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Ansatz
In physics and mathematics, an ansatz (; , meaning: "initial placement of a tool at a work piece", plural Ansätze ; ) is an educated guess or an additional assumption made to help solve a problem, and which may later be verified to be part of the solution by its results. Use An ansatz is the establishment of the starting equation(s), the theorem(s), or the value(s) describing a mathematical or physical problem or solution. It typically provides an initial estimate or framework to the solution of a mathematical problem, and can also take into consideration the boundary conditions (in fact, an ansatz is sometimes thought of as a "trial answer" and an important technique in solving differential equations). After an ansatz, which constitutes nothing more than an assumption, has been established, the equations are solved more precisely for the general function of interest, which then constitutes a confirmation of the assumption. In essence, an ansatz makes assumptions about the form o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coupled Cluster
Coupled cluster (CC) is a numerical technique used for describing many-body systems. Its most common use is as one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry, but it is also used in nuclear physics. Coupled cluster essentially takes the basic Hartree–Fock molecular orbital method and constructs multi-electron wavefunctions using the exponential cluster operator to account for electron correlation. Some of the most accurate calculations for small to medium-sized molecules use this method. The method was initially developed by Fritz Coester and Hermann Kümmel in the 1950s for studying nuclear-physics phenomena, but became more frequently used when in 1966 Jiří Čížek (and later together with Josef Paldus) reformulated the method for electron correlation in atoms and molecules. It is now one of the most prevalent methods in quantum chemistry that includes electronic correlation. CC theory is simply the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Method Of Undetermined Coefficients
In mathematics, the method of undetermined coefficients is an approach to finding a particular solution to certain nonhomogeneous ordinary differential equations and recurrence relations. It is closely related to the annihilator method, but instead of using a particular kind of differential operator (the annihilator) in order to find the best possible form of the particular solution, an ansatz or 'guess' is made as to the appropriate form, which is then tested by differentiating the resulting equation. For complex equations, the annihilator method or variation of parameters is less time-consuming to perform. Undetermined coefficients is not as general a method as variation of parameters, since it only works for differential equations that follow certain forms.Ralph P. Grimaldi (2000). "Nonhomogeneous Recurrence Relations". Section 3.3.3 of ''Handbook of Discrete and Combinatorial Mathematics''. Kenneth H. Rosen, ed. CRC Press. . Description of the method Consider a linear non-h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heuristic
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, short-term goal or approximation. Where finding an optimal solution is impossible or impractical, heuristic methods can be used to speed up the process of finding a satisfactory solution. Heuristics can be mental shortcuts that ease the cognitive load of making a decision. Examples that employ heuristics include using trial and error, a rule of thumb or an educated guess. Heuristics are the strategies derived from previous experiences with similar problems. These strategies depend on using readily accessible, though loosely applicable, information to control problem solving in human beings, machines and abstract issues. When an individual applies a heuristic in practice, it generally performs as expected. However it can alternativ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, with its main goal being to understand how the universe behaves. "Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concepts In Physics
Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks of the concept behind principles, thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by several disciplines, such as linguistics, psychology, and philosophy, and these disciplines are interested in the logical and psychological structure of concepts, and how they are put together to form thoughts and sentences. The study of concepts has served as an important flagship of an emerging interdisciplinary approach called cognitive science. In contemporary philosophy, there are at least three prevailing ways to understand what a concept is: * Concepts as mental representations, where concepts are entities that exist in the mind (mental objects) * Concepts as abilities, where concepts are abilities peculiar to cognitive agents (mental states) * Concepts as Fregean senses, where concepts are abstract objects, as opposed to mental obj ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Physics
In philosophy, philosophy of physics deals with conceptual and interpretational issues in modern physics, many of which overlap with research done by certain kinds of theoretical physicists. Philosophy of physics can be broadly divided into three areas: * interpretations of quantum mechanics: mainly concerning issues with how to formulate an adequate response to the measurement problem and understand what the theory says about reality. * the nature of space and time: Are space and time substances, or purely relational? Is simultaneity conventional or only relative? Is temporal asymmetry purely reducible to thermodynamic asymmetry? * inter-theoretic relations: the relationship between various physical theories, such as thermodynamics and statistical mechanics. