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In 2020, it was announced that Google's AlphaFold, a neural network based on DeepMind artificial intelligence, is capable of predicting a protein's final shape based solely on its amino-acid chain with an accuracy of around 90% on a test sample of proteins used by the team.
If a system initially rests at its equilibrium position, from where it is acted upon by a unit-impulse at the instance t=0, i.e., p(t) in the equation above is a Dirac delta function δ(t), () = | = =, then by solving the differential equation one can get a fundamental solution (known as a unit-impulse response function)
As a result, the nascent delta functions that arise as fundamental solutions of the associated Cauchy problems are generally oscillatory integrals. An example, which comes from a solution of the Euler–Tricomi equation of transonic gas dynamics , [ 61 ] is the rescaled Airy function ε − 1 / 3 Ai ( x ε − 1 / 3 ) . {\displaystyle ...
the solution of the initial-value problem = is the convolution (). Through the superposition principle , given a linear ordinary differential equation (ODE), L y = f {\displaystyle Ly=f} , one can first solve L G = δ s {\displaystyle LG=\delta _{s}} , for each s , and realizing that, since the source is a sum of delta functions , the solution ...
In chemistry, reactivity is the impulse for which a chemical substance undergoes a chemical reaction, either by itself or with other materials, with an overall release of energy. Reactivity refers to: the chemical reactions of a single substance, the chemical reactions of two or more substances that interact with each other,
An advantage of the plug flow model is that no part of the solution of the problem can be perpetuated "upstream". This allows one to calculate the exact solution to the differential equation knowing only the initial conditions. No further iteration is required. Each "plug" can be solved independently provided the previous plug's state is known.
The impulse responses of two exponentially stable systems. The graph on the right shows the impulse response of two similar systems. The green curve is the response of the system with impulse response () =, while the blue represents the system () = ().
In solution chemistry and biochemistry, the Gibbs free energy decrease (∂G/∂ξ, in molar units, denoted cryptically by ΔG) is commonly used as a surrogate for (−T times) the global entropy produced by spontaneous chemical reactions in situations where no work is being done; or at least no "useful" work; i.e., other than perhaps ± P dV.