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Sodium- and chloride-dependent glycine transporter 1-Selective inhibitors-Elevation of extracellular synaptic glycine concentration by blockade of GlyT1 has been hypothesized to potentiate NMDA receptor function in vivo and to represent a rational approach for the treatment of schizophrenia and cognitive disorders. Sev... | milkshake721/2.1M-wiki-STEM |
Dynamical Theory of Crystal Lattices-Dynamical Theory of Crystal Lattices-Dynamical Theory of Crystal Lattices is a book in solid state physics, authored collaboratively by Max Born and Kun Huang. The book was originally started by Born in c. 1940, and was finished in the 1950s by Huang in consultation with Born. The t... | milkshake721/2.1M-wiki-STEM |
Warm inflation-Warm inflation-In physical cosmology, warm inflation is one of two dynamical realizations of cosmological inflation. The other is the standard scenario, sometimes called cold inflation.In warm inflation radiation production occurs concurrently with inflationary expansion. This is consistent with the cond... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Kepler conjecture-The Kepler conjecture, named after the 17th-century mathematician and astronomer Johannes Kepler, is a mathematical theorem about sphere packing in three-dimensional Euclidean space. It states that no arrangement of equally sized spheres filling space has a greater average density th... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Kepler conjecture-In 1998, Thomas Hales, following an approach suggested by Fejes Tóth (1953), announced that he had a proof of the Kepler conjecture. Hales' proof is a proof by exhaustion involving the checking of many individual cases using complex computer calculations. Referees said that they were... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Background-Imagine filling a large container with small equal-sized spheres: Say a porcelain gallon jug with identical marbles. The "density" of the arrangement is equal to the total volume of all the marbles, divided by the volume of the jug. To maximize the number of marbles in the jug means to crea... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Background-Experiment shows that dropping the marbles in randomly, with no effort to arrange them tightly, will achieve a density of around 65%. However, a higher density can be achieved by carefully arranging the marbles as follows: For the first layer of marbles, arrange them in a hexagonal lattice ... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Origins-The conjecture was first stated by Johannes Kepler (1611) in his paper 'On the six-cornered snowflake'. He had started to study arrangements of spheres as a result of his correspondence with the English mathematician and astronomer Thomas Harriot in 1606. Harriot was a friend and assistant of ... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Nineteenth century-Kepler did not have a proof of the conjecture, and the next step was taken by Carl Friedrich Gauss (1831), who proved that the Kepler conjecture is true if the spheres have to be arranged in a regular lattice. | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Nineteenth century-This meant that any packing arrangement that disproved the Kepler conjecture would have to be an irregular one. But eliminating all possible irregular arrangements is very difficult, and this is what made the Kepler conjecture so hard to prove. In fact, there are irregular arrangeme... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Nineteenth century-After Gauss, no further progress was made towards proving the Kepler conjecture in the nineteenth century. In 1900 David Hilbert included it in his list of twenty three unsolved problems of mathematics—it forms part of Hilbert's eighteenth problem. | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Twentieth century-The next step toward a solution was taken by László Fejes Tóth. Fejes Tóth (1953) showed that the problem of determining the maximum density of all arrangements (regular and irregular) could be reduced to a finite (but very large) number of calculations. This meant that a proof by ex... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Twentieth century-Meanwhile, attempts were made to find an upper bound for the maximum density of any possible arrangement of spheres. English mathematician Claude Ambrose Rogers (see Rogers (1958)) established an upper bound value of about 78%, and subsequent efforts by other mathematicians reduced t... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Twentieth century-In 1990, Wu-Yi Hsiang claimed to have proven the Kepler conjecture. The proof was praised by Encyclopædia Britannica and Science and Hsiang was also honored at joint meetings of AMS-MAA. Wu-Yi Hsiang (1993, 2001) claimed to prove the Kepler conjecture using geometric methods. However... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Hales' proof-Following the approach suggested by Fejes Tóth (1953), Thomas Hales, then at the University of Michigan, determined that the maximum density of all arrangements could be found by minimizing a function with 150 variables. In 1992, assisted by his graduate student Samuel Ferguson, he embark... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Hales' proof-When presenting the progress of his project in 1996, Hales said that the end was in sight, but it might take "a year or two" to complete. In August 1998 Hales announced that the proof was complete. At that stage, it consisted of 250 pages of notes and 3 gigabytes of computer programs, dat... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Hales' proof-Despite the unusual nature of the proof, the editors of the Annals of Mathematics agreed to publish it, provided it was accepted by a panel of twelve referees. In 2003, after four years of work, the head of the referee's panel, Gábor Fejes Tóth, reported that the panel were "99% certain" ... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Hales' proof-Hales (2005) published a 100-page paper describing the non-computer part of his proof in detail.
