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1 ημέρα πριν · This non-commutativity has some unexpected consequences, among them that a polynomial equation over the quaternions can have more distinct solutions than the degree of the polynomial. For example, the equation z 2 + 1 = 0 , has infinitely many quaternion solutions, which are the quaternions z = b i + c j + d k such that b 2 + c 2 + d 2 = 1 .
1 ημέρα πριν · These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
1 ημέρα πριν · Jules Henri Poincaré (UK: / ˈ p w æ̃ k ɑːr eɪ /, US: / ˌ p w æ̃ k ɑː ˈ r eɪ /; French: [ɑ̃ʁi pwɛ̃kaʁe] ⓘ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science.He is often described as a polymath, and in mathematics as "The Last Universalist", since he excelled in all fields of the discipline as it existed ...
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1 ημέρα πριν · Summarise this content to 300 words 1. Introduction Alzheimer's disease (AD) is a neurodegenerative disease with insidious onset and progressive development. Clinically, AD is characterized by memory disorder, aphasia, apraxia, agnosia, visual skill damage, and general dementia with personality and behavior changes. However, the cause of the disease remains unknown. Currently, there is no accurate
