More precisely, only totally ramified primes have a chance of being Eisenstein primes for the polynomial. (In quadratic fields, ramification is always total, so the distinction is not seen in the quadratic case like above.) In fact, Eisenstein polynomials are directly linked to totally ramified primes, as follows: if a field extension of the rationals is generated by the root of a polynomial that is Eisenstein at then is totally ramified in the extension, and conversely if is totally ramified in a number field then the field is generated by the root of an Eisenstein polynomial at .
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The Riemann–Hurwitz formula concerning (ramified) maps between Riemann surfaces or algebraic curves is a consequence of the Riemann–Roch theorem.
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In Philosophy of Religion, McGrew focuses on historical arguments for and against miracle claims, natural theology and atheology, and ramified natural theology.
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The right-handed trefoil knot. In geometric topology a basic type are embeddings, of which knot theory is a central example, and generalizations such as immersions, submersions, covering spaces, and ramified covering spaces. Basic results include the Whitney embedding theorem and Whitney immersion theorem. Riemann surface for the function f(z) = , shown as a ramified covering space of the complex plane.
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Paraloricaria shows a strongly flattened body, weak postorbital notches, long and ramified maxillary barbels, and overall, conspicuous fringed barbels. Male Paraloricaria are abdomino-lip brooders.
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Continuing in this vein, compact Riemann surfaces can map to surfaces of lower genus, but not to higher genus, except as constant maps. This is because holomorphic and meromorphic maps behave locally like z \mapsto z^n, so non- constant maps are ramified covering maps, and for compact Riemann surfaces these are constrained by the Riemann–Hurwitz formula in algebraic topology, which relates the Euler characteristic of a space and a ramified cover. For example, hyperbolic Riemann surfaces are ramified covering spaces of the sphere (they have non-constant meromorphic functions), but the sphere does not cover or otherwise map to higher genus surfaces, except as a constant.
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For archimedean local fields or in the unramified case the Hilbert symbol is easy to write down explicitly. The main problem is to evaluate it in the ramified case.
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The most typical relief is a ridge- hollow. The site is a highly ramified beam web, located in a Chernaya Balka that flows directly into the valley of Seversky Donets.
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Unlike activated or ameboid microglia, ramified microglia do not phagocytose cells and secrete fewer immunomolecules (including the MHC class I/II proteins). Microglia in this state are able to search for and identify immune threats while maintaining homeostasis in the CNS. Although this is considered the resting state, microglia in this form are still extremely active in chemically surveying the environment. Ramified microglia can be transformed into the activated form at any time in response to injury or threat.
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In mathematics, Belyi's theorem on algebraic curves states that any non- singular algebraic curve C, defined by algebraic number coefficients, represents a compact Riemann surface which is a ramified covering of the Riemann sphere, ramified at three points only. This is a result of G. V. Belyi from 1979. At the time it was considered surprising, and it spurred Grothendieck to develop his theory of dessins d'enfant, which describes nonsingular algebraic curves over the algebraic numbers using combinatorial data.
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Lubin–Tate theory is important in explicit local class field theory. The unramified part of any abelian extension is easily constructed, Lubin–Tate finds its value in producing the ramified part. This works by defining a family of modules (indexed by the natural numbers) over the ring of integers consisting of what can be considered as roots of the power series repeatedly composed with itself. The compositum of all fields formed by adjoining such modules to the original field gives the ramified part.
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The sixth bonus track is "Ramified", which had been specially recorded by the band for Underground Magazine and provided on a free cassette that was included with the debut issue of that publication in 1987.
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Several results in algebraic topology and complex analysis follow. Firstly, there are no ramified covering maps from a curve of lower genus to a curve of higher genus – and thus, since non-constant meromorphic maps of curves are ramified covering spaces, there are no non-constant meromorphic maps from a curve of lower genus to a curve of higher genus. As another example, it shows immediately that a curve of genus 0 has no cover with N > 1 that is unramified everywhere: because that would give rise to an Euler characteristic > 2.
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The Sepik Hill languages form the largest and most ramified branch of the Sepik languages of northern Papua New Guinea. They are spoken along the southern margin of the Sepik floodplain in the foothills of Central Range of south-central East Sepik Province.
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The Mucoraceae are a family of fungi of the order Mucorales, characterized by having the thallus not segmented or ramified. Pathogenic genera include Absidia, Apophysomyces, Mucor, Rhizomucor, and Rhizopus. According to a 2008 estimate, the family contains 25 genera and 129 species.
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The dessin d'enfant on the Klein quartic associated with the quotient map by its automorphism group (with quotient the Riemann sphere) is precisely the 1-skeleton of the order-3 heptagonal tiling.. That is, the quotient map is ramified over the points , and ; dividing by 1728 yields a Belyi function (ramified at , and ), where the 56 vertices (black points in dessin) lie over 0, the midpoints of the 84 edges (white points in dessin) lie over 1, and the centers of the 24 heptagons lie over infinity. The resulting dessin is a "platonic" dessin, meaning edge- transitive and "clean" (each white point has valence 2).
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DLCA clusters are loose and ramified (d ≈ 1.8), while the RLCA clusters are more compact (d ≈ 2.1). The cluster size distribution is also different in these two regimes. DLCA clusters are relatively monodisperse, while the size distribution of RLCA clusters is very broad. The larger the cluster size, the faster their settling velocity.
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Dugesia digestion tract consists of a central non-pigmented tubular pharynx. Like the other triclads, Dugesia's gut consists in three ramified branches. Each branch consists of ceca, which delivers the nutrients to the body. This worm has a sac digestive plan, that is, it does not have a separate opening for waste excretion.
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There are three pairs of these lateral appendages situated along the margin of the sides. These appendages have a ramified apex. Each ramification of the apex has a rounded base and a long, thin and sharp prolongation. The whole length of each of these appendages is covered by little and acute ramifications.
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183–186 In March, he joined the committee which was to present Cuza with the Assembly's stances, but he resigned over disagreements with his colleagues.Catargiu, pp. 171–172 During the ramified scandal, his alleged direct threats against Cuza resulted in his arrest."Correo estanjero", in La Discusión. Diário Democrático, April 4, 1860, p.
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It possesses a yellowish-green thallus that measures wide, its laciniae are plane and adnate. Its surface is continuous and somewhat irregularly cracked, being isodichotomously ramified. The species' axilla is oval, it counts with truncate apices, and a black-lined margin. It shows no lacinules nor soredia while showing weakly laminal maculae.
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It possesses a whitish-green thallus that measures wide, its lobes measuring between wide. Its surface is continuous, laterally overlapping and adnate, being dichotomously ramified. The species' axillary sinus is oval, it counts with rounded apices, and a black-lined margin with no cilia. It shows no lacinules while possessing laminal maculae.
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The body shape is elongate, limaciform and anteriorly rounded. The oral veil has 18 ramified appendages that differ in length. The oral tentacles are flat. Plocamopherus lemur has a brownish background color heavily speckled all over the body with minute brown dots, and minute orange dots that are clustered to form orange patches.
