494 research outputs found
The Extended Bigraded Toda hierarchy
We generalize the Toda lattice hierarchy by considering N+M dependent
variables. We construct roots and logarithms of the Lax operator which are
uniquely defined operators with coefficients that are -series of
differential polynomials in the dependent variables, and we use them to provide
a Lax pair definition of the extended bigraded Toda hierarchy. Using R-matrix
theory we give the bihamiltonian formulation of this hierarchy and we prove the
existence of a tau function for its solutions. Finally we study the
dispersionless limit and its connection with a class of Frobenius manifolds on
the orbit space of the extended affine Weyl groups of the series.Comment: 32 pages, corrected typo
Integrable discrete systems on R and related dispersionless systems
The general framework for integrable discrete systems on R in particular
containing lattice soliton systems and their q-deformed analogues is presented.
The concept of regular grain structures on R, generated by discrete
one-parameter groups of diffeomorphisms, through which one can define algebras
of shift operators is introduced. Two integrable hierarchies of discrete chains
together with bi-Hamiltonian structures are constructed. Their continuous limit
and the inverse problem based on the deformation quantization scheme are
considered.Comment: 19 page
Tau function and Hirota bilinear equations for the Extended bigraded Toda Hierarchy
In this paper we generalize the Sato theory to the extended bigraded Toda
hierarchy (EBTH). We revise the definition of the Lax equations,give the Sato
equations, wave operators, Hirota bilinear identities (HBI) and show the
existence of function . Meanwhile we prove the validity of its
Fay-like identities and Hirota bilinear equations (HBEs) in terms of vertex
operators whose coefficients take values in the algebra of differential
operators. In contrast with HBEs of the usual integrable system, the current
HBEs are equations of product of operators involving and
.Comment: 29 pages, to appear Journal of Mathematical Physics(2010
Motor Parameter-Free Predictive Current Control of Synchronous Motors by Recursive Least-Square Self-Commissioning Model
This article deals with a finite-set model predictive current control in synchronous motor drives. The peculiarity is that it does not require the knowledge of any motor parameter. The inherent advantage of this method is that the control is self-adapting to any synchronous motor, thus easing the matching between motor and inverter coming from different manufacturers. Overcoming the flaws of the existing lookup table based parameter-free techniques, the article elaborates the past current measurements by a recursive least-square algorithm to estimate the future behavior of the current in response to a finite set of voltage vectors. The article goes through the mathematical basis of the algorithm till a complete set of experiments that prove the feasibility and the advantages of the proposed technique
An Effective Model-Free Predictive Current Control for Synchronous Reluctance Motor Drives
The performances of a model predictive control algorithm largely depend on the knowledge of the system model. A model-free predictive control approach skips all the effects of parameters variations or mismatches, as well as of model nonlinearity and uncertainties. A finite-set model-free current predictive control is proposed in this paper. The current variations predictions induced by the eight base inverter voltage vectors are estimated by means of the previous measurements stored into lookup tables. To keep the current variations information up to date, the three current measurements due to the three most recent feeding voltages are combined together to reconstruct all the others. The reconstruction is performed by taking advantage of the relationships between the three different base voltage vectors involved in the process. In particular, 210 possible combinations of three-state voltage vectors can be found, but they can be gathered together in six different groups. A light and computationally fast algorithm for the group identification is proposed in this paper. Finally, the current reconstruction for the prediction of future steps is thoroughly analyzed. A compensation of the motor rotation effect on the input voltages is proposed, too. The control scheme is evaluated by means of both simulation and experimental evidences on two different synchronous reluctance motors
The multicomponent 2D Toda hierarchy: Discrete flows and string equations
The multicomponent 2D Toda hierarchy is analyzed through a factorization
problem associated to an infinite-dimensional group. A new set of discrete
flows is considered and the corresponding Lax and Zakharov--Shabat equations
are characterized. Reductions of block Toeplitz and Hankel bi-infinite matrix
types are proposed and studied. Orlov--Schulman operators, string equations and
additional symmetries (discrete and continuous) are considered. The
continuous-discrete Lax equations are shown to be equivalent to a factorization
problem as well as to a set of string equations. A congruence method to derive
site independent equations is presented and used to derive equations in the
discrete multicomponent KP sector (and also for its modification) of the theory
as well as dispersive Whitham equations.Comment: 27 pages. In the revised paper we improved the presentatio
Doubly Perfect Nonlinear Boolean Permutations
Due to implementation constraints the XOR operation is widely used in order
to combine plaintext and key bit-strings in secret-key block ciphers. This
choice directly induces the classical version of the differential attack by the
use of XOR-kind differences. While very natural, there are many alternatives to
the XOR. Each of them inducing a new form for its corresponding differential
attack (using the appropriate notion of difference) and therefore block-ciphers
need to use S-boxes that are resistant against these nonstandard differential
cryptanalysis. In this contribution we study the functions that offer the best
resistance against a differential attack based on a finite field
multiplication. We also show that in some particular cases, there are robust
permutations which offers the best resistant against both multiplication and
exponentiation base differential attacks. We call them doubly perfect nonlinear
permutations
On the Complexity of Computing Two Nonlinearity Measures
We study the computational complexity of two Boolean nonlinearity measures:
the nonlinearity and the multiplicative complexity. We show that if one-way
functions exist, no algorithm can compute the multiplicative complexity in time
given the truth table of length , in fact under the same
assumption it is impossible to approximate the multiplicative complexity within
a factor of . When given a circuit, the problem of
determining the multiplicative complexity is in the second level of the
polynomial hierarchy. For nonlinearity, we show that it is #P hard to compute
given a function represented by a circuit
Efeito da solarização na germinação de esclerócios (scLerotínia sclerotiorum) em estufa plástica
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