The universal covering homomorphism in o‐minimal expansions of groups

Suppose G is a definably connected, definable group in an o‐minimal expansion of an ordered group. We show that the o‐minimal universal covering homomorphism : → G is a locally definable covering homomorphism and π₁(G) is isomorphic to the o‐minimal fundamental group π (G) of G defined using locally definable covering homomorphisms. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Series with monotone coefficients by Walsh system

The paper studies the series $\sum\limits_{n = 0}^\infty {a_n } W_n (x)$ by Walsh system, where |a _n | monotone tends to zero and $\sum\limits_{n = 1}^\infty {a_{_n }^2 } = \infty $ . Some theorems on correction in L ¹ and representability of functions from L ^p , p ∈ (0, 1) by subseries of the Walsh series are proved.     

Universal spaces for almost -dimensionality

We find universal functions for the class of lower semi-continuous (LSC) functions with at most -dimensional domain. In an earlier paper we proved that a space is almost -dimensional if and only if it is homeomorphic to the graph of an LSC function with an at most -dimensional domain. We conclude that the class of almost -dimensional spaces contains universal elements (that are topologically complete). These universal spaces can be thought of as higher-dimensional analogues of complete Erdos space.

     

On rational isomorphisms of Lie algebras

Let \(\mathfrak{n}\) be a finite-dimensional noncommutative nilpotent Lie algebra for which the ring of polynomial invariants of the coadjoint representation is generated by linear functions. Let \(\mathfrak{g}\) be an arbitrary Lie algebra. We consider semidirect sums \(\mathfrak{n} \dashv _\rho \mathfrak{g}\) with respect to an arbitrary representation ρ: \(\mathfrak{g}\) → der \(\mathfrak{n}\) such that the center z \(\mathfrak{n}\) of \(\mathfrak{n}\) has a ρ-invariant complement.We establish that some localization \(\tilde P(\mathfrak{n} \dashv _\rho \mathfrak{g})\) of the Poisson algebra of polynomials in elements of the Lie algebra \(\mathfrak{n} \dashv _\rho \mathfrak{g}\) is isomorphic to the tensor product of the standard Poisson algebra of a nonzero symplectic space by a localization of the Poisson algebra of the Lie subalgebra \((z\mathfrak{n}) \dashv \mathfrak{g}\). If \([\mathfrak{n},\mathfrak{n}] \subseteq z\mathfrak{n}\), then a similar tensor product decomposition is established for the localized universal enveloping algebra of the Lie algebra \(\mathfrak{n} \dashv _\rho \mathfrak{g}\). For the case in which \(\mathfrak{n}\) is a Heisenberg algebra, we obtain explicit formulas for the embeddings of \(\mathfrak{g}_P \) in \(\tilde P(\mathfrak{n} \dashv _\rho \mathfrak{g})\). These formulas have applications, some related to integrability in mechanics and others to the Gelfand-Kirillov conjecture.     

普遍服务、市场竞争与消费者福利

通过构建一个简单的模型分析了普遍服务约束下的垄断产业在引入竞争后的市场竞争,模型很好地展现了垄断产业引入竞争后所出现的“撇脂现象”.通过分析得出:引入竞争后,在位者的盈利和亏损同时减少,但盈利减少得更多;竞争对消费者总体上是有利的,但竞争的好处更多地被低成本的城市消费者所获得,高成本的农村消费者则没有分享到改革的成果;...     

Synthesis,Physicochemical Properties,and Hydrogen Bonding of 4(5)‐Substituted 1‐H‐Imidazole‐2‐carboxamide,a Potential Universal Reader for DNA Sequencing by Recognition Tunneling

We have developed a chemical reagent that recognizes all naturally occurring DNA bases, a so called universal reader, for DNA sequencing by recognition tunneling in nanopores. 1 The primary requirements for this type of molecules are the ability to form non‐covalent complexes with individual DNA bases and to generate recognizable electronic signatures under an electrical bias. 1‐H‐imidazole‐2‐carboxamide was designed as such a recognition moiety to interact with the DNA bases through hydrogen bonding. In the present study, we first furnished a synthetic route to 1‐H‐imidazole‐2‐carboxamide containing a short ω‐functionalized alkyl chain at its 4(5) position for its attachment to metal and carbon electrodes. The acid dissociation constants of the imidazole‐2‐carboxamide were then determined by UV spectroscopy. The data show that the 1‐H‐imidazole‐2‐carboxamide exists in a neutral form between pH 6–10. Density functional theory (DFT) and NMR studies indicate that the imidazole ring exists in prototropic tautomers. We propose an intramolecular mechanism for tautomerization of 1‐H‐imidazole‐2‐carboxamide. In addition, the imidazole‐2‐carboxamide can self‐associate to form hydrogen bonded dimers. NMR titration found that naturally occurring nucleosides interacted with 1‐H‐imidazole‐2‐carboxamide through hydrogen bonding in a tendency of dG>dC?dT>dA. These studies are indispensable to assisting us in understanding the molecular recognition that takes place in the nanopore where routinely used analytical tools such as NMR and FTIR cannot be conveniently applied.     

Universal Calibration Method for the Determination of Polycyclic Aromatic Hydrocarbons by High Performance Liquid Chromatography with Broadband Diode-Array Detection

Abstract

The response of polycyclic aromatic hydrocarbons (PAH) at different UV wavelengths was measured using high performance liquid chromatography with spectrophotometric diode-array detection. By utilizing the total UV absorption bandwidth (200-400 nm), it was found that a narrow distribution of normalized response factors (area/g) could be obtained for 16 PAH in a reference mixture of frequently-occurring species, even though the PAH represented a wide variety of different chromophores.

Using the mean response factor for the 16 PAH, a universal calibration factor was obtained that formed the basis of a method for the determination of PAH for which calibration data cannot otherwise be obtained. It utilized normal phase high performance liquid chromatography (HPLC) with a cyanopropyl column and a hexane-dichloromethane mobile phase. The HPLC conditions were optimized for the separation of PAH according to their aromatic ring number. The method was developed for the characterization of complex mixtures of fossil fuels-derived PAH that cannot be analyzed by traditional methods. It is applicable to PAH having from 1 to 10 or more fused aromatic rings.     

Gröbner bases for the Hilbert ideal and coinvariants of the dihedral group D2p

We consider a finite dimensional representation of the dihedral group D_2p over a field of characteristic two where p is an odd integer and study the corresponding Hilbert ideal I_H. We show that I_H has a universal Gröbner basis consisting of invariants and monomials only. We provide sharp bounds for the degree of an element in this basis and in a minimal generating set for I_H. We also compute the top degree of coinvariants when p is prime.     

Universal absolute extensors in extension theory

Let be a countable and locally finite CW complex. Suppose that the class of all metrizable compacta of extension dimension contains a universal element which is an absolute extensor in dimension . Our main result shows that is quasi-finite.