id stringlengths 14 14 | text stringlengths 9 3.55k | source stringlengths 1 250 |
|---|---|---|
c_m4ryfbylahen | Molecular modeling software often provides graphical images of electron density. For example, in aniline (see image at right). | Electronic density |
c_p2rnc1zel4pm | Graphical models, including electron density are a commonly employed tool in chemistry education. Note in the left-most image of aniline, high electron densities are associated with the carbons and nitrogen, but the hydrogens with only one proton in their nuclei, are not visible. This is the reason that X-ray diffracti... | Electronic density |
c_dcjr7e5bj41g | Most molecular modeling software packages allow the user to choose a value for the electron density, often called the isovalue. Some software also allows for specification of the electron density in terms of percentage of total electrons enclosed. Depending on the isovalue (typical units are electrons per cubic bohr), ... | Electronic density |
c_dnaywdoubtcd | The electrostatic potential map (the property of electrostatic potential mapped upon the electron density) provides an indicator for charge distribution in a molecule. The local ionisation potential map (the property of local ionisation potential mapped upon the electron density) provides an indicator of electrophilici... | Electronic density |
c_p741oo57wohh | In molecules, the nonadiabatic couplings between two adiabatic potentials build the avoided crossing (AC) region. The rovibronic resonances in the AC region of two-coupled potentials are very special, since they are not in the bound state region of the adiabatic potentials, and they usually do not play important roles ... | Feshbach resonance |
c_7orbir8a9bzn | Exemplified in particle scattering, resonances in the AC region are comprehensively investigated. The effects of resonances in the AC region on the scattering cross sections strongly depend on the nonadiabatic couplings of the system, it can be very significant as sharp peaks, or inconspicuous buried in the background.... | Feshbach resonance |
c_a55effc9rkwo | In molecules, the situation becomes more complex, as each molecule has a different orbital structure. The molecular orbitals are labelled according to their symmetry, rather than the atomic orbital labels used for atoms and monatomic ions: hence, the electron configuration of the dioxygen molecule, O2, is written 1σg2 ... | Noble gas configuration |
c_16zkh27u0h5n | From Hund's rules, these electrons have parallel spins in the ground state, and so dioxygen has a net magnetic moment (it is paramagnetic). The explanation of the paramagnetism of dioxygen was a major success for molecular orbital theory. The electronic configuration of polyatomic molecules can change without absorptio... | Noble gas configuration |
c_5ttceavydu6i | In momentum transfer, the fluid is treated as a continuous distribution of matter. The study of momentum transfer, or fluid mechanics can be divided into two branches: fluid statics (fluids at rest), and fluid dynamics (fluids in motion). When a fluid is flowing in the x-direction parallel to a solid surface, the fluid... | Momentum flux |
c_p0ocz9uqbz91 | Hence the x-directed momentum has been transferred in the z-direction from the faster- to the slower-moving layer. The equation for momentum transfer is Newton's law of viscosity written as follows: τ z x = − ν ∂ ρ υ x ∂ z {\displaystyle \tau _{zx}=-\nu {\frac {\partial \rho \upsilon _{x}}{\partial z}}} where τzx is th... | Momentum flux |
c_8vh3dkeq994l | In monarchies with either an uncodified or partly unwritten constitution (such as the United Kingdom or Canada) or a wholly written constitution that consists of a text augmented by additional conventions, traditions, letters patent, etc., the monarch generally possesses reserve powers. Typically these powers are: to g... | Discretionary power |
c_ulps29kv96kf | Most constitutional monarchies employ a system that includes the principle of responsible government. In such an order, the reserve powers are thought to be the means by which the monarch and his or her viceregal representatives can legitimately exist as "constitutional guardians" or "umpires", tasked with guaranteeing... | Discretionary power |
c_6w26axcdyy4a | In monastic houses, monks were expected to pray the Divine Office daily in Latin, the liturgical language of the Western Christian Church. Christian monastics, in addition to clergymen, "recited or chanted the 150 Psalms as a major source of hourly worship." To count these repetitions, they used beads strung upon a cor... | Rosary based prayers |
c_k4ifc3pcct7c | Lay people adopted this practice as a form of popular worship. In the eighth century the penitentials, or rule books pertaining to penitents, prescribed various penances of twenty, fifty, or more, paters. | Rosary based prayers |
