In this note I establish a ’’Birkhoff’s type theorem’’ for the most general second‐order vector–tensor theory of gravitation and electromagnetism, which is such that its field equations are (i) ...

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The reciprocal relationship between conservation laws and symmetries is established for those theories wherein the equations of motion are derivable from a variational principle. It is shown, for a ...

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In this paper, a semilinear elliptic equation of fractional order is constructed by combining the semilinear elliptic equation with the fractional order equation. On this basis, the “standardized” ...

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The Pythagorean Theorem—discovered by the Greek mathematician Pythagoras in the 6th century BCE—is a cornerstone of mathematics. Simply stated as a 2 + b 2 = c 2, the theorem posits that the sum of ...

Two high school seniors have presented their proof of the Pythagorean theorem using trigonometry — which mathematicians thought to be impossible — at an American Mathematical Society meeting. When you ...

Abstract: A simple variational theorem for the dispersion relations and propagation constants of periodic waveguides is derived. The trial fields used in the variational formula incorporate all the ...