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Glossary of classical algebraic geometry-Q-quarto-quartic A Quarto-quartic transformation is a Cremona transformation such that the homaloids of the transformation and its inverse all have degree 4. (Semple & Roth 1949, p.187) quaternary Depending on four variables, as in quaternary form.
quartic Degree 4, especially a... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-R-ramphoid Beak-like. A ramphoid cusp is one whose two branches curve in the same direction; see keratoid cusp. Salmon (1879, p.46) rank 1. The rank of a projective curve is the number of tangents to the curve meeting a generic linear subspace of codimension 2. (Semple & Roth 19... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-R-range 1. The set of all points on a line. (Coxeter 1969, p.242) 2. A labeled or finite ordered set of points on a line.
rational 1. Birational to projective space.
2. Defined over the rational numbers.
ray A line, especially one in a family of lines regular 1. A regular surfac... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-R-resultant 1. The resultant of two polynomials, given by the determinant of the Sylvester matrix of two binary forms, that vanishes if they have a common root. 2. A Cremona transformation formed from n correlations of n-dimensional projective space. (Semple & Roth 1949, p.180)... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-S-Sn Projective space of dimension n. | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-S-Salmon conic The Salmon conic of a pair of plane conics is the locus of points such that the pairs of tangents to the two conics are harmonically conjugate. (Dolgachev 2012, p. 119) satellite 1. If a line meets a cubic curve in 3 points, the residual intersections of the tang... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-S-2. A certain plane curve of degree (n–1)(n–2) constructed from a plane curve of degree n and a generic point. (Coolidge 1931, p. 159–161) 3. For satellite points see (Zariski 1935, p.8). Possibly something to do with base points. scroll A ruled surface with an embedding into... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-S-secant 1. A line intersecting a variety in 2 points, or more generally an n-dimensional projective space meeting a variety in n+1 points.
2. A secant variety is the union of the secants of a variety.
second kind All residues at poles are zero secundum An intersection of two pr... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-S-3. A self-conjugate tetrad is a set of 4 points such that the pole of each side lies on the opposite side. (Dolgachev 2012, p.123) septic septimic 1. (Adjective) Degree 7 2. (Noun) A degree 7 projective variety 3. (Noun) A degree 7 form sextactic point One of the 27 points of... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-S-singular Special in some way, including but not limited to the current sense of having a singularity skew Intersecting in a set that is either empty or of the "expected" dimension. For example skew lines in projective 3-space do not intersect, while skew planes in projective 4... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-S-symmetroid The zeros of the determinant of a symmetric matrix of linear forms syntheme A partition of a set of 6 elements into 3 pairs, or an element of the symmetric group on 6 points of cycle shape 222. (Dolgachev 2012) system A family of algebraic sets in projective space; ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-S-syzygetic Paired. Opposite of azygetic, meaning unpaired. Example: syzygetic triad, syzygetic tetrad, syzygetic set, syzygetic pencil.
syzygy 1. A point is in syzygy with some other points if it is in the linear subspace generated by them. (Baker 1922a, vol 1, p. 33) A syzygy ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-T-tacnode A tacnode is a point of a curve where two branches meet in the same direction. (Cayley 1852) tacnode-cusp A singularity of a plane curve where a tacnode and a cusp are combined at the same point. (Salmon 1879, p.207) tact-invariant An invariant of two curves that vanis... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-T-twisted A twisted cubic is a degree 3 embedding of the projective line in projective 3-space total A set of 5 partitions of a 6-element set into three pairs, such that no two elements of the total have a pair in common. For example, {(12)(36)(45), (13)(24)(56), (14)(26)(35), (... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-U-undulation A point of undulation of a curve is where the tangent meets the curve to fourth order; also called a hyperflex. See inflection point. (Salmon 1879, p.35, 211) unibranch Having only one branch at a point. For example, a cusp of a plane curve is unibranch, while a nod... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-V-valence valency The valence or valency of a correspondence T on a curve is a number k such that the divisors T(P)+kP are all linearly equivalent. A correspondence need not have a valency. (Semple & Roth 1949, p.368) Veronese surface An embedding of the projective plane in 5-di... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-V-virtual An estimate for something that is often but not always correct, such as virtual genus, virtual dimension, and so on. If some number is given by the dimension of a space of sections of some sheaf, the corresponding virtual number is sometimes given by the corresponding ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-W-web A 3-dimensional linear system. See "net" and "pencil". (Semple & Roth 1949, p.160) Weddle surface A quartic surface in projective space given by the locus of the vertex of a cone passing through 6 points in general position.
