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991.
Prof. Dr. Werner Raab 《Monatshefte für Mathematik》1984,98(4):311-322
The inequalities $$P_{k,l} = \frac{1}{{B(l + 1,k)}}\int\limits_0^{l/(k + l)} {x^l (1 - x)^{k - 1} dx = I_{l/(k + l)} (l + 1,k)< \frac{1}{2}}$$ and $$\Phi _{k,l,\mu } = \frac{1}{{B(k,k\mu + 1)}}\int\limits_0^1 {x^{k - 1} (1 - x)^{k\mu } I_x (l + 1,l\mu )dx< \frac{1}{2}}$$ are shown to be valid for any positive real numbersk, l, μ. 相似文献
992.
Zusammenfassung Ein neues Verfahren, das eine unmittelbare und kontinuierliche Registrierung des mechanischen Verlustwinkels über einen weiten
Temperaturbereich erm?glicht, wird beschrieben. Die Probe wird einer periodischen Biegung (f=2,5 Hz) unterworfen; die Zeit des Kraftnulldurchgangs relativ zur Bewegung ist dem Verlustwinkel proportional und wird elektronisch
ermittelt. Das Me\ergebnis ist weitgehend von der Probenform und deren ?nderung w?hrend der Messung (Krümmung der Probe, thermische
Ausdehnung usw). unabh?ngig.
Der Deutschen Forschungsgemeinschaft sei für die Unterstützung dieser Arbeit verbindlichst gedankt. 相似文献
993.
994.
Dr. Hans Peter Paukowitsch 《Monatshefte für Mathematik》1978,85(2):137-148
For such curves we know a moving frame and a complete system of invariants (affine curvatures) with respect to the group of volume-conserving transformations (unimodular group) of the order 2n?1 respectively 2n (see [1], p. 171). In this paper we study for a curvec a moving frame and a system of invariants of the minimal ordern+1, respectivelyn+2, by means of a curve with vanishing affine curvatures that has contact of maximal order withc. Forn=3 this is a result ofA. Winternitz ([1], p. 171 or [3], p. 86). 相似文献
995.
Prof. Dr. Ulrich Krengel 《Monatshefte für Mathematik》1978,86(1):3-6
Given any ergodic invertible measure preserving transformation τ of [0,1] and any null-sequence (α N ) of positive reals, there exists a continuousf such that $$\lim \sup \alpha _{\rm N}^{ - 1} \left| {N^{ - 1} \sum\limits_{k = 0}^{N - 1} {f \circ \tau ^k - \smallint f} } \right| = \infty a. e.,$$ i.e. there is no “speed of convergence” in the ergodic theorem for any τ. The analogous result holds also for norm-convergence. 相似文献
996.
Dr. Christoph Lübbert 《Journal of Geometry》1978,11(1):35-54
On a ruled closed surface in the elliptic 3-space two integral invariants are considered: the aperture distance of a curve orthogonal to the generating lines of , and the aperture angle of an orthogonally circumscribed tangent surfaces. By means of these integral invariants and by considering certain ruled surfaces associated to one finds the geometric meaning of further integral invariants. If is generated by the binormals of a curve one obtains some properties of closed curves in the elliptic 3-space. 相似文献
997.
Dr.-Ing. W. Ahrens Dr.-Ing. G. Dehnert H. J. Gerber 《Mathematical Methods of Operations Research》1978,22(1):B85-B103
Zusammenfassung Tourenprobleme bei der Hausmüllsammlung lassen sich in die Reihe der Lieferplanprobleme einordnen. Zur Lösung praktischer Größenordnungen werden hier einfache heuristische Verfahren (Prioritätsregeln) vorgestellt, weniger um der Vielzahl heuristischer Verfahren weitere hinzuzufügen als vielmehr dem Praktiker einen vielversprechenden Weg beim Lösen seiner Probleme aufzuzeigen.
Zusammenfassung dreier Vorträge im 4. planungstechnischen Seminar Tourenplanung bei der Abfallbeseitigung am Institut für Siedlungswasserwirtschaft der Universität Karlsruhe am 1.10.1976. 相似文献
Summary The discussed solid waste collection problem shows the properties of the so called truck dispatching problem. To solve problems for typical problem structure heuristic rules are pointed out in order to show the planner an efficient way of problem solving.
Zusammenfassung dreier Vorträge im 4. planungstechnischen Seminar Tourenplanung bei der Abfallbeseitigung am Institut für Siedlungswasserwirtschaft der Universität Karlsruhe am 1.10.1976. 相似文献
998.
