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Special Issue “CMMSE 2020” in Mathematical Methods in the Applied Sciences (MMA)

Authors:
Jesús Vigo Aguiar
Jesús Vigo Aguiar
Jesús Vigo Aguiar
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Sandra Ranilla-Cortina at University of Oviedo
Sandra Ranilla-Cortina
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DOI: 10.1002/mma.9194
EDITORIAL
Special Issue “CMMSE 2020” in Mathematical Methods in
the Applied Sciences (MMA)
The aim of this special issue is to provide a deep look into today's challenging mathematical and technological problems.
The authors examine and present innovative and rigorous solutions to a wide range of topics in the field of applied
mathematics and engineering, including quantum cryptography, fuzzy logic, physics, and more.
These studies demonstrate the importance of interdisciplinary collaboration and the combination of mathematical and
technological approaches in solving the most complex problems of our time. Each of the articles is an example of the
dedication of researchers in seeking effective and sustainable solutions to novel problems in science.
For instance, in [1], the authors develop a quantum key distribution protocol, a method for secure communication, on
qudits, to deal with the problem of cryptography systems in terms of quantum computing. The authors present a solution
using quantum operators to achieve a secure key distribution on these systems.
In [2], the focus is on fuzzy logic, a branch of mathematics that allows for the creation of more flexible and adaptable
systems that can better handle the uncertainty and complexity of real-world problems. Specifically, in this work they
provide a first notion of inconsistency by means of the absence of models, and they define two measures of consistency
that belong purely to the fuzzy paradigm.
The articles [3, 4] and [5] present important advances in mathematical methods applied to biology and physics.The
first deals with the Keller-Segel model, a mathematical model used to describe the movement of biological organisms.
The second presents a direct method for finding solutions to split quaternion matrix equations, which is an important
mathematical equation used to model physical systems. And the last one provides a method for determining the integra-
bility of GL(2,R)invariant fourth-order ordinary differential equations, which is crucial for understanding the behavior
of physical systems modeled by these equations.
Lastly, the work[6] provides a solution for controlling multi-input linear systems using Kalman reduced form and state
feedback. The authors apply this solution over Hermite rings, a type of mathematical ring, to achieve a more effective
control of the system.
In summary, these articles are a testament to the importance of scientific research and technological innovation in
seeking solutions to the most complex problems we face today.
Jesús Vigo Aguiar1
Sandra Ranilla-Cortina2
1University Salamanca, 37008, Spain
2Credit Suisse Bank, Madrid, 28001, Spain
Correspondence
Jesús Vigo Aguiar, University Salamanca, 37008, Spain.
Email: jvigo@usal.es
REFERENCES
1. P. Kumam, A Quantum Key Distribution On Qudits Using Quantum Operators. CMMSE 2020, MMA 6988, MMA-20-18819.R1.
2. N. Madrid, A Measure of Consistency for Fuzzy Logic Theories. CMMSE 2020, MMA 7470, MMA-20-19155.
3. R. de la Rosa Silva, Symmetry reductions of a (2+1)-dimensional Keller-Segel model. CMMSE 2020, MMA 7330, MMA-20-18753.R1.
4. S.-F. Yuan, Direct methods on 𝜂-Hermitian solutions of the split quaternion matrix equation (AXB,CXD)=(E,F). CMMSE 2020, MMA 7273,
MMA-20-19029.R1.
5. A. Ruiz Serván, On the integrability of GL(2,R)-invariant fourth-order ordinary differential equations. CMMSE 2020, MMA 7242,
MMA-20-19044.
6. M. V. Carriegos, Kalman reduced form and pole placement by state feedback for multi-input linear systems over hermite rings. CMMSE 2020,
MMA8240, MMA-20-19153.R1.
Math. Meth. Appl. Sci. 2023;46:15923. wileyonlinelibrary.com/journal/mma © 2023 John Wiley & Sons, Ltd. 15923
ResearchGate has not been able to resolve any citations for this publication.
Kalman reduced form and pole placement by state feedback for multi‐input linear systems over Hermite rings
Article
Full-text available
  • Mar 2022
  • MATH METHOD APPL SCI
A Kalman reduced form is obtained for linear systems over Hermite rings. This reduced form gives information of the set of assignable polynomials to a given linear system.
