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https://en.wikipedia.org/wiki/Quadratus%20lumborum%20muscle | The quadratus lumborum muscle, informally called the QL, is a paired muscle of the left and right posterior abdominal wall. It is the deepest abdominal muscle, and commonly referred to as a back muscle. Each is irregular and quadrilateral in shape.
The quadratus lumborum muscles originate from the wings of the ilium; their insertions are on the transverse processes of the upper four lumbar vertebrae plus the lower posterior border of the twelfth rib. Contraction of one of the pair of muscles causes lateral flexion of the lumbar spine, elevation of the pelvis, or both. Contraction of both causes extension of the lumbar spine.
A disorder of the quadratus lumborum muscles is pain due to muscle fatigue from constant contraction due to prolonged sitting, such as at a computer or in a car. Kyphosis and weak gluteal muscles can also contribute to the likelihood of quadratus lumborum pain.
Structure
The quadratus lumborum muscle originates by aponeurotic fibers into the iliolumbar ligament and the internal lip of the iliac crest for about . It inserts from the lower border of the last rib for about half its length and by four small tendons from the apices of the transverse processes of the upper four lumbar vertebrae.
The number of attachments to the vertebræ, and the extent of its attachment to the last rib, may vary. Also, occasionally, a second portion of this muscle is found in front of the preceding. It arises from the upper borders of the transverse processes of the lower three or four lumbar vertebræ, and is inserted into the lower margin of the last rib.
Relationships
Anterior to the quadratus lumborum are the colon, the kidney, the psoas major muscle, (if present) the psoas minor muscle, and the diaphragm; between the fascia and the muscle are the twelfth thoracic, ilioinguinal, and iliohypogastric nerves. The quadratus lumborum muscle is a continuation of transverse abdominal muscle.
Nerve supply
Anterior branches of the ventral rami of T12 to L4.
Funct |
https://en.wikipedia.org/wiki/Corrugator%20cutis%20ani%20muscle | The corrugator cutis ani is a muscle of the human body, also known as the Ellis' muscle, after the anatomist George Viner Ellis.
Around the anus is a thin stratum of involuntary muscle fiber, which radiates from the orifice. Medially the fibers fade off into the submucous tissue, while laterally they blend with the true skin. By its contraction it raises the skin into ridges around the margin of the anus. The name of this muscle is primarily limited to older texts.
External links |
https://en.wikipedia.org/wiki/External%20anal%20sphincter | The external anal sphincter (or sphincter ani externus) is an oval tube skeletal muscle fibers. Distally, it is adherent to the skin surrounding the margin of the anus. The sphincter exhibits a resting state of tonical contraction.
Anatomy
The external anal sphincter is far more substantial than the internal anal sphincter. The proximal portion of external anal sphincter overlaps the internal anal sphincter (which terminates distally a little distance proximal to the anal orifice) superficially; where the two overlap, they are separated by the intervening conjoint longitudinal muscle.
Structure
Historically, the sphincter was described as consisting of three parts (deep, superficial, and subcontinuous), however, this is not supported by current anatomical knowledge. Some sources still describe it as consisting of two layers: deep (or proximal) superficial (or distal or subcutaneous).
Some of the muscles fibres decussate at the anterior midline and posterior midline, so forming an anterior commissure and posterior commissure.
Attachments
The muscle attaches anteriorly onto the perineal body, and posteriorly onto the anococcygeal ligament.
Innervation
The sphincter receives innervation from the bilaterally paired inferior anal nerve (each a branch of the pudendal nerve which is derived from ventral rami of S2-S4). It may also receive additional motor innervation from the nerve to levator ani.
Histology
The sphincter consists mostly of slow twitch fibers that allow extended continuous contraction.
Function
(1) Like other muscles, it is always in a state of tonic contraction, and having no antagonistic muscle it keeps the anal canal and orifice shut.
(2) It can be put into a condition of greater contraction under the influence of the will, so as more firmly to occlude the anal aperture, in expiratory efforts unconnected with defecation.
(3) Taking its fixed point at the coccyx, it helps to fix the central point of the perineum, so that the bulbospongiosus |
https://en.wikipedia.org/wiki/Internal%20anal%20sphincter | The internal anal sphincter, IAS, (or sphincter ani internus) is a ring of smooth muscle that surrounds about 2.5–4.0 cm of the anal canal. It is about 5 mm thick, and is formed by an aggregation of the smooth (involuntary) circular muscle fibers of the rectum. it terminates distally about 6 mm from the anal orifice.
The internal anal sphincter aids the sphincter ani externus to occlude the anal aperture and aids in the expulsion of the feces. Its action is entirely involuntary. It is normally in a state of continuous maximal contraction to prevent leakage of faeces or gases. Sympathetic stimulation stimulates and maintains the sphincter's contraction, and parasympathetic stimulation inhibits it. It becomes relaxed in response to distention of the rectal ampulla, requiring voluntary contraction of the puborectalis and external anal sphincter to maintain continence.
Anatomy
The internal anal sphincter is the specialised thickened terminal portion of the inner circular layer of smooth muscle of the large intestine. It extends from the pectinate line (anorectal junction) proximally to just proximal to the anal orifice distally (the distal termination is palpable). Its muscle fibres are arranged in a spiral (rather than a circular) manner.
At its distal extremity, it is in contact with but separate from the external anal sphincter.
Innervation
The sphincter receives extrinsic autonomic innervation via the inferior hypogastric plexus, with sympathetic innervation derived from spinal levels L1-L2, and parasympathetic innervation derived from S2-S4.
The internal anal sphincter is not innervated by the pudendal nerve (which provides motor and sensory innervation to the external anal sphincter).
Function
The sphincter is contracted in its resting state, but reflexively relaxes in certain contexts (most notably during defecation).
Transient relaxation of its proximal portion occurs with rectal distension and post-prandial rectal contraction (the recto-anal inhibitory |
https://en.wikipedia.org/wiki/External%20sphincter%20muscle%20of%20male%20urethra | The external sphincter muscle of male urethra, also sphincter urethrae membranaceae, sphincter urethrae externus, surrounds the whole length of the membranous urethra, and is enclosed in the fascia of the urogenital diaphragm.
Its external fibers arise from the junction of the inferior pubic ramus and ischium to the extent of 1.25 to 2 cm., and from the neighboring fascia.
They arch across the front of the urethra and bulbourethral glands, pass around the urethra, and behind it unite with the muscle of the opposite side, by means of a tendinous raphe.
Its innermost fibers form a continuous circular investment for the membranous urethra.
Function
The muscle helps maintain continence of urine along with the internal urethral sphincter which is under control of the autonomic nervous system. The external sphincter muscle prevents urine leakage as the muscle is tonically contracted via somatic fibers that originate in Onuf's nucleus and pass through sacral spinal nerves S2-S4 then the pudendal nerve to synapse on the muscle.
Voiding urine begins with voluntary relaxation of the external urethral sphincter. This is facilitated by inhibition of the somatic neurons in Onuf's nucleus via signals arising in the pontine micturition center and traveling through the descending reticulospinal tracts. During ejaculation, the external sphincter opens and the internal sphincter closes.
Additional images
See also
Levator ani
External sphincter muscle of female urethra
Internal urethral sphincter
Prostatic urethra |
https://en.wikipedia.org/wiki/Subclavius%20muscle | The subclavius is a small triangular muscle, placed between the clavicle and the first rib. Along with the pectoralis major and pectoralis minor muscles, the subclavius muscle makes up the anterior axioappendicular muscles, also known as anterior wall of the axilla.
Structure
It arises by a short, thick tendon from the first rib and its cartilage at their junction, in front of the costoclavicular ligament.
The fleshy fibers proceed obliquely superolaterally, to be inserted into the groove on the under surface of the clavicle.
Innervation
The nerve to subclavius (or subclavian nerve) innervates the muscle. This arises from the junction of the fifth and sixth cervical nerves, from the superior/upper trunk of the brachial plexus.
Variation
Insertion into coracoid process instead of clavicle or into both clavicle and coracoid process. Sternoscapular fasciculus to the upper border of scapula. Sternoclavicularis from manubrium to clavicle between pectoralis major and coracoclavicular fascia. Rarely, the subclavius may be missing entirely.
Function
It depresses the lateral clavicle, acts to stabilize the clavicle while the shoulder moves the arm. It also raises the first rib while lowering the clavicle during breathing.
The subclavius protects the underlying brachial plexus and subclavian vessels from a broken clavicle - the most frequently broken long bone.
Additional images |
https://en.wikipedia.org/wiki/Subscapularis%20muscle | The subscapularis is a large triangular muscle which fills the subscapular fossa and inserts into the lesser tubercle of the humerus and the front of the capsule of the shoulder-joint.
Structure
The subscapularis is covered by a dense fascia which attaches to the scapula at the margins of the subscapularis' attachment (origin) on the scapula.
The muscle's fibers pass laterally from its origin before coalescing into a tendon of insertion. The tendon intermingles with the glenohumeral (shoulder) joint capsule.
A bursa (which communicates with the cavity of the shoulder joint via an aperture in the joint capsule) intervenes between the tendon and a bare area at the lateral angle of the scapula/the neck of the scapula. The subscapularis (supraserratus) bursa separates the subscapularis is from the serratus anterior.
Origin
It arises from its medial two-thirds of the costal surface of the scapula, the intermuscular septa (which create ridges upon the scapula), and the lower two-thirds of the groove on the axillary border (subscapular fossa) of the scapula.
Some fibers arise from tendinous laminae, which intersect the muscle and are attached to ridges on the bone; others from an aponeurosis, which separates the muscle from the teres major and the long head of the triceps brachii.
Insertion
It inserts onto the lesser tubercle of the humerus and the anterior part of the shoulder-joint capsule. Tendinous fibers extend to the greater tubercle with insertions into the bicipital groove.
Innervation
The subscapularis is supplied by the upper and lower subscapular nerves (C5-C6), branches of the posterior cord of the brachial plexus.
Actions/movements
The subscapularis medially (internally) rotates the humerus (acting here as a prime mover) and adducts it. When the arm is raised, it draws the humerus forward and downward.
Function
The subscapularis stabilises the shoulder joint by contributing to the fixation of the proximal humerus during movements of the elbow, wr |
https://en.wikipedia.org/wiki/Teres%20major%20muscle | The teres major muscle is a muscle of the upper limb. It attaches to the scapula and the humerus and is one of the seven scapulohumeral muscles. It is a thick but somewhat flattened muscle.
The teres major muscle (from Latin teres, meaning "rounded") is positioned above the latissimus dorsi muscle and assists in the extension and medial rotation of the humerus. This muscle is commonly confused as a rotator cuff muscle, but it is not because it does not attach to the capsule of the shoulder joint, unlike the teres minor muscle for example.
Structure
The teres major muscle originates on the dorsal surface of the inferior angle and the lower part of the lateral border of the scapula.
The fibers of teres major insert into the medial lip of the intertubercular sulcus of the humerus.
Relations
The tendon, at its insertion, lies behind that of the latissimus dorsi, from which it is separated by a bursa, the two tendons being, however, united along their lower borders for a short distance. The fibers of these two muscles run parallel to each other, and both muscles insert at the crest of the lesser tubercle of the humerus (also described as the medial lip of the intertubercular sulcus).
Together with teres minor muscle, teres major muscle forms the axillary space, through which several important arteries and veins pass.
Innervation
Teres major is supplied primarily by the lower subscapular nerve and additionally by the thoracodorsal nerve (middle subscapular nerve). These are distal to the upper subscapular nerve. These three nerves branch off the posterior cord of the brachial plexus. The nerves that innervate teres major consist of fibers from spinal nerves C5-C8.
Function
The teres major is a medial rotator and adductor of the humerus and assists the latissimus dorsi in drawing the previously raised humerus downwards and backwards (extension, but not hyperextension). It also helps stabilise the humeral head in the glenoid cavity.
Injury
Isolated teres major inj |
https://en.wikipedia.org/wiki/Coracobrachialis%20muscle | The coracobrachialis muscle is a muscle in the upper medial part of the arm. It is located within the anterior compartment of the arm. It originates from the coracoid process of the scapula; it inserts onto the middle of the medial aspect of the body of the humerus. It is innervated by the musculocutaneous nerve. It acts to adduct and flex the arm.
Structure
Origin
Coracobrachialis muscle arises from the (deep surface of the) apex of the coracoid process of the scapula (a common origin with the short head of the biceps brachii). It additionally also arises from the proximal portion of tendon of origin of the biceps brachii muscle.
Insertion
It is inserted (by means of a flat tendon) into an impression at the middle of the medial border of the body of the humerus (shaft of the humerus) between the attachments of the medial head of the triceps brachii and the brachialis.
Innervation
Coracobrachialis muscle is perforated by and innervated by the musculocutaneous nerve, which arises from the anterior division of the upper trunk (C5, C6) and middle trunk (C7) of the brachial plexus.
Variation
The coracobrachialis muscle has been classified into distinct superficial and deep layers. In 16% of individuals the muscle is fully divided into these layers, in 8% of individuals there is incomplete separation, and in the 76% there is no discernible separation of the layers.
Function
The coracobrachialis is functionally insignificant. It is a weak flexor and adductor of the arm at the glenohumeral joint (shoulder joint).
It additionally also resists deviation of the arm from the frontal plane during abduction.
Clinical significance
The overuse of the coracobrachialis can lead to stiffening of the muscle. Common causes of injury include chest workouts or activities that require one to press the arm very tight towards the body, e.g. work on the rings in gymnastics.
Symptoms of overuse or injury are pain in the arm and shoulder, radiating down to the back of the hand. I |
https://en.wikipedia.org/wiki/Extensor%20digitorum%20muscle | The extensor digitorum muscle (also known as extensor digitorum communis) is a muscle of the posterior forearm present in humans and other animals. It extends the medial four digits of the hand. Extensor digitorum is innervated by the posterior interosseous nerve, which is a branch of the radial nerve.
Structure
The extensor digitorum muscle arises from the lateral epicondyle of the humerus, by the common tendon; from the intermuscular septa between it and the adjacent muscles, and from the antebrachial fascia. It divides below into four tendons, which pass, together with that of the extensor indicis proprius, through a separate compartment of the dorsal carpal ligament, within a mucous sheath. The tendons then diverge on the back of the hand, and are inserted into the middle and distal phalanges of the fingers in the following manner.
Opposite the metacarpophalangeal articulation each tendon is bound by fasciculi to the collateral ligaments and serves as the dorsal ligament of this joint; after having crossed the joint, it spreads out into a broad aponeurosis, which covers the dorsal surface of the first phalanx and is reinforced, in this situation, by the tendons of the interossei and lumbricalis.
Opposite the first interphalangeal joint this aponeurosis divides into three slips; an intermediate and two collateral: the former is inserted into the base of the second phalanx; and the two collateral, which are continued onward along the sides of the second phalanx, unite by their contiguous margins, and are inserted into the dorsal surface of the last phalanx. As the tendons cross the interphalangeal joints, they furnish them with dorsal ligaments. The tendon to the index finger is accompanied by the tendon of extensor indicis, which lies on its ulnar side. On the back of the hand, the tendons to the middle, ring, and little fingers are connected by two obliquely placed bands, one from the third tendon passing inferior and laterally to the second tendon, and the o |
https://en.wikipedia.org/wiki/Extensor%20pollicis%20longus%20muscle | In human anatomy, the extensor pollicis longus muscle (EPL) is a skeletal muscle located dorsally on the forearm. It is much larger than the extensor pollicis brevis, the origin of which it partly covers and acts to stretch the thumb together with this muscle.
Structure
The extensor pollicis longus arises from the dorsal surface of the ulna and from the interosseous membrane, next to the origins of abductor pollicis longus and extensor pollicis brevis.
Passing through the third tendon compartment, lying in a narrow, oblique groove on the back of the lower end of the radius, it crosses the wrist close to the dorsal midline before turning towards the thumb using Lister's tubercle on the distal end of the radius as a pulley.
It obliquely crosses the tendons of the extensores carpi radialis longus and brevis, and is separated from the extensor pollicis brevis by a triangular interval, the anatomical snuff box in which the radial artery is found.
At the proximal phalanx, the tendon is joined by expansions from abductor pollicis brevis and adductor pollicis.
The tendon is finally inserted on the base of the distal phalanx of the thumb.
in length, the tendon passes through a long and superficial synovial sheath which, passing obliquely from the radial border of the forearm into the thumb, extends from the proximal border of the extensor retinaculum to the first carpometacarpal joint. In the synovial sheath a proximal and a distal mesotendon connect the tendon to the floor of the sheath.
Relations
Together with the tendons of the extensor pollicis brevis and the abductor pollicis longus, its tendon crosses the radial artery.
Blood supply
The tendon of extensor pollicis longus is supplied by branches from various arteries. Before the tendon enters its synovial sheath, arteries from the anterior interosseous artery or its muscular branches enter the tendon. The sheath itself is supplied by the posterior ramus of the same artery. In the metacarpal region, beyond |
https://en.wikipedia.org/wiki/Flexor%20pollicis%20brevis%20muscle | The flexor pollicis brevis is a muscle in the hand that flexes the thumb. It is one of three thenar muscles. It has both a superficial part and a deep part.
Origin and insertion
The muscle's superficial head arises from the distal edge of the flexor retinaculum and the tubercle of the trapezium, the most lateral bone in the distal row of carpal bones. It passes along the radial side of the tendon of the flexor pollicis longus.
The deeper (and medial) head "varies in size and may be absent." It arises from the trapezoid and capitate bones on the floor of the carpal tunnel, as well as the ligaments of the distal carpal row.
Both heads become tendinous and insert together into the radial side of the base of the proximal phalanx of the thumb; at the junction between the tendinous heads there is a sesamoid bone.
Innervation
The superficial head is usually innervated by the lateral terminal branch of the median nerve. The deep part is often innervated by the deep branch of the ulnar nerve (C8, T1).
Blood supply
The flexor pollicis brevis receives its blood supply from the superficial palmar branches of radial artery.
Action
The flexor pollicis brevis flexes the thumb at the metacarpophalangeal joint, as well as flexion and medial rotation of the 1st metacarpal bone at the carpometacarpal joint.
Pathology
Flexor pollicis brevis can, rarely, be completely absent at birth due to a congenital issue (as can the other muscles of the thenar eminence).
