The manifold of a planar array in a direction finding system may be considered as two families of azimuth and elevation curves, where the-parameter curves are as well as while the-parameter curves hyperhelical geodesic are. Since the-curves are not hyperhelical, their curvatures depend on and neither so analytical evaluation of curvatures of order greater than two can become exceedingly laborio...

Spin models for link invariants were introduced by Jones [7], and their connection to combinatorics was revealed first in [4]. Jaeger and Nomura [6] constructed nonsymmetric spin models for link invariants from Hadamard matrices, and showed that these models give link invariants which depend nontrivially on link orientation. These models are a modification of the Hadamard model originally const...

We characterize the natural diagonal almost product (locally product) structures on the tangent bundle of a Riemannian manifold. We obtain the conditions under which the tangent bundle endowed with the determined structure and with a metric of natural diagonal lift type is a Riemannian almost product (locally product) manifold, or an (almost) para-Hermitian manifold. We find the natural diagona...

The moment map is a mathematical expression of the concept of the conservation associated with the symmetries of a Hamiltonian system. The abstract moment map is defined from G-manifold M to dual Lie algebra of G. We will interested study maps from G-manifold M to spaces that are more general than dual Lie algebra of G. These maps help us to reduce the dimension of a manifold much more.

The precoding scheme based on real Hadamard transform is an effective and flexible way for reducing the peak-to-average power ratio (PAPR) of OFDM signals. However, the reduction capacity of PAPR is limited for real Hadamard transform method. In this paper, the new scheme based on complex Hadamard transform is proposed. The simulation results indicate that the proposed scheme may obtain a 1.2 d...

In 1933 a family of skew Hadamard difference sets was described by Paley using matrix language and was called the Paley–Hadamard difference sets in the literature. During the last 70 years, no new skew Hadamard difference sets were found. It was conjectured that there are no further examples of skew Hadamard difference sets. This conjecture was proved to be true for the cyclic case in 1954, and...

Let (X, g) be a product cone with the metric $$g=dr^2+r^2h$$ , where $$X=C(Y)=(0,\infty )_r\times Y$$ and cross section Y is $$(n-1)$$ -dimensional closed Riemannian manifold (Y, h). We study upper boundedness of heat kernel associated operator $${\mathcal {L}}_V=-\Delta _g+V_0 r^{-2}$$ $$-\Delta _g$$ positive Friedrichs extension Laplacian on X $$V=V_0(y) $$V_0\in {\mathcal {C}}^\infty (Y)$$ r...

It is known that there are exactly b t−1 2 c and b t 2c nonequivalent Z2Z4-linear Hadamard codes of length 2t , with α = 0 and α 6= 0, respectively, for all t ≥ 3. In this paper, it is shown that each Z2Z4-linear Hadamard code with α = 0 is equivalent to a Z2Z4-linear Hadamard code with α 6= 0, so there are only b t 2c nonequivalent Z2Z4-linear Hadamard codes of length 2t . Moreover, the orders...

In this paper, we generalize the Hadamard transform to the the case of lapped transform A matrix A(z) is a lapped Hadamard transform if it satisfies A ~ ( ~ ' ) A ( ~ ) = a~ for some integer a and all the entries of its coefficient matrices are i1. Many methods have been proposed to construct lapped Hadamard matrices. In this paper, we will study these matrices using the theory of paraunitary f...