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However, the clavus is red-brown with a white spot at the tip. The rhinophoral sheath is short. There are three pairs of short lateral appendages, with the last pair having a prominent rounded globular structure that is white in color. All lateral appendages are slightly ramified and whitish at the tip.
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Quine explains the ramified theory as follows: "It has been so called because the type of a function depends both on the types of its arguments and on the types of the apparent variables contained in it (or in its expression), in case these exceed the types of the arguments". Stephen Kleene in his 1952 Introduction to Metamathematics describes the ramified theory of types this way: :The primary objects or individuals (i.e. the given things not being subjected to logical analysis) are assigned to one type (say type 0), the properties of individuals to type 1, properties of properties of individuals to type 2, etc.; and no properties are admitted which do not fall into one of these logical types (e.g.
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This state is actually part of a graded response as microglia move from their ramified form to their fully active phagocytic form. Microglia can be activated by a variety of factors including: pro-inflammatory cytokines, cell necrosis factors, lipopolysaccharide, and changes in extracellular potassium (indicative of ruptured cells). Once activated the cells undergo several key morphological changes including the thickening and retraction of branches, uptake of MHC class I/II proteins, expression of immunomolecules, secretion of cytotoxic factors, secretion of recruitment molecules, and secretion of pro-inflammatory signaling molecules (resulting in a pro-inflammation signal cascade). Activated non-phagocytic microglia generally appear as "bushy," "rods," or small ameboids depending on how far along the ramified to full phagocytic transformation continuum they are.
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Mucoralean fungi are typically fast-growing, and their wide hyphae (long, filamentous structures), lack septa (multi- perforate septa, are present only in sporangiophores and gametangia). The hyphae grow mostly within the substrate. Sporangiophores are upright (simple or ramified) hyphae, that support sac-like sporangia filled with asexual sporangiospores. Other structures include merospores, oidia, and sporangiola.
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In the example above, the discriminant of the number field Q(x) with x3 − x − 1 = 0 is −23, and as we have seen the 23-adic place ramifies. The Dedekind discriminant tells us it is the only ultrametric place which does. The other ramified place comes from the absolute value on the complex embedding of F.
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In complex geometry, ramified covering spaces are used to model Riemann surfaces, and to analyze maps between surfaces, such as by the Riemann–Hurwitz formula. In Riemannian geometry, one may ask for maps to preserve the Riemannian metric, leading to notions of isometric embeddings, isometric immersions, and Riemannian submersions; a basic result is the Nash embedding theorem.
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In the mathematical discipline of set theory, ramified forcing is the original form of forcing introduced by to prove the independence of the continuum hypothesis from Zermelo–Fraenkel set theory. Ramified forcing starts with a model of set theory in which the axiom of constructibility, , holds, and then builds up a larger model of Zermelo–Fraenkel set theory by adding a generic subset of a partially ordered set to , imitating Kurt Gödel's constructible hierarchy. Dana Scott and Robert Solovay realized that the use of constructible sets was an unnecessary complication, and could be replaced by a simpler construction similar to John von Neumann's construction of the universe as a union of sets for ordinals . Their simplification was originally called "unramified forcing" , but is now usually just called "forcing".
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Structure of larger aggregates formed can be different. In the fast aggregation regime or DLCA regime, the aggregates are more ramified, while in the slow aggregation regime or RLCA regime, the aggregates are more compact. As the aggregation process continues, larger clusters form. The growth occurs mainly through encounters between different clusters, and therefore one refers to cluster-cluster aggregation process.
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De la Caballeria (or De la Cavallería), Sephardic family of Aragon, Spain, widely ramified, and influential through its wealth and scholarship, especially in Saragossa. The family descended from D. Solomon ibn Labi de la Caballeria, who had nine sons. The eldest, Bonafos Caballeria, was baptized, and all the others followed his example except Benveniste. Bonafos and Samuel took the name "Pedro" (Micer Pedro).
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The main body of the octopus is normally long and including the arms, approximately long. The octopus displays a typical color pattern with dark ramified lines similar to veins, usually with a yellow siphon. The arms are usually dark in color, with contrasting white suckers. In many color displays, a lighter trapezoidal area can be seen immediately below the eye.
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The rhinophoral sheath is short with clusters of orange dots. There are three pairs of lateral appendages, with only the last pair forming a rounded, brown, and prominent globular structure. All lateral appendages are conical having a short but highly ramified prolongation at the apex. The first two lateral appendages are very short and the last pair is very elongate.
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Usually the posterior most pair has the larger globular structure, although exceptions have been observed. All lateral appendages are slightly ramified and whitish at the tip. There are three principal tripinnate branchial leaves, which do not form a complete circle around the anus. The posterior portion of the foot forms a well- developed keel that has a small crest tipped with white.
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Corticium diamantense is a species of sea sponge in the order Homosclerophorida, first found in vertical walls of reef caves at depths of about in the Caribbean Sea. This species has oscula situated near its border; regular non-lophose calthrops of one size, rare tetralophose calthrops and candelabra, the fourth actine of which is basally ramified into 4 or 5 microspined rays.
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In mathematics, the Hilbert–Speiser theorem is a result on cyclotomic fields, characterising those with a normal integral basis. More generally, it applies to any finite abelian extension of , which by the Kronecker–Weber theorem are isomorphic to subfields of cyclotomic fields. :Hilbert–Speiser Theorem. A finite abelian extension has a normal integral basis if and only if it is tamely ramified over .
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Schnell belonged to a widely ramified family of musicians that originally came from the Allgäu. His father Bernhard Schnell was footman in the service of the music-loving count in Wiesentheid. In 1714 Schnell became oboist and violinist at the court of Bamberg. In July 1727 he was appointed court and chamber music director by the Bamberg prince-bishop Lothar Franz von Schönborn.
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There are also two buccal suckers at the anterior extremity. The digestive organs include an anterior subterminal mouth, a pharynx, an oesophagus and a posterior intestine that bifurcates near the level of the genital atrium in two lateral branches. The intestinal branches are ramified medially and laterally and are not confluent posteriorly. Each adult contains male and female reproductive organs.
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In mathematics, the Riemann–Hurwitz formula, named after Bernhard Riemann and Adolf Hurwitz, describes the relationship of the Euler characteristics of two surfaces when one is a ramified covering of the other. It therefore connects ramification with algebraic topology, in this case. It is a prototype result for many others, and is often applied in the theory of Riemann surfaces (which is its origin) and algebraic curves.
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The nudibranchs in this superfamily share with the Aeolidida the possession of dorsal cerata. Unlike the cerata of aeolids they have either no digestive gland or short digestive gland intrusions into the cerata and no cnidosacs. In the Goniaeolididae the digestive gland is ramified beneath the skin but does not extend into the cerata. The cerata are easily cast off and are probably defensive in purpose.
