1,090 research outputs found
A New Computational Schema for Euphonic Conjunctions in Sanskrit Processing
Automated language processing is central to the drive to enable facilitated referencing of increasingly available Sanskrit E-texts. The first step towards processing Sanskrit text involves the handling of Sanskrit compound words that are an integral part of Sanskrit texts. This firstly necessitates the processing of euphonic conjunctions or sandhi-s, which are points in words or between words, at which adjacent letters coalesce and transform. The ancient Sanskrit grammarian P??iniâs codification of the Sanskrit grammar is the accepted authority in the subject. His famed s?tra-s or aphorisms, numbering approximately four thousand, tersely, precisely and comprehensively codify the rules of the grammar, including all the rules pertaining to sandhi-s. This work presents a fresh new approach to processing sandhi-s in terms of a computational schema. This new computational model is based on P??iniâs complex codification of the rules of grammar. The model has simple beginnings and is yet powerful, comprehensive and computationally lean
On the simplest (2+1) dimensional integrable spin systems and their equivalent nonlinear Schr\"odinger equations
Using a moving space curve formalism, geometrical as well as gauge
equivalence between a (2+1) dimensional spin equation (M-I equation) and the
(2+1) dimensional nonlinear Schr\"odinger equation (NLSE) originally discovered
by Calogero, discussed then by Zakharov and recently rederived by Strachan,
have been estabilished. A compatible set of three linear equations are obtained
and integrals of motion are discussed. Through stereographic projection, the
M-I equation has been bilinearized and different types of solutions such as
line and curved solitons, breaking solitons, induced dromions, and domain wall
type solutions are presented. Breaking soliton solutions of (2+1) dimensional
NLSE have also been reported. Generalizations of the above spin equation are
discussed.Comment: 32 pages, no figures, accepted for publication in J. Math. Phy
Transition from anticipatory to lag synchronization via complete synchronization in time-delay systems
The existence of anticipatory, complete and lag synchronization in a single
system having two different time-delays, that is feedback delay and
coupling delay , is identified. The transition from anticipatory to
complete synchronization and from complete to lag synchronization as a function
of coupling delay with suitable stability condition is discussed. The
existence of anticipatory and lag synchronization is characterized both by the
minimum of similarity function and the transition from on-off intermittency to
periodic structure in laminar phase distribution.Comment: 14 Pages and 12 Figure
Bright-dark solitons and their collisions in mixed N-coupled nonlinear Schr\"odinger equations
Mixed type (bright-dark) soliton solutions of the integrable N-coupled
nonlinear Schr{\"o}dinger (CNLS) equations with mixed signs of focusing and
defocusing type nonlinearity coefficients are obtained by using Hirota's
bilinearization method. Generally, for the mixed N-CNLS equations the bright
and dark solitons can be split up in ways. By analysing the collision
dynamics of these coupled bright and dark solitons systematically we point out
that for , if the bright solitons appear in at least two components,
non-trivial effects like onset of intensity redistribution, amplitude dependent
phase-shift and change in relative separation distance take place in the bright
solitons during collision. However their counterparts, the dark solitons,
undergo elastic collision but experience the same amplitude dependent
phase-shift as that of bright solitons. Thus in the mixed CNLS system there
co-exist shape changing collision of bright solitons and elastic collision of
dark solitons with amplitude dependent phase-shift, thereby influencing each
other mutually in an intricate way.Comment: Accepted for publication in Physical Review
Quantal Two-Centre Coulomb Problem treated by means of the Phase-Integral Method I. General Theory
The present paper concerns the derivation of phase-integral quantization
conditions for the two-centre Coulomb problem under the assumption that the two
Coulomb centres are fixed. With this restriction we treat the general
two-centre Coulomb problem according to the phase-integral method, in which one
uses an {\it a priori} unspecified {\it base function}. We consider base
functions containing three unspecified parameters and .
When the absolute value of the magnetic quantum number is not too small, it
is most appropriate to choose . When, on the other hand,
is sufficiently small, it is most appropriate to choose .
Arbitrary-order phase-integral quantization conditions are obtained for these
choices of . The parameters and are determined from the
requirement that the results of the first and the third order of the
phase-integral approximation coincide, which makes the first-order
approximation as good as possible.
In order to make the paper to some extent self-contained, a short review of
the phase-integral method is given in the Appendix.Comment: 23 pages, RevTeX, 4 EPS figures, submitted to J. Math. Phy
- âŠ