides. LXVI. Synthesis and X-ray crystal structure of [O(CH2CH2C5H4)2Y(μ-OH]2 and (MeC5H4)3Ho(H2O), two unusual products of the hydrolysis of organolanthanoide compounds

The partial hydrolysis of [O(CH₂CH₂C₅H₄)₂]Y(C₅H₄CH₃) 1 , [O(CH₂CH₂C₅H₄)₂]Y(C₅H₅) 3 , and [O(CH₂CH₂C₅H₄)₂]Ho(C₅H₄CH₃) 5 results in the formation of [O(CH₂CH₂CH₂C₅H₄)₂Y(μ-OH)₂]₂ 2 , (C₅H₅)₃Y(OH₂) 9 and (MeC₅H₄)₃Ho(OH₂) 11 . The new compounds have been characterized by elemental analyses, IR and NMR spectra. The X-ray structural analyses shows 2 to be monoclinic, space group P2₁/n with a = 1146.0(3), b= 1046.6(3), c = 1514.9(3) pm, β = 94.83(2)°. The molecular structure shows bridging hydroxyl groups with a mean distance Y? O = 223.8(3) pm. 11 crystallizes in the cubic space group 14 3d with a = 1847.9(3)pm with Z = 16 molecules per unit cell. The molecules posses symmetry C₃-3, the coordination is trigonal pyramidal with three methylcyclopentadienyl anions and one water molecule as ligands. The distance Ho? O is 231 pm.     

Landscape of supersymmetric particle mass hierarchies and their signature space at the CERN Large Hadron Collider

The minimal supersymmetric standard model with soft breaking has a large landscape of supersymmetric particle mass hierarchies. This number is reduced significantly in well-motivated scenarios such as minimal supergravity and alternatives. We carry out an analysis of the landscape for the first four lightest particles and identify at least 16 mass patterns, and provide benchmarks for each. We study the signature space for the patterns at the CERN Large Hadron Collider by analyzing the lepton+ (jet> or =2) + missing P{T} signals with 0, 1, 2, and 3 leptons. Correlations in missing P{T} are also analyzed. It is found that even with 10 fb{-1} of data a significant discrimination among patterns emerges.     

1,3‐Dehydro‐o‐Carborane: Generation and Reaction with Arenes

Like the importance of benzyne, witnessed in modern arene chemistry for decades, 1,2‐dehydro‐o‐carborane (o‐carboryne), a three‐dimensional relative of benzyne, has been used as a synthon for generating a wide range of cage, carbon‐functionalized carboranes over the past 20 years. However, the selective B functionalization of the cage still represents a challenging task. Disclosed herein is the first example of 1,3‐dehydro‐o‐carborane featuring a cage C? B bond having multiple bonding characters, and is successfully generated by treatment of 3‐diazonium‐o‐carborane tetrafluoroborate with non‐nucleophilic bases. This presents a new methodology for simultaneous functionalization of both cage carbon and boron vertices.     

Regioselective Insertion of o‐Carborynes into the α‐CH Bond of Tertiary Amines: Synthesis of α‐Carboranylated Amines

o‐Carboryne can undergo α‐C? H bond insertion with tertiary amines, thus affording α‐carboranylated amines in very good regioselectivity and isolated yields. In this process, the nucleophilic addition of tertiary amines to the multiple bond of o‐carboryne generates a zwitterionic intermediate. An intramolecular proton transfer, followed by a nucleophilic attack leads to the formation of the final product. Thus, regioselectivity is highly dependent upon the acidity of α‐C? H proton of tertiary amines. This approach serves as an efficient methodology for the preparation of a series of 1‐aminoalkyl‐o‐carboranes.     

基于金属有机骨架材料的磁固相萃取与高效液相色谱-紫外检测法分析饮料和方便面中4种防腐剂

通过简单的搅拌共混方式制备了磁性氨基功能化的金属有机骨架化合物（MOFs）材料,得到的复合材料磁性和热稳定性良好,比表面积大,被用于不同极性防腐剂（苯甲酸、山梨酸、对羟基苯甲酸丙酯和对羟基苯甲酸丁酯）的萃取。优化磁固相萃取及解吸条件后,将解吸液引入高效液相色谱-紫外检测分析仪器,采用Purospher^® STAR LP C18色谱柱（250 mm×4.6 mm,5 μm）分离,以甲醇-10 mmol/L醋酸铵水溶液（50：50,v/v）为流动相进行梯度洗脱。结果表明,目标防腐剂的检出限为0.51~1.89 μg/L;苏打水、维生素饮料和方便面面饼中目标防腐剂的加标回收率为72.2%~109%。该方法简单快速,准确可靠,适用于饮料和食品中不同极性防腐剂的分析,为食品安全及质量监控提供了有效的技术有段。     

Synthesis and structural characterization of imido-lanthanide complexes with a metal-nitrogen multiple bond

Treatment of an amido-ytterbium complex with n-BuLi leads to the isolation and structural characterization of a mixed amido-imido-ytterbium or imido-ytterbium complex, respectively, depending upon the molar ratios of the reactants; the Yb-N distance and the linearity of the imido N atom strongly suggest the presence of a formal Yb=N multiple bond in these novel complexes.