Correspondence between geometrical and differential definitions of the sine and cosine functions and connection with kinematics

In classical physics, the familiar sine and cosine functions appear in two forms: (1) geometrical, in the treatment of vectors such as forces and velocities, and (2) differential, as solutions of oscillation and wave equations. These two forms correspond to two different definitions of trigonometric functions, one geometrical using right triangles and unit circles, and the other employing differential equations. Although the two definitions must be equivalent, this equivalence is not demonstrated in textbooks. In this manuscript, the equivalence between the geometrical and the differential definition is presented assuming no a priori knowledge of the properties of sine and cosine functions. We start with the usual length projections on the unit circle and use elementary geometry and elementary calculus to arrive to harmonic differential equations. This more general and abstract treatment not only reveals the equivalence of the two definitions but also provides an instructive perspective on circular and harmonic motion as studied in kinematics. This exercise can help develop an appreciation of abstract thinking in physics.Comment: 6 pages including 1 figur

Metabolomics Reveals Target and Off-Target Toxicities of a Model Organophosphate Pesticide to Roach (Rutilus rutilus): Implications for Biomonitoring

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The Fifth International Congress of Mathematicians.

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Polyester composite water uptake and organic contaminant release affected by carbon nanofiber reinforcements

The incorporation of carbon nanofiber (CNF) into glass fiber (GF) composites is a potential route to extend polymer composite service-life and enhance mechanical properties. Under nonstatic conditions, only limited information concerning water uptake and contaminant release properties of nanocomposite materials is currently available. Polyester composites containing GF and oxidized CNF were immersed in water for 30 days under nominal pressure at 23 °C, below the polymer\u27s glass-transition temperature. Water was analyzed and changed every three days to simulate water chemistry regeneration similar to exposures in flowing systems. Composites with oxidized CNF had greater water sorption capacity and leaching rates than CNF-free composites. The total mass of organic contaminant released correlated with the amount of water sorbed by each composite (r2 = 0.91), although CNF dispersion was found to vary greatly within composites. The greatest and least contaminant release rates were found for the polyester-CNF and the polyester-GF composites, respectively. While volatile aromatic resin solvents and stabilizer compounds were detected, their concentrations declined over the 30 day exposure period. We hypothesize that the hydrophilic nature of the oxidized CNF increased the water sorption capacity of the polyester composites. Additional studies are warranted that examine the impact of this phenomenon on composite mechanical and long-term durability properties

Role of autoantibody levels as biomarkers in the management of patients with myasthenia gravis: A systematic review and expert appraisal

Background and purpose Although myasthenia gravis (MG) is recognized as an immunoglobulin G autoantibody-mediated disease, the relationship between autoantibody levels and disease activity in MG is unclear. We sought to evaluate this landscape through systematically assessing the evidence, testing the impact of predefined variables on any relationship, and augmenting with expert opinion. Methods In October 2020, a forum of leading clinicians and researchers in neurology from across Europe (Expert Forum for Rare Autoantibodies in Neurology in Myasthenia Gravis) participated in a series of virtual meetings that took place alongside the conduct of a systematic literature review (SLR). Results Forty-two studies were identified meeting inclusion criteria. Of these, 10 reported some correlation between a patient's autoantibody level and disease severity. Generally, decreased autoantibody levels (acetylcholine receptor, muscle-specific kinase, and titin) were positively and significantly correlated with improvements in disease severity (Quantitative Myasthenia Gravis score, Myasthenia Gravis Composite score, Myasthenia Gravis Activities of Daily Living score, Myasthenia Gravis Foundation of America classification). Given the limited evidence, testing the impact of predefined variables was not feasible. Conclusions This first SLR to assess whether a correlation exists between autoantibody levels and disease activity in patients with MG has indicated a potential positive correlation, which could have clinical implications in guiding treatment decisions. However, in light of the limited and variable evidence, we cannot currently recommend routine clinical use of autoantibody level testing in this context. For now, patient's characteristics, clinical disease course, and laboratory data (e.g., autoantibody status, thymus histology) should inform management, alongside patient-reported outcomes. We highlight the need for future studies to reach more definitive conclusions on this relationship.Neurological Motor Disorder

The effectiveness and cost-effectiveness of erythropoiesis-stimulating agents (epoetin and darbepoetin) for treating cancer treatment-induced anaemia (including review of technology appraisal no. 142): a systematic review and economic model.

Anaemia is a common side effect of cancer treatments and can lead to a reduction in quality of life. Erythropoiesis-stimulating agents (ESAs) are licensed for use in conjunction with red blood cell transfusions to improve cancer treatment-induced anaemia (CIA).This report is freely available via the NIHR Journals Library. Click on the 'Additional Link' above to access the full-text

Immunosuppressive agents in adult kidney transplantation in the National Health Service: a model-based economic evaluation.

Immunosuppression is required in kidney transplantation to prevent rejection and prolong graft survival. We conducted an economic evaluation to support England's National Institute for Health and Care Excellence in developing updated guidance on the use of immunosuppression, incorporating new immunosuppressive agents, and addressing changes in pricing and the evidence base