Hales & Ferguson (2006) and several subsequent papers described the computational portions. Hales and Ferguson received the Fulkerson Prize for outstanding papers in the area of discrete mathe... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Hales' proof-A formal proof In January 2003, Hales announced the start of a collaborative project to produce a complete formal proof of the Kepler conjecture. The aim was to remove any remaining uncertainty about the validity of the proof by creating a formal proof that can be verified by automated pr... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Related problems-Thue's theorem The regular hexagonal packing is the densest circle packing in the plane (1890). The density is π⁄√12.
The 2-dimensional analog of the Kepler conjecture; the proof is elementary. Henk and Ziegler attribute this result to Lagrange, in 1773 (see references, pag. 770).
A s... | milkshake721/2.1M-wiki-STEM |
Kepler conjecture-Related problems-A related problem, whose proof uses similar techniques to Hales' proof of the Kepler conjecture. Conjecture by L. Fejes Tóth in the 1950s.The Kelvin problem What is the most efficient foam in 3 dimensions? This was conjectured to be solved by the Kelvin structure, and this was widely ... | milkshake721/2.1M-wiki-STEM |
Learning disability-Learning disability-Learning disability, learning disorder, or learning difficulty (British English) is a condition in the brain that causes difficulties comprehending or processing information and can be caused by several different factors. Given the "difficulty learning in a typical manner", this ... | milkshake721/2.1M-wiki-STEM |
Learning disability-Learning disability-Individuals with learning disabilities can face unique challenges that are often pervasive throughout the lifespan. Depending on the type and severity of the disability, interventions, and current technologies may be used to help the individual learn strategies that will foster f... | milkshake721/2.1M-wiki-STEM |
Learning disability-Definition-Representatives of organizations committed to the education and welfare of individuals with learning disabilities are known as National Joint Committee on Learning Disabilities (NJCLD). The NJCLD used the term 'learning disability' to indicate a discrepancy between a child's apparent capa... | milkshake721/2.1M-wiki-STEM |
Learning disability-Definition-In the 1980s, NJCLD, therefore, defined the term learning disability as: a heterogeneous group of disorders manifested by significant difficulties in the acquisition and use of listening, speaking, reading, writing, reasoning or mathematical abilities. These disorders are intrinsic to the... | milkshake721/2.1M-wiki-STEM |
Learning disability-Definition-The 2002 LD Roundtable produced the following definition:Concept of LD: Strong converging evidence supports the validity of the concept of specific learning disabilities (SLD). This evidence is particularly impressive because it converges across different indicators and methodologies. The... | milkshake721/2.1M-wiki-STEM |
Learning disability-Definition-United States and Canada In the United States and Canada, the terms learning disability and learning disorder (LD) refer to a group of disorders that affect a broad range of academic and functional skills including the ability to speak, listen, read, write, spell, reason, organize informa... | milkshake721/2.1M-wiki-STEM |
Learning disability-Definition-Legislation in the United States The Section 504 of the Rehabilitation Act 1973, effective May 1977, guarantees certain rights to people with disabilities, especially in the cases of education and work, such being in schools, colleges and university settings.The Individuals with Disabilit... | milkshake721/2.1M-wiki-STEM |
Learning disability-Definition-Canada In Canada, the first association in support of children with learning disabilities was founded in 1962 by a group of concerned parents. Originally called the Association for Children with Learning Disabilities, the Learning Disabilities Association of Canada – LDAC was created to p... | milkshake721/2.1M-wiki-STEM |
Learning disability-Definition-United Kingdom In the UK, terms such as specific learning difficulty (SpLD), developmental dyslexia, developmental coordination disorder and dyscalculia are used to cover the range of learning difficulties referred to in the United States as "learning disabilities". In the UK, the term "l... | milkshake721/2.1M-wiki-STEM |
Learning disability-Definition-Japan In Japan, acknowledgement and support for students with learning disabilities has been a fairly recent development, and has improved drastically since the start of the 21st Century. The first definition for learning disability was coined in 1999, and in 2001, the Enrichment Project ... | milkshake721/2.1M-wiki-STEM |
