the main objective of an extrusion die is flow balancing as an unbalanced flow causes a distorted product together with residual stress. in this paper a strategy is presented for flow balancing a u-shaped profile with different wall thicknesses. for this purpose, a choker bar is provided at thicker wall to locally restrict excessive flow passing through the thicker section. for optimal design s...

Balancing numbers n and balancers r are solutions of the Diophantine equation 1 + 2 + . . . + (n 1) = (n + 1) + (n + 2) + . . . + (n + r). It is well-known that if n is a balancing number, then 8n2 + 1 is a perfect square and its positive square root is called a Lucas-balancing number. In this paper, some new identities involving balancing and Lucas-balancing numbers are obtained. Some divisibi...

1. BALANCING NUMBERS We call an Integer n e Z a balancing number if 1+ 2+ --+ (»l ) = (w + l) + (w + 2) +••• + (» + >•) (1) for some r e Z. Here r is called the balancer corresponding to the balancing number n. For example, 6, 35, and 204 are balancing numbers with balancers 2, 14, and 84, respectively. It follows from (1) that, if n is a balancing number with balancer r, then n2^(n + r)(n + r ...

designing the self-balancing two-wheeled mobile robots and reducing undesired vibrations are of great importance. for this purpose, the majority of researches are focused on application of relatively complex control approaches without improving the robot structure. therefore, in this paper we introduce a new two-wheeled mobile robot which, despite its relative simple structure, fulfills the req...

Load Balancing is the standout amongst the most noteworthy parts in circulated situations. As Cloud Computing is outstanding amongst other stage that gives stockpiling of information in extremely insignificant cost and available forever finished the internet, load balancing for the cloud computing has transformed into an exceptionally intriguing and imperative investigation region. Load balanci...