4,042 research outputs found
On and Off-diagonal Sturmian operator: dynamic and spectral dimension
We study two versions of quasicrystal model, both subcases of Jacobi
matrices. For Off-diagonal model, we show an upper bound of dynamical exponent
and the norm of the transfer matrix. We apply this result to the Off-diagonal
Fibonacci Hamiltonian and obtain a sub-ballistic bound for coupling large
enough. In diagonal case, we improve previous lower bounds on the fractal
box-counting dimension of the spectrum.Comment: arXiv admin note: text overlap with arXiv:math-ph/0502044 and
arXiv:0807.3024 by other author
Spectral properties of the renormalization group at infinite temperature
The renormalization group (RG) approach is largely responsible for the
considerable success that has been achieved in developing a quantitative theory
of phase transitions. Physical properties emerge from spectral properties of
the linearization of the RG map at a fixed point. This article considers RG for
classical Ising-type lattice systems. The linearization acts on an
infinite-dimensional Banach space of interactions. At a trivial fixed point
(zero interaction), the spectral properties of the RG linearization can be
worked out explicitly, without any approximation. The results are for the RG
maps corresponding to decimation and majority rule. They indicate spectrum of
an unusual kind: dense point spectrum for which the adjoint operators have no
point spectrum at all, only residual spectrum. This may serve as a lesson in
what one might expect in more general situations.Comment: 12 page
Local quasi hidden variable modelling and violations of Bell-type inequalities by a multipartite quantum state
We introduce for a general correlation scenario a new simulation model, a
local quasi hidden variable (LqHV) model, where locality and the
measure-theoretic structure inherent to an LHV model are preserved but
positivity of a simulation measure is dropped. We specify a necessary and
sufficient condition for LqHV modelling and, based on this, prove that every
quantum correlation scenario admits an LqHV simulation. Via the LqHV approach,
we construct analogs of Bell-type inequalities for an N-partite quantum state
and find a new analytical upper bound on the maximal violation by an N-partite
quantum state of S_{1}x...xS_{N}-setting Bell-type inequalities - either on
correlation functions or on joint probabilities and for outcomes of an
arbitrary spectral type, discrete or continuous. This general analytical upper
bound is expressed in terms of the new state dilation characteristics
introduced in the present paper and not only traces quantum states admitting an
S_{1}x...xS_{N}-setting LHV description but also leads to the new exact
numerical upper estimates on the maximal Bell violations for concrete N-partite
quantum states used in quantum information processing and for an arbitrary
N-partite quantum state. We, in particular, prove that violation by an
N-partite quantum state of an arbitrary Bell-type inequality (either on
correlation functions or on joint probabilities) for S settings per site cannot
exceed (2S-1)^{N-1} even in case of an infinite dimensional quantum state and
infinitely many outcomes.Comment: Improved, edited versio
Generalized Solutions for Quantum Mechanical Oscillator on K\"{a}hler Conifold
We study the possible generalized boundary conditions and the corresponding
solutions for the quantum mechanical oscillator model on K\"{a}hler conifold.
We perform it by self-adjoint extension of the the initial domain of the
effective radial Hamiltonian. Remarkable effect of this generalized boundary
condition is that at certain boundary condition the orbital angular momentum
degeneracy is restored! We also recover the known spectrum in our formulation,
which of course correspond to some other boundary condition.Comment: 7 pages, latex, no figur
Fr\'echet frames, general definition and expansions
We define an {\it -frame} with Banach spaces , , and a -space (\Theta, \snorm[\cdot]).
Then by the use of decreasing sequences of Banach spaces
and of sequence spaces , we define a general Fr\'
echet frame on the Fr\' echet space . We give
frame expansions of elements of and its dual , as well of some of
the generating spaces of with convergence in appropriate norms. Moreover,
we give necessary and sufficient conditions for a general pre-Fr\' echet frame
to be a general Fr\' echet frame, as well as for the complementedness of the
range of the analysis operator .Comment: A new section is added and a minor revision is don
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Teaching schools evaluation. Research Brief
This Research Brief reports the findings from a two-year study (2013-15) in to the work of teaching schools and their alliances commissioned by the National College for Teaching and Leadership (NCTL). The broad aim of the study was to investigate the effectiveness and impact of teaching schools on improvement, and identify the quality and scope of external support that are required to enhance these . This was achieved through combining qualitative and quantitative data collection and analysis derived from three research activities: case studies of 26 teaching schools alliances (TSAs), a national survey of the first three cohorts of 345 TSAs, and secondary research and analysis of national performance and inspection results
Microalgae Growth in Physically Pre-Treated Wastewater Generated During Hydraulic Fracturing
Hydraulic fracturing technique frequently used during gas and oil production generates large amounts of wastewaters (WWs). High cost of the conventional techniques used to treat such waters adversely affect their economic feasibility. Hence, novel technologies that will facilitate remediation and subsequent re-use of these WWs are welcomed. In this study, growth profile of four Oklahoma native microalgae (Geitlerinema carotinosum, Komvophoron sp., Pseudanabaena sp., Picochlorum oklahomensis) cultivated in physically pre-treated flowback and produced water generated during hydraulic fracturing were characterized. A mechanical step based on oil removal by an oil skimmer was introduced during pre-treatment. The experimental results demonstrated that all four strains could grow in pre-treated flowback and produced water. Biomass productivity varied significantly with the microalgae strain and type of the WW used in the growth experiments. The best performing strain, cyanobacterium Komvophoron sp., was able to grow with a specific growth rate ranging from 0.03 to 0.18 day-1 depending on the type of WW. The process was capable of removing ammonium and phosphorus with efficiencies up to 99 and 63%, respectively
Spectral theory of some non-selfadjoint linear differential operators
We give a characterisation of the spectral properties of linear differential
operators with constant coefficients, acting on functions defined on a bounded
interval, and determined by general linear boundary conditions. The boundary
conditions may be such that the resulting operator is not selfadjoint.
We associate the spectral properties of such an operator with the
properties of the solution of a corresponding boundary value problem for the
partial differential equation . Namely, we are able to
establish an explicit correspondence between the properties of the family of
eigenfunctions of the operator, and in particular whether this family is a
basis, and the existence and properties of the unique solution of the
associated boundary value problem. When such a unique solution exists, we
consider its representation as a complex contour integral that is obtained
using a transform method recently proposed by Fokas and one of the authors. The
analyticity properties of the integrand in this representation are crucial for
studying the spectral theory of the associated operator.Comment: 1 figur
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