Additional images |
https://en.wikipedia.org/wiki/Flexor%20pollicis%20longus%20muscle | The flexor pollicis longus (; FPL, Latin flexor, bender; pollicis, of the thumb; longus, long) is a muscle in the forearm and hand that flexes the thumb. It lies in the same plane as the flexor digitorum profundus. This muscle is unique to humans, being either rudimentary or absent in other primates. A meta-analysis indicated accessory flexor pollicis longus is present in around 48% of the population.
Human anatomy
Origin and insertion
It arises from the grooved anterior (side of palm) surface of the body of the radius, extending from immediately below the radial tuberosity and oblique line to within a short distance of the pronator quadratus muscle. An occasionally present accessory long head of the flexor pollicis longus muscle is called 'Gantzer's muscle'. It may cause compression of the anterior interosseous nerve.
It arises also from the adjacent part of the interosseous membrane of the forearm, and generally by a fleshy slip from the medial border of the coronoid process of the ulna. In 40 percent of cases, it is also inserted from the medial epicondyle of the humerus, and in those cases a tendinous connection with the humeral head of the flexor digitorum superficialis is present.
The fibers end in a flattened tendon, which passes beneath the flexor retinaculum of the hand through the carpal tunnel. It is then lodged between the lateral head of the flexor pollicis brevis and the oblique part of the adductor pollicis, and, entering an osseoaponeurotic canal similar to those for the flexor tendons of the fingers, is inserted into the base of the distal phalanx of the thumb.
Relations
The anterior interosseous nerve (a branch of the median nerve) and the anterior interosseous artery and vein pass downward on the front of the interosseous membrane between the flexor pollicis longus and flexor digitorum profundus.
Injuries to tendons are particularly difficult to recover from due to the limited blood supply they receive.
Actions
The flexor pollicis longus |
https://en.wikipedia.org/wiki/Pronator%20teres%20muscle | The pronator teres is a muscle (located mainly in the forearm) that, along with the pronator quadratus, serves to pronate the forearm (turning it so that the palm faces posteriorly when from the anatomical position). It has two origins, at the medial humeral supracondylar ridge and the ulnar tuberosity, and inserts near the middle of the radius.
Structure
The pronator teres has two heads—humeral and ulnar.
The humeral head, the larger and more superficial, arises from the medial supracondylar ridge immediately superior to the medial epicondyle of the humerus, and from the common flexor tendon (which arises from the medial epicondyle).
The ulnar head (or ulnar tuberosity) is a thin fasciculus, which arises from the medial side of the coronoid process of the ulna, and joins the preceding at an acute angle.
The median nerve enters the forearm between the two heads of the muscle, and is separated from the ulnar artery by the ulnar head.
The muscle passes obliquely across the forearm, and ends in a flat tendon, which is inserted into a rough impression at the middle of the lateral surface of the body of the radius, just distal to the insertion of the supinator.
The lateral border of the muscle forms the medial boundary of the triangular hollow known as the cubital fossa, which is situated anterior to the elbow.
Nerve supply
The pronator teres is innervated by the median nerve and nerve roots C6 and C7.
To stimulate the pronator teres, a signal begins in the precentral gyrus in the brain and goes down through the internal capsule. It continues down the corticospinal tracts through the capsule, midbrain, and pons where it arrives at the medullar pyramids. Once at the pyramids, the corticospinal tracts decussate and the signal goes down the lateral corticospinal tract until it reaches the ventral horns of C5, C6, C7, C8, and T1. The signal then goes through the ventral rami and down the root ganglions of C5, C6, C7, C8, and T1 (which together form the brachial plexu |
https://en.wikipedia.org/wiki/Palmaris%20longus%20muscle | The palmaris longus is a muscle visible as a small tendon located between the flexor carpi radialis and the flexor carpi ulnaris, although it is not always present. It is absent in about 14 percent of the population; this number can vary in African, Asian, and Native American populations, however. Absence of the palmaris longus does not have an effect on grip strength. The lack of palmaris longus muscle does result in decreased pinch strength in fourth and fifth fingers. The absence of palmaris longus muscle is more prevalent in females than males.
The palmaris longus muscle can be seen by touching the pads of the fourth finger and thumb and flexing the wrist. The tendon, if present, will be visible in the midline of the anterior wrist.
Structure
Palmaris longus is a slender, elongated, spindle shaped muscle, lying on the medial side of the flexor carpi radialis. It is widest in the middle, and narrowest at the proximal and distal attachments.
It arises mainly from the medial epicondyle of the humerus via the common flexor tendon. It also takes origin from the adjacent intermuscular septa and from the antebrachial fascia.
It ends in a slender, flattened tendon, which passes over the upper part of the flexor retinaculum and inserts onto the central part of the flexor retinaculum and lower part of the palmar aponeurosis. Frequently, it sends a tendinous slip to the short muscles of the thumb.
Nerve supply
The palmaris longus is innervated by the median nerve.
Variation
The palmaris longus muscle is a variable muscle. The most common variation is its absence. Several in vivo and in vitro studies have documented the prevalence or absence of the PL tendon in different ethnic groups. Between 5.5 and 24% of Caucasian populations (European and North American) and 4.6 to 26.6% of Asian populations (Chinese, Japanese, Indian, Turkish, Malaysian) have been reported to lack the PL tendon.
There are also variations related to its form. It may be tendinous above and muscu |
https://en.wikipedia.org/wiki/Supinator%20muscle | In human anatomy, the supinator is a broad muscle in the posterior compartment of the forearm, curved around the upper third of the radius. Its function is to supinate the forearm.
Structure
Supinator consists of two planes of fibers, between which passes the deep branch of the radial nerve. The two planes arise in common — the superficial one by tendinous (the initial portion of the muscle is actually just tendon) and the deeper by muscular fibers — from the supinator crest of the ulna, the lateral epicondyle of humerus, the radial collateral ligament, and the annular radial ligament.
The superficial fibers (pars superficialis) surround the upper part of the radius, and are inserted into the lateral edge of the radial tuberosity and the oblique line of the radius, as low down as the insertion of the pronator teres. The upper fibers (pars profunda) of the deeper plane form a sling-like fasciculus, which encircles the neck of the radius above the tuberosity and is attached to the back part of its medial surface; the greater part of this portion of the muscle is inserted into the dorsal and lateral surfaces of the body of the radius, midway between the oblique line and the head of the bone.
The proximal aspect of the superficial head is known as the arcade of Frohse or the supinator arch.
Innervation
It is innervated by the deep branch of the radial nerve. The deep branch then becomes the posterior interosseous nerve upon exiting the supinator muscle. Its nerve roots are primarily from C6, with some C5 involvement. There is also possible additional C7 innervation.
The radial nerve divides into deep and sensory superficial branches just proximal to the supinator muscle — an arrangement that can lead to entrapment and compression of the deep part, potentially resulting in selective paralysis of the muscles served by this nerve (the extensor muscles and the abductor pollicis longus.) Many possible causes are known for this nerve syndrome, known as supinator entrapme |
https://en.wikipedia.org/wiki/Abductor%20pollicis%20brevis%20muscle | The abductor pollicis brevis is a muscle in the hand that functions as an abductor of the thumb.
Structure
The abductor pollicis brevis is a flat, thin muscle located just under the skin. It is a thenar muscle, and therefore contributes to the bulk of the palm's thenar eminence.
It originates from the flexor retinaculum of the hand, the tubercle of the scaphoid bone, and additionally sometimes from the tubercle of the trapezium.
Running lateralward and downward, it is inserted by a thin, flat tendon into the lateral side of the base of the first phalanx of the thumb, and the capsule of the metacarpophalangeal joint.
Nerve supply
The abductor pollicis brevis is supplied by the recurrent branch of the median nerve (Roots C8-T1).
Function
Abduction of the thumb is defined as the movement of the thumb anteriorly, a direction perpendicular to the palm. The abductor pollicis brevis does this by acting across both the carpometacarpal joint and the metacarpophalangeal joint.
It also assists in opposition and extension of the thumb.
Additional images |
https://en.wikipedia.org/wiki/Adductor%20pollicis%20muscle | In human anatomy, the adductor pollicis muscle is a muscle in the hand that functions to adduct the thumb. It has two heads: transverse and oblique.
It is a fleshy, flat, triangular, and fan-shaped muscle deep in the thenar compartment beneath the long flexor tendons and the lumbrical muscles at the center of the palm. It overlies the metacarpal bones and the interosseous muscles.
Structure
Oblique head
The oblique head (Latin: adductor obliquus pollicis) arises by several slips from the capitate bone, the bases of the second and third metacarpals, the intercarpal ligaments, and the sheath of the tendon of the flexor carpi radialis.
From this origin the greater number of fibers pass obliquely downward and converge to a tendon, which, uniting with the tendons of the medial portion of the flexor pollicis brevis and the transverse head of the adductor pollicis, is inserted into the ulnar side of the base of the proximal phalanx of the thumb, a sesamoid bone being present in the tendon.
A considerable fasciculus, however, passes more obliquely beneath the tendon of the flexor pollicis longus to join the lateral portion of the flexor pollicis brevis and the abductor pollicis brevis.
Transverse head
The transverse head (Latin: adductor transversus pollicis) is deeply seated.
It is triangular, arising by a broad base from the lower two-thirds of the palmar surface of the third metacarpal bone; the fibers converge, to be inserted with the medial part of the flexor pollicis brevis and the oblique head into the ulnar side of the base of the proximal phalanx of the thumb.
Relations
The radial artery passes between the two heads, travelling from the back of the hand into the palm, where it forms the deep palmar arch.
Innervation
The adductor pollicis is innervated by the deep branch of the ulnar nerve (C8–T1).
Between the oblique and transverse heads is a thin fibrous arcade which the nerve passes as it traverses the palm laterally. The nerve is accompanied by the |
https://en.wikipedia.org/wiki/Dorsal%20interossei%20of%20the%20foot | In human anatomy, the dorsal interossei of the foot are four muscles situated between the metatarsal bones.
Origin
The four interossei muscles are bipenniform muscles each originating by two heads from the proximal half of the sides of adjacent metatarsal bones.
Insertion
The two heads of each muscle form a central tendon which passes forwards deep to the deep transverse metatarsal ligament. The tendons are inserted on the bases of the second, third, and fourth proximal phalanges and into the aponeurosis of the tendons of the extensor digitorum longus without attaching to the extensor hoods of the toes.
Thus, the first is inserted into the medial side of the second toe; the other three are inserted into the lateral sides of the second, third, and fourth toes.
Action
The dorsal interossei abduct at the metatarsophalangeal joints of the third and fourth toes. Because there is a pair of dorsal interossei muscles attached on both sides of the second toe, simultaneous contraction of these muscles results in no movement. This arrangement of dorsal interossei makes the second toe the midline of the foot, whereas the midline of the hand (marked by dorsal interossei of hand) is in the third finger.
Abduction is of little importance in the foot, but, together with the plantar interossei, the dorsal interossei also produce flexion at the metatarsophalangeal joints. Although small, the dorsal interossei are powerful muscles that, together with their plantar counterparts, control the direction of the toes during violent activity, thus allowing the long and short flexors to perform their actions.
Because of the relationship to the metatarsophalangeal joints, the interossei muscles also contribute to maintaining the anterior metatarsal arch of the foot and also, to a limited extent, the medial and lateral longitudinal arches of the foot.
Innervation
All dorsal interossei are innervated by the lateral plantar nerve (S2–3). Those in the fourth interosseous space are i |
https://en.wikipedia.org/wiki/Extensor%20pollicis%20brevis%20muscle | In human anatomy, the extensor pollicis brevis is a skeletal muscle on the dorsal side of the forearm. It lies on the medial side of, and is closely connected with, the abductor pollicis longus. The extensor pollicis brevis (EPB) belongs to the deep group of the posterior fascial compartment of the forearm.[1] It is a part of the lateral border of the anatomical snuffbox.
Structure
The extensor pollicis brevis arises from the ulna distal to the abductor pollicis longus, from the interosseous membrane, and from the dorsal surface of the radius.
Its direction is similar to that of the abductor pollicis longus, its tendon passing the same groove on the lateral side of the lower end of the radius, to be inserted into the base of the first phalanx of the thumb.
Variation
Absence; fusion of tendon with that of the extensor pollicis longus or abductor pollicis longus muscle.
Function
In a close relationship to the abductor pollicis longus, the extensor pollicis brevis both extends and abducts the thumb at the carpometacarpal and metacarpophalangeal joints.
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https://en.wikipedia.org/wiki/Palmaris%20brevis%20muscle | Palmaris brevis muscle is a thin, quadrilateral muscle, placed beneath the integument of the ulnar side of the hand. It acts to fold the skin of the hypothenar eminence transversally.
Structure
Origin and insertion
Palmaris brevis muscle is located on the ulnar side of the hand. It arises from the tendinous fasciculi from the transverse carpal ligament and palmar aponeurosis. The muscle fibres are inserted into the skin on the ulnar border of the palm of the hand, and occasionally on the pisiform bone.
Innervation
Palmaris brevis muscle is the only muscle innervated by the superficial branch of the ulnar nerve (C8, T1).
Blood supply
Palmaris brevis muscle is supplied by the palmar metacarpal artery of the deep palmar arch.
Discovery
The first recorded observation of the muscle is by Italian anatomist Giambattista Canano sometime before 1543. The muscle was independently discovered a few years later by Realdo Colombo before being pushed to general acceptance in the works of Andreas Vesalius.
Function
Palmaris brevis muscle tenses the skin of the palm on the ulnar side during a grip action. It also deepens the hollow of the palm. The palmaris brevis may protect the ulnar nerve and ulnar artery from compressive forces during repetitive grasping actions. The muscle has a fatigue-resistant fiber type profile, which supports the idea of a protective function to the ulnar neurovasculature during repetitive intermittent grasping tasks.
See also
Thenar eminence
Palmar interossei muscles
Palmaris longus muscle
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https://en.wikipedia.org/wiki/Opponens%20digiti%20minimi%20muscle%20of%20hand | The opponens digiti minimi (opponens digiti quinti in older texts) is a muscle in the hand. It is of a triangular form, and placed immediately beneath the palmaris brevis, abductor digiti minimi and flexor digiti minimi brevis. It is one of the three hypothenar muscles that control the little finger.
It arises from the convexity of the hamulus of the hamate bone and the contiguous portion of the transverse carpal ligament; it is inserted into the whole length of the metacarpal bone of the little finger, along its ulnar margin.
The opponens digiti minimi muscle serves to flex and laterally rotate the 5th metacarpal about the 5th carpometacarpal joint, as when bringing the little finger and thumb into opposition. It is innervated by the deep branch of the ulnar nerve.
See also
Hypothenar
Opponens pollicis muscle
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https://en.wikipedia.org/wiki/Opponens%20pollicis%20muscle | The opponens pollicis is a small, triangular muscle in the hand, which functions to oppose the thumb. It is one of the three thenar muscles. It lies deep to the abductor pollicis brevis and lateral to the flexor pollicis brevis.
Structure
The opponens pollicis muscle is one of the three thenar muscles. It originates from the flexor retinaculum of the hand and the tubercle of the trapezium. It passes downward and laterally, and is inserted into the whole length of the metacarpal bone of the thumb on its radial side.
Innervation
Like the other thenar muscles, the opponens pollicis is innervated by the recurrent branch of the median nerve. In 20% of the population, opponens pollicis is innervated by the ulnar nerve.
Blood supply
The opponens pollicis receives its blood supply from the superficial palmar arch.
Function
Opposition of the thumb is a combination of actions that allows the tip of the thumb to touch the tips of other fingers. The part of apposition that this muscle is responsible for is the flexion of the thumb's metacarpal at the first carpometacarpal joint. This specific action cups the palm. Many texts, for simplicity, use the term opposition to represent this component of true apposition. In order to truly appose the thumb, the actions of a number of other muscles are needed at the thumb's metacarpophalangeal joint. Note that the two opponens muscles (opponens pollicis and opponens digiti minimi) are named so because they oppose each other, but their actions appose the bones.
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https://en.wikipedia.org/wiki/External%20obturator%20muscle | The external obturator muscle, obturator externus muscle (; OE) is a flat, triangular muscle, which covers the outer surface of the anterior wall of the pelvis.
It is sometimes considered part of the medial compartment of thigh, and sometimes considered part of the gluteal region.
Structure
It arises from the margin of bone immediately around the medial side of the obturator membrane and surrounding bone, viz., from the inferior pubic ramus, and the ramus of the ischium; it also arises from the medial two-thirds of the outer surface of the obturator membrane, and from the tendinous arch which completes the canal for the passage of the obturator vessels and nerves.
The fibers springing from the pubic arch extend on to the inner surface of the bone, where they obtain a narrow origin between the margin of the foramen and the attachment of the obturator membrane.
The fibers converge and pass posterolateral and upward, and end in a tendon which runs across the back of the neck of the femur and lower part of the capsule of the hip joint and is inserted into the trochanteric fossa of the femur.
Relations
The obturator vessels lie between the muscle and the obturator membrane; the anterior branch of the obturator nerve reaches the thigh by passing in front of the muscle, and the posterior branch by piercing it.
Variation
In 33% of people a supernumerary muscle is found between the adductor brevis and minimus. While this muscle, when present, is similar to its neighbouring adductors, it is formed by separation from the superficial layer of the external obturator, and is thus not ontogenetically related to the adductor muscles of the hip. This muscle originates from the upper part of the inferior pubic ramus from where it runs downwards and laterally. In half of cases, it inserts into the anterior surface of the insertion aponeurosis of the adductor minimus. In the remaining cases, it is either inserted into the upper part of the pectineal line or the posterior part |
https://en.wikipedia.org/wiki/Quadratus%20femoris%20muscle | The quadratus femoris is a flat, quadrilateral skeletal muscle. Located on the posterior side of the hip joint, it is a strong external rotator and adductor of the thigh, but also acts to stabilize the femoral head in the acetabulum. Quadratus femoris use in the Meyer's muscle pedicle grafting to prevent avascular necrosis of femur head.
Course
It originates on the lateral border of the ischial tuberosity of the ischium of the pelvis. From there, it passes laterally to its insertion on the posterior side of the head of the femur: the quadrate tubercle on the intertrochanteric crest and along the quadrate line, the vertical line which runs downward to bisect the lesser trochanter on the medial side of the femur. Along its course, quadratus is aligned edge to edge with the inferior gemellus above and the adductor magnus below, so that its upper and lower borders run horizontal and parallel.
At its origin, the upper margin of the adductor magnus is separated from it by the terminal branches of the medial femoral circumflex vessels.
A bursa is often found between the front of this muscle and the lesser trochanter. Sometimes absent.
