Results 221 to 230 of about 256,372 (245)
Associations between temporomandibular disorders/bruxism and head and neck pains: a bidirectional Mendelian randomization study. [PDF]
J Oral Facial Pain HeadacheDu SS, Hu YY, Niu YM.
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Association between asthma and changes in brain cortical structure: a Mendelian randomization study. [PDF]
BMC Pulm MedCai Y +5 more
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Knowledge-driven teaching-learning-based optimization algorithm for bi-objective flexible job-shop scheduling problem with tool allocation. [PDF]
PLoS OneChen K, Yuan X, Tan W.
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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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