c_s5u57biz7rek | The strings of beads, with the aid of which such penances were accurately said, gradually came to be known as paternosters. The Paternoster could be of various lengths, but was often made up of 5 "decades" of 10 beads, which when performed three times made up 150 prayers. Today, some Anglican religious orders, such as ... | Rosary based prayers |
c_4f1jotbme28p | In monetary economics, a money multiplier is one of various closely related ratios of commercial bank money to central bank money (also called the monetary base) under a fractional-reserve banking system. It relates to the maximum amount of commercial bank money that can be created, given a certain amount of central ba... | Money multiplier |
c_g3pg5vup4yaq | The actual ratio of money to central bank money, also called the money multiplier, is lower because some funds are held by the non-bank public as currency. Also, banks may hold excess reserves, being reserves above the reserve requirement set by the central bank.Although the money multiplier concept is a traditional po... | Money multiplier |
c_cg35fivyjmi4 | The Federal Reserve, Bank of England, Deutsche Bundesbank, and the Standard & Poor's rating agency have issued criticisms of the concept's use. Several countries (such as Canada, the UK, Australia and Sweden) set no legal reserve requirements. The same is true for the United States since March 2020. | Money multiplier |
c_0gkgoivc32rt | Even in those countries that do, the reserve requirement is as a ratio to deposits held, not a ratio to loans that can be extended. Basel III does stipulate a liquidity requirement to cover 30 days net cash outflow expected under a modeled stressed scenario (note this is not a ratio to loans that can be extended); howe... | Money multiplier |
c_vbcnqguvc15b | (In March 2020, the minimum reserve requirement for all deposit institutions in the United States was abolished, setting RR=0. In practice, however, banks continue to be limited by their capital requirement.) If banks lend out close to the maximum allowed by their reserves, then the inequality becomes an approximate eq... | Money multiplier |
c_lw9uj9yullyc | If banks instead lend less than the maximum, accumulating excess reserves, then commercial bank money will be less than central bank money times the theoretical multiplier. In the United States since 1959, banks lent out close to the maximum allowed for the 49-year period from 1959 until August 2008, maintaining a low ... | Money multiplier |
c_q7xcfj309lna | In monetary economics, fiat money is an intrinsically valueless object or record that is accepted widely as a means of payment. Accordingly, the value of fiat money is greater than the value of its metal or paper content. One justification for fiat money comes from a micro-founded model. In most economic models, agents... | Fiat currency |
c_s01oy98vxp4a | In a model by Lagos and Wright, fiat money doesn't have an intrinsic worth but agents get more of the goods they want when they trade assuming fiat money is valuable. Fiat money's value is created internally by the community and, at equilibrium, makes otherwise infeasible trades possible.Another mathematical model that... | Fiat currency |
c_oir1cbxzfic0 | In monetary economics, inside money is money issued by private intermediaries (i.e. commercial banks) in the form of debt (credit). This money is typically in the form of demand deposits or other deposits, and hence is part of the money supply. The money, which is an asset of the depositor but coincides with a liabilit... | Inside money |
c_uhlw6gxj5rjw | In monetary economics, redenomination is the process of changing the face value of banknotes and coins in circulation. It may be done because inflation has made the currency unit so small that only large denominations of the currency are in circulation. In such cases the name of the currency may change or the original ... | Redenomination |
c_t310y0043d0f | Redenomination itself is considered symbolic as it does not have any impact on a country's exchange rate in relation to other currencies. It may, however, have a psychological impact on the population by suggesting that a period of hyperinflation is over, and is not a reminder of how much inflation has impacted them. | Redenomination |
c_qm43qxzkmx1x | The reduction in the number of zeros also improves the image of the country abroad. Inflation over time is the main cause for the purchasing power of the monetary unit decreasing; but there are a variety of political reasons for the government not reining in inflation or for not redenominating the currency when its val... | Redenomination |
c_ta1dv820zdc5 | In monetary economics, the demand for money is the desired holding of financial assets in the form of money: that is, cash or bank deposits rather than investments. It can refer to the demand for money narrowly defined as M1 (directly spendable holdings), or for money in the broader sense of M2 or M3. Money in the sens... | Demand for money |
