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71.
Two main existence conditions for solutions of variational relation problems are established without convexity. The first one is based on a finite solvability property and the second one on generalized KKM mappings. These conditions unify and strengthen several existing results in the literature on the topic. A model of satisficing process by rejection is considered which gives an economic interpretation of the introduced concepts. 相似文献
72.
We developed a novel microfluidic cell culture device in which magnetic beads repetitively collide with osteoblast cells, MC3T3‐E1, owing to attractive forces generated by pulsed electromagnetic fields and consequently the cells were physically stimulated by bead impacts. Our device consists of an on‐chip microelectromagnet and a microfluidic channel which were fabricated by a microelectromechanical system technique. The impact forces and stresses acting on a cell were numerically analyzed and experimentally generated with different sizes of bead (4.5, 7.6 and 8.4 μm) and at various pulse frequencies (60 Hz, 1 kHz and 1 MHz). Cells were synchronized at each specific phase of the cell cycle before stimulation in order to determine the most susceptible phase against bead impacts. The cells were stimulated with different sizes of bead at various pulse frequencies for 1 min at G1, S and G2 phases, respectively, and then counted immediately after one doubling time. The growth rate of cells was highly accelerated when they were stimulated with 4.5 μm beads at G1 phase and a pulse frequency of 1 MHz. Almost all of the cells were viable after stimulation, indicating that our cell stimulator did not cause any cellular damage and is suitable for use in new physical stimulus modalities. 相似文献
73.
Jan Andres Tom Fürst Karel Pastor 《Journal of Mathematical Analysis and Applications》2008,340(2):1132-1144
A full analogy of the celebrated Sharkovsky cycle coexistence theorem is established for lower semicontinuous (multivalued) maps on metrizable linear continua. This result is further extended to triangular maps. 相似文献
74.
Kazutoshi Maegawa 《Proceedings of the American Mathematical Society》2008,136(8):2875-2879
For a dominant algebraically stable rational self-map of the complex projective plane of degree at least 2, we will consider three different definitions of the Fatou set and show the equivalence of them (Ascoli-Arzelà type theorem). As a corollary, it follows that all Fatou components are Stein. This is an improvement of an early result by Fornæss and Sibony.
75.
The expansion coefficient CD|L| of Coulomb potential 1/r12 of atomic system in hyper‐spherical harmonics is derived and the explicit expression is given. 相似文献
76.
Parrondo’s paradox [J.M.R. Parrondo, G.P. Harmer, D. Abbott, New paradoxical games based on Brownian ratchets, Phys. Rev. Lett. 85 (2000), 5226–5229] (see also [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68–72]) states that two losing gambling games when combined one after the other (either deterministically or randomly) can result in a winning game: that is, a losing game followed by a losing game = a winning game. Inspired by this paradox, a recent study [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] asked an analogous question in discrete time dynamical system: can two chaotic systems give rise to order, namely can they be combined into another dynamical system which does not behave chaotically? Numerical evidence is provided in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] that two chaotic quadratic maps, when composed with each other, create a new dynamical system which has a stable period orbit. The question of what happens in the case of random composition of maps is posed in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124–132] but left unanswered. In this note we present an example of a dynamical system where, at each iteration, a map is chosen in a probabilistic manner from a collection of chaotic maps. The resulting random map is proved to have an infinite absolutely continuous invariant measure (acim) with spikes at two points. From this we show that the dynamics behaves in a nearly ordered manner. When the foregoing maps are applied one after the other, deterministically as in [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68–72], the resulting composed map has a periodic orbit which is stable. 相似文献
77.
We study a version of Whitney’s embedding problem in projective geometry: What is the smallest dimension of an affine space that can contain an n-dimensional submanifold without any pairs of parallel or intersecting tangent lines at distinct points? This problem is related to the generalized vector field problem, existence of non-singular bilinear maps, and the immersion problem for real projective spaces. We use these connections and other methods to obtain several specific and general bounds for the desired dimension. 相似文献
78.
79.
S. Kumar 《Acta Mathematica Hungarica》2008,118(1-2):9-28
We prove expansion mappings theorems in various spaces i.e., metric spaces, generalized metric spaces, probabilistic metric
spaces and fuzzy metric spaces, which generalize the results of various authors like Daffer and Kaneko [11], Ahmad, Ashraf
and Rhoades [1], Vasuki [38], Rhoades [31] and Wang, Li, Gao and Iseki [40] etc.
In the memory of 65th birthday anniversary of his Father Late Sh. Ram Phool Sharma 相似文献
80.
Armen Glebovich Sergeev 《中国科学A辑(英文版)》2008,51(4):695-706
We study harmonic maps from Riemann surfaces M to the loop spaces ΩG of compact Lie groups G, using the twistor approach. We conjecture that harmonic maps of the Riemann sphere ℂℙ1 into ΩG are related to Yang-Mills G-fields on ℝ4.
This work was partly supported by the RFBR (Grant Nos. 04-01-00236, 06-02-04012), by the program of Support of Scientific
Schools (Grant No. 1542.2003.1), and by the Scientific Program of RAS “Nonlinear Dynamics” 相似文献