The Experts below are selected from a list of 488574 Experts worldwide ranked by ideXlab platform
Kirk Pruhs - One of the best experts on this subject based on the ideXlab platform.
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speed scaling with an arbitrary Power Function
ACM Transactions on Algorithms, 2013Co-Authors: Nikhil Bansal, Holeung Chan, Kirk PruhsAbstract:This article initiates a theoretical investigation into online scheduling problems with speed scaling where the allowable speeds may be discrete, and the Power Function may be arbitrary, and develops algorithmic analysis techniques for this setting. We show that a natural algorithm, which uses Shortest Remaining Processing Time for scheduling and sets the Power to be one more than the number of unfinished jobs, is 3-competitive for the objective of total flow time plus energy. We also show that another natural algorithm, which uses Highest Density First for scheduling and sets the Power to be the fractional weight of the unfinished jobs, is a 2-competitive algorithm for the objective of fractional weighted flow time plus energy.
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speed scaling with an arbitrary Power Function
Symposium on Discrete Algorithms, 2009Co-Authors: Nikhil Bansal, Holeung Chan, Kirk PruhsAbstract:All of the theoretical speed scaling research to date has assumed that the Power Function, which expresses the Power consumption P as a Function of the processor speed s, is of the form P = sα, where α > 1 is some constant. Motivated in part by technological advances, we initiate a study of speed scaling with arbitrary Power Functions. We consider the problem of minimizing the total flow plus energy. Our main result is a (3+e)-competitive algorithm for this problem, that holds for essentially any Power Function. We also give a (2+e)-competitive algorithm for the objective of fractional weighted flow plus energy. Even for Power Functions of the form sα, it was not previously known how to obtain competitiveness independent of α for these problems. We also introduce a model of allowable speeds that generalizes all known models in the literature.
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SODA - Speed scaling with an arbitrary Power Function
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, 2009Co-Authors: Nikhil Bansal, Holeung Chan, Kirk PruhsAbstract:All of the theoretical speed scaling research to date has assumed that the Power Function, which expresses the Power consumption P as a Function of the processor speed s, is of the form P = sα, where α > 1 is some constant. Motivated in part by technological advances, we initiate a study of speed scaling with arbitrary Power Functions. We consider the problem of minimizing the total flow plus energy. Our main result is a (3+e)-competitive algorithm for this problem, that holds for essentially any Power Function. We also give a (2+e)-competitive algorithm for the objective of fractional weighted flow plus energy. Even for Power Functions of the form sα, it was not previously known how to obtain competitiveness independent of α for these problems. We also introduce a model of allowable speeds that generalizes all known models in the literature.
Nikhil Bansal - One of the best experts on this subject based on the ideXlab platform.
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speed scaling with an arbitrary Power Function
ACM Transactions on Algorithms, 2013Co-Authors: Nikhil Bansal, Holeung Chan, Kirk PruhsAbstract:This article initiates a theoretical investigation into online scheduling problems with speed scaling where the allowable speeds may be discrete, and the Power Function may be arbitrary, and develops algorithmic analysis techniques for this setting. We show that a natural algorithm, which uses Shortest Remaining Processing Time for scheduling and sets the Power to be one more than the number of unfinished jobs, is 3-competitive for the objective of total flow time plus energy. We also show that another natural algorithm, which uses Highest Density First for scheduling and sets the Power to be the fractional weight of the unfinished jobs, is a 2-competitive algorithm for the objective of fractional weighted flow time plus energy.
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speed scaling with an arbitrary Power Function
Symposium on Discrete Algorithms, 2009Co-Authors: Nikhil Bansal, Holeung Chan, Kirk PruhsAbstract:All of the theoretical speed scaling research to date has assumed that the Power Function, which expresses the Power consumption P as a Function of the processor speed s, is of the form P = sα, where α > 1 is some constant. Motivated in part by technological advances, we initiate a study of speed scaling with arbitrary Power Functions. We consider the problem of minimizing the total flow plus energy. Our main result is a (3+e)-competitive algorithm for this problem, that holds for essentially any Power Function. We also give a (2+e)-competitive algorithm for the objective of fractional weighted flow plus energy. Even for Power Functions of the form sα, it was not previously known how to obtain competitiveness independent of α for these problems. We also introduce a model of allowable speeds that generalizes all known models in the literature.
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SODA - Speed scaling with an arbitrary Power Function
Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, 2009Co-Authors: Nikhil Bansal, Holeung Chan, Kirk PruhsAbstract:All of the theoretical speed scaling research to date has assumed that the Power Function, which expresses the Power consumption P as a Function of the processor speed s, is of the form P = sα, where α > 1 is some constant. Motivated in part by technological advances, we initiate a study of speed scaling with arbitrary Power Functions. We consider the problem of minimizing the total flow plus energy. Our main result is a (3+e)-competitive algorithm for this problem, that holds for essentially any Power Function. We also give a (2+e)-competitive algorithm for the objective of fractional weighted flow plus energy. Even for Power Functions of the form sα, it was not previously known how to obtain competitiveness independent of α for these problems. We also introduce a model of allowable speeds that generalizes all known models in the literature.
L P Khoroshun - One of the best experts on this subject based on the ideXlab platform.
