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1.
2.
We treat here of the question of absorbing boundary conditionsfor nonlinear diffusion equations. We use the conditions designedfor the linear equation, we prove them to be well posed forthe nonlinear problem, and through numerical experiments thatthey are well suited for reactiondiffusion equations. 相似文献
3.
Giovanni Cupini Marcello Guidorzi Cristina Marcelli 《Journal of Differential Equations》2007,243(2):329-348
Classical one-dimensional, autonomous Lagrange problems are considered. In absence of any smoothness, convexity or coercivity condition on the energy density, we prove a DuBois-Reymond type necessary condition, expressed as a differential inclusion involving the subdifferential of convex analysis. As a consequence, a non-existence result is obtained. 相似文献
4.
In this note we make a correction in the paper [1] by two of the authors. Specifically we modify an auxiliary localization
result and prove that the applications to the saturation theory of some outstanding conservative operators remain valid. Moreover,
we enrich a corollary dealing with the well-known Szász-Mirakjan operators.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
Alexander J. Zaslavski 《Journal of Mathematical Analysis and Applications》2007,335(2):962-973
The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions. In this paper we consider a large class of optimal control problems which is identified with a complete metric space of integrands without convexity assumptions and show that for a generic integrand the corresponding optimal control problem possesses a unique solution and this solution is Lipschitzian. 相似文献
6.
7.
High quality factor of dynamic structures at micro and nano scale is exploited in various applications of micro electro-mechanical
systems (MEMS) and nano electro-mechanical system. The quality factor of such devices can be very high in vacuum. However,
when vacuum is not desirable or not possible, the tiny structures must vibrate in air or some other gas at pressure levels
that may vary from atmospheric to low vacuum. The interaction of the surrounding fluid with the vibrating structure leads
to dissipation, thus bringing down the quality factor. Depending on the ambient fluid pressure or the gap between the vibrating
and the fixed structure, the fluid motion can range from continuum flow to molecular flow giving a wide range of dissipation.
The relevant fluid flow characteristics are determined by the Knudsen number which is the ratio of the mean free path of the
gas molecule to the characteristic flow length of the device. This number is very small for continuum flow and reasonably
big for molecular flow. In this paper, we study the effect of fluid pressure on the quality factor by carrying out experiments
on a MEMS device that consists of a double gimbaled torsional resonator. Such devices are commonly used in optical cross-connects
and switches. We only vary fluid pressure to make the Knudsen number go through the entire range of continuum flow, slip flow,
transition flow, and molecular flow. We experimentally determine the quality factor of the torsional resonator at different
air pressures ranging from 760 Torr to 0.001 Torr. The variation of this pressure over six orders of magnitude ensures required
rarefaction to range over all flow conditions. Finally, we get the variation of quality factor with pressure. The result indicates
that the quality factor, Q, follows a power law, Q ∝P
–r
, with different values of the exponent r in different flow regimes. In the second part of the paper, we propose the use of effective viscosity for considering velocity
slip conditions in solving Navier–Stokes equation numerically. This concept is validated with analytical results for a simple
case and then compared with the experimental results presented in this paper. The study shows that the effective viscosity
concept can be used effectively even for the molecular regime if the air-gap to length ratio is sufficiently small (h
0/L<0.01). As this ratio increases, the range of validity decreases. 相似文献
8.
We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game (Section 1 and Appendix). Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game (which is two-dimensional but without labels), by a simple and natural interpretation (Section 2). Jervell proposed another type of a combinatorial game, by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show (Section 3) that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φω (0) (while that of PA or of Kirby-Paris' Game is φ1 (0) = ?0) in the Veblen hierarchy of ordinals. 相似文献
9.
WU Xiu-Lan WANG Fen REN Qiang 《结构化学》2007,26(6):732-736
Homogeneous cordierite has been synthesized at low cost by talc-magnesite and coal gangue as the main raw materials. The mechanism of synthesizing cordierite under such a com- posing system of raw materials, and the effect of temperature on the crystal cell parameters and microstructure and thermal expansion coefficient of cordierite crystal have been studied via testing methods of XRD, SEM, etc. The result shows that the homogeneous cordierite can be synthesized by the systematic composing materials of “talc-magnesite—coal gangue—talc” with heat pre- servation at 1350 ℃ for 1 h; as the keeping time is prolonged, Al3+ and Mg2+ in cordierite crystal are replaced by a few impurity ions such as Fe3+, Fe2+, etc., and the crystal cell parameters of cordierite present an increase trend; as the high-temperature heat preservation is prolonged, the content of glassy phase in the sample is increased, its density is improved, and its thermal expansion coeffi- cient presents an increase trend. 相似文献
10.
A novel coordination polymer [{Cd(hmbdc)(H2O)3}·2H2O]n (hmbdc=5-hydroxy- isophthalic acid) has been synthesized and characterized by elemental analysis, IR spectra and single-crystal X-ray diffraction. The crystal belongs to monoclinic, space group P21/c, with a=9.599(3), b=18.699(5), c=7.557(2) (A), β= 108.198(4)°, V=1288.6(6) (A)3, Z=4, Mr=382.60, Dc=1.972 g/cm3, F(000)=760, μ=1.740, the final R=0.0555 and wR=0.0995 for 1732 observed reflections with Ⅰ > 2σ(Ⅰ). The structural analysis shows that the intermolecular hydrogen bonds and π-π interactions result in a three-dimensional supramolecular framework. 相似文献