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31.
Dassios George; Giapalaki Sofia N.; Kandili Anastasia N.; Kariotou Fotini 《The Quarterly Journal of Mechanics and Applied Mathematics》2007,60(1):1-25
The magnetic induction field in the exterior of an ellipsoidallyinhomogeneous, four-conducting-layer model of the human headis obtained analytically up to its quadrupole approximation.The interior ellipsoidal core represents the homogeneous brainwhile each one of the shells represents the cerebrospinal fluid,the skull and the scalp, all characterized by different conductivities.The inhomogeneities of these four domains, together with theanisotropy imposed by the use of the ellipsoidal geometry, providethe most realistic physical and geometrical model of the brainfor which an analytic solution of the biomagnetic forward problemis possible. It is shown that in contrast to the spherical model,where shells of different conductivity are magnetically invisible,the magnetic induction field in ellipsoidal geometry is stronglydependent on the conductivity supports. The fact that sphericalshells of different conductivity are invisible has enhancedthe common belief that the biomagnetic forward solution doesnot depend on the conductivity profiles. As we demonstrate inthe present work, this is not true. Hence, the proposed multilayeredellipsoidal model provides a qualitative improvement of therealistic interpretation of magnetoencephalography (MEG) measurements.We show that the presence of the shells of different conductivitycan be incorporated in the form of the dipole vector for thehomogeneous model. Numerical investigations show that the effectsof shell inhomogeneities are almost as sound as the level ofMEG measurements themselves. The degenerate cases, where eitherthe differences of the conductivities within the shells disappear,or the ellipsoidal geometry is reduced to the spherical one,are also considered. 相似文献
32.
George N. Facas 《International Journal of Heat and Fluid Flow》1995,16(6):519-526
Numerical solutions are presented for the natural convection heat transfer from an elliptic heat source buried beneath a semi-infinite, saturated, porous medium. The surface of the medium is assumed to be permeable. The governing equations for Darcy flow are solved using finite differences. The complicated geometry is handled through the use of a body-fitted curvilinear coordinate system. Results are presented for Ra values ranging from 10 to 200 and ellipse aspect ratio values from 1.0 (circular cylinder) to 0.167. Two body orientations have been considered. The slender orientation yields much higher hear transfer rates (especially at low ellipse aspect ratio values) than the blunt orientation. The numerical simulations indicate that the boundary-layer approximations cannot be employed for low ellipse aspect ratios. In addition, the heat loss does not depend on the burial depth. 相似文献
33.
34.
Robert Carroll George Delic R. P. Gilbert 《Mathematical Methods in the Applied Sciences》1989,11(1):43-63
It is shown how Newton–Sabatier methods (arising in inverse scattering at fixed energy) can be related to spectral measures and typically when they correspond to regular potentials. A number of spectral formulae for various transmutation kernels are also given in terms of general Kontorovi?–Lebedev theory and connections to generating functions, generalized orthogonal polynomials, etc. are indicated. 相似文献
35.
We study the approximability of minimum total weighted tardiness with a modified objective which includes an additive constant. This ensures the existence of a positive lower bound for the minimum value. Moreover the new objective has a natural interpretation in just-in-time production systems. 相似文献
36.
An optimization approach for planning daily drayage operations 总被引:1,自引:0,他引:1
Yetkin Ileri Mokhtar Bazaraa Ted Gifford George Nemhauser Joel Sokol Erick Wikum 《Central European Journal of Operations Research》2006,14(2):141-156
Daily drayage operations involve moving loaded or empty equipment between customer locations and rail ramps. Our goal is to
minimize the cost of daily drayage operations in a region on a given day. Drayage orders are generally pickup and delivery
requests with time windows. The repositioning of empty equipment may also be required in order to facilitate loaded movements.
The drayage orders are satisfied by a heterogeneous fleet of drivers. Driver routes must satisfy various operational constraints.
We present an optimization methodology for finding cost-effective schedules for regional daily drayage operations. The core
of the formulation is a set partitioning model whose columns represent routes. Routes are added to the formulation by column
generation. We present numerical results for real-world data which demonstrate that our methodology produces low cost solutions
in a reasonably short time. 相似文献
37.
Adel A. George Michael 《Arkiv f?r Matematik》2006,44(1):92-96
In this paper, we generalize a theorem of Kallman [2, Theorem 1.1] and we resolve the unsettled case there. 相似文献
38.
39.
Scott P. Lewis Cengiz Alacaci George E. O'Brien Zhonghong Jiang 《School science and mathematics》2002,102(4):172-180
The use of a project‐based science (PBS) approach to teaching encourages students to integrate mathematics and science in meaningful ways as they create projects. As a beginning study of how students use mathematics in such an approach, an analysis of 23 projects developed by preservice elementary teachers enrolled in an elementary science course was conducted. Findings showed that students made a number of different types of mathematical errors and underutilized data representation and summary forms. Implications included the importance of developing methods for supporting the use of mathematical tools in utilizing a project‐based approach and considering ways that such tools mediate scientific thinking. 相似文献
40.