scholarly journals A reformulation-linearization based algorithm for the smallest enclosing circle problem

2017 ◽  
Vol 13 (5) ◽  
pp. 0-0
Author(s):  
Yi Jiang ◽  
◽  
Yuan Cai
Keyword(s):  
Circle Problem ◽  
Reformulation Linearization

Allocating nodes to hubs for minimizing the hubs processing resources: A case study

2019 ◽  
Vol 53 (3) ◽  
pp. 807-827
Author(s):  
Ali Balma ◽  
Mehdi Mrad
Keyword(s):  
Telecommunication Network ◽  
Real Life ◽  
Optimal Solutions ◽  
Total Flow ◽  
Nonlinear Formulation ◽  
Large Size ◽  
Processing Resources ◽  
Reformulation Linearization

This paper addresses the problem of allocating the terminal nodes to the hub nodes in a telecommunication network. Since the flow processing induces some undesirable delay, the objective is to minimize the total flow processed by the hubs. This study focuses on a real life network of the tunisian operator Tunisie Telecom whose operations managers are concerned by the quality of service. We provide three compact formulations that give optimal solutions for networks of large size. In particular, the last two are obtained by applying the Reformulation-Linearization Technique to a nonlinear formulation of the problem. The latter formulation derived within this approach is the most computationally effective, as pointed out by the computational experiments conducted on the real life network of Tunisie Telecom with 110 nodes and 5 hubs. Finally, we discuss and compare between the single allocation and double allocation configurations.

ON A NEW CIRCLE PROBLEM

2016 ◽  
Vol 103 (2) ◽  
pp. 231-249
Author(s):  
JUN FURUYA ◽  
MAKOTO MINAMIDE ◽  
YOSHIO TANIGAWA
Keyword(s):  
Asymptotic Formula ◽  
Error Term ◽  
Dirichlet Character ◽  
Arithmetical Function ◽  
Circle Problem ◽  
The Riemann Zeta Function ◽  
Primitive Dirichlet Character ◽  
Riemann Zeta ◽  
The Mean ◽  
Voronoi Formula

We attempt to discuss a new circle problem. Let $\unicode[STIX]{x1D701}(s)$ denote the Riemann zeta-function $\sum _{n=1}^{\infty }n^{-s}$ ($\text{Re}\,s>1$) and $L(s,\unicode[STIX]{x1D712}_{4})$ the Dirichlet $L$-function $\sum _{n=1}^{\infty }\unicode[STIX]{x1D712}_{4}(n)n^{-s}$ ($\text{Re}\,s>1$) with the primitive Dirichlet character mod 4. We shall define an arithmetical function $R_{(1,1)}(n)$ by the coefficient of the Dirichlet series $\unicode[STIX]{x1D701}^{\prime }(s)L^{\prime }(s,\unicode[STIX]{x1D712}_{4})=\sum _{n=1}^{\infty }R_{(1,1)}(n)n^{-s}$$(\text{Re}\,s>1)$. This is an analogue of $r(n)/4=\sum _{d|n}\unicode[STIX]{x1D712}_{4}(d)$. In the circle problem, there are many researches of estimations and related topics on the error term in the asymptotic formula for $\sum _{n\leq x}r(n)$. As a new problem, we deduce a ‘truncated Voronoï formula’ for the error term in the asymptotic formula for $\sum _{n\leq x}R_{(1,1)}(n)$. As a direct application, we show the mean square for the error term in our new problem.

scholarly journals Almost periodic functions and hyperbolic counting

2018 ◽  
Vol 14 (09) ◽  
pp. 2343-2368
Author(s):  
Giacomo Cherubini
Keyword(s):  
Asymptotic Variance ◽  
Limiting Distribution ◽  
Almost Periodic Functions ◽  
Specific Class ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Circle Problem

We prove the existence of asymptotic moments and an estimate on the tails of the limiting distribution for a specific class of almost periodic functions. Then we introduce the hyperbolic circle problem, proving an estimate on the asymptotic variance of the remainder that improves a result of Chamizo. Applying the results of the first part we prove the existence of limiting distribution and asymptotic moments for three functions that are integrated versions of the remainder, and were considered originally (with due adaptations to our settings) by Wolfe, Phillips and Rudnick, and Hill and Parnovski.

A Graphics Processing Unit Algorithm to Solve the Quadratic Assignment Problem Using Level-2 Reformulation-Linearization Technique

2017 ◽  
Vol 29 (4) ◽  
pp. 676-687 ◽  
Author(s):  
Alexandre Domingues Gonçalves ◽  
Artur Alves Pessoa ◽  
Cristiana Bentes ◽  
Ricardo Farias ◽  
Lúcia Maria de A. Drummond
Keyword(s):  
Assignment Problem ◽  
Graphics Processing Unit ◽  
Quadratic Assignment Problem ◽  
Quadratic Assignment ◽  
Processing Unit ◽  
Linearization Technique ◽  
Graphics Processing ◽  
Reformulation Linearization ◽  
Level 2

scholarly journals Bilateral-type solutions to the fixed-circle problem with rectified linear units application

2020 ◽  
Vol 44 (4) ◽  
pp. 1330-1344
Author(s):  
Nihal TAŞ
Keyword(s):  
Circle Problem

On the nonlinear limit-point/limit-circle problem

1983 ◽  
Vol 7 (8) ◽  
pp. 851-871 ◽  
Author(s):  
John R. Graef ◽  
Paul W. Spikes
Keyword(s):  
Limit Point ◽  
Limit Circle ◽  
Circle Problem

A twist of the Gauss circle problem by holomorphic cusp forms

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ratnadeep Acharya
Keyword(s):  
Cusp Forms ◽  
Circle Problem ◽  
Holomorphic Cusp Forms ◽  
Gauss Circle Problem
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