Revistas académicas de la Universidad Católica del Norte
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New approach for Somos’s Dedekind eta-function identities of level 6
No full textIn the present work, we prove few new Dedekind eta-function identities of level 6 discovered by Somos in two different methods. Also during this process, we give an alternate method to Somos’s Dedekind eta-function identities of level 6 proved by B. R. Srivatsa Kumar et al. As an application of this, we establish colored partition identities
Linear maps on ℬ(ℋ) preserving some operator properties
No full textIn this paper, for a complex Hilbert space ℋ with dim ℋ ≥ 2, we study the linear maps on ℬ(ℋ), the bounded linear operators on ℋ, that preserves projections and idempotents. As a result, we characterize the linear maps on ℬ(ℋ) that preserves involutions in both directions
Graphs of edge-to-vertex detour number 2
No full textFor two vertices u and v in a graph G = (V,E), the detour distance D(u, v) is the length of a longest u − v path in G. A u − v path of length D(u, v) is called a u − v detour. For subsets A and B of V , the detour distance D(A,B) is defined as D(A,B) = min{D(x, y) : x ∈ A, y ∈ B}. A u − v path of length D(A,B) is called an A-B detour joining the sets A,B ⊆ V where u ∈ A and v ∈ B. A vertex x is said to lie on an A − B detour if x is a vertex of some A−B detour. A set S ⊆ E is called an edge-to-vertex detour set if every vertex of G is incident with an edge of S or lies on a detour joining a pair of edges of S. The edge-to-vertex detour number dn2(G) of G is the minimum order of its edge-to-vertex detour sets and any edge-to-vertex detour set of order dn2(G) is an edge-to-vertex detour basis of G. Graphs G of size q for which dn2(G) = 2 are characterized
The probability of an automorphism of an abelian group fixing a group element
No full textIn this paper, we consider the probability of an automorphism of a finite abelian group fixing a group element. Explicit computations are made to find the fusion classes of a finite abelian groups. The probability of an automorphism fixing a group element is obtained in terms of fusion classes. We also compute the bounds of the probability for some particular cases
Ortiz Nicolás, J. C. y Alatorre Gúzman, D. (Comps.). (2019). Innovación Social y Diseño. UNAM. ISBN: 9786073025683
Get PDFThe main contributions of Social Innovation and Design, book compiled by two Mexican academics, Dr. Juan Carlos Ortiz Nicolás and Mtr. Diego Alatorre, are described and analyzed. This article emphasizes on the didactic and pedagogical objectives for the teaching and practice of the design of a publication that helps the reader to understand the trajectory of this discipline; a journey in wich the designer becomes a change maker and is led toward the praxis of social innovation. In this book, researchers and academics provide theoretical contributions and describe processes and scopes of social innovation for design, agreeing that the benefits of this approach not only lie in the success of the development of innovative products and / or the profit of business, but also positively influences the quality of life of people through the construction of systemic relationships that can be socially beneficial.Se describen y analizan las principales aportaciones del libro Innovación Social y Diseño, una obra compilada por dos académicos mexicanos: Dr. Juan Carlos Ortiz Nicolás y Mtro. Diego Alatorre. Se enfatiza en los objetivos didácticos y pedagógicos para la enseñanza y práctica del diseño de una obra que ayuda al lector a comprender la trayectoria de esta disciplina; una travesía donde el diseñador se convierte en un agente de cambio y se conduce hacia la praxis de la innovación social. En este libro, investigadores y académicos brindan aportes teóricos y describen procesos y alcances de la innovación social para el diseño, coincidiendo en que las bondades de este enfoque no solo recaen en el éxito del desarrollo de productos innovadores y/o el provecho de los negocios, sino que también pueden influir positivamente en la calidad de vida de las personas a través de la construcción de relaciones sistémicas que pueden ser socialmente beneficiosas
21 lecciones para el siglo XXI: Yuval Noah Harari
Get PDFThere are two relevant elements for the work of any university. Work and Education are themes that give foundation and meaning to the university. Educators must consider a new cultural context, influenced by artificial intelligence and new technologies that profoundly influence these two areas of human life. How to respond in a meaningful way to the challenges posed by the new culture, what type of education, what content, what perspectives and forms will have to be considered and for what Jobs the citizens of the new century must be trained. These are some of the questions posed by Yuval Noah Harari, in his work 21 Lessons for the XXI Century.Dos dimensiones relevantes para la labor de toda universidad: el Trabajo y la Educación, son temas que dan fundamento y sentido a la universidad. Hay que considerar un nuevo contexto cultural, influenciado por la inteligencia artificial, y las nuevas tecnologías que influyen profundamente en estos dos ámbitos de la vida humana. Cómo responder de buena forma a los desafíos que nos propone la nueva cultura, qué tipo de educación, qué contenidos, qué perspectivas y formas se tendrán que considerar y para que trabajos hay que formar los ciudadanos del nuevo siglo. Estas son algunas de las interrogantes que plantea Yuval Noah Harari, en su obra 21 Lecciones para el Siglo XXI
New algebraic properties of middle Bol loops II
No full textA loop (Q, ·, \, /) is called a middle Bol loop (MBL) if it obeys the identity x(yz\x)=(x/z)(y\x). To every MBL corresponds a right Bol loop (RBL) and a left Bol loop (LBL). In this paper, some new algebraic properties of a middle Bol loop are established in a different style. Some new methods of constructing a MBL by using a non-abelian group, the holomorph of a right Bol loop and a ring are described. Some equivalent necessary and sufficient conditions for a right (left) Bol loop to be a middle Bol loop are established. A RBL (MBL, LBL, MBL) is shown to be a MBL (RBL, MBL, LBL) if and only if it is a Moufang loop
A subclass with bi-univalence involving Horadam polynomials and its coefficient bounds
No full textIn this research contribution, we have constructed a subclass of analytic bi-univalent functions using Horadam polynomials. Bounds for certain coefficients and Fekete- Szegö inequalities have been estimated
Some generalized results related to Fibonacci sequence
No full textCassini's identity states that for the nth Fibonacci number Fn+1Fn-1-Fn2=(-1)n, We generalize Fibonacci sequence in terms of the number of sequences. Fibonacci sequence is the particular case of generating only one sequence. This generalization is used to generalize Cassini’s identity. Moreover we prove few more results which can be seen as generalized form of the results which hold for Fibonacci sequence
Fixed point theorems in the study of positive strict set-contractions operator
No full textThe author use fixed point index properties and the general minorant principle(see Theorem 7:B in [11]) to prove new fixed point theorems for strict set-contractionoperators leaving invariant a cone in a Banach space