Maximizing the amount of work harvested from an environment is important for
a wide variety of biological and technological processes, from
energy-harvesting processes such as photosynthesisto energy storage systems
such as fuels and batter...
The phase transition in bounded-size Achlioptas processes
April 27, 2017
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Mathematics
Physics
Probability
Statistical Mechanics
Combinatorics
Probability
Statistical Mechanics
Combinatorics
Perhaps the best understood phase transition is that in the component
structure of the uniform random graph process introduced by Erd\H{o}s and
R\'enyi around 1960. Since the model is so fundamental, it is very interesting
to know which fea...
The First Syzygy of Hibi Rings Associated with Planar distributive
lattices
April 26, 2017
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Mathematics
Commutative Algebra
Let L be a finite distributive lattice and S=K[xα:α∈L] be a polynomial ring over a field K and $I=\langle x_\alpha
x_\beta - x_{\alpha\vee \beta} x_{\alpha\wedge\beta} : \alpha \nsim
\beta,\alpha,\b...
Vaidya Spacetime in the Diagonal Coordinates
April 23, 2017
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Physics
General Relativity and Quantum Cosmology
We have analyzed the transformation from initial coordinates (v,r) of the
Vaidya metric with light coordinate v to the most physical diagonal
coordinates (t,r). An exact solution has been obtained for the corresponding
metric tensor i...
The lost proof of Fermat's last theorem
April 20, 2017
Mathematics
General Mathematics
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
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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
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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
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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...