Abstract : In this paper, we investigate the portfolio optimization problem under the SVCEV model, which is a hybrid model of constant elasticity of variance (CEV) and stochastic volatility, by taking into account of minimum-entropy robustness. The Hamilton-Jacobi-Bellman (HJB) equation is derived and the first two orders of optimal strategies are obtained by utilizing an asymptotic approximation approach. We also derive the first two orders of practical optimal strategies by knowing that the underlying Ornstein-Uhlenbeck process is not observable. Finally, we conduct numerical experiments and sensitivity analysis on the leading optimal strategy and the first correction term with respect to various values of the model parameters.
Abstract : Given a dimension function $\omega$, we introduce the notion of an $\omega$-vector weighted digraph and an $\omega$-equivalence between them. Then we establish a bijection between the weakly $(\mathbb{Z}/2)^n$-equivariant homeomorphism classes of small covers over a product of simplices $\Delta^{\omega(1)}\times\cdots \times \Delta^{\omega(m)}$ and the set of $\omega$-equivalence classes of $\omega$-vector weighted digraphs with $m$-labeled vertices, where $n$ is the sum of the dimensions of the simplicies. Using this bijection, we obtain a formula for the number of weakly $(\mathbb{Z}/2)^n$-equivariant homeomorphism classes of small covers over a product of three simplices.
Abstract : Recently, Gireesh, Shivashankar, and Naika [11] found some infinite classes of congruences for the 3- and the 9-regular cubic partitions modulo powers of 3. We extend their study to all the $3^k$-regular cubic partitions. We also find new families of congruences.
Abstract : We construct generalized Cauchy-Riemann equations of the first order for a pair of two $\mathbb{R}$-valued functions to deform a minimal graph in ${\mathbb{R}}^{3}$ to the one parameter family of the two dimensional minimal graphs in ${\mathbb{R}}^{4}$. We construct the two parameter family of minimal graphs in ${\mathbb{R}}^{4}$, which include catenoids, helicoids, planes in ${\mathbb{R}}^{3}$, and complex logarithmic graphs in ${\mathbb{C}}^{2}$. We present higher codimensional generalizations of Scherk's periodic minimal surfaces.
Abstract : Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with $\beta$-Kenmotsu structure. It is proven that a $(2n+1)$-dimensional generalized Sasakian-space-form with $\beta$-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with $\beta$-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either $\Psi \backslash T^{k} \times M^{2n+1-k}$ or gradient $\eta$-Yamabe soliton.
Abstract : In this study, we consider a heat equation with a variable-coefficient linear forcing term and a time-periodic boundary condition. Under some decay and smoothness assumptions on the coefficient, we establish the existence and uniqueness of a time-periodic solution satisfying the boundary condition. Furthermore, possible connections to the closed boundary layer equations were discussed. The difficulty with a perturbed leading order coefficient is demonstrated by a simple example.
Abstract : For every $n\geq 2$, let $\mathbb{R}^n_{\|\cdot\|}$ be $\mathbb{R}^n$ with a norm $\|\cdot\|$ such that its unit ball has finitely many extreme points more than $2n$. We devote to the description of the sets of extreme and exposed points of the closed unit balls of ${\mathcal L}(^2\mathbb{R}^n_{\|\cdot\|})$ and ${\mathcal L}_s(^2\mathbb{R}^n_{\|\cdot\|})$, where ${\mathcal L}(^2\mathbb{R}^n_{\|\cdot\|})$ is the space of bilinear forms on $\mathbb{R}^n_{\|\cdot\|}$, and ${\mathcal L}_s(^2\mathbb{R}^n_{\|\cdot\|})$ is the subspace of ${\mathcal L}(^2\mathbb{R}^n_{\|\cdot\|})$ consisting of symmetric bilinear forms. Let ${\mathcal F}={\mathcal L}(^2\mathbb{R}^n_{\|\cdot\|})$ or ${\mathcal L}_s(^2\mathbb{R}^n_{\|\cdot\|})$. First we classify the extreme and exposed points of the closed unit ball of ${\mathcal F}$. We also show that every extreme point of the closed unit ball of ${\mathcal F}$ is exposed. It is shown that ${ext}B_{{\mathcal L}_s(^2\mathbb{R}^n_{\|\cdot\|})}={ext}B_{{\mathcal L}(^2\mathbb{R}^n_{\|\cdot\|})}\cap {\mathcal L}_s(^2\mathbb{R}^n_{\|\cdot\|})$ and ${exp}B_{{\mathcal L}_s(^2\mathbb{R}^n_{\|\cdot\|})}={exp}B_{{\mathcal L}(^2\mathbb{R}^n_{\|\cdot\|})}\cap {\mathcal L}_s(^2\mathbb{R}^n_{\|\cdot\|})$, which expand some results of \cite{18, 23, 28, 29, 35, 38, 40, 41, 43}.