c_1kcv5y11oc5p | This creates a trade-off between the liquidity advantage of holding money for near-future expenditure and the interest advantage of temporarily holding other assets. The demand for M1 is a result of this trade-off regarding the form in which a person's funds to be spent should be held. In macroeconomics motivations for... | Demand for money |
c_z13icalj2ke5 | The demand for those parts of the broader money concept M2 that bear a non-trivial interest rate is based on the asset demand. These can be further subdivided into more microeconomically founded motivations for holding money. Generally, the nominal demand for money increases with the level of nominal output (price leve... | Demand for money |
c_keqk2v82fzoc | The real demand for money is defined as the nominal amount of money demanded divided by the price level. For a given money supply the locus of income-interest rate pairs at which money demand equals money supply is known as the LM curve. The magnitude of the volatility of money demand has crucial implications for the o... | Demand for money |
c_3z5ckqcgvio3 | Conditions under which the LM curve is flat, so that increases in the money supply have no stimulatory effect (a liquidity trap), play an important role in Keynesian theory. This situation occurs when the demand for money is infinitely elastic with respect to the interest rate. A typical money-demand function may be wr... | Demand for money |
c_14n5ipv1cfdi | In monetary economics, the equation of exchange is the relation: M ⋅ V = P ⋅ Q {\displaystyle M\cdot V=P\cdot Q} where, for a given period, M {\displaystyle M\,} is the total money supply in circulation on average in an economy. V {\displaystyle V\,} is the velocity of money, that is the average frequency with which a ... | Equation of exchange |
c_ptm9ch9sy2j4 | This equation is a rearrangement of the definition of velocity: V = PQ / M. As such, without the introduction of any assumptions, it is a tautology. The quantity theory of money adds assumptions about the money supply, the price level, and the effect of interest rates on velocity to create a theory about the causes of ... | Equation of exchange |
c_fh1zamamd9wc | In monetary economics, the quantity theory of money (often abbreviated QTM) is one of the directions of Western economic thought that emerged in the 16th-17th centuries. The QTM states that the general price level of goods and services is directly proportional to the amount of money in circulation, or money supply. For... | Quantity Theory of Money |
c_13lhqrxdkeye | In monitoring and security, an important contribution to alarm detection and alarm verification can be supplied, using sound recognition techniques. In particular, these methods could be helpful for intrusion detection in places like offices, stores, private homes or for the supervision of public premises exposed to pe... | Audio recognition |
c_65jtghe3hsut | In monitoring, the region of deposition of this material onto the filter medium is continuously viewed by a radiation detector, concurrent with the collection. This is as opposed to a sampling system, in which the airborne material is collected by pumping air, usually at a much higher volumetric flowrate than a CPAM, t... | Airborne particulate radioactivity monitoring |
c_tnf7in01h9r1 | In monocot seeds, the embryo's radicle and cotyledon are covered by a coleorhiza and coleoptile, respectively. The coleorhiza is the first part to grow out of the seed, followed by the radicle. The coleoptile is then pushed up through the ground until it reaches the surface. There, it stops elongating and the first lea... | Germination rate |
c_hw3012qitawq | In monolithic kernels, a driver can write to any word of memory and thus accidentally corrupt user programs. In Minix 3, when a user expects data from, for example, the file system, it builds a descriptor telling who has access and at what addresses. It then passes an index to this descriptor to the file system, which ... | Minix 3 |
c_rekd6j03b42j | In monolithic kernels, device drivers reside in the kernel. Thus, when a new peripheral is installed, unknown, untrusted code is inserted in the kernel. One bad line of code in a driver can bring down the system. | Minix 3 |
c_7o03fa32mfll | Instead, in Minix 3, each device driver is a separate user-mode process. Drivers cannot execute privileged instructions, change the page tables, perform arbitrary input/output (I/O), or write to absolute memory. They must make kernel calls for these services and the kernel checks each call for authority. | Minix 3 |
c_emybdzq9ia7y | In monometallic complexes, aldehydes and ketones can bind to metals in either of two modes, η1-O-bonded and η2-C,O-bonded. These bonding modes are sometimes referred to sigma- and pi-bonded. These forms may sometimes interconvert. The sigma bonding mode is more common for higher valence, Lewis-acidic metal centers (e.g... | Transition metal complexes of aldehydes and ketones |
c_b6ifqbobu11d | The pi-bonded mode is observed for low valence, electron-rich metal centers (e.g., Fe(0) and Os(0)).For the purpose of electron-counting, O-bonded ligands count as 2-electron "L ligands": they are Lewis bases. η2-C,O ligands are described as analogues of alkene ligands, i.e. the Dewar-Chatt-Duncanson model.η2-C,O keton... | Transition metal complexes of aldehydes and ketones |
c_bxx2uksvpwg1 | In monostatic sonar the receiver is listening to the echo which is reflected (scattered) right back from the target. Bistatic sonar can work in two ways: by utilizing either the target backscattering or forward scattering. Backscattering bistatic sonar is the sonar in which the bistatic angle φ is less than 90°. Forwar... | Bistatic sonar |
c_ulshycpm4n7c | In monostatic sonar, the first thing the receiver can hear is the sound of the transmitted ping. This sound level is very high, and it is impossible to detect the echo during the ping duration τ. That means targets are undetectable within the circle of Cτ/2 radius, where C is sound speed in water. This area is usually ... | Bistatic sonar |
c_yk3i68qtxcu9 | In bistatic sonar, the travel distance from projector to target and from target to receiver is R = Rpt + Rtr . As the projector is separated from receiver by Rpr distance, first Rpr /C seconds after the ping starts, the receiver is just waiting. | Bistatic sonar |
c_1h1wafv82u29 | After that time, it receives direct signal from the projector (often referred to as “direct blast”,) which lasts τ seconds. So the sonar cannot detect targets within the ellipse R = Rpr + Cτ, as shown at the picture. High level reverberation in the projector area does not affect the dead zone. | Bistatic sonar |
c_x4ebmdbbzy80 | In monotheistic theology, the doctrine of Divine Simplicity says that God is simple (without parts). This is the idea that God does not exist in parts but is one unified entity, with no distinct attributes; that is, God’s existence is identical to God’s essence. | Divine simplicity |
c_mi84kz88z6b7 | In monotheistic thought, God is usually viewed as the supreme being, creator, and principal object of faith. In polytheistic thought, a god is "a spirit or being believed to control some part of the universe or life and often worshipped for doing so, or something that represents this spirit or being". Belief in the exi... | Monotheistic God |
c_wzorbjjtw4oy | Atheism rejects the belief in any deity. Agnosticism is the belief that the existence of God is unknown or unknowable. Some theists view knowledge concerning God as derived from faith. | Monotheistic God |
c_jxcbmklab7ng | God is often conceived as the greatest entity in existence. God is often believed to be the cause of all things and so is seen as the creator and sustainer and the ruler of the universe. God is often thought of as incorporeal and independent of the material creation while pantheism holds God is the universe itself. | Monotheistic God |
c_373h327xpcmi | God is sometimes seen as the most benevolent, while deism holds that God is not involved in humanity apart from creation. Some traditions attach spiritual significance to the relationship with God and see God as the source of all moral obligation, with acts such as worship and prayer. God is sometimes described without... | Monotheistic God |
c_s27b14sf7rd3 | In monotone comparative statics, the single-crossing condition or single-crossing property refers to a condition where the relationship between two or more functions is such that they will only cross once. For example, a mean-preserving spread will result in an altered probability distribution whose cumulative distribu... | Single-crossing condition |
c_g1lyhnbx3klg | In monotone drawing of graphs, in 2-visibility representation of graphs. | Good spanning tree |
c_7os4y9sg3u07 | In moral and political philosophy, the social contract is a theory or model that originated during the Age of Enlightenment and usually, although not always, concerns the legitimacy of the authority of the state over the individual.Social contract arguments typically are that individuals have consented, either explicit... | Social contract |
c_imt557ct2swx | The starting point for most social contract theories is an examination of the human condition absent of any political order (termed the "state of nature" by Thomas Hobbes). In this condition, individuals' actions are bound only by their personal power and conscience. From this shared starting point, social contract the... | Social contract |
c_tym2kp3389n6 | Prominent 17th- and 18th-century theorists of the social contract and natural rights included Hugo de Groot (1625), Thomas Hobbes (1651), Samuel von Pufendorf (1673), John Locke (1689), Jean-Jacques Rousseau (1762) and Immanuel Kant (1797), each approaching the concept of political authority differently. Grotius posite... | Social contract |
c_gn0g8cj7aewx | Thomas Hobbes famously said that in a "state of nature", human life would be "solitary, poor, nasty, brutish and short". In the absence of political order and law, everyone would have unlimited natural freedoms, including the "right to all things" and thus the freedom to plunder, rape and murder; there would be an endl... | Social contract |
c_5h5b53rx4yfg | Though the sovereign's edicts may well be arbitrary and tyrannical, Hobbes saw absolute government as the only alternative to the terrifying anarchy of a state of nature. Hobbes asserted that humans consent to abdicate their rights in favor of the absolute authority of government (whether monarchical or parliamentary).... | Social contract |
c_oyyi9j1iaqw2 | The central assertion that social contract theory approaches is that law and political order are not natural, but human creations. The social contract and the political order it creates are simply the means towards an end—the benefit of the individuals involved—and legitimate only to the extent that they fulfill their ... | Social contract |
c_0vemdzd1n53o | In moral philosophy, deontological ethics or deontology (from Greek: δέον, 'obligation, duty' + λόγος, 'study') is the normative ethical theory that the morality of an action should be based on whether that action itself is right or wrong under a series of rules and principles, rather than based on the consequences of ... | Deontological ethics |
c_6x6no3sfsv1r | In this terminology, action is more important than the consequences. The term deontological was first used to describe the current, specialised definition by C. D. Broad in his 1930 book, Five Types of Ethical Theory. Older usage of the term goes back to Jeremy Bentham, who coined it prior to 1816 as a synonym of dicas... | Deontological ethics |
c_ma5lkf04uhxk | The more general sense of the word is retained in French, especially in the term code de déontologie (ethical code), in the context of professional ethics. Depending on the system of deontological ethics under consideration, a moral obligation may arise from an external or internal source, such as a set of rules inhere... | Deontological ethics |
c_m7k4z2drzxoy | In moral philosophy, instrumental and intrinsic value are the distinction between what is a means to an end and what is as an end in itself. Things are deemed to have instrumental value if they help one achieve a particular end; intrinsic values, by contrast, are understood to be desirable in and of themselves. A tool ... | Instrumental value |
c_q7usfyp0uyps | The classic names instrumental and intrinsic were coined by sociologist Max Weber, who spent years studying good meanings people assigned to their actions and beliefs. The Oxford Handbook of Value Theory provides three modern definitions of intrinsic and instrumental value: They are "the distinction between what is goo... | Instrumental value |
c_llr9np3dzdgz | By contrast, extrinsic value has been characterized mainly as what is valuable as a means, or for something else's sake. ": 29 "Among nonfinal values, instrumental value—intuitively, the value attaching a means to what is finally valuable—stands out as a bona fide example of what is not valuable for its own sake. | Instrumental value |
c_vu0pzkno44ny | ": 34 When people judge efficient means and legitimate ends at the same time, both can be considered as good. However, when ends are judged separately from means, it may result in a conflict: what works may not be right; what is right may not work. Separating the criteria contaminates reasoning about the good. | Instrumental value |
c_st6o0x70tebl | Philosopher John Dewey argued that separating criteria for good ends from those for good means necessarily contaminates recognition of efficient and legitimate patterns of behavior. Economist J. Fagg Foster explained why only instrumental value is capable of correlating good ends with good means. Philosopher Jacques El... | Instrumental value |
c_pv57bkv0z0m5 | Philosopher Anjan Chakravartty argued that instrumental value is only legitimate when it produces good scientific theories compatible with the intrinsic truth of mind-independent reality. The word value is ambiguous in that it is both a verb and a noun, as well as denoting both a criterion of judgment itself and the re... | Instrumental value |
c_uxds8uszeoss | In more "free" forms, and in free verse in particular, conventions for the use of line become, arguably, more arbitrary and more visually determined such that they may only be properly apparent in typographical representation and/or page layout. One extreme deviation from a conventional rule for line can occur in concr... | Line break (poetry) |
c_p63q3b6dcdkg | In more advanced areas of mathematics, when viewing Euclidean space as a vector space, its distance is associated with a norm called the Euclidean norm, defined as the distance of each vector from the origin. One of the important properties of this norm, relative to other norms, is that it remains unchanged under arbit... | Pythagorean distance |
c_4xyu8kk9rp4f | It can be extended to infinite-dimensional vector spaces as the L2 norm or L2 distance. The Euclidean distance gives Euclidean space the structure of a topological space, the Euclidean topology, with the open balls (subsets of points at less than a given distance from a given point) as its neighborhoods.Other common di... | Pythagorean distance |
