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151.
Music as Embodied Mathematics: A Study of a Mutually Informing Affinity   总被引:1,自引:0,他引:1  
The argument examined in this paper is that music – when approached through making and responding to coherent musical structures,facilitated by multiple, intuitively accessible representations – can become a learning context in which basic mathematical ideas can be elicited and perceived as relevant and important. Students' inquiry into the bases for their perceptions of musical coherence provides a path into the mathematics of ratio,proportion, fractions, and common multiples. Ina similar manner, we conjecture that other topics in mathematics – patterns of change,transformations and invariants – might also expose, illuminate and account for more general organizing structures in music. Drawing on experience with 11–12 year old students working in a software music/math environment, we illustrate the role of multiple representations, multi-media, and the use of multiple sensory modalities in eliciting and developing students' initially implicit knowledge of music and its inherent mathematics. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   
152.
We investigate the six-dimensional Schrödinger equation for a three-body system with central pair interactions of a more general form than Coulomb interactions. Regular general and special physical solutions of this equation are represented by infinite asymptotic series in integer powers of the distance between two particles and in the sought functions of the other three-body coordinates. Constructing such functions in angular bases composed of spherical and bispherical harmonics or symmetrized Wigner D-functions is reduced to solving simple recursive algebraic equations. For projections of physical solutions on the angular bases functions, we derive boundary conditions at the pair impact point.  相似文献   
153.
Suppose that the signal X to be estimated is a diffusion process in a random medium W and the signal is correlated with the observation noise. We study the historical filtering problem concerned with estimating the signal path up until the current time based upon the back observations. Using Dirichlet form theory, we introduce a filtering model for general rough signal X W and establish a multiple Wiener integrals representation for the unnormalized pathspace filtering process. Then, we construct a precise nonlinear filtering model for the process X itself and give the corresponding Wiener chaos decomposition.  相似文献   
154.
For an integer n3 and any positive number , we establish the existence of smooth functions K on n {0} with |K–1|, such that the equation has a smooth positive solution which blows up at the origin (i.e., u does not have slow decay near the origin). Furthermore, we show that in some situations K can be extended as a Lipschitz function on n . These provide counter-examples to a conjecture of C.-S. Lin when n>4, and a question of Taliaferro. Mathematics Subject Classification (2000)Primary 35J60; Secondary 53C21  相似文献   
155.
Filippov  V. V. 《Mathematical Notes》2003,73(5-6):859-870
In this paper, we continue extending the theory of boundary-value problems to ordinary differential equations and inclusions with discontinuous right-hand side. To this end, we construct a new version of the method of shifts along trajectories. We compare the results obtained by the new approach and those obtained by the method of Fuik spectra.  相似文献   
156.
Convergence dynamics of Hopfield-type neural networks subjected to almost periodic external stimuli are investigated. In this article, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures. By employing Halanay inequalities, we obtain delay independent sufficient conditions for the networks to converge exponentially toward encoded patterns associated with the external stimuli. The networks are guaranteed to have exponentially hetero-associative stable encoding of the external stimuli.  相似文献   
157.
Gorbunov  K. Yu. 《Mathematical Notes》2003,74(3-4):483-490
A generalization of the Hilbert basis theorem in the geometric setting is proposed. It asserts that, for any well-describable (in a certain sense) family of polynomials, there exists a number C such that if P is an everywhere dense (in a certain sense) subfamily of this family, a is an arbitrary point, and the first C polynomials in any sequence from P vanish at the point a, then all polynomials from P vanish at a.  相似文献   
158.
使用变系数的广义Ricatti方程映射法,对(2+1)维Broer-Kaup—Kupershmidt方程进行了研究,得到了包括Weierstrass函数解、孤立子解、似孤立子解和三角函数解等.由于解的表达式中存在2个或3个任意函数,因此解中存在丰富的结构.  相似文献   
159.
Lp(Rm × Rn) boundedness is considered for the multiple Marcinkiewicz integral. Some size conditions implying the Lp(Rm × Rn) boundedness of the multiple Marcinkiewicz integral for some fixed 1 > p > ∞ are obtained.  相似文献   
160.
In the context of the weak solutions of the Navier-Stokes equations we study the regularity of the pressure and its derivatives in the space-time neighbourhood of regular points. We present some global and local conditions under which the regularity is further improved.  相似文献   
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