Results 231 to 240 of about 21,411 (263)
Some of the next articles are maybe not open access.
On optimal weighted-sum rates for the modulo sum problem
2020 IEEE International Symposium on Information Theory (ISIT), 2020In a seminal work Korner and Marton showed that for computing the module-two sum of doubly symmetric binary sources, linear codes achieved the optimal rates and outperformed random coding and binning based arguments. Korner also showed the optimality of Slepian-Wolf based random coding for the same problem for a different class of pairwise ...
Chandra Nair, Yan Nan Wang
openaire +1 more source
Sum of weighted distances in trees
Discrete Applied Mathematics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qingqiong Cai +3 more
openaire +1 more source
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 ...
openaire +1 more source
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 ...
openaire +1 more source
Number of Weighted Subsequence Sums with Weights in {1, –1}
Integers, 2011AbstractLet
Sukumar Das Adhikari +1 more
openaire +3 more sources
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.
openaire +1 more source
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.
openaire +1 more source
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.
openaire +1 more source
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.
openaire +1 more source
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 \((a,p)=1\).
openaire +2 more sources
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 \((a,p)=1\).
openaire +2 more sources
Sums and weighted sums of a gamma Markov sequence
Journal of Applied Probability, 1988We derive the Laplace transforms of sums and weighted sums of random variables forming a Markov chain whose stationary distribution is gamma. Both seasonal and non-seasonal cases are considered. The results are applied to two problems in stochastic reservoir theory.
openaire +1 more source
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 $$\mathop {\min }\limits_{x\varepsilon X} \sum\limits_{i = 1}^Q {\lambda _i f_i \left( x
openaire +1 more source
In this chapter we will investigate to what extent an MOP of the Pareto class $$\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
openaire +1 more source
Sylvester power and weighted sums on the Frobenius set in arithmetic progression
Discrete Applied Mathematics, 2022Takao Komatsu
exaly