Weierstrass point A point on a curve where the d... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-XYZ-Zeuthen–Segre invariant The Zeuthen–Segre invariant is 4 less than the Euler characteristic of a non-singular projective surface. | milkshake721/2.1M-wiki-STEM |
ELOB-ELOB-Elongin B is a protein that in humans is encoded by the ELOB gene. | milkshake721/2.1M-wiki-STEM |
ELOB-Function-Elongin B is a subunit of the transcription factor B (SIII) complex. The SIII complex is composed of elongins A/A2, B and C. It activates elongation by RNA polymerase II by suppressing transient pausing of the polymerase at many sites within transcription units. Elongin A functions as the transcriptionall... | milkshake721/2.1M-wiki-STEM |
ELOB-Interactions-TCEB2 has been shown to interact with: CUL2, TCEB1, and Von Hippel-Lindau tumor suppressor. | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process miniaturization-Chemical process miniaturization refers to a philosophical concept within the discipline of process design that challenges the notion of "economy of scale" or "bigger is better". In this context, process design refers to the discipline taught primarily to chemical enginee... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process miniaturization-One of the challenges of chemical engineering has been to design processes based on chemical laboratory-scale methods, and to scale-up processes so that products can be manufactured that are economically affordable. | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process miniaturization-As a process becomes larger, more product can be produced per unit time, so when a process technology becomes established or mature, and operates consistently without upsets or “downtime”, more economic efficiency can be gained from scale-up. Given a fixed price for the f... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process miniaturization-The economy of scale concept, as taught to chemical engineers, has led to the notion that one of the objectives of process development and design is to achieve “economy of scale” by scaling-up to the largest possible size processing plant so that the product cost can be e... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process miniaturization-Fluids, by definition are materials that flow and can be transferred using pumps or gravity. Therefore, large pumps, valves, and pipelines exist to transfer large amounts of fluids in the process industries. Process miniaturization, in contrast, will involve processing of... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process miniaturization-The concept of a microprocess has been defined by S. S. Sofer while a professor at the New Jersey Institute of Technology. A microprocess has the following characteristics: 1) Portability 2) Capable of being mass produced using advanced robotic manufacturing methods 3) Ap... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Miniaturization of Electronic Devices-The microprocess design philosophy has been largely envisioned by historical analysis of the role that component miniaturization has played in the information technology industry. It is the evolution of the miniaturization of computer hardware that has enabl... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Miniaturization of Electronic Devices-Electrical and electronic devices have always played an important role in chemical process plant automation. However, initially, simple thermometers such as those containing mercury, and pressure gauges which were completely mechanical in nature were used to... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Miniaturization of Electronic Devices-Process control of the future will involve the widespread utilization of intelligent sensors, and mass-produced intelligent miniaturized devices such as programmable logic controllers that communicate wirelessly to process actuators. Since these devices will... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Miniaturization of Electronic Devices-The intelligence of the process will be developed using process simulation models based on scientific fundamentals. Heuristic rules will be programmed into the micro-controllers, which will largely eliminate the need for constant monitoring by human heuristi... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process Miniaturization for Knowledge-based Businesses-Advanced process control systems for process miniaturization will increase the need for controlling the security and ownership of process intelligence in a knowledge-based business. It will become more difficult to control intellectual prope... