Query complexity,or why is it difficult to separateNP A ∩coNP A fromP A by random oraclesA?

By thequery-time complexity of a relativized algorithm we mean the total length of oracle queries made; thequery-space complexity is the maximum length of the queries made. With respect to these cost measures one can define polynomially time- or space-bounded deterministic, nondeterministic, alternating, etc. Turing machines and the corresponding complexity classes. It turns out that all known relativized separation results operate essentially with this cost measure. Therefore, if certain classes do not separate in the query complexity model, this can be taken as an indication that their relativized separation in the classical cost model will require entirely new principles.A notable unresolved question in relativized complexity theory is the separation of NP^A co NP^A fromP ^A under random oraclesA. We conjecture that the analogues of these classes actually coincide in the query complexity model, thus indicating an answer to the question in the title. As a first step in the direction of establishing the conjecture, we prove the following result, where polynomial bounds refer to query complexity.If two polynomially query-time-bounded nondeterministic oracle Turing machines accept precisely complementary (oracle dependent) languages L^A and {0, 1}^*L^A under every oracle A then there exists a deterministic polynomially query-time-bounded oracle Turing machine that accept L^A. The proof involves a sort of greedy strategy to selecting deterministically, from the large set of prospective queries of the two nondeterministic machines, a small subset that suffices to perform an accepting computation in one of the nondeterministic machines. We describe additional algorithmic strategies that may resolve the same problem when the condition holds for a (1–) fraction of the oracles A, a step that would bring us to a non-uniform version of the conjecture. Thereby we reduce the question to a combinatorial problem on certain pairs of sets of partial functions on finite sets.     

Symmetries and conservation laws of Kadomtsev-Pogutse equations

Kadomtsev-Pogutse equations are of great interest from the viewpoint of the theory of symmetries and conservation laws and, in particular, enable us to demonstrate their potentials in action. This paper presents, firstly, the results of computations of symmetries and conservation laws for these equations and the methods of obtaining these results. Apparently, all the local symmetries and conservation laws admitted by the considered equations are exhausted by those enumerated in this paper. Secondly, we point out some reductions of Kadomtsev-Pogutse equations to more simpler forms which have less independent variables and which, in some cases, allow us to construct exact solutions. Finally, the technique of solution deformation by symmetries and their physical interpretation are demonstrated.     

Solutions rationnelles de certaines équations fonctionnelles

Dans cet article, nous démontrons essentiellement les deux résultats suivants, qui montrent que les solutions séries formelles à coefficients dans de certaines équations fonctionnelles sont rationnelles. Soient tout d'abords un entier naturel non nul, eta _i ,b _i ,(i = 1, , s), 2s nombres complexes, lesa _i étant non nuls. On définit l'ensembleA comme étant l'intersection des parties de , contenant l'origine et stables par toutes les applicationsg _i (x) = a _i x + b _i . On a alors le résultat suivant: Théorème 1.Soient f, R ₁, ,R _s s + 1 fractions rationnelles de (x), régulières à l'origine, et a_i, b_i (i = 1,, s), 2s éléments de . On suppose que les a_i sont non nuls et de module strictement inférieur à un pour tout i = 1,, s. Soit y(x) un élément de [[x]], vérifiant l'équation fonctionnelle

The many limits of mixed means

The sequences introduced by Carlson (1971) are variants of the Gauss arithmetic geometric sequences (which have been elegantly discussed by D. A. Cox (1984, 1985)). Given (complex)a ₀,b ₀ we define

分子筛修饰电极的研究（Ⅰ）──氢醌／醌电对在分子筛修饰电极上的电化学行为

考察了中性分子电对Ｈ_２Ｑ／Ｑ在１３Ｘ型分子筛修饰电极上的电化学行为。发现Ｈ_２Ｑ／Ｑ电对在修饰电极上电响应迅速，为双电子可逆反应，不受溶液温度及电极与溶液相对运动的影响，而与溶液的ｐＨ值有关。当ｐＨ≤２．０时，修饰电极对Ｈ_２Ｑ／Ｑ电对的氧化／还原有明显的催化作用．     

QSPR Modeling of the Reactivity Parameters of Monomers in Radical Copolymerizations

For a series of monomers, QSPR test analysis is performed by optimizing the correlation weights of the local invariants of molecular graphs representing monomer structures in order to construct models of the reactivity parameters of monomers Q and e. This approach may be used as a tool in reactivity predictions for monomers for which no experimental data on Q and e are available.Original Russian Text Copyright © 2004 by A. A. Toropov, V. O. Kudyshkin, N. L. Voropaeva, I. N. Ruban, and S. Sh. Rashidova__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 994–998, November–December, 2004.     