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The juxtaoral organ in humans is a small longish structure (10–14 mm in length, 1–2 mm in diameter), situated medially to the medial pterygoid muscle. The organ consists of a central ramified cord of epithelial parenchyma, embedded in connective tissue particularly rich in nerve fibers and sensory receptors. Close relations exist between epithelial cells and nerve endings. Histochemically, the parenchyma displays a characteristic pattern of various enzymes.
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The height at the shoulder can range from . (2011). The hoof, which is large in relation to the body, has elastic interdigital membranes which are useful for swimming and walking on marshy surfaces. Only the males possess antlers which are ramified and reach a length of 60 cm (23 inches). An adult typically grows to a weight of , although an occasional big male can weigh up to . (2011).
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The ovary is densely pubescent; style terete, silvery gray tomentose on lower half. The nut is ovoid or narrowly ovoid, densely appressed tomentose; the calyx tube is up to 2.8 cm in diameter, glabrous and glaucous; the winglike calyx segments are linear-lanceolate, 12-15 × ca. 3 cm, glabrous, minutely papillate near much- ramified solitary midvein. Flowering is from March to April, and fruiting occurs in June and July.
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In algebraic geometry a generalized Jacobian is a commutative algebraic group associated to a curve with a divisor, generalizing the Jacobian variety of a complete curve. They were introduced by , and can be used to study ramified coverings of a curve, with abelian Galois group. Generalized Jacobians of a curve are extensions of the Jacobian of the curve by a commutative affine algebraic group, giving nontrivial examples of Chevalley's structure theorem.
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Schematic depiction of ramification: the fibers of almost all points in Y below consist of three points, except for two points in Y marked with dots, where the fibers consist of one and two points (marked in black), respectively. The map f is said to be ramified in these points of Y. Ramification, generally speaking, describes a geometric phenomenon that can occur with finite-to-one maps (that is, maps f: X → Y such that the preimages of all points y in Y consist only of finitely many points): the cardinality of the fibers f−1(y) will generally have the same number of points, but it occurs that, in special points y, this number drops. For example, the map :C → C, z ↦ zn has n points in each fiber over t, namely the n (complex) roots of t, except in t = 0, where the fiber consists of only one element, z = 0. One says that the map is "ramified" in zero.
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98 In computability theory, Putnam investigated the structure of the ramified analytical hierarchy, its connection with the constructible hierarchy and its Turing degrees. He showed that there exist many levels of the constructible hierarchy which do not add any subsets of the integers and later, with his student George Boolos, that the first such "non-index" is the ordinal \beta_0 of ramified analysis (this is the smallest \beta such that L_\beta is a model of full second-order comprehension), and also, together with a separate paper with Richard Boyd (another of Putnam's students) and Gustav Hensel, how the Davis–Mostowski–Kleene hyperarithmetical hierarchy of arithmetical degrees can be naturally extended up to \beta_0. In computer science, Putnam is known for the Davis–Putnam algorithm for the Boolean satisfiability problem (SAT), developed with Martin Davis in 1960. The algorithm finds if there is a set of true or false values that satisfies a given Boolean expression so that the entire expression becomes true.
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Each of these reactions is characterized by the respective aggregation coefficients kAA, kBB, and kAB. For example, when particles A and B bear positive and negative charge, respectively, the homoaggregation rates may be slow, while the heteroaggregation rate is fast. In contrast to homoaggregation, the heteroaggregation rate accelerates with decreasing salt concentration. Clusters formed at later stages of such heteroaggregation processes are even more ramified that those obtained during DLCA (d ≈ 1.4).
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Much of the significance of the discriminant lies in the fact that ramified ultrametric places are all places obtained from factorizations in Qp where p divides the discriminant. This is even true of the polynomial discriminant; however the converse is also true, that if a prime p divides the discriminant, then there is a p-place which ramifies. For this converse the field discriminant is needed. This is the Dedekind discriminant theorem.
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It is certainly therefore necessary for it to be a free module. It leaves the question of the gap between free and projective, for which a large theory has now been built up. A classical result, based on a result of David Hilbert, is that a tamely ramified abelian number field has a normal integral basis. This may be seen by using the Kronecker–Weber theorem to embed the abelian field into a cyclotomic field.
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Lobopods with curved termial claws may have given some lobopodians the ability to climb on substrances. Not much is known about the physiology of lobopodians. There are evidence suggest that lobopodians moult just like other ecdysozoan taxa, but the outline and ornamentation of the harden sclerite did not vary during ontogeny. The gill-like structures on the body flaps of gilled lobopodians and ramified extensions on the lobopods of Jianshanopodia may provide respiratory function (gills).
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Libraries, University, University Librarian, Rose Arny, R.R. Company, and Nicole Rafter. White Trash. Northeastern University Press, 1988. Print, pp. 49-54. McCulloch put the number of families in the study at thirty, with the Ishmaels being the “central, the oldest and the most widely ramified family.” It appears likely that McCulloch also chose to publicize the Ishmael family due to the name's association to the Orient, of which McCulloch had studied intensely.
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The ability to view and characterize different neural cells including microglia began in 1880 when Nissl staining was developed by Franz Nissl. Franz Nissl and F. Robertson first described microglial cells during their histology experiments. The cell staining techniques in the 1880s showed that microglia are related to macrophages. The activation of microglia and formation of ramified microglial clusters was first noted by Victor Babeş while studying a rabies case in 1897.
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In mathematics, Abhyankar's lemma (named after Shreeram Shankar Abhyankar) allows one to kill tame ramification by taking an extension of a base field. More precisely, Abhyankar's lemma states that if A, B, C are local fields such that A and B are finite extensions of C, with ramification indices a and b, and B is tamely ramified over C and b divides a, then the compositum AB is an unramified extension of A.
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Polyclads range from in length with a flattened, roughly oval, body shape and, in many cases, a pair of short tentacles on the head. They are distinguished from other related animals by the presence of a folded pharynx, an elongated intestine with numerous complex diverticula, and multiple ocelli. The etymology of the order name Polycladida corresponds to the two ancient Greek words (), meaning "numerous", and (), meaning "branch". It refers to the ramified shape of the intestine in these flatworms.
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Corynebacterium renale is a pathogenic bacterium that causes cystitis and pyelonephritis in cattle. C. renale is a facultatively anaerobic Gram-positive organism, characterized by nonencapsulated, nonsporulated, immobile, straight or curved rods with a length of 1 to 8 µm and width of 0.3 to 0.8 µm, which forms ramified aggregations in culture (looking like "Chinese characters"). The bacterium is sensitive to the majority of antibiotics, such as the penicillins, ampicillin, cephalosporins, quinolones, chloramphenicol, tetracyclines, cefuroxime, and trimethoprim.
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In mathematics, Weierstrass's elliptic functions are elliptic functions that take a particularly simple form; they are named for Karl Weierstrass. This class of functions are also referred to as p-functions and generally written using the symbol ℘ (a calligraphic lowercase p). The ℘ functions constitute branched double coverings of the Riemann sphere by the torus, ramified at four points. They can be used to parametrize elliptic curves over the complex numbers, thus establishing an equivalence to complex tori.