Learning disability-Effects-The effects of having a learning disability or learning difference are not limited to educational outcomes: individuals with learning disabilities may experience social problems as well. Neuropsychological differences can affect the accurate perception of social cues with peers. Researchers ... | milkshake721/2.1M-wiki-STEM |
Learning disability-Causes-The causes for learning disabilities are not well understood, and sometimes there is no apparent cause for a learning disability. However, some causes of neurological impairments include: Heredity and genetics: Learning disabilities are often linked through genetics and run in the family. Chi... | milkshake721/2.1M-wiki-STEM |
Learning disability-Causes-Problems during pregnancy and birth: A learning disability can result from anomalies in the developing brain, illness or injury. Risk factors are fetal exposure to alcohol or drugs and low birth weight (3 pounds or less). These children are more likely to develop a disability in math or readi... | milkshake721/2.1M-wiki-STEM |
Learning disability-Causes-Accidents after birth: Learning disabilities can also be caused by head injuries, malnutrition, or by toxic exposure (such as heavy metals or pesticides). | milkshake721/2.1M-wiki-STEM |
Learning disability-Diagnosis-IQ-achievement discrepancy Learning disabilities can be identified by psychiatrists, speech language pathologists, school psychologists, clinical psychologists, counseling psychologists, neuropsychologists, speech language pathologists, and other learning disability specialists through a c... | milkshake721/2.1M-wiki-STEM |
Learning disability-Diagnosis-Although the discrepancy model has dominated the school system for many years, there has been substantial criticism of this approach among researchers. Recent research has provided little evidence that a discrepancy between formally measured IQ and achievement is a clear indicator of LD. F... | milkshake721/2.1M-wiki-STEM |
Learning disability-Diagnosis-Since 1998 there have been attempts to create a reference index more useful than IQ to generate predicted scores on achievement tests. For example, for a student whose vocabulary and general knowledge scores matches their reading comprehension score a teacher could assume that reading comp... | milkshake721/2.1M-wiki-STEM |
Learning disability-Diagnosis-A primary benefit of such a model is that it would not be necessary to wait for a child to be sufficiently far behind to qualify for assistance. This may enable more children to receive assistance before experiencing significant failure, which may, in turn, result in fewer children who nee... | milkshake721/2.1M-wiki-STEM |
Learning disability-Diagnosis-The process does not take into account children's individual neuropsychological factors such as phonological awareness and memory, that can inform design instruction. By not taking into account specific cognitive processes, RTI fails to inform educators about a students' relative strengths... | milkshake721/2.1M-wiki-STEM |
Learning disability-Diagnosis-Latino English language learners Demographers in the United States report that there has been a significant increase in immigrant children in the United States over the past two decades. This information is vital because it has been and will continue to affect both students and how educato... | milkshake721/2.1M-wiki-STEM |
Learning disability-Diagnosis-Spanish-speaking ELL A well trained bilingual school psychologist will be able to administer and interpret assessment all psychological testing tool. Also, an emphasis is placed on informal assessment measures such as language samples, observations, interviews, and rating scales as well as... | milkshake721/2.1M-wiki-STEM |
Learning disability-Diagnosis-Assessment Many normed assessments can be used in evaluating skills in the primary academic domains: reading, including word recognition, fluency, and comprehension; mathematics, including computation and problem solving; and written expression, including handwriting, spelling and composit... | milkshake721/2.1M-wiki-STEM |
Learning disability-Diagnosis-The most commonly used comprehensive achievement tests include the Woodcock-Johnson IV (WJ IV), Wechsler Individual Achievement Test II (WIAT II), the Wide Range Achievement Test III (WRAT III), and the Stanford Achievement Test–10th edition. These tests include measures of many academic d... | milkshake721/2.1M-wiki-STEM |
Learning disability-Diagnosis-However, caution should be made when suspecting the person with a learning disability may also have dementia, especially as people with Down's syndrome may have the neuroanatomical profile but not the associated clinical signs and symptoms. Examination can be carried out of executive funct... | milkshake721/2.1M-wiki-STEM |
Learning disability-Types-Learning disabilities can be categorized by either the type of information processing affected by the disability or by the specific difficulties caused by a processing deficit.
