On Local LYM Identities

The LYMinequality (Lubell, Yamamoto, Meshalkin) is a generalization of Sperner’s theorem for antichains. Kleitman and Harper independently proved that the LYM inequality and the normalized matching property (or local LYM inequality) are equivalent. Many contributions have been proposed to sharpen the LYM inequality. Noticeably, Ahlswede and Zhang lifted the LYM inequality to an identity, called the AZ identity. Thus, one expects that the same sharpening of the local LYM inequality is equivalent to the AZ identity. In this paper, we introduce a local LYM identity which sharpens the local LYM inequality and prove that it is equivalent to the AZ identity. The local LYM identity shows local relationships between components in the AZ identity.     

Review of stationary phases for microelectromechanical systems in gas chromatography: feasibility and separations

This review covers the recent development of stationary phases for chip-based gas chromatography (GC). Portable systems for rapid and reliable analysis are urgently needed. One way to achieve this is to miniaturize the entire analysis. Because the column is the central component of the GC system and determines the feasibility and quality of separation, this review focuses on stationary phases reported in the literature and their use in different fields during the last two decades, with emphasis on different methods for introducing the stationary phase into the GC column.     

Synthesis,Complexes and Metal Extraction Ability of R1R2NC(X)NHP(Y)(0Ph)2

Abstract

The new 1,1-disubstituted 3-diphenoxy(thio)phosphoryl-(thio)ureas, R¹R²NC(X)NHP(0Ph)₂, HA, with X,Y = O,S, were synthesized by addition of secondary mines to the corresponding P-iso(thio)cyanates. This reaction is reversible if X,Y = S. (PhO)₂P(Y)Cl reacts with H₂NC(X)NR₂ in the presence of an HCl acceptor only if X,Y a 0. Side reactions are observed. Phosphorylated derivatives of biuret were isolated from such a reaction mixture.     

Novel Copolymers of Styrene and Halogen Ring‐Disubstituted 2‐Cyano‐N,N‐Dimethyl‐3‐Phenyl‐2‐Propenamides

Electrophilic trisubstituted ethylene monomers, halogen ring‐disubstituted 2‐cyano‐N,N‐dimethyl‐3‐phenyl‐2‐propenamides, RC₆H₃CH?C(CN)CON(CH₃)₂ (where R is 2,3‐dichloro, 2,4‐dichloro, 2,6‐dichloro, 3,4‐dichloro, 3,5‐dichloro, 2,3‐difluoro, 2,4‐difluoro, 2,6‐difluoro, 3,4‐difluoro, 3,5‐difluoro), were synthesized by potassium hydroxide catalyzed Knoevenagel condensation of ring‐substituted benzaldehydes and N,N‐dimethyl cyanoacetamide, and characterized by CHN elemental analysis, IR, ¹H‐ and ¹³C‐NMR. Novel copolymers of the ethylenes and styrene were prepared at equimolar monomer feed composition by solution copolymerization in the presence of a radical initiator, ABCN at 70°C. The composition of the copolymers was calculated from nitrogen analysis, and the structures were analyzed by IR, ¹H and ¹³C NMR, GPC, DSC, and TGA. High T_g of the copolymers in comparison with that of polystyrene indicates a substantial decrease in chain mobility of the copolymer due to the high dipolar character of the trisubstituted ethylene monomer unit. The gravimetric analysis indicated that the copolymers decompose in the 300–450°C range.     

A Complex between C-Methylcalix[4]resorcinarene and Triethylammonium Nitrate

Abstract

The synthesis and crystal structure of the complex formed by the all-cis epimer of C-methylcalix[4]resorcinarene (1) and triethylammonium nitrate are reported. “1.(HNEt⁺ ₃)₄. (NO^? ₃)₄(2)”, crystallizes in the monoclinic space group P2₁/n, a=25.796(2), b=16.6048(11), c=29.5659(10) Å, β=94.636(4)°, V=12623(2) ų, Z=8. Refinement led to a final conventional R₁ value of 0.128 for 12428 reflections and 1473 parameters. The resorcinarene displays the usual bowl-type shape, with four hydroxyl protons involved in intramolecular hydrogen bonds, whereas the remaining four make hydrogen bonds with four bridging nitrate ions, which results in the formation of infinite chains. Those chains are arranged so as to form layers, between which the triethylammonium ions and the remaining nitrate ions are hydrogen-bonded one to another.     

Calixarenes as Polyhapto-aromatic Ligands: Alkali Metal Ions and Sulfonated Calixarenes

Crystal structure determinations for the hexarubidium and octacesium derivatives of calix[6]arene hexasulfonic acid, as well as of a new solvate of the pentasodium derivative of calix[4]arene tetrasulfonic acid, and comparison with structural data from the literature for alkali metal complexes of sulfonated calixarenes, have provided further evidence for the importance of interactions with aromatic ~ -electrons for the heavier alkali metal cations. There is evidence as well that this interaction can be enhanced by extended ionization of the sulfonated calixarene.     

A Bis(p-tert-butyloctahomotetraoxacalix[8]arene) Capsule with [(UO2)2(OH)2] Links and a Disordered [Rb4(H2O)4] Inner Core

p-tert-Butyloctahomotetraoxacalix[8]arene (LH⁸) reacts with uranyl nitrate hexahydrate in the presence of rubidium hydroxide to give a mixed complex that can be viewed as a tetrauranate dimer [(UO²)⁴(LH⁴)²(OH)⁴] containing four disordered rubidium ions and water molecules. Two uranyl ions are complexed in an “external” fashion by each macrocycle, each of them bound to two phenoxide groups and one ether group, as well as to two bridging hydroxide ions. The latter ensure the formation of a dimeric capsule that contains the disordered set of alkali metal ions. Apart from water molecules, the Rb⁺ ions are bound to the uranyl oxo groups directed towards the inner cavity, and to phenol and ether oxygen atoms from the macrocycle. The resulting octanuclear complex presents an unprecedented geometry evidencing the assembling potential of uranyl ions.

p-tert-Butyloctahomotetraoxacalix[8]arene (LH₈) reacts with uranyl nitrate hexahydrate in the presence of rubidium hydroxide to give a mixed complex that can be viewed as a tetrauranate dimer [(UO₂)₄(LH₄)₂(OH)₄] containing four disordered rubidium ions and water molecules. Two uranyl ions are complexed in an “external” fashion by each macrocycle, each of them bound to two phenoxide groups and one ether group, as well as to two bridging hydroxide ions. The latter ensure the formation of a dimeric capsule that contains the disordered set of alkali metal ions. Apart from water molecules, the Rb^+| ions are bound to the uranyl oxo groups directed towards the inner cavity, and to phenol and ether oxygen atoms from the macrocycle. The resulting octanuclear complex presents an unprecedented geometry evidencing the assembling potential of uranyl ions.