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...

Soybean is a type of food crop with economic benefits. Whether they are damaged or not directly affects the survival and nutritional value soybean plants. In machine learning, unbalanced data represent major factor affecting learning efficiency, refer to category in which number samples one much larger than that other, biases classification results towards large thus accuracy. Therefore, effect...

We consider the wave equation on a strictly convex domain of dimension at least two with smooth non empty boundary and Dirichlet conditions. construct sharp local in time parametrix then proceed to obtain dispersion estimates: our fixed decay rate for Green function exhibits $t^{1/4}$ loss respect less case. Moreover, we precisely describe where when these losses occur relate them swallowtail t...