c_1b60u2wys2ct | In more advanced diving (particularly penetration diving) divers often use additional underwater communication methods, including signalling with lights, pulls along connecting lines, or tapping on tanks.Ultrasonic signalling devices that attract the buddy's attention by vibration have been marketed and may have some l... | Buddy line |
c_fayqp4gyphb6 | In more advanced mathematics, cancelling out can be used in the context of infinite series, whose terms can be cancelled out to get a finite sum or a convergent series. In this case, the term telescoping is often used. Considerable care and prevention of errors is often necessary to ensure the amended equation will be ... | Cancelling out |
c_2bdo5cilkv9p | In more advanced systems, such as the US Federal Aviation Administration (FAA)-labeled 'Enhanced Flight Vision System', a real-world visual image can be overlaid onto the combiner. Typically an infrared camera (either single or multi-band) is installed in the nose of the aircraft to display a conformed image to the pil... | Head Up Display |
c_gb6l4xwb7bfw | "Registration," or the accurate overlay of the EVS image with the real world image, is one feature closely examined by authorities prior to approval of a HUD based EVS. This is because of the importance of the HUD matching the real world. | Head Up Display |
c_sxnjx1pbznjh | While the EVS display can greatly help, the FAA has only relaxed operating regulations so an aircraft with EVS can perform a CATEGORY I approach to CATEGORY II minimums. In all other cases the flight crew must comply with all "unaided" visual restrictions. (For example, if the runway visibility is restricted because of... | Head Up Display |
c_4mfkak5iwuzv | In more advanced treatments, one further distinguishes pseudovector fields and pseudoscalar fields, which are identical to vector fields and scalar fields, except that they change sign under an orientation-reversing map: for example, the curl of a vector field is a pseudovector field, and if one reflects a vector field... | Vector Calculus |
c_1rh7cdxedpgb | In more ancient times, some marriages between distinctly different tribes and nations were due to royalty trying to form alliances with or to influence other kingdoms or to dissuade marauders or slave traders. Two examples, Hermodike I c.800BC and Hermodike II c.600BC were Greek princesses from the house of Agamemnon w... | Melting pot |
c_ua3ax6767u6w | In more common usage, an oxidizing agent transfers oxygen atoms to a substrate. In this context, the oxidizing agent can be called an oxygenation reagent or oxygen-atom transfer (OAT) agent. Examples include MnO−4 (permanganate), CrO2−4 (chromate), OsO4 (osmium tetroxide), and especially ClO−4 (perchlorate). Notice tha... | Electron acceptors |
c_1455b8f00356 | In more complex cases, some fields in a copy should have shared values with the original object (as in a shallow copy), corresponding to an "association" relationship; and some fields should have copies (as in a deep copy), corresponding to an "aggregation" relationship. In these cases a custom implementation of copyin... | Shallow copy |
c_jibonkm95m8z | In more complicated cases, it is impossible to construct exact pivots. However, having approximate pivots improves convergence to asymptotic normality. Suppose a sample of size n {\displaystyle n} of vectors ( X i , Y i ) ′ {\displaystyle (X_{i},Y_{i})'} is taken from a bivariate normal distribution with unknown correl... | Pivotal quantity |
c_5d8z34aodya5 | The sample statistic r {\displaystyle r} has an asymptotically normal distribution: n r − ρ 1 − ρ 2 ⇒ N ( 0 , 1 ) {\displaystyle {\sqrt {n}}{\frac {r-\rho }{1-\rho ^{2}}}\Rightarrow N(0,1)} .However, a variance-stabilizing transformation z = t a n h − 1 r = 1 2 ln 1 + r 1 − r {\displaystyle z={\rm {{tanh}^{-1}r={\fra... | Pivotal quantity |
c_sq9g7rjzpoju | In more complicated usage, O(·) can appear in different places in an equation, even several times on each side. For example, the following are true for n → ∞ {\displaystyle n\to \infty }: The meaning of such statements is as follows: for any functions which satisfy each O(·) on the left side, there are some functions s... | Landau symbol |
c_8f2fc0wzlkan | In more concrete terms, the uniform word problem can be expressed as a rewriting question, for literal strings. For a presentation P of a group G, P will specify a certain number of generators x, y, z, ...for G. We need to introduce one letter for x and another (for convenience) for the group element represented by x−1... | Word problem for groups |
c_jlrou1y7z28t | The effect of the relations in G is to make various such strings represent the same element of G. In fact the relations provide a list of strings that can be either introduced where we want, or cancelled out whenever we see them, without changing the 'value', i.e. the group element that is the result of the multiplicat... | Word problem for groups |