Dr. Rudolf J. Taschner 《Monatshefte für Mathematik》1978,86(3):221-237
It is the aim of this paper to introduce two new notions of discrepancy. They are defined by the formulas $$\begin{gathered} \Delta _N^r \left( {\omega ;f} \right) = \mathop {\sup }\limits_{\left| z \right| = r} \left| {\left( {{1 \mathord{\left/ {\vphantom {1 N}} \right. \kern-\nulldelimiterspace} N}} \right)\sum\limits_{n = 1}^N {f\left( {z e^2 \pi i\omega \left( n \right)} \right)} - f\left( 0 \right)} \right|, and \hfill \\ \delta _N^r \left( {\omega ;f} \right) = \mathop {\sup }\limits_{\left| z \right| = r} \left| {\left( {{1 \mathord{\left/ {\vphantom {1 N}} \right. \kern-\nulldelimiterspace} N}} \right)\sum\limits_{n = 1}^N {f\left( {z \omega \left( n \right)} \right)} \cdot z - \int\limits_0^z {f\left( \zeta \right)d\zeta } } \right|, \hfill \\ \end{gathered} $$ wheref is a holomorphic function defined in the unit disc withf (k) (0)≠0 for allk∈?,r<1 is a positive number, and ω is a sequence in [0, 1]. The first of these discrepancies can be generalized for multidimensional sequences. ω is uniform distributed if and only if lim N→∞ Δ N r (ω;f)=0 resp. lim N→∞δ N r (ω;f)=0. These results are proved in a quantitative way by estimating the classical discrepancyD N (ω) by means ofΔ N r (ω;f) and δ N r (ω;f): $$\begin{gathered} \Delta _N^r \left( {\omega ;f} \right) \ll D_N \left( \omega \right) \ll \Phi \left( {\Delta _N^r \left( {\omega ;f} \right)} \right), \hfill \\ \delta _N^r \left( {\omega ;f} \right) \ll D_N \left( \omega \right) \ll \Psi \left( {\delta _N^r \left( {\omega ;f} \right)} \right). \hfill \\ \end{gathered} $$ The functions Φ and Ψ only depend onf andr. These estimations are based on the inequalities ofKoksma-Hlawka andErdös-Turán. 相似文献
999.
Ji-Lai Li Cai-Yun Geng Xu-Ri Huang Chia-Chung Sun 《Theoretical chemistry accounts》2007,117(3):417-429
The reaction of atomic radical F with propyne has been studied theoretically using ab initio quantum chemistry methods and
transition state theory. The potential energy surface was calculated at the CCSD(T)/aug-cc-pVDZ (single-point) level using
the UMP2/6-311++G(d,p) optimized structures. Two reaction mechanisms including the addition–isomerization–elimination reaction
mechanism and the directed hydrogen abstraction reaction mechanism are considered. For the hydrogen abstraction reactions,
i.e., the most probable evolution pathway in the title reaction, the HF formation occurs via direct abstraction mechanism
dominantly and the H atom picked up by the atomic radical F should come mostly from the methyl group of normal propyne. On
the other hand, for the addition–isomerization–elimination mechanism, the most feasible pathway should be the atomic radical
F attacking on the C≡C triple bond in propyne (CH3C≡CH) to form a weakly-bound adduct A1 with no barrier, followed by F addition to the C≡C triple bond to form the low-lying
intermediate isomer 5. Subsequently, isomer 5 directly dissociates to P3 H2CCCHF + H via transition state TS5/P3. The other reaction pathways on the doublet PES are less competitive due to thermodynamical or kinetic factors. Furthermore,
based on the analysis of the kinetics of all channels through which the addition and abstraction reaction proceed, we expect
that the competitive power of reaction channels may vary with experimental conditions for the title reaction. The present
work will provide useful information for understanding the processes of atomic radical F reaction with other unsaturated hydrocarbons.
This material is available from author via E-mail. 相似文献
1000.
Xiu-Kui Qu Lan-Ying Zhu Ling Li Xi-Lian Wei Feng Liu De-Zhi Sun 《Journal of solution chemistry》2007,36(5):643-650
As a continuation of our previous investigation, interactions between cyclodextrin (β-CD), γ-cyclodextrin (γ-CD) and alkyl trimethylammonium bromides in aqueous solutions have been studied with titration calorimetry and 1H NMR at 298.15 K. The results are discussed in terms of the amphiphilic interaction of CD with surfactants and the iceberg
structure formed by water molecules existing around the hydrophobic tail of surfactant molecules. The stoichiometry of the β-CD–surfactant system is 1:1 whereas that of the γ-CD–surfactant system is 1:2. The corresponding formation enthalpy (negative) of the complexes of the two systems decreases
with an increase in the number of carbon atoms (n) in hydrophobic chain of surfactant molecule, C
n
H2n+1, whereas the entropy increases with the enlargement of n. 相似文献