List of group theory topics

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, may be modelled by symmetry groups, thus group theory and the related representation theory have many important applications in physics and materials science. Group theory is central to public key cryptography. Classification of finite simple groups Algebraic geometry Algebraic topology Discrete space Fundamental group Geometry Homology Minkowski's theorem Topological group Affine representation Character theory Great orthogonality theorem Maschke's theorem Monstrous moonshine Projective representation Representation theory Schur's lemma Coset enumeration Schreier's subgroup lemma Schreier–Sims algorithm Todd–Coxeter algorithm Computer algebra system Cryptography Discrete logarithm Triple DES Caesar cipher Exponentiating by squaring Knapsack problem Shor's algorithm Standard Model Symmetry in physics Burnside's problem Classification of finite simple groups Herzog-Schönheim conjecture Subset sum problem Whitehead problem Word problem for groups List of abstract algebra topics List of category theory topics List of Lie group topics

Neuromuscular monitoring

In anesthesia, neuromuscular blocking agents may be required to facilitate endotracheal intubation and provide optimal surgical conditions. When neuromuscular blocking agents are administered, neuromuscular function of the patient must be monitored. Neuromuscular function monitoring is a technique that involves the electrical stimulation of a motor nerve and monitoring the response of the muscle supplied by that nerve, it may be used from the induction of to recovery from neuromuscular blockade. It is used to confirm adequacy of recovery after the administration of neuromuscular blocking agents; the response of the muscles to electrical stimulation of the nerves can be recorded subjectively or objectively. Quantitative techniques include electromyography, acceleromyography, kinemyography and mechanomyography. Neuromuscular monitoring is recommended when neuromuscular-blocking drugs have been part of the general anesthesia and the doctor wishes to avoid postoperative residual curarization in the patient, that is, the residual paralysis of muscles stemming from these drugs.

When train of four monitoring is "used continuously, each set of stimuli is repeated every 10th to 12th second. Each stimulus in the train causes the muscle to contract, and'fade' in the response provides the basis for evaluation." These sets are called trains. In train of four monitoring, "peripheral nerve stimulation can ensure proper medication dosing and thus decrease the incidence of side effects" by "assessing the depth of neuromuscular blockade". Before the patient is awake, voluntary muscle testing is not possible and indirect clinical tests, such as apparent muscle tone and pulmonary compliance, can be affected by factors other than PORC. Direct neuromuscular monitoring avoids these problems and allows the doctor to remedy PORC before it becomes a source of patient distress. Various nerve stimulation patterns may be used in neuromuscular function monitoring and the response to these stimulation patterns is used to assess the depth of neuromuscular blockade; some patterns of stimulation used today include, single twitch, train-of four, double burst stimulation, tetanic stimulation and the post tetanic count.

The response of the muscle to stimulation of the nerve supplying it can be assessed by subjective techniques or quantitative devices that provide a numeric value relating to the depth of neuromuscular blockade. Quantitative neuromuscular monitors can be subdivided into monitors that measure the electrical response, the compound evoked muscle action potential, those that monitor the contractile response to stimulation; the measurement of the electrical response to muscle stimulation is called electromyography. The mechanical response to stimulation of the muscle can be measured by mechanomyography and acceleromyography In 2018 recommendations by an international panel of experts on neuromuscular monitoring to assist anaesthesia care providers and professional organisations that develop practice advisories and guidelines regarding the minimum standards for monitoring patients that receive neuromuscular blockade during anaesthesia; the recommendations include the following: "Quantitative NMB monitoring should be used whenever non-depolarising neuromuscular blocking drug is administered."

"Subjective or clinical tests of NMB are not predictive of adequate neuromuscular recovery and are not sensitive to detect residual weakness. "Professional organisations should develop practice standards and guidelines detailing how best to monitor and manage perioperative administration of NMBDs." "Terms that describe the levels of NMB should be standardised. New proposed definitions are published in the consensus statement based on quantitative NMB monitoring criteria." The Association of Anaesthetists of Great Britain and Ireland published recommendations for standards of monitoring during anaesthesia and recovery in 2015. These included that a peripheral nerve stimulator is mandatory for all patients receiving neuromuscular blocking drugs and that they should be applied and used from induction until recovery from blockade and return of consciousness, they state that a more reliable guarantee of return of safe motor function is a train of four ratio of greater than 0.9. A quantitative neuromuscular monitor is required to assess the train of four ratio.

The Australian and New Zealand College of Anaesthetists publishes professional standards and guidelines on monitoring during anaesthesia. In respect to neuromuscular function monitoring - They state " Neuromuscular function monitoring, preferably quantitative, must be available for every patient in whom neuromuscular blockade is induced and should be used whenever the anaesthetist is considering extubation following the use of non-depolarising neuromuscular blockade."

Ingleby Arncliffe

Ingleby Arncliffe is a village and civil parish in the Hambleton district of North Yorkshire, England. It is situated between the A172 and A19 roads, 6.5 miles north-east from Northallerton and 7 miles south-east from the small market town of Stokesley, is on the edge of the North York Moors National Park. The village is conjoined to Ingleby Cross. According to A Dictionary of British Place Names, Ingleby is derived from the Old Scandinavian "Englar + by", meaning "farmstead or village of the Englishmen", Arncliffe, Old English "earn + cliff", meaning "eagles' cliff". Ingleby Arncliffe Grade II * listed, it includes 14th-century effigies. The church is situated less than 0.5 miles south-east from the centre of the village, 60 yards from the church is Arncliffe Hall, a Grade I listed house from 1753–54, designed by John Carr, that replaced a 16th-century house of the Mauleverer family. At the centre of the village is a Grade II listed water tower, built in 1915 to supply water to the village. Rev. David Simpson, Anglican priest was born here in 1745 Media related to Ingleby Arncliffe at Wikimedia Commons The ancient parish of Ingleby Arncliffe: historical and genealogical information at GENUKI