Problems of Lifts in Symplectic Geometry

Let(M,ω)be a symplectic manifold.In this paper,the authors consider the notions of musical(bemolle and diesis)isomorphisms ω~b:T M→T~*M and ω~?:T~*M→TM between tangent and cotangent bundles.The authors prove that the complete lifts of symplectic vector field to tangent and cotangent bundles is ω~b-related.As consequence of analyze of connections between the complete lift ~cω_(T M )of symplectic 2-form ω to tangent bundle and the natural symplectic 2-form dp on cotangent bundle,the authors proved that dp is a pullback o f~cω_(TM)by ω~?.Also,the authors investigate the complete lift ~cφ_T~*_M )of almost complex structure φ to cotangent bundle and prove that it is a transform by ω~?of complete lift~cφ_(T M )to tangent bundle if the triple(M,ω,φ)is an almost holomorphic A-manifold.The transform of complete lifts of vector-valued 2-form is also studied.     

A FACILE CONVERSION OF THE BAYLIS-HILLMAN ADDUCTS INTO TRIMETHYLSILYL ETHERS WITH HEXAMETHYLDISILAZANE CATALYSED BY IODINE

The hydroxy group of the Baylis-Hillman adducts was protected with trimethylsilyl (TMS) group using the reaction of adducts 1a–h with hexamethyldisilazane (HMDS) catalyzed by iodine under nearly neutral reaction conditions.     

SYNTHESIS OF THE CHIRAL α,β-UNSATURATED N-ACYL-OXAZOLIDIN-2-ONES BY WITTIG REACTION

A new, universal, and versatile method has been developed for the synthesis of the chiral α,β-unsaturated N-acyl-oxazolidin-2-ones 4 based on the Wittig reaction of the triphenylphosphonium salt 7 derived from the (R)-3-(2-Chloro-acetyl)-5,5-dimethyl-4-phenyl-oxazolidin-2-one 6.     

Discovery of 4,6-bis(2-((E)-benzylidene)hydrazinyl)pyrimidin-2-Amine with Antibiotic Activity

Robenidine (E)-N′-((E)-1-(4-chlorophenyl)ethylidene)-2-(1-(4-chlorophenyl)ethylidene)hydrazine-1-carboximidhydrazide displays methicillin-resistant Staphyoccoccus aureus (MRSA) and vancomycin-resistant Enterococci (VRE) MICs of 2 μg mL⁻¹. Herein we describe the structure-activity relationship development of a novel series of guanidine to 2-aminopyrimidine isosteres that ameliorate the low levels of mammalian cytotoxicity in the lead compound while retaining good antibiotic activity. Removal of the 2-NH₂ pyrimidine moiety renders these analogues inactive. Introduction of a central 2-NH₂ triazine moiety saw a 10-fold activity reduction. Phenyl to cyclohexyl isosteres were inactive. The 4-BrPh and 4-CH₃Ph with MIC values of 2 and 4 μg mL⁻¹, against MRSA and VRE respectively, are promising candidates for future development.     

A convenient two-step preparation of monodeuteriated tetramethylsilane

Purified partially mono-deuteriatedTMS was synthesized by preparing lithiomethyltrimethylsilane from chloromethyltrimethylsilane and reaction of the former with deuteriated water. Using this reference deuterium chemical shifts in parts per million can be reported with respect to [²H] resonance frequency of internalTMS in deuterium nmr spectroscopy.

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Eine einfache zweistufige Synthese von monodeuteriertem Tetramethylsilan (Kurze Mitteilung)

Zusammenfassung Es wird die Synthese von partiell monodeuteriertemTMS beschrieben. Dazu wurde Monochlormethyltrimethylsilan in Lithiomethyltrimethylsilan übergeführt und dieses mit D₂O weiter zum Zielprodukt umgesetzt.

     

Maximum transversal in partial Latin squares and rainbow matchings

In a partial Latin square P a set of distinct entries, such that no two of which are in the same row or column is called a transversal. By the size of a transversal T, we mean the number of its entries. We define a duplex to be a partial Latin square of order n containing 2n entries such that exactly two entries lie in each row and column and each of n symbols occurs exactly twice. We show that determining the maximum size of a transversal in a given duplex is an NP-complete problem. This problem relates to independent sets in certain subfamilies of cubic graphs. Generalizing the concept of transversals in edge coloring of graphs we are led to introduce the concept of rainbow matching. We show that if each color appears at most twice then it is a polynomial time problem to know whether there exists a rainbow matching of size at least ⌊n/2⌋-t for each fixed t, where n is the order of the graph. As an application we show that for any fixed t, there is a polynomial time algorithm which decides whether α(G)?n-t, for any graph G on 2n vertices containing a perfect matching. At the end we mention some other applications of rainbow matching.     

Time‐Resolved Phase Transitions of the Nanocrystalline Cubic to Submicron Monoclinic Phase in Zirconia

The nanocrystalline cubic, tetragonal, and submicron monoclinic phases of pure zirconia were prepared by thermal decomposition of carbonate and hydroxide precursors. The crystallization and isothermal phase transformations of the oxide were studied using high temperature X‐ray diffraction, X‐ray diffraction and Raman spectra of quenched samples. Cubic zirconia formed first, and then progressively transformed to tetragonal and monoclinic phases at temperatures as low as 320°C. The cubic, tetragonal, and monoclinic phases for ZrO₂ were found to be distinct functions of crystallite size, indicating the nanocrystalline nature of these phases. They were found to exist within critical size ranges of 50 to 140 Å, 100 to 220 Å and 190 to 420 Å (±5 Å), respectively. Thus, as the crystallites grow during annealing, they first transform from cubic to tetragonal and then from tetragonal to monoclinic at critical sizes. The classical Avrami equation for nucleation and growth was applied to the tetragonal to monoclinic phase transition.     

Introduction of Ag/CuO/MCM‐48 as an efficient catalyst for the one‐pot synthesis of novel pyran‐pyrrole hybrids

Bimetallic silver and copper incorporated mesoporous MCM‐48 (Ag/CuO/MCM‐48) was synthesized by simple wet‐impregnation method. The knowledge about its structural properties was gathered by means of Fourier transform‐infrared, energy‐dispersive X‐ray, X‐ray diffraction, field emission‐scanning electron microscopy, transmission electron microscopy and Brunauer–Emmett–Teller analyses. The catalytic activity of Ag/CuO/MCM‐48 was examined in the one‐pot three‐component reaction of 3‐(1‐methyl‐1H‐pyrrol‐2‐yl)‐3‐oxopropanenitrile, malononitrile and various aromatic aldehydes leading to novel pyran‐pyrrole hybrid derivatives in reduced reaction times (5–10 min) and excellent yields (88–97%). Application of Ag/CuO/MCM‐48 as a potent heterogeneous catalyst with good reusability up to five times, use of ethanol as an eco‐compatible medium and chromatography‐free work‐up are some crucial green aspects of this procedure.