Search results for "Linear Algebra"
showing 10 items of 552 documents
Relativistic coupled-cluster calculations on XeF6: Delicate interplay between electron-correlation and basis-set effects
2015
A systematic relativistic coupled-cluster study is reported on the harmonic vibrational frequencies of the O(h), C(3v), and C(2v) conformers of XeF6, with scalar-relativistic effects efficiently treated using the spin-free exact two-component theory in its one-electron variant (SFX2C-1e). Atomic natural orbital type basis sets recontracted for the SFX2C-1e scheme have been shown to provide rapid basis-set convergence for the vibrational frequencies. SFX2C-1e as well as complementary pseudopotential based computations consistently predicts that both O(h) and C(3v) structures are local minima on the potential energy surface, while the C(2v) structure is a transition state. Qualitative disagre…
Public administration sustainability and its organizational basis
2019
Benefiting from a novel data set spanning nearly half a century, this study probes the sustainability of public governance. Theoretically, it examines how sustainable public governance rests on its organizational fabric. The study illuminates how organizational factors systematically influence decision-making behaviour and thus public governance sustainability. Moreover, the study argues that since organizational structure is amendable to deliberate manipulative change, it may thus be an important design instrument of the context of choice in public governance. Accordingly, the article offers an avenue to build bridges between the academic and practitioner worlds of public administration. E…
A note on faithful traces on a von Neumann algebra
2009
In this short note we give some techniques for constructing, starting from a {\it sufficient} family $\mc F$ of semifinite or finite traces on a von Neumann algebra $\M$, a new trace which is faithful.
The diamond partial order in rings
2013
In this paper we introduce a new partial order on a ring, namely the diamond partial order. This order is an extension of a partial order defined in a matrix setting in [J.K. Baksalary and J. Hauke, A further algebraic version of Cochran's theorem and matrix partial orderings, Linear Algebra and its Applications, 127, 157--169, 1990]. We characterize the diamond partial order on rings and study its relationships with other partial orders known in the literature. We also analyze successors, predecessors and maximal elements under the diamond order.
On symplectically rigid local systems of rank four and Calabi–Yau operators
2013
AbstractWe classify all Sp4(C)-rigid, quasi-unipotent local systems and show that all of them have geometric origin. Furthermore, we investigate which of those having a maximal unipotent element are induced by fourth order Calabi–Yau operators. Via this approach, we reconstruct all known Calabi–Yau operators inducing an Sp4(C)-rigid monodromy tuple and obtain closed formulae for special solutions of them.
Hamiltonians Generated by Parseval Frames
2021
AbstractIt is known that self-adjoint Hamiltonians with purely discrete eigenvalues can be written as (infinite) linear combination of mutually orthogonal projectors with eigenvalues as coefficients of the expansion. The projectors are defined by the eigenvectors of the Hamiltonians. In some recent papers, this expansion has been extended to the case in which these eigenvectors form a Riesz basis or, more recently, a ${\mathcal{D}}$ D -quasi basis (Bagarello and Bellomonte in J. Phys. A 50:145203, 2017, Bagarello et al. in J. Math. Phys. 59:033506, 2018), rather than an orthonormal basis. Here we discuss what can be done when these sets are replaced by Parseval frames. This interest is moti…
Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals in the theory of Haar and Walsh series
2015
Abstract The problem of recovering the coefficients of rectangular convergent multiple Haar and Walsh series from their sums, by generalized Fourier formulas, is reduced to the one of recovering a function (the primitive) from its derivative with respect to the appropriate derivation basis. Multidimensional dyadic Kurzweil–Henstock- and Perron-type integrals are compared and it is shown that a Perron-type integral, defined by major and minor functions having a special continuity property, solves the coefficients problem for series which are convergent everywhere outside some uniqueness sets.
On stable geometries
1994
Within the concept of projective lattice geometry we are considering the class of stable geometries which have also been introduced in [14]. The investigation of their basic properties will result in fundamental structure theorems which especially give a lattice-geometric characterization of free left modules of rank ≥6 over proper right Bezout rings of stable rank 2. This yields a proper generalization of previous results of ours.
The first Chevalley–Eilenberg Cohomology group of the Lie algebra on the transverse bundle of a decreasing family of foliations
2010
Abstract In [L. Lebtahi, Lie algebra on the transverse bundle of a decreasing family of foliations, J. Geom. Phys. 60 (2010), 122–133], we defined the transverse bundle V k to a decreasing family of k foliations F i on a manifold M . We have shown that there exists a ( 1 , 1 ) tensor J of V k such that J k ≠ 0 , J k + 1 = 0 and we defined by L J ( V k ) the Lie Algebra of vector fields X on V k such that, for each vector field Y on V k , [ X , J Y ] = J [ X , Y ] . In this note, we study the first Chevalley–Eilenberg Cohomology Group, i.e. the quotient space of derivations of L J ( V k ) by the subspace of inner derivations, denoted by H 1 ( L J ( V k ) ) .
Distributions Frames and bases
2018
In this paper we will consider, in the abstract setting of rigged Hilbert spaces, distribution valued functions and we will investigate, in particular, conditions for them to constitute a "continuous basis" for the smallest space $\mathcal D$ of a rigged Hilbert space. This analysis requires suitable extensions of familiar notions as those of frame, Riesz basis and orthonormal basis. A motivation for this study comes from the Gel'fand-Maurin theorem which states, under certain conditions, the existence of a family of generalized eigenvectors of an essentially self-adjoint operator on a domain $\mathcal D$ which acts like an orthonormal basis of the Hilbert space $\mathcal H$. The correspond…