A PROOF BY ELEMENTARY METHODS, WITHOUT COMPLEX QUANTITIES, THAT EVERY ALGEBRAIC FUNCTION (WITH REAL COEFFICIENTS) HAS FACTORS OF THE FORM (x2-px+q(p, q, REAL) AND HENCE, EVERY ALGEBRAIC EQUATION WITH COEFFICIENTS REAL OR IMAGINARY, HAS REAL OR IMAGINARY ROOTS EQUAL IN NUMBER TO THE DEGREE OF THE EQUATION

Initial coefficients of starlike functions with real coefficients

The sharp bounds for the third and fourth coefficients of Ma-Minda starlike functions having fixed second coefficient are determined. These results are proved by using certain constraint coefficient problem for functions with positive real part whose coefficients are real and the first coefficient is kept fixed. Analogous results are obtained for a general class of close-to-convex functions

[Bird flu: a real or imaginary threat?].

The therapeutic value of cannabinoids in MS: real or imaginary?

On the Number of Real Roots of a Random Algebraic Equation

1 . SOME time ago Littlewood and Offordt gave estimates of the number of real roots that an equation of degree n selected at random might be expected to have for various classes of equations in which the coefficients were selected on some probability basis . They found that, when each coefficient was treated on the same basis, the results were practically the same in all cases considered and ag...

Real Zeros of Algebraic Polynomials with Dependent Random Coefficients

The expected number of real zeros of polynomials a0+a1x+a2x+ · · · + an−1xn−1 with random coefficients is well studied. For n large and for the normal zero mean independent coefficients, irrespective of the distribution of coefficients, this expected number is known to be asymptotic to (2/π) logn. For the dependent cases studied so far it is shown that this asymptotic value remains O(logn). In ...