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A measure of consistency for fuzzy logic theories
Article
Full-text available
  • May 2021
  • MATH METHOD APPL SCI
Fuzzy logic has shown to be a suitable framework to handle contradictions in which, unsurprisingly, the notion of inconsistency can be defined in different ways. This paper starts with a short survey of different ways to define the notion of inconsistency in fuzzy logic systems. As a result, we provide a first notion of inconsistency by means of the absence of models. Subsequently, we define two measures of consistency that belong purely to the fuzzy paradigm; in the sense that both measures coincide with the crisp notion of consistency when the set of truth values is {0, 1}. Accordingly, we can state that the two provided measures of consistence are notions of consistence based on degrees, bringing back the spirit of fuzzy logic into the notion of consistency.
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Symmetry reductions of a (2 + 1)‐dimensional Keller–Segel model
Article
Full-text available
  • Mar 2021
  • MATH METHOD APPL SCI
In this work, symmetry groups are used to determine symmetry reductions of a (2 + 1)‐dimensional Keller–Segel system depending on two arbitrary functions. We show that the point symmetries of the considered Keller–Segel system comprise an infinite‐dimensional Lie algebra which involves three arbitrary functions. By way of example, we have used these point symmetries to reduce straightaway the given system of second‐order partial differential equations to a system of second‐order ordinary differential equations. Moreover, we are allowed to substitute one of the dependent variables from one of the equations into the other, leading to an equivalent fourth‐order nonlinear ordinary differential equation. This equation is reduced through the use of solvable symmetry subalgebras, and some exact solutions are obtained for a particular case.
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Direct methods on η ‐Hermitian solutions of the split quaternion matrix equation (AXB,CXD)=(E,F)
Article
Full-text available
  • Feb 2021
  • MATH METHOD APPL SCI
This paper provides two direct methods for solving the split quaternion matrix equation ( A X B , C X D ) = ( E , F ) , where X is an unknown split quaternion η‐Hermitian matrix, and A, B, C, D, E, F are known split quaternion matrices with suitable size. Our tools are the Kronecker product, Moore–Penrose generalized inverse, real representation, and complex representation of split quaternion matrices. Our main work is to find the necessary and sufficient conditions for the existence of a solution of the matrix equation mentioned above, derive the explicit solution representation, and provide four numerical algorithms and two numerical examples.
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On the integrability of GL(2, R)-invariant fourth-order ordinary differential equations
Article
Full-text available
  • Feb 2021
  • MATH METHOD APPL SCI
The integrability of fourth-order ordinary differential equations admitting gl(2, R) as Lie symmetry algebra is addressed in this work. The classical Lie's method of reduction cannot be applied to solve by quadrature this kind of equations because gl(2, R) is nonsolvable. In order to avoid such difficulty, a solvable structure involving the vector field identified with the equation is constructed by using the symmetry generators of gl(2, R). This permits to compute a first integral of the equation by quadrature. In the aftermath, it is shown that the general solution of any GL(2, R)-invariant fourth-order ordinary differential equation can be obtained in parametric form, involving linearly independent solutions to a related one-parameter family of linear second-order equations. Particular examples are also shown with the end of illustrating the presented approach.
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A quantum key distribution on qudits using quantum operators
Article
Full-text available
  • Nov 2020
  • MATH METHOD APPL SCI
Cryptography is processing for securing communication between two people. The opponent wants to know the message that is encrypted using a secret key. Although the opponent can eavesdrop the message sent between the sender and the receiver, the opponent is unable to decrypt to read the message. Therefore, the secret key is very important. The sender and the receiver agree with the secret key in an insecure channel by using key distribution protocol such as the Diffie–Hellman protocol. Since quantum computer is coming soon, Diffie–Hellman protocol is not secure. We will develop a quantum key distribution protocol. The benefit of the quantum system is the quantum state that cannot copy by no‐cloning theorem. Thus, the opponent does not copy and keeps the message that is quantum. In this paper, a novel quantum key distribution protocol between two people (Alice and Bob) based on quantum operators is developed. The opponent (Eve) wants to know the secret key. Although Eve knows this quantum key distribution protocol, Eve does not behave similarly to Alice and Bob. For example, Eve eavesdrops Alice's quantum state that was sent to Bob, and Eve sends another quantum state. Therefore, we cannot control Eve's behavior. So we give the upper bound of mutual information between the user and opponent by using Holevo's bound. We verify the usual security definition for quantum key distribution that is equality‐and‐uniformity and privacy in the mutual information sense.
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Symmetry reductions of a (2 + 1)-dimensional Keller-Segel model
  • R De La
  • Rosa Silva
R. de la Rosa Silva, Symmetry reductions of a (2 + 1)-dimensional Keller-Segel model. CMMSE 2020, MMA 7330, MMA-20-18753.R1.