Clinical significance
Groin pain can be a disabling ailment with many potential root causes: one such cause, often overlooked, is quadratus femoris tendinitis. Magnetic resonance imaging can show abnormal signal intensity at the insertion of the right quadratus femoris tendon, which suggests inflammation of the area. Since the muscle works to laterally rotate and adduct the femur, actions involving the lower body can strain the muscle. In addition, patients present with hip pain and an increased signal intensity of the MRI of the quadratus femoris have been shown to also have a significantly narrower ischiofemoral space compared to the general populace. The ischiofemoral impingement may be a cause of the hip pain associated with quadratus femoris tendinitis.
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Notes |
https://en.wikipedia.org/wiki/Adductor%20brevis%20muscle | The adductor brevis is a muscle in the thigh situated immediately deep to the pectineus and adductor longus. It belongs to the adductor muscle group. The main function of the adductor brevis is to pull the thigh medially. The adductor brevis and the rest of the adductor muscle group is also used to stabilize left to right movements of the trunk, when standing on both feet, or to balance when standing on a moving surface. The adductor muscle group is used pressing the thighs together to ride a horse, and kicking with the inside of the foot in soccer or swimming. Last, they contribute to flexion of the thigh when running or against resistance (squats, jumping, etc.).
Structure
It is somewhat triangular in form, and arises by a narrow origin from the outer surfaces of the body of the pubis and inferior ramus of the pubis, between the gracilis and obturator externus.
The Adductor brevis muscle widens in triangular fashion to be inserted into the upper part of the linea aspera immediately lateral to the insertion of pectineus and above that of adductor longus.
Relations
By its anterior surface, the adductor brevis is in relation with the pectineus, adductor longus, and anterior branches of the obturator artery, the obturator vein, and the obturator nerve.
By its posterior surface with the adductor magnus and the posterior branches of the obturator artery, the obturator vein, and the obturator nerve.
By its outer border with the obturator externus, and the iliopsoas. By its inner border with the gracilis and adductor magnus.
It is pierced near its insertion by the middle perforating artery.
Innervation
The adductor brevis is innervated dually by the anterior and posterior branches of the obturator nerve.
Function
The muscle is primarily known as a hip adductor. It also functions as a hip flexor. Whether it acts to rotate the femur laterally or medially is dependent on position. |
https://en.wikipedia.org/wiki/Adductor%20magnus%20muscle | The adductor magnus is a large triangular muscle, situated on the medial side of the thigh.
It consists of two parts. The portion which arises from the ischiopubic ramus (a small part of the inferior ramus of the pubis, and the inferior ramus of the ischium) is called the pubofemoral portion, adductor portion, or adductor minimus, and the portion arising from the tuberosity of the ischium is called the ischiocondylar portion, extensor portion, or "hamstring portion". Due to its common embryonic origin, innervation, and action the ischiocondylar portion (or hamstring portion) is often considered part of the hamstring group of muscles. The ischiocondylar portion of the adductor magnus is considered a muscle of the posterior compartment of the thigh while the pubofemoral portion of the adductor magnus is considered a muscle of the medial compartment.
Structure
Pubofemoral (adductor) portion
Those fibers which arise from the ramus of the pubis are short, horizontal in direction, and are inserted into the rough line of the femur leading from the greater trochanter to the linea aspera, medial to the gluteus maximus.
Those fibers from the ramus of the ischium are directed downward and laterally with different degrees of obliquity, to be inserted, by means of a broad aponeurosis, into the linea aspera and the upper part of its medial prolongation below.
Ischiocondylar (hamstring) portion
The medial portion of the muscle, composed principally of the fibers arising from the tuberosity of the ischium, forms a thick fleshy mass consisting of coarse bundles which descend almost vertically, and end about the lower third of the thigh in a rounded tendon which is inserted into the adductor tubercle on the medial condyle of the femur, and is connected by a fibrous expansion to the line leading upward from the tubercle to the linea aspera.
Relations
By its anterior surface the adductor magnus is in relation with the pectineus, adductor brevis, adductor longus, femoral art |
https://en.wikipedia.org/wiki/Vastus%20intermedius%20muscle | The vastus intermedius () (Cruraeus) arises from the front and lateral surfaces of the body of the femur in its upper two-thirds, sitting under the rectus femoris muscle and from the lower part of the lateral intermuscular septum. Its fibers end in a superficial aponeurosis, which forms the deep part of the quadriceps femoris tendon.
The vastus medialis and vastus intermedius appear to be inseparably united, but when the rectus femoris has been reflected during dissection a narrow interval will be observed extending upward from the medial border of the patella between the two muscles, and the separation may be continued as far as the lower part of the intertrochanteric line, where, however, the two muscles are frequently continuous.
Due to being the deeper middle-most of the quadriceps muscle group, the intermedius is the most difficult to stretch once maximum knee flexion is attained. It cannot be further stretched by hip extension as the rectus femoris can, nor is it accessible to manipulate with massage therapy to stretch the fibres sideways as the vastus lateralis and vastus medialis are.
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https://en.wikipedia.org/wiki/Vastus%20lateralis%20muscle | The vastus lateralis (), also called the vastus externus, is the largest and most powerful part of the quadriceps femoris, a muscle in the thigh. Together with other muscles of the quadriceps group, it serves to extend the knee joint, moving the lower leg forward. It arises from a series of flat, broad tendons attached to the femur, and attaches to the outer border of the patella. It ultimately joins with the other muscles that make up the quadriceps in the quadriceps tendon, which travels over the knee to connect to the tibia. The vastus lateralis is the recommended site for intramuscular injection in infants less than 7 months old and those unable to walk, with loss of muscular tone.
Structure
The vastus lateralis muscle arises from several areas of the femur, including the upper part of the intertrochanteric line; the lower, anterior borders of the greater trochanter, to the outer border of the gluteal tuberosity, and the upper half of the outer border of the linea aspera. These form an aponeurosis, a broad flat tendon that covers the upper three-quarters of the muscle. From the inner surface of the aponeurosis, many muscle fibers originate. Some additional fibers arise from the tendon of the gluteus maximus muscle, and from the septum between the vastus lateralis and short head of the biceps femoris.
The fibers form a large fleshy mass, attached to a second strong aponeurosis, placed on the deep surface of the lower part of the muscle. This lower aponeurosis becomes contracted and thickened into a flat tendon that attaches to the outer border of the patella, and subsequently joins with the quadriceps femoris tendon, expanding the capsule of the knee-joint.
Innervation
The vastus lateralis muscle is innervated by the muscular branches of the femoral nerve (L2, L3, and L4).
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https://en.wikipedia.org/wiki/Gracilis%20muscle | The gracilis muscle (; Latin for "slender") is the most superficial muscle on the medial side of the thigh. It is thin and flattened, broad above, narrow and tapering below.
Structure
It arises by a thin aponeurosis from the anterior margins of the lower half of the symphysis pubis and the upper half of the pubic arch.
The muscle's fibers run vertically downward, ending in a rounded tendon. This tendon passes behind the medial condyle of the femur, curves around the medial condyle of the tibia where it becomes flattened, and inserts into the upper part of the medial surface of the body of the tibia, below the condyle. For this reason, the muscle is a lower limb adductor. At its insertion the tendon is situated immediately above that of the semitendinosus muscle, and its upper edge is overlapped by the tendon of the sartorius muscle, which it joins to form the pes anserinus. The pes anserinus is separated from the medial collateral ligament of the knee-joint by a bursa.
A few of the fibers of the lower part of the tendon are prolonged into the deep fascia of the leg.
Relations
By its inner or superficial surface gracilis is in relation with the fascia lata, and below with the sartorius and internal saphenous nerve; the internal saphenous vein crosses it lying superficially to the fascia lata.
By its outer or deep surface with the adductor longus, brevis, and magnus, and the internal lateral ligament of the knee-joint, from which it is separated by a synovial bursa common to the tendons of the gracilis and semitendinosus.
Nerve supply
The obturator nerve innervates the gracilis muscle via the lumbar spinal vertebrae.
Function
The muscle adducts, medially rotates (with hip flexion), laterally rotates, and flexes the hip as above, and also aids in flexion of the knee.
Clinical significance
The gracilis muscle is commonly used as a flap in microsurgery. According to the classification of Mathes and Nahai, it presents a type II blood supply, allowing it to be tran |
https://en.wikipedia.org/wiki/Semimembranosus%20muscle | The semimembranosus muscle () is the most medial of the three hamstring muscles in the thigh. It is so named because it has a flat tendon of origin. It lies posteromedially in the thigh, deep to the semitendinosus muscle. It extends the hip joint and flexes the knee joint.
Structure
The semimembranosus muscle, so called from its membranous tendon of origin, is situated at the back and medial side of the thigh. It is wider, flatter, and deeper than the semitendinosus (with which it shares very close insertion and attachment points). The muscle overlaps the upper part of the popliteal vessels.
Origin
The semimembranosus muscle originates by a thick tendon from the superolateral aspect of the ischial tuberosity. It arises above and medial to the biceps femoris muscle and semitendinosus muscle. The tendon of origin expands into an aponeurosis, which covers the upper part of the anterior surface of the muscle; from this aponeurosis, muscular fibers arise, and converge to another aponeurosis which covers the lower part of the posterior surface of the muscle and contracts into the tendon of insertion.
Insertion
The semimembranosus muscle inserts on the:
medial condyle of the tibia.
medial margin of the tibia.
lateral condyle of femur.
fascia of the popliteus muscle.
The tendon of insertion gives off certain fibrous expansions: one, of considerable size, passes upward and laterally to be inserted into the posterior lateral condyle of the femur, forming part of the oblique popliteal ligament of the knee-joint; a second is continued downward to the fascia which covers the popliteus muscle; while a few fibers join the medial collateral ligament of the joint and the fascia of the leg.
Nerve supply
The semimembranosus is innervated by the tibial part of the sciatic nerve. The sciatic nerve consists of the anterior divisions of ventral nerve roots from L4 through S3. These nerve roots are part of the larger nerve network–the sacral plexus. The tibial part of the sc |
https://en.wikipedia.org/wiki/Semitendinosus%20muscle | The semitendinosus () is a long superficial muscle in the back of the thigh. It is so named because it has a very long tendon of insertion. It lies posteromedially in the thigh, superficial to the semimembranosus.
Structure
The semitendinosus, remarkable for the great length of its tendon of insertion, is situated at the posterior and medial aspect of the thigh.
It arises from the lower and medial impression on the upper part of the tuberosity of the ischium, by a tendon common to it and the long head of the biceps femoris; it also arises from an aponeurosis which connects the adjacent surfaces of the two muscles to the extent of about 7.5 cm. from their origin.
The muscle is fusiform and ends a little below the middle of the thigh in a long round tendon which lies along the medial side of the popliteal fossa; it then curves around the medial condyle of the tibia and passes over the medial collateral ligament of the knee-joint, from which it is separated by a bursa, and is inserted into the upper part of the medial surface of the body of the tibia, nearly as far forward as its anterior crest.
The semitendinosus is more superficial than the semimembranosus (with which it shares very close insertion and attachment points). However, because the semimembranosus is wider and flatter than the semitendinosus, it is still possible to palpate the semimembranosus directly.
At its insertion it gives off from its lower border a prolongation to the deep fascia of the leg and lies behind the tendon of the sartorius, and below that of the gracilis, to which it is united. These three tendons form what is known as the pes anserinus, so named because it looks like the foot of a goose.
Innervation
A lower motor neuron exits to the sacral plexus exiting through the spinal levels L5-S2. From the sacral plexus, the lower motor neuron travels down the sciatic nerve. The sciatic nerve branches into the deep fibular nerve and the tibial nerve. The tibial nerve innervates the semi |
https://en.wikipedia.org/wiki/Rectus%20femoris%20muscle | The rectus femoris muscle is one of the four quadriceps muscles of the human body. The others are the vastus medialis, the vastus intermedius (deep to the rectus femoris), and the vastus lateralis. All four parts of the quadriceps muscle attach to the patella (knee cap) by the quadriceps tendon.
The rectus femoris is situated in the middle of the front of the thigh; it is fusiform in shape, and its superficial fibers are arranged in a bipenniform manner, the deep fibers running straight () down to the deep aponeurosis. Its functions are to flex the thigh at the hip joint and to extend the leg at the knee joint.
Structure
It arises by two tendons: one, the anterior or straight, from the anterior inferior iliac spine; the other, the posterior or reflected, from a groove above the rim of the acetabulum.
The two unite at an acute angle and spread into an aponeurosis that is prolonged downward on the anterior surface of the muscle, and from this the muscular fibers arise.
The muscle ends in a broad and thick aponeurosis that occupies the lower two-thirds of its posterior surface, and, gradually becoming narrowed into a flattened tendon, is inserted into the base of the patella.
Nerve supply
The neurons for voluntary thigh contraction originate near the summit of the medial side of the precentral gyrus (the primary motor area of the brain). These neurons send a nerve signal that is carried by the corticospinal tract down the brainstem and spinal cord. The signal starts with the upper motor neurons carrying the signal from the precentral gyrus down through the internal capsule, through the cerebral peduncle, and into the medulla. In the medullary pyramid, the corticospinal tract decussates and becomes the lateral corticospinal tract. The nerve signal will continue down the lateral corticospinal tract until it reaches spinal nerve L4. At this point, the nerve signal will synapse from the upper motor neurons to the lower motor neurons. The signal will travel through the |
https://en.wikipedia.org/wiki/Flexor%20hallucis%20longus%20muscle | The flexor hallucis longus muscle (FHL) attaches to the plantar surface of phalanx of the great toe and is responsible for flexing that toe. The FHL is one of the three deep muscles of the posterior compartment of the leg, the others being the flexor digitorum longus and the tibialis posterior. The tibialis posterior is the most powerful of these deep muscles. All three muscles are innervated by the tibial nerve which comprises half of the sciatic nerve.
Structure
The flexor hallucis longus is situated on the fibular side of the leg. It arises from the inferior two-thirds of the posterior surface of the body of the fibula, with the exception of 2.5 cm. at its lowest part; from the lower part of the interosseous membrane; from an intermuscular septum between it and the peroneus muscles, laterally, and from the fascia covering the tibialis posterior, medially.
The fibers pass obliquely downward and backward, where it passes through the tarsal tunnel on the medial side of the foot and end in a tendon which occupies nearly the whole length of the posterior surface of the muscle.
This tendon lies in a groove which crosses the posterior surface of the lower end of the tibia, between the medial and lateral tubercles of the posterior surface of the talus, and the under surface of the sustentaculum tali of the calcaneus; in the sole of the foot it runs forward between the two heads of the flexor hallucis brevis, and is inserted into the base of the last phalanx of the great toe. The grooves on the talus and calcaneus, which contain the tendon of the muscle, are converted by tendinous fibers into distinct canals, lined by a mucous sheath.
As the tendon passes forward in the sole of the foot, it is situated above, and crosses from the lateral to the medial side of the tendon of the flexor digitorum longus, to which it is connected by a fibrous slip.
Variation
Usually a slip runs to the flexor digitorum and frequently an additional slip runs from the flexor digitorum to |
https://en.wikipedia.org/wiki/Flexor%20digitorum%20longus%20muscle | The flexor digitorum longus muscle is situated on the tibial side of the leg. At its origin it is thin and pointed, but it gradually increases in size as it descends. It serves to flex the second, third, fourth, and fifth toes.
Structure
The flexor digitorum longus muscle arises from the posterior surface of the body of the tibia, from immediately below the soleal line to within 7 or 8 cm of its lower extremity, medial to the tibial origin of the tibialis posterior muscle. It also arises from the fascia covering the tibialis posterior muscle.
The fibers end in a tendon, which runs nearly the whole length of the posterior surface of the muscle. This tendon passes behind the medial malleolus, in a groove, common to it and the tibialis posterior, but separated from the latter by a fibrous septum, each tendon being contained in a special compartment lined by a separate mucous sheath. The tendon of the tibialis posterior and the tendon of the flexor digitorum longus cross each other, in a spot above the medial malleolus, the crural tendinous chiasm. It passes through the tarsal tunnel.
It passes obliquely forward and lateralward, superficial to the deltoid ligament of the ankle-joint, into the sole of the foot, where it crosses over the tendon of the flexor hallucis longus at the level of the navicular bone at a location known as the knot of henry (also referred to as plantar tendinous chiasm), and receives from it a strong tendinous slip.
It then expands and is joined by the quadratus plantæ muscle, and finally divides into four tendons, which are inserted into the bases of the last phalanges of the second, third, fourth, and fifth toes, each tendon passing through an opening in the corresponding tendon of the flexor digitorum brevis muscle opposite the base of the first interphalangeal joint.
Variation
Flexor accessorius longus digitorum, not infrequent, origin from fibula, or tibia, or the deep fascia and ending in a tendon which, after passing beneath the lacin |
https://en.wikipedia.org/wiki/Extensor%20digitorum%20longus%20muscle | The extensor digitorum longus is a pennate muscle, situated at the lateral part of the front of the leg.
Structure
It arises from the lateral condyle of the tibia; from the upper three-quarters of the anterior surface of the body of the fibula; from the upper part of the interosseous membrane; from the deep surface of the fascia; and from the intermuscular septa between it and the tibialis anterior on the medial, and the peroneal muscles on the lateral side. Between it and the tibialis anterior are the upper portions of the anterior tibial vessels and deep peroneal nerve.
The muscle passes under the superior and inferior extensor retinaculum of foot in company with the fibularis tertius, and divides into four slips, which run forward on the dorsum of the foot, and are inserted into the second and third phalanges of the four lesser toes.
The tendons to the second, third, and fourth toes are each joined, opposite the metatarsophalangeal articulations, on the lateral side by a tendon of the extensor digitorum brevis. The tendons are inserted in the following manner: each receives a fibrous expansion from the interossei and lumbricals, and then spreads out into a broad aponeurosis, which covers the dorsal surface of the first phalanx: this aponeurosis, at the articulation of the first with the second phalanx, divides into three slips—an intermediate, which is inserted into the base of the second phalanx; and two collateral slips, which, after uniting on the dorsal surface of the second phalanx, are continued onward, to be inserted into the base of the third phalanx.
Variations
This muscle varies considerably in the modes of origin and the arrangement of its various tendons.
The tendons to the second and fifth toes may be found doubled, or extra slips are given off from one or more tendons to their corresponding metatarsal bones, or to the short extensor, or to one of the interosseous muscles.
A slip to the great toe from the innermost tendon has been found.
