Computational complexity of inner and outerj-radii of polytopes in finite-dimensional normed spaces

This paper studies the complexity of computing (or approximating, or bounding) the various inner and outer radii of ann-dimensional convex polytope in the space ⁿ equipped with an _p norm or a polytopal norm. The polytopeP is assumed to be presented as the convex hull of finitely many points with rational coordinates (V-presented) or as the intersection of finitely many closed halfspaces defined by linear inequalities with rational coefficients (-presented). The innerj-radius ofP is the radius of a largestj-ball contained inP; it isP's inradius whenj = n and half ofP's diameter whenj = 1. The outerj-radius measures how wellP can be approximated, in a minimax sense, by an (n — j)-flat; it isP's circumradius whenj = n and half ofP's width whenj = 1. The binary (Turing machine) model of computation is employed. The primary concern is not with finding optimal algorithms, but with establishing polynomial-time computability or NP-hardness. Special attention is paid to the case in whichP is centrally symmetric. When the dimensionn is permitted to vary, the situation is roughly as follows: (a) for general -presented polytopes in _p spaces with 1相似文献   

Inequalities for tails of adapted processes with an application to Wald's lemma

In this paper we introduce a new tail probability version of Wald's lemma for expectations of randomly stopped sums of independent random variables. We also make a connection between the works of Klass^{(18, 19)} and Gundy⁽¹¹⁾ on Wald's lemma. In making the connection, we develop new Lenglart and Good Lambda inequalities comparing the tails of various types of adapted processes. As a consequence of our Good Lambda inequalities we include the following result. Let {d _i }, {e _i } be two sequences of variables adapted to the same increasing sequence of σ-fields ? _n ↗?, (e.g., ? _n =σ({d _i } _i=1 ⁿ , {E _i } _i=1 ⁿ ), and letN?∞ be a stopping time adapted to {? _n }. Then for allp>0, there exists a constant 0<C _p <∞ depending onp only, such that $$\mathop {\overline {\lim } }\limits_\lambda \lambda ^p P\left( {\mathop {\sup }\limits_{1 \leqslant n \leqslant N} \left\| {\sum\limits_{i = 1}^n {d_i } } \right\| > \lambda } \right) \leqslant C_p \mathop {\overline {\lim } }\limits_\lambda \lambda ^p P\left( {\mathop {\sup }\limits_{1 \leqslant n \leqslant N} \left\| {\sum\limits_{i = 1}^n {e_i } } \right\| > \lambda } \right)$$ This result holds when the sequences are real, tangent, and either conditionally symmetric or nonnegative, or alternatively, if {d _i } is a sequence of independent random variables and {e _i } is an independent copy of {d _i }, withN a stopping time adapted to the filtration generated by {d _i } only. Other examples include Hilbert space valued differentially subordinate conditionally symmetric martingale differences. The result is true for more general operators applied to sequences as shown by an example comparing the square function of a conditionally symmetric sequence to the maximum of its absolute partial sums.     

Michael addition reactions between chiral equivalents of a nucleophilic glycine and (S)- or (R)-3-[(E)-enoyl]-4-phenyl-1,3-oxazolidin-2-ones as a general method for efficient preparation of beta-substituted pyroglutamic acids. Case of topographically controlled stereoselectivity

This paper describes a systematic study of addition reactions between the chiral Ni(II) complex of the Schiff base of glycine with (S)-o-[N-(N-benzylprolyl)amino]benzophenone and (S)- or (R)-3-[(E)-enoyl]-4-phenyl-1,3-oxazolidin-2-ones as a general and synthetically efficient approach to beta-substituted pyroglutamic acids and relevant compounds. These reactions were shown to occur at room temperature in the presence of nonchelating organic bases and, most notably, with very high (>98% diastereomeric excess (de)) stereoselectivity at both newly formed stereogenic centers. The stereochemical outcome of the reactions was found to be overwhelmingly controlled by the stereochemical preferences of the Michael acceptors, and the chirality of the glycine complex influenced only the reaction rate. Thus, in the reactions of both the (S)-configured Ni(II) complex and the Michael acceptors, the reaction rates were exceptionally high, allowing preparation of the corresponding products with virtually quantitative (>98%) chemical and stereochemical yields. In contrast, reactions of the (S)-configured Ni(II) complex and (R)-configured Michael acceptors proceeded at noticeably lower rates, but the addition products were obtained in high diastereo- and enantiomeric purity. To rationalize the remarkably high and robust stereoselectivity observed in these reactions, we consider an enzyme-substrate-like mode of interaction involving a topographical match or mismatch of two geometric figures. Excellent chemical and stereochemical yields, combined with the simplicity and operational convenience of the experimental procedures, render the present method of immediate use for preparing various beta-substituted pyroglutamic acids and related compounds.     

Determination of Pt in urine of tram drivers by sector field inductively coupled plasma mass spectrometry

The Platinum Group Elements (PGEs) used in automotive catalytic converters are partly emitted into the air during use and can enter the human respiratory system. Due to the increasing use of automotive catalytic converters, the importance of this problem cannot be overlooked.The goal of this investigation was to determine the concentration of Pt in the urine of individuals occupationally exposed to urban air with heavy traffic. Sector field inductively coupled plasma mass spectrometry (SF–ICP–MS) was used for determination of Pt in the urine of tram drivers. 38 and 34 subjects were investigated in Vienna and Budapest, respectively. Samples were taken from the tram drivers both before and after the shift.The results for Pt were compared to those from a previous study performed by our team. The comparison showed that the concentration medians were 4 times higher than the previous ones. Moreover, the values in Budapest were about twice as high as those from Vienna. A partly significant change could be observed between the two sets of data: before, and after the shift.     

