Asymptotic Normality of Cross-correlogram Estimates of the Response Function

The problem of estimation of an unknown response function of a time-invariant continuous linear system is considered. Discrete-time sample input–output cross-correlograms are taken as estimates of the response function. The inputs are supposed to be zero-mean stationary Gaussian processes close, in some sense, to a white noise. Both asymptotic normality of finite-dimensional distributions of the estimates and their asymptotic normality in spaces of continuous functions are studied. Our basic tool is a new integral representation for cumulants of the estimate as a finite sum of integrals involving cyclic products of kernels. Some inequalities for these integrals are obtained and their asymptotic behaviour is studied.     

Intersection Cohomology on Nonrational Polytopes⋆

We consider a fan as a ringed space (with finitely many points). We develop the corresponding sheaf theory and functors, such as direct image R_* ( is a subdivision of a fan), Verdier duality, etc. The distinguished sheaf , called the minimal sheaf plays the role of an equivariant intersection cohomology complex on the corresponding toric variety (which exists if is rational). Using we define the intersection cohomology space IH(). It is conjectured that a strictly convex piecewise linear function on acts as a Lefschetz operator on IH(). We show that this conjecture implies Stanley's conjecture on the unimodality of the generalized h-vector of a convex polytope.     

Steric effects on the mechanism of reaction of nucleophilic substitution of β‐substituted alkoxyvinyl trifluoromethyl ketones with four secondary amines

The kinetics of the reaction of β‐substituted β‐alkoxyvinyl trifluoromethyl ketones R¹O‐CR²?CH‐COCF₃ ( 1a – e ) [( 1a ), R¹?C₂H₅, R²?H; ( 1b ), R¹?R²?CH₃; ( 1c ), R¹?C₂H₅, R²?C₆H₅; ( 1d ), R¹?C₂H₅, R²?V^?pNO₂C₆H₄; ( 1e ), R¹?C₂H₅, R²?C(CH₃)₃] with four aliphatic amines ( 2a – d ) [( 2a ), (C₂H₅)₂NH; ( 2b ), (i‐C₃H₇)₂NH; ( 2c ), (CH₂)₅NH; ( 2d ), O(CH₂CH₂)₂NH] was studied in two aprotic solvents, hexane and acetonitrile. The least reactive stereoisomeric form of ( 1a – d ) was the most populated ( E‐s‐Z‐o‐Z ) form, whereas in ( 1e ), the more reactive form ( Z‐s‐Z‐o‐Z ) dominated. The reactions studied proceeded via common transition state formation whose decomposition occurred by ‘uncatalyzed’ and/or ‘catalyzed’ route. Shielding of the reaction centre by bulky β‐substituents lowered abruptly both k′ (‘uncatalyzed’ rate constant) and k″ (‘catalyzed’ rate constant) of this reaction. Bulky amines reduced k″ to a greater extent than k′ as a result of an additional steric retardation to the approach of the bulky amine to its ammonium ion in the transition state. An increase in the electron‐withdrawing ability of the β‐substituent increased ‘uncatalyzed’ k′ due to the acceleration of the initial nucleophile attack (k₁) and ‘uncatalyzed’ decomposition of transition state (k₂) via promoting electrophilic assistance (through transition state 8 ). The amine basicity determined the route of the reaction: the higher amine basicity, the higher k₃/k₂ ratio (a measure of the ‘catalyzed’ route contribution as compared to the ‘uncatalyzed’ process) was. ‘Uncatalyzed’ route predominated for all reactions; however in polar acetonitrile the contribution of the ‘catalyzed’ route was significant for amines with high pK_a and small bulk. Copyright © 2007 John Wiley & Sons, Ltd.     

