摘要 :
Elliptic problems with parameters in the boundary conditions are called Steklov problems. With the toolof computational approximation (finite-element method), we estimate the solution of a nonlinear Stekloveigenvalue problem for a...
展开
Elliptic problems with parameters in the boundary conditions are called Steklov problems. With the toolof computational approximation (finite-element method), we estimate the solution of a nonlinear Stekloveigenvalue problem for a second-order, self-adjoint, elliptic differential problem. We discussed the be-havior of the nonlinear problem with the help of computational results using Matlab
收起
摘要 :
This article focuses on the problem and its types, and describes the methodology for solving non-standard problems. Recommendations are given for solving non-standard issues by dividing them into specific categories.
摘要 :
In a classic Markov decision problem of Derman et al. (Oper. Res. 23(6): 1120-1130, 1975) an investor has an initial capital x from which to make investments, the opportunities for which occur randomly over time. An investment of ...
展开
In a classic Markov decision problem of Derman et al. (Oper. Res. 23(6): 1120-1130, 1975) an investor has an initial capital x from which to make investments, the opportunities for which occur randomly over time. An investment of size y results in profit P(y), and the aim is maximize the sum of the profits obtained within a given time t. The problem is similar to a groundwater management problem of Burt (Manag. Sci. 11(1):80-93, 1964), the notorious bomber problem of Klinger and Brown (Stochastic Optimization and Control, pp. 173-209, 1968), and types of fighter problems addressed by Weber (Stochastic Dynamic Optimization and Applications in Scheduling and Related Fields, p. 148, 1985), Shepp et al. (Adv. Appl. Probab. 23:624-641, 1991) and Bartroff et al. (Adv. Appl. Probab. 42(3):795-815, 2010a). In all these problems, one is allocating successive portions of a limited resource, optimally allocating y(x, t), as a function of remaining resource x and remaining time t. For their investment problem, Derman et al. (Oper. Res. 23(6): 1120-1130, 1975) proved that an optimal policy has three monotonicity properties: (A) y(x, t) is nonin-creasing in t, (B) y(x, t) is nondecreasing in x, and (C) x - y(x, t) is nondecreasing in x. Theirs is the only problem of its type for which all three properties are known to be true.In the bomber problem the status of (B) is unresolved. For the general fighter problem the status of (A) is unresolved. We survey what is known about these exceedingly difficult problems. We show that (A) and (C) remain true in the bomber problem, but that (B) is false if we very slightly relax the assumptions of the usual model. We give other new results, counterexamples and conjectures for these problems.
收起
摘要 :
In a classic Markov decision problem of Derman et al. (Oper. Res. 23(6):1120–1130, 1975) an investor has an initial capital x from which to make investments, the opportunities for which occur randomly over time. An investment of ...
展开
In a classic Markov decision problem of Derman et al. (Oper. Res. 23(6):1120–1130, 1975) an investor has an initial capital x from which to make investments, the opportunities for which occur randomly over time. An investment of size y results in profit P(y), and the aim is maximize the sum of the profits obtained within a given time t. The problem is similar to a groundwater management problem of Burt (Manag. Sci. 11(1):80–93, 1964), the notorious bomber problem of Klinger and Brown (Stochastic Optimization and Control, pp. 173–209, 1968), and types of fighter problems addressed by Weber (Stochastic Dynamic Optimization and Applications in Scheduling and Related Fields, p. 148, 1985), Shepp et al. (Adv. Appl. Probab. 23:624–641, 1991) and Bartroff et al. (Adv. Appl. Probab. 42(3):795–815, 2010a). In all these problems, one is allocating successive portions of a limited resource, optimally allocating y(x,t), as a function of remaining resource x and remaining time t. For their investment problem, Derman et al. (Oper. Res. 23(6):1120–1130, 1975) proved that an optimal policy has three monotonicity properties: (A) y(x,t) is nonincreasing in t, (B) y(x,t) is nondecreasing in x, and (C) x−y(x,t) is nondecreasing in x. Theirs is the only problem of its type for which all three properties are known to be true.
