9,543 research outputs found
Tensor models and 3-ary algebras
Tensor models are the generalization of matrix models, and are studied as
models of quantum gravity in general dimensions. In this paper, I discuss the
algebraic structure in the fuzzy space interpretation of the tensor models
which have a tensor with three indices as its only dynamical variable. The
algebraic structure is studied mainly from the perspective of 3-ary algebras.
It is shown that the tensor models have algebraic expressions, and that their
symmetries are represented by 3-ary algebras. It is also shown that the 3-ary
algebras of coordinates, which appear in the nonassociative fuzzy flat
spacetimes corresponding to a certain class of configurations with Gaussian
functions in the tensor models, form Lie triple systems, and the associated Lie
algebras are shown to agree with those of the Snyder's noncommutative
spacetimes. The Poincare transformations on the fuzzy flat spacetimes are shown
to be generated by 3-ary algebras.Comment: 21 pages, no essential changes of contents, but explanations added
for clarit
Multi-instantons in seven dimensions
We consider the self-dual Yang-Mills equations in seven dimensions. Modifying
the t'Hooft construction of instantons in , we find -instanton
solutions which depend on effective parameters and are -invariant.Comment: 9 pages, LaTeX, no figure
The Ginzburg-Landau Free Energy Functional of Color Superconductivity at Weak Coupling
We derive the Ginzburg-Landau free energy functional of color
superconductivity in terms of the thermal diagrams of QCD in its perturbative
region. The zero mode of the quadratic term coefficient yields the same
transition temperature, including the pre-exponential factor, as the one
obtained previously from the Fredholm determinant of the two quark scattering
amplitude. All coefficients of the free energy can be made identical to those
of a BCS model by setting the Fermi velocity of the latter equal to the speed
of light. We also calculate the induced symmetric color condensate near
and find that it scales as the cubic power of the dominant antisymmetric color
component. We show that in the presence of an inhomogeneity and a nonzero gauge
potential, while the color-flavor locked condensate dominates in the bulk, the
unlocked condensate, the octet, emerges as a result of a simultaneous
color-flavor rotation in the core region of a vortex filament or at the
junction of super and normal phases.Comment: 32 pages, Plain Tex, 3 figure
The use of the Winograd matrix multiplication algorithm in digital multispectral processing
The Winograd procedure for matrix multiplication provides a method whereby general matrix products may be computed more efficiently than the normal method. The algorithm and the time savings that can be effected are described. A FORTRAN program is provided which performs a general matrix multiply according to this algorithm. A variation of this procedure that may be used to calculate Gaussian probability density functions is also described. It is shown how a time savings can be effected in this calculation. The extension of this method to other similar calculations should yield similar savings
Digital control of magnetic bearings supporting a multimass flexible rotor
The characteristics of magnetic bearings used to support a three mass flexible rotor operated at speeds up to 14,000 RPM are discussed. The magnetic components of the bearing are of a type reported in the literature previously, but the earlier analog controls were replaced by digital ones. Analog-to-digital and digital-to-analog converters and digital control software were installed in an AT&T PC. This PC-based digital controller was used to operate one of the magnetic bearings on the test rig. Basic proportional-derivative control was applied to the bearings, and the bearing stiffness and damping characteristics were evaluated. Particular attention is paid to the frequency dependent behavior of the stiffness and damping properties, and comparisons are made between the actual controllers and ideal proportional-derivative control
Effective Gap Equation for the Inhomogeneous LOFF Superconductive Phase
We present an approximate gap equation for different crystalline structures
of the LOFF phase of high density QCD at T=0. This equation is derived by using
an effective condensate term obtained by averaging the inhomogeneous condensate
over distances of the order of the crystal lattice size. The approximation is
expected to work better far off any second order phase transition. As a
function of the difference of the chemical potentials of the up and down
quarks, , we get that the octahedron is energetically favored from
to , where is the gap for
the homogeneous phase, while in the range the face
centered cube prevails. At a first order phase
transition to the normal phase occurs.Comment: 11 pages, 5 figure
Self-dual Yang-Mills fields in pseudoeuclidean spaces
The self-duality Yang-Mills equations in pseudoeuclidean spaces of dimensions
are investigated. New classes of solutions of the equations are
found. Extended solutions to the D=10, N=1 supergravity and super Yang-Mills
equations are constructed from these solutions.Comment: 9 pages, LaTeX, no figure
Alternativity and reciprocity in the Cayley-Dickson algebra
We calculate the eigenvalue \rho of the multiplication mapping R on the
Cayley-Dickson algebra A_n. If the element in A_n is composed of a pair of
alternative elements in A_{n-1}, half the eigenvectors of R in A_n are still
eigenvectors in the subspace which is isomorphic to A_{n-1}.
The invariant under the reciprocal transformation A_n \times A_{n} \ni (x,y)
-> (-y,x) plays a fundamental role in simplifying the functional form of \rho.
If some physical field can be identified with the eigenspace of R, with an
injective map from the field to a scalar quantity (such as a mass) m, then
there is a one-to-one map \pi: m \mapsto \rho. As an example, the electro-weak
gauge field can be regarded as the eigenspace of R, where \pi implies that the
W-boson mass is less than the Z-boson mass, as in the standard model.Comment: To be published in J. Phys. A: Mathematical and Genera
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From Gain Score t to ANCOVA F (and vice versa)
Although they test somewhat different hypotheses, analysis of gain scores (or its repeated-measures analog) and analysis of covariance are both common methods that researchers use for pre-post data. The results of the two approaches yield non-comparable outcomes, but since the same generic data are used, it is possible to transform the test statistic of one into that of the other. We derive a formula that can be used to accomplish a conversion between the two and give an example. Such a result could be helpful to meta-analysts, where the outcomes in different research reports may be of either of the two types, yet need to be synthesized. Suggestions for additional research that can improve the usefulness of the formula are offered. Accessed 30,293 times on https://pareonline.net from March 20, 2009 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right
Dynamics of methane ebullition from a peat monolith revealed from a dynamic flux chamber system
Methane (CH4) ebullition in northern peatlands is poorly quantified in part due to its high spatiotemporal variability. In this study, a dynamic flux chamber (DFC) system was used to continuously measure CH4 fluxes from a monolith of nearâsurface Sphagnum peat at the laboratory scale to understand the complex behavior of CH4 ebullition. Coincident transmission ground penetrating radar measurements of gas content were also acquired at three depths within the monolith. A graphical method was developed to separate diffusion, steady ebullition, and episodic ebullition fluxes from the total CH4 flux recorded and to identify the timing and CH4 content of individual ebullition events. The results show that the application of the DFC had minimal disturbance on airâpeat CH4 exchange and estimated ebullition fluxes were not sensitive to the uncertainties associated with the graphical model. Steady and episodic ebullition fluxes were estimated to be averagely 36 ± 24% and 38 ± 24% of the total fluxes over the study period, respectively. The coupling between episodic CH4 ebullition and gas content within the three layers supports the existence of a threshold gas content regulating CH4 ebullition. However, the threshold at which active ebullition commenced varied between peat layers with a larger threshold (0.14 m3 mâ3) observed in the deeper layers, suggesting that the peat physical structure controls gas bubble dynamics in peat. Temperature variation (23°C to 27°C) was likely only responsible for small episodic ebullition events from the upper peat layer, while large ebullition events from the deeper layers were most likely triggered by drops in atmospheric pressure
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