1,135 research outputs found
Reducible Correlations in Dicke States
We apply a simple observation to show that the generalized Dicke states can
be determined from their reduced subsystems. In this framework, it is
sufficient to calculate the expression for only the diagonal elements of the
reudced density matrices in terms of the state coefficients. We prove that the
correlation in generalized Dicke states can be reduced to
-partite level. Application to the Quantum Marginal Problem is also
discussed.Comment: 12 pages, single column; accepted in J. Phys. A as FT
The ball in play demands of international rugby union
Objectives: Rugby union is a high intensity intermittent sport, typically analysed via set time periods or rolling average methods. This study reports the demands of international rugby union via global positioning system (GPS) metrics expressed as mean ball in play (BiP), maximum BiP (max BiP), and whole match outputs.
Design: Single cohort cross sectional study involving 22 international players, categorised as forwards and backs.
Methods: A total of 88 GPS files from eight international test matches were collected during 2016. An Opta sportscode timeline was integrated into the GPS software to split the data into BiP periods. Metres per min (m.min-1), high metabolic load per min (HML), accelerations per min (Acc), high speed running per min (HSR), and collisions per min (Coll) were expressed relative to BiP periods and over the whole match (>60min).
Results: Whole match metrics were significantly lower than all BiP metrics (p < 0.001). Mean and max BiP HML, (p < 0.01) and HSR (p < 0.05) were significantly higher for backs versus forwards, whereas Coll were significantly higher for forwards (p < 0.001). In plays lasting 61s or greater, max BiP m.min-1 were higher for backs. Max BiP m.min-1, HML, HSR and Coll were all time dependant (p < 0.05) showing that both movement metrics and collision demands differ as length of play continues.
Conclusions: This study uses a novel method of accurately assessing the BiP demands of rugby union. It also reports typical and maximal demands of international rugby union that can be used by practitioners and scientists to target training of worst-case scenario's equivalent to international intensity. Backs covered greater distances at higher speeds and demonstrated higher HML, in general play as well as 'worst case scenarios'; conversely forwards perform a higher number of collisions
Estimation Of Fluid Loading On Offshore Structures
This paper is a working guide to methods and associated data for estimating loading on offshore structures due to waves and currents. Its primary concern is with existing practice in which the formula known as Morison' s equation is extensively used but some attention is given to diffraction theory methods now quite widely adopted for large monolithic types of structure and a section on the influence of marine roughness on loading is included. Regarding Morison's equation, a comprehensive review of published data on the relevant coefficients is presented, stressing the considerable uncertainties which still exist in some areas but offering advice on the best values to be used in the light of current knowledge, systematically documented by references to the corresponding data sources. Other important questions discussed include selection of appropriate wave theories and associated particle kinematics, the effects on fluid loading of proximity and inclination of structural members and the special problems of estimating impact or 'slamming' forces. The section on diffraction theory analysis discusses the interpretation of the results for both fixed and moving bodies and problems of practical application. It also reviews published information on both analytical and numerical solutions including comments on reliability and experimental validation and tabular summaries of the capabilities of an extensive range of methods and computer programs already available. In discussing marine roughness recent published data indicating the substantial effects which it can have on drag coefficients in both waves and currents are reviewed and advice is given on how these should be estimated. A general conclusion of the paper is that although data on fluid loading available in the literature is very plentiful there are still many serious uncertainties and gaps in knowledge. It is therefore important that research should continue with emphasis on the need for more reliable data from large scale structures in the real environment
A Comparison between the Zero Forcing Number and the Strong Metric Dimension of Graphs
The \emph{zero forcing number}, , of a graph is the minimum
cardinality of a set of black vertices (whereas vertices in are
colored white) such that is turned black after finitely many
applications of "the color-change rule": a white vertex is converted black if
it is the only white neighbor of a black vertex. The \emph{strong metric
dimension}, , of a graph is the minimum among cardinalities of all
strong resolving sets: is a \emph{strong resolving set} of
if for any , there exists an such that either
lies on an geodesic or lies on an geodesic. In this paper, we
prove that for a connected graph , where is
the cycle rank of . Further, we prove the sharp bound
when is a tree or a unicyclic graph, and we characterize trees
attaining . It is easy to see that can be
arbitrarily large for a tree ; we prove that and
show that the bound is sharp.Comment: 8 pages, 5 figure
Signatures of partition functions and their complexity reduction through the KP II equation
A statistical amoeba arises from a real-valued partition function when the
positivity condition for pre-exponential terms is relaxed, and families of
signatures are taken into account. This notion lets us explore special types of
constraints when we focus on those signatures that preserve particular
properties. Specifically, we look at sums of determinantal type, and main
attention is paid to a distinguished class of soliton solutions of the
Kadomtsev-Petviashvili (KP) II equation. A characterization of the signatures
preserving the determinantal form, as well as the signatures compatible with
the KP II equation, is provided: both of them are reduced to choices of signs
for columns and rows of a coefficient matrix, and they satisfy the whole KP
hierarchy. Interpretations in term of information-theoretic properties,
geometric characteristics, and the relation with tropical limits are discussed.Comment: 42 pages, 11 figures. Section 7.1 has been added, the organization of
the paper has been change
The Enhanced Principal Rank Characteristic Sequence for Hermitian Matrices
The enhanced principal rank characteristic sequence (epr-sequence) of an n x n matrix is a sequence l(1) l(2) . . .l(n), where each l(k) is A, S, or N according as all, some, or none of its principal minors of order k are nonzero. There has been substantial work on epr-sequences of symmetric matrices (especially real symmetric matrices) and real skew-symmetric matrices, and incidental remarks have been made about results extending (or not extending) to (complex) Hermitian matrices. A systematic study of epr-sequences of Hermitian matrices is undertaken; the differences with the case of symmetric matrices are quite striking. Various results are established regarding the attainability by Hermitian matrices of epr-sequences that contain two Ns with a gap in between. Hermitian adjacency matrices of mixed graphs that begin with N A N are characterized. All attainable epr-sequences of Hermitian matrices of orders 2, 3, 4, and 5, are listed with justifications
Algebraic inversion of the Dirac equation for the vector potential in the non-abelian case
We study the Dirac equation for spinor wavefunctions minimally coupled to an
external field, from the perspective of an algebraic system of linear equations
for the vector potential. By analogy with the method in electromagnetism, which
has been well-studied, and leads to classical solutions of the Maxwell-Dirac
equations, we set up the formalism for non-abelian gauge symmetry, with the
SU(2) group and the case of four-spinor doublets. An extended isospin-charge
conjugation operator is defined, enabling the hermiticity constraint on the
gauge potential to be imposed in a covariant fashion, and rendering the
algebraic system tractable. The outcome is an invertible linear equation for
the non-abelian vector potential in terms of bispinor current densities. We
show that, via application of suitable extended Fierz identities, the solution
of this system for the non-abelian vector potential is a rational expression
involving only Pauli scalar and Pauli triplet, Lorentz scalar, vector and axial
vector current densities, albeit in the non-closed form of a Neumann series.Comment: 21pp, uses iopar
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