This work contains two papers: the first published in 2022 and entitled "On
the nature of some Euler's double equations equivalent to Fermat's last
theorem" provides a marvellous proof through the so-called discordant forms of
appropriate E...
To compute orientations of Morse flow trees in Legendrian contact
homology
April 17, 2017
Mathematics
Symplectic Geometry
Let Λ be a closed, connected Legendrian submanifold of the 1-jet
space of a smooth n-dimensional manifold. Associated to Λ there is a
Legendrian invariant called Legendrian contact homology, which is defined by
counting ri...
Algorithmic releases on the spanning trees of suitable graphs
April 17, 2017
| |
Mathematics
Combinatorics
In this paper algebraic and combinatorial properties and a computation of the
number of the spanning trees are developed for certain graphs. To this purpose,
an original method, independent of the spectrum of the Laplacian matrix
associated...
A proof of Riemann Hypothesis
April 16, 2017
|
Mathematics
General Mathematics
Let Ξ(t) be a function relating to the Riemann zeta function ζ(s)
with s=21+it. In this paper, we construct a function v
containing t and Ξ(t), and prove that v satisfies a nonadjoint boundary
value prob...
Fast Similarity Sketching
April 14, 2017
| | |
Computer Science
Data Structures and Algorithms
We consider the Similarity Sketching problem: Given a universe
[u]={0,…,u−1} we want a random function S mapping subsets
A⊆[u] into vectors S(A) of size t, such that similarity is
preserved. More prec...
Generalized Three and Four Person Hat Game
April 13, 2017
Mathematics
Computer Science
Combinatorics
Discrete Mathematics
Information Theory
Information Theory
This paper studies Ebert's hat problem for three and four players and two
colors, where the probabilities of the colors may be different for each player.
Our goal is to maximize the probability of winning the game and to describe
winning st...
Classification of Lie algebras of specific type in complexified Clifford
algebras
April 12, 2017
|
Physics
Mathematics
Mathematical Physics
Mathematical Physics
Mathematical Physics
Mathematical Physics
We give a full classification of Lie algebras of specific type in
complexified Clifford algebras. These sixteen Lie algebras are direct sums of
subspaces of quaternion types. We obtain isomorphisms between these Lie
algebras and classical m...
Star flows: a characterization via Lyapunov functions
April 6, 2017
Mathematics
Dynamical Systems
In this work, it is presented a characterization of star property for a C1
vector field based on Lyapunov functions. It is also obtained conditions to
strong homogeneity for singular sets by using the notion of infinitesimal
Lyapunov fun...
Primordial black holes from collapsing antimatter
April 6, 2017
Physics
High Energy Physics - Theory
General Relativity and Quantum Cosmology
In this paper a simple (i.e. free of fine-tuning, etc.) new mechanism for
primordial black hole formation based on the collapse of large antimatter
systems in the early Universe is introduced. A peculiarity of this process is
that, compared...
A Mathematical Framework for Consciousness in Neural Networks
April 4, 2017
|
Quantitative Biology
Neurons and Cognition
Neurons and Cognition
This paper presents a novel mathematical framework for bridging the
explanatory gap (Levine, 1983) between consciousness and its physical
correlates. Specifically, we propose that qualia correspond to singularities in
the mathematical repre...