In this paper, we first give the maximal and minimal values of the ranks and inertias of the quadratic matrix functions q1(X) = Q1 − XP1X and q2(X) = Q2 − XP2X subject to a consistent matrix equation AX = B, where Q1, Q2, P1 and P2 are Hermitian matrices. As applications, we derive necessary and sufficient conditions for the solution of AX = B to satisfy the quadratic equality XP1X ∗ = Q1 and X...

Let K be a quadratic extension of Q, B a quaternion algebra over Q and A = B ⊗Q K. Let O be a maximal order in A extending an order in B. The projective norm one group PO1 is shown to be isomorphic to the spinorial kernel group O′(L), for an explicitly determined quadratic Z-lattice L of rank four, in several general situations. In other cases, only the local structures of O and L are given at ...

2. QUADRATIC TIME-FREQUENCY DISTRIBUTIONS AND AMBIGUITY FUNCTION In this paper, the properties Of the recently Proposed B-distribution are investigated. We show that this distribution satisfies most of the desirable properties sought for a time-frequency distribution. Quadratic (also known as Cohen’s) class of time-frequency distributions is defined by the following expression [31: That is, we ...

The paper deals with modeling of human head surface on the basis of quadratic triangular B-splines for the standard videocodec MPEG-4 SNHC. First, we define a triangular B-spline surface of any degree and then we present its calculation for modeling of the quadratic form. Next, we apply the quadratic triangular B-splines on modeling of the human head surface using 3D polygonal model Candide 3-1...

Let K be a field (characteristic # 2), and let L be a quadratic extension of K. Then L = K{yja) for some aeK. Let D be the quaternion algebra (a, b/K) generated by elements i, j satisfying i = a, j 2 = b, ij = —ji. We will assume that D is a division algebra, i.e. that the quadratic form <1> ~> ~b, ab} is anisotropic. Let — denote the standard involution on L and on D so that y/a = —*Ja on L an...

We consider the class of algebras of rank 4 equipped with a standard involution over an arbitrary base ring. In particular, we characterize quaternion rings, those algebras defined by the construction of the even Clifford algebra. A quaternion algebra is a central simple algebra of dimension 4 over a field F . Generalizations of the notion of quaternion algebra to other commutative base rings R...

For a considerable number of years, Oscar Kempthorne and I were colleagues in the Iowa State University Department of Statistics and shared the responsibility for the teaching of two graduate-level courses on linear models. The first of these was an M.S.-level course in which most, but not all, of the students were statistics majors and for which an introductory course in linear or matrix algeb...

The morphology of glacial valley can be described in terms of power law or quadratic equations fitted to valley cross-profiles. These two models are used to study the cross-profiles of 86 valley cross-profiles in the Zardkuh Mountain in order to understand the evolutional patterns of valleys. Assessment of using the power law function indicates that b values for both valley sides range from 1.0...

In this paper two disturbance decoupling problems without stability and with quadratic stability via dynamic output feedback for switched linear systems are investigated. Firstly, simultaneous (C,A,B)-pair which incorporates both the concept of simultaneous (A,B)-invariant subspace and its dual simultaneous (C,A)-invariant subspace for a family of linear systems are investigated. Secondly, dist...

In swine nutrition, little is known about the role of vitamin B(12) in the reproductive processes. The current study was undertaken to obtain information on the dose-response pattern of different metabolic criteria related to the homeostasis of vitamin B(12) and homocysteine in gestating sows receiving various concentrations of dietary vitamin B(12) (cyanocobalamin). Homocysteine is a detriment...