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process Miniaturization for Knowledge-based Businesses-Techno-economic analysis, as taught in traditional chemical process design, will also dramatically shift from a conservative viewpoint of utilization of historical trend economics and cash flow analysis. Economic viability of a given enterpr... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process Miniaturization for Future Societies Based on Renewable Materials-Rather than one large central plant, that has to be fed a large amount of feedstock, such as a refinery that can unload a tanker shipment of petroleum if located next to an ocean, the discipline of process miniaturization ... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process Miniaturization for Future Societies Based on Renewable Materials-Historically, small processes or microprocesses per se have always existed. For example, small vineyards and breweries have produced feedstock, processed it, and stored product in what could be considered “microprocess” wh... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process Miniaturization for Future Societies Based on Renewable Materials-The design philosophy of process miniaturization envisions that “scale-down” of complex processes involving multiple process unit operations can be achieved, and that economy of scale will be more related to the size of a ... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process Miniaturization for Future Societies Based on Renewable Materials-Since fossil fuels by definition are being consumed and are non-renewable, future fuel and materials will be based on renewable biomass. | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process Miniaturization for Microbial Fuel Cells-The conversion of biomass into energy is perhaps more challenging to the technologist than energy from fossil fuels. Water, dissolved organic and inorganic compounds, and solid particulates of various size can be present in biomass processes. It i... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process Miniaturization for Microbial Fuel Cells-The challenges of microbial fuel cells relate mainly to finding lower cost manufacturing methods, materials of construction, and systems design. Bruce Logan from the Penn State University has described in several research articles and reviews thes... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process Miniaturization for mini Nuclear Reactors-Nuclear power is considered "green technology" in that it does not produce carbon dioxide, a green house gas, as do traditional natural gas or coal-fired power plants. The economics of the deployment of mini nuclear reactors has been discussed in... | milkshake721/2.1M-wiki-STEM |
Process miniaturization-Process Miniaturization for mini Nuclear Reactors-The advantages of mini nuclear reactors has also been discussed by Secretary of Energy, Steven Chu. As discussed by Chu, the reactors would be manufactured in a factory-like situation and then transported, intact by rail or ship to different part... | milkshake721/2.1M-wiki-STEM |
Living Reviews (journal series)-Living Reviews (journal series)-Living Reviews is an open access journal series, which publishes regularly updated peer-reviewed review articles in various fields of science. Its concept of "living" articles takes advantage of web-based electronic publishing and allows authors to update ... | milkshake721/2.1M-wiki-STEM |
Living Reviews (journal series)-Living Reviews (journal series)-The concept of Living Reviews was developed by Bernard Schutz and Jennifer Wheary, who started the first journal, Living Reviews in Relativity, in 1998 at the Max Planck Institute for Gravitational Physics. The series now contains three entries Living Revi... | milkshake721/2.1M-wiki-STEM |
Field lens-Field lens-In imaging optics, a field lens is a positive-powered lens or group of lenses that comes after the objective lens and before the image plane or the eyepiece, serving to change the size of the image or to provide image-space telecentricity. It is used for the reduction of detector size and, in inst... | milkshake721/2.1M-wiki-STEM |
Field lens-Field lens-In X-Ray microscopy, the field lens is used to produce parallel and homogeneous illumination of the stencil. | milkshake721/2.1M-wiki-STEM |