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Senecio inaequidens is a perennial chamaephyte up to 1 m in height, often much ramified, with each stem ending in one or a few capitula yellow in colour, forming a loose floral display. A single plant produces 26 to 500 capitula each year, with approximately 90 florets, 74% of them developing a viable achene. The leaves are linear, entire or almost so and without petioles. S. inaequidens exists as a diploid genotype and a tetraploid cytotype.
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In mathematics, the Lubin–Tate formal group law is a formal group law introduced by to isolate the local field part of the classical theory of complex multiplication of elliptic functions. In particular it can be used to construct the totally ramified abelian extensions of a local field. It does this by considering the (formal) endomorphisms of the formal group, emulating the way in which elliptic curves with extra endomorphisms are used to give abelian extensions of global fields.
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Retrieved 2009-02-21 It does not show definite air-floats.Jones, W.E. 1964. The British Phycological Society. A key to the genera of the British Seaweeds. Reprinted from Field Studies Volume 1, (4) pp 1 - 32 All species’ sporophytes consist of a ramified holdfast, an unbranched cylindrical stipe, and a blade with a percurrent, cartilaginous midrib, Alaria is frequently found with lacerations running from the margin to the midrib caused by the ravages of the sea.
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The herbarium material examined by Cheek and Jebb exhibited spurs that were basally 5-branched, with each branch being secondarily ramified. Upper pitchers are similar in shape to their terrestrial counterparts, though usually more elongated, growing to 7–25 cm in height by 1.2–6 cm in width. The basal fifth to third of the trap is ovate, narrowing and becoming cylindrical to slightly infundibular above. As in lower pitchers, a conspicuous hip often marks the boundary between these two parts.
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Boyd earned his Ph.D. from MIT in 1970. Boyd's doctoral thesis, directed by Richard Cartwright, was titled A Recursion-Theoretic Characterization of the Ramified Analytical Hierarchy. Boyd taught for most of his career at Cornell University, though he also taught briefly at Harvard University, the University of Michigan, Ann Arbor, and the University of California, Berkeley. He has also been a visiting professor at the University of Canterbury in Christchurch, New Zealand, and the University of Melbourne in Melbourne, Victoria, Australia.
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Vascularity in an adult forearm. Vascularity, in bodybuilding, is the condition of having many highly-visible, prominent, and often extensively- ramified superficial veins. The skin appears "thin" — sometimes virtually transparent — due to an extreme reduction of subcutaneous fat, allowing for maximum muscle definition. Vascularity is enhanced by extremely low body fat (usually below 10%) and low retained water, as well as the muscle engorgement ("pump") and venous distension accentuated by the vigorous flexing and potentially hazardous Valsalva effect which characterize competitive posing.
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M65 was discovered by Charles Messier and included in his Messier Objects list. However, William Henry Smyth accidentally attributed the discovery to Pierre Méchain in his popular 19th-century astronomical work A Cycle of Celestial Objects (stating "They [M65 and M66] were pointed out by Méchain to Messier in 1780"). This error was in turn picked up by Kenneth Glyn Jones in Messier's Nebulae and Star Clusters. This has since ramified into a number of other books by a variety of authors.
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As we know, Richard Wagner's operatic performances were the fullest embodiment of the Gesamtkunst-werk. Alex Salaueu was to become actively involved in the theatre movements of both large and small forms. The work of the Salaueu was always figurative and anthropomorphic; his pictures have an intriguing subject and his figures fixed, typical features. The ramified associative nature of his painterly mise-en-scenes elevated his work to the level of a mythological reality that was more authentic than the visible and everyday.
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In mathematics, the ELSV formula, named after its four authors Torsten Ekedahl, Sergei Lando, Michael Shapiro, Alek Vainshtein, is an equality between a Hurwitz number (counting ramified coverings of the sphere) and an integral over the moduli space of stable curves. Several fundamental results in the intersection theory of moduli spaces of curves can be deduced from the ELSV formula, including the Witten conjecture, the Virasoro constraints, and the \lambda_g-conjecture. It is generalized by the Gopakumar–Mariño–Vafa formula.
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Although, in theory, there were no discriminatory laws against the Jews in democratic Latvia and they enjoyed equality of rights, in practice the economic policy of the government was intended to restrict their activities. This was also reflected in the area of credit. The Jews of Latvia developed a ramified network of loan banks for the granting of credit with the support of the American Jewish Joint Distribution Committee and the Jewish Colonization Association (JCA). Cooperative credit societies for craftsmen, small tradesmen, etc.
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Corynebacterium bovis is a pathogenic bacterium that causes mastitis and pyelonephritis in cattle. C. bovis is a facultatively anaerobic, Gram-positive organism, characterized by nonencapsulated, nonsporulated, immobile, straight or curved rods with a length of 1 to 8 µm and width of 0.3 to 0.8 µm, which forms ramified aggregations in culture (looking like "Chinese characters"). In mastitic infections, C. bovis is spread from cow to cow most commonly through improper milking technique. However, it is usually a mild infection resulting in an elevated somatic cell count.
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Russell discovered that Basic Law V is inconsistent (this is Russell's paradox). Frege abandoned his logicist program soon after this, but it was continued by Russell and Whitehead. They attributed the paradox to "vicious circularity" and built up what they called ramified type theory to deal with it. In this system, they were eventually able to build up much of modern mathematics but in an altered, and excessively complex form (for example, there were different natural numbers in each type, and there were infinitely many types).
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Constructions, and the entities they construct, are organized into a ramified type theory incorporating a simple type theory. The semantics is tailored to the hardest case, as constituted by hyperintensional contexts, and generalized from there to intensional and extensional contexts. The underlying logic is a Frege-style function/argument one, treating functions, rather than relations or sets, as primitive, together with a Church-style logic, centred on the operations of functional abstraction and application. Key constraints informing TIL approach to semantic analysis are compositionality and anti-contextualism.
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The system of connections and processes described above can be "ramified" to any size. During the development of an application, monitoring processes may be added between pairs of processes, processes may be "exploded" to subnets, or simulations of processes may be replaced by the real process logic. FBP therefore lends itself to rapid prototyping. This is really an assembly line image of data processing: the IPs travelling through a network of processes may be thought of as widgets travelling from station to station in an assembly line.
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Many curves, for example hyperelliptic curves, may be presented abstractly, as ramified covers of the projective line. According to the Riemann–Hurwitz formula, the genus then depends only on the type of ramification. A rational curve is a curve that is birationally equivalent to a projective line (see rational variety); its genus is 0. A rational normal curve in projective space Pn is a rational curve that lies in no proper linear subspace; it is known that there is only one example (up to projective equivalence),.
