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The Laplacian spectral ratio R_L(G) of a connected graph G is defined as the ratio of its Laplacian spectral radius to its algebraic connectivity. If a connected graph of ...

For any algebraic number x of degree n>2, a rational approximation p/q to x must satisfy |x-p/q|>1/(q^n) for sufficiently large q. Writing r=n leads to the definition of the ...

A field which is complete with respect to a discrete valuation is called a local field if its field of residue classes is finite. The Hasse principle is one of the chief ...

The term "loop" has a number of meanings in mathematics. Most simply, a loop is a closed curve whose initial and final points coincide in a fixed point p known as the ...

Low-dimensional topology usually deals with objects that are two-, three-, or four-dimensional in nature. Properly speaking, low-dimensional topology should be part of ...

A surface which a monkey can straddle with both legs and his tail. A simple Cartesian equation for such a surface is z=x(x^2-3y^2), (1) which can also be given by the ...

In a set X equipped with a binary operation · called a product, the multiplicative identity is an element e such that e·x=x·e=x for all x in X. It can be, for example, the ...

The Ochoa curve is the elliptic curve 3Y^2=2X^3+386X^2+256X-58195, given in Weierstrass form as y^2=x^3-440067x+106074110. The complete set of 23 integer solutions (where ...

Let two disks of radius r intersect one another perpendicularly and have a diameter in common. If the distance between the centers of the disks is sqrt(2) times their radius, ...

Consider the decimal expansion of the reciprocal of the number seven, 1/7=0.142857142857...=0.142857^_, (1) which is a repeating decimal. Now take overlapping pairs of these ...