‎‎In the category of Mordell curves (E_D:y^2=x^3+D) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (E_1), ‎and of the generic rank at least two and at least three as cubic twists of (E_1). ‎Previous work‎, ‎in the category of Mordell curves with trivial torsion groups‎, ‎has found infinitely many elliptic curves with ...

‎‎in the category of mordell curves (e_d:y^2=x^3+d) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (e_1), ‎and of the generic rank at least two and at least three as cubic twists of (e_1). ‎previous work‎, ‎in the category of mordell curves with trivial torsion groups‎, ‎has found infinitely many elliptic curves with rank at least seven as sextic tw...

This paper is a continuation of Kantor (4, 6] and Ronan [10]. We will construct finite and infinite 'geometries' admitting flag-transitive groups and having buildings as universal covers. The first building is that of {1+ (6, (Ji2); the remaining ones are new and strange. As in the aforementioned papers, our motivation is the search for finite geometries that strongly resemble buildings, and fo...

By combining results from a Doppler-free two-photon laser excitation study on several lines in the EF'g X 'g (0,0) band of H2 with results from a Fourier-transform spectroscopic study on a low-pressure discharge in hydrogen, absolute level energies, with respect to the X g , v1⁄4 0, N1⁄4 0 ground level, were determined for 547 rovibronically excited states in H2. While for some of the levels in...

In this paper, assuming that (X, Y1, Y2)T has a trivariate normal distribution, we derive the exact joint distribution of ( X, Y(1), Y(2))^T, where Y(1) and Y(2) are order statistics arising from (Y1, Y2)T . We show that this joint distribution is a mixture of truncated trivariate normal distributions and then use this mixture representation to derive the best (nonlinear) predictiors of X...

In this paper‎, ‎we study the extremal‎ ‎ranks and inertias of the Hermitian matrix expression $$‎ ‎f(X,Y)=C_{4}-B_{4}Y-(B_{4}Y)^{*}-A_{4}XA_{4}^{*},$$ where $C_{4}$ is‎ ‎Hermitian‎, ‎$*$ denotes the conjugate transpose‎, ‎$X$ and $Y$ satisfy‎ ‎the following consistent system of matrix equations $A_{3}Y=C_{3}‎, ‎A_{1}X=C_{1},XB_{1}=D_{1},A_{2}XA_{2}^{*}=C_{2},X=X^{*}.$ As‎ ‎consequences‎, ‎we g...