Influence of target surface degradation on the properties of r.f. magnetron‐sputtered calcium phosphate coatings

This paper reports a detailed study of how repeated r.f. magnetron sputtering from a hydroxyapatite (HA) powder target affects the nature and reproducibility of a sequential series of thin‐film coatings deposited onto Ti6Al4V substrates. An evaluation of the effective lifespan of the HA sputter targets and the reproducibility of the calcium phosphate (CaP) coatings produced from them has been made from Fourier transform infrared spectroscopy, XPS and, as appropriate, atomic force microscopy and SEM/energy dispersive x‐ray analyses. The annulus region of the target surface, from which sputtering under r.f. magnetron conditions normally occurs, showed severe surface degradation after only one deposition run, as indicated by significant PO₄^3? and OH^? depletion. This deterioration continued after each subsequent deposition cycle but to a much lesser extent than that observed in the initial sputtering period. The layers produced from all of the sputter runs contained the expected Ca²⁺ and PO₄^3? species characteristic of a CaP system but were OH^? deficient in the as‐deposited state. However, the chemical and morphological properties of the coatings did not change significantly until after the third consecutive sputter cycle. Hence, these data indicate that, even though a significant level of degradation of the HA target occurs at the outset of the sputtering procedure, the general plasma conditions employed here have a dominant influence on the coating properties until a critical degradation condition is met. As such, the compacted HA powder targets of interest can have a life‐cycle greater than single usage without detriment to the chemistry and morphology of the coatings produced from them. Copyright © 2003 John Wiley & Sons, Ltd.     

丙烯酸β-羧乙酯-苯乙烯共聚合的研究

<正> 丙烯酸酯类聚合物是一类性能优良的橡胶、涂料和粘合剂,酯的结构不同可得到性能各异的均聚物和共聚物。 丙烯酸β-羧乙酯(APA)是一种具有多种反应功能的丙烯酸酯单体,结构式为:CH_2=CH—COOCH_2CH_2COOH,其双键可发生加成聚合,制得的大分子带有反应性酯基和羧基侧基,以其制备反应性大分子具有广泛的应用前景。我们研究了丙烯酸β-羧     

Chiral base route to functionalised cyclopentenyl amines: formal synthesis of the cyclopentene core of nucleoside Q

A chiral base route to a range of highly functionalised amino cyclopentenes has been developed. The key asymmetric step involved the chiral lithium amide base-mediated rearrangement of a protected trans-4-hydroxy cyclopentene oxide to give an allylic alcohol (88% ee). Subsequent Overman rearrangement gave a protected trans-1,2-aminocyclopentenol whereas Mitsunobu substitution with BocNHNs gave a protected cis-amino cyclopentenol. Both are proven intermediates for natural product synthesis. The protected cis-aminocyclopentenol was transformed in a few steps into a precursor of the cyclopentene core of nucleoside Q, a natural product whose deficiency in animals is related to tumour growth.     

Synthesis, Crystal Structure and Inhibition of the K562 Cell Proliferation of N＇-Tertbutylaminocarbonyl-N-2-chlorophenoxyacetylthiourea

The title compound N'-tert-butylaminocarbonyl-N-2-chlorophenoxyacetylthiou- rea has been synthesized for the first time. Complete assignments were achieved by IR, 1H NHR and single-crystal X-ray diffraction analyses. The inhibitory rate of the cellular growth of K562 cells (chronic myeloid 1eukemic cells) was measured using MTT [3-(4,5-dimethylthiazo-2-y1)-2,5-di- phenyltetra-zolium bromide] assay. The cell apoptosis was assessed by agarose gel electrophoresis to find that the title compound has antiproliferation and apoptosis inducing effects on K562 cells. In order to investigate the relationship between structure and activity of the target compound, we report its crystal structure and biological behavior in the present paper. Crystallographic data: C14H18- ClN3O3S, Mr = 343.82, orthorhombic, space group Pnma, a = 19.786(6), b = 6.789(2), c = 12.938(4) , V = 1738.0(9) 3, Z = 4, Dc = 1.314 g/cm3, F(000) = 720, μ(MoKα) = 0.354 mm-1, R = 0.0378 and wR = 0.0941. The molecule is a planar structure.