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991.
George E. Andrews Arnold Knopfmacher Burkhard Zimmermann 《Journal of Number Theory》2006,118(1):15-30
We study M(n), the number of distinct values taken by multinomial coefficients with upper entry n, and some closely related sequences. We show that both pP(n)/M(n) and M(n)/p(n) tend to zero as n goes to infinity, where pP(n) is the number of partitions of n into primes and p(n) is the total number of partitions of n. To use methods from commutative algebra, we encode partitions and multinomial coefficients as monomials. 相似文献
992.
In the 1960s Gisbert Hasenjaeger built Turing Machines from electromechanical relays and uniselectors. Recently, Glaschick reverse engineered the program of one of these machines and found that it is a universal Turing machine. In fact, its program uses only four states and two symbols, making it a very small universal Turing machine. (The machine has three tapes and a number of other features that are important to keep in mind when comparing it to other small universal machines.) Hasenjaeger’s machine simulates Hao Wang’s B machines, which were proved universal by Wang. Unfortunately, Wang’s original simulation algorithm suffers from an exponential slowdown when simulating Turing machines. Hence, via this simulation, Hasenjaeger’s machine also has an exponential slowdown when simulating Turing machines. In this work, we give a new efficient simulation algorithm for Wang’s B machines by showing that they simulate Turing machines with only a polynomial slowdown. As a second result, we find that Hasenjaeger’s machine also efficiently simulates Turing machines in polynomial time. Thus, Hasenjaeger’s machine is both small and fast. In another application of our result, we show that Hooper’s small universal Turing machine simulates Turing machines in polynomial time, an exponential improvement. 相似文献
993.
In this paper, we present a new method for solving 1D time dependent partial differential equations based on the Laplace transform (LT). As a result, the problem is converted into a stationary boundary value problem (BVP) which depends on the parameter of LT. The resulting BVP is solved by the polynomial Trefftz method (PTM), which can be regarded as a meshless method. In PTM, the source term is approximated by a truncated series of Chebyshev polynomials and the particular solution is obtained from a recursive procedure. Talbot’s method is employed for the numerical inversion of LT. The method is tested with the help of some numerical examples. 相似文献
994.
A. R. Nasr-Isfahani 《代数通讯》2017,45(1):443-445
995.
高阶模激光束通过会聚光学系统的聚焦特性 总被引:5,自引:0,他引:5
以惠更斯 -菲涅尔原理和取样理论为基础 ,利用计算机编程计算和绘图软件 Graftool得到高阶模激光束 (如厄米 -高斯光束 TEM1 1 、TEM1 2 (或 TEM2 1 )、TEM2 2 和拉盖尔 -高斯光束 TEM1 0 、TEM1 1 )经过会聚光学系统 (以双透镜聚焦系统为例 )传播后的聚焦曲线 (r- z)。在聚焦曲线上 ,r的极小值 rmin就是激光束会聚的聚焦光斑尺寸 ,对应的 z值是束腰位置 zfocus。这样就从理论上获得了上述激光束通过会聚光学系统后的束腰位置和聚焦光斑尺寸 ,从而为研究高阶模激光束的聚焦问题提供了一种新方法 相似文献
996.
997.
Restarted generalized Krylov subspace methods for solving large-scale polynomial eigenvalue problems
In this paper, we introduce a generalized Krylov subspace based on a square matrix sequence {A
j
} and a vector sequence {u
j
}. Next we present a generalized Arnoldi procedure for generating an orthonormal basis of . By applying the projection and the refined technique, we derive a restarted generalized Arnoldi method and a restarted refined
generalized Arnoldi method for solving a large-scale polynomial eigenvalue problem (PEP). These two methods are applied to
solve the PEP directly. Hence they preserve essential structures and properties of the PEP. Furthermore, restarting reduces
the storage requirements. Some theoretical results are presented. Numerical tests report the effectiveness of these methods.
Yimin Wei is supported by the National Natural Science Foundation of China and Shanghai Education Committee. 相似文献
998.
999.
Animesh Lahiri 《代数通讯》2019,47(3):1099-1101
1000.