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Chaos theory is an interdisciplinary area of scientific study and branch of mathematics. It focuses on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions. These were once thought to have completely random states of disorder and irregularities. [1]
The Mandelbrot set (/ ˈmændəlbroʊt, - brɒt /) [1][2] is a two-dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified. It is popular for its aesthetic appeal and fractal structures. The set is defined in the complex plane as the complex numbers for which the function does not ...
Hopfield network. A Hopfield network (associative memory or Ising–Lenz–Little model or Nakano-Amari-Hopfield network) is a spin glass system used to model neural networks, based on Ernst Ising 's work with Wilhelm Lenz on the Ising model of magnetic materials. [1]
Falsifiability (or refutability) is a deductive standard of evaluation of scientific theories and hypotheses, introduced by the philosopher of science Karl Popper in his book The Logic of Scientific Discovery (1934). [B] A theory or hypothesis is falsifiable if it can be logically contradicted by an empirical test.
The Centers for Disease Control (CDC) says recalled eggs supplied by are linked to an ongoing salmonella outbreak. To date, 65 people across nine states have gotten sick from the same strain of ...
Although the complement of a fuzzy set has a single most common definition, the other main operations, union and intersection, do have some ambiguity. For a given fuzzy set A {\displaystyle A} , its complement ¬ A {\displaystyle \neg {A}} (sometimes denoted as A c {\displaystyle A^{c}} or c A {\displaystyle cA} ) is defined by the following ...
A fractal is formed when pulling apart two glue-covered acrylic sheets. High-voltage breakdown within a 4 in (100 mm) block of acrylic glass creates a fractal Lichtenberg figure. Romanesco broccoli, showing self-similar form approximating a natural fractal. Fractal defrosting patterns, polar Mars.
In mathematical analysis, the spaces of test functions and distributions are topological vector spaces (TVSs) that are used in the definition and application of distributions. Test functions are usually infinitely differentiable complex -valued (or sometimes real -valued) functions on a non-empty open subset that have compact support.