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111.
Our work is a foundational study of the notion of approximation in Q-categories and in (U,Q)-categories, for a quantale Q and the ultrafilter monad U. We introduce auxiliary, approximating and Scott-continuous distributors, the way-below distributor, and continuity of Q- and (U,Q)-categories. We fully characterize continuous Q-categories (resp. (U,Q)-categories) among all cocomplete Q-categories (resp. (U,Q)-categories) in the same ways as continuous domains are characterized among all dcpos. By varying the choice of the quantale Q and the notion of ideals, and by further allowing the ultrafilter monad to act on the quantale, we obtain a flexible theory of continuity that applies to partial orders and to metric and topological spaces. We demonstrate on examples that our theory unifies some major approaches to quantitative domain theory. 相似文献
112.
In this paper we investigate the efficiency of the Orthogonal Matching Pursuit algorithm (OMP) for random dictionaries. We
concentrate on dictionaries satisfying the Restricted Isometry Property. We also introduce a stronger Homogenous Restricted
Isometry Property which we show is satisfied with overwhelming probability for random dictionaries used in compressed sensing.
For these dictionaries we obtain upper estimates for the error of approximation by OMP in terms of the error of the best n-term
approximation (Lebesgue-type inequalities). We also present and discuss some open problems about OMP. This is a development
of recent results obtained by D.L. Donoho, M. Elad and V.N. Temlyakov. 相似文献
113.
Pawe? Pra?at 《Graphs and Combinatorics》2011,27(4):567-584
A model for cleaning a graph with brushes was recently introduced. Let α = (v
1, v
2, . . . , v
n
) be a permutation of the vertices of G; for each vertex v
i
let ${N^+(v_i)=\{j: v_j v_i \in E {\rm and} j>\,i\}}${N^+(v_i)=\{j: v_j v_i \in E {\rm and} j>\,i\}} and N-(vi)={j: vj vi ? E and j < i}{N^-(v_i)=\{j: v_j v_i \in E {\rm and} j<\,i\}} ; finally let ba(G)=?i=1n max{|N+(vi)|-|N-(vi)|,0}{b_{\alpha}(G)=\sum_{i=1}^n {\rm max}\{|N^+(v_i)|-|N^-(v_i)|,0\}}. The Broom number is given by B(G) = max
α
b
α
(G). We consider the Broom number of d-regular graphs, focusing on the asymptotic number for random d-regular graphs. Various lower and upper bounds are proposed. To get an asymptotically almost sure lower bound we use a degree-greedy
algorithm to clean a random d-regular graph on n vertices (with dn even) and analyze it using the differential equations method (for fixed d). We further show that for any d-regular graph on n vertices there is a cleaning sequence such at least n(d + 1)/4 brushes are needed to clean a graph using this sequence. For an asymptotically almost sure upper bound, the pairing
model is used to show that at most n(d+2?{d ln2})/4{n(d+2\sqrt{d \ln 2})/4} brushes can be used when a random d-regular graph is cleaned. This implies that for fixed large d, the Broom number of a random d-regular graph on n vertices is asymptotically almost surely
\fracn4(d+Q(?d)){\frac{n}{4}(d+\Theta(\sqrt{d}))}. 相似文献
114.
The main goal of present paper is to demonstrate the separation and detection capability of micro-TLC technique involving simple one step liquid extraction protocols of complex materials without multi-steps sample pre-purification. In the present studies target components (cyanobacteria pigments, lipids and fullerenes) were isolated from heavy loading complex matrices including spirulina dried cells, birds’ feathers and fatty oils as well as soot samples derived from biomass fuel and fossils-fired home heating systems. In each case isocratic separation protocol involving less that 1 mL of one component or binary mixture mobile phases can be completed within time of 5–8 min. Sensitive detection of components of interest was performed via fluorescence or staining techniques using iodine or phosphomolybdic acid. Described methodology can be applied for fast fractionation or screening of whole range of target substances as well as chemo-taxonomic studies and fingerprinting of complex mixtures, which are present in raw biological or environmental samples. 相似文献
115.
The Fukui functions based on the computable local polarizability vector have been presented for a group of simple molecules. The necessary approximation for the density functional theory softness kernel has been supported by a theoretical analysis unifying and generalizing early concepts produced by the several authors. The exact relation between local polarizability vector and the derivative of the nonlocal part of the electronic potential over the electric field has been demonstrated. The resulting Fukui functions are unique and represent a reasonable refinement when compared to the classical ones that are calculated as the finite difference of the density in molecular ions. The new Fukui functions are strongly validated by their direct link to electron dipole polarizabilities that are reported experimentally and by other computational methods. 相似文献
116.