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In Riemann surface theory, the Bolza surface, sometimes called the Bolza curve, is obtained as the ramified double cover of the Riemann sphere, with ramification locus at the set of vertices of the regular inscribed octahedron. Its automorphism group includes the hyperelliptic involution which flips the two sheets of the cover. The quotient by the order 2 subgroup generated by the hyperelliptic involution yields precisely the group of symmetries of the octahedron. Among the many remarkable properties of the Bolza surface is the fact that it maximizes the systole among all genus 2 hyperbolic surfaces.
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Over bases with positive characteristic or more arithmetic structure, additional isomorphism types exist. For example, if 2 is invertible over the base, all group schemes of order 2 are constant, but over the 2-adic integers, μ2 is non-constant, because the special fiber isn't smooth. There exist sequences of highly ramified 2-adic rings over which the number of isomorphism types of group schemes of order 2 grows arbitrarily large. More detailed analysis of commutative finite flat group schemes over p-adic rings can be found in Raynaud's work on prolongations.
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Tomas Schmit (born 13 July 1943 in Thier, now part of Wipperfürth; died 4 October 2006 in Berlin, Germany) was an artist and author, one of the pioneers of the Fluxus movement of the early 1960s. During the subsequent 40 years, he developed a ramified work of drawings, texts, books and concepts of artists' books. From the late 1960s until his death, he continuously exhibited in international galleries. With his series of drawings, he is represented in renowned museums and collections (among them Museum Ludwig, Cologne; Collection Harald Falckenberg, Hamburg).
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Its ascomata are orange-brown, rounded and measure approximately 100-350 μm in diameter, exclusive of its appendages. Its asci are hyaline and rounded, containing 8 lens-shaped, orange, ascospores, 7 μm in diameter. In addition, their peridial appendages are pale-orange and have a membranous inner layer with an outer layer of orange-brown, septate, thick-walled and prickly hyphae that form a highly ramified mesh-like peridium with anastamosing connections. With its teleomorphic stages being more commonly found, its anamorph state is absent or rare, having large amounts of arthroconidia.
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La Sorbonne The French educational system is highly centralised, organised, and ramified. It is divided into three stages: # primary education (enseignement primaire); # secondary education (enseignement secondaire); # tertiary or college education (enseignement supérieur) Schooling in France is mandatory as of age 6, the first year of primary school. Many parents start sending their children earlier though, around age 3 as kindergarten classes (maternelle) are usually affiliated to a borough's (commune) primary school. Some even start earlier at age 2 in pré-maternelle or garderie class, which is essentially a daycare facility.
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This form of microglial cell is commonly found at specific locations throughout the entire brain and spinal cord in the absence of foreign material or dying cells. This "resting" form of microglia is composed of long branching processes and a small cellular body. Unlike the amoeboid forms of microglia, the cell body of the ramified form remains in place while its branches are constantly moving and surveying the surrounding area. The branches are very sensitive to small changes in physiological condition and require very specific culture conditions to observe in vitro.
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For a field contained in it, the field trace can be used to construct such a basis in also (see the article on Gaussian periods). Then in the case of squarefree and odd, is a compositum of subfields of this type for the primes dividing (this follows from a simple argument on ramification). This decomposition can be used to treat any of its subfields. proved a converse to the Hilbert–Speiser theorem: :Each finite tamely ramified abelian extension of a fixed number field has a relative normal integral basis if and only if .
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The discriminant of K can be referred to as the absolute discriminant of K to distinguish it from the relative discriminant of an extension K/L of number fields. The latter is an ideal in the ring of integers of L, and like the absolute discriminant it indicates which primes are ramified in K/L. It is a generalization of the absolute discriminant allowing for L to be bigger than Q; in fact, when L = Q, the relative discriminant of K/Q is the principal ideal of Z generated by the absolute discriminant of K.
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This is introduced because of a counting theorem: on a Riemann surface the sum of the weights of the Weierstrass points is g(g^2 - 1). For example, a hyperelliptic Weierstrass point, as above, has weight g(g - 1)/2. Therefore, there are (at most) 2(g + 1) of them. The 2g+2 ramification points of the ramified covering of degree two from a hyperelliptic curve to the projective line are all hyperelliptic Weierstrass points and these exhausts all the Weierstrass points on a hyperelliptic curve of genus g.
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134-135); the proof in Russell 1927 PM Appendix B that "the integers of any order higher than 5 are the same as those of order 5" is "not conclusive" and "the question whether (or to what extent) the theory of integers can be obtained on the basis of the ramified hierarchy [classes plus types] must be considered as unsolved at the present time". Gödel concluded that it wouldn't matter anyway because propositional functions of order n (any n) must be described by finite combinations of symbols (all quotes and content derived from page 135).
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The desert zone, an area lying west and southwest of the Euphrates River, is a part of the Syrian Desert and Arabian Desert, which covers sections of Syria, Jordan, and Saudi Arabia and most of the Arabian Peninsula. The region, sparsely inhabited by pastoral bedouins, consists of a wide stony plain interspersed with rare sandy stretches. A widely ramified pattern of wadis–watercourses that are dry most of the year–runs from the border to the Euphrates. Some wadis are over long and carry brief but torrential floods during the winter rains.
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The Kungur Ice Cave is located in the vicinity of Kungur, on the right bank of the Sylva River. Ramified passages stretch under the ground for over 6,000 meters, and only a small part has already been explored. To this day old slides and crumblings do not allow to determine the total length of the passages. In the explored part of the cave there are several dozens of grottoes; the largest one, which is called the Druzhba (Friendship) Grotto, was given its name in honor of the participants of the International Geological Congress who visited the cave in 1937.
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Like most lectins, ConA is a homotetramer: each sub-unit (26.5kDa, 235 amino-acids, heavily glycated) binds a metallic atom (usually Mn2+ and a Ca2+). It has the D2 symmetry. Its tertiary structure has been elucidated, as have the molecular basis of its interactions with metals as well as its affinity for the sugars mannose and glucose are well known. ConA binds specifically α-D-mannosyl and α-D-glucosyl residues (two hexoses differing only in the alcohol on carbon 2) in terminal position of ramified structures from B-Glycans (reach in α-mannose, or hybrid and bi-antennary glycan complexes).
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Among the latter are the steep edge of the Bârlad Plateau (), known as the Iași Ridge (), the edge of the Central Moldavian Plateau (), known as the Cornești Hills, and the edge of the Dniester Hills, known as the Dniester Ridge. The relief in the valleys of the rivers and creeks is quite conspicuous, so that the valleys have large terraces and hillocks. The Siret Passage (), ramified in the north with the Moldova Valley, and Suceava Valley cuts the main part of the plateau from the Moldavian Subcarpathians. The Prut Passage cuts the Plateau in half in the north-south direction.
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The flowers are the most brilliant aspect of this plant, with the production of a great quantity of vermillion, magenta or pink flowers that will often cover the entire site, hence the popular name "pink carpet". The plant contains ramified stems that are spread out, carrying sheets opposed, and are long and narrow, with the end of the stems increasing into a quantity of isolated small flowers, with diameters ranging from . These abundant and long-lasting flowers will remain in bloom from July to September. The plant is sun-loving, and thrives well in very dry and hot environments.
