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Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 [1] and republished in 1999. [2] Smale composed this list in reply to a request from Vladimir Arnold, then vice-president of the International Mathematical Union, who asked several mathematicians to propose a list of problems for the 21st century.
de Bruijn's theorem: A box can be packed with a harmonic brick a × a b × a b c if the box has dimensions a p × a b q × a b c r for some natural numbers p, q, r (i.e., the box is a multiple of the brick.) [15]
In number theory, the divisor summatory function is a function that is a sum over the divisor function. It frequently occurs in the study of the asymptotic behaviour of the Riemann zeta function . The various studies of the behaviour of the divisor function are sometimes called divisor problems .
g(x) is a constant, a polynomial function, exponential function , sine or cosine functions or , or finite sums and products of these functions (, constants). The method consists of finding the general homogeneous solution y c {\displaystyle y_{c}} for the complementary linear homogeneous differential equation
Pressed Spring is seen to expand while valve is opened manually, so helps to open the valve. In reality this spring functions the opposite way. 2. No blank frames between emptied tube (elastic vessel) and filled tube give the impression that the tube is filled quick but live in the animation. Being in conflict with the valve that stays closed.
The control grid is an electrode used in amplifying thermionic valves (vacuum tubes) such as the triode, tetrode and pentode, used to control the flow of electrons from the cathode to the anode (plate) electrode. The control grid usually consists of a cylindrical screen or helix of fine wire surrounding the cathode, and is surrounded in turn by ...
One of the more natural choices is the box topology, where a base is given by the Cartesian products of open sets in the component spaces. [1] Another possibility is the product topology , where a base is also given by the Cartesian products of open sets in the component spaces, but only finitely many of which can be unequal to the entire ...
The problem is the following question: can every continuous function of three variables be expressed as a composition of finitely many continuous functions of two variables? The affirmative answer to this general question was given in 1957 by Vladimir Arnold, then only nineteen years old and a student of Andrey Kolmogorov. Kolmogorov had shown ...