The generalized Kupershmidt deformation for constructing new integrable systems from integrable bi-Hamiltonian systems

Based on the Kupershmidt deformation for any integrable bi-Hamiltonian systems presented in [4], we propose the generalized Kupershmidt deformation to construct new systems from integrable bi-Hamiltonian systems, which provides a nonholonomic perturbation of the bi-Hamiltonian systems. The generalized Kupershmidt deformation is conjectured to preserve integrability. The conjecture is verified in a few representative cases: KdV equation, Boussinesq equation, Jaulent-Miodek equation and Camassa-Holm equation. For these specific cases, we present a general procedure to convert the generalized Kupershmidt deformation into the integrable Rosochatius deformation of soliton equation with self-consistent sources, then to transform it into a $t$-type bi-Hamiltonian system. By using this generalized Kupershmidt deformation some new integrable systems are derived. In fact, this generalized Kupershmidt deformation also provides a new method to construct the integrable Rosochatius deformation of soliton equation with self-consistent sources.Comment: 21 pages, to appear in Journal of Mathematical Physic

Trajectories of Self-compassion and Psychological Symptoms in Newly Diagnosed Cancer Patients

Objectives More self-compassion has been related to a better psychological functioning in cancer patients, but little is known about the course of self-compassion over time in the trajectory of illness and cancer treatment. This longitudinal study aimed to examine subgroups of cancer patients with differential trajectories of self-compassion and associations of these trajectories with the course of psychological symptoms. Methods A total of 153 cancer patients participated in this longitudinal study. Self-reported questionnaires were used to measure self-compassion (i.e., overall self-compassion and, separately, positive self-compassion, and negative self-compassion), and depressive and anxiety symptoms. These assessments were taken directly after cancer diagnosis (T1), and at the start (T2) and the end (T3) of medical treatment. Latent class growth modelling and repeated measures ANOVA were applied to examine the research questions. Results We identified three trajectories of overall self-compassion ("stable low" 82.2%, "late increase" 11.8%, and "late decrease" 6.0%), four trajectories of positive self-compassion ("late decline" 57.2%, "early decline" 22.4%, "large increase" 15.1%, and "large decline" 5.3%), and four trajectories of negative self-compassion ("late decline" 42.1%, "stable negative self-compassion" 40.8%, "large fluctuation" 9.9%, and "large increase" 7.2%). Only the negative self-compassion trajectories were significantly related to the course of depressive and anxiety symptoms. Conclusions Our findings suggest that subgroups of cancer patients exist that show distinct trajectories of self-compassion over time. We identified a small group of patients at a higher risk of losing self-compassion throughout the cancer trajectory and experiencing psychological symptoms

Effects of pore widening vs oxygenation on capacitance of activated carbon in aqueous sodium sulfate electrolyte

The commercial activated carbon has a relatively low specific capacitance in the Na2SO4 electrolyte, which hinder the development of asymmetrical supercapacitors with high voltage. Re-activation and oxidative etching methods were applied to change the pore structure of activated carbon, respectively, to study the capacitive behavior of carbon in the Na2SO4 electrolyte. The pore distributions combining with capacitive properties deduce that 0.85 nm is the threshold diameter of the ion-accessible micropores for hydrated Na+ and SO42−. The specific capacitances of both the carbon materials by re-activation and oxidative etching methods are increased by 40 %, in comparison with the commercial activated carbon. The enhanced capacitive performances of the carbon materials were mainly attributed to the increased ion-accessible specific surface area and pseudocapacitance, respectively. The oxidative etching is a more facile and economical method for practice application. Combining with MnO2 as the positive electrode, the asymmetrical supercapacitor with a high voltage of 1.8 V exhibits a maximum specific cell capacitance of 50 F g–1 and specific energy of 22.5 Wh kg–1

Self-Compassion and Symptoms of Depression and Anxiety in Chinese Cancer Patients:the Mediating Role of Illness Perceptions

Objectives An adaptive role of self-compassion for psychological functioning in cancer patients has been highlighted, yet less is known about the underlying mechanisms. This study aimed to examine the mediating role of cancer patients' illness perceptions in the relations between self-compassion and psychological symptoms. Methods This cross-sectional study focused on 301 people with heterogeneous types of cancer. A self-reported questionnaire was used to collect participants' levels of self-compassion, illness perceptions, and symptoms of depression and anxiety. Parallel mediation analyses were performed to examine the research questions. Results The relation between self-compassion and depressive symptoms was mediated by perceived consequences and a timeline cyclical of cancer. Perceived consequences also mediated the relation between self-compassion and symptoms of anxiety, with an additional mediating role of personal control. Conclusions These findings suggest that both self-compassion and illness perceptions were closely linked with cancer patients' psychological symptoms. Particularly, cancer patients who feel more self-compassionate perceive fewer negative consequences of cancer, a less timeline cyclical, and more personal control over their life and report fewer psychological symptoms