By stage of information processing Learning disabilities fall into broad categories based on the four stages of infor... | milkshake721/2.1M-wiki-STEM |
Learning disability-Types-Input: This is the information perceived through the senses, such as visual and auditory perception. Difficulties with visual perception can cause problems with recognizing the shape, position, or size of items seen. There can be problems with sequencing, which can relate to deficits with proc... | milkshake721/2.1M-wiki-STEM |
Learning disability-Types-Integration: This is the stage during which perceived input is interpreted, categorized, placed in a sequence, or related to previous learning. Students with problems in these areas may be unable to tell a story in the correct sequence, unable to memorize sequences of information such as the d... | milkshake721/2.1M-wiki-STEM |
Learning disability-Types-Storage: Problems with memory can occur with short-term or working memory, or with long-term memory. Most memory difficulties occur with one's short-term memory, which can make it difficult to learn new material without more repetitions than usual. Difficulties with visual memory can impede le... | milkshake721/2.1M-wiki-STEM |
Learning disability-Types-Output: Information comes out of the brain either through words, that is, language output, or through muscle activity, such as gesturing, writing or drawing. Difficulties with language output can create problems with spoken language. Such difficulties include answering a question on demand, in... | milkshake721/2.1M-wiki-STEM |
Learning disability-Types-By function impaired Deficits in any area of information processing can manifest in a variety of specific learning disabilities. It is possible for an individual to have more than one of these difficulties. This is referred to as comorbidity or co-occurrence of learning disabilities. In the UK... | milkshake721/2.1M-wiki-STEM |
Learning disability-Types-Reading disorder (ICD-10 and DSM-IV codes: F81.0/315.00) Reading disorder is the most common learning disability. Of all students with specific learning disabilities, 70–80% have deficits in reading. The term "Developmental Dyslexia" is often used as a synonym for reading disability; however, ... | milkshake721/2.1M-wiki-STEM |
Learning disability-Types-Disorder of written expression (ICD-10 and DSM-IV-TR codes 315.2) The DSM-IV-TR criteria for a disorder of written expression is writing skills (as measured by a standardized test or functional assessment) that fall substantially below those expected based on the individual's chronological age... | milkshake721/2.1M-wiki-STEM |
Learning disability-Types-By a number of organizations, the term "dysgraphia" has been used as an overarching term for all disorders of written expression.
Math disability (ICD-10 and DSM-IV codes F81.2-3/315.1) Sometimes called dyscalculia, a math disability involves difficulties such as learning math concepts (such a... | milkshake721/2.1M-wiki-STEM |
Learning disability-Management-Interventions include: Mastery model: Learners work at their own level of mastery.