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In the 1920s, Leon Chwistek and Frank P. Ramsey proposed an unramified type theory, now known as the "theory of simple types" or simple type theory, which collapsed the hierarchy of the types in the earlier ramified theory and as such did not require the axiom of reducibility. The common usage of "type theory" is when those types are used with a term rewrite system. The most famous early example is Alonzo Church's simply typed lambda calculus. Church's theory of types helped the formal system avoid the Kleene–Rosser paradox that afflicted the original untyped lambda calculus.
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In the 1920s, Leon ChwistekL. Chwistek, Antynomje logikiformalnej, Przeglad Filozoficzny 24 (1921) 164–171 and Frank P. RamseyF. P. Ramsey, The foundations of mathematics, Proceedings of the London Mathematical Society, Series 2 25 (1926) 338–384. noticed that, if one is willing to give up the vicious circle principle, the hierarchy of levels of types in the "ramified theory of types" can be collapsed. The resulting restricted logic is called the theory of simple typesGödel 1944, pages 126 and 136–138, footnote 17: "Russell's mathematical logic" appearing in Kurt Gödel: Collected Works: Volume II Publications 1938–1974, Oxford University Press, New York NY, (v.2.pbk).
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Moore is well known not only for his work in the areas or metaphysics and history of philosophy, but also for his contributions to the philosophy of logic and the philosophy of mathematics. In particular, Moore has done much work on the nature of infinity which illustrates his ramified interests. In his book The Infinite, Moore offers a thorough discussion of the idea of infinity and its history, and a defence of finitism. He engages with a wide range of approaches and issues in the history of thought about the infinite, including various paradoxes, as well as the problems of human finitude and death.
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In mathematics, the interplay between the Galois group G of a Galois extension L of a number field K, and the way the prime ideals P of the ring of integers OK factorise as products of prime ideals of OL, provides one of the richest parts of algebraic number theory. The splitting of prime ideals in Galois extensions is sometimes attributed to David Hilbert by calling it Hilbert theory. There is a geometric analogue, for ramified coverings of Riemann surfaces, which is simpler in that only one kind of subgroup of G need be considered, rather than two. This was certainly familiar before Hilbert.
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Further, codimension 0 immersions do not behave like other immersions, which are largely determined by the stable normal bundle: in codimension 0 one has issues of fundamental class and cover spaces. For instance, there is no codimension 0 immersion , despite the circle being parallelizable, which can be proven because the line has no fundamental class, so one does not get the required map on top cohomology. Alternatively, this is by invariance of domain. Similarly, although S3 and the 3-torus T3 are both parallelizable, there is no immersion – any such cover would have to be ramified at some points, since the sphere is simply connected.
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Although Gerz's texts are conceived as part of his artworks, they are also highly acclaimed on their own merits. “The most extensive and richest of these books”, writes Petra Kipphoff of “The Centaur’s Difficulty When Dismounting the Horse”, created in parallel with the installation at the 1976 Venice Biennale, “is on the one hand a reflection and a reckoning and on the other a collection of aphorisms that with its intricately ramified phrases is unrivalled in contemporary literature.”Petra Kipphoff: “Trau keinem Bild”, in: Die Zeit, Hamburg, 15 September 1978, quoted in Detlef Bluemler: “Jochen Gerz. Weitermachen gegen das Aufhören”, Kritisches Lexikon der Gegenwartskunst, edition 6, Munich, 1989, p. 7.
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Riemann surface theory shows that a compact Riemann surface has enough meromorphic functions on it, making it an algebraic curve. Under the name Riemann's existence theorem a deeper result on ramified coverings of a compact Riemann surface was known: such finite coverings as topological spaces are classified by permutation representations of the fundamental group of the complement of the ramification points. Since the Riemann surface property is local, such coverings are quite easily seen to be coverings in the complex- analytic sense. It is then possible to conclude that they come from covering maps of algebraic curves--that is, such coverings all come from finite extensions of the function field.
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Similarly, the projection X → D is a degree 2 morphism ramified over the contact points on D of the four lines tangent to both C and D, and the corresponding involution \tau has the form x → q − x for some q. Thus the composition \tau \sigma is a translation on X. If a power of \tau \sigma has a fixed point, that power must be the identity. Translated back into the language of C and D, this means that if one point c ∈ C (equipped with a corresponding d) gives rise to an orbit that closes up (i.e., gives an n-gon), then so does every point.
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Rhamnogalacturonan endolyase (, rhamnogalacturonase B, alpha-L- rhamnopyranosyl-(1->4)-alpha-D-galactopyranosyluronide lyase, Rgase B, rhamnogalacturonan alpha-L-rhamnopyranosyl-(1,4)-alpha-D- galactopyranosyluronide lyase, RG-lyase, YesW, RGL4, Rgl11A, Rgl11Y, RhiE) is an enzyme with systematic name alpha-L-rhamnopyranosyl-(1->4)-alpha-D- galactopyranosyluronate endolyase. This enzyme catalyses the following chemical reaction : Endotype eliminative cleavage of L-alpha- rhamnopyranosyl-(1->4)-alpha-D-galactopyranosyluronic acid bonds of rhamnogalacturonan I domains in ramified hairy regions of pectin leaving L-rhamnopyranose at the reducing end and 4-deoxy-4,5-unsaturated D-galactopyranosyluronic acid at the non-reducing end. The enzyme is part of the degradation system for rhamnogalacturonan I in Bacillus subtilis strain 168 and Aspergillus aculeatus.
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Assume that ƒ is finite. For a point P ∈ X, the ramification index eP is defined as follows. Let Q = ƒ(P) and let t be a local uniformizing parameter at P; that is, t is a regular function defined in a neighborhood of Q with t(Q) = 0 whose differential is nonzero. Pulling back t by ƒ defines a regular function on X. Then :e_P = v_P(t\circ f) where vP is the valuation in the local ring of regular functions at P. That is, eP is the order to which t\circ f vanishes at P. If eP > 1, then ƒ is said to be ramified at P. In that case, Q is called a branch point.
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The international cooperation of University "Ukraine" is ramified and integrated in European research and education process. The priority of the University is the elaboration of educational technologies and simultaneous social, educational, psychological and physical rehabilitation of students with special needs. In this field the University takes a positive experience of foreign colleagues including educators from the U.S.A. Because the U.S.A as well as all developed European countries has been deeply involved in addressing to the people with special needs for a long time. Particularly in matters of equal opportunities for education of healthy and disabled, rich and poor, educators of the University "Ukraine" see the meaning of international cooperation with foreign colleagues.
