查询词典 resolution of singularities

Fenton has given particular attention to the treatment of singularities in the governing integral equation involving the symmetric Green's function — a feature apparently not accounted for by Black — and he reduces the relevant line integral equations to forms possessing series which are rapidly convergent.

Fenton 已经把特别的注意给奇异的治疗在那统治包括对称的格林的功能的整体的相等-一个特征显然地不根据黑色解释-而且他让有关的线整体相等变成持有快速趋集于一点的系列的表格。

The earth is modeled as an oblate and rotating spheroid, and higher order terms in the multiple expansion of gravitational fields are considered. To avoid singularities in computations, the quaternion representation of the spacecraft attitude is used in the angular kinetic model equations.

其中地球被描述为绕短轴自转的椭球体，重力场梯度由四阶Jeffery常数描述，航天飞机的姿态运动用四元素法描述，以避免模型方程中的数值奇异点。

Note the periodicity in t and the singularities at .

注意t 中的周期性以及处的奇异性。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

While still a graduate student, he and Mathematician Roger Penrose developed new techniques proving mathematically that if general relativity is correct, singularities must exist.

当还是一个研究生时，他和数学家罗格·培恩罗慈发展了新的技术来精确地证明，如果普遍相对论是正确的，非凡现象肯定存在。

Working with mathematician roger penrose and using einstein's relativity equations, he developed new techniques to prove mathematically that at the heart of black/holes were singularities—infinitely dense, dimensionless points with irresistible gravity.

他同数学家罗杰·潘罗斯合作，运用爱因斯坦的相对论等式找到了新的计算方法来证明：在黑洞的中心是一堆密密麻麻的、无边无际的、具有巨大引力的奇异小点。

Work ing with mathematician Roger Penrose and us ing Einstein's relativity equations, he developed new techniques to prove mathematically that at the heart of black/holes were singularities-infinitely dense, dimensionless points with irresistible gravity.

他同数学家罗杰。潘罗斯合作，运用爱因斯坦的相对论等式找到了新的计算方法来证明：在黑洞的中心是一堆密密麻麻的、无边无际的、具有巨大引力的奇异小点。

Working with mathematician Roger Penrose and using Einsteins relativity equations, he developed new techniques to prove mathematically that at the heart of black/holes were singularities—infinitely dense, dimensionless points with irresistible gravity.

他同数学家罗杰·潘罗斯合作，运用爱因斯坦的相对论等式找到了新的计算方法来证明：在黑洞的中心是一堆密密麻麻的、无边无际的、具有巨大引力的奇异小点。

Working with mathematician Roger Penrose using Einstein's relativity equations, he developed new techniques to prove mathematically that at the heart of black/holes were singularities—infinitely dense, dimensionless points with irresistible gravity.

他同数学家罗杰·潘罗斯合作，运用爱因斯坦的相对 www.8t t t8.com 论等式找到了新的计算方法来证明：在黑洞的中心是一堆密密麻麻的、无边无际的、具有巨大引力的奇异小点。

Working wit h mat h ematician Roger Penrose and using Einstein's relativity equations, h e developed new tec h niques to prove mat h ematically t h at at t h e h eart of black/ h oles were singularities—infinitely dense, dimensionless points wit h irresistible gravity.

他同数学家罗杰·潘罗斯合作，运用爱因斯坦的相对论等式找到了新的计算方法来证明：在黑洞的中心是一堆密密麻麻的、无边无际的、具有巨大引力的奇异小点。

His female bullfighter Lydia gradually Health love, but she was in a vegetative state after the Bulls Zhuangcheng away from her, just because Lydia's ex-boyfriend showed more affectionate than he is like love.

他对女斗牛士莉迪亚渐生爱意，却在她被公牛撞成植物人后离她而去，仅仅因为莉迪亚的前男友表现出好似比他更深情的爱。

I know of none which are not easy to answer, but what I am trying to do now is only by a series of hints to throw some light on the narrow path of legal doctrine, and upon two pitfalls which, as it seems to me, lie perilously near to it.

我不认为有什么难以回答的问题，但我现在要做的仅仅是通过一系列线索，来给法律理论的狭窄路径以及在我看来离它近得危险的两个陷阱提供一些启示。