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Often, constructing local balance equations is equivalent to removing the outer summations in the global balance equations for certain terms. [ 1 ] During the 1980s it was thought local balance was a requirement for a product-form equilibrium distribution , [ 10 ] [ 11 ] but Gelenbe 's G-network model showed this not to be the case.
Al-Jabr (Arabic: الجبر), also known as The Compendious Book on Calculation by Completion and Balancing (Arabic: الكتاب المختصر في حساب الجبر والمقابلة, al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah; [b] or Latin: Liber Algebræ et Almucabola), is an Arabic mathematical treatise on algebra written in Baghdad around 820 by the Persian polymath ...
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Balancing and buck passing are the main strategies for preserving the balance of power and preventing a potential hegemon's rise. [78] Instead of balancing against an aggressor, some states instead choose to "pass the buck" whereby instead of taking action to prevent a potential rise, it will pass the responsibility on to another state.
Balancing can be carried out through internal or external efforts and means. Internal balancing involves efforts to enhance state's power by increasing one's economic resources and military strength in order to be able to rely on independent capabilities in response to a potential hegemon and be able to compete more effectively in the international system.
A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [13] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...
Consider the average number of particles with particle properties denoted by a particle state vector (x,r) (where x corresponds to particle properties like size, density, etc. also known as internal coordinates and, r corresponds to spatial position or external coordinates) dispersed in a continuous phase defined by a phase vector Y(r,t) (which again is a function of all such vectors which ...
The first "balancing" of books, or the balance sheet financial statement in accounting is to check iterations (trial balance) to be sure the equation above applies, and where assets and liabilities are unequal, to equalize them by debiting or crediting owner's equity [2] (i.e. if assets exceed liabilities, equity is increased, if liabilities ...