On the number of solutions of a diophantine system

1969 ◽  
Vol 20 (1-2) ◽  
pp. 185-191 ◽  
Author(s):  
I. Kátai ◽  
J. Mogyoródi
Keyword(s):  
Number Of Solutions ◽  
Diophantine System

scholarly journals Almost prime solutions to diophantine systems of high rank

2016 ◽  
Vol 13 (06) ◽  
pp. 1491-1514 ◽  
Author(s):  
Ákos Magyar ◽  
Tatchai Titichetrakun
Keyword(s):  
High Rank ◽  
Expected Number ◽  
Number Of Solutions ◽  
Linear Forms ◽  
Bounded Number ◽  
Integral Forms ◽  
Diophantine System ◽  
Linearly Independent ◽  
Integer Solutions ◽  
Almost Prime

Let [Formula: see text] be a family of [Formula: see text] integral forms of degree [Formula: see text] and [Formula: see text] be a family of pairwise linearly independent linear forms in [Formula: see text] variables [Formula: see text]. We study the number of solutions [Formula: see text] to the diophantine system [Formula: see text] under the restriction that [Formula: see text] has a bounded number of prime factors for each [Formula: see text]. We show that the system [Formula: see text] that has the expected number of such “almost prime” solutions under similar conditions was established for existence of integer solutions by Birch.

Researching the factors influencing the satisfaction of master students at VNU School of Interdisciplinary Studies

2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Do Huy Thuong ◽  
Nguyen Thi Phuong Hong
Keyword(s):  
Service Industry ◽  
Interdisciplinary Studies ◽  
Number Of Solutions ◽  
Factors Affecting ◽  
Training Institutions ◽  
Market Needs ◽  
Market Strategies ◽  
Students Satisfaction ◽  
Training Service

Improving the quality in order to keep up with the trend in the world is the vital task of training institutions today. Training institutions need to grasp market needs and satisfy the requirements of customers - learners. Nadiri, H., Kandampully, J & Hussain, K. (2009) argue that the managers in education need to apply market strategies that are being used by manufacturing and business enterprises and need to be aware that the role of training institutions is a service industry which is responsible for satisfying learner needs (Elliott & Shin, 2002). Currently, there have been many researches on students’ satisfaction. However, each research has its own objectives and is conducted on different scales. This study is implemented to provide information about the factors affecting master students’ satisfaction with the training service at VNU School of Interdisciplinary Studies (VNU SIS). Through it, the research offers a number of solutions to improving the satisfaction level of the master students at VNU SIS in the coming time.

scholarly journals Existence and Concentration Behavior of Solutions of the Critical Schrödinger–Poisson Equation in R3

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 464
Author(s):  
Jichao Wang ◽  
Ting Yu
Keyword(s):  
Poisson Equation ◽  
Existence Result ◽  
Critical Growth ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Number Of Solutions ◽  
Concentration Behavior ◽  
The Relationship ◽  
Concentration Phenomenon

In this paper, we study the singularly perturbed problem for the Schrödinger–Poisson equation with critical growth. When the perturbed coefficient is small, we establish the relationship between the number of solutions and the profiles of the coefficients. Furthermore, without any restriction on the perturbed coefficient, we obtain a different concentration phenomenon. Besides, we obtain an existence result.

scholarly journals On polytopes and generalizations of the KLT relations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Nikhil Kalyanapuram
Keyword(s):  
Scattering Amplitudes ◽  
Large Class ◽  
Moduli Space ◽  
Differential Forms ◽  
Natural Generalization ◽  
Intersection Theory ◽  
Hyperplane Arrangements ◽  
Number Of Solutions ◽  
Scalar Theories ◽  
Double Copy

Abstract We combine the technology of the theory of polytopes and twisted intersection theory to derive a large class of double copy relations that generalize the classical relations due to Kawai, Lewellen and Tye (KLT). To do this, we first study a generalization of the scattering equations of Cachazo, He and Yuan. While the scattering equations were defined on ℳ0, n — the moduli space of marked Riemann spheres — the new scattering equations are defined on polytopes known as accordiohedra, realized as hyperplane arrangements. These polytopes encode as patterns of intersection the scattering amplitudes of generic scalar theories. The twisted period relations of such intersection numbers provide a vast generalization of the KLT relations. Differential forms dual to the bounded chambers of the hyperplane arrangements furnish a natural generalization of the Bern-Carrasco-Johansson (BCJ) basis, the number of which can be determined by counting the number of solutions of the generalized scattering equations. In this work the focus is on a generalization of the BCJ expansion to generic scalar theories, although we use the labels KLT and BCJ interchangeably.

scholarly journals Characterization of Degenerate Configurations in Attitude Determination of Three-Vehicle Heterogeneous Formations

Sensors ◽  
2021 ◽  
Vol 21 (14) ◽  
pp. 4631
Author(s):  
Pedro Cruz ◽  
Pedro Batista
Keyword(s):  
Unique Solution ◽  
Multiple Solutions ◽  
Attitude Determination ◽  
Line Of Sight ◽  
Number Of Solutions ◽  
Relative Line ◽  
Heterogeneous Formations ◽  
Heterogeneous Formation

The existence of multiple solutions to an attitude determination problem impacts the design of estimation schemes, potentially increasing the errors by a significant value. It is therefore essential to identify such cases in any attitude problem. In this paper, the cases where multiple attitudes satisfy all constraints of a three-vehicle heterogeneous formation are identified. In the formation considered herein, the vehicles measure inertial references and relative line-of-sight vectors. Nonetheless, the line of sight between two elements of the formation is restricted, and these elements are denoted as deputies. The attitude determination problem is characterized relative to the number of solutions associated with each configuration of the formation. There are degenerate and ambiguous configurations that result in infinite or exactly two solutions, respectively. Otherwise, the problem has a unique solution. The degenerate configurations require some collinearity between independent measurements, whereas the ambiguous configurations result from symmetries in the formation measurements. The conditions which define all such configurations are determined in this work. Furthermore, the ambiguous subset of configurations is geometrically interpreted resorting to the planes defined by specific measurements. This subset is also shown to be a zero-measure subset of all possible configurations. Finally, a maneuver is simulated to illustrate and validate the conclusions. As a result of this analysis, it is concluded that, in general, the problem has one attitude solution. Nonetheless, there are configurations with two or infinite solutions, which are identified in this work.

scholarly journals Ranked solutions of the matric equationA1X1=A2X2

1980 ◽  
Vol 3 (2) ◽  
pp. 293-304 ◽  
Author(s):  
A. Duane Porter ◽  
Nick Mousouris
Keyword(s):  
Finite Field ◽  
Number Of Solutions

LetGF(pz)denote the finite field ofpzelements. LetA1bes×mof rankr1andA2bes×nof rankr2with elements fromGF(pz). In this paper, formulas are given for finding the number ofX1,X2overGF(pz)which satisfy the matric equationA1X1=A2X2, whereX1ism×tof rankk1, andX2isn×tof rankk2. These results are then used to find the number of solutionsX1,…,Xn,Y1,…,Ym,m,n>1, of the matric equationA1X1…Xn=A2Y1…Ym.

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