scholarly journals Non-Clausal Multi-ary a-Generalized Resolution Calculus for a Finite Lattice-Valued Logic

2018 ◽  
Vol 11 (1) ◽  
pp. 384 ◽  
Author(s):  
Yang Xu ◽  
Jun Liu ◽  
Xingxing He ◽  
Xiaomei Zhong ◽  
Shuwei Chen
Keyword(s):  
Finite Lattice ◽  
Generalized Resolution ◽  
Resolution Calculus

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.

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

Matchings and Radon transforms in lattices II. Concordant sets

1987 ◽  
Vol 101 (2) ◽  
pp. 221-231 ◽  
Author(s):  
Joseph P. S. Kung
Keyword(s):  
Incidence Matrix ◽  
Finite Lattice ◽  
Möbius Function ◽  
Radon Transforms ◽  
Modular Lattices ◽  
Covering Theorem ◽  
Mobius Function ◽  
Finite Lattices ◽  
Semimodular Lattices

AbstractLet and ℳ be subsets of a finite lattice L. is said to be concordant with ℳ if, for every element x in L, either x is in ℳ or there exists an element x+ such that (CS1) the Möbius function μ(x, x+) ≠ 0 and (CS2) for every element j in , x ∨ j ≠ x+. We prove that if is concordant with ℳ, then the incidence matrix I(ℳ | ) has maximum possible rank ||, and hence there exists an injection σ: → ℳ such that σ(j) ≥ j for all j in . Using this, we derive several rank and covering inequalities in finite lattices. Among the results are generalizations of the Dowling-Wilson inequalities and Dilworth's covering theorem to semimodular lattices, and a refinement of Dilworth's covering theorem for modular lattices.

Efficiency of encounter-controlled reaction between diffusing reactants in a finite lattice

2000 ◽  
Vol 113 (18) ◽  
pp. 8168-8174 ◽  
Author(s):  
John J. Kozak ◽  
C. Nicolis ◽  
G. Nicolis
Keyword(s):  
Finite Lattice

scholarly journals Two-species hardcore reversible cellular automaton: matrix ansatz for dynamics and nonequilibrium stationary state

2019 ◽  
Vol 6 (6) ◽  
Author(s):  
Marko Medenjak ◽  
Vladislav Popkov ◽  
Tomaz Prosen ◽  
Eric Ragoucy ◽  
Matthieu Vanicat
Keyword(s):  
Cellular Automaton ◽  
Time Evolution ◽  
Stationary State ◽  
Finite Lattice ◽  
Matrix Product ◽  
Density Profiles ◽  
Reversible Cellular Automaton ◽  
Product Expression ◽  
Particle Current ◽  
Exact Matrix

In this paper we study the statistical properties of a reversible cellular automaton in two out-of-equilibrium settings. In the first part we consider two instances of the initial value problem, corresponding to the inhomogeneous quench and the local quench. Our main result is an exact matrix product expression of the time evolution of the probability distribution, which we use to determine the time evolution of the density profiles analytically. In the second part we study the model on a finite lattice coupled with stochastic boundaries. Once again we derive an exact matrix product expression of the stationary distribution, as well as the particle current and density profiles in the stationary state. The exact expressions reveal the existence of different phases with either ballistic or diffusive transport depending on the boundary parameters.

scholarly journals Generalized resolution matrix for neutron spin-echo three-axis spectrometers

2018 ◽  
Vol 51 (3) ◽  
pp. 818-830 ◽  
Author(s):  
Felix Groitl ◽  
Thomas Keller ◽  
Klaus Habicht
Keyword(s):  
Energy Resolution ◽  
Spin Echo ◽  
Neutron Spin ◽  
Matrix Formalism ◽  
Prior Work ◽  
Gradient Vector ◽  
Neutron Spin Echo ◽  
Dispersion Surface ◽  
Generalized Resolution ◽  
Line Widths

This article describes the energy resolution of spin-echo three-axis spectrometers (SE-TASs) by a compact matrix formalism. SE-TASs allow one to measure the line widths of elementary excitations in crystals, such as phonons and magnons, with an energy resolution in the µeV range. The resolution matrices derived here generalize prior work: (i) the formalism works for all crystal structures; (ii) spectrometer detuning effects are included; these arise typically from inaccurate knowledge of the excitation energy and group velocity; (iii) components of the gradient vector of the dispersion surface dω/dq perpendicular to the scattering plane are properly treated; (iv) the curvature of the dispersion surface is easily calculated in reciprocal units; (v) the formalism permits analysis of spin-echo signals resulting from multiple excitation modes within the three-axis spectrometer resolution ellipsoid.

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