EaseUS Partition Master-EaseUS Partition Master-EaseUS Partition Master is a disk partition software that allows users to manage hard disk drives or solid-state drives on the 32-bit or 64-bit Windows PCs and Windows servers. | milkshake721/2.1M-wiki-STEM |
EaseUS Partition Master-Overview-Created by EaseUS Software, the program was initially released in 2006. It comes in three versions: Home, Professional, and Enterprise. It performs tasks that Windows default device manager doesn't offer, including disk surface test, hiding partitions, re-building MBR, and WinPE boot di... | milkshake721/2.1M-wiki-STEM |
Signal velocity-Signal velocity-The signal velocity is the speed at which a wave carries information. It describes how quickly a message can be communicated (using any particular method) between two separated parties. No signal velocity can exceed the speed of a light pulse in a vacuum (by Special Relativity). Signal ... | milkshake721/2.1M-wiki-STEM |
Signal velocity-Signal velocity-vs=cεrμr≈cεr where εr is the relative permittivity of the medium, μr is the relative permeability of the medium, and c is the speed of light in vacuum. The approximation shown is used in many practical context because for most common materials μr≈1 | milkshake721/2.1M-wiki-STEM |
Flyte (chocolate bar)-Flyte (chocolate bar)-Flyte was a chocolate bar manufactured by Mars, Incorporated weighing 45 grams. The product was introduced in 1996.Each bar came wrapped in two individual halves. It consisted of a chocolatey, whipped nougat-style centre coated in milk chocolate. It was essentially the same a... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Industrial water treatment-There are many uses of water in industry and, in most cases, the used water also needs treatment to render it fit for re-use or disposal. Raw water entering an industrial plant often needs treatment to meet tight quality specifications to be of use in specific indus... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Overview-Water treatment is used to optimize most water-based industrial processes, such as heating, cooling, processing, cleaning, and rinsing so that operating costs and risks are reduced. Poor water treatment lets water interact with the surfaces of pipes and vessels which contain it. Stea... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Objectives-Industrial water treatment seeks to manage four main problem areas: scaling, corrosion, microbiological activity and disposal of residual wastewater. Boilers do not have many problems with microbes as the high temperatures prevent their growth. | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Objectives-Scaling occurs when the chemistry and temperature conditions are such that the dissolved mineral salts in the water are caused to precipitate and form solid deposits. These can be mobile, like a fine silt, or can build up in layers on the metal surfaces of the systems. Scale is a p... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Objectives-Corrosion occurs when the parent metal oxidises (as iron rusts, for example) and gradually the integrity of the plant equipment is compromised. The corrosion products can cause similar problems to scale, but corrosion can also lead to leaks, which in a pressurised system can lead t... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Objectives-Microbes can thrive in untreated cooling water, which is warm and sometimes full of organic nutrients as wet cooling towers are very efficient air scrubbers. Dust, flies, grass, fungal spores, and others collect in the water and create a sort of "microbial soup" if not treated with... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Disposal of residual industrial wastewaters-Disposal of residual wastewaters from an industrial plant is a difficult and costly problem. Most petroleum refineries, chemical and petrochemical plants have onsite facilities to treat their wastewaters so that the pollutant concentrations in the t... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Processes-Two of the main processes of industrial water treatment are boiler water treatment and cooling water treatment. A large amount of proper water treatment can lead to the reaction of solids and bacteria within pipe work and boiler housing. Steam boilers can suffer from scale or corros... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Processes-Corrosion in low pressure boilers can be caused by dissolved oxygen, acidity and excessive alkalinity. Water treatment therefore should remove the dissolved oxygen and maintain the boiler water with the appropriate pH and alkalinity levels. Without effective water treatment, a cooli... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Processes-Boiler water treatment Boiler water treatment is a type of industrial water treatment focused on removal or chemical modification of substances potentially damaging to the boiler. Varying types of treatment are used at different locations to avoid scale, corrosion, or foaming. Exter... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Processes-Cooling water treatment Water cooling is a method of heat removal from components of machinery and industrial equipment. Water may be a more efficient heat transfer fluid where air cooling is ineffective. In most occupied climates water offers the thermal conductivity advantages of ... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Technologies-Advancements in water treatment technology have affected all areas of industrial water treatment. Although mechanical filtration, such as reverse osmosis, is widely employed to filter contaminants, other technologies including the use of ozone generators, wastewater evaporation, ... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Technologies-Chemical treatment Chemical treatments utilizes the additive of chemicals to make industrial water suitable for use or discharge. These includes processes like chemical precipitation, chemical disinfection, Advanced oxidation process (AOP), ion exchange, and chemical neutralizati... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Technologies-Physical treatment Physical treatment involves the separation of solids form industrial wastewater either through Filtration or Dissolved air flotation. Filtration involves the use of Membrane or filters such as mechanical filters like sand filtration etc to achieve solid-liquid ... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Technologies-Biological treatment Biological treatment is needed to treat wastewater containing biodegradable elements. It is commonly used in municipal and industrial wastewater management facilities and usually consists in adding common bacteria and other microbes, mostly environmentally fr... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Technologies-Slow sand filters use a biological process to purify raw water to produce potable water. They work by using a complex biological film that grows naturally on the surface of sand. This gelatinous biofilm called the hypogeal layer or Schmutzdecke is located in the upper few millime... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Technologies-Ultraviolet irradiation Ultraviolet (UV) disinfection technology has been a common water treatment technology in the past two decades due to its ability to provide disinfected water without the use of harmful chemicals. The UV-C portion represents wavelengths from 200 nm - 280 nm... | milkshake721/2.1M-wiki-STEM |
Industrial water treatment-Technologies-Process water treatment technology Process water is water that is used in a variety of manufacturing operations, such as: coating and plating; rinsing and spraying; washing, etc. Municipal and ground water often contain dissolved minerals which make it unsuitable for these proces... | milkshake721/2.1M-wiki-STEM |
Facies (medical)-Facies (medical)-In medical contexts, a facies is a distinctive facial expression or appearance associated with a specific medical condition. The term comes from Latin for "face". As a fifth declension noun, facies can be both singular and plural. | milkshake721/2.1M-wiki-STEM |
Facies (medical)-Types-Examples include: Hippocratic facies – eyes are sunken, temples collapsed, nose is pinched with crusts on the lips, and the forehead is clammy Moon face (also known as "Cushingoid facies") – Cushing's syndrome Elfin facies – Williams syndrome Potter facies – oligohydramnios Mask like facies – par... | milkshake721/2.1M-wiki-STEM |
Facies (medical)-Types-Lion-like facies – involvement of craniofacial bones in Paget disease of Bone Chipmunk facies – beta thalassemia Treacher Collins syndrome – deformities of the ears, eyes, cheekbones, and chin | milkshake721/2.1M-wiki-STEM |
Facies (medical)-Other disorders associated with syndromic facies-Pitt–Hopkins syndrome Beta thalassemia is associated with distinctive facial features due to ineffective erythropoiesis. The ineffective erythropoiesis causes marrow hyperplasia or expansion and bony changes, including the bones of the face; this causes ... | milkshake721/2.1M-wiki-STEM |
