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The problem was subsequently shown to be equivalent to numerous open problems in pure mathematics, applied mathematics, engineering and computer science. [ 2 ] [ 3 ] Kadison, Singer, and most later authors believed the statement to be false, [ 2 ] [ 3 ] but, in 2013, it was proven true by Adam Marcus , Daniel Spielman and Nikhil Srivastava ...
In spite of these successes, there are still many problems that remain to be solved. One of the deepest problems in modern physics is the problem of quantum gravity. [1] The general theory of relativity is formulated within the framework of classical physics, whereas the other fundamental forces are described within the framework of quantum ...
The longitudinal stability of an aircraft, also called pitch stability, [2] refers to the aircraft's stability in its plane of symmetry [2] about the lateral axis (the axis along the wingspan). [1] It is an important aspect of the handling qualities of the aircraft, and one of the main factors determining the ease with which the pilot is able ...
Figure 1 shows a typical plot of the rate of crack growth as a function of the alternating stress intensity or crack tip driving force plotted on log scales. The crack growth rate behaviour with respect to the alternating stress intensity can be explained in different regimes (see, figure 1) as follows
The transformation can be thought of as the projection of the three phase quantities (voltages or currents) onto two stationary axes, the alpha axis and the beta axis. However, no information is lost if the system is balanced, as the equation I a + I b + I c = 0 {\displaystyle I_{a}+I_{b}+I_{c}=0} is equivalent to the equation for I γ ...
Angle of attack of an airfoil. In fluid dynamics, angle of attack (AOA, α, or ) is the angle between a reference line on a body (often the chord line of an airfoil) and the vector representing the relative motion between the body and the fluid through which it is moving. [1]
Transformation of three phase electrical quantities to two phase quantities is a usual practice to simplify analysis of three phase electrical circuits. Polyphase a.c machines can be represented by an equivalent two phase model provided the rotating polyphases winding in rotor and the stationary polyphase windings in stator can be expressed in a fictitious two axes coils.
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.