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Analysis of a class of two-delay fractional differential equation.

Chaos

January 2025

School of Mathematics and Statistics, University of Hyderabad, Hyderabad 500046, India.

The differential equations involving two discrete delays are helpful in modeling two different processes in one model. We provide the stability and bifurcation analysis in the fractional order delay differential equation Dαx(t)=ax(t)+bx(t-τ)-bx(t-2τ) in the ab-plane. Various regions of stability include stable, unstable, single stable region (SSR), and stability switch (SS).

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Delayed fracture healing (DFH), a common complication of post-fracture surgery, exhibits an incompletely understood pathogenesis. The present study endeavors to investigate the roles and underlying mechanisms of miR-656-3p and Bone Morphogenetic Protein-2 (BMP-2) in DFH. It was recruited 94 patients with normal fracture healing (NFH) and 88 patients with DFH of the femoral neck.

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High tibial osteotomy (HTO) is a widely used procedure for delaying knee arthroplasty, correcting alignment, and relieving symptoms in patients with knee osteoarthritis. Recently, proximal fibular osteotomy (PFO) has emerged as a less invasive and more cost-effective alternative. This study compares the outcomes of HTO and PFO to evaluate whether PFO can deliver results comparable to HTO in similar patient populations.

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Bubble coalescence principle in saline water.

Proc Natl Acad Sci U S A

February 2025

School of Chemical Engineering and Technology, China University of Mining and Technology, Xuzhou 221116, China.

Bubbles present in saline water typically exhibit a prolonged lifetime, making them attractive for various engineering processes. Herein, we unveil a transition from delayed bubble coalescence to rapid bursting within about one millisecond in salty solutions. The key aspect in understanding this transition lies in the combined influences of surface deformation and ion surface excess instead of characterizing the ions alone.

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Introduction: After the release of the Bayley Scales of Infant and Toddler Development, third edition (Bayley-III), US norms, an overestimation of outcome was observed. But, the conformity between the Bayley Scales of Infant Development, second edition (BSID-II), and the Bayley-III German norms is unknown. This retrospective analysis aimed to compare outcomes of very preterm infants tested with BSID-II and Bayley-III German norms.

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