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Note that the foregoing proof of analyticity derived an expression for a system of n different function elements fi(x), provided that x is not a critical point of p(x, y). A critical point is a point where the number of distinct zeros is smaller than the degree of p, and this occurs only where the highest degree term of p vanishes, and where the discriminant vanishes. Hence there are only finitely many such points c1, ..., cm. A close analysis of the properties of the function elements fi near the critical points can be used to show that the monodromy cover is ramified over the critical points (and possibly the point at infinity).
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Schematic depiction of ramification: the fibers of almost all points in Y below consist of three points, except for two points in Y marked with dots, where the fibers consist of one and two points (marked in black), respectively. The map f is said to be ramified in these points of Y. In geometry, ramification is 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign. The term is also used from the opposite perspective (branches coming together) as when a covering map degenerates at a point of a space, with some collapsing of the fibers of the mapping.
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Given an arbitrary (n; m; p) machine S, such that every two states can be distinguished from each other, there exists an experiment of length n(n-1)/2 that identifies the state of S at the end of this experiment.'' In 1957 Karatsuba proved two theorems which completely solved the Moore problem on improving the estimate of the length of experiment in his Theorem 8. : Theorem A (Karatsuba). If S is a (n; m; p) machine such that each two its states can be distinguished from each other then there exists a ramified experiment of length at most , by means of which one can find the state S at the end of the experiment.
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Aleksandr Solzhenitsyn in his 1973 novel, The Gulag Archipelago characterized the enormous scope of the article in this way: > One can find more epithets in praise of this article than Turgenev once > assembled to praise the Russian language, or Nekrasov to praise Mother > Russia: great, powerful, abundant, highly ramified, multiform, wide sweeping > 58, which summed up the world not so much through the exact terms of its > sections as in their extended dialectical interpretation. > Who among us has not experienced its all-encompassing embrace? In all truth, > there is no step, thought, action, or lack of action under the heavens which > could not be punished by the heavy hand of Article 58.Aleksandr > Solzhenitsyn.
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Massa's helmet was blue with a fluorescent yellow X on the sides and a yellow triangle that covers the upper helmet with the top section coloured with a green gradient (prior to F1, this section was blue), in Ferrari early years until 2010, Massa's helmet featured also a white ring surrounding the top. In 2008 the tips of the fluoro yellow X were more ramified. In 2011 on the yellow triangle covered the entire upper front with 2 blue lines in the sides. For his 100th race with Ferrari at the 2011 Brazilian Grand Prix, Massa sported a chrome and gold prancing horse on the top with a further 100 horses representing the races Massa contested with Ferrari.
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The digestive organs include an anterior, terminal mouth, a spherical pharynx, an esophagus extending just posterior to the genital atrium, and a posterior intestine with two lateral branches ramified laterally and fusing in a single peduncle that extends into the haptor. Each adult contains male and female reproductive organs. The reproductive organs include an genital atrium, armed with numerous conical spines arranged in concentric circles, opening near anterior end, a single relatively long ovary, a uterus, vitelline glands that extends along both sides from the genital atrium to the beginning of the haptor and are joined posteriorly, and 13-24 testes which are posterior to the ovary. The eggs are elongate with a short filament at both poles.
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Between 1902 and 1908 Bertrand Russell proposed various "theories of type" in response to his discovery that Gottlob Frege's version of naive set theory was afflicted with Russell's paradox. By 1908 Russell arrived at a "ramified" theory of types together with an "axiom of reducibility" both of which featured prominently in Whitehead and Russell's Principia Mathematica published between 1910 and 1913. They attempted to resolve Russell's paradox by first creating a hierarchy of types, then assigning each concrete mathematical (and possibly other) entity to a type. Entities of a given type are built exclusively from entities of those types that are lower in their hierarchy, thus preventing an entity from being assigned to itself.
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Since Duke Bretislaus I of Bohemia had implemented the inheritance principle of agnatic seniority in the 11th century, the order of succession in Bohemia, many rivalling scions of the ramified Přemyslid dynasty waged war against each other. The claimants to the Prague throne sought for formal recognition by the Holy Roman Emperor, actually, the accession required the active support by the Bohemian nobility. The Přemyslid duke Vladislaus I of Bohemia, ruling since 1109, likewise had to struggle to consolidate his authority, defying the claims raised by his brother Bořivoj II who had reached his enfeoffment by Emperor Henry IV in 1101. When Vladislaus died in 1125 his succession was disputed among his surviving brother Soběslav I and his Moravian cousin Otto II, duke in Olomouc and Brno.
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This they called their "Ginger Group." After Milner's death in 1925, the leadership was largely shared by the survivors of Milner's "Kindergarten," that is, the group of young Oxford men whom he used as civil servants in his reconstruction of South Africa in 1901-1910. Brand was the last survivor of the "Kindergarten"; since his death, the greatly reduced activities of the organization have been exercised largely through the Editorial Committee of The Round Table magazine under Adam Marris. Money for the widely ramified activities of this organization came originally from the associates and followers of Cecil Rhodes, chiefly from the Rhodes Trust itself, and from wealthy associates such as the Beit brothers, from Sir Abe Bailey, and (after 1915) from the Astor family.
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He helped to advance the exact quantification of logic trees with a myriad of basic events via binary decision diagrams (BBD) and the modeling of human (crew)-system- interactions during accident scenarios by accident dynamic simulator (ADS) and discrete dynamical event trees (DDET). His reflections of limitations of PSA, based on "lessons learned from Fukushima disaster", gained international recognition. More recently, a project has been started to complement PSA by precursor analysis based on simplified generic models and data and by making use of a curated comprehensive open database with more than one thousand events which has been established for open online use. # He has pioneered the modeling and simulation of complex, widely ramified critical infrastructure networks and their interdependencies, turning them into "systems-of-systems", e.g.
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Another protection were the then widely ramified, sometimes almost impenetrable and marshy floodplain of the Upper RhineHöckmann: 1986 S. 415th and the presence of numerous meandering tributaries, which also considerably more difficult to approach the border zone.Bockius: 2006 S. 212th Furthermore, in a fight the Germanic tribes on the Rhine couldn't muster anything remotely equivalent to the Romans' highly developed river-going battleships. Had the invaders somehow managed to overcome all these difficulties, there was still the possibility that they could be intercepted at the very last moment back on the Rhine again on the return trip from one of their marauding attacks, and have all their booty confiscated, just to see it redistributed among the border soldiers who had taken part in the battle (see also ).
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Its vassals included the von Blumenthal family, whom it brought from Blumenthal in the diocese of Magdeburg to Blumenthal in the Prignitz. In the Middle Ages the family ramified throughout Northern Germany and numerous different branches descend from them - among others, the lines of von Plotho zu Grabow, Räckendorf, Codlewe and Zerben, and of particular note the Flanders branch of von Plotho zu Ingelmunster - many of which survive today. In 1643 Wolfgang Edler von Plotho was made a baron of the Holy Roman Empire by Emperor Ferdinand III for his military services. In modern times the family is best known for the fact that Elisabeth von Plotho (1853-1952) was the model for Effi Briest in Theodore Fontane's novel of that name.