Voder-Voder-The Bell Telephone Laboratory's Voder (from Voice Operating Demonstrator) was the first attempt to electronically synthesize human speech by breaking it down into its acoustic components. It was invented by Homer Dudley in 1937–1938 and developed on his earlier work on the vocoder. The quality of the speech... | milkshake721/2.1M-wiki-STEM |
Voder-Voder-The Voder synthesized human speech by imitating the effects of the human vocal tract. The operator could select one of two basic sounds by using a wrist bar. A buzz tone generated by a relaxation oscillator produced the voiced vowels and nasal sounds, with the pitch controlled by a foot pedal. A hissing noi... | milkshake721/2.1M-wiki-STEM |
Voder-Voder-Performances on the Voder were featured at the 1939 New York World's Fair and in San Francisco. Twenty operators were trained by Helen Harper, particularly noted for her skill with the machine. The machine said the words "Good afternoon, radio audience."The Voder was developed from research into compression... | milkshake721/2.1M-wiki-STEM |
Voder-Voder-Whereas the vocoder analyzes speech, transforms it into electronically transmitted information, and recreates it, the voder generates synthesized speech by means of a console with fifteen touch-sensitive keys and a pedal. It basically consists of the "second half" of the vocoder, but with manual filter cont... | milkshake721/2.1M-wiki-STEM |
Central core disease-Central core disease-Central core disease (CCD), also known as central core myopathy, is an autosomal dominantly inherited muscle disorder present from birth that negatively affects the skeletal muscles. It was first described by Shy and Magee in 1956. It is characterized by the appearance of the m... | milkshake721/2.1M-wiki-STEM |
Central core disease-Signs and symptoms-The symptoms of CCD are variable, but usually involve hypotonia (decreased muscle tone) at birth, mild delay in child development (highly variable between cases), weakness of the facial muscles, and skeletal malformations such as scoliosis and hip dislocation.CCD is usually diagn... | milkshake721/2.1M-wiki-STEM |
Central core disease-Pathophysiology-Central core disease is inherited in an autosomal dominant fashion. Most cases have demonstrable mutations in the ryanodine receptor type 1 (RYR1) gene, which are often de novo (newly developed). People with CCD are at increased risk for developing malignant hyperthermia (MH) when r... | milkshake721/2.1M-wiki-STEM |
Central core disease-Diagnosis-The diagnosis is made based on the combination of typical symptoms and the appearance on biopsy (tissue sample) from muscle. The name derives from the typical appearance of the biopsy on light microscopy, where the muscle cells have cores that are devoid of mitochondria and specific enzym... | milkshake721/2.1M-wiki-STEM |
Central core disease-Treatment-There is no specific treatment but triggering anesthetics are avoided and relatives are screened for RYR1 mutations as these may make them susceptible to MH. | milkshake721/2.1M-wiki-STEM |
Cognate object-Cognate object-In linguistics, a cognate object (or cognate accusative) is a verb's object that is etymologically related to the verb. More specifically, the verb is one that is ordinarily intransitive (lacking any object), and the cognate object is simply the verb's noun form. For example, in the senten... | milkshake721/2.1M-wiki-STEM |
Cognate object-Examples-In English, the construction can occur with a number of intransitive verbs, which then become transitive: He slept a troubled sleep. (He slept, and his sleep was troubled.) He laughed a bitter laugh. (He laughed bitterly.) He dreamed a strange dream. (He dreamed, and his dream was strange.) He w... | milkshake721/2.1M-wiki-STEM |
Hardy–Littlewood Tauberian theorem-Hardy–Littlewood Tauberian theorem-In mathematical analysis, the Hardy–Littlewood Tauberian theorem is a Tauberian theorem relating the asymptotics of the partial sums of a series with the asymptotics of its Abel summation. In this form, the theorem asserts that if the sequence an≥0 i... | milkshake721/2.1M-wiki-STEM |
Hardy–Littlewood Tauberian theorem-Hardy–Littlewood Tauberian theorem-The theorem was proved in 1914 by G. H. Hardy and J. E. Littlewood.: 226 In 1930, Jovan Karamata gave a new and much simpler proof.: 226 | milkshake721/2.1M-wiki-STEM |
Hardy–Littlewood Tauberian theorem-Statement of the theorem-Series formulation This formulation is from Titchmarsh.: 226 Suppose an≥0 for all n∈N , and we have as 1.
Then as n→∞ we have ∑k=0nak∼n.
