New constructions for amicable orthogonal designs are given. These new designs then give new amicable Hadamard matrices and new skew-Hadamard matrices. In particular we show that if p is the order of normalized amicable Hadamard matrices there are normalized amicable Hadamard matrices of order (p 1)u + 1, u > 0 an odd integer. Tables are given for the existence of amicable and skew-Hadamard mat...

We prove that if there exist Hadamard matrices of order 4m, 4n, 4p, 4q then there exists an Hadamard matrix of order 16mnpq. This improves and extends the known result of Agayan that there exists an Hadamard matrix of order 8mn if there exist Hadamard matrices of order 4m and 4n.

‎This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$‎. ‎Some applications to these inequalities are also given‎. ‎In addi...

The present article serves the purpose of pursuing Geometrization of heat flow on volumetrically isothermal manifold by means of RF approach. In this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of Riemannian manifold and fundamental properties of thermodynamic systems. By making use of the notions of various curva...

We define several operations that switch substructures of Hadamard matrices thereby producing new, generally inequivalent, Hadamard matrices. These operations have application to the enumeration and classification of Hadamard matrices. To illustrate their power, we use them to greatly improve the lower bounds on the number of equivalence classes of Hadamard matrices in orders 32 and 36 to 3,578...

In this paper we study a one-dimensional quantum random walk with the Hadamard transformation which is often called the Hadamard walk. We construct the Hadamard walk using a transition matrix on probability amplitude and give some results on symmetry of probability distributions for the Hadamard walk.

A manifold with a smooth action of a Lie group G is called G-manifold. In this paper we consider a complete Riemannian manifold M with the action of a closed and connected Lie subgroup G of the isometries. The dimension of the orbit space is called the cohomogeneity of the action. Manifolds having actions of cohomogeneity zero are called homogeneous. A classic theorem about Riemannian manifolds...

In this paper, we obtain a necessary and sufficient condition for a conformal mapping between two Weyl manifolds to preserve Einstein tensor. Then we prove that some basic curvature tensors of $W_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. Also, we obtained the relation between the scalar curvatures of the Weyl manifolds r...

Abstract We obtain a comparison formula for integrals of mean curvatures Riemannian hypersurfaces via Reilly’s identities. As applications, we derive several geometric inequalities convex hypersurface Γ \Gamma in Cartan-Hadamard manifold M M . In particular, show that the first curvatu...

Abstract Given a pair of normally hyperbolic operators over (possibnly different) globally spacetimes on given smooth manifold, the existence geometric isomorphism, called Møller operator , between space solutions is studied. This achieved by exploiting new equivalence relation in metrics, paracausal . In particular, it shown that associated to paracausally related metrics and also intertwines ...