We give two new proofs of Winquist’s identity. In the first proof, we use basic properties of cube roots of unity and the Jacobi triple product identity. The latter does not use the Jacobi triple product identity.

We exhibit several families of Jacobi–Videv pseudo-Riemannian manifolds which are not Einstein. We also exhibit Jacobi–Videv algebraic curvature tensors where the Ricci operator defines an almost complex structure.

In this note, we give some estimate of the generalized quadrature formula of Gauss-Jacobi$$underset{a}{overset{a+eta left( b,aright) }{int }}left( x-aright)^{p}left( a+eta left( b,aright) -xright) ^{q}fleft( xright) dx$$in the cases where $f$ and $left| fright| ^{lambda }$ for $lambda >1$, are $s$-preinvex functions in the second sense.

We present a numerical method for a class of boundary value problems on the unit interval which feature a type of exponential and product nonlinearities. Also, we consider singular case. We construct a kind of spectral collocation method based on shifted Jacobi polynomials to implement this method. A number of specific numerical examples demonstrate the accuracy and the efficiency of the propos...

This report discusses the application of Jacobi-Davidson style methods in electric circuit simulation. Using the generalised eigenvalue problem, which arises from pole-zero analysis, as a starting point, both the JDQR-method and the JDQZ-method are studied. Although the JDQR-method (for the ordinary eigenproblem) and the JDQZ-method (for the generalised eigenproblem) are designed to converge fa...