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Citation: "[The] first historically documented Kolowrat, recognised by historians as the founder of the family, is Albrecht of Kolowrat the Elder († 1391). [...] He married three times and fathered eight children, six of them sons, laying the foundations of one of the most ramified among Czech aristocratic families." that had a prominent role in the history and administration of their native Kingdom of Bohemia as well as the Holy Roman Empire and later the Habsburg Monarchy as high-ranking officials and supporters of the Czech National Revival. The family origins are so far back in time that they are not recorded in any extant Bohemian historical documents. Only a few legends, such as those recounted by historians Bohuslav Balbín and František Palacký, give an account of those origins.
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Let X be the subvariety of C × D consisting of (c,d) such that ℓd passes through c. Given c, the number of d with (c,d) ∈ X is 1 if c ∈ C ∩ D and 2 otherwise. Thus the projection X → C ≃ P1 presents X as a degree 2 cover ramified above 4 points, so X is an elliptic curve (once we fix a base point on X). Let \sigma be the involution of X sending a general (c,d) to the other point (c,d′) with the same first coordinate. Any involution of an elliptic curve with a fixed point, when expressed in the group law, has the form x → p − x for some p, so \sigma has this form.
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The residue class ring modulo a Gaussian integer is a field if and only if z_0 is a Gaussian prime. If is a decomposed prime or the ramified prime (that is, if its norm is a prime number, which is either 2 or a prime congruent to 1 modulo 4), then the residue class field has a prime number of elements (that is, ). It is thus isomorphic to the field of the integers modulo . If, on the other hand, is an inert prime (that is, is the square of a prime number, which is congruent to 3 modulo 4), then the residue class field has elements, and it is an extension of degree 2 (unique, up to an isomorphism) of the prime field with elements (the integers modulo ).
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Now assume that S and S' are Riemann surfaces, and that the map \pi is complex analytic. The map \pi is said to be ramified at a point P in S′ if there exist analytic coordinates near P and π(P) such that π takes the form π(z) = zn, and n > 1\. An equivalent way of thinking about this is that there exists a small neighborhood U of P such that π(P) has exactly one preimage in U, but the image of any other point in U has exactly n preimages in U. The number n is called the ramification index at P and also denoted by eP. In calculating the Euler characteristic of S′ we notice the loss of eP − 1 copies of P above π(P) (that is, in the inverse image of π(P)).
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Now assume that S and S′ are Riemann surfaces, and that the map π is complex analytic. The map π is said to be ramified at a point P in S′ if there exist analytic coordinates near P and π(P) such that π takes the form π(z) = zn, and n > 1\. An equivalent way of thinking about this is that there exists a small neighborhood U of P such that π(P) has exactly one preimage in U, but the image of any other point in U has exactly n preimages in U. The number n is called the ramification index at P and also denoted by eP. In calculating the Euler characteristic of S′ we notice the loss of eP − 1 copies of P above π(P) (that is, in the inverse image of π(P)).
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TEK seceded from the first established college in Hungary, the Rajk László College for Advanced Studies. However, in the beginning - before the fall of the Iron Curtain - the College's main topic was the reinterpretation of Marx's ouvre, since liberal and alternative thinking was only possible if it was related to Marxist studies. With the fall of the iron curtain, this coercion disappeared, and since the College's main profile was its diversity and openness to new ideas, philosophies and theories, the College's profile now freely and rapidly ramified into diverse - and pioneering among the Hungarian colleges at that time - topics: environmentalism, sustainability, postmodernism, anarchism, postmarxism, sociolinguistics, phenomenology, post-structuralism, Buddhist economics, feminism, sociology of minorities, queer studies, postcolonialism, network theory. The College also dealt with the topic of squatting, the sociological causes of poverty and since the establishment the farmost detailed analysis of critical theory/Frankfurt school among other colleges.
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More precisely, let V be an algebraic variety over K (assumptions here are: V is an irreducible set, a quasi-projective variety, and K has characteristic zero). A type I thin set is a subset of V(K) that is not Zariski-dense. That means it lies in an algebraic set that is a finite union of algebraic varieties of dimension lower than d, the dimension of V. A type II thin set is an image of an algebraic morphism (essentially a polynomial mapping) φ, applied to the K-points of some other d-dimensional algebraic variety V′, that maps essentially onto V as a ramified covering with degree e > 1. Saying this more technically, a thin set of type II is any subset of :φ(V′(K)) where V′ satisfies the same assumptions as V and φ is generically surjective from the geometer's point of view.
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In abstract algebra, Abhyankar's conjecture is a 1957 conjecture of Shreeram Abhyankar, on the Galois groups of algebraic function fields of characteristic p.. The soluble case was solved by Serre in 1990 and the full conjecture was proved in 1994 by work of Michel Raynaud and David Harbater... The problem involves a finite group G, a prime number p, and the function field K(C) of a nonsingular integral algebraic curve C defined over an algebraically closed field K of characteristic p. The question addresses the existence of a Galois extension L of K(C), with G as Galois group, and with specified ramification. From a geometric point of view, L corresponds to another curve C′, together with a morphism :π : C′ → C. Geometrically, the assertion that π is ramified at a finite set S of points on C means that π restricted to the complement of S in C is an étale morphism. This is in analogy with the case of Riemann surfaces.
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28 November 2016 The British historian and social writer, William Lecky (1880), notes that around 1200 AD: "Christianity for the first time made charity a rudimentary virtue, giving it a leading place in the moral type, and in the exhortation of its teachers. Besides its general influence in stimulating the affections, it effected a complete revolution in this sphere, by regarding the poor as the special representatives of the Christian Founder, and thus making the love of Christ, rather than the love of man the principle of charity... A vast organization of charity, presided over by Bishops, and actively directed by the deacons, soon ramified over Christendom, till the bond of charity became the bond of unity, and the most distant sections of the Christian Church corresponded by the interchange of mercy." The quote above reflects the start of organized charitable work in the Christian world in the Middle Ages. It was a major break in theological thinking and it was brokered by the Catholic Church.
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As Stewart Shapiro explains in his Thinking About Mathematics, Russell's attempts to solve the paradoxes led to the ramified theory of types, which, though it is highly complex and relies on the doubtful axiom of reducibility, actually manages to solve both syntactic and semantic paradoxes at the expense of rendering the logicist project suspect and introducing much complexity in the PM system. Philosopher and logician F.P. Ramsey would later simplify the theory of types arguing that there was no need to solve both semantic and syntactic paradoxes to provide a foundation for mathematics. The philosopher and logician George Boolos discusses the power of the PM system in the preface to his Logic, logic & logic, stating that it is powerful enough to derive most classical mathematics, equating the power of PM to that of Z, a weaker form of set theory than ZFC (Zermelo-Fraenkel Set theory with Choice). In fact, ZFC actually does circumvent Russell's paradox by restricting the comprehension axiom to already existing sets by the use of subset axioms.
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