Abstract : We study a class of left-invariant pseudo-Riemannian Sasaki metrics on solvable Lie groups, which can be characterized by the property that the zero level set of the moment map relative to the action of some one-parameter subgroup $\{\exp tX\}$ is a normal nilpotent subgroup commuting with $\{\exp tX\}$, and $X$ is not lightlike. We characterize this geometry in terms of the Sasaki reduction and its pseudo-K\"ahler quotient under the action generated by the Reeb vector field. We classify pseudo-Riemannian Sasaki solvmanifolds of this type in dimension $5$ and those of dimension $7$ whose K\"ahler reduction in the above sense is abelian.
Abstract : The 4-dimensional Sklyanin algebras are a well-studied 2-parameter family of non-commutative graded algebras, often denoted $A(E,\tau)$, that depend on a quartic elliptic curve $E \subseteq \mathbb{P}^3$ and a translation automorphism $\tau$ of $E$. They are graded algebras generated by four degree-one elements subject to six quadratic relations and in many important ways they behave like the polynomial ring on four indeterminates except that they are not commutative. They can be seen as ``elliptic analogues'' of the enveloping algebra of $\mathfrak{gl}(2,\mathbb{C})$ and the quantized enveloping algebras $U_q(\mathfrak{gl}_2)$. Recently, Cho, Hong, and Lau conjectured that a certain 2-parameter family of algebras arising in their work on homological mirror symmetry consists of 4-dimensional Sklyanin algebras. This paper shows their conjecture is false in the generality they make it. On the positive side, we show their algebras exhibit features that are similar to, and differ from, analogous features of the 4-dimensional Sklyanin algebras in interesting ways. We show that most of the Cho-Hong-Lau algebras determine, and are determined by, the graph of a bijection between two 20-point subsets of the projective space $\mathbb{P}^3$. The paper also examines a 3-parameter family of 4-generator 6-relator algebras admitting presentations analogous to those of the 4-dimensional Sklyanin algebras. This class includes the 4-dimensional Sklyanin algebras and most of the Cho-Hong-Lau algebras.
Abstract : In this paper, two weight conditions are introduced and the multiple weighted strong and weak characterizations of the multilinear fractional new maximal operator $\mathcal{M}_{\varphi,\beta}$ are established. Meanwhile, we introduce the $S_{(\vec{p},q),\beta}(\varphi)$ and $B_{(\vec{p},q),\beta}(\varphi)$ conditions and obtain the characterization of two-weighted inequalities for $\mathcal{M}_{\varphi,\beta}$. Finally, the relationships of the conditions $S_{(\vec{p},q),\beta}(\varphi)$, $\mathcal{A}_{(\vec{p},q),\beta}(\varphi)$ and $B_{(\vec{p},q),\beta}(\varphi)$ and the characterization of the one-weight $A_{(\vec{p},q),\beta}(\varphi)$ are given.
Noureddine Ghiloufi , Safa Snoun
J. Korean Math. Soc. 2022; 59(3): 449-468
https://doi.org/10.4134/JKMS.j200373
Li Zhu
J. Korean Math. Soc. 2022; 59(2): 407-420
https://doi.org/10.4134/JKMS.j210371
J. Korean Math. Soc. 2022; 59(1): 171-192
https://doi.org/10.4134/JKMS.j210271
Daeyung Gim, Hyungbin Park
J. Korean Math. Soc. 2022; 59(2): 311-335
https://doi.org/10.4134/JKMS.j210168
Namjip Koo, Hyunhee Lee
J. Korean Math. Soc. 2023; 60(5): 1043-1055
https://doi.org/10.4134/JKMS.j220595
Manseob Lee
J. Korean Math. Soc. 2023; 60(5): 987-998
https://doi.org/10.4134/JKMS.j220359
Ankita Jindal, Nabin Kumar Meher
J. Korean Math. Soc. 2023; 60(5): 1073-1085
https://doi.org/10.4134/JKMS.j230031
Xiaolei Zhang
J. Korean Math. Soc. 2023; 60(3): 521-536
https://doi.org/10.4134/JKMS.j220055
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd