In this paper, we present an important property of smooth function germs of orbit tangent space, and apply it to discuss the proof of Morse's Lemma. More >

In prostate cancer treatment, intermittent androgen deprivation therapy can delay the emergence of drug resistance, yet its efficacy is influenced by environmental fluctuations, treatment parameters, and competition among tumor cell populations. To investigate the mechanisms underlying resistance during intermittent therapy, we developed a stochastic impulsive differential equation model. First, a global analysis of the model without environmental noise is conducted. Subsequently, sufficient conditions for tumor extinction and persistence are established based on stochastic stability theory. Numerical simulations further demonstrate that moderate noise suppresses tumor growth, and an optimal... More >

This article delves into the trajectory structure rules of a specific fifth-order rational difference equation: $$ s_{m+1}=\frac{s_ms_{m-2}s_{m-3}s_{m-4}+s_ms_{m-2}+s_ms_{m-3}+s_{m-2}s_{m-3}+s_{m-4}+a}{s_ms_{m-2}s_{m-3}+s_ms_{m-2}s_{m-4}+s_ms_{m-3}s_{m-4}+s_{m-2}s_{m-3}s_{m-4}+1+a} $$ where the initial conditions satisfy $s_i\in (0,\infty)$, $i=-4,-3,-2,-1,0$, and the parameters $a\in [0,\infty).$ As the initial values vary, the lengths of consecutive positive and negative semi-cycles for non-trivial solutions exhibit a periodic pattern with a prime period of 31. The rule within one period is $1^-, 2^+, 1^-, 1^+, 1^-, 1^+, 2^-, 4^+, 3^-, 2^+, 2^-, 1^+, 5^-, 1^+, 1^-,$ $ 3^+ $. Through t... More >

The accurate classification of cervical cytology in Pap smear images remains a critical challenge in computer-aided diagnosis, largely due to the inherent uncertainty and subtle morphological variations among different pathological categories. To address this, we propose a novel uncertainty-aware ensemble framework that integrates statistical quantile analysis with deep learning for robust and interpretable classification. Our framework first leverages three deep convolutional neural networks DenseNet121, MobileNetV2, and ResNet-50 as base feature extractors. Instead of employing naive ensemble strategies, we introduce a quantile deviation based weighting mechanism to dynamically assess and... More >

(1) Objective: This study aims to examine the relationships between college students' cell phone addiction, anxiety, and depression, and to explore the mediating role of anxiety in the association between cell phone addiction and depression. (2) Methods: Data were statistically analyzed using SPSS and AMOS. Independent samples t-tests and F-tests were employed to analyze differences in cell phone addiction (and its dimensions) across demographic variables. Pearson correlation analysis was conducted to assess the relationships among cell phone addiction, anxiety, and depression. Structural equation modeling (SEM) via AMOS was used to validate the hypothetical model, and regression analysis co... More >