Showing papers in "Journal of The Korean Mathematical Society in 2020"
16 citations
TL;DR: In this paper, the authors derived sufficient conditions for normalized analytic functions f to belong to various subclasses of starlike functions, or to satisfy | log(zf ′(z)/f(z))| < 1, | (zf ǫ (z)/ǫ(z)2 − 1 | < 1 and zf Ã(z/ǫ ) lying in the parabolic region v2 < 2u− 1.
Abstract: Let p be an analytic function defined on the open unit disk D. We obtain certain differential subordination implications such as ψ(p) := pλ(z)(α+βp(z)+γ/p(z)+δzp′(z)/pj(z)) ≺ h(z) (j = 1, 2) implies p ≺ q, where h is given by ψ(q) and q belongs to P, by finding the conditions on α, β, γ, δ and λ. Further as an application of our derived results, we obtain sufficient conditions for normalized analytic function f to belong to various subclasses of starlike functions, or to satisfy | log(zf ′(z)/f(z))| < 1, |(zf ′(z)/f(z))2 − 1| < 1 and zf ′(z)/f(z) lying in the parabolic region v2 < 2u− 1.
6 citations
6 citations
5 citations
TL;DR: In this article, the authors proved complete formulas for counting quasipolynomials for small numbers of pieces and other formulas for high-order coefficients of the general counting qua-polynomials.
Abstract: Parts I-IV showed that the number of ways to place $q$ nonattacking queens or similar chess pieces on an $n\times n$ chessboard is a quasipolynomial function of $n$ whose coefficients are essentially polynomials in $q$. For partial queens, which have a subset of the queen's moves, we proved complete formulas for these counting quasipolynomials for small numbers of pieces and other formulas for high-order coefficients of the general counting quasipolynomials. We found some upper and lower bounds for the periods of those quasipolynomials by calculating explicit denominators of vertices of the inside-out polytope.
Here we discover more about the counting quasipolynomials for partial queens, both familiar and strange, and the nightrider and its subpieces, and we compare our results to the empirical formulas found by Kotěsovec. We prove some of Kotěsovec's formulas and conjectures about the quasipolynomials and their high-order coefficients, and in some instances go beyond them.
5 citations
5 citations
4 citations
4 citations
TL;DR: In this article, the authors considered the case of pricing discretely-sampled variance swaps under the class of equity-interest rate hybridization, and obtained an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions.
Abstract: This paper considers the case of pricing discretely-sampled variance swaps under the class of equity-interest rate hybridization. Our modeling framework consists of the equity which follows the dynamics of the Heston stochastic volatility model, and the stochastic interest rate is driven by the Cox-Ingersoll-Ross (CIR) process with full correlation structure imposed among the state variables. This full correlation structure possesses the limitation to have fully analytical pricing formula for hybrid models of variance swaps, due to the non-affinity property embedded in the model itself. We address this issue by obtaining an efficient semi-closed form pricing formula of variance swaps for an approximation of the hybrid model via the derivation of characteristic functions. Subsequently, we implement numerical experiments to evaluate the accuracy of our pricing formula. Our findings confirm that the impact of the correlation between the underlying and the interest rate is significant for pricing discretely-sampled variance swaps.
4 citations
TL;DR: In this paper, the authors studied the Zariski closure of the set of 1-jets on a weighted homogeneous plane curve singularity with tangent space πC : TC/k → C.
Abstract: Let k be a field of characteristic 0. Let C = Spec(k[x, y]/〈f〉) be a weighted homogeneous plane curve singularity with tangent space πC : TC/k → C . In this article, we study, from a computational point of view, the Zariski closure G (C ) of the set of the 1-jets on C which define formal solutions (in F [[t]]2 for field extensions F of k) of the equation f = 0. We produce Groebner bases of the ideal N1(C ) defining G (C ) as a reduced closed subscheme of TC/k and obtain applications in terms of logarithmic differential operators (in the plane) along C .
3 citations
TL;DR: In this paper, the authors introduced the notion of orbit equivalence to canonically associated dynamical systems of self-similar groups and showed that the limit dynamical system of two groups are orbit equivalent if and only if their associated Deaconu groupoids are isomorphic as topological groupoids.
