Results 291 to 300 of about 1,301,558 (327)
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Journal of Mathematical Sciences, 2006
Let \(\{a_n\}\) be a sequence of nonnegative real numbers and for a fixed natural number \(r\geq2\) let \(\tau_r(n)\) be the divisor function whose generating function is \(\zeta(s)^r\). Set \(A(x)=\sum_{n\leq x}a_n\) and \(D_r(x)=\sum_{n\leq x}\tau_r(n)a_n\).
Friedlander, J. B., Iwaniec, H.
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Let \(\{a_n\}\) be a sequence of nonnegative real numbers and for a fixed natural number \(r\geq2\) let \(\tau_r(n)\) be the divisor function whose generating function is \(\zeta(s)^r\). Set \(A(x)=\sum_{n\leq x}a_n\) and \(D_r(x)=\sum_{n\leq x}\tau_r(n)a_n\).
Friedlander, J. B., Iwaniec, H.
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Deuteron bremsstrahlung-weighted photonuclear sum rule
Physical Review C, 1987The various contributions to the deuteron bremsstrahlung-weighted photonuclear sum rule sigma/sub -1/ are analyzed. It is shown that the unretarded normal L = 1 sum rule is model independent and that retardation, higher multipoles, and interaction effects are negligible. An accurate estimation of sigma/sub -1/ is provided by the knowledge of the charge
Bohigas, O., Lipparini, E.
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Combinatorics, Probability and Computing, 1995
The main result of this paper has the following consequence. Let G be an abelian group of order n. Let {xi: 1 ≤ 2n − 1} be a family of elements of G and let {wi: 1 ≤ i ≤ n − 1} be a family of integers prime relative to n. Then there is a permutation & of [1,2n − 1] such thatApplying this result with wi = 1 for all i, one obtains the Erdős–Ginzburg ...
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The main result of this paper has the following consequence. Let G be an abelian group of order n. Let {xi: 1 ≤ 2n − 1} be a family of elements of G and let {wi: 1 ≤ i ≤ n − 1} be a family of integers prime relative to n. Then there is a permutation & of [1,2n − 1] such thatApplying this result with wi = 1 for all i, one obtains the Erdős–Ginzburg ...
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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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