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The abstract science of numbers, quantity, and space, either as abstract concepts (pure mathematics), or as applied to other disciplines such as physics and engineering (applied mathematics). Join now and publish your research and/or review what has been already published.

31/01/2024| By
Álvaro Álvaro Antón-Sancho

Let X be a compact Riemann surface of genus g ≥ 2 and M(E6) be the moduli space of E6-Higgs bundles over X. We consider the automorphisms σ+ of M(E6) defined by σ (E, φ) = (E∗ , −φt) , induced by the action of the outer involution of E6 in M(E6), and σ− defined by σ (E, φ) = (E* , -φt), which results from the combination of σ+ with the involution of M(E6), which consists on a change of sign in the Higgs field. In this work, we describe the fixed points of σ+ and σ−, as F4-Higgs bundles, F4-Higgs pairs associated with the fundamental irreducible representation of F4, and PSp(8, C)-Higgs pairs associated with the second symmetric power or the second wedge power of the fundamental representation of Sp(8, C). Finally, we describe the reduced notions of semistability and polystability for these objects. Citation: Antón-Sancho, Álvaro. F4 and PSp (8, ℂ)-Higgs pairs understood as fixed points of the moduli space of E6-Higgs bundles over a compact Riemann surface. Open Mathematics, vol. 20, no. 1, 2022, pp. 1723-1733.

Version 1
Factorization of the real part of complex numbers squared
16/10/2023| By
Pedro Hugo Pedro Hugo Garcia Peláez

This refers to the process of expressing the square of the real part of complex numbers as a product of its factors. In mathematical terms, if you have a complex number z = a biz=a+bi, where a-a is the real part and bb is the imaginary part, the factorization involves breaking down {Re}(z))^2(Re(z)) into its constituent factors. This process can be useful in various mathematical contexts, such as simplifying expressions.

21/05/2023| By
Gennady Gennady Butov

This is just an attempt to associate sums or differences of prime numbers with points lying on an ellipse or hyperbola. Certain pairs of prime numbers can be represented as radius-distances from the focuses to points lying either on the ellipse or on the hyperbola. The ellipse equation can be written in the following form: |p(k)| |p(t)| = 2n. The hyperbola equation can be written in the following form: ||p(k)| - |p(t)|| = 2n. Here p(k) and p(t) are prime numbers (p(1) = 2, p(2) = 3, p(3) = 5, p(4) = 7,...), k and t are indices of prime numbers, 2n is a given even number, k, t, n ∈ N. If we construct ellipses and hyperbolas based on the above, we get the following: 1) there are only 5 non-intersecting curves (for 2n=4; 2n=6; 2n=8; 2n=10; 2n=16). The remaining ellipses have intersection points. 2) there is only 1 non-intersecting hyperbola (for 2n=2) and 1 non-intersecting vertical line. The remaining hyperbolas have intersection points.

12/01/2023| By
Fernando Gustavo Fernando Gustavo Isa Massa

La educación como sabemos es el eje del crecimiento y desarrollo; y de una verdadera humanidad. El fractal cruz es un modelo de geometría fractal, que se usa para derivar datos discretos, y encontrar junto a un nuevo modelo de estadísticas circulares; la probabilidad de uniformidad de la serie de datos. También útil en la predicción de la continuación de la serie de datos. El segundo modelo denominado estadística circular es demostrado con integrales y límites y encuentra razón en la predicción de dramas sociales como lo son: la violencia contra las mujeres, la delincuencia, la trata de personas y secuestro extorsivo.

11/01/2023| By
Leopoldo Leopoldo Viveros-Rosas ,
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José Antonio José Antonio Vega-González

Se utiliza el modelo clasificador Naive como propuesta de herramienta para dar claridad en la decisión sobre las alternativas en la contratación de personal académico del Tecnológico de Estudios Superiores de Coacalco (TESCo). Se considera una base de datos de 232 personas como personal académico de las cuales se utilizan 180 para el cálculo de probabilidades, mismas que se prueban con el resto de la base de datos. Se calculan las probabilidades conjuntas y se utilizan para evaluar el clasificador. El modelo permite asignar probabilidades para cada uno de los nuevos prospectos de contratación de personal académico.

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