Identification of the function of gene lndM2 encoding a bifunctional oxygenase-reductase involved in the biosynthesis of the antitumor antibiotic landomycin E by Streptomyces globisporus 1912 supports the originally assigned structure for landomycinone

The angucycline antibiotic family of the landomycins displays potent antitumor activity. To elucidate early post polyketide synthase (PKS) tailoring steps of the landomycin E biosynthetic pathway in Streptomyces globisporus 1912, the mutant S. globisporus M12 was prepared through gene replacement experiment of lndM2. It encodes an enzyme with putative oxygenase and reductase domains, according to sequencing of the gene and its counterpart lanM2 from S. cyanogenus S136 landomycin A biosynthetic gene cluster. The isolation of the novel shunt products 11-hydroxytetrangomycin and 4-hydroxytetrangomycin along with the well-known angucyclines tetrangomycin and tetrangulol from the culture of S. globisporus M12 provides evidence for the involvement of lndM2 in the early biosynthetic pathway of the landomycins, in particular in the formation of the alicyclic 6-hydroxy function of the landomycin aglycon. We therefore propose LndM2 to be responsible for both hydroxylation of the 6-position and its subsequent reduction. These reactions are necessary before the glycosylation reactions can occur. The results are in agreement with the originally published structure of landomycin but do not support the recently suggested revised structure.     

The Role of Carnitine Acyltransferases in the Maintenance of Cell Function

Summary. Carnitine acyltransferases catalyse equilibria between acyl-CoA esters and the respective acylcarnitines. Therefore, they act not only as pathway enzymes, but also as modulators of acyl-CoA concentrations within individual sub-cellular compartments. Because acyl-CoA esters are potent biologically active metabolites, carnitine acyltransferase activities are potentially able to affect a diverse range of physiological processes, ranging from insulin secretion, to appetite control, and insulin sensitivity of tissues. The distinctive subcellular distributions of the different types of carnitine acyltransferases also enables them to participate in the transfer of acyl moieties across intracellular membranes, and of particular acylcarnitine esters across the plasma membrane and into the plasma. Pharmacological strategies that make use of these properties to improve cell function are discussed.     

Assembly and Dissociation of Α-Cyclodextrin [2]Pseudorotaxanes with α,ω-Bis(N-(N,N′-dimethylethylenediamine)alkane Threads

A series of novel bischelate bridging ligands, CH₃NH(CH₂)₂N(CH₃)(CH₂) _n N(CH₃)(CH₂)₂NHCH₃ (n = 9, 10, 11, and 12) were synthesized as hydrochloride salts and characterized by elemental analyses, electrospray mass spectrometry, and ¹H and ¹³C NMR spectroscopy. These ligands form [2]pseudorotaxanes with α-cyclodextrin (α-CD) and the stability constants have been determined from ¹H NMR titrations in D₂O. The kinetics and mechanism of the assembly and dissociation of a [2]pseudorotaxane in which α-CD has been threaded by the CH₃NH₂(CH₂)₂N(CH₃)(CH₂)₁₂N(CH₃)(CH₂)₂NH₂CH ₃ ²⁺ ligand were determined in aqueous solution using ¹H NMR spectroscopy. A weak inclusion of the dimethylethylenediamine end group precedes the passage of the α-CD onto the hydrophobic dodecamethylene chain.     

A facile approach to architecturally defined nanoparticles via intramolecular chain collapse

A novel approach is presented for the controlled intramolecular collapse of linear polymer chains to give well-defined single-molecule nanoparticles whose structure is directly related to the original linear polymer. By employing a combination of living free radical polymerization and benzocyclobutene (BCB) chemistry, nanoparticles can be routinely prepared in multigram quantities with the size being accurately controlled by either the initial degree of polymerization of the linear chain or the level of incorporation of the BCB coupling groups. The latter also allows the cross-link density of the final nanoparticles to be manipulated. In analogy with dendritic macromolecules, a significant reduction of up to 75% in the hydrodynamic volume is observed on going from the starting random coil linear chains to the corresponding nanoparticles. The facile nature of the living free radical process also permits wide variation in monomer selection and functional group incorporation and allows novel macromolecular architectures to be prepared. Furthermore, the use of block copolymers functionalized with benzocyclobutene groups in only one of the blocks gives, after intramolecular collapse, a hybrid architecture in which a single linear polymer chain is attached to the globular nanoparticle.     

Comparative Studies of Cathodically-Promoted and Base-Catalyzed Michael Addition Reactions of Levoglucosenone

Regioselective Michael addition of nitro and heterocyclic compounds to levoglucosenone, 1, is effectively catalyzed by amines and also by cathodic electrolysis. In comparison to the base-catalyzed reaction, it was found that under electrochemical conditions the reaction proceeds under milder conditions and with higher yields. Cathodically-initiated Michael addition of thiols to levoglucosenone using small currents produces the previously unknown threo addition product in several instances. The normal erythro isomer, identified as the kinetic product, tends to be formed when large currents are used. In contrast, slow, low current electrolyses promote equilibration of the two forms so that erythro can be converted to threo by the retro reaction and readdition. Addition of 2-naphthalenethiol to (R)-(+)-apoverbenone is also reported.