We investigate a probabilistic approach for the valuation of exchange option with stochastic liquidity risk. To measure market liquidity risk, Ornstein-Uhlenbeck (OU) process with the mean reversion feature is used. A liquidity discount factor is applied to the underlying assets to allow for possible effects. We derive the characteristic function using a probabilistic approach, and subsequently obtain the pricing formula for the option using the measure change technique and the Fourier inversion formula.

This paper is mostly a survey paper on algorithmic approaches to compute sheaf cohomology groups of a coherent sheaf on a projective variety. We review various computational methods together with an algorithmic point of view. We also review further generalizations to compute higher direct image sheaves of a coherent sheaf under a morphism between two projective varieties. We also discuss a few open problems and working ideas on those computations and functorial properties.

In this note we consider hyponormality of Toeplitz operators T_𝜑 with symbols ${\varphi}={\bar{g}}+f$, where f, g ∈ H^∞(𝕋) are bounded type functions and also discuss about the Cowen's set.

Oral squamous cell carcinoma (OSCC) is a leading cause of cancer-related deaths globally, with 177,757 fatalities reported in 2020 World Health Organization. Early detection significantly improves survival rates. This study proposes an automated machine-learning approach for OSCC detection using histopathological images. Deep features extracted from the pre-trained model (ResNet-101) achieved 91.61% classification accuracy. Furthermore, using ReliefF-based feature selection filters enhanced performance by 97.3%. The ReliefF-ResNet-101 deep feature-trained support vector machine model required only 500 features. The comparative analysis confirmed the reliability and superiority of the proposed ReliefF-ResNet-101 framework over existing feature selection methods and state-of-the-art approaches. These findings suggest potential clinical applications for aiding OSCC diagnosis.

This paper is concerned with the optimal control via the initial conditions for the self-organizing target detection in 1D domains. That is, we obtain the continuous dependence on the initial conditions and show the global existence of strong solution. And then, we consider the optimal control problem whose control variables are the initial conditions.

We establish weighted a priori L^q-regularity estimates for weak solutions to p-Laplacian type equations involving differential forms. These equations are analyzed under minimal assumptions on the coefficient a(x), satisfying a bounded mean oscillation (BMO) type condition, and the data F, belonging to weighted Lebesgue spaces with Muckenhoupt weights. By extending Calderón-Zygmund estimates to the weighted setting, our results provide a unified framework for studying p-Laplacian systems in complex scenarios, significantly broadening the scope of regularity theory in nonlinear partial differential equations.

This paper is a research for a perpetual American lookback option introduced in Dai [3, 4] under a stochastic volatility model. We derive the formula in closed form for the price of the perpetual American lookback option under the mean-reverting stochastic volatility introduced by Fouque et al. [6]. As this work is a direct extension of the work of Lee [11] where the zero and first order terms are derived, we focus on improving accuracy in an asymptotic series expansion. Based on the second order approach used in Fouque et al. [8], we extend the approximation by incorporating the third order asymptotics for the stochastic volatility.

Recently, Kozma et al. (2023) constructed a measurable set S ⊂ [0, 1] such that no exponential system can be a Riesz basis for L²(S). In this paper, we review their construction method and explore its potential generalizations to higher dimensions. We conjecture that for each d ∈ ℕ, there exists a measurable set S ⊂ [0, 1]^d such that no exponential system can be a Riesz basis for L²(S).