c_dg1ayj5dj9s1 | We should also remember to strike out AAA; this says that since the cube of a is the identity element of G, so is the cube of the inverse of a. Under these conditions the word problem becomes easy. First reduce strings to the empty string, a, aa, A or AA. Then note that we may also multiply by aaa, so we can convert A ... | Word problem for groups |
c_n6lk7t92j6lq | This is not, however, the typical case. For the example, we have a canonical form available that reduces any string to one of length at most three, by decreasing the length monotonically. In general, it is not true that one can get a canonical form for the elements, by stepwise cancellation. One may have to use relatio... | Word problem for groups |
c_b4xqzqmos9y5 | In more contemporary times, thunderstorms have taken on the role of a scientific curiosity. Every spring, storm chasers head to the Great Plains of the United States and the Canadian Prairies to explore the scientific aspects of storms and tornadoes through use of videotaping. Radio pulses produced by cosmic rays are b... | Lightning storm |
c_l6stxx9z5fu1 | In more current research, Schultz (1999) found that households that received more normative messages describing the frequency and amount of weekly recycling began to have a direct impact on both the households' frequency and amount of their curbside recycling. The sudden change was due to the fact that "the other neigh... | Normative social influence |
c_qfirx98otk2n | In more detail, an arithmetic surface S {\displaystyle S} (over the Dedekind domain R {\displaystyle R} ) is a scheme with a morphism p: S → S p e c ( R ) {\displaystyle p:S\rightarrow \mathrm {Spec} (R)} with the following properties: S {\displaystyle S} is integral, normal, excellent, flat and of finite type over R {... | Arithmetic surface |
c_crv9goa900v5 | In more detail, let X and Y be topological spaces. Given a continuous mapping f: X → Y {\displaystyle f\colon X\to Y} and a point x in X, consider for any n ≥ 1 the induced homomorphism f ∗: π n ( X , x ) → π n ( Y , f ( x ) ) , {\displaystyle f_{*}\colon \pi _{n}(X,x)\to \pi _{n}(Y,f(x)),} where πn(X,x) denotes the n-... | Whitehead theorem |
c_e5zaxv022kjw | (For X and Y path-connected, the first condition is automatic, and it suffices to state the second condition for a single point x in X.) The Whitehead theorem states that a weak homotopy equivalence from one CW complex to another is a homotopy equivalence. (That is, the map f: X → Y has a homotopy inverse g: Y → X, whi... | Whitehead theorem |
c_rudasn1am5we | In more detail, the star unfolding is obtained from a polyhedron P {\displaystyle P} by choosing a starting point p {\displaystyle p} on the surface of P {\displaystyle P} , in general position, meaning that there is a unique shortest geodesic from p {\displaystyle p} to each vertex of P {\displaystyle P} . The star po... | Star unfolding |
c_efcfw8d5kjj6 | In more detail, when the radio-labelled molecule is attached or is in proximity to bead, light emission is stimulated. However, if the bead does not become bound to the radio-labelled molecule, the bead will not be stimulated to emit light. This is because the beta particles (high-velocity electrons) released from the ... | Scintillation proximity assay |
c_ks990ogabryk | Tritium releases electrons as one of the subatomic particles. The energy of these particles influences the distance traveled by the particles itself through a medium such as water, because there is an inverse correlation between particle kinetic energy and strength of interaction with matter. The SPA method depends on ... | Scintillation proximity assay |
c_z0io13myfp9c | For instance, the decay of a Tritium atom releases a beta particle, which is well-suited to SPA due to a very short (1.5 µm) path length through water. So, when the β-particle is within 1.5 µm of the scintillant bead, there is sufficient energy to stimulate the bead to emit light. If the distance between them is greate... | Scintillation proximity assay |
c_9pkvvi5yi7rr | The beads in SPA are formed from the incorporation of scintillant into small beads known as fluomicrospheres. These are specially designed to bind with specific molecules. | Scintillation proximity assay |
c_3rymjdkrbqe1 | When the bead is in close proximity to the radioactive molecule, light is stimulated. The photonmultiplier tube (PMT) can be used to detect the emitted photons. This device converts the emitted photon energy into electrical energy by a photocathode via a series of other electrodes. Another device is known as CCD Imager... | Scintillation proximity assay |
c_3vsdwe7ny4qc | In more extreme cases, plasmapheresis can be considered. This technique is used to remove the blood plasma or fluid in the red blood cells and then return the cells to the body. It "removes a circulating factor from the blood that may be involved in causing the urticaria," but is still being tested and is not always ef... | Solar urticaria |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.