Results 231 to 240 of about 18,643 (267)
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Izvestiya: Mathematics, 2000
The paper investigates weighted character sums of type \[ \sum_{n \leq N} \tau_k(n) \chi(n+a). \] Here, \(\chi\) is a non-principal Dirichlet character modulo a prime number \(p\), \(\tau_k(n)\) the number of positive integer solutions \(x_1, \ldots , x_k\) of the equation \(x_1 \cdots x_k = n\) and \((a,p)=1\).
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The paper investigates weighted character sums of type \[ \sum_{n \leq N} \tau_k(n) \chi(n+a). \] Here, \(\chi\) is a non-principal Dirichlet character modulo a prime number \(p\), \(\tau_k(n)\) the number of positive integer solutions \(x_1, \ldots , x_k\) of the equation \(x_1 \cdots x_k = n\) and \((a,p)=1\).
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Publicationes Mathematicae Debrecen, 2005
Summary: In this paper, we study the equation \(z^n=\sum_{k=0}^{n-1} a_k z^k\), where \(\sum_{k=0}^{n-1}a_k =1\), \(a_k\geq 0\) for each \(k\). We show that, given \(p>1\), there exist \(C(1/p)\)-polynomials with the degree of weighted sum \(n-1\). However, we obtain sufficient conditions for nonexistence of certain lacunary \(C(1/p)\)-polynomials.
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Summary: In this paper, we study the equation \(z^n=\sum_{k=0}^{n-1} a_k z^k\), where \(\sum_{k=0}^{n-1}a_k =1\), \(a_k\geq 0\) for each \(k\). We show that, given \(p>1\), there exist \(C(1/p)\)-polynomials with the degree of weighted sum \(n-1\). However, we obtain sufficient conditions for nonexistence of certain lacunary \(C(1/p)\)-polynomials.
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2000
In this chapter we will investigate to what extent an MOP of the Pareto class $$\mathop {\min }\limits_{x\varepsilon X} \left( {f_1 \left( x \right), \ldots,f_Q \left( x \right)} \right)$$ (3.1) can be solved by solving scalarized problems of the type $$\mathop {\min }\limits_{x\varepsilon X} \sum\limits_{i = 1}^Q {\lambda _i f_i \left( x
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In this chapter we will investigate to what extent an MOP of the Pareto class $$\mathop {\min }\limits_{x\varepsilon X} \left( {f_1 \left( x \right), \ldots,f_Q \left( x \right)} \right)$$ (3.1) can be solved by solving scalarized problems of the type $$\mathop {\min }\limits_{x\varepsilon X} \sum\limits_{i = 1}^Q {\lambda _i f_i \left( x
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Weighted Cumulative Sum Technique
Technometrics, 1989A class of weighted control schemes that generalizes the basic cumulative sum (CUSUM) technique is introduced. The schemes of the first type, in which the weights represent information concomitant with the data, prove to be especially useful when handling charts corresponding to samples of varying sizes.
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Journal of the Operational Research Society, 2009
The problem of scheduling in permutation flowshops is considered in this paper with the objectives of minimizing the sum of weighted flowtime/sum of weighted tardiness/sum of weighted flowtime and weighted tardiness/sum of weighted flowtime, weighted tardiness and weighted earliness of jobs, with each objective considered separately.
N Madhushini, C Rajendran, Y Deepa
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The problem of scheduling in permutation flowshops is considered in this paper with the objectives of minimizing the sum of weighted flowtime/sum of weighted tardiness/sum of weighted flowtime and weighted tardiness/sum of weighted flowtime, weighted tardiness and weighted earliness of jobs, with each objective considered separately.
N Madhushini, C Rajendran, Y Deepa
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On the general trigonometric sums weighted by character sums
Applied Mathematics and Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tian, Qing, Yang, Wei, Ding, Liping
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Sums and Products of Weighted Shifts
Canadian Mathematical Bulletin, 2001AbstractIn this article it is shown that every bounded linear operator on a complex, infinite dimensional, separable Hilbert space is a sum of at most eighteen unilateral (alternatively, bilateral) weighted shifts. As well, we classify products of weighted shifts, as well as sums and limits of the resulting operators.
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Inverse energy weighted sum-rules
Pramana, 1989A new derivation of the inverse energy-weighted sum-rules is given by applying the spectral distribution methods to the Rayleigh-Schrodinger perturbation theory. The scalar space result is then extended to the configurations. This is applied to obtain corrections to the ground-state energy estimates when the effective interaction is approximated by a ...
V K B Kota +3 more
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Two Theorems in Multi-Weighted Sums
Journal of the Society for Industrial and Applied Mathematics, 1961Systems of linear relationships have received an increasing amount of attention in recent years, partly in their own right as mathematical entities, but probably more so because of their frequent occurrence in physical situations. Multilinear systems, however, involving linear combinations of linear expressions, seem to have been almost completely ...
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Weighted Sum Method and Weighted Product Method
2012In this chapter we look at two simple multi-criteria decision-making methods, the Weighted Sum method and the Weighted Product method. In the Weighted Sum method the score of an alternative is equal to the weighted sum of its evaluation ratings, where the weights are the importance weights associated with each attribute. In the Weighted Product method,
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