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Superposition (EP)
Superposition may refer to: Science and mathematics * Law of superposition in geology and archaeology, which states that sedimentary layers are deposited in a time sequence, with the oldest on the bottom and the youngest on the top * Superposition calculus, used in logic for equational first-order reasoning * Superposition principle in physics and engineering, asserting the linearity of many physical systems, including: ** Superposition theorem for electric circuits ** Superposition of gravitational potentials ** Dalton's law of partial pressures, superposition in fluid mechanics ** Quantum superposition, in quantum physics * In chemistry, a property of two structures that have the same chirality * In Euclidean geometry, the principle of superposition is a method of proof * The Kolmogorov–Arnold superposition theorem, representing a multivariate function as a superposition of univariate functions Music and art *" Superposition", a song by Young the Giant from the 2018 albu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of Superposition
The law of superposition is an axiom that forms one of the bases of the sciences of geology, archaeology, and other fields pertaining to geological stratigraphy. In its plainest form, it states that in undeformed stratigraphic sequences, the oldest strata will lie at the bottom of the sequence, while newer material stacks upon the surface to form new deposits over time. This is paramount to stratigraphic dating, which requires a set of assumptions, including that the law of superposition holds true and that an object cannot be older than the materials of which it is composed. To illustrate the practical applications of superposition in scientific inquiry, sedimentary rock that has not been deformed by more than 90° will exhibit the oldest layers on the bottom, thus enabling paleontologists and paleobotanists to identify the relative ages of any fossils found within the strata, with the remains of the most archaic lifeforms confined to the lowest. These findings can inform th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superposition Calculus
The superposition calculus is a calculus for reasoning in equational first-order logic. It was developed in the early 1990s and combines concepts from first-order resolution with ordering-based equality handling as developed in the context of (unfailing) Knuth–Bendix completion. It can be seen as a generalization of either resolution (to equational logic) or unfailing completion (to full clausal logic). As most first-order calculi, superposition tries to show the ''unsatisfiability'' of a set of first-order clauses, i.e. it performs proofs by refutation. Superposition is refutation-complete—given unlimited resources and a ''fair'' derivation strategy, from any unsatisfiable clause set a contradiction will eventually be derived. , most of the (state-of-the-art) theorem provers for first-order logic are based on superposition (e.g. the E equational theorem prover), although only a few implement the pure calculus. Implementations * E * SPASS * Vampire * Waldmeisterbr>(off ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superposition Principle
The superposition principle, also known as superposition property, states that, for all linear systems, the net response caused by two or more stimuli is the sum of the responses that would have been caused by each stimulus individually. So that if input ''A'' produces response ''X'' and input ''B'' produces response ''Y'' then input (''A'' + ''B'') produces response (''X'' + ''Y''). A function F(x) that satisfies the superposition principle is called a linear function. Superposition can be defined by two simpler properties: additivity F(x_1+x_2)=F(x_1)+F(x_2) \, and homogeneity F(a x)=a F(x) \, for scalar . This principle has many applications in physics and engineering because many physical systems can be modeled as linear systems. For example, a beam can be modeled as a linear system where the input stimulus is the load on the beam and the output response is the deflection of the beam. The importance of linear systems is that they are easier to analyze mathematically; the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superposition Theorem
The superposition theorem is a derived result of the superposition principle suited to the network analysis of electrical circuits. The superposition theorem states that for a linear system (notably including the subcategory of time-invariant linear systems) the response (voltage or current) in any branch of a bilateral linear circuit having more than one independent source equals the algebraic sum of the responses caused by each independent source acting alone, where all the other independent sources are replaced by their internal impedances. To ascertain the contribution of each individual source, all of the other sources first must be "turned off" (set to zero) by: * Replacing all other independent voltage sources with a short circuit (thereby eliminating difference of potential i.e. ''V''=0; internal impedance of ideal voltage source is zero (short circuit)). * Replacing all other independent current sources with an open circuit (thereby eliminating current i.e. ''I''=0; int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Potential
In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move an object to that location from a fixed reference location. It is analogous to the electric potential with mass playing the role of charge. The reference location, where the potential is zero, is by convention infinitely far away from any mass, resulting in a negative potential at any finite distance. In mathematics, the gravitational potential is also known as the Newtonian potential and is fundamental in the study of potential theory. It may also be used for solving the electrostatic and magnetostatic fields generated by uniformly charged or polarized ellipsoidal bodies. Potential energy The gravitational potential (''V'') at a location is the gravitational potential energy (''U'') at that location per unit mass: V = \frac, where ''m'' is the mass of the object. Potential energy is equal (in magnitude, but negative) to the w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dalton's Law Of Partial Pressures
