Enciphering with Arbitrary Small Finite Domains

Author(s):  
Valery Pryamikov
Keyword(s):  
2009 ◽  
Vol 24 (18n19) ◽  
pp. 3243-3255 ◽  
Author(s):  
GERARD 't HOOFT

Matter interacting classically with gravity in 3+1 dimensions usually gives rise to a continuum of degrees of freedom, so that, in any attempt to quantize the theory, ultraviolet divergences are nearly inevitable. Here, we investigate a theory that only displays a finite number of degrees of freedom in compact sections of space-time. In finite domains, one has only exact, analytic solutions. This is achieved by limiting ourselves to straight pieces of string, surrounded by locally flat sections of space-time. Next, we suggest replacing in the string holonomy group, the Lorentz group by a discrete subgroup, which turns space-time into a 4-dimensional crystal with defects.


2000 ◽  
Vol 145 (3-4) ◽  
pp. 191-206 ◽  
Author(s):  
M.R.E. Proctor ◽  
S.M. Tobias ◽  
E. Knobloch

2002 ◽  
Vol 37 (3) ◽  
pp. 259-264 ◽  
Author(s):  
Q. Z Wang

First, based on an approximate analysis, simple closed-form expressions of the stress concentration factor (SCF) for two- or three-dimensional models with a circular hole or a spherical cavity in a finite domain are derived. Then, an asymptotic method is adopted to improve the accuracy of the derived solutions for an extremely large circular hole or spherical cavity, when the remaining ligament approaches zero. Exact limit SCF values for these two kinds of models were given by Koiter; these values are used for the adjustment of the coefficients in the SCF expressions. Finally, simple SCF formulae for these finite domain problems are obtained, their accuracy is demonstrated to be very good by comparison with the available data from the literature, and the asymptotic validity is guaranteed.


Author(s):  
Joxan Jaffar ◽  
Michael J. Maher ◽  
Peter J. Stuckey ◽  
Roland H. C. Yap
Keyword(s):  

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