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Abstract In this paper, some new nonlinear delay integral inequalities on time scales are established, which provide a handy tool in the research of boundedness of unknown functions in delay dynamic equations on time scales. The established results generalize some of the results in Lipovan [J. Math. Anal. Appl. 322, 349-358 (2006)], Pachpatte [J. Math. Anal. Appl. 251, 736-751 (2000)], Li [Comput. Math. Appl. 59, 1929-1936 (2010)], and Sun [J. Math. Anal. Appl. 301, 265-275 (2005)]. MSC 2010: 26E70; 26D15; 26D10.

Abstract In this paper, some new nonlinear Gronwall-Bellman-type discrete inequalities are established, which can be used as a handy tool in the research of qualitative and quantitative properties of solutions of certain difference equations. The established results generalize some of the recent results obtained by Cheung and Ma, respectively. Mathematics Subject Classification (2010) 26D15

Abstract In this work, some new finite difference inequalities in two independent variables are established, which can be used in the study of qualitative as well as quantitative properties of solutions of certain difference equations. The established results extend some existing results in the literature. MSC 2010: 26D15

Developing advanced engineering polymers that combine high strength and toughness represents not only a necessary path to excellence but also a major technical challenge. Here for the first time a rigid‐flexible interlocking polymer (RFIP) is reported featuring remarkable mechanical properties, consisting of flexible polyurethane (PU) and rigid polyimide (PI) chains cleverly woven together around the copper(I) ions center. By rationally weaving PI, PU chains, and copper(I) ions, RFIP exhibits ultra‐high strength (twice that of unwoven polymers, 91.4 ± 3.3 MPa), toughness (448.0 ± 14.2 MJ m−3), fatigue resistance (recoverable after 10 000 cyclic stretches), and shape memory properties. Simulation results and characterization analysis together support the correlation between microstructure and macroscopic features, confirming the greater cohesive energy of the interwoven network and providing insights into strengthening toughening mechanisms. The essence of weaving on the atomic and molecular levels is fused to obtain brilliant and valuable mechanical properties, opening new perspectives in designing robust and stable polymers. [ABSTRACT FROM AUTHOR]

The presence of underlying mined-out layer and developed joints have an important impact on the fragmentation process of landslide collapse. In order to further explore the cutting and fragmentation effects and characteristics of joints on rock masses, based on UAV aerial photography and field investigations of debris flows in the Madaling landslide, the particle discrete element method was used to simulate the flow force crushing process of landslide debris with joints in the underlying layer. Changes in the quantity and particle size distribution of fragmented bodies were analyzed. The conclusions are as follows: 1. The development process of debris flow in the Madaling landslide can be summarized as the following: trailing edge tension fracture, stepped creeping tension fracture, shear deformation, slip surface connection, and overall failure of the sliding mass. The collapse of joints and underlying layer promotes the failure and fragmentation process of the sliding mass; 2. Fragmentation occurs during both the failure and movement deposition processes of the sliding mass, with fragmentation dominating during movement deposition; 3. Results fitted with the Weibull dual-parameter model show continuous increase in fine particle fragmentation within the sliding body, ultimately resulting in predominantly medium to small particle size fragmentation in the deposited mass, demonstrating the phenomenon of fragmentation and disintegration during the movement and deposition of the sliding body. This study provides new insights for the analysis of the fracture mechanism of the landslide debris flow with joints in such underlying layer, and proves that the effect of the caving and joint cutting of the underlying layer on the rock mass fracture has a certain guiding significance for the prevention and control of landslide debris flow disasters in areas with similar geological conditions. [ABSTRACT FROM AUTHOR]

Byline: Tianming. Lian, Gaomin. Liu, Yaoming. Zhang Double common bile duct is a rare congenital anomaly among biliary anomalies. The anomaly has an important clinical implication because of its association [...]