The characterization of automorphisms of Bernstein algebras is an open problem. We only know some particular results. Previously we have characterized the automorphisms of quasiorthogonal, orthogonal, and strongly orthogonal weak Bernstein-Jordan algebras. In this paper we work on the minimal dimension with respect to quasiorthogonality, orthogonality, and strong orthogonality. We establish som...

In this article, we present what we believe to be a simple way to motivate the use of Hilbert spaces in quantum mechanics. To achieve this, we study the way the notion of dimension can, at a very primitive level, be defined as the cardinality of a maximal collection of mutually orthogonal elements (which, for instance, can be seen as spatial directions). Following this idea, we develop a formal...

A logic of orthogonality characterizes all “orthogonality consequences” of a given class Σ of morphisms, i.e. those morphisms s such that every object orthogonal to Σ is also orthogonal to s. A simple four-rule deduction system is formulated which is sound in every cocomplete category. In locally presentable categories we prove that the deduction system is also complete (a) for all classes Σ of...

In this paper, transmit Beamforming (BF) for Space Division Multiple Access (SDMA) is studied in the downlink of wireless cellular systems based on Multi-Carrier Code Division Multiple Access (MC-CDMA). This combination allows a separation of users’ signals in space, thanks to BF, and frequency, thanks to CDMA, and thus improves mitigation of multiple access interference. We propose to perform ...

The arguments by Pandres that the double valued spherical harmonics provide a basis for the irreducible spinor representation of the three dimensional rotation group are further developed and justified. The usual arguments against the inadmissibility of such functions, concerning hermiticity, orthogonality, behavior under rotations, etc., are all shown to be related to the unsuitable choice of ...

Let (S1,S2) be a bi-isometry, that is, pair of commuting isometries S1 and S2 on complex Hilbert space H. By the von Neumann-Wold decomposition, hyper-range H∞(S1):=∩n=0∞S1nH reduces to unitary operator. Although H∞(S1) is an invariant subspace for S2, in general, not reducing S2. We show isometry if only subspaces S2(ker⁡S1⁎) H are orthogonal. Further, we describe all bi-isometries satisfying ...

This paper describes the results obtained from the merging of two techniques that provide improvements to search and retrieval using Latent Semantic Indexing (LSI): Essential Dimensions of LSI (EDLSI) and partial singular value decomposition (PSVD) updating. EDLSI utilizes an implementation of LSI that requires the use of only a few dimensions in the LSI space. The PSVD updating and folding-up ...

We explain why and how the Hilbert space comes about in quantum theory. The axiomatic structures of vector space, scalar product, orthogonality, linear functional are derivable from statistical description micro-events Hilbertian sum squares $|\mathfrak{a}_1|^2+|\mathfrak{a}_2|^2+\cdots$. latter leads (non-axiomatically) to standard writing Born formula $\mathtt{f} = |\langle\psi|\varphi\rangle...

Under the mild condition of continuity at a single point we describe all the bijections of the set of all partial isometries on a Hilbert space which preserve the order and the orthogonality in both directions. Moreover, we present a natural analogue of Wigner’s theorem on quantum mechanical symmetries for the set of all rank-1 partial isometries. In the mathematical foundations of quantum mech...