36 research outputs found
Quantum Barnes function as the partition function of the resolved conifold
We suggest a new strategy for proving large duality by interpreting
Gromov-Witten, Donaldson-Thomas and Chern-Simons invariants of a Calabi-Yau
threefold as different characterizations of the same holomorphic function. For
the resolved conifold this function turns out to be the quantum Barnes
function, a natural -deformation of the classical one that in its turn
generalizes Euler's gamma function. Our reasoning is based on a new formula for
this function that expresses it as a graded product of -shifted
multifactorials.Comment: 47 pages, 7 figure
Invasion waves in the presence of a mutualist
This paper studies invasion waves in the diffusive
Competitor-Competitor-Mutualist model generalizing the 2-species Lotka-Volterra
model studied by Weinberger et al. The mutualist may benefit the invading or
the resident species producing two different types of invasions. Sufficient
conditions for linear determinacy are derived in both cases, and when they
hold, explicit formulas for linear spreading speeds of the invasions are
obtained by linearizing the model. While in the first case the linear speed is
increased by the mutualist, it is unaffected in the second case. Mathematical
methods are based on converting the model into a cooperative reaction-diffusion
system.Comment: 21 pages, 4 figure
From Golden to Unimodular Cryptography
We introduce a natural generalization of the golden cryptography, which uses
general unimodular matrices in place of the traditional Q-matrices, and prove
that it preserves the original error correction properties of the encryption.
Moreover, the additional parameters involved in generating the coding matrices
make this unimodular cryptography resilient to the chosen plaintext attacks
that worked against the golden cryptography. Finally, we show that even the
golden cryptography is generally unable to correct double errors in the same
row of the ciphertext matrix, and offer an additional check number which, if
transmitted, allows for the correction.Comment: 20 pages, no figure