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991.
We introduce the fuzzy supersphere as sequence of finite-dimensional, noncommutative
2-graded algebras tending in a suitable limit to a dense subalgebra of the
2-graded algebra of
∞-functions on the (2|2)-dimensional supersphere. Noncommutative analogues of the body map (to the (fuzzy) sphere) and the super-deRham complex are introduced. In particular we reproduce the equality of the super-deRham cohomology of the supersphere and the ordinary deRham cohomology of its body on the “fuzzy level”. 相似文献
992.
Myron W. Evans 《Foundations of Physics Letters》2004,17(1):25-47
The first and second Maurer-Cartan structure relations are combined with the Evans field equation [1] for differential forms to build a grand unified field theory based on differential geometry. The tetrad or vielbein plays a central role in this theory, and all four fields currently thought to exist in nature can be described by the same equations, the tangent space index of the tetrad in general relativity being identified with the tetrad's internal (gauge group) index guage theory. 相似文献
993.
Mathemstics is used to study the nature. Straight lines, circles, ellipses,continuous and differentiable curves and surfaces etc. are the first approximations of forms of concrete objects. But in reality, these forms are very irregular. Consequentily B. Mandebrot introduces since 1975 fractals and the fractal geometry to study the second approximaions of such forms. Si 相似文献
994.
N. J. Wildberger 《Geometriae Dedicata》2007,128(1):145-166
One dimensional metrical geometry may be developed in either an affine or projective setting over a general field using only
algebraic ideas and quadratic forms. Some basic results of universal geometry are already present in this situation, such
as the Triple quad formula, the Triple spread formula and the Spread polynomials, which are universal analogs of the Chebyshev
polynomials of the first kind. Chromogeometry appears here, and the related metrical and algebraic properties of the projective
line are brought to the fore.
相似文献
995.
基于多项式组主项解耦消元法 ,将几何定理的假设条件 (多项式组 PS)化为主项只含主变元的三角型多项式组 DTS,可得到定理命题成立的不含变元的非退化条件 ,即充分必要或更接近充分必要的非退化条件 .由于多项式主系数不含变元 ,已不存在 DTS多项式之间的约化问题 ,故方法有普遍意义 .文中例为西姆松定理的机器证明 . 相似文献
996.
In this paper an ultraspherical integral method is proposed to solve optimal control problems governed by ordinary differential equations. Ultraspherical approximation method reduced the problem to a constrained optimization problem. Penalty leap frog method is presented to solve the resulting constrained optimization problem. Error estimates for the ultraspherical approximations are derived and a technique that gives an optimal approximation of the problems is introduced. Numerical results are included to confirm the efficiency and accuracy of the method. 相似文献
997.
G. E. Schröder-Turk A. Fogden S. T. Hyde 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,54(4):509-524
Balanced infinite periodic minimal surface families that contain the cubic Gyroid (G), Diamond (D) and Primitive (P) surfaces
are studied in terms of their global packing and local curvature properties. These properties are central to understanding
the formation of mesophases in amphiphile and copolymer molecular systems. The surfaces investigated are the tetragonal, rhombohedral
and hexagonal tD, tP, tG, rG, rPD and H surfaces. These non-cubic minimal surfaces furnish topology-preserving transformation
pathways between the three cubic surfaces. We introduce `packing (or global) homogeneity', defined as the standard deviation
Δd of the distribution of the channel diameter throughout the labyrinth, where the channel diameter d is determined from the
medial surface skeleton centered within the labyrinthine domains. Curvature homogeneity is defined similarly as the standard
deviation ΔK of the distribution of Gaussian curvature. All data are presented for distinct length normalisations: constant
surface-to-volume ratio, constant average Gaussian curvature and constant average channel diameter. We provide first and second
moments of the distribution of channel diameter for all members of these surfaces complementing curvature data from [A. Fogden,
S. Hyde, Eur. Phys. J. B 7, 91 (1999)]. The cubic G and D surfaces are deep local minima of Δd along the surface families (with G more homogeneous than
D), whereas the cubic P surface is an inflection point of Δd with adjacent, more homogeneous surface members. Both curvature
and packing homogeneity favour the tetragonal route between G and D (via tG and tD surfaces) in preference to the rhombohedral
route (via rG and rPD). 相似文献
998.
A. V. Marshakov 《Theoretical and Mathematical Physics》2006,147(2):583-636
We consider the simplest gauge theories given by one-and two-matrix integrals and concentrate on their stringy and geometric
properties. We recall the general integrable structure behind the matrix integrals and turn to the geometric properties of
planar matrix models, demonstrating that they are universally described in terms of integrable systems directly related to
the theory of complex curves. We study the main ingredients of this geometric picture, suggesting that it can be generalized
beyond one complex dimension, and formulate them in terms of semiclassical integrable systems solved by constructing tau functions
or prepotentials. We discuss the complex curves and tau functions of one-and two-matrix models in detail.
[This article was written at the request of the Editorial Board. It is based on several lectures presented at schools of mathematical
physics and talks at the conference “Complex Geometry and String Theory” and the Polivanov memorial seminar.]
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 163–228, May, 2006. 相似文献
999.
We investigate a special type of singularity in non-smooth solutions
of first-order partial differential equations, with emphasis on
Isaacs’ equation. This type, called focal manifold, is
characterized by the incoming trajectory fields on the two sides and a
discontinuous gradient. We provide a complete set of constructive
equations under various hypotheses on the singularity, culminating
with the case where no a priori hypothesis on its geometry is known,
and where the extremal trajectory fields need not be collinear. We
show two examples of differential games exhibiting non-collinear
fields of extremal trajectories on the focal manifold, one with a
transversal approach and one with a tangential approach. 相似文献
1000.
S BugaV Blank Å FranssonN Serebryanaya B Sundqvist 《Journal of Physics and Chemistry of Solids》2002,63(2):331-343
C60 and C70 fullerenes polymerized under pressures between 9.5 and 13 GPa and temperatures between 670 and 1850 K were investigated by differential scanning calorimetry (DSC) in the range 240-640 K. Endothermal heat effects were observed with a peak maximum just below 540 K, a temperature characteristic for breakdown of (2+2) intermolecular links in dimers, 1D and 2D polymers. Exothermal effects, starting from 380 K, were observed for the first time in polymeric fullerenes. These effects are attributed to relaxation processes and to breakdown of other types of intermolecular bonds such as common four-sided rings and (3+3) interlinks. 相似文献