See a |
https://en.wikipedia.org/wiki/Popliteus%20muscle | The popliteus muscle in the leg is used for unlocking the knees when walking, by laterally rotating the femur on the tibia during the closed chain portion of the gait cycle (one with the foot in contact with the ground). In open chain movements (when the involved limb is not in contact with the ground), the popliteus muscle medially rotates the tibia on the femur. It is also used when sitting down and standing up. It is the only muscle in the posterior (back) compartment of the lower leg that acts just on the knee and not on the ankle. The gastrocnemius muscle acts on both joints.
Structure
The popliteus muscle originates from the lateral surface of the lateral condyle of the femur by a rounded tendon. Its fibers pass downward and medially. It inserts onto the posterior surface of tibia, above the soleal line. The popliteus tendon runs beneath the lateral collateral ligament and tendon of biceps femoris. The muscle also runs above the lateral meniscus but has no connection with the meniscus in 45% of the cases, but has strong connection with it in 17.5% of the cases. Therefore, popliteus muscle is extrasynovial, extra-articular, and intracapsular.
Nerve supply
The popliteus muscle is supplied by the tibial nerve, from spinal roots L5 and S1.
Variation
There is sometimes an additional head from the sesamoid bone in the lateral (outer) head of the gastrocnemius muscle.
Rarely an additional inconstant muscle; the popliteus minor is seen. It originates from the femur on the inner side of the plantaris muscle and inserts into the posterior ligament of the knee-joint.
Peroneotibialis, 14% of population. Origin is inner side of the head of the fibula, insertion into the upper end of the oblique line of the tibia, it lies beneath the popliteus.
Another variant, the cyamella, is a small sesamoid bone embedded in the tendon of the popliteus muscle. It is rarely seen in humans, with prevalence rates from 0.57–1.8%, but has been described more often in other primates a |
https://en.wikipedia.org/wiki/Fibularis%20brevis | In human anatomy, the fibularis brevis (or peroneus brevis) is a muscle that lies underneath the fibularis longus within the lateral compartment of the leg. It acts to tilt the sole of the foot away from the midline of the body (eversion) and to extend the foot downward away from the body at the ankle (plantar flexion).
Structure
The fibularis brevis arises from the lower two-thirds of the lateral, or outward, surface of the fibula (inward in relation to the fibularis longus) and from the connective tissue between it and the muscles on the front and back of the leg.
The muscle passes downward and ends in a tendon that runs behind the lateral malleolus of the ankle in a groove that it shares with the tendon of the fibularis longus; the groove is converted into a canal by the superior fibular retinaculum, and the tendons in it are contained in a common mucous sheath.
The tendon then runs forward along the lateral side of the calcaneus, above the calcaneal tubercle and the tendon of the fibularis longus. It inserts into the tuberosity at the base of the fifth metatarsal on its lateral side.
The fibularis brevis is supplied by the superficial fibular (peroneal) nerve.
Function
The fibularis brevis is the strongest abductor of the foot. Together with the fibularis longus and the tibialis posterior, it extends the foot downward away from the body at the ankle (plantar flexion). It opposes the tibialis anterior and the fibularis tertius, which pull the foot upward toward the body (dorsiflexion). The fibularis longus also tilts the sole of the foot away from the midline of the body (eversion).
Together, the fibularis muscles help to steady the leg upon the foot, especially in standing on one leg.
Clinical significance
When the base of the fifth metatarsal is fractured, the fibularis brevis may pull on and displace the upper fragment (known as a Jones fracture). An inversion sprain of the foot may pull the tendon such that it avulses the tuberosity at the base of th |
https://en.wikipedia.org/wiki/Fibularis%20tertius | In human anatomy, the fibularis tertius (also known as the peroneus tertius) is a muscle in the anterior compartment of the leg. It acts to tilt the sole of the foot away from the midline of the body (eversion) and to pull the foot upward toward the body (dorsiflexion).
Structure
The fibularis tertius arises from the lower third of the front surface of the fibula, the lower part of the interosseous membrane, and septum, or connective tissue, between it and the fibularis brevis. The septum is sometimes called the intermuscular septum of Otto.
The muscle passes downward and ends in a tendon that passes under the superior extensor retinaculum and the inferior extensor retinaculum of the foot in the same canal as the extensor digitorum longus muscle. It may be mistaken as a fifth tendon of the extensor digitorum longus. The tendon inserts into the medial part of the posterior surface of the shaft of the fifth metatarsal bone.
The fibularis tertius is supplied by the deep fibular nerve. In rare cases, it may also be supplied by the common fibular nerve. This is unlike the other fibularis muscles, which are located in the lateral compartment of the leg and are supplied by the superficial fibular nerve, since the fibularis tertius is found in the anterior compartment of the leg.
The fibularis tertius may be absent in humans. It may be absent in as few as 5% of people, or as many as 72%, depending on the population surveyed. It is rarely found in other primates, which is one reason its function has been linked to efficient bipedalism.
Function
As a weak dorsiflexor of the ankle joint, the fibularis tertius assists in pulling the foot upward toward the body. It also assists in tilting the sole of the foot away from midline of the body at the ankle (eversion). It is likely to be helpful though not essential in bipedal walking.
Clinical significance
The fibularis tertius may be involved in ankle injuries and may rupture. This is caused by hyperextension.
The fibular |
https://en.wikipedia.org/wiki/Abductor%20hallucis%20muscle | The abductor hallucis muscle is an intrinsic muscle of the foot. It participates in the abduction and flexion of the great toe.
Structure
The abductor hallucis muscle is located in the medial border of the foot and contributes to form the prominence that is observed on the region. It is inserted behind on the tuberosity of the calcaneus, the flexor retinaculum, and the plantar aponeurosis. Its muscle body, relatively thick behind, flattens as it goes forward. It ends in a common tendon with the medial head of the flexor hallucis brevis that inserts on the medial surface of the base of the first proximal phalanx and its related sesamoid bone. Its medial surface is superficial and covered with the muscle's fascia and the skin.
Nerve supply
Abductor hallucis is supplied by the medial plantar nerve. The nerves that supply it enter the muscle from its upper border.
Additional images
See also
Intrinsic muscles of the foot
Sole of the foot |
https://en.wikipedia.org/wiki/Adductor%20hallucis%20muscle | The Adductor hallucis (Adductor obliquus hallucis) arises by two heads—oblique and transverse and is responsible for adducting the big toe. It has two heads, both are innervated by the lateral plantar nerve.
Structure
Oblique head
The oblique head is a large, thick, fleshy mass, crossing the foot obliquely and occupying the hollow space under the first, second, third and fourth metatarsal bones. It arises from the bases of the second, third, and fourth metatarsal bones, and from the sheath of the tendon of the Peroneus longus, and is inserted, together with the lateral portion of the Flexor hallucis brevis, into the lateral side of the base of the first phalanx of the great toe.
Transverse head
The transverse head (Transversus pedis) is a narrow, flat fasciculus which arises from the plantar metatarsophalangeal ligaments of the third, fourth, and fifth toes (sometimes only from the third and fourth), and from the transverse ligament of the metatarsals.
It is inserted into the lateral side of the base of the first phalanx of the great toe, its fibers blending with the tendon of insertion of the oblique head.
Variation
Slips to the base of the first phalanx of the second toe. Opponens hallucis, occasional slips from the adductor to the metatarsal bone of the great toe.
Additional images |
https://en.wikipedia.org/wiki/Flexor%20hallucis%20brevis%20muscle | Flexor hallucis brevis muscle is a muscle of the foot that flexes the big toe.
Structure
Flexor hallucis brevis muscle arises, by a pointed tendinous process, from the medial part of the under surface of the cuboid bone, from the contiguous portion of the third cuneiform, and from the prolongation of the tendon of the tibialis posterior muscle which is attached to that bone. It divides in front into two portions, which are inserted into the medial and lateral sides of the base of the first phalanx of the great toe, a sesamoid bone being present in each tendon at its insertion. The medial portion is blended with the abductor hallucis muscle previous to its insertion; the lateral portion (sometimes described as the first plantar interosseus) with the adductor hallucis muscle. The tendon of the flexor hallucis longus muscle lies in a groove between the two. Its tendon usually contains two sesamoid bones at the point under the first metatarsophalangeal joint.
Innervation
The medial and lateral head of the flexor hallucis brevis is innervated by the medial plantar nerve. Both heads are represented by spinal segments S1, S2.
Variation
Origin subject to considerable variation; it often receives fibers from the calcaneus or long plantar ligament. Attachment to the cuboid bone sometimes wanting. Slip to first phalanx of the second toe.
Function
Flexor hallucis brevis flexes the first metatarsophalangeal joint, or the big toe. It helps to maintain the medial longitudinal arch. It assists with the toe-off phase of gait providing increased push-off.
Clinical significance
Sesamoid bones contained within the tendon of flexor hallucis brevis muscle may become damaged during exercise.
Additional images |
https://en.wikipedia.org/wiki/Flexor%20digitorum%20brevis%20muscle | The flexor digitorum brevis is a muscle which lies in the middle of the sole of the foot, immediately above the central part of the plantar aponeurosis, with which it is firmly united.
Its deep surface is separated from the lateral plantar vessels and nerves by a thin layer of fascia.
Structure
It arises by a narrow tendon, from the medial process of the tuberosity of the calcaneus, from the central part of the plantar aponeurosis, and from the intermuscular septa between it and the adjacent muscles.
It passes forward, and divides into four tendons, one for each of the four lesser toes.
Opposite the bases of the first phalanges, each tendon divides into two slips, to allow of the passage of the corresponding tendon of the flexor digitorum longus; the two portions of the tendon then unite and form a grooved channel for the reception of the accompanying long Flexor tendon.
Finally, it divides a second time, and is inserted into the sides of the second phalanx about its middle. The mode of division of the tendons of the flexor digitorum brevis, and of their insertion into the phalanges, is analogous to that of the tendons of the flexor digitorum superficialis in the hand.
Innervation
Innervation is by the medial plantar nerve.
Variation
Slip to the little toe may occasionally be absent, where it may be replaced by a small fusiform muscle arising from the long flexor tendon or from the quadratus plantæ.
Additional images |
https://en.wikipedia.org/wiki/Plantar%20interossei%20muscles | In human anatomy, plantar interossei muscles are three muscles located between the metatarsal bones in the foot.
Structure
The three plantar interosseous muscles are unipennate, as opposed to the bipennate structure of dorsal interosseous muscles, and originate on a single metatarsal bone. The three muscles originate on the medial aspect of metatarsals III-V. The muscles cross the metatarsophalangeal joint of toes III-V so the insertions correspond with the origin and there is no crossing between toes.
The muscles then continue distally along the foot and insert in the proximal phalanges III-V. The muscles cross the metatarsophalangeal joint of toes III-V so the insertions correspond with the origin and there is no crossing between toes.
Innervation
All three plantar interosseous muscles are innervated by the lateral plantar nerve. The lateral plantar nerve is a branch from the tibial nerve, which originally branches off the sciatic nerve from the sacral plexus.
Function
Since the intersseous muscles cross on the metatarsophalangeal joint, then they act on that specific joint and cause adduction of toes III, IV, and V.
Adduction itself is not of extreme importance to the toes, but these muscles work together with the dorsal interosseous muscles in flexion of the foot. They also work together to strengthen the metatarsal arch.
Additional images
See also
Interosseous muscles of the hand
Dorsal interossei of the hand
Palmar interossei
Interosseous muscles of the foot
Dorsal interossei of the foot |
https://en.wikipedia.org/wiki/Quadratus%20plantae%20muscle | The quadratus plantae (flexor accessorius) is separated from the muscles of the first layer by the lateral plantar vessels and nerve. It acts to aid in flexing the 2nd to 5th toes (offsetting the oblique pull of the flexor digitorum longus) and is one of the few muscles in the foot with no homolog in the hand.
Origin and insertion
It arises by two heads, which are separated from each other by the long plantar ligament: the medial or larger head is muscular, and is attached to the medial concave surface of the calcaneus, below the groove which lodges the tendon of the flexor hallucis longus; the lateral head, flat and tendinous, arises from the lateral border of the inferior surface of the calcaneus, in front of the lateral process of its tuberosity, and from the long plantar ligament.
The two portions join at an acute angle, and end in a flattened band which is inserted into the lateral margin and upper and under surfaces of the tendon of the flexor digitorum longus, forming a kind of groove, in which the tendon is lodged. It usually sends slips to those tendons of the Flexor digitorum longus which pass to the second, third, and fourth toes.
Variations
Lateral head often wanting; entire muscle absent. Variation in the number of digital tendons to which fibers can be traced. Most frequent offsets are sent to the second, third and fourth toes; in many cases to the fifth as well; occasionally to two toes only.
Additional images |
https://en.wikipedia.org/wiki/Lumbricals%20of%20the%20foot | The lumbricals are four small skeletal muscles, accessory to the tendons of the flexor digitorum longus muscle. They are numbered from the medial side of the foot.
Structure
The lumbricals arise from the tendons of the flexor digitorum longus muscle, as far back as their angles of division, each springing from two tendons, except the first. The first lumbrical is unipennate, while the second, third and fourth are bipennate.
The muscles end in tendons, which pass forward on the medial sides of the four lesser toes, and are inserted into the expansions of the tendons of the extensor digitorum longus muscle on the dorsal surfaces of the proximal phalanges. All four lumbricals insert into extensor hoods of the phalanges, thus creating extension at the inter-phalangeal (PIP and DIP) joints. However, as the tendons also pass inferior to the metatarsal phalangeal (MTP) joints it creates flexion at this joint.
Innervation
The most medial lumbrical is innervated by the medial plantar nerve while the remaining three lumbricals are supplied by the lateral plantar nerve.
Variation
Absence of one or more; doubling of the third or fourth even the fifth. Insertion partly or wholly into the first phalanges.
History
The term "lumbrical" comes from the Latin, meaning "worm".
Additional images |
https://en.wikipedia.org/wiki/International%20Mathematics%20Competition | The International Mathematics Competition (IMC) for University Students is an annual mathematics competition open to all undergraduate students of mathematics. Participating students are expected to be at most twenty three years of age at the time of the IMC. The IMC is primarily a competition for individuals, although most participating universities select and send one or more teams of students. The working language is English.
The IMC is a residential competition and all student participants are required to stay in the accommodation provided by the organisers. It aims to provide a friendly, comfortable and secure environment for university mathematics students to enjoy mathematics with their peers from all around the world, to broaden their world perspective and to be inspired to set mathematical goals for themselves that might not have been previously imaginable or thought possible. Notably, in 2018 Caucher Birkar (born Fereydoun Derakhshani), an Iranian Kurdish mathematician, who participated in the 7th IMC held at University College London in 2000, received mathematics' most prestigious award, the Fields Medal. He is now a professor at Tsinghua University and at the University of Cambridge. In 2022 a Kyiv-born mathematician, Maryna Viazovska, was also awarded the Fields Medal. She participated in the IMC as a student four times, in 2002, 2003, 2004 and 2005. She is now a Professor and the Chair of Number Theory at the Institute of Mathematics of the École Polytechnique Fédérale de Lausanne in Switzerland.
Students from over 200 universities from over 50 countries have participated over the first thirty competitions. At the 29th IMC in 2022 participants were awarded Individual Result Prizes, Fair Play Prizes and Most Efficient Team Leader Prizes.
University College London has been involved in the organisation of the IMC and Professor John E. Jayne has served as the President from the beginning in 1994. The IMC runs over five or six days during which the compe |
https://en.wikipedia.org/wiki/Incinerating%20toilet | An incinerating toilet is a type of dry toilet that burns human feces instead of flushing them away with water, as does a flush toilet.
History
The first commercially successful incinerating toilet was the Destroilet, patented in 1946. Destroilets were used on ships in the 1960s when laws were passed to prevent the dumping of raw sewage into American waterways.
In 2011, the Bill & Melinda Gates Foundation launched the "Reinvent the Toilet Challenge" to promote safer, more effective ways to treat human excreta. Several research teams have received funding to work on developing toilets based on solid waste combustion. For example, a toilet under development by RTI International is based on electrochemical disinfection and solid waste combustion. This technology converts feces into burnable pieces and then uses thermoelectric devices to convert the thermal energy into electrical energy.
Design
Incinerating toilets may be powered by electricity, gas, dried feces or other energy sources. Incinerating toilets gather excrement in an integral ashpan and then incinerate it, reducing it to pathogen-free ash. Some will also incinerate "grey water" created from showers and sinks.
Applications
Incinerating toilets are used only for niche applications, which include:
Apartments with limited or difficult access to waste plumbing.
Houses without access to drains, and where building a septic tank would be difficult or uneconomic.
On yachts and canal barges, as an alternative to a blackwater holding tank, which needs to be pumped out occasionally.
On mobile homes, recreational vehicles and caravans/(trailers). |
https://en.wikipedia.org/wiki/Modern%20valence%20bond%20theory | Modern valence bond theory is the application of valence bond theory (VBT) with computer programs that are competitive in accuracy and economy with programs for the Hartree–Fock or post-Hartree-Fock methods. The latter methods dominated quantum chemistry from the advent of digital computers because they were easier to program. The early popularity of valence bond methods thus declined. It is only recently that the programming of valence bond methods has improved. These developments are due to and described by Gerratt, Cooper, Karadakov and Raimondi (1997); Li and McWeeny (2002); Joop H. van Lenthe and co-workers (2002); Song, Mo, Zhang and Wu (2005); and Shaik and Hiberty (2004)
While molecular orbital theory (MOT) describes the electronic wavefunction as a linear combination of basis functions that are centered on the various atoms in a species (linear combination of atomic orbitals), VBT describes the electronic wavefunction as a linear combination of several valence bond structures. Each of these valence bond structures can be described using linear combinations of either atomic orbitals, delocalized atomic orbitals (Coulson-Fischer theory), or even molecular orbital fragments. Although this is often overlooked, MOT and VBT are equally valid ways of describing the electronic wavefunction, and are actually related by a unitary transformation. Assuming MOT and VBT are applied at the same level of theory, this relationship ensures that they will describe the same wavefunction, but will do so in different forms.
