Coined Walks on Infinite Lattices

2018 ◽  
pp. 69-88
Author(s):  
Renato Portugal
Keyword(s):  
Infinite Lattices

Surface tension and surface modes in semi-infinite lattices

1965 ◽  
Vol 3 (1) ◽  
pp. 19-32 ◽  
Author(s):  
D.C. Gazis ◽  
R.F. Wallis
Keyword(s):  
Surface Tension ◽  
Surface Modes ◽  
Infinite Lattices

Multi-bump solutions of -Δn = K(x)u (n+2)/(n-2) on lattices in ℝ n

2018 ◽  
Vol 2018 (743) ◽  
pp. 163-211 ◽  
Author(s):  
Yanyan Li ◽  
Juncheng Wei ◽  
Haoyuan Xu
Keyword(s):  
Elliptic Equation ◽  
Critical Exponent ◽  
Critical Point ◽  
Semilinear Elliptic Equation ◽  
Natural Conditions ◽  
Semilinear Elliptic ◽  
Infinite Lattices

Abstract We consider the following semilinear elliptic equation with critical exponent: Δ u = K(x) u^{(n+2)/(n-2)} , u > 0 in \mathbb{R}^{n} , where {n\geq 3} , {K>0} is periodic in ( x_{1} ,…, x_{k} ) with 1 \leq k < (n-2)/2. Under some natural conditions on K near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in {\mathbb{R}^{k}} , including infinite lattices. We also show that for k \geq (n-2)/2, no such solutions exist.

scholarly journals Twin edge coloring of infinite lattices

2018 ◽  
Vol 1087 ◽  
pp. 052020
Author(s):  
Qing Yang ◽  
Shuang Liang Tian ◽  
Lang Wang Qing Suo
Keyword(s):  
Edge Coloring ◽  
Infinite Lattices

Magnetism, electronic spectra, and structure of transition metal alkoxides. I. methoxides and ethoxides of chromium(II), manganese(II), Iron(II), cobalt(II), nickel(II), copper(II), titanium(III), chromium(III), and iron(III)

1966 ◽  
Vol 19 (2) ◽  
pp. 207 ◽  
Author(s):  
RW Adams ◽  
E Bishop ◽  
RL Martin ◽  
G Winter
Keyword(s):  
Transition Metal ◽  
Spectral Data ◽  
Electronic Spectra ◽  
Magnetic Moments ◽  
Field Parameter ◽  
Ligand Field ◽  
Metal Alkoxides ◽  
Infinite Lattices ◽  
Ligand Field Parameter

The magnetic moments and electronic spectra are reported for the following divalent transition metal methoxides: Cr(OCH3)2, Mn(OCH3)2, Fe(OCH3)2, Co(OCH3)2, Ni(OCH3)2, and Cu(OCH3)2. These measurements when coupled with the involatility and insolubility of the compounds favour structures based on infinite lattices composed either of regular (Mn, Fe, Co, and Ni) or distorted (Cr and Cu) MO6 octahedra. The spectral data place the ligand field parameter, Δ, for the methoxide group very close to that of water.

On generation of aggregation functions on infinite lattices

2018 ◽  
Vol 23 (16) ◽  
pp. 7279-7286 ◽  
Author(s):  
Radomír Halaš ◽  
Radko Mesiar ◽  
Jozef Pócs
Keyword(s):  
Aggregation Functions ◽  
Infinite Lattices

ABUNDANCE OF MOSAIC PATTERNS FOR CNN WITH SPATIALLY VARIANT TEMPLATES

2002 ◽  
Vol 12 (06) ◽  
pp. 1321-1332 ◽  
Author(s):  
CHENG-HSIUNG HSU ◽  
TING-HUI YANG
Keyword(s):  
Neural Network ◽  
Boundary Conditions ◽  
Cellular Neural Network ◽  
One Dimensional ◽  
Various Boundary Conditions ◽  
Exact Number ◽  
Finite Lattices ◽  
Infinite Lattices ◽  
Spatially Variant

This work investigates the complexity of one-dimensional cellular neural network mosaic patterns with spatially variant templates on finite and infinite lattices. Various boundary conditions are considered for finite lattices and the exact number of mosaic patterns is computed precisely. The entropy of mosaic patterns with periodic templates can also be calculated for infinite lattices. Furthermore, we show the abundance of mosaic patterns with respect to template periods and, which differ greatly from cases with spatially invariant templates.

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