Improved Even Order Magic Square Construction Algorithms and Their Applications

2014 ◽  
pp. 666-680
Author(s):  
Zhenhua Duan ◽  
Jin Liu ◽  
Jie Li ◽  
Cong Tian
Keyword(s):  
Magic Square ◽  
Even Order ◽  
Construction Algorithms

Algorithm 117: Magic square (even order)

1962 ◽  
Vol 5 (8) ◽  
pp. 435
Author(s):  
D. M. Collison
Keyword(s):  
Magic Square ◽  
Even Order

scholarly journals Magic square

2009 ◽  
Vol 6 (3) ◽  
pp. 618-620
Author(s):  
Baghdad Science Journal
Keyword(s):  
Magic Square ◽  
Odd Order ◽  
Even Order

In this paper we introduce two Algorithms, the first Algorithms when it is odd order and how we calculate magic square and rotation for it. The second Algorithms when it be even order and how to find magic square and rotation for it.

WDM Multicast Tree Construction Algorithms and Their Comparative Evaluations

2010 ◽  
Vol E93-B (9) ◽  
pp. 2282-2290
Author(s):  
Tsutomu MAKABE ◽  
Taiju MIKOSHI ◽  
Toyofumi TAKENAKA
Keyword(s):  
Multicast Tree ◽  
Tree Construction ◽  
Construction Algorithms ◽  
Multicast Tree Construction

scholarly journals Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems

2007 ◽  
Vol 14 (4) ◽  
pp. 775-792
Author(s):  
Youyu Wang ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Even Order

Abstract In this paper, we consider the existence of multiple positive solutions for the 2𝑛th order 𝑚-point boundary value problem: where (0,1), 0 < ξ 1 < ξ 2 < ⋯ < ξ 𝑚–2 < 1. Using the Leggett–Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The associated Green's function for the above problem is also given.

scholarly journals Even-order differential equation with continuous delay: nonexistence criteria of Kneser solutions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ali Muhib ◽  
M. Motawi Khashan ◽  
Osama Moaaz
Keyword(s):  
Differential Equation ◽  
Order Differential Equation ◽  
Delay Argument ◽  
Even Order ◽  
Continuous Delay ◽  
New Criteria

AbstractIn this paper, we study even-order DEs where we deduce new conditions for nonexistence Kneser solutions for this type of DEs. Based on the nonexistence criteria of Kneser solutions, we establish the criteria for oscillation that take into account the effect of the delay argument, where to our knowledge all the previous results neglected the effect of the delay argument, so our results improve the previous results. The effectiveness of our new criteria is illustrated by examples.

scholarly journals Two-color two-dimensional terahertz spectroscopy: A new approach for exploring even-order nonlinearities in the nonperturbative regime

2021 ◽  
Vol 154 (15) ◽  
pp. 154203
Author(s):  
Michael Woerner ◽  
Ahmed Ghalgaoui ◽  
Klaus Reimann ◽  
Thomas Elsaesser
Keyword(s):  
Terahertz Spectroscopy ◽  
Two Dimensional ◽  
New Approach ◽  
Even Order

A nonlocal problem for a differential operator of even order with involution

2020 ◽  
Vol 26 (2) ◽  
pp. 297-307
Author(s):  
Petro I. Kalenyuk ◽  
Yaroslav O. Baranetskij ◽  
Lubov I. Kolyasa
Keyword(s):  
Differential Operator ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Riesz Basis ◽  
Existence And Uniqueness ◽  
Spectral Properties ◽  
Nonlocal Problem ◽  
Even Order

AbstractWe study a nonlocal problem for ordinary differential equations of {2n}-order with involution. Spectral properties of the operator of this problem are analyzed and conditions for the existence and uniqueness of its solution are established. It is also proved that the system of eigenfunctions of the analyzed problem forms a Riesz basis.

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