Dalton's law (also called Dalton's law of partial pressures) states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. This empirical law was observed by John Dalton in 1801 and published in 1802.J. Dalton (1802)"Essay IV. On the expansion of elastic fluids by heat,"''Memoirs of the Literary and Philosophical Society of Manchester'', vol. 5, pt. 2, pages 595–602; see page 600. Dalton's law is related to the ideal gas laws. Formula Mathematically, the pressure of a mixture of non-reactive gases can be defined as the summation: p_\text = \sum_^n p_i = p_1+p_2+p_3+\cdots+p_n where ''p''1, ''p''2, ..., ''pn'' represent the partial pressures of each component. p_ = p_\text x_i where ''xi'' is the mole fraction of the ''i''th component in the total mixture of ''n'' components . Volume-based concentration The relationship below provides a way to determine the volume-based concentration of any i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Superposition
Quantum superposition is a fundamental principle of quantum mechanics. It states that, much like waves in classical physics, any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum state; and conversely, that every quantum state can be represented as a sum of two or more other distinct states. Mathematically, it refers to a property of solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of solutions will also be a solution(s) . An example of a physically observable manifestation of the wave nature of quantum systems is the interference peaks from an electron beam in a double-slit experiment. The pattern is very similar to the one obtained by diffraction of classical waves. Another example is a quantum logical qubit state, as used in quantum information processing, which is a quantum superposition of the "basis states" , 0 \rangle and , 1 \rangle . Here , 0 \r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chirality (chemistry)
In chemistry, a molecule or ion is called chiral () if it cannot be superposed on its mirror image by any combination of rotation (geometry), rotations, translation (geometry), translations, and some Conformational isomerism, conformational changes. This geometric property is called chirality (). The terms are derived from Ancient Greek χείρ (''cheir'') 'hand'; which is the canonical example of an object with this property. A chiral molecule or ion exists in two stereoisomers that are mirror images of each other, called enantiomers; they are often distinguished as either "right-handed" or "left-handed" by their absolute configuration or some other criterion. The two enantiomers have the same chemical properties, except when reacting with other chiral compounds. They also have the same physics, physical properties, except that they often have opposite optical activity, optical activities. A homogeneous mixture of the two enantiomers in equal parts is said to be racemic mixtu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry: the ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small set of intuitively appealing axioms (postulates) and deducing many other propositions (theorems) from these. Although many of Euclid's results had been stated earlier,. Euclid was the first to organize these propositions into a logic, logical system in which each result is ''mathematical proof, proved'' from axioms and previously proved theorems. The ''Elements'' begins with plane geometry, still taught in secondary school (high school) as the first axiomatic system and the first examples of mathematical proofs. It goes on to the solid geometry of three dimensions. Much of the ''Elements'' states results of what are now called algebra and number theory, explained in geometrical language. For more than two thousand years, the adjective " ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kolmogorov–Arnold Representation Theorem
In real analysis and approximation theory, the Kolmogorov-Arnold representation theorem (or superposition theorem) states that every multivariate continuous function can be represented as a superposition of the two-argument addition and continuous functions of one variable. It solved a more constrained, yet more general form of Hilbert's thirteenth problem. The works of Vladimir Arnold and Andrey Kolmogorov established that if ''f'' is a multivariate continuous function, then ''f'' can be written as a finite composition of continuous functions of a single variable and the binary operation of addition. More specifically, : f(\mathbf x) = f(x_1,\ldots ,x_n) = \sum_^ \Phi_\left(\sum_^ \phi_(x_)\right) . There are proofs with specific constructions. In a sense, they showed that the only true multivariate function is the sum, since every other function can be written using univariate functions and summing.Persi Diaconis and Mehrdad Shahshahani, ''On Linear Functions of Linear Combinat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superposition (song)
"Superposition" is a song by American alternative rock band Young the Giant, promoted as the second single off of the band's fourth album, ''Mirror Master''. It was released on August 23, 2018, through Elektra Records. Background and recording Beyond the original version, two remakes were released: the first one was dubbed "Superposition (Reprise)", recorded in a single day in the Layman Drug Company Studio in Nashville, and uploaded to YouTube on January 16, 2019 while the second was named "Superposition (Reflection)" and posted online on April 12, 2019. On social media posts, the band has described "Superposition" as "a song about quantum physics that has defied odds". On the ''Reprise'' version, they stated it is "a deconstructed negative of the original: a flipper zip on the double helix". Furthermore, on the ''Reflection'' version, they added it "is about recognizing the constant that hides behind infinite variations". Critical reception While parent album ''Mirror Mas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Case Study 01
''Case Study 01'' (stylized in all caps) is the second studio album by Canadian singer and songwriter Daniel Caesar, released on June 28, 2019, through Golden Child Recordings. It features guest appearances from Brandy, Pharrell Williams, John Mayer, Sean Leon and Jacob Collier. Promotion Caesar held a listening party in Los Angeles in the week leading up to the album's release. Along with invited music industry figures, the event was also open to the first 200 guests that arrived. Caesar also teased the album on social media, including with a video of a person walking across a desert set to a "muted keyboard melody" and a quote from scientist J. Robert Oppenheimer. Critical reception Jacob Carey of '' Exclaim!'' noted the "experimental nature" of the album, concluding: "Although ''Case Study 01'' may not receive the same critical reception as Freudian, it's a solid effort by an artist who is, more or less, still a rookie, attempting to diversify his sound early on in order ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
