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Second-order logic. In logic and mathematics, second-order logic is an extension of first-order logic, which itself is an extension of propositional logic. [ 1] Second-order logic is in turn extended by higher-order logic and type theory . First-order logic quantifies only variables that range over individuals (elements of the domain of ...
A recurrence relation is an equation that expresses each element of a sequence as a function of the preceding ones. More precisely, in the case where only the immediately preceding element is involved, a recurrence relation has the form. where. is a function, where X is a set to which the elements of a sequence must belong.
The coefficient of relationship is sometimes used to express degrees of kinship in numeric terms in human genealogy. In human relationships, the value of the coefficient of relationship is usually calculated based on the knowledge of a full family tree extending to a comparatively small number of generations, perhaps of the order of three or four.
Higher order coherence. In quantum optics, correlation functions are used to characterize the statistical and coherence properties – the ability of waves to interfere – of electromagnetic radiation, like optical light. Higher order coherence or n-th order coherence (for any positive integer n >1) extends the concept of coherence to quantum ...
In mathematical finance, the Greeks are the quantities (known in calculus as partial derivatives; first-order or higher) representing the sensitivity of the price of a derivative instrument such as an option to changes in one or more underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent.
The relationship of first-order and second-order cybernetics can be compared to that between Isaac Newton's view of the universe and that of Albert Einstein. [1] Just as Newton's description remains appropriate and usable in many circumstances, even flights to the moon, so first-order cybernetics also provides everything that is needed in many ...
A second-order Butterworth filter (i.e., continuous-time filter with the flattest passband frequency response) has an underdamped Q = 1 ⁄ √ 2. [ 11 ] A pendulum's Q-factor is: Q = M ω / Γ {\textstyle Q={M\omega }/{\Gamma }} , where M is the mass of the bob, ω = 2π/ T is the pendulum's radian frequency of oscillation, and Γ is the ...
Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and provides basic definitions.