9,291 research outputs found
Balanced Symmetric Functions over
Under mild conditions on , we give a lower bound on the number of
-variable balanced symmetric polynomials over finite fields , where
is a prime number. The existence of nonlinear balanced symmetric
polynomials is an immediate corollary of this bound. Furthermore, we conjecture
that are the only nonlinear balanced elementary symmetric
polynomials over GF(2), where , and we prove various results in support of this conjecture.Comment: 21 page
Enumeration of Balanced Symmetric Functions over GF(p)
It is proved that the construction and enumeration of the number of balanced symmetric functions over GF(p) are equivalent to solving an equation system and enumerating the solutions. Furthermore, we give an lower bound on number of balanced symmetric functions over GF(p), and the lower bound provides best known results
Improved lower bound on the number of balanced symmetric functions over GF(p)
The lower bound on the number of n-variable balanced symmetric
functions over finite fields GF(p) presented in
{\cite{Cusick}} is improved in this paper
Rogers functions and fluctuation theory
Extending earlier work by Rogers, Wiener-Hopf factorisation is studied for a
class of functions closely related to Nevanlinna-Pick functions and complete
Bernstein functions. The name 'Rogers functions' is proposed for this class.
Under mild additional condition, for a Rogers function f, the Wiener--Hopf
factors of f(z)+q, as well as their ratios, are proved to be complete Bernstein
functions in both z and q. This result has a natural interpretation in
fluctuation theory of L\'evy processes: for a L\'evy process X_t with
completely monotone jumps, under mild additional condition, the Laplace
exponents kappa(q;z), kappa*(q;z) of ladder processes are complete Bernstein
functions of both z and q. Integral representation for these Wiener--Hopf
factors is studied, and a semi-explicit expression for the space-only Laplace
transform of the supremum and the infimum of X_t follows.Comment: 70 pages, 2 figure
Supersymmetric quantum mechanics on the lattice: III. Simulations and algorithms
In the fermion loop formulation the contributions to the partition function
naturally separate into topological equivalence classes with a definite sign.
This separation forms the basis for an efficient fermion simulation algorithm
using a fluctuating open fermion string. It guarantees sufficient tunnelling
between the topological sectors, and hence provides a solution to the fermion
sign problem affecting systems with broken supersymmetry. Moreover, the
algorithm shows no critical slowing down even in the massless limit and can
hence handle the massless Goldstino mode emerging in the supersymmetry broken
phase. In this paper -- the third in a series of three -- we present the
details of the simulation algorithm and demonstrate its efficiency by means of
a few examples.Comment: 21 pages, 10 figures; typos in text correcte
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