We show how to apply the Collatz function and the modified Collatz function to the ternary representation of a positive integer, and we present the ternary modified Collatz sequence starting with a multiple of 3N for an arbitrary large integer N . Each ternary string in the sequence is shown to have a repeating string, and the number of occurrences of each digit in each repeating string is iden...

We combine I. background independent Loop Quantum Gravity (LQG) quantization techniques, II. the mathematically rigorous framework of Algebraic Quantum Field Theory (AQFT) and III. the theory of integrable systems resulting in the invariant Pohlmeyer Charges in order to set up the general representation theory (superselection theory) for the closed bosonic quantum string on flat target space. W...

The AdS/CFT correspondence of elementary string theory has been recently suggested as a “microscopic” approach to QCD string theory in various dimensions. We use the microscopic theory to show that the ultraviolet regime on the string world-sheet is mapped to the ultraviolet effects in QCD. In the case of QCD2, a world-sheet path integral representation of QCD strings is known, in terms of a to...

The X.500 Directory uses distinguished names as the primary keys to entries in the directory. Distinguished Names are encoded in ASN.1 in Zeilenga LDAPv3 DN [Page 1] INTERNET-DRAFT draft-ietf-ldapbis-dn-03.txt 1 April 2001 the X.500 Directory protocols. In the Lightweight Directory Access Protocol, a string representation of distinguished names is transferred. This specification defines the str...

The X.500 Directory uses distinguished names as the primary keys to entries in the directory. Distinguished Names are encoded in ASN.1 in Zeilenga LDAPv3 DN [Page 1] INTERNET-DRAFT draft-ietf-ldapbis-dn-03.txt 1 April 2001 the X.500 Directory protocols. In the Lightweight Directory Access Protocol, a string representation of distinguished names is transferred. This specification defines the str...

In this paper fields of quantum reference frames based on gauge transformations of rational string states are described in a way that, hopefully, makes them more understandable than their description in an earlier paper. The approach taken here is based on three main points: (1) There are a large number of different quantum theory representations of natural numbers, integers, and rational numbe...

In this paper, a model for the interaction of the strings with the frets in a guitar or other fretted string instruments is introduced. In the two-polarization representation of the string oscillations it is observed that the string interacts with the fret in different ways. While the vertical oscillation is governed by perfect or imperfect clamping of the string on the fret, the horizontal osc...

String diagrams provide an intuitive language for expressing networks of interacting processes graphically. A discrete representation of string diagrams, called string graphs, allows for mechanised equational reasoning by double-pushout rewriting. However, one often wishes to express not just single equations, but entire families of equations between diagrams of arbitrary size. To do this we de...

Tree-to-string translation rules are widely used in linguistically syntax-based statistical machine translation systems. In this paper, we propose to use deep syntactic information for obtaining fine-grained translation rules. A head-driven phrase structure grammar (HPSG) parser is used to obtain the deep syntactic information, which includes a fine-grained description of the syntactic property...

We consider the realization of affine ADE Lie algebras as string junctions on mutually non-local 7-branes in Type IIB string theory. The existence of the affine algebra is signaled by the presence of the imaginary root junction δ, which is realized as a string encircling the 7-brane configuration. The level k of an affine representation partially constrains the asymptotic (p, q) charges of stri...