Practice Gain fundamental skills before moving onto the next level Note: this approach is most likely to be used with adult learners or outside the mainstream school system. | milkshake721/2.1M-wiki-STEM |
Learning disability-Management-Direct instruction:Emphasizes carefully planned lessons for small learning increments Scripted lesson plans Rapid-paced interaction between teacher and students Correcting mistakes immediately Achievement-based grouping Frequent progress assessments Classroom adjustments: Special seating ... | milkshake721/2.1M-wiki-STEM |
Learning disability-Management-Helping Individuals with Learning Disabilities Many individuals with learning disabilities may not openly disclose their condition. Some experts say that an instructor directly asking or assuming potential disabilities could cause potential harm to an individual's self esteem. In addition... | milkshake721/2.1M-wiki-STEM |
Learning disability-Society and culture-School laws Schools in the United States have a legal obligation to new arrivals to the country, including undocumented students. The landmark Supreme Court ruling Plyler v. Doe (1982) grants all children, no matter their legal status, the right to a free education. This ruling s... | milkshake721/2.1M-wiki-STEM |
Learning disability-Society and culture-Issues Regarding Standardized Testing Problems still exist regarding the fairness of standardized testing. Providing testing accommodations to students with learning disabilities has become increasingly common. One of such issues that introduce iniquity to those with disabilities... | milkshake721/2.1M-wiki-STEM |
Learning disability-Society and culture-Critique of the medical model Learning disability theory is founded in the medical model of disability, in that disability is perceived as an individual deficit that is biological in origin. Researchers working within a social model of disability assert that there are social or s... | milkshake721/2.1M-wiki-STEM |
Learning disability-Society and culture-Culture There are three patterns that are well known in regards to mainstream students and minority labels in the United States: "A higher percentage of minority children than of white children are assigned to special education"; "within special education, white children are assi... | milkshake721/2.1M-wiki-STEM |
Learning disability-Society and culture-Social roots of learning disabilities in the U.S. | milkshake721/2.1M-wiki-STEM |
Learning disability-Society and culture-Learning disabilities have a disproportionate identification of racial and ethnic minorities and students who have low socioeconomic status (SES). While some attribute the disproportionate identification of racial/ethnic minorities to racist practices or cultural misunderstanding... | milkshake721/2.1M-wiki-STEM |
Learning disability-Society and culture-While many studies have considered only one characteristic of the student at a time, or used district- or school-level data to examine this issue, more recent studies have used large national student-level datasets and sophisticated methodology to find that the disproportionate i... | milkshake721/2.1M-wiki-STEM |
Learning disability-Society and culture-Learning disabilities in adulthood A common misconception about those with learning disabilities is that they outgrow it as they enter adulthood. This is often not the case and most adults with learning disabilities still require resources and care to help manage their disability... | milkshake721/2.1M-wiki-STEM |
Learning disability-Contrast with other conditions-People with an IQ lower than 70 are usually characterized as having an intellectual disability and are not included under most definitions of learning disabilities because their difficulty in learning are considered to be related directly to their overall low intellige... | milkshake721/2.1M-wiki-STEM |
Learning disability-Contrast with other conditions-Attention-deficit hyperactivity disorder (ADHD) is often studied in connection with learning disabilities, but it is not actually included in the standard definitions of learning disabilities. Individuals with ADHD may struggle with learning, but can often learn adequa... | milkshake721/2.1M-wiki-STEM |
Learning disability-Learning disabilities affects the writing process-The ability to express one's thoughts and opinions in an organized fashion and in written form is an essential life skill that individuals have been taught and practiced repetitively since youth. The writing process includes, but is not limited to: u... | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification group-In number theory, more specifically in local class field theory, the ramification groups are a filtration of the Galois group of a local field extension, which gives detailed information on the ramification phenomena of the extension. | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification theory of valuations-In mathematics, the ramification theory of valuations studies the set of extensions of a valuation v of a field K to an extension L of K. It is a generalization of the ramification theory of Dedekind domains.The structure of the set of extensions is known better when... | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification theory of valuations-Decomposition group and inertia group Let (K, v) be a valued field and let L be a finite Galois extension of K. Let Sv be the set of equivalence classes of extensions of v to L and let G be the Galois group of L over K. Then G acts on Sv by σ[w] = [w ∘ σ] (i.e. w is ... | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification theory of valuations-Given a fixed extension w of v to L, the decomposition group of w is the stabilizer subgroup Gw of [w], i.e. it is the subgroup of G consisting of all elements that fix the equivalence class [w] ∈ Sv. | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification theory of valuations-Let mw denote the maximal ideal of w inside the valuation ring Rw of w. The inertia group of w is the subgroup Iw of Gw consisting of elements σ such that σx ≡ x (mod mw) for all x in Rw. In other words, Iw consists of the elements of the decomposition group that act... | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification theory of valuations-The reduced ramification index e(w/v) is independent of w and is denoted e(v). Similarly, the relative degree f(w/v) is also independent of w and is denoted f(v). | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification groups in lower numbering-Ramification groups are a refinement of the Galois group G of a finite L/K Galois extension of local fields. We shall write w,OL,p for the valuation, the ring of integers and its maximal ideal for L . As a consequence of Hensel's lemma, one can write OL=OK[... | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification groups in lower numbering-(i) s operates trivially on OL/pi+1.
