Articles publicats (Matemàtica)

Permanent URI for this collection

Browse

Recent Submissions

Now showing 1 - 5 of 412
  • Item
    Open Access
    On the Apparent Discretization of Spacetime and Its Connection with the Cosmological Constant
    (MDPI, 2024) Giné, Jaume; Luciano, Giuseppe Gaetano
    The emergence of a minimal observable length of order of the Planck scale is a prediction of many quantum theories of gravity. However, the question arises as to whether this is a real fundamental length affecting nature in all of its facets, including spacetime. In this work, we show that the quantum measurement process implies the existence of a minimal measurable length and consequently the apparent discretization of spacetime. The obtained result is used to infer the value of zero-point energy in the universe, which is found to be in good agreement with the observed cosmological constant. This potentially offers some hints towards the resolution of the cosmological constant problem.
  • Item
    Open Access
    E-Coin-Based Priced Oblivious Transfer with a Fast Item Retrieval
    (MDPI, 2024) Sebé Feixas, Francesc; Simón, Sergi
    Priced oblivious transfer (POT) is a cryptographic protocol designed for privacy-preserving e-commerce of digital content. It involves two parties: the merchant, who provides a set of priced items as input, and a customer, who acquires one of them. After the protocol has run, the customer obtains the item they chose, while the merchant cannot determine which one. Moreover, the protocol guarantees that the customer gets the content only if they have paid the price established by the merchant. In a recent paper, the authors proposed a POT system where the payments employed e-coin transactions. The strong point of the proposal was the absence of zero-knowledge proofs required in preceding systems to guarantee the correctness of payments. In this paper, we propose a novel e-coin-based POT system with a fast item retrieval procedure whose running time does not depend on the number of items for sale. This is an improvement over the aforementioned existing proposal whose execution time becomes prohibitively long when the catalog is extensive. The use of zero-knowledge proofs is neither required.
  • Item
    Open Access
    On the permutation cycle structures for almost Moore digraphs of degrees 4 and 5
    (Shahin Digital Publisher, 2023) Miret, Josep M. (Josep Maria); Simanjuntak, Rinovia; Simón, Sergi
    Almost Moore digraphs of degree d and diameter k, for short (d, k)-digraphs, appear in the degree/diameter problem as a class of extremal directed graphs. Their order is one less than the unattainable Moore bound M(d, k) = 1 + d + · · · + d k . So far, their existence has only been shown for k = 2. Their nonexistence has been proven for k = 3, 4 and for d = 2, 3, when k ≥ 3. In this paper, we study the possible cycle structures of the permutation of repeats for the (4, k) and (5, k)-digraphs.
  • Item
    Open Access
    Lower bounds for the local cyclicity for families of centers
    (Elsevier, 2021) Giné, Jaume; Gouveia, Luiz F. S.; Torregrosa, Joan
    In this paper, we are interested in how the local cyclicity of a family of centers depends on the parameters. This fact was pointed out in [21], to prove that there exists a family of cubic centers, labeled by in [25], with more local cyclicity than expected. In this family, there is a special center such that at least twelve limit cycles of small amplitude bifurcate from the origin when we perturb it in the cubic polynomial general class. The original proof has some crucial missing points in the arguments that we correct here. We take advantage of a better understanding of the bifurcation phenomenon in nongeneric cases to show two new cubic systems exhibiting 11 limit cycles and another exhibiting 12. Finally, using the same techniques, we study the local cyclicity of holomorphic quartic centers, proving that 21 limit cycles of small amplitude bifurcate from the origin, when we perturb in the class of quartic polynomial vector fields.
  • Item
    Open Access
    Privacy-Preserving Electricity Trading for Connected Microgrids
    (MDPI, 2024) Alàs Cercós, Oriol; Sebé Feixas, Francesc
    The electricity market is evolving from the traditional unidirectional model into a bidirectional one in which households also generate and sell energy. This new scenario requires technology able to manage the available energy and guarantee that all the participants pay or are paid appropriately. Unfortunately, fine-grained monitoring of energy production and consumption makes it possible to infer sensitive information about confidential aspects of people’s private life. In this paper, we propose a system designed for privacy-preserving electricity trading in a connected microgrid. The system guarantees that at the end of a billing period, the distribution system operator can compute the quantity to be charged or paid to each household while being unable to trace its consumption details.