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61.
62.
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
63.
Victor H. de la Peña 《Journal of Theoretical Probability》1993,6(2):285-302
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. 相似文献
64.
The inertia defects of some vinyl halides and their deuterated derivatives have been calculated on the basis of the general formulation developed by Oka and Morino. The initial sets of Urey-Bradley force constants, based on published data, were adjusted by a least squares procedure until they reproduced the fundamental vibrational frequencies satisfactorily. The Coriolis coupling constants which satisfy the sum rules derived were evaluated and used to calculate the inertia defect in the ground vibrational state. The theoretical values of the inertia defect are used to determine the rotational constant A which cannot otherwise be accurately determined from an “a” type transition. 相似文献
65.
Atri Mukhopadhyay Raj Kumar Moitra Debashis Mukherjee 《International journal of quantum chemistry》1975,9(3):545-554
We introduce here a new partitioning of the Hamiltonian in calculating pair-correlation energies using many-body perturbation theory, by which we are able to eliminate the off-diagonal particle–hole (p–h) ladders exactly to all orders in the perturbation expansion. In this formulation, the particle states turn out to be different for each distinct pair of hole states in the correlation energy calculation. We have also included the contributions of the diagonal particle–particle (p–p) and hole–hole ladders exactly to all orders. The effect of the off-diagonal p–p ladders has been estimated for each pair by computing the third-, foruth- and fifth-order energies. For highly symmetric systems the present partitioning yields in general symmetry-broken orbitals. Here one may use an average kind of partitioning for all the partners of the degenerate sets, which restores the symmetry and at the same time ensures cancellation of the p–h ladders exactly at the lowest order and approximately at the higher orders. Results are presented for a selection of 6π-electron conjugated systems. The correlation energy for each pair is in excellent agreement with that obtained from a partial CI calculation involving all double excitations from this pair. The advantages of implementing the present scheme in larger systems has been discussed. 相似文献
66.
Tran TT Zeng J Treutlein H Burgess AW 《Journal of the American Chemical Society》2002,124(18):5222-5230
Thiopeptides, formed by replacing the amide oxygen atom with a sp(2) sulfur atom, are useful in protein engineering and drug design because they confer resistance to enzymatic degradation and are predicted to be more rigid. This report describes our free molecular dynamics simulations with explicit water and free energy calculations on the effects of thio substitutions on the conformation of alpha-helices, 3(10)-helices, and their relative stability. The most prominent structural effect of thio substitution is the increase in the hydrogen bond distance from 2.1 A for normal peptides to 2.7 A for thiopeptides. To accommodate for the longer C[double bond]S...H-N hydrogen bond, the (phi, psi) dihedral angles of the alpha-helix changed from (-66 degrees, -42 degrees) to (-68 degrees, -38 degrees), and the rise per turn increased from 5.5 to 6.3 A. For 3(10)-helices, the (phi, psi) dihedral angles (-60 degrees, -20 degrees) and rise per turn (6.0 A) changed to (-66 degrees, -12 degrees) and 6.8 A, respectively. In terms of relative stability, the most prominent change upon thio substitution is the decrease in the free energy difference, Delta A(alpha --> 3(10)), from 14 to 3.5 kcal/mol. Therefore, normal peptides are less likely to form 3(10)-helix than are thiopeptides. Component analysis of the Delta A(alpha --> 3(10)) reviews that the entropy advantage of the 3(10)-helix for both Ac-Ala(10)-NHMe and Act-Alat(10)-NHMe is attributed to the 3(10)-helix being more flexible than the alpha-helix. Interestingly, upon thio substitution, this differential flexibility is even more apparent because the alpha-helix conformation of Act-Alat(10)-NHMe becomes more rigid due to the bulkier sulfur atom. 相似文献
67.
68.
Victor A.?ZammitEmail author Nigel T.?Price Vicky N.?Jackson Byun-Sung?Park 《Monatshefte für Chemie / Chemical Monthly》2005,136(8):1299-1309
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. 相似文献
69.
Victor X. Jin Donal H. Macartney Erwin Buncel 《Journal of inclusion phenomena and macrocyclic chemistry》2005,53(3-4):197-203
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. 相似文献
70.
Brahmananda?Ghosh David A.?LightnerEmail author Antony F.?McDonaghEmail author 《Monatshefte für Chemie / Chemical Monthly》2004,135(9):1189-1199
Summary. A symmetrical C(10)-selena-bilirubin analog, 8,12-bis(2-carboxyethyl)-7,13-dimethyl-2,3,17,18-tetraethyl-10-selenabiladiene-ac-1,19(21H,24H)-dione was synthesized from 8-(2-carboxyethyl)-2,3-diethyl-7-methyl-(10H)-dipyrrin-1-one in one step by reaction with diselenyl dichloride. The selena-rubin exhibited UV-vis and NMR spectroscopic properties similar to those of the parent mesobilirubin, and like bilirubin and mesobilirubin, it adopts an intramolecularly hydrogen-bonded conformation, shaped like a ridge-tile but with a steeper pitch. The longer C–Se bond lengths (2.2Å) and smaller bond angles at C–Se–C (88°), as compared to C–CH2–C (1.5Å, 106°), lead to an interplanar angle between the two dipyrrinones of only 72°, which is considerably less than that of bilirubin (100°) and close to that (74°) of its 10-thia-rubin analog. Despite the conformational distortion, the sensitivity of Se toward oxidation and the typically weak C–Se bond, the selena-rubin is metabolized in normal rats, like bilirubin, to acyl glucuronides, which are secreted into bile. In mutant (Gunn) rats lacking bilirubin glucuronosyl transferase (UGT1A1), glucuronide or other metabolites of the selena-rubin were not detected in bile, demonstrating the importance of hepatic glucuronidation for its biliary excretion. 相似文献