Asymptotic expansion for the number of solutions of the diophantine system of Hilbert-Kamke with increasing number of variables

1985 ◽  
Vol 29 (3) ◽  
pp. 1275-1289
Author(s):  
M. I. Israilov
Keyword(s):  
Asymptotic Expansion ◽  
Number Of Solutions ◽  
Diophantine System

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.

Influence of free convection on the diffusion current to a sphere in a laminar forced flow regime

1985 ◽  
Vol 50 (12) ◽  
pp. 2697-2714
Author(s):  
Arnošt Kimla ◽  
Jiří Míčka
Keyword(s):  
Asymptotic Expansion ◽  
Free Convection ◽  
Boundary Value Problem ◽  
Concentration Gradient ◽  
Empirical Formula ◽  
Convective Diffusion ◽  
Forced Flow ◽  
Diffusion Current ◽  
Wide Range ◽  
Free And Forced Convection

The formulation and solution of a boundary value problem is presented, describing the influence of the free convective diffusion on the forced one to a sphere for a wide range of Rayleigh, Ra, and Peclet, Pe, numbers. It is assumed that both the free and forced convection are oriented in the same sense. Numerical results obtained by the method of finite differences were approximated by an empirical formula based on an analytically derived asymptotic expansion for Pe → ∞. The concentration gradient at the surface and the total diffusion current calculated from the empirical formula agree with those obtained from the numerical solution within the limits of the estimated errors.

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