The theorem is sometimes quoted in equivalent forms, where instead of requiring an≥0 , we require an=O(1) , or we req... | milkshake721/2.1M-wiki-STEM |
Hardy–Littlewood Tauberian theorem-Statement of the theorem-Here Γ denotes the Gamma function. One obtains the theorem for series as a special case by taking ρ=1 and F(t) to be a piecewise constant function with value ∑k=0nak between t=n and t=n+1 A slight improvement is possible. According to the definition of a... | milkshake721/2.1M-wiki-STEM |
Hardy–Littlewood Tauberian theorem-Karamata's proof-Karamata (1930) found a short proof of the theorem by considering the functions g such that lim x→1(1−x)∑anxng(xn)=∫01g(t)dt An easy calculation shows that all monomials g(x)=xk have this property, and therefore so do all polynomials g . This can be extended to a f... | milkshake721/2.1M-wiki-STEM |
Hardy–Littlewood Tauberian theorem-Examples-Non-positive coefficients The theorem can fail without the condition that the coefficients are non-negative. For example, the function 1(1+x)2(1−x)=1−x+2x2−2x3+3x4−3x5+⋯ is asymptotic to 1/4(1−x) as x→1 , but the partial sums of its coefficients are 1, 0, 2, 0, 3, 0, 4, ...... | milkshake721/2.1M-wiki-STEM |
Hardy–Littlewood Tauberian theorem-Examples-This came historically before the Hardy–Littlewood Tauberian theorem, but can be proved as a simple application of it.: 233–235 Prime number theorem In 1915 Hardy and Littlewood developed a proof of the prime number theorem based on their Tauberian theorem; they proved ∑n=2∞Λ... | milkshake721/2.1M-wiki-STEM |
Hardy–Littlewood Tauberian theorem-Notes-Karamata, J. (December 1930). "Über die Hardy-Littlewoodschen Umkehrungen des Abelschen Stetigkeitssatzes". Mathematische Zeitschrift (in German). 32 (1): 319–320. doi:10.1007/BF01194636. | milkshake721/2.1M-wiki-STEM |
Wind turbines on public display-Wind turbines on public display-The great majority of wind turbines around the world belong to individuals or corporations who use them to generate electric power or to perform mechanical work. As such, wind turbines are primarily designed to be working devices. However, the large size a... | milkshake721/2.1M-wiki-STEM |
Wind turbines on public display-Notable wind turbines on public display-AustraliaBlayney Wind Farm, New South Wales has a viewing area and interpretive centre Wattle Point Wind Farm, South Australia has an information centre Albany Wind Farm has board walks, viewing towers, interpretive displays and picnic areas on and... | milkshake721/2.1M-wiki-STEM |
Wind turbines on public display-Notable wind turbines on public display-Green Park Business Park has an Enercon E-70 2 MW wind turbine adjacent to the M4 motorway, billed as the UK's most visible turbine Renewable Energy Systems has a Vestas V29 225 kW wind turbine visible from the M25 motorway at its headquarters at B... | milkshake721/2.1M-wiki-STEM |
Wind turbines on public display-Notable wind turbines on public display-Dorchester, Massachusetts – Local 103 of the International Brotherhood of Electrical Workers installed the first commercial-scale wind turbine within the City of Boston, a 100 kW unit from Fuhrlaender on a 35-meter tower with rotor diameter of 21 m... | milkshake721/2.1M-wiki-STEM |
Wind turbines on public display-Notable wind turbines on public display-Dorchester, Massachusetts - Local 103 of the International Brotherhood of Electrical Workers installed the first commercial-scale wind turbine within the City of Boston, a 100 kW unit from Fuhrlaender on a 35-meter tower with rotor diameter of 21 m... | milkshake721/2.1M-wiki-STEM |
Wind turbines on public display-Notable wind turbines on public display-Lubbock, Texas has a Vestas V47 at the American Wind Power Center McKinney, Texas has a Wal-Mart store with several sustainability features, including two wind turbines manufactured by Bergey Windpower, of 1 kW and 50 kW nameplate capacity respecti... | milkshake721/2.1M-wiki-STEM |
Wind turbines on public display-Observation deck-Some wind turbines on public display go one further, with observation decks beneath their nacelles. The observation decks are accessed with stairs inside the tower. | milkshake721/2.1M-wiki-STEM |
Wind turbines on public display-Observation deck-AustriaWind turbine at Pesendorf, Lichtenegg, Lower Austria. Type Enercon E-66 One turbine at the wind farm Energiepark near Bruck an der Leitha, Type Enercon E-66CanadaGrouse Mountain Resorts in North Vancouver, British Columbia installed a Leitwind 1.5MW wind turbine w... | milkshake721/2.1M-wiki-STEM |
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