Theory
Bonding in H2
Heitler and London's original work on VBT attempts to approximate the electronic wavefunction as a covalent combination of localized basis functions on the bonding atoms. In VBT, wavefunctions are described as the sums and differences of VB determinants, which enforce the antisymmetric properties required by the Pauli exclusion principle. Taking H2 as an example, the VB determinant is
In this expression, N is a normalization constant |
https://en.wikipedia.org/wiki/Leaf%20protein%20concentrate | Leaf protein concentrate (LPC) refers to the proteinaceous mass extracted from leaves. It can be a lucrative source of low-cost and sustainable protein for food as well as feed applications. Although the proteinaceous extracts from leaves have been described as early as 1773 by Rouelle, large scale extraction and production of LPC was pioneered post the World War II. In fact, many innovations and advances made with regards to LPC production occurred in parallel to the Green Revolution. In some respects, these two technologies were complimentary in that the Green Revolution sought to increase agrarian productivity through increased crop yields via fertiliser use, mechanisation and genetically modified crops, while LPC offered the means to better utilise available agrarian resources through efficient protein extraction.
Sources
Over the years, numerous sources have been experimented. Pirie and Telek described LPC production using a combination of pulping and heat coagulation. Leaves are typically sourced from shrubs or agricultural wastes given their ease of access and relative abundance. Trees are generally considered a poor source of leaf mass for the production of LPC given restrictions on the ease of access. Fallen leaves / leaf litter have negligible protein-content and are of no extractive value.
Plants belonging to the Fabaceae family such as clover, peas and legumes have also been prime candidates for LPC production. While most plants have a mean leaf protein content of 4 to 6% w/v. Fabaceae plants tend to have nearly double that value at 8 to 10% v/w, depending on the protein estimation method employed. Other non-traditional sources include agricultural wastes such as pea (Pisum sativum) pods, cauliflower (Brassica oleracea) leaves, as well as invasive plants such as Gorse (Ulex europeaus), Broom (Cytisus scoparius), and Bracken (Pteridium aquilinum).
Methods of production
LPC production processes are two-staged, with the first focusing on the expression |
https://en.wikipedia.org/wiki/Nuclear%20binding%20energy | Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable nuclei is always a positive number, as the nucleus must gain energy for the nucleons to move apart from each other. Nucleons are attracted to each other by the strong nuclear force. In theoretical nuclear physics, the nuclear binding energy is considered a negative number. In this context it represents the energy of the nucleus relative to the energy of the constituent nucleons when they are infinitely far apart. Both the experimental and theoretical views are equivalent, with slightly different emphasis on what the binding energy means.
The mass of an atomic nucleus is less than the sum of the individual masses of the free constituent protons and neutrons. The difference in mass can be calculated by the Einstein equation, , where E is the nuclear binding energy, c is the speed of light, and m is the difference in mass. This 'missing mass' is known as the mass defect, and represents the energy that was released when the nucleus was formed.
The term "nuclear binding energy" may also refer to the energy balance in processes in which the nucleus splits into fragments composed of more than one nucleon. If new binding energy is available when light nuclei fuse (nuclear fusion), or when heavy nuclei split (nuclear fission), either process can result in release of this binding energy. This energy may be made available as nuclear energy and can be used to produce electricity, as in nuclear power, or in a nuclear weapon. When a large nucleus splits into pieces, excess energy is emitted as gamma rays and the kinetic energy of various ejected particles (nuclear fission products).
These nuclear binding energies and forces are on the order of one million times greater than the electron binding energies of light atoms like hydrogen.
Introduction
Nucl |
https://en.wikipedia.org/wiki/Fixed%20points%20of%20isometry%20groups%20in%20Euclidean%20space | A fixed point of an isometry group is a point that is a fixed point for every isometry in the group. For any isometry group in Euclidean space the set of fixed points is either empty or an affine space.
For an object, any unique centre and, more generally, any point with unique properties with respect to the object is a fixed point of its symmetry group.
In particular this applies for the centroid of a figure, if it exists. In the case of a physical body, if for the symmetry not only the shape but also the density is taken into account, it applies to the centre of mass.
If the set of fixed points of the symmetry group of an object is a singleton then the object has a specific centre of symmetry. The centroid and centre of mass, if defined, are this point. Another meaning of "centre of symmetry" is a point with respect to which inversion symmetry applies. Such a point needs not be unique; if it is not, there is translational symmetry, hence there are infinitely many of such points. On the other hand, in the cases of e.g. C3h and D2 symmetry there is a centre of symmetry in the first sense, but no inversion.
If the symmetry group of an object has no fixed points then the object is infinite and its centroid and centre of mass are undefined.
If the set of fixed points of the symmetry group of an object is a line or plane then the centroid and centre of mass of the object, if defined, and any other point that has unique properties with respect to the object, are on this line or plane.
1D
Line
Only the trivial isometry group leaves the whole line fixed.
Point
The groups generated by a reflection leave a point fixed.
2D
Plane
Only the trivial isometry group C1 leaves the whole plane fixed.
Line
Cs with respect to any line leaves that line fixed.
Point
The point groups in two dimensions with respect to any point leave that point fixed.
3D
Space
Only the trivial isometry group C1 leaves the whole space fixed.
Plane
Cs with respect to a plane leaves that plane fix |
https://en.wikipedia.org/wiki/Generic%20point | In algebraic geometry, a generic point P of an algebraic variety X is a point in a general position, at which all generic properties are true, a generic property being a property which is true for almost every point.
In classical algebraic geometry, a generic point of an affine or projective algebraic variety of dimension d is a point such that the field generated by its coordinates has transcendence degree d over the field generated by the coefficients of the equations of the variety.
In scheme theory, the spectrum of an integral domain has a unique generic point, which is the zero ideal. As the closure of this point for the Zariski topology is the whole spectrum, the definition has been extended to general topology, where a generic point of a topological space X is a point whose closure is X.
Definition and motivation
A generic point of the topological space X is a point P whose closure is all of X, that is, a point that is dense in X.
The terminology arises from the case of the Zariski topology on the set of subvarieties of an algebraic set: the algebraic set is irreducible (that is, it is not the union of two proper algebraic subsets) if and only if the topological space of the subvarieties has a generic point.
Examples
The only Hausdorff space that has a generic point is the singleton set.
Any integral scheme has a (unique) generic point; in the case of an affine integral scheme (i.e., the prime spectrum of an integral domain) the generic point is the point associated to the prime ideal (0).
History
In the foundational approach of André Weil, developed in his Foundations of Algebraic Geometry, generic points played an important role, but were handled in a different manner. For an algebraic variety V over a field K, generic points of V were a whole class of points of V taking values in a universal domain Ω, an algebraically closed field containing K but also an infinite supply of fresh indeterminates. This approach worked, without any need to deal dire |
https://en.wikipedia.org/wiki/Compensation%20point | The light compensation point (Ic) is the light intensity on the light curve where the rate of photosynthesis exactly matches the rate of cellular respiration. At this point, the uptake of CO2 through photosynthetic pathways is equal to the respiratory release of carbon dioxide, and the uptake of O2 by respiration is equal to the photosynthetic release of oxygen. The concept of compensation points in general may be applied to other photosynthetic variables, the most important being that of CO2 concentration – CO2 compensation point (Γ).Interval of time in day time when light intensity is low due to which net gaseous exchange is zero is called as compensation point.
In assimilation terms, at the compensation point, the net carbon dioxide assimilation is zero. Leaves release CO2 by photorespiration and cellular respiration, but CO2 is also converted into carbohydrate by photosynthesis. Assimilation is therefore the difference in the rate of these processes. At a given partial pressure of CO2 (0.343 hPa in 1980 atmosphere), there is an irradiation at which the net assimilation of CO2 is zero. For instance, in the early morning and late evenings, the light compensation point Ic may be reached as photosynthetic activity decreases and respiration increases. The concentration of CO2 also affects the rates of photosynthesis and photorespiration. Higher CO2 concentrations favour photosynthesis whereas low CO2 concentrations favor photorespiration, producing a CO2 compensation point Γ for a given irradiation.
Light compensation point
As defined above, the light compensation point Ic is when no net carbon assimilation occurs. At this point, the organism is neither consuming nor building biomass. The net gaseous exchange is also zero at this point.
Ic is a practical value that can be reached during early mornings and early evenings. Respiration is relatively constant with regard to light, whereas photosynthesis depends on the intensity of sunlight.
Depth
For aquatic plants |
https://en.wikipedia.org/wiki/Series%2080%20%28software%20platform%29 | Nokia's Series 80 (formerly Crystal) was a short-lived mobile software platform for their enterprise and professional level smartphones, introduced in 2000. It uses the Symbian OS. Common physical properties of this Symbian OS user interface platform are a screen resolution of 640×200 pixels and a full QWERTY keyboard. Series 80 used the large size of the Communicator screens to good effect, but software had to be developed specifically for it, for a relatively small market.
The final Series 80 device was the Nokia 9300i, announced in 2005 and shipped in 2006. Nokia used S60 3rd Edition instead of the Series 80 platform on its final "Communicator" branded device, the Nokia E90 Communicator, released in 2007.
Features
Support for editing popular office documents
Full QWERTY keyboard
Integrated mouse for navigation
SSL/TLS support
Full web browser based on Opera
VPN support
Devices
S80 v1.0:
Jun 2001 – Nokia 9210 Communicator
Jun 2001 – Nokia 9290 Communicator
May 2002 – Nokia 9210i Communicator
S80 v2.0:
Feb 2005 – Nokia 9500 Communicator
Jul 2005 – Nokia 9300 (not branded as "Communicator")
Mar 2006 – Nokia 9300i (not branded as "Communicator") |
https://en.wikipedia.org/wiki/Carbonate%20compensation%20depth | The carbonate compensation depth (CCD) is the depth, in the oceans, at which the rate of supply of calcium carbonates matches the rate of solvation. That is, solvation 'compensates' supply. Below the CCD solvation is faster, so that carbonate particles dissolve and the carbonate shells (tests) of animals are not preserved. Carbonate particles cannot accumulate in the sediments where the sea floor is below this depth.
Calcite is the least soluble of these carbonates, so the CCD is normally the compensation depth for calcite. The aragonite compensation depth (ACD) is the compensation depth for aragonitic carbonates. Aragonite is more soluble than calcite, and the aragonite compensation depth is generally shallower than both the calcite compensation depth and the CCD.
Overview
As shown in the diagram, biogenic calcium carbonate (CaCO3) tests are produced in the photic zone of the oceans (green circles). Upon death, those tests escaping dissolution near the surface settle, along with clay materials. In seawater, a dissolution boundary is formed as a result of temperature, pressure, and depth, and is known as the saturation horizon. Above this horizon, waters are supersaturated and CaCO3 tests are largely preserved. Below it, waters are undersaturated, because of both the increasing solubility with depth and the release of CO2 from organic matter decay, and CaCO3 will dissolve. The sinking velocity of debris is rapid (broad pale arrows), so dissolution occurs primarily at the sediment surface.
At the carbonate compensation depth, the rate of dissolution exactly matches the rate of supply of CaCO3 from above. At steady state this depth, the CCD, is similar to the snowline (the first depth where carbonate-poor sediments occur). The lysocline is the depth interval between the saturation and carbonate compensation depths.
Solubility of carbonate
Calcium carbonate is essentially insoluble in sea surface waters today. Shells of dead calcareous plankton sinking to dee |
https://en.wikipedia.org/wiki/Why%20We%20Nap | Why We Nap: Evolution, Chronobiology, and Functions of Polyphasic and Ultrashort Sleep is a 1992 book edited by Claudio Stampi, sole proprietor of the Chronobiology Research Institute. It is frequently mentioned by "polyphasic sleepers", as it is one of the few published books about the subject of systematic short napping in extreme situations where consolidated sleep is not possible.
According to the book, in a sleep deprived condition, measurements of a polyphasic sleeper's memory retention and analytical ability show increases as compared with monophasic and biphasic sleep (but still a decrease of 12% as compared with free running sleep). According to Stampi, the improvement is due to an extraordinary evolutionary predisposition to adopt such a sleep schedule; he hypothesizes this is possibly because polyphasic sleep was the preferred schedule of ancestors of the human race for thousands of years prior to the adoption of the monophasic schedule.
According to EEG measurements collected by Dr. Stampi during a 50-day trial of polyphasic ultrashort sleep with a test subject and published in his book Why We Nap, the proportion of sleep stages remains roughly the same during both polyphasic and monophasic sleep schedules. The major differences are that the ratio of lighter sleep stages to deeper sleep stages is slightly reduced and that sleep stages are often taken out of order or not at all, that is, some naps may be composed primarily of slow wave sleep while rapid eye movement sleep dominates other naps. |
https://en.wikipedia.org/wiki/E350%20%28food%20additive%29 | E350 is an EU recognised food additive. It comes in two forms,
E350 (i) Sodium malate
E350 (ii) Sodium hydrogen malate
Sodium malate is a sodium salt of malic acid (E296), a natural acid present in fruit, its alate is used as a buffer and flavouring in soft drinks, confectionery and other foods. The D,L - and D-isomers are not allowed for infants - who lack the enzymes to metabolise these compounds. |
https://en.wikipedia.org/wiki/Riverstone%20Networks | Riverstone Networks, was a provider of networking switching hardware based in Santa Clara, California. Originally part of Cabletron Systems, and based on an early acquisition of YAGO, it was one of the many Gigabit Ethernet startups in the mid-1990s. It is now a part of Alcatel-Lucent and its operations are being wound down via a Chapter 11 filing by their current owners.
Company history
7 February 2006 - Riverstone's partner Lucent Technologies signed an Asset Purchase agreement to acquire Riverstone Networks
21 March 2006 - Lucent Technologies wins the auction for Riverstone Networks over rival Ericsson. The final price was $207 million
18 April 2006 - Lucent Technologies are currently in the process of a merger of equals with Alcatel
1 December 2006 - Lucent Technologies completed the process of a merger of equals with Alcatel. Assets of Riverstone Networks are now part of Alcatel-Lucent
Products
All of Riverstone Networks products were geared towards IP over Ethernet, often for a Metro Ethernet solution. All the products were multilayer switches (or switch-routers) and specialized in MPLS VPNs.
15000 Family
The 15000 Family (referred to as the 15K) differed from the RS family as the 15K is not flow-based. Flow-based routers use the main CPU to process new flows and packets through the switch. The 15K differed by letting the line card processors do the work for the network traffic, leaving the main CPU to work on the system itself. This type of network processing is similar to Cisco's dCEF.
The 15K products were based on a different operating system than other Riverstone products, called ROS-X. It was designed to be modular and more like the common command line interface of Cisco.
15008 - The highest performance product from Riverstone. It supported a 96 port 10/100 Ethernet card, 12 or 24 port 1GB Ethernet cards and 1 or 2 port 10GB Ethernet cards. Support for ATM and PoS was planned.
15100/15200 - Designed with the same architecture and operating s |
https://en.wikipedia.org/wiki/Semantic%20URL%20attack | In a semantic URL attack, a client manually adjusts the parameters of its request by maintaining the URL's syntax but altering its semantic meaning. This attack is primarily used against CGI driven websites.
A similar attack involving web browser cookies is commonly referred to as cookie poisoning.
Example
Consider a web-based e-mail application where users can reset their password by answering the security question correctly, and allows the users to send the password
to the e-mail address of their choosing. After they answer the security question correctly, the web page will arrive to the following web form where the users can enter their alternative e-mail address:
<form action="resetpassword.php" method="GET">
<input type="hidden" name="username" value="user001" />
<p>Please enter your alternative e-mail address:</p>
<input type="text" name="altemail" /><br />
<input type="submit" value="Submit" />
</form>
The receiving page, resetpassword.php, has all the information it needs to send the password to the new e-mail. The hidden variable username contains the value user001, which is the username of the e-mail account.
Because this web form is using the GET data method, when the user submits alternative@emailexample.com as the e-mail address where the user wants the password to be sent to,
the user then arrives at the following URL:
http://semanticurlattackexample.com/resetpassword.php?username=user001&altemail=alternative%40emailexample.com
This URL appears in the location bar of the browser, so the user can identify the username and the e-mail address through the URL parameters. The user may decide to steal other people's (user002) e-mail address by visiting the following URL as an experiment:
http://semanticurlattackexample.com/resetpassword.php?username=user002&altemail=alternative%40emailexample.com
If the resetpassword.php accepts these values, it is vulnerable to a semantic URL attack. The new password of the user002 e-mail address will be ge |
https://en.wikipedia.org/wiki/AMD%20Horus | The Horus system, designed by Newisys for AMD, was created to enable AMD Opteron machines to extend beyond the current limit of 8-way (CPU sockets) architectures. The Opteron CPUs feature a cache-coherent HyperTransport (ccHT) bus to permit glueless, multiprocessor interconnect between physical CPU packages but as there is a maximum of three ccHT interfaces per chip, the systems are limited to a maximum of 8 sockets. The HyperTransport bus is also distance restricted and does not permit off-system interconnect.
The Horus system overcomes these limitations by creating a pseudo-Opteron, the Horus chip, which connects to four real Opterons via the HyperTransport bus. As far as the Opterons are concerned they are in a five-way system and this is the basic Horus node (as called 'quad'). The Horus chip then provides an additional off-board interface (based on the InfiniBand standards) which can link to additional Horus nodes (up to 8). The chip handles the necessary translation between local and off-board ccHT communications. By building the CPUs around the Horus chip with 12-bit lanes running at 3125 MHz with InfiniBand technology (8b/10b encoding), this system has an effective internal speed of 30 Gbit/s.
With 8 'quads' connected together, each with the maximum of four Opteron sockets per node, the Horus system allows a total of 32 CPU sockets in a single machine. Dual and future quad-core chips will also be supported, allowing a single system to scale to over a hundred processing cores.
See also
Heterogeneous System Architecture
External links
Horus white paper.
Google groups discussion by engineer.
AMD technologies
Computer buses |
https://en.wikipedia.org/wiki/Incremental%20build%20model | The incremental build model is a method of software development where the product is designed, implemented and tested incrementally (a little more is added each time) until the product is finished. It involves both development and maintenance. The product is defined as finished when it satisfies all of its requirements. This model combines the elements of the waterfall model with the iterative philosophy of prototyping.
According to the Project Management Institute, an incremental approach is an "adaptive development approach in which the deliverable is produced successively, adding
functionality until the deliverable contains the necessary and
sufficient capability to be considered complete."
The product is decomposed into a number of components, each of which is designed and built separately (termed as builds).
Each component is delivered to the client when it is complete. This allows partial utilization of the product and avoids a long
development time. It also avoids a large initial capital outlay and subsequent long waiting period. This model of development also helps ease the traumatic effect of introducing a completely new system all at once.
Incremental model
The incremental model applies the waterfall model incrementally.
The series of releases is referred to as “increments”, with each increment providing more functionality to the customers. After the first increment, a core product is delivered, which can already be used by the customer. Based on customer feedback, a plan is developed for the next increments, and modifications are made accordingly. This process continues, with increments being delivered until the complete product is delivered. The incremental philosophy is also used in the agile process model (see agile modeling).
