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Estimates of Hyperbolic Metric with Applications to Teichmuller Spaces
TOSHIYUKI SUGAWA 경북대학교 자연과학대학 수학과 2002 Kyungpook mathematical journal Vol.42 No.1
We show a monotonicity property of the hyperbolic metric of a punctured rectangular torus. We will then deduce a lower estimate of the hyperbolic metric of the domain C\{0,1}. We also determine the value of hyperbolic sup-norm of standard quadratic differentials on the once-punctured square torus or the symmetric four-times punctured sphere. This enables us to compute numerically the inner and outer radii of the Bers embedding of the corrdesponding Teichmuller space under the hypothesis of some conjectural properties of it
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Ideal Classes and Cappell-Shaneson Homotopy 4-Spheres
김민훈,Shohei Yamada 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.3
Gompf proposed a conjecture on Cappell-Shaneson matrices whose affirmative answer implies that all Cappell-Shaneson homotopy 4-spheres are diffeomorphic to the standard 4-sphere. We study Gompf conjecture on Cappell-Shaneson matrices using various algebraic number theoretic techniques. We find a hidden symmetry between trace n Cappell-Shaneson matrices and trace 5-n Cappell-Shaneson matrices which was suggested by Gompf experimentally. Using this symmetry, we prove that Gompf conjecture for the trace n case is equivalent to the trace 5-n case. We confirm Gompf conjecture for the special cases that -64 ≤ trace ≤ 69 and corresponding Cappell-Shaneson homotopy 4-spheres are diffeomorphic to the standard 4-sphere. We also give a new infinite family of Cappell-Shaneson spheres which are diffeomorphic to the standard 4-sphere.
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Ly Kim Ha 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.3
The main purpose of this paper is to show that over a large class of bounded domains Ω ⊂ C2, for 1 < p < ∞, the Bergman projection P is bounded from Lp(Ω, dV ) to the Bergman space Ap(Ω); from L∞(Ω) to the holomorphic Bloch space BlHol(Ω); and from L1(Ω, P(z, z)dV ) to the holomorphic Besov space Besov(Ω), where P(ζ, z) is the Bergman kernel for Ω.
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Miyachi’s Theorem for the k-Hankel Transform on R^d
Mohamed Amine Boubatra 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.3
The classical Hardy theorem on R states that a function f and its Fourier transform cannot both be very smal simultaneously, this fact was generalized by Miyachi in terms L1 + L∞ and log+-functions. In this paper, we consider the k-Hankel transform which is a deformation of the Hankel transform by a parameter k > 0 arising from Dunkl’s theory. Moreover, we study Miyachi’s theorem for the k-Hankel transform on Rd.
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Existence and Uniqueness Results for a Coupled System of Nonlinear Fractional Langevin Equations
Sushma Basil,Santhi Antony,Muralisankar Subramanian 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.3
In this paper, we present a sufficient condition for the unique existence of solutions for a coupled system of nonlinear fractional Langevin equations, with a new class of multipoint and nonlocal integral boundary conditions. We define a Z*λ-contraction mapping and present the sufficient condition by identifying the problem with an equivalent fixed point problem in the context of b-metric spaces. Finally, some numerical examples are given to validate our main results.
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Some Results on Generalized Asymptotically Nonexpansive Mappings in p-Hadamard Spaces
Kaewta Juanak,Aree Varatechakongka,Withun Phuengrattana 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.3
In this paper, we study the fixed point property for generalized asymptoti cally nonexpansive mappings in the setting of p-Hadamard spaces, with p ≥ 2. We also prove the strong convergence of the sequence generated by the modified two-step iterative sequence for finding a fixed point of a generalized asymptotically nonexpansive mapping in p-Hadamard spaces.
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Multinomial Probability Distribution and Quantum Deformed Algebras
Fridolin Melong 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.3
An examination is conducted on the multinomial coefficients derived from generalized quantum deformed algebras, and on their recurrence relations. The R(p, q)-deformed multinomial probability distribution and the negative R(p, q)-deformed multino mial probability distribution are constructed, and the recurrence relations are determined. From our general result, we deduce particular cases that correspond to quantum algebras considered in the literature.
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On Extended Hurwitz-Lerch Zeta Function
Mohannad Jamal Said Shahwan,Maged Gumman Bin-Saad,Mohammed Ahmed Pathan 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.3
This paper investigates an extended form Hurwitz-Lerch zeta function, as well as related integral images, ordinary and fractional derivatives, and series expan sions, using the term extended beta function. In addition, we establish a connection between the extended Hurwitz-Lerch zeta function and the Laguerre polynomials. Fur thermore, we present a probability distribution application of the extended Hurwitz-Lerch zeta functionζδ,µν,λ. Several (known and new) results are shown to follow as special cases of our findings.
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Towards A Dichotomy for the List Switch Homomorphism Problem for Signed Graph
김효빈,시거스, 마크 할버 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.3
We make advances towards a structural characterisation of the signed graphs H for which the list switch H-colouring problem List-S-Hom(H) can be solved in polynomial time. We conjecture two different characterisations, the second refining the first, in the case that the graph H can be switched to a graph in which every negative edge is also positive. Using a recent proof of the first characterisations for reflexive signed graphs, by Bok et. al., we prove the second characterisation for reflexive signed graphs. We also provide several tools for reducing the problem to the bipartite case, and prove a full complexity dichotomy for a related problem.
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Weak u-S-flat Modules and Dimensions
Refat Abdelmawla Khaled Assaad,Xiaolei Zhang 경북대학교 자연과학대학 수학과 2023 Kyungpook mathematical journal Vol.63 No.3
In this paper, we generalize the notions uniformly S-flat, briefly u-S-flat, modules and dimensions. We introduce and study the notions of weak u-S-flat modules. An R-module M is said to be weak u-S-flat if TorR 1 (R/I, M) is u-S-torsion for any ideal I of R. This new class of modules will be used to characterize u-S-von Neumann regular rings. Hence, we introduce the weak u-S-flat dimensions of modules and rings. The rela tions between the introduced dimensions and other (classical) homological dimensions are discussed.
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