Ohta K Yamada S Kamada K Slepkov AD Hegmann FA Tykwinski RR Shirtcliff LD Haley MM Sałek P Gel'mukhanov F Ågren H 《The journal of physical chemistry. A》2011,115(2):105-117
The two-photon absorption (TPA) properties of four TPEB [tetrakis(phenylethynyl)benzene] derivatives (TD, para, ortho, and meta) with different donor/acceptor substitution patterns have been investigated experimentally by the femtosecond open-aperture Z-scan method and theoretically by the time-dependent density-functional theory (TDDFT) method. The four compounds show relatively large TPA cross sections, and the all-donor substituted species (TD) displays the largest TPA cross-section σ(2) = 520 ± 30 GM. On the basis of the calculated electronic structure, TD shows no TPA band in the lower energy region of the spectrum because the transition density is concentrated on particular transitions due to the high symmetry of the molecular structure. The centrosymmetric donor-acceptor TPEB para shows excitations resulting from transitions centered on D-π-D and A-π-A moieties, as well as transition between the D-π-D and A-π-A moieties; this accounts for the broad nature of the TPA bands for this compound. Calculations for two noncentrosymmetric TPEBs (ortho and meta) reveal that the diminished TPA intensities of higher-energy bands result from destructive interference between the dipolar and three-state terms. The molecular orbitals (MOs) of the TPEBs are derivable with linear combinations of the MOs of the two crossing BPEB [bis(phenylethynyl)benzene] derivatives. Overall, the characteristics of the experimental spectra are well-described based on the theoretical analysis. 相似文献
117.
Jaros?aw A. Pytka Piotr Tarkowski Stefan Fija?kowski Piotr Budzyński Jaros?aw D?browski W?odzimierz Kupicz Pawe? Pytka 《Journal of Terramechanics》2011,48(5):384-395
The paper presents an instrumented vehicle that was equipped with measuring systems to perform complete dynamics tests, especially in off-road conditions. The equipment consists of four wheel dynamometers, a steering robot, and a differential GPS system together with an inertial platform, a non-contact vehicle speed sensor, and an on-board computer with software to control the devices and collect experimental data. The four wheel dynamometers measure six elements; based on strain gage force transducers, it measures three orthogonal forces and three moments. The steering robot can control the steering wheel of the vehicle at a variety of excitation modes; it can carry out typical vehicle dynamics tests (ISO 7401, ISO 4138, ISO/TR3888, etc.) as well as custom engineered tests at a wide range of setting parameters (steer angle rate up to 1600 deg/s). The differential GPS system gives true time vehicle kinematics data (velocities, accelerations, angles, etc.) at 10-ns sample rate and 20-mm accuracy. The base vehicle, a Suzuki Vitara 4 × 4, required no special modifications or changes to install the measuring equipment. The paper also describes typical tests performed with the use of the instrumented vehicle together with sample results. 相似文献
118.
We develop the concept of integral Menger curvature for a large class of nonsmooth surfaces. We prove uniform Ahlfors regularity and a C1,λ-a priori bound for surfaces for which this functional is finite. In fact, it turns out that there is an explicit length scale R>0 which depends only on an upper bound E for the integral Menger curvature Mp(Σ) and the integrability exponent p, and not on the surface Σ itself; below that scale, each surface with energy smaller than E looks like a nearly flat disc with the amount of bending controlled by the (local) Mp-energy. Moreover, integral Menger curvature can be defined a priori for surfaces with self-intersections or branch points; we prove that a posteriori all such singularities are excluded for surfaces with finite integral Menger curvature. By means of slicing and iterative arguments we bootstrap the Hölder exponent λ up to the optimal one, λ=1−(8/p), thus establishing a new geometric ‘Morrey–Sobolev’ imbedding theorem.As two of the various possible variational applications we prove the existence of surfaces in given isotopy classes minimizing integral Menger curvature with a uniform bound on area, and of area minimizing surfaces subjected to a uniform bound on integral Menger curvature. 相似文献
119.
Cui Yunan Hudzik Henryk Kaczmarek Radosław Kolwicz Paweł 《Aequationes Mathematicae》2019,93(1):311-343
Aequationes mathematicae - The paper deals with F-normed functions and sequence spaces. First, some general results on such spaces are presented. But most of the results in this paper concern... 相似文献
120.