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coupled processes of deformation and long term damage of fibrous materials with the microdurability of the matrix described by an exponential Power Function
International Applied Mechanics, 2010Co-Authors: L P Khoroshun, E N ShikulaAbstract:The theory of long-term damage is generalized to fibrous composites. The damage of the matrix is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Huber–von Mises criterion, and assumed to be a random Function of coordinates. An equation of damage (porosity) balance in the matrix at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of stress-rupture microstrength described by an exponential Power Function
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deformation and long term damage of fibrous materials with the stress rupture microstrength of the matrix described by a fractional Power Function
International Applied Mechanics, 2009Co-Authors: L P Khoroshun, E N ShikulaAbstract:The theory of long-term damage is generalized to unidirectional fibrous composites. The damage of the matrix is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Huber–Mises criterion, and assumed to be a random Function of coordinates. An equation of damage (porosity) balance in the matrix at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of stress-rupture microstrength described by a fractional Power Function
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Long-term damage of discrete-fiber-reinforced composites with transversely isotropic inclusions and stress-rupture microstrength described by an exponential Power Function
International Applied Mechanics, 2009Co-Authors: L P Khoroshun, L. V. NazarenkoAbstract:The theory of long-term damage of homogeneous materials, which is based on the equations of the mechanics of stochastically inhomogeneous materials, is generalized to discrete-fiber-reinforced composite materials. The microdamage of the composite components is modeled by randomly dispersed micropores. The failure criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit. Given macrostresses and macrostrains, an equation of damage (porosity) balance in the composite components at an arbitrary time is formulated. The time dependence of microdamage and macrostresses or macrostrains is established in the case of stress-rupture microstrength described by an exponential Power Function
Kolosov Petro - One of the best experts on this subject based on the ideXlab platform.
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Series Representation of Power Function
arXiv: Number Theory, 2016Co-Authors: Kolosov PetroAbstract:In this paper described numerical expansion of natural-valued Power Function $x^n$, in point $x=x_0$ where $n, \ x_0$ - natural numbers. Applying numerical methods, that is calculus of finite differences, namely, discrete case of Binomial expansion is reached. Received results were compared with solutions according to Newton's Binomial theorem and MacMillan Double Binomial sum. Additionally, in section 4 exponential Function's $e^x$ representation is shown.
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series representation of Power Function
2016Co-Authors: Kolosov PetroAbstract:This paper presents the way to make expansion for the next form Function: y = x, ∀(x, n) ∈ N to the numerical series. The most widely used methods to solve this problem are Newton’s Binomial Theorem and Fundamental Theorem of Calculus (that is, derivative and integral are inverse operators). The paper provides the other kind of solution, except above described theorems.
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series expansion for Power Function
2015Co-Authors: Kolosov PetroAbstract:This paper presents the way to make expansion for the next form Function: = , ∈ N, ∈ N to the numerical series. The most widely used ways to solve this problem are Newton’s Binomial Theorem and Fundamental Theorem of Calculus (that is, derivative and integral are inverse operators). The paper provides the other kind of solution, except above described theorems. INTRODUCTION Let basically describe Newton’s Binomial Theorem and Fundamental Theorem of Calculus and some their properties. In elementary algebra, the binomial theorem (or binomial expansion) describes the algebraic expansion of Powers of a binomial. According to the theorem, it is possible to expand the Power + into a sum involving terms of the form , where the exponents and are nonnegative integers with + = , and the coefficient of each term is a specific positive integer depending on and . The coefficient in the term of is known as the binomial coefficient. The main properties of the binominal theorem are next: I. the Powers of go down until it reaches = 1starting value is (the in ( + ) ) II. the Powers of go up from 0 ( = 1) until it reaches (also the in ( + ) ) III. the -th row of the Pascal's Triangle will be the coefficients of the expanded binomial. IV. for each line, the number of products (i.e. the sum of the coefficients) is equal to 2 V. for each line, the number of product groups is equal to + 1 By using binomial theorem for our case we obtain next form Function [1]: = + 2 + ⋯ + − 1 + 1 We can reach the same result by using Fundamental Theorem of Calculus, according it we have [2]:
E N Shikula - One of the best experts on this subject based on the ideXlab platform.
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coupled processes of deformation and long term damage of fibrous materials with the microdurability of the matrix described by an exponential Power Function
International Applied Mechanics, 2010Co-Authors: L P Khoroshun, E N ShikulaAbstract:The theory of long-term damage is generalized to fibrous composites. The damage of the matrix is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Huber–von Mises criterion, and assumed to be a random Function of coordinates. An equation of damage (porosity) balance in the matrix at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of stress-rupture microstrength described by an exponential Power Function
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deformation and long term damage of fibrous materials with the stress rupture microstrength of the matrix described by a fractional Power Function
International Applied Mechanics, 2009Co-Authors: L P Khoroshun, E N ShikulaAbstract:The theory of long-term damage is generalized to unidirectional fibrous composites. The damage of the matrix is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the ultimate strength, according to the Huber–Mises criterion, and assumed to be a random Function of coordinates. An equation of damage (porosity) balance in the matrix at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of stress-rupture microstrength described by a fractional Power Function