(ii) w(s(x)−x)≥i+1 for all x∈OL (iii) 1.
The group Gi is called i -th ramification group. They form a decreasing filtration, G−1=G⊃G0⊃G1⊃…{∗}.
In fact, the Gi are normal by (i) and trivial for sufficiently large i by... | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification groups in lower numbering-G1=1⇔L/K is tamely ramified (i.e., the ramification index is prime to the residue characteristic.)The study of ramification groups reduces to the totally ramified case since one has Gi=(G0)i for i≥0 One also defines the function iG(s)=w(s(α)−α),s∈G . (ii) in ... | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification groups in lower numbering-Fix a uniformizer π of L . Then s↦s(π)/π induces the injection Gi/Gi+1→UL,i/UL,i+1,i≥0 where UL,0=OL×,UL,i=1+pi . (The map actually does not depend on the choice of the uniformizer.) It follows from this G0/G1 is cyclic of order prime to p Gi/Gi+1 is a pro... | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification groups in lower numbering-The ramification groups can be used to compute the different DL/K of the extension L/K and that of subextensions: w(DL/K)=∑s≠1iG(s)=∑i=0∞(|Gi|−1).
If H is a normal subgroup of G , then, for σ∈G , iG/H(σ)=1eL/K∑s↦σiG(s) .Combining this with the above one ob... | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification groups in lower numbering-Example: the cyclotomic extension The ramification groups for a cyclotomic extension := Qp(ζ)/Qp , where ζ is a pn -th primitive root of unity, can be described explicitly: Gs=Gal(Kn/Ke), where e is chosen such that pe−1≤s<pe Example: a quartic extension Let... | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification groups in lower numbering-Now x1 − x3 = 2 x1 , which is in π5.
and x1−x2=4−22, which is in π3.
Various methods show that the Galois group of K is C4 , cyclic of order 4. Also: G0=G1=G2=C4.
and 13 24 ).
11 , so that the different 11 x1 satisfies X4 − 4X2 + 2, which has discriminant ... | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification groups in upper numbering-If u is a real number ≥−1 , let Gu denote Gi where i the least integer ≥u . In other words, 1. | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification groups in upper numbering-Define ϕ by ϕ(u)=∫0udt(G0:Gt) where, by convention, (G0:Gt) is equal to (G−1:G0)−1 if t=−1 and is equal to 1 for −1<t≤0 . Then ϕ(u)=u for −1≤u≤0 . It is immediate that ϕ is continuous and strictly increasing, and thus has the continuous inverse function... | milkshake721/2.1M-wiki-STEM |
Ramification group-Ramification groups in upper numbering-The upper numbering for an abelian extension is important because of the Hasse–Arf theorem. It states that if G is abelian, then the jumps in the filtration Gv are integers; i.e., Gi=Gi+1 whenever ϕ(i) is not an integer.The upper numbering is compatible with... | milkshake721/2.1M-wiki-STEM |
Schumacher criteria-Schumacher criteria-Schumacher criteria are diagnostic criteria that were previously used for identifying multiple sclerosis (MS). Multiple sclerosis, understood as a central nervous system (CNS) condition, can be difficult to diagnose since its signs and symptoms may be similar to other medical pro... | milkshake721/2.1M-wiki-STEM |
Schumacher criteria-Schumacher criteria-Sometimes it has been stated that the only proved diagnosis of MS is autopsy, or occasionally biopsy, where lesions typical of MS can be detected through histopathological techniques, and that sensitivity and specificity should be calculated for any given criteria | milkshake721/2.1M-wiki-STEM |
Schumacher criteria-Context-Historically, the first widespread set of criteria were the Schumacher criteria (also spelled sometimes Schumacker). Currently, testing of cerebrospinal fluid obtained from a lumbar puncture can provide evidence of chronic inflammation of the central nervous system, looking for oligoclonal b... | milkshake721/2.1M-wiki-STEM |
Schumacher criteria-Context-The most commonly used diagnostic tools at that time were evoked potentials. The nervous system of a person with MS responds less actively to stimulation of the optic nerve and sensory nerves due to demyelination of such pathways. These brain responses can be examined using visual and sensor... | milkshake721/2.1M-wiki-STEM |
