MINIMAL SEMIGROUPS GENERATING VARIETIES WITH COMPLEX SUBVARIETY LATTICES

2007 ◽  
Vol 17 (08) ◽  
pp. 1553-1572 ◽  
Author(s):  
EDMOND W. H. LEE
Keyword(s):  
Finite Lattice ◽  
Minimal Order ◽  
Subvariety Lattice

A semigroup is complex if it generates a variety with the property that every finite lattice is embeddable in its subvariety lattice. In this paper, subvariety lattices of varieties generated by small semigroups will be investigated. Specifically, all complex semigroups of minimal order will be identified.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

scholarly journals Eigenvalue spectrum and scaling dimension of lattice $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Georg Bergner ◽  
David Schaich
Keyword(s):  
Anomalous Dimension ◽  
Finite Lattice ◽  
Continuum Theory ◽  
Lattice Volume ◽  
Yang Mills ◽  
Lattice Regularization ◽  
Perturbative Renormalization ◽  
Zero Values ◽  
Definition Of ◽  
Group Flow

Abstract We investigate the lattice regularization of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory, by stochastically computing the eigenvalue mode number of the fermion operator. This provides important insight into the non-perturbative renormalization group flow of the lattice theory, through the definition of a scale-dependent effective mass anomalous dimension. While this anomalous dimension is expected to vanish in the conformal continuum theory, the finite lattice volume and lattice spacing generically lead to non-zero values, which we use to study the approach to the continuum limit. Our numerical results, comparing multiple lattice volumes, ’t Hooft couplings, and numbers of colors, confirm convergence towards the expected continuum result, while quantifying the increasing significance of lattice artifacts at larger couplings.

scholarly journals Differential resolvents of minimal order and weight

2004 ◽  
Vol 2004 (54) ◽  
pp. 2867-2893
Author(s):  
John Michael Nahay
Keyword(s):  
Upper Bound ◽  
Minimal Order ◽  
Determinantal Formula ◽  
Differential Field ◽  
Nonzero Coefficient ◽  
Univariate Polynomial ◽  
Linear Differential ◽  
Indicial Equation

We will determine the number of powers ofαthat appear with nonzero coefficient in anα-power linear differential resolvent of smallest possible order of a univariate polynomialP(t)whose coefficients lie in an ordinary differential field and whose distinct roots are differentially independent over constants. We will then give an upper bound on the weight of anα-resolvent of smallest possible weight. We will then compute the indicial equation, apparent singularities, and Wronskian of the Cockleα-resolvent of a trinomial and finish with a related determinantal formula.

Finite lattice systems with true critical behavior

1992 ◽  
Vol 46 (4) ◽  
pp. 1643-1657 ◽  
Author(s):  
J. L. deLyra ◽  
S. K. Foong ◽  
T. E. Gallivan
Keyword(s):  
Critical Behavior ◽  
Finite Lattice ◽  
Lattice Systems
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