Uniform expansion

We prove that Cayley graphs of SL2 (Fp ) are expanders with respect to the projection of any fixed elements in SL(2, Z) generating a non-elementary subgroup, and with respect to generators chosen at random in SL2 (Fp ). 1. Introduction Expanders are highly-connected sparse graphs widely used in computer science, in areas ranging from parallel computation to complexity theory and cryptography; recently they also have found some remarkable applications in pure mathematics; see [5],[10], [15], [20], [21] and references therein. ...

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The atomic theory of matter asserts that material bodies are made up of small particles. This theory was founded in ancient times by Democritus and expressed in poetic form by Lucretius. This view was challenged by the opposite theory, according to which matter is a continuous expanse.

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Responding to the demands of increased regulatory requirements, international expansion, and increased acquisition activity requires flexibility. Rules, network reliability, and business processes can vary widely across geographies and product lines. IT systems must accommodate these challenges both functionally and technically. Oracle FLEXCUBE Core Banking supports several deployment options that allow banks to provide services uniformly across all channels and markets.

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