In this paper we define a Poincaré-Reidemeister scalar product on the determinant line of the cohomology of any flat vector bundle over a closed orientable odd-dimensional manifold. It is a combinatorial “torsion-type” invariant which refines the PR-metric introduced in [Fa] and contains an additional sign or phase information. We compute the PR-scalar product in terms of the torsions of Euler ...

The standard block orthogonal (SBO) polynomials Pi;n(x), 0 ≤ i ≤ n are real polynomials of degree n which are orthogonal with respect to a first Euclidean scalar product to polynomials of degree less than i. In addition, they are mutually orthogonal with respect to a second Euclidean scalar product. Applying the general results obtained in a previous paper, we determine and investigate these po...

SUMMARY We investigate the performance characteristics of a numerically enhanced scalar product (dot) kernel loop that uses the Kahan algorithm to compensate for numerical errors, and describe efficient SIMD-vectorized implementations on recent multi-and manycore processors. Using low-level instruction analysis and the execution-cache-memory (ECM) performance model we pinpoint the relevant perf...

This letter continues the program [17][12][20][21] aimed at analysis of the scalar product of states in the Chern-Simons theory. It treats the elliptic case with group SU2. The formal scalar product is expressed as a multiple finite dimensional integral which, if convergent for every state, provides the space of states with a Hilbert space structure. The convergence is checked for states with a...

The aim of this paper is to give a characterization in Hilbert spaces of the generators of C0-semigroups associated with closed, sectorial forms in terms of the convergence of a generalized Trotter’s product formula. In the course of the proof of the main result we also present a similarity result which can be of independent interest: for any unbounded generator A of a C0-semigroup e tA it is p...

We investigate the performance characteristics of a numerically enhanced scalar product (dot) kernel loop that uses the Kahan algorithm to compensate for numerical errors, and describe efficient SIMD-vectorized implementations on recent Intel processors. Using low-level instruction analysis and the execution-cache-memory (ECM) performance model we pinpoint the relevant performance bottlenecks f...

In this paper we define a Poincaré-Reidemeister scalar product on the determinant line of the cohomology of any flat vector bundle over a closed orientable odd-dimensional manifold. It is a combinatorial “torsion-type” invariant which refines the PR-metric introduced in [Fa] and contains an additional sign or phase information. We compute the PR-scalar product in terms of the torsions of Euler ...

A secure scalar product protocol is a type of specific SMC problem, and has found various applications in many areas such as privacy-preserving data mining, privacy-preserving cooperative statistical analysis, and privacy-preserving geometry computation. In this paper, we firstly extend to a solution of homomorphic-encryption based secure scalar product protocol such that it enables the scheme ...

Privacy-preserving data mining seeks to empower conventional data mining techniques with the desirable property of preserving data privacy during the mining process. Given existing approaches on privacy-preserving decision tree induction for horizontally and vertically partitioned data involving multiple parties, we extend current work to multiple parties holding arbitrarily partitioned data. A...

This paper contains a detailed analysis of the properties of the scalar product of short and long living superpositions of neutral |K0〉, |K0〉 mesons. It is shown for the exact effective Hamiltonian for neutral meson subsystem that the scalar product of its eigenvectors, which correspond with these short and long living superpositions, can not be real with the assumption of CPT conserved and CP ...