收起
摘要 :
Several journal articles, websites, and conferences have recently focused on the emerging discipline of statistical engineering. This discipline focuses on developing the theory and practice of how to address large, complex, unstr...
展开
Several journal articles, websites, and conferences have recently focused on the emerging discipline of statistical engineering. This discipline focuses on developing the theory and practice of how to address large, complex, unstructured problems, particularly those that require data and analysis. While good statisticians and engineers have always applied statistical engineering, they did not generally document the critical thinking they applied to resolve such big problems. In this sense, statistical engineering is not new, but the discipline of statistical engineering is. As a professional society, the International Statistical Engineering Association (ISEA) is even newer. This expository article explains the basics of statistical engineering: what it is, why it is needed, how it works, how it is unique, and so on. Furthermore, it provides a history of the development of statistical engineering going back to Churchill Eisenhart during the early years after World War II. It then discusses the origins and rapid development of ISEA as an international professional society devoted to the emerging discipline of statistical engineering.
收起
摘要 :
Let Λ be the four subspace algebra. We show that for any Λ-module M there exists an algorithm (up to the problem of finding roots of the so-called characteristic polynomial of M) with relatively low polynomial complexity of dete...
展开
Let Λ be the four subspace algebra. We show that for any Λ-module M there exists an algorithm (up to the problem of finding roots of the so-called characteristic polynomial of M) with relatively low polynomial complexity of determining multiplicities of all direct summands of M. Moreover, we give a fully algorithmic criterion for deciding if two Λ-modules M and N are isomorphic.
收起
摘要 :
The transportation problem is a classic problem in operations research that involves finding the optimal way to move goods from one place to another. With the increase of globalization and the development of complex distribution n...
展开
The transportation problem is a classic problem in operations research that involves finding the optimal way to move goods from one place to another. With the increase of globalization and the development of complex distribution networks, the transportation problem has become increasingly important in the field of operations research. This article provides a literature review of transportation problems and their solutions. The authors explore the various types of transportation problems and the available solutions that can be used to address them. The article looks at the different objectives and constraints that can be used to formulate transportation problems and presents the main algorithms used to solve them. The authors discuss the applications of transportation problems in different areas including logistics, supply chain management, urban planning, and others. They also examine the potential benefits and drawbacks of using transportation problems in these areas and conclude by suggesting further research in the field.
收起
摘要 :
We consider the direct problem of aerial electric sounding for a layered medium with a vertical cylindri-cal anomaly. We determine the minimum size of the anomaly when it is indistinguishable from an infi-nite layer of the same co...
展开
We consider the direct problem of aerial electric sounding for a layered medium with a vertical cylindri-cal anomaly. We determine the minimum size of the anomaly when it is indistinguishable from an infi-nite layer of the same conductivity. The integral equation is solved by the integral current method. Theconcept of apparent conductivity is introduced for sounding problems using a magnetic dipole. The cal-culations support the conjecture of the locality of aerial sounding and prove the high efficiency of the in-tegral current method for such problems.
收起
摘要 :
We discuss a problem posed by Ronald Graham about the minimum number,over all 2-colorings of [1, n], of monochromatic {x, y, x + ay} triples for a > 1. Wegive a new proof of the original case of a = 1. We show that the minimum num...
展开
We discuss a problem posed by Ronald Graham about the minimum number,over all 2-colorings of [1, n], of monochromatic {x, y, x + ay} triples for a > 1. Wegive a new proof of the original case of a = 1. We show that the minimum numberof such triples is at most + O(n) when a ≥ 2. We also find a new upper 2a(a~2+2a+3) bound for the minimum number, over all r-colorings of [1, n], of monochromaticSchur triples, for r > 3.
收起
原文获取