Abstract: Following Matsumoto’s definition of continuous orbit equivalence for one-sided subshifts of finite type, we introduce the notion of orbit equivalence to canonically associated dynamical systems, called the limit dynamical systems, of self-similar groups. We show that the limit dynamical systems of two self-similar groups are orbit equivalent if and only if their associated Deaconu groupoids are isomorphic as topological groupoids. We also show that the equivalence class of Cuntz-Pimsner groupoids and the stably isomorphism class of Cuntz-Pimsner algebras of self-similar groups are invariants for orbit equivalence of limit dynamical systems.
TL;DR: In this paper, a measure expanding diffeomorphism on compact smooth manifolds is characterized via the notion of Ω-stability, and it is shown that f is invariant measure expanding on X if and only if its restriction on CR(f) is invariantly measure expanding.
Abstract: In this paper we present a measurable version of the Smale’s spectral decomposition theorem for homeomorphisms on compact metric spaces. More precisely, we prove that if a homeomorphism f on a compact metric space X is invariantly measure expanding on its chain recurrent set CR(f) and has the eventually shadowing property on CR(f), then f has the spectral decomposition. Moreover we show that f is invariantly measure expanding on X if and only if its restriction on CR(f) is invariantly measure expanding. Using this, we characterize the measure expanding diffeomorphisms on compact smooth manifolds via the notion of Ω-stability.
TL;DR: In this paper, a parallel iterative method for finding a common fixed point of a finite family of strongly nonexpansive mappings in a real reflexive Banach space is introduced.
Abstract: In this paper, we introduce a parallel iterative method for finding a common fixed point of a finite family of Bregman strongly nonexpansive mappings in a real reflexive Banach space. Moreover, we give some applications of the main theorem for solving some related problems. Finally, some numerical examples are developed to illustrate the behavior of the new algorithms with respect to existing algorithms.
TL;DR: In this article, the authors classify all solutions bounded from below to uniformly elliptic equations of second order in the form of Lu(x) = aij(x),Diju (x) + bi(x,Diu(x)) + c(x)-u(x)/u(X) = f(x).
Abstract: In this paper, we classify all solutions bounded from below to uniformly elliptic equations of second order in the form of Lu(x) = aij(x)Diju(x) + bi(x)Diu(x) + c(x)u(x) = f(x) or Lu(x) = Di(aij(x) Dju(x)) + bi(x)Diu(x) + c(x)u(x) = f(x) in unbounded cylinders. After establishing that the Aleksandrov maximum principle and boundary Harnack inequality hold for bounded solutions, we show that all solutions bounded from below are linear combinations of solutions, which are sums of two special solutions that exponential growth at one end and exponential decay at the another end, and a bounded solution that corresponds to the inhomogeneous term f of the equation.
TL;DR: In this article, the authors studied the group structures and irreducible representations of simply reducible groups, namely, dihedral groups, point groups, dicyclic groups, generalized quaternion groups, Heisenberg groups over prime field of characteristic 2, some Clifford groups, and some Coxeter groups.
Abstract: Simply reducible groups are important in physics and chemistry, which contain some of the important groups in condensed matter physics and crystal symmetry. By studying the group structures and irreducible representations, we find some new examples of simply reducible groups, namely, dihedral groups, some point groups, some dicyclic groups, generalized quaternion groups, Heisenberg groups over prime field of characteristic 2, some Clifford groups, and some Coxeter groups. We give the precise decompositions of product of irreducible characters of dihedral groups, Heisenberg groups, and some Coxeter groups, giving the ClebschGordan coefficients for these groups. To verify some of our results, we use the computer algebra systems GAP and SAGE to construct and get the character tables of some examples.
TL;DR: In this paper, a rigidity of a Kähler potential of Poincaré metric with a constant length differential was shown, and the rigidity was shown for Poincare metric with constant length.
Abstract: We will show a rigidity of a Kähler potential of the Poincaré metric with a constant length differential.
TL;DR: In this paper, the authors studied bifurcation for the following fractional Schrödinger equation and established the asymptotic behavior of the solution around the bifurlcation point.
Abstract: We study bifurcation for the following fractional Schrödinger equation (−∆)su+ V (x)u = λ f(u) in Ω u > 0 in Ω u = 0 inRn \ Ω where 0 < s < 1, n > 2s, Ω is a bounded smooth domain of Rn, (−∆)s is the fractional Laplacian of order s, V is the potential energy satisfying suitable assumptions and λ is a positive real parameter. The nonlinear term f is a positive nondecreasing convex function, asymptotically linear that is lim t→+∞ f(t) t = a ∈ (0,+∞). We discuss the existence, uniqueness and stability of a positive solution and we also prove the existence of critical value and the uniqueness of extremal solutions. We take into account the types of Bifurcation problem for a class of quasilinear fractional Schrödinger equations, we also establish the asymptotic behavior of the solution around the bifurcation point.