The Incremental model can be applied to DevOps. In DevOps it centers around the idea of minimizing risk and cost of a DevOps adoption whilst building the necessary in-house skillset and momentum.
Characteristics of Increment |
https://en.wikipedia.org/wiki/Gibbs%20state | In probability theory and statistical mechanics, a Gibbs state is an equilibrium probability distribution which remains invariant under future evolution of the system. For example, a stationary or steady-state distribution of a Markov chain, such as that achieved by running a Markov chain Monte Carlo iteration for a sufficiently long time, is a Gibbs state.
Precisely, suppose is a generator of evolutions for an initial state , so that the state at any later time is given by . Then the condition for to be a Gibbs state is
.
In physics there may be several physically distinct Gibbs states in which a system may be trapped, particularly at lower temperatures.
They are named after Josiah Willard Gibbs, for his work in determining equilibrium properties of statistical ensembles. Gibbs himself referred to this type of statistical ensemble as being in "statistical equilibrium".
See also
Gibbs algorithm
Gibbs measure
KMS state |
https://en.wikipedia.org/wiki/Credit%20card%20interest | Credit card interest is a way in which credit card issuers generate revenue. A card issuer is a bank or credit union that gives a consumer (the cardholder) a card or account number that can be used with various payees to make payments and borrow money from the bank simultaneously. The bank pays the payee and then charges the cardholder interest over the time the money remains borrowed. Banks suffer losses when cardholders do not pay back the borrowed money as agreed. As a result, optimal calculation of interest based on any information they have about the cardholder's credit risk is key to a card issuer's profitability. Before determining what interest rate to offer, banks typically check national, and international (if applicable), credit bureau reports to identify the borrowing history of the card holder applicant with other banks and conduct detailed interviews and documentation of the applicant's finances.
Interest rates
Interest rates vary widely. Some credit card loans are secured by real estate, and can be as low as 6to 12% in the U.S. (2005). Typical credit cards have interest rates between 7and 36% in the U.S., depending largely upon the bank's risk evaluation methods and the borrower's credit history. Brazil has much higher interest rates, about 50% over that of most developing countries, which average about 200% (Economist, May 2006). A Brazilian bank-issued Visa or MasterCard to a new account holder can have annual interest as high as 240% even though inflation seems to have gone up per annum (Economist, May 2006). Banco do Brasil offered its new checking account holders Visa and MasterCard credit accounts for 192% annual interest, with somewhat lower interest rates reserved for people with dependable income and assets (July 2005). These high-interest accounts typically offer very low credit limits (US$40 to $400). They also often offer a grace period with no interest until the due date, which makes them more popular for use as liquidity accounts, whic |
https://en.wikipedia.org/wiki/Gibbs%20algorithm | In statistical mechanics, the Gibbs algorithm, introduced by J. Willard Gibbs in 1902, is a criterion for choosing a probability distribution for the statistical ensemble of microstates of a thermodynamic system by minimizing the average log probability
subject to the probability distribution satisfying a set of constraints (usually expectation values) corresponding to the known macroscopic quantities. in 1948, Claude Shannon interpreted the negative of this quantity, which he called information entropy, as a measure of the uncertainty in a probability distribution. In 1957, E.T. Jaynes realized that this quantity could be interpreted as missing information about anything, and generalized the Gibbs algorithm to non-equilibrium systems with the principle of maximum entropy and maximum entropy thermodynamics.
Physicists call the result of applying the Gibbs algorithm the Gibbs distribution for the given constraints, most notably Gibbs's grand canonical ensemble for open systems when the average energy and the average number of particles are given. (See also partition function).
This general result of the Gibbs algorithm is then a maximum entropy probability distribution. Statisticians identify such distributions as belonging to exponential families. |
https://en.wikipedia.org/wiki/Moishezon%20manifold | In mathematics, a Moishezon manifold is a compact complex manifold such that the field of meromorphic functions on each component has transcendence degree equal the complex dimension of the component:
Complex algebraic varieties have this property, but the converse is not true: Hironaka's example gives a smooth 3-dimensional Moishezon manifold that is not an algebraic variety or scheme. showed that a Moishezon manifold is a projective algebraic variety if and only if it admits a Kähler metric. showed that any Moishezon manifold carries an algebraic space structure; more precisely, the category of Moishezon spaces (similar to Moishezon manifolds, but are allowed to have singularities) is equivalent with the category of algebraic spaces that are proper over . |
https://en.wikipedia.org/wiki/Konami%27s%20Ping%20Pong | Konami's Ping Pong is a sports arcade game created in 1985 by Konami. It is the first video game to accurately reflect the gameplay of table tennis, as opposed to earlier simplifications like Pong. It was ported to the Amstrad CPC, Commodore 64, Famicom Disk System, MSX, and ZX Spectrum.
Gameplay
Konami's Ping Pong can be played singleplayer or multiplayer, using 11 point scoring rules; the first player to attain a score of 11 or higher, leading by two points, wins the game (to a maximum of 14-14, at which point the next point wins). The player must win the best of two out of three games in order to beat the match. The playfield is shown from an isometric perspective with the players shown as disembodied hands; players placed on the far-side of the table will find hitting the ball is much more difficult. However, the player is always positioned on the near side during the single player mode. All the essential moves are represented: forehand, backhand, lob, and smash.
The game includes the penguin protagonist from Konami's earlier title Antarctic Adventure on the title screen and as a member of the audience in the game. This penguin would be later be known as Penta. In the introductory animation, a pingpong ball bounces along the table, and finally hits Penta on the head, who appears to faint.
Reception
In Japan, Game Machine listed Konami's Ping Pong on their September 1, 1985 issue as being the nineteenth most-successful table arcade unit of the month.
Ports
In 1985 the game was released by Konami for MSX computers and in 1986 the game was ported to the Amstrad CPC, Commodore 64 and ZX Spectrum by Imagine Software and Bernie Duggs, under the name Ping Pong. Apart from scaled-down graphics and sound due to limited system capabilities, the ports perfectly replicate the arcade gameplay.
In 1987 the game was ported to the Famicom Disk System as Smash Ping Pong and published by Nintendo. Nintendo's character Donkey Kong Jr. replaces Konami's Penta in the crowd. D |
https://en.wikipedia.org/wiki/Kelly%20criterion | In probability theory, the Kelly criterion (or Kelly strategy or Kelly bet) is a formula for sizing a bet. The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate. It assumes that the expected returns are known and is optimal for a bettor who values their wealth logarithmically. J. L. Kelly Jr, a researcher at Bell Labs, described the criterion in 1956. Under the stated assumptions, the Kelly criterion leads to higher wealth than any other strategy in the long run (i.e., the theoretical maximum return as the number of bets goes to infinity).
The practical use of the formula has been demonstrated for gambling, and the same idea was used to explain diversification in investment management. In the 2000s, Kelly-style analysis became a part of mainstream investment theory and the claim has been made that well-known successful investors including Warren Buffett and Bill Gross use Kelly methods. Also see Intertemporal portfolio choice.
Gambling formula
Where losing the bet involves losing the entire wager, the Kelly bet is:
where:
is the fraction of the current bankroll to wager.
is the probability of a win.
is the probability of a loss ().
is the proportion of the bet gained with a win. E.g., if betting $10 on a 2-to-1 odds bet (upon win you are returned $30, winning you $20), then .
As an example, if a gamble has a 60% chance of winning (, ), and the gambler receives 1-to-1 odds on a winning bet (), then to maximize the long-run growth rate of the bankroll, the gambler should bet 20% of the bankroll at each opportunity ().
If the gambler has zero edge, i.e., if , then the criterion recommends for the gambler to bet nothing.
If the edge is negative () the formula gives a negative result, indicating that the gambler should take the other side of the bet. For example, in American roulette, the bettor is offered an even money payoff () on red, when there are |
https://en.wikipedia.org/wiki/Functional%20near-infrared%20spectroscopy | Functional near-infrared spectroscopy (fNIRS) is an optical brain monitoring technique which uses near-infrared spectroscopy for the purpose of functional neuroimaging. Using fNIRS, brain activity is measured by using near-infrared light to estimate cortical hemodynamic activity which occur in response to neural activity. Alongside EEG, fNIRS is one of the most common non-invasive neuroimaging techniques which can be used in portable contexts. The signal is often compared with the BOLD signal measured by fMRI and is capable of measuring changes both in oxy- and deoxyhemoglobin concentration, but can only measure from regions near the cortical surface. fNIRS may also be referred to as Optical Topography (OT) and is sometimes referred to simply as NIRS.
Description
fNIRS estimates the concentration of hemoglobin from changes in absorption of near infrared light. As light moves or propagates through the head, it is alternately scattered or absorbed by the tissue through which it travels. Because hemoglobin is a significant absorber of near-infrared light, changes in absorbed light can be used to reliably measure changes in hemoglobin concentration. Different fNIRS techniques can also use the way in which light propagates to estimate blood volume and oxygenation. The technique is safe, non-invasive, and can be used with other imaging modalities.
fNIRS is a non-invasive imaging method involving the quantification of chromophore concentration resolved from the measurement of near infrared (NIR) light attenuation or temporal or phasic changes. The technique takes advantage of the optical window in which (a) skin, tissue, and bone are mostly transparent to NIR light (700–900 nm spectral interval) and (b) hemoglobin (Hb) and deoxygenated-hemoglobin (deoxy-Hb) are strong absorbers of light.
There are six different ways for infrared light to interact with the brain tissue: direct transmission, diffuse transmission, specular reflection, diffuse reflection, scattering, and a |
https://en.wikipedia.org/wiki/Moons%20of%20Pluto | The dwarf planet Pluto has five natural satellites. In order of distance from Pluto, they are Charon, Styx, Nix, Kerberos, and Hydra. Charon, the largest, is mutually tidally locked with Pluto, and is massive enough that Pluto–Charon is sometimes considered a double dwarf planet.
History
The innermost and largest moon, Charon, was discovered by James Christy on 22 June 1978, nearly half a century after Pluto was discovered. This led to a substantial revision in estimates of Pluto's size, which had previously assumed that the observed mass and reflected light of the system were all attributable to Pluto alone.
Two additional moons were imaged by astronomers of the Pluto Companion Search Team preparing for the New Horizons mission and working with the Hubble Space Telescope on 15 May 2005, which received the provisional designations S/2005 P 1 and S/2005 P 2. The International Astronomical Union officially named these moons Nix (or Pluto II, the inner of the two moons, formerly P 2) and Hydra (Pluto III, the outer moon, formerly P 1), on 21 June 2006. Kerberos, announced on 20 July 2011, was discovered while searching for Plutonian rings. Styx, announced on 7 July 2012, was discovered while looking for potential hazards for New Horizons.
Charon
Charon is about half the diameter of Pluto and is massive enough (nearly one eighth of the mass of Pluto) that the system's barycenter lies between them, approximately 960 km above Pluto's surface. Charon and Pluto are also tidally locked, so that they always present the same face toward each other. The IAU General Assembly in August 2006 considered a proposal that Pluto and Charon be reclassified as a double planet, but the proposal was abandoned.
Like Pluto, Charon is a perfect sphere to within measurement uncertainty.
Small moons
Pluto's four small circumbinary moons orbit Pluto at two to four times the distance of Charon, ranging from Styx at 42,700 kilometres to Hydra at 64,800 kilometres from the barycenter of the |
https://en.wikipedia.org/wiki/Reverse%20learning | Reverse learning is a neurobiological theory of dreams. In 1983, in a paper published in the science journal Nature, Crick and Mitchison's reverse learning model likened the process of dreaming to a computer in that it was "off-line" during dreaming or the REM phase of sleep. During this phase, the brain sifts through information gathered throughout the day and throws out all unwanted material. According to the model, we dream in order to forget and this involves a process of 'reverse learning' or 'unlearning'.
The cortex cannot cope with the vast amount of information received throughout the day without developing "parasitic" thoughts that would disrupt the efficient organisation of memory. During REM sleep, these unwanted connections in cortical networks are wiped out or damped down by the Crick-Mitchison process making use of impulses bombarding the cortex from sub-cortical areas.
The Crick-Mitchison theory is a variant upon Hobson and McCarley's activation-synthesis hypothesis, published in December 1977. Hobson and McCarley hypothesized that a brain stem neuronal mechanism sends pontine-geniculo-occipital (or PGO) waves that automatically activate the mammalian forebrain. By comparing information generated in specific brain areas with information stored in memory, the forebrain synthesizes dreams during REM sleep.
Crick verbatim on the function of REM sleep
Suppose one did not have REM, then one would mix things up. That is not necessarily a bad thing — it is the basis of fantasy, imagination, and so forth. Imagination means seeing a connection between two things that are different but which have something in common which you had not noticed before. If one had too much REM, one would predict one would be a rather prosaic person without too much imagination. But the process is not 100% efficient. If one goes on too far, one begins to wipe out everything.
Another way to look at it is to say "How could you prevent the brain being overloaded"? One way would b |
https://en.wikipedia.org/wiki/Chirurgia%20magna | Chirurgia magna (Latin for "Great [work on] Surgery"), fully titled the Inventarium sive chirurgia magna (Latin for "The Inventory, or the Great [work on] Surgery"), is a guide to surgery and practical medicine completed in 1363. Guy de Chauliac, Pope Clement VI's attending physician, compiled the information from his own field experience and research of historical medical texts. The original text is in Latin and comprises 465 pages. It was translated into various European languages: the version in Middle English has been published. This work became one of the most important reference manuals of practical medicine for the next three centuries. It was translated into Irish by Cormac Mac Duinnshléibhe.
The physician and bibliophile Tibulle Desbarreaux-Bernard (1798–1880) believed that the Chirurgia magna was originally written in Catalan at the medical school in Montpellier and that the extant Latin text is an early translation.
A modern edition of the Latin text, with commentary on sources, has been printed. |
https://en.wikipedia.org/wiki/Sodium%20trimetaphosphate | Sodium trimetaphosphate (also STMP), with formula Na3P3O9, is one of the metaphosphates of sodium. It has the formula but the hexahydrate is also well known. It is the sodium salt of trimetaphosphoric acid. It is a colourless solid that finds specialised applications in food and construction industries.
Although drawn with a particular resonance structure, the trianion has high symmetry.
Synthesis and reactions
Trisodium trimetaphosphate is produced industrially by heating sodium dihydrogen phosphate to 550 °C, a method first developed in 1955:
The trimetaphosphate dissolves in water and is precipitated by the addition of sodium chloride (common ion effect), affording the hexahydrate. STMP can also prepared by heating samples of sodium polyphosphate, or by a thermal reaction of orthophosphoric acid and sodium chloride at 600°C.
Hydrolysis of the ring leads to the acyclic sodium triphosphate:
Na3P3O9 + H2O → H2Na3P3O10
The analogous reaction of the metatriphosphate anion involves ring-opening by amine nucleophiles. |
https://en.wikipedia.org/wiki/Anterior%20communicating%20artery | In human anatomy, the anterior communicating artery is a blood vessel of the brain that connects the left and right anterior cerebral arteries.
Anatomy
The anterior communicating artery connects the two anterior cerebral arteries across the commencement of the longitudinal fissure. Sometimes this vessel is wanting, the two arteries joining to form a single trunk, which afterward divides; or it may be wholly, or partially, divided into two. Its length averages about 4 mm, but varies greatly. It gives off some of the anteromedial ganglionic vessels, but these are principally derived from the anterior cerebral artery.
It is part of the cerebral arterial circle, also known as the circle of Willis.
Physiology
Anatomical variations of the anterior communicating artery are relatively common. The artery is sometimes duplicated, multiplicated, fenestrated ("net-like") or very short, giving the impression that two anterior cerebral arteries are fused at the point where the anterior communicating artery is usually expected to arise.
Normally, the anterior communicating artery does not significantly contribute to cerebral blood supply, as there is negligible net blood flow within it, and some of its anteromedial branches seem to be specially adapted to ease forebrain sodium sensing, rather than to supply the brain with blood.
Pathology
Aneurysms of the anterior communicating artery are the most common circle of Willis aneurysm and can cause visual field defects such as bitemporal heteronymous hemianopsia (due to compression of the optic chiasm), psychopathology and frontal lobe pathology.
In case of narrowing of other arteries of the circle of Willis or the arteries supplying the circle, the anterior communicating artery can provide a way to supply blood to the opposite (affected) side of the circle. This can often preserve the cerebral blood supply well enough to avoid the symptoms of ischemia. |
https://en.wikipedia.org/wiki/Peppermint%20extract | Peppermint extract is a herbal extract of peppermint (Mentha × piperita) made from the essential oil of peppermint leaves. Peppermint is a hybrid of water mint and spearmint. The oil has been used for various purposes over centuries.
Peppermint extract is commonly used in cooking, as a dietary supplement, as an herbal or alternative medicine, as a pest repellent, and a flavor or fragrance agent for cleaning products, cosmetics, mouthwash, chewing gum, and candies. Its active ingredient menthol causes a cold sensation when peppermint extract is consumed or used topically. There is insufficient evidence to conclude it is effective in treating any medical condition.
Extraction
Peppermint extract is obtained through steam distillation, solvent extraction, and soxhlet extraction.
Uses
Peppermint extract is commonly used as a flavoring agent; it is also used in alternative medical treatments, although there is no sufficient evidence that peppermint extract is effective in treating any medical condition. Moderate levels can be safely mixed into food items, or applied topically, sprayed on surfaces as a household cleaner, or inhaled using aromatherapy. However, the menthol in peppermint oil may cause serious side effects in children and infants if inhaled. Peppermint oil may have adverse interactions with prescription drugs.
Uses in cooking
Peppermint extract can be used to add a peppermint flavor to baked goods, desserts, and candy, particularly candy canes, mints, and peppermint patties. Extracts for cooking may be labeled as pure, natural, imitation, or artificial. While pure and natural extracts contain peppermint oil specifically, imitation and artificial extracts generally use a mix of ingredients to achieve a flavor resembling peppermint.
Peppermint extract can be substituted in recipes with peppermint oil (a stronger ingredient primarily used in candy-making), crème de menthe, or peppermint schnapps. If the food is not heated, the alcoholic properties of liqu |
https://en.wikipedia.org/wiki/Model%20horse%20showing | Model horse showing is a hobby built around the collection of scale model horses, with equal focus on honouring the (real) horse show industry as well as the artistic merit of the miniatures.