Crown‐ether and azobenzene‐containing liquid crystalline polymers: An influence of macromolecular architecture on optical properties and photo‐orientation processes

A series of novel crown ether‐containing photochromic comb‐shaped liquid crystalline polyacrylates with different macromolecular structure of side groups were synthesized and investigated. Phase behavior, optical and photo‐optical properties of thin spin‐coated films of these polymers were studied. A special attention was paid to a comparative study of the photo‐orientation phenomena occurring in the polymer films under a polarized light action. It was shown that complex formation with the potassium ions results in the decrease in degree of the photoinduced order that can be used for the creation of new materials for sensor devices. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

New 5-arylamino-4-(5-nitrofuran-2-yl)pyrimidines as promising antibacterial agents

A facile synthetic approach to 5-arylamino-4-(5-nitrofuran- 2-yl)pyrimidines by the Buchwald–Hartwig cross-coupling with various anilines has been developed. All synthesized compounds demonstrated a significant level of in vitro antibacterial activity against Neisseria gonorrhoeae, Streptococcus pyogene and Staphylococcus aureus, including their drug-resistant strains, which is much higher than that of the commercial drug Spectinomycin.     

A novel generation of photoactive comb‐shaped polyamides for the photoalignment of liquid crystals

A new approach to the synthesis of photoactive comb‐shaped homo‐ and copolyamides containing azobenzene, cinnamate, and coumarin side groups for photoalignment of liquid crystals was elaborated. Photooptical properties and photoorientational ability of these polymers with respect to liquid crystals were studied. It was shown that polarized UV irradiation of all spin‐coated polyamides leads to orientation of liquid crystalline molecules deposited on the polyamide thin films. The synthesized polymers containing cinnamate and coumarin side groups as well as azobenzene‐containing cyano‐ and nitro‐substituted polymers demonstrated good orientation ability in relation to liquid crystals displaying photoinduced planar orientation with high dichroism values within the range of 0.68–0.72. Contrary to the above‐mentioned polyamides, azobenzene‐containing fluorosubstituted polymers induced a homeotropic orientation of liquid crystals. It was shown that the synthesized photoactive polyamides can be considered as promising photoalignment materials for application in display technology, photonics, and other “smart” optical devices. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4031–4041     

Application of synchronous fluorescence to parchment characterization

A nondestructive method for quantitative parchment characterization and sensitive indication of its deterioration stage was developed. Synchronous fluorescence (SF) measurements were applied for the first time to parchment samples. The method provides detailed spectral features, which are useful for parchment characterization. The discrimination of parchment samples into groups (modern, historical, and artificially aged) was successfully performed. The SF spectra could be resolved into specific fluorophores, which were related to the parchment condition. The spectral data indicate a continuous change in the collagen-to-gelatin ratio during the aging process. Depth-resolved synchronous fluorescence spectra were also measured. The data indicate that parchments possess a layered structure, and the dominant fluorophore in the upper layer is different from those in the lower layers. Layer-resolved profiling allows for quantifying the contribution of each fluorophore in each given layer. This way, significant differences between modern, artificially aged, and historical samples can be observed.     

Palladium-catalyzed Suzuki cross-coupling reactions in a microemulsion

An enhancement of palladium-catalyzed Suzuki cross-coupling reactions between substrates possessing long-chain alkyl or oxyalkyl substituents in two-phase media, in the presence of sodium dodecylsulfate, is shown. Quantitative evaluations of the influence of SDS on the reaction rates were determined.     

Ferrocenylalkyl azoles: bioactivity,synthesis, structure

The toxicity of ferrocenylethyl benzotriazole ( 1 ) and other ferrocene compounds including ferrocenylmethyl benzimidazoles ( 4,5,6,11 ), ferricenium salts ( 3,9,10 ) and ferrocenylmethyl adenine ( 7 ), was studied. All ferrocene complexes under investigation showed low or medium toxicities. On the basis of an earlier model of chemical carcinogenesis, the antitumor activity of ferrocenylalkyl azoles 1, 8 and ferricenium salts 9, 10 was studied in vivo in the so‐called sub‐capsular test on human tumors. This effectiveness was compared with that of cisplatin. A series of ferrocenylalkyl azoles were synthesized by interacting azoles either with α‐hydroxyalkyl ferrocenes FcC(OH)R₁R₂ in organic solvent in the presence of aqueous HBF₄ in quantitative yields or with trimethyl(aminomethyl)ferrocene iodide in an aqueous‐basic medium in good yields. The X‐ray determinations of molecular and crystal structures of α‐(1‐benzotriazolyl)ethylferrocene ( 1 ) and α‐(1‐naphthatriazolyl)ethylferrocene ( 12 ) were performed. Copyright © 2008 John Wiley & Sons, Ltd.