TL;DR: In this article, it was shown that the radical layer length of a right Λ-module is an upper bound for its injective dimension, which is a lower bound for the radical length of the whole right module.
Abstract: Let Λ be an Artin algebra and mod Λ the category of finitely generated right Λ-modules. We prove that the radical layer length of Λ is an upper bound for the radical layer length of mod Λ. We give an upper bound for the extension dimension of mod Λ in terms of the injective dimension of a certain class of simple right Λ-modules and the radical layer length of DΛ.
TL;DR: In this paper, generalized Dedekind sums in dimension n, defined as sum of products of values of periodic Bernoulli functions, were considered and an exponential sum of a Laurent polynomial was shown to satisfy the equidistribution criterion of Weyl.
Abstract: We consider generalized Dedekind sums in dimension n, defined as sum of products of values of periodic Bernoulli functions. For the generalized Dedekind sums, we associate a Laurent polynomial. Using this, we associate an exponential sum of a Laurent polynomial to the generalized Dedekind sums and show that this exponential sum has a nontrivial bound that is sufficient to fulfill the equidistribution criterion of Weyl and thus the fractional part of the generalized Dedekind sums are equidistributed in R/Z.
TL;DR: Using the complex parabolic rotations of holomorphic null curves in Euclidean space, a family of degenerate minimal surfaces was discovered in this paper, foliated by conic sections with eccentricity grater than 1$: hyperbolas or straight lines.
Abstract: Using the complex parabolic rotations of holomorphic null curves in ${\mathbb{C}}^{4}$, we transform minimal surfaces in Euclidean space ${\mathbb{R}}^{3} \subset {\mathbb{R}}^{4}$ to a family of degenerate minimal surfaces in Euclidean space ${\mathbb{R}}^{4}$. Applying our deformation to holomorphic null curves in ${\mathbb{C}}^{3} \subset {\mathbb{C}}^{4}$ induced by helicoids in ${\mathbb{R}}^{3}$, we discover new minimal surfaces in ${\mathbb{R}}^{4}$ foliated by conic sections with eccentricity grater than $1$: hyperbolas or straight lines. Applying our deformation to holomorphic null curves in ${\mathbb{C}}^{3}$ induced by catenoids in ${\mathbb{R}}^{3}$, we can rediscover the Hoffman-Osserman catenoids in ${\mathbb{R}}^{4}$ foliated by conic sections with eccentricity smaller than $1$: ellipses or circles. We prove the existence of minimal surfaces in ${\mathbb{R}}^{4}$ foliated by ellipses, which converge to circles at infinity. We construct minimal surfaces in ${\mathbb{R}}^{4}$ foliated by parabolas: conic sections which have eccentricity $1$.
TL;DR: In this paper, the authors provide detailed proofs for local gradient estimates for elliptic equations in divergence form with partial Dini mean oscillation coefficients in a ball and a half ball.
Abstract: We provide detailed proofs for local gradient estimates for elliptic equations in divergence form with partial Dini mean oscillation coefficients in a ball and a half ball.
TL;DR: In this paper, the properties of operator matrices in the class S were investigated and conditions for such matrices to satisfy a-Weyl's theorem and a-Browder's theorem, respectively.
Abstract: Let S be the collection of the operator matrices ( A C Z B ) where the range of C is closed. In this paper, we study the properties of operator matrices in the class S. We first explore various local spectral relations, that is, the property (β), decomposable, and the property (C) between the operator matrices in the class S and their component operators. Moreover, we investigate Weyl and Browder type spectra of operator matrices in the class S, and as some applications, we provide the conditions for such operator matrices to satisfy a-Weyl’s theorem and a-Browder’s theorem, respectively.
TL;DR: In this paper, the authors investigated the complete f -moment convergence for extended negatively dependent (END, for short) random variables under sublinear expectations, and they extended some results on complete f −moments convergence from the classical probability space to the sublinear expectation space.
Abstract: In this paper, we investigate the complete f -moment convergence for extended negatively dependent (END, for short) random variables under sub-linear expectations. We extend some results on complete f -moment convergence from the classical probability space to the sub-linear expectation space. As applications, we present some corollaries on complete moment convergence for END random variables under sub-linear expectations.