scholarly journals A note on asymptotic existence results for orthogonal designs

Author(s):  
Peter Eades ◽  
Jennifer Seberry Wallis ◽  
Nicholas Wormald
2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Ebrahim Ghaderpour

Orthogonal designs and weighing matrices have many applications in areas such as coding theory, cryptography, wireless networking, and communication. In this paper, we first show that if positive integer k cannot be written as the sum of three integer squares, then there does not exist any skew-symmetric weighing matrix of order 4n and weight k, where n is an odd positive integer. Then we show that, for any square k, there is an integer N(k) such that, for each n≥N(k), there is a symmetric weighing matrix of order n and weight k. Moreover, we improve some of the asymptotic existence results for weighing matrices obtained by Eades, Geramita, and Seberry.


2020 ◽  
Vol 57 (3) ◽  
pp. 775-791
Author(s):  
David Dereudre ◽  
Thibaut Vasseur

AbstractWe provide a new proof of the existence of Gibbs point processes with infinite range interactions, based on the compactness of entropy levels. Our main existence theorem holds under two assumptions. The first one is the standard stability assumption, which means that the energy of any finite configuration is superlinear with respect to the number of points. The second assumption is the so-called intensity regularity, which controls the long range of the interaction via the intensity of the process. This assumption is new and introduced here since it is well adapted to the entropy approach. As a corollary of our main result we improve the existence results by Ruelle (1970) for pairwise interactions by relaxing the superstabilty assumption. Note that our setting is not reduced to pairwise interaction and can contain infinite-range multi-body counterparts.


Author(s):  
Shengli Xie

AbstractIn this paper we prove the existence and uniqueness of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay in Banach spaces. We generalize the existence theorem for integer order differential equations to the fractional order case. The results obtained here improve and generalize many known results.


2002 ◽  
Vol 9 (2) ◽  
pp. 287-294
Author(s):  
Tadeusz Jankowski

Abstract The method of lower and upper solutions combined with the monotone iterative technique is used for ordinary differential equations with nonlinear boundary conditions. Some existence results are formulated for such problems.


2020 ◽  
Vol 7 (1) ◽  
pp. 272-280
Author(s):  
Mamadou Abdoul Diop ◽  
Kora Hafiz Bete ◽  
Reine Kakpo ◽  
Carlos Ogouyandjou

AbstractIn this work, we present existence of mild solutions for partial integro-differential equations with state-dependent nonlocal local conditions. We assume that the linear part has a resolvent operator in the sense given by Grimmer. The existence of mild solutions is proved by means of Kuratowski’s measure of non-compactness and a generalized Darbo fixed point theorem in Fréchet space. Finally, an example is given for demonstration.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed Nouara ◽  
Abdelkader Amara ◽  
Eva Kaslik ◽  
Sina Etemad ◽  
Shahram Rezapour ◽  
...  

AbstractIn this research work, a newly-proposed multiterm hybrid multi-order fractional boundary value problem is studied. The existence results for the supposed hybrid fractional differential equation that involves Riemann–Liouville fractional derivatives and integrals of multi-orders type are derived using Dhage’s technique, which deals with a composition of three operators. After that, its stability analysis of Ulam–Hyers type and the relevant generalizations are checked. Some illustrative numerical examples are provided at the end to illustrate and validate our obtained results.


Author(s):  
Haiffa Muhsan B. Alrikabi ◽  
Ayed E. Hashoosh ◽  
Ahmed A. H. Alkhalidi

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