In this letter, we introduce some mathematical and numerical tools to analyze and interpret inhomogeneous quadratic forms. The resulting characterization is in some aspects similar to that given by experimental studies of cortical cells, making it particularly suitable for application to second-order approximations and theoretical models of physiological receptive fields. We first discuss two w...

We study 2-incompressible Grassmannians of isotropic subspaces of a quadratic form, of a hermitian form over a quadratic extension of the base field, and of a hermitian form over a quaternion algebra.

This paper studies the solution of quadratic eigenvalue problems by the quadratic residual iteration method. The focus is on applications arising from nite-element simulations in acoustics. One approach is the shift-invert Arnoldi method applied to the linearized problem. When more than one eigenvalue is wanted, it is advisable to use locking or de-ation of converged eigenvectors (or Schur vect...

It is well known that the Riemann Zeta function ζ ( p ) = ∑∞n=1 1/np can be represented in closed form for p an even integer. We will define a shifted quadratic Zeta series as ∑∞ n=1 1/ ( 4n2−α2)p . In this paper, we will determine closed-form representations of shifted quadratic Zeta series from a recursion point of view using the Riemann Zeta function. We will also determine closed-form repre...

It is well known that every non-degenerate quadratic form admits a decomposition into an orthogonal sum of its anisotropic part and hyperbolic form. This unique up to isometry. In this paper we present algorithm for constructing given with coefficients in arbitrary number field.

‎A conditional test based on quadratic form using type-2 censored sample for testing exponentiality against Weibull alternative is proposed‎. ‎The simulated percentage points and powers are given‎. ‎The proposed test performs well for identifying Weibull DFR alternative even for small sample‎. ‎An example is also given.

This article presents a test based on quadratic form using Type-2 with replacement-censored sample for testing exponentiality against weibull IFR/DFR alternative. The percentile points and powers are simulated. The proposed test is compared with that of Bain and Engelhardt (1986) test. An example based on Type-2 censoring is also discussed.