Schumacher criteria-Summary-To get a diagnosis of CDMS a patient must show the following: Clinical signs of a problem in the CNS Dissemination in space, shown by clinical evidence of damage in two or more areas of CNS. | milkshake721/2.1M-wiki-STEM |
Schumacher criteria-Summary-Evidence of white matter involvement Dissemination in time shown by one of these: Two or more relapses (each lasting ≥ 24 hr and separated by at least 1 month) or disability progression (slow or stepwise) Patient should be between 10 and 50 yr old at time of examination No better explanation... | milkshake721/2.1M-wiki-STEM |
Schumacher criteria-Influence-These criteria were later substituted by Poser criteria and McDonald criteria. Poser criteria introduced the CNS oligoclonal bands into the diagnosis criteria, while McDonald criteria focus on a demonstration with clinical, laboratory and radiologic data of the dissemination of MS lesions ... | milkshake721/2.1M-wiki-STEM |
Srimad Bhagavata Book 2-Srimad Bhagavata Book 2-The Srimad Bhagavata is one of the main books of Hindu philosophy. The Bhagavata is a devotional account of the Supreme Being and His incarnations. The second book of the Srimad Bhagavata covers the creation of the universe according to Hindu Mythology and gives a summary... | milkshake721/2.1M-wiki-STEM |
Srimad Bhagavata Book 2-Chapter 1-Suka Rishi is very happy to hear Parikshit's question, as its answer will benefit mankind.
Suka Rishi tells Parikshit that even though he was already completely established in the formless, infinite Atman, his mind was still attracted to Narayana’s playful acts in His incarnations.
Thi... | milkshake721/2.1M-wiki-STEM |
Srimad Bhagavata Book 2-Chapter 2-Importance of renunciation Meditate on the form of Narayana in the space within the heart This form is similar to Vishnu's 4-armed form with the lotus, discus, mace, and conch One should meditate on the whole form until the mind is steady One should then meditate on each part of the Lo... | milkshake721/2.1M-wiki-STEM |
Srimad Bhagavata Book 2-Chapter 2-For example, jewelry (a gross substance) is made of gold (a subtler substance) One should raise the energy from the lower Chakra (Muladhara) all the way to the highest one (Brahmarandhra).
The idea of renunciation is to merge the gross senses/elements/organs into their subtler versions... | milkshake721/2.1M-wiki-STEM |
Srimad Bhagavata Book 2-Chapter 3-People who want a specific object or status should worship a specific deity.
Worshipping Brahma gives Vedic learning and powers Worshipping Sri (Lakshmi) gives wealth However, all the deities get their powers from the Supreme.
By worshipping the Supreme, one gets all their material and... | milkshake721/2.1M-wiki-STEM |
Srimad Bhagavata Book 2-Chapter 4-Parikshit asks Suka Rishi numerous questions about the Supreme, his power Maya (the power of illusion), and the knowledge of the Atman (soul) Suka Rishi's praises of the Supreme Director of the creation, preservation, and dissolution of the universe One who gives all rewards (including... | milkshake721/2.1M-wiki-STEM |
Srimad Bhagavata Book 2-Chapter 5-Narada believes that Brahma created the universe and praises Brahma as the Supreme, but wonders then why Brahma had to do great austerities Brahma takes the opportunity to praise Vasudeva, the true creator of the universe, as the one even above Brahma Brahma describes the creation of t... | milkshake721/2.1M-wiki-STEM |
Srimad Bhagavata Book 2-Chapter 5-This led to the creation of Mahattattva, which led to the creation of the subsequent categories.
The first of the categories is the 3 Gunas (or modes of nature). They are Sattva (good), Rajas (average), and Tamas (bad).
Ahankara (the ego) is mostly Tamas The elements were evolved from ... | milkshake721/2.1M-wiki-STEM |
Srimad Bhagavata Book 2-Chapter 6-Brahma continues explaining about Narayana's Universal Form to Narada The Purusha is Narayana's Universal Form, which is described in Purusha Sukta Each part of the Purusha is the original and complete prototype and contains all the related senses and objects.
An infinitesimal part is ... | milkshake721/2.1M-wiki-STEM |
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