Classes & Divisions
Model horse shows consist primarily of two divisions: Halter and Performance. There are both Halter-only and Performance-only shows, though many larger shows will include both. Often there are up to three shows run side-by-side: Youth, Novice and/or Open. Individual shows will make their own guidelines for what qualifies entry to each of these categories.
Several abbreviations commonly occur: OF (Original Finish), CM (Custom) and AR (Artist Resin).
Halter Division
These classes evaluate how a model represents the actual breed of horse. The divisions and judging criteria are derived from their real-life counterparts. Although known as "Halter", no tack or costume is required on the model, and it is generally omitted.
Halter can be further broken down into subdivisions based on manufacturing medium to equalize the different fields of craftsmanship. Common subdivisions include:
OF Plastic or Original Finish Plastic, refers to the original plastic horses produced by companies such as the Breyer Horse Company or the Peter Stone Company. Many shows now further break this down to give separate classes to Breyer and Peter Stone Company horses.
OF China/Resin or Original Finish Chinas and Resins, refers to professionally produced porcelain horses produced by companies such as Animal Artistry, Pour Horse Pottery, or Alchemy Fine China.
Artist Resin refers to professionally produced resin models which have been individually painted by professional or amateur artists.
CM Plastic typically refers to OF Plastic horses that have been repainted, haired, or resculpted, regardless of original material or manufacturer. The custom may be a drastic custom, where the original model is no longer recognisable, or a minimal custom.
CM China or Custom Glazed Chinas, refers to |
https://en.wikipedia.org/wiki/Paracelsianism | Paracelsianism (also Paracelsism; German: ) was an early modern medical movement based on the theories and therapies of Paracelsus.
It developed in the second half of the 16th century, during the decades following Paracelsus' death in 1541, and it flourished during the first half of the 17th century, representing one of the most comprehensive alternatives to learned medicine, the traditional system of therapeutics derived from Galenic physiology.
Based on the by then antiquated principle of maintaining harmony between the microcosm and macrocosm, Paracelsianism fell rapidly into decline in the later 17th century, but left its mark on medical practices. It was responsible for the widespread introduction of mineral therapies and several other iatrochemical techniques.
Spagyric
Spagyric, or spagyria, is a method developed by Paracelsus and his followers which was thought to improve the efficacy of existing medicines by separating them into their primordial elements (the : sulphur, mercury, and salt) and then again recombining them. Paracelsian physicians held that through this method the medically beneficial ingredients of a compound (the purified ) were separated from the harmful and toxic ones, turning even some poisons into medicines.
This procedure involved fermentation, distillation, and extraction of mineral components from the ash of the plant. These processes were in use in medieval alchemy generally for the separation and purification of metals from ores (see Calcination), and salts from brines and other aqueous solutions.
Etymology
Originally coined by Paracelsus, the word comes from the Ancient Greek σπάω spao ('to separate, to draw out') and ἀγείρω ageiro ('to combine', 'to recombine', 'to gather'). In its original use, the word spagyric was commonly used synonymously with the word alchemy, however, in more recent times it has often been adopted by alternative medicine theorists and various techniques of holistic medicine.
See also
Sulfur-mercury the |
https://en.wikipedia.org/wiki/Solo%20garlic | Solo garlic, also known as single clove garlic, monobulb garlic, single bulb garlic, or pearl garlic, is a type of Allium sativum (garlic). The size of the single clove differs from approximately 25 to 50 mm in diameter. It has the flavour of the garlic clove but is somewhat milder and slightly perfumed. The appearance is akin to that of a pickling onion, with white skin and often purple stripes. Compared to traditional garlic, Solo garlic offers the advantage of being easy to peel quickly.
Single clove garlic originated in the mountainous Yunnan province of southwestern China. It is not a single variety of garlic, but rather a product of specific planting practices. As a result, single cloved versions of other garlic species such as Allium nigrum and Allium ampeloprasum are also available.
Growth
Small bulbs of solo garlic can be obtained by planting the bulbils of any variety of garlic. However, commercial production comes from areas where garlic is likely to produce a solo bulb due to environmental factors. The climate in these areas, combined with careful cultivation, leads to a large percentage of the garlic crop failing to split into multiple cloves.
Cultivation
Solo garlic is believed to have originated in Yunnan, China, a mountainous area. The product is known as "only-child garlic".
See also
Black garlic (food) |
https://en.wikipedia.org/wiki/Keychain%20%28software%29 | Keychain is the password management system in macOS, developed by Apple. It was introduced with Mac OS 8.6, and has been included in all subsequent versions of the operating system, now known as macOS. A Keychain can contain various types of data: passwords (for websites, FTP servers, SSH accounts, network shares, wireless networks, groupware applications, encrypted disk images), private keys, certificates, and secure notes.
Storage and access
In macOS, keychain files are stored in ~/Library/Keychains/ (and subdirectories), /Library/Keychains/, and /Network/Library/Keychains/, and the Keychain Access GUI application is located in the Utilities folder in the Applications folder. It is free, open source software released under the terms of the APSL-2.0. The command line equivalent of Keychain Access is /usr/bin/security.
The keychain database is encrypted per-table and per-row with AES-256-GCM. The time which each credential is decrypted, how long it will remain decrypted, and whether the encrypted credential will be synced to iCloud varies depending on the type of data stored, and is documented on the Apple support website.
Locking and unlocking
The default keychain file is the login keychain, typically unlocked on login by the user's login password, although the password for this keychain can instead be different from a user's login password, adding security at the expense of some convenience. The Keychain Access application does not permit setting an empty password on a keychain.
The keychain may be set to be automatically "locked" if the computer has been idle for a time, and can be locked manually from the Keychain Access application. When locked, the password has to be re-entered next time the keychain is accessed, to unlock it. Overwriting the file in ~/Library/Keychains/ with a new one (e.g. as part of a restore operation) also causes the keychain to lock and a password is required at next access.
Password synchronization
If the login keychain is protect |
https://en.wikipedia.org/wiki/NetInfo | NetInfo is the system configuration database in NeXTSTEP and Mac OS X versions up through Mac OS X v10.4 "Tiger". NetInfo replaces most of the Unix system configuration files, though they are still present for running the machine in single user mode; most Unix APIs wrap around NetInfo instead. NetInfo stores system wide network-type configuration information, such as users and groups, in binary databases; while Mac OS X machine and application specific settings are stored as plist files.
History
NetInfo was introduced in NeXTSTEP version 0.9, and replaced both the Unix system configuration files and Sun Microsystems' Network Information Service (Yellow Pages) on NeXT computers. It immediately caused controversy, much unfavorable. Not only was NetInfo unique to NeXT computers (although NeXT later licensed NetInfo to Xedoc, an Australian software company who produced NetInfo for other UNIX systems), DNS queries went through NetInfo. This led to a situation where basic tasks such as translating a UNIX UID to a user name string would not complete because NetInfo was stalled on a DNS lookup. At first, it was possible to disable NetInfo and use the Unix system files, but as of NeXTSTEP version 2 disabling NetInfo also disabled DNS support. Thus, NeXT computers became notorious for locking a user out of everyday tasks because a DNS server had stopped responding.
The Mac OS X version of NetInfo remedied this (and many other problems), but due to the early problems, NetInfo never took over the world of Unix system configuration.
Apple has moved away from using NetInfo towards LDAP, particularly in Mac OS X Server. . Mac OS X v10.4 is the last version to support Netinfo. Beginning with Mac OS X v10.5, Netinfo has been completely phased out and replaced by a new local search node named dslocal, which files are located in /var/db/dslocal/ and are standard property list (XML-based) files.
Files
The NetInfo Database is stored in , and can only be accessed by root. It ca |
https://en.wikipedia.org/wiki/Static%20universe | In cosmology, a static universe (also referred to as stationary, infinite, static infinite or static eternal) is a cosmological model in which the universe is both spatially and temporally infinite, and space is neither expanding nor contracting. Such a universe does not have so-called spatial curvature; that is to say that it is 'flat' or Euclidean. A static infinite universe was first proposed by English astronomer Thomas Digges (1546–1595).
In contrast to this model, Albert Einstein proposed a temporally infinite but spatially finite model - static eternal universe - as his preferred cosmology during 1917, in his paper Cosmological Considerations in the General Theory of Relativity.
After the discovery of the redshift-distance relationship (deduced by the inverse correlation of galactic brightness to redshift) by American astronomers Vesto Slipher and Edwin Hubble, the astrophysicist and priest Georges Lemaître interpreted the redshift as evidence of universal expansion and thus a Big Bang, whereas Swiss astronomer Fritz Zwicky proposed that the redshift was caused by the photons losing energy as they passed through the matter and/or forces in intergalactic space. Zwicky's proposal would come to be termed 'tired light'—a term invented by the major Big Bang proponent Richard Tolman.
The Einstein universe
During 1917, Albert Einstein added a positive cosmological constant to his equations of general relativity to counteract the attractive effects of gravity on ordinary matter, which would otherwise cause a static, spatially finite universe to either collapse or expand forever.
This model of the universe became known as the Einstein World or Einstein's static universe.
This motivation ended after the proposal by the astrophysicist and Roman Catholic priest Georges Lemaître that the universe seems to be not static, but expanding. Edwin Hubble had researched data from the observations made by astronomer Vesto Slipher to confirm a relationship between redshift and |
https://en.wikipedia.org/wiki/Gerald%20Sacks | Gerald Enoch Sacks (1933 – October 4, 2019) was a logician whose most important contributions were in recursion theory. Named after him is Sacks forcing, a forcing notion based on perfect sets and the Sacks Density Theorem, which asserts that the partial order of the recursively enumerable Turing degrees is dense. Sacks had a joint appointment as a professor at the Massachusetts Institute of Technology and at Harvard University starting in 1972 and became emeritus at M.I.T. in 2006 and at Harvard in 2012.
Sacks was born in Brooklyn in 1933. He earned his Ph.D. in 1961 from Cornell University under the direction of J. Barkley Rosser, with his dissertation On Suborderings of Degrees of Recursive Insolvability. Among his notable students are Lenore Blum, Harvey Friedman, Sy Friedman, Leo Harrington, Richard Shore, Steve Simpson and Theodore Slaman.
Selected publications
Degrees of unsolvability, Princeton University Press 1963, 1966
Saturated Model Theory, Benjamin 1972; 2nd edition, World Scientific 2010
Higher Recursion theory, Springer 1990
Selected Logic Papers, World Scientific 1999
Mathematical Logic in the 20th Century, World Scientific 2003 |
https://en.wikipedia.org/wiki/Mesh%20generation | Mesh generation is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells.
Often these cells form a simplicial complex.
Usually the cells partition the geometric input domain.
Mesh cells are used as discrete local approximations of the larger domain. Meshes are created by computer algorithms, often with human guidance through a GUI , depending on the complexity of the domain and the type of mesh desired.
A typical goal is to create a mesh that accurately captures the input domain geometry, with high-quality (well-shaped) cells, and without so many cells as to make subsequent calculations intractable.
The mesh should also be fine (have small elements) in areas that are important for the subsequent calculations.
Meshes are used for rendering to a computer screen and for physical simulation such as finite element analysis or computational fluid dynamics. Meshes are composed of simple cells like triangles because, e.g., we know how to perform operations such as finite element calculations (engineering) or ray tracing (computer graphics) on triangles, but we do not know how to perform these operations directly on complicated spaces and shapes such as a roadway bridge. We can simulate the strength of the bridge, or draw it on a computer screen, by performing calculations on each triangle and calculating the interactions between triangles.
A major distinction is between structured and unstructured meshing. In structured meshing the mesh is a regular lattice, such as an array, with implied connectivity between elements. In unstructured meshing, elements may be connected to each other in irregular patterns, and more complicated domains can be captured. This page is primarily about unstructured meshes.
While a mesh may be a triangulation, the process of meshing is distinguished from point set triangulation in that meshing includes the freedom to add vertices not present in the input. "Facetting" (triangul |
https://en.wikipedia.org/wiki/Model%20yachting | Model yachting is the pastime of building and racing model yachts. It has always been customary for ship-builders to make a miniature model of the vessel under construction, which is in every respect a copy of the original on a small scale, whether steamship or sailing ship. There are fine collections to be seen at both general interest museums such as the Victoria and Albert Museum in London and at many specialized maritime museums worldwide. Many of these models are of exquisite workmanship, every rope, pulley or portion of the engine being faithfully reproduced. In the case of sailing yachts, these models were often pitted against each other on small bodies of water, and hence arose the modern pastime. It was soon seen that elaborate fittings and complicated rigging were a detriment to rapid handling, and that, on account of the comparatively stronger winds in which models were sailed, they needed a greater draught. For these reasons modern model yachts, which usually have fin keels, are of about 15% or 20% deeper draught than full-sized vessels, while rigging and fittings have been reduced to absolute simplicity. This applies to models built for racing and not to elaborate copies of steamers and ships, made only for show or for " toy cruising."
Model yacht clubs
Model yacht clubs have existed for many years in Great Britain, Ireland and the United States, most of them holding a number of regattas during each season. The rules do not generally require the owner or skipper of a model to build his own craft, but among model yachtsmen the designing and the construction of the boats constitute as important and interesting a part of the sport as the actual sailing.
Sail–driven yachts
Construction and rigging
Traditional models are constructed of some light, seasoned wood, such as pine, preferably white pine, white cedar or mahogany free from knots. The hull may either be hollowed out of a solid block of wood, or cut from layers of planks in the so-called bread-and- |
https://en.wikipedia.org/wiki/Fredholm%20alternative | In mathematics, the Fredholm alternative, named after Ivar Fredholm, is one of Fredholm's theorems and is a result in Fredholm theory. It may be expressed in several ways, as a theorem of linear algebra, a theorem of integral equations, or as a theorem on Fredholm operators. Part of the result states that a non-zero complex number in the spectrum of a compact operator is an eigenvalue.
Linear algebra
If V is an n-dimensional vector space and is a linear transformation, then exactly one of the following holds:
For each vector v in V there is a vector u in V so that . In other words: T is surjective (and so also bijective, since V is finite-dimensional).
A more elementary formulation, in terms of matrices, is as follows. Given an m×n matrix A and a m×1 column vector b, exactly one of the following must hold:
Either: A x = b has a solution x
Or: AT y = 0 has a solution y with yTb ≠ 0.
In other words, A x = b has a solution if and only if for any y such that AT y = 0, it follows that yTb = 0 .
Integral equations
Let be an integral kernel, and consider the homogeneous equation, the Fredholm integral equation,
and the inhomogeneous equation
The Fredholm alternative is the statement that, for every non-zero fixed complex number , either the first equation has a non-trivial solution, or the second equation has a solution for all .
A sufficient condition for this statement to be true is for to be square integrable on the rectangle (where a and/or b may be minus or plus infinity). The integral operator defined by such a K is called a Hilbert–Schmidt integral operator.
Functional analysis
Results about Fredholm operators generalize these results to complete normed vector spaces of infinite dimensions; that is, Banach spaces.
The integral equation can be reformulated in terms of operator notation as follows. Write (somewhat informally)
to mean
with the Dirac delta function, considered as a distribution, or generalized function, in two variables.
Then by |
https://en.wikipedia.org/wiki/Runaway%20breakdown | Runaway breakdown is a theory of lightning initiation proposed by Alex Gurevich in 1992.
Electrons in air have a mean free path of ~1 cm. Fast electrons which move at a large fraction of the speed of light have a mean free path up to 100 times longer. Given the long free paths, an electric field can accelerate these electrons to energies far higher than that of initially static electrons. If they strike air molecules, more relativistic electrons will be released, creating an avalanche multiplication of "runaway" electrons. This process, relativistic runaway electron avalanche, has been hypothesized to lead to electrical breakdown in thunderstorms, but only when a source of high-energy electrons from a cosmic ray is present to start the "runaway" process.
The resulting conductive plasma trail, many tens of meters long, is suggested to supply the "seed" which triggers a lightning flash.
See also
List of plasma (physics) articles
Spark gap
Avalanche breakdown
Electron avalanche |
https://en.wikipedia.org/wiki/Homography | In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive. It is a bijection that maps lines to lines, and thus a collineation. In general, some collineations are not homographies, but the fundamental theorem of projective geometry asserts that is not so in the case of real projective spaces of dimension at least two. Synonyms include projectivity, projective transformation, and projective collineation.
Historically, homographies (and projective spaces) have been introduced to study perspective and projections in Euclidean geometry, and the term homography, which, etymologically, roughly means "similar drawing", dates from this time. At the end of the 19th century, formal definitions of projective spaces were introduced, which differed from extending Euclidean or affine spaces by adding points at infinity. The term "projective transformation" originated in these abstract constructions. These constructions divide into two classes that have been shown to be equivalent. A projective space may be constructed as the set of the lines of a vector space over a given field (the above definition is based on this version); this construction facilitates the definition of projective coordinates and allows using the tools of linear algebra for the study of homographies. The alternative approach consists in defining the projective space through a set of axioms, which do not involve explicitly any field (incidence geometry, see also synthetic geometry); in this context, collineations are easier to define than homographies, and homographies are defined as specific collineations, thus called "projective collineations".
For sake of simplicity, unless otherwise stated, the projective spaces considered in this article are supposed to be defined over a (commutative) field. Equivalently Pappus's hexagon theorem and Desargues's theorem are supposed to be true. A large part of the res |
https://en.wikipedia.org/wiki/Pale%20%28heraldry%29 | A pale is a term used in heraldic blazon and vexillology to describe a charge on a coat of arms (or flag), that takes the form of a band running vertically down the centre of the shield. Writers broadly agree that the width of the pale ranges from about one-fifth to about one-third of the width of the shield, but this width is not fixed. A narrow pale is more likely if it is uncharged, that is, if it does not have other objects placed on it. If charged, the pale is typically wider to allow room for the objects drawn there.
The pale is one of the ordinaries in heraldry, along with the bend, chevron, fess, and chief. There are several other ordinaries and sub-ordinaries.
The word pale originally referred to a picket (a piece of wood much taller than it is wide such as is used to build a picket fence) and it is from the resemblance to this that the heraldic pale derives its name.
Derived terms
pallet
In British heraldry when two or more pales appear on a field, they are conventionally termed pallets. While a pallet is generally classified as a diminutive of the pale, the pallets on a shield of two pallets may be no narrower than the pale on another where it has been narrowed to accommodate other charges on either side.
paly
A shield with numerous pales may be termed paly, especially in early heraldry, though this term is now properly reserved to describe a variation of the field.
in pale
In pale refers to the appearance of several items on the shield being lined up in the direction of a pale.
palewise
A charge palewise is vertical like a pale.
party per pale
A shield party per pale is divided into two parts by a single line which runs in the direction of a pale.
Special cases
A pale may be couped ("cut off" at either end, and so not reaching the top or bottom of the shield); however, while other charges if couped at the top would just be blazoned as "couped in chief," the special term for this in the case of the pale is "a pale retrait" (this also applies to pa |
https://en.wikipedia.org/wiki/Polyspermy | In biology, polyspermy describes the fertilization of an egg by more than one sperm. Diploid organisms normally contain two copies of each chromosome, one from each parent. The cell resulting from polyspermy, on the other hand, contains three or more copies of each chromosome—one from the egg and one each from multiple sperm. Usually, the result is an unviable zygote. This may occur because sperm are too efficient at reaching and fertilizing eggs due to the selective pressures of sperm competition. Such a situation is often deleterious to the female: in other words, the male–male competition among sperm spills over to create sexual conflict.
Physiological polyspermy
Physiological polyspermy happens when the egg normally accepts more than one sperm but only one of the multiple sperm will fuse its nucleus with the nucleus of the egg. Physiological polyspermy is present in some species of vertebrates and invertebrates. Some species utilize physiological polyspermy as the proper mechanism for developing their offspring. Some of these animals include birds, ctenophora, reptiles and amphibians. Some vertebrates that are both amniote or anamniote, including urodele amphibians, cartilaginous fish, birds and reptiles, undergo physiological polyspermy because of the internal fertilization of their yolky eggs. Sperm triggers egg activation by the induction of free calcium ion concentration in the cytoplasm of the egg. This induction plays a very critical role in both physiological polyspermy and monomeric polyspermy species. The rise in calcium causes activation of the egg. The egg will then be altered on both a biochemical and morphological level. In mammals as well as sea urchins, the sudden rise in calcium concentration occurs because of the influx of calcium ions within the egg. These calcium ions are responsible for the cortical granule reaction, and are also stored in the egg's endoplasmic reticulum.
Unlike physiological polyspermy, monospermic fertilization deals wit |
https://en.wikipedia.org/wiki/Ocular%20myasthenia | Ocular myasthenia gravis (MG) is a disease of the neuromuscular junction resulting in hallmark variability in muscle weakness and fatigability. MG is an autoimmune disease where anomalous antibodies are produced against the naturally occurring acetylcholine receptors in voluntary muscles. MG may be limited to the muscles of the eye (ocular MG), leading to abrupt onset of weakness/fatigability of the eyelids or eye movement. MG may also involve other muscle groups (generalized MG).
Signs and symptoms
Although these blocking antibodies may be confined to one of the larger muscles responsible for moving the face or appendages or for breathing, about 90% of MG patients eventually have eye involvement. The most common symptoms are double vision (diplopia) and eyelid drooping (ptosis), whereas the pupil is always spared. Diplopia occurs when MG affects a single extraocular muscle in one eye, limiting eye movement and leading to double vision when the eye is turned toward the affected muscle. Ptosis occurs when the levator palpebrae superioris (the muscle responsible for eyelid elevation) is affected on one or both sides, leading to eyelid drooping. Although these symptoms may not be readily apparent in well-rested patients, weakness can usually be induced with exercise of the commonly affected muscles (e.g. by having the patient look upward for about 60 seconds).
In 75% of MG cases, the initial manifestation is in the eye. Within 2 years, 80% of patients with ocular onset of MG will progress to involve other muscle groups, thereby developing generalized MG. If MG is confined to the ocular muscles for more than 3 years, there is a 94% likelihood that the symptoms will not worsen or generalize.
Aside from asymmetric ptosis (which becomes worse with fatigue, sustained upgaze, and at the end of the day) and variable limitation of extraocular muscles/diplopia, other clinical signs of ocular MG include gaze-evoked nystagmus (rapid, involuntary, oscillatory motion of the eye |
https://en.wikipedia.org/wiki/Glan%E2%80%93Thompson%20prism | A Glan–Thompson prism is a type of polarizing prism similar to the Nicol prism and Glan–Foucault prism.
Design
A Glan–Thompson prism consists of two right-angled calcite prisms that are cemented together by their long faces. The optical axes of the calcite crystals are parallel and aligned perpendicular to the plane of reflection. Birefringence splits light entering the prism into two rays, experiencing different refractive indices; the p-polarized ordinary ray is totally internally reflected from the calcite–cement interface, leaving the s-polarized extraordinary ray to be transmitted. The prism can therefore be used as a polarizing beam splitter.
Traditionally Canada balsam was used as the cement in assembling these prisms, but this has largely been replaced by synthetic polymers.
Characteristics
Compared to the similar Glan–Foucault prism, the Glan–Thompson has a wider acceptance angle, but a much lower limit of maximal irradiance (due to optical damage limitations of the cement layer).
See also
Glan–Taylor prism |
https://en.wikipedia.org/wiki/Glan%E2%80%93Foucault%20prism | A Glan–Foucault prism (also called a Glan–air prism) is a type of prism which is used as a polarizer. It is similar in construction to a Glan–Thompson prism, except that two right-angled calcite prisms are spaced with an air gap instead of being cemented together. Total internal reflection of p-polarized light at the air gap means that only s-polarized light is transmitted straight through the prism.
Design
Compared to the Glan–Thompson prism, the Glan–Foucault has a narrower acceptance angle over which it works, but because it uses an air gap rather than cement, much higher irradiances can be used without damage. The prism can thus be used with laser beams. The prism is also shorter (for a given usable aperture) than the Glan–Thompson design, and the deflection angle of the rejected beam can be made close to 90°, which is sometimes useful. Glan–Foucault prisms are not typically used as polarizing beamsplitters because while the transmitted beam is completely polarized, the reflected beam is not.
Polarization
The Glan–Taylor prism is similar, except that the crystal axes and transmitted polarization direction are orthogonal to the Glan–Foucault design. This yields higher transmission and better polarization of the reflected light. Calcite Glan–Foucault prisms are now rarely used, having been mostly replaced by Glan–Taylor polarizers and other more recent designs.
Yttrium orthovanadate (YVO4) prisms based on the Glan–Foucault design have superior polarization of the reflected beam and higher damage threshold, compared with calcite Glan–Foucault and Glan–Taylor prisms. YVO4 prisms are more expensive, however, and can accept beams over a very limited range of angles of incidence. |
https://en.wikipedia.org/wiki/Bateman%20Manuscript%20Project | The Bateman Manuscript Project was a major effort at collation and encyclopedic compilation of the mathematical theory of special functions. It resulted in the eventual publication of five important reference volumes, under the editorship of Arthur Erdélyi.
Overview
The theory of special functions was a core activity of the field of applied mathematics, from the middle of the nineteenth century to the advent of high-speed electronic computing. The intricate properties of spherical harmonics, elliptic functions and other staples of problem-solving in mathematical physics, astronomy and right across the physical sciences, are not easy to document completely, absent a theory explaining the inter-relationships. Mathematical tables to perform actual calculations needed to mesh with an adequate theory of how functions could be transformed into those already tabulated.
Harry Bateman, a distinguished applied mathematician, undertook the somewhat quixotic task of trying to collate the content of the very large literature. On his death in 1946, his papers on this project were still in a uniformly rough state. The publication of the edited version provided special functions texts more up-to-date than, for example, the classic Whittaker & Watson.
The volumes were out of print for many years, and copyright in the works reverted to the California Institute of Technology, who renewed them in the early 1980s. Dover planned to reprint them for publication in 2007, but this never occurred . In 2011, the California Institute of Technology gave permission for scans of the volumes to be made publicly available.
Other mathematicians involved in the project include Wilhelm Magnus, Fritz Oberhettinger and Francesco Tricomi.
Askey–Bateman project
In 2007, the Askey–Bateman project was announced by Mourad Ismail as a five- or six-volume encyclopedic book series on special functions, based on the works of Harry Bateman and Richard Askey.
Starting in 2020, Cambridge University Press bega |
https://en.wikipedia.org/wiki/Crystal%20growth | A crystal is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. Crystal growth is a major stage of a crystallization process, and consists of the addition of new atoms, ions, or polymer strings into the characteristic arrangement of the crystalline lattice. The growth typically follows an initial stage of either homogeneous or heterogeneous (surface catalyzed) nucleation, unless a "seed" crystal, purposely added to start the growth, was already present.
The action of crystal growth yields a crystalline solid whose atoms or molecules are close packed, with fixed positions in space relative to each other.
The crystalline state of matter is characterized by a distinct structural rigidity and very high resistance to deformation (i.e. changes of shape and/or volume). Most crystalline solids have high values both of Young's modulus and of the shear modulus of elasticity. This contrasts with most liquids or fluids, which have a low shear modulus, and typically exhibit the capacity for macroscopic viscous flow.
Overview
After successful formation of a stable nucleus, a growth stage ensues in which free particles (atoms or molecules) adsorb onto the nucleus and propagate its crystalline structure outwards from the nucleating site. This process is significantly faster than nucleation. The reason for such rapid growth is that real crystals contain dislocations and other defects, which act as a catalyst for the addition of particles to the existing crystalline structure. By contrast, perfect crystals (lacking defects) would grow exceedingly slowly. On the other hand, impurities can act as crystal growth inhibitors and can also modify crystal habit.
Nucleation
Nucleation can be either homogeneous, without the influence of foreign particles, or heterogeneous, with the influence of foreign particles. Generally, heterogeneous nucleation takes place more quickly since the foreign pa |
https://en.wikipedia.org/wiki/Sensitization | Sensitization is a non-associative learning process in which repeated administration of a stimulus results in the progressive amplification of a response. Sensitization often is characterized by an enhancement of response to a whole class of stimuli in addition to the one that is repeated. For example, repetition of a painful stimulus may make one more responsive to a loud noise.
History
Eric Kandel was one of the first to study the neural basis of sensitization, conducting experiments in the 1960s and 1970s on the gill withdrawal reflex of the seaslug Aplysia. Kandel and his colleagues first habituated the reflex, weakening the response by repeatedly touching the animal's siphon. They then paired noxious electrical stimulus to the tail with a touch to the siphon, causing the gill withdrawal response to reappear. After this sensitization, a light touch to the siphon alone produced a strong gill withdrawal response, and this sensitization effect lasted for several days. (After Squire and Kandel, 1999). In 2000, Eric Kandel was awarded the Nobel Prize in Physiology or Medicine for his research in neuronal learning processes.
Neural substrates
The neural basis of behavioral sensitization is often not known, but it typically seems to result from a cellular receptor becoming more likely to respond to a stimulus. Several examples of neural sensitization include:
Electrical or chemical stimulation of the rat hippocampus causes strengthening of synaptic signals, a process known as long-term potentiation or LTP. LTP of AMPA receptors is a potential mechanism underlying memory and learning in the brain.
In "kindling", repeated stimulation of hippocampal or amygdaloid neurons in the limbic system eventually leads to seizures in laboratory animals. After sensitization, very little stimulation may be required to produce seizures. Thus, kindling has been suggested as a model for temporal lobe epilepsy in humans, where stimulation of a repetitive type (flickering lights for i |
https://en.wikipedia.org/wiki/Spesmilo | The spesmilo (, plural spesmiloj ) is an obsolete decimal international currency, proposed in 1907 by René de Saussure and used before World War I by a few British and Swiss banks, primarily the Ĉekbanko Esperantista.
The spesmilo was equivalent to one thousand spesoj, and worth of pure gold (0.8 grams of 22 karat gold), which at the time was about one-half United States dollar, two shillings (one-tenth of a pound sterling) in Britain, one Russian ruble, or Swiss francs. On 6 November 2022, that quantity of gold would be worth about US$43.50, £38 sterling, €44, ₽2692 Russian roubles, and SFr 43 Swiss francs.
The basic unit, the speso (from Italian spesa or German Spesen; spesmilo is Esperanto for "a thousand pennies"), was purposely made very small to avoid fractions.
Sign
The spesmilo sign, called spesmilsigno in Esperanto, is a monogram of a cursive capital "S", from whose tail emerges an "m". The currency sign is often typeset as the separate letters Sm.
In Unicode, the character is assigned in version 5.2.
Miscellaneous
The stelo was another currency unit used by the Universala Ligo from 1942 to the 1990s.
An Esperanto version of the board game Monopoly uses play money in denominations of spesmiloj. |
https://en.wikipedia.org/wiki/Kasanka%20National%20Park | Kasanka National Park is a park located in the Chitambo District of Zambia’s Central Province. At roughly , Kasanka is one of Zambia’s smallest national parks. Kasanka was the first of Zambia’s national parks to be managed by a private-public partnership. The privately funded Kasanka Trust Ltd has been in operation since 1986 and undertakes all management responsibilities, in partnership with the Department of National Parks and Wildlife (DNPW - previously ZAWA). The park has an average elevation between and above mean sea level. It has a number permanent shallow lakes and water bodies with the largest being Wasa. There are five perennial rivers in the park, with the largest being the Luwombwa River. The Luwombwa is the only river that drains the NP, which flows out in the northwestern corner. It is a tributary of the Luapula, which further upstream also drains the Bangweulu Swamp and forms the main source of the Congo River. Although Kasanka NP is part of the Greater Bangweulu Ecosystem, there is no direct hydrological connection between the park and the Bangweulu Wetlands.
A total of 114 mammal species have been recorded in the park including elephant, hippopotamus and sitatunga. A number of species have been reintroduced in the park by Kasanka Trust - the most successful of which are zebra and buffalo. Close to ten million Eidolon helvum (African straw-coloured fruit bat) migrate to the Mushitu swamp evergreen forest in the park for three months during October to December, making it the largest mammal migration in the world. Over 471 bird species have been identified in the park. An airfield lies there.
Topography and vegetation
Kasanka has a varying altitude of and above mean sea level. The park is located in the Zambia in Serenje District of Zambia. While most sources quote the area of the park to be around , others record the area close to , making it one of the smaller national parks in the country. It has a relatively flat topography with few notewo |
https://en.wikipedia.org/wiki/Apodization | In signal processing, apodization (from Greek "removing the foot") is the modification of the shape of a mathematical function. The function may represent an electrical signal, an optical transmission, or a mechanical structure. In optics, it is primarily used to remove Airy disks caused by diffraction around an intensity peak, improving the focus.
Apodization in electronics
Apodization in signal processing
The term apodization is used frequently in publications on Fourier-transform infrared (FTIR) signal processing. An example of apodization is the use of the Hann window in the fast Fourier transform analyzer to smooth the discontinuities at the beginning and end of the sampled time record.
Apodization in digital audio
An apodizing filter can be used in digital audio processing instead of the more common brick-wall filters, in order to reduce the pre- and post-ringing that the latter introduces.
Apodization in mass spectrometry
During oscillation within an Orbitrap, ion transient signal may not be stable until the ions settle into their oscillations. Toward the end, subtle ion collisions have added up to cause noticeable dephasing. This presents a problem for the Fourier transformation, as it averages the oscillatory signal across the length of the time-domain measurement. The software allows “apodization”, the removal of the front and back section of the transient signal from consideration in the FT calculation. Thus, apodization improves the resolution of the resulting mass spectrum. Another way to improve the quality of the transient is to wait to collect data until ions have settled into stable oscillatory motion within the trap.
Apodization in nuclear magnetic resonance spectroscopy
Apodization is applied to NMR signals before discrete Fourier Transformation. Typically, NMR signals are truncated due to time constraints (indirect dimension) or to obtain a higher signal-to-noise ratio. In order to reduce truncation artifacts, the signals are subjected |
https://en.wikipedia.org/wiki/Fina%27denne%27 | Fina'denne' (many alternate spellings, commonly finadene, fina'denni', or fina'dene) is a spicy, all-purpose condiment that is a staple of Chamorro cuisine. In the Chamorro language, it translates as "made with chili pepper." It may be drizzled over meat dish or rice, or placed in a separate, small dipping saucer. Anthropologists visiting Guam in the early 20th century noted the frequent use of fina'denne' by Chamorros.
History
There are many historical and contemporary versions of fina'denne'. The earliest fina'denne', predating Spanish colonization in the late seventeenth century, was simply salt and pepper. Filipino immigrants during the Spanish period introduced the technique of tapping coconut trees and fermenting the sap to make tubâ vinegar. The fina'denne' of this time was made with tubâ, salt, lemon, water, and fresh pepper. The Japanese subsequently introduced soy sauce to the Mariana Islands, resulting in the typical contemporary version of fina'denne' with soy sauce, lemon juice, onion, and fresh bird's eye chili, known locally as "boonie peppers." The acidic ingredient may also be white vinegar, cider vinegar, coconut vinegar, or lime.
Other versions that are still made are binakle fina'denne' made with tubâ; chigu'an fina'denne', made with fish brine and resembling fish sauces of Southeast Asia; and a common fina'denne' made entirely with lemon and no soy sauce. Soy sauce-based fina'denne' typically accompanies red meat, pork, and chicken dishes. Lemon-based fina'denne' is typically used for fish and more delicately flavoured dishes.
See also
List of dips
List of sauces
Cuisine of the Mariana Islands |
https://en.wikipedia.org/wiki/Three-dimensional%20space | In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point. Most commonly, it is the three-dimensional Euclidean space, the Euclidean n-space of dimension n=3 that models physical space. More general three-dimensional spaces are called 3-manifolds.
The term may also refer colloquially to a subset of space, a three-dimensional region (or 3D domain), a solid figure.
Technically, a tuple of numbers can be understood as the Cartesian coordinates of a location in a -dimensional Euclidean space. The set of these -tuples is commonly denoted and can be identified to the pair formed by a -dimensional Euclidean space and a Cartesian coordinate system.
When , this space is called the three-dimensional Euclidean space (or simply "Euclidean space" when the context is clear). It serves as a model of the physical universe (when relativity theory is not considered), in which all known matter exists. While this space remains the most compelling and useful way to model the world as it is experienced, it is only one example of a large variety of spaces in three dimensions called 3-manifolds. In this classical example, when the three values refer to measurements in different directions (coordinates), any three directions can be chosen, provided that vectors in these directions do not all lie in the same 2-space (plane). Furthermore, in this case, these three values can be labeled by any combination of three chosen from the terms width/breadth, height/depth, and length.
History
Books XI to XIII of Euclid's Elements dealt with three-dimensional geometry. Book XI develops notions of orthogonality and parallelism of lines and planes, and defines solids including parallelpipeds, pyramids, prisms, spheres, octahedra, icosahedra and dodecahedra. Book XII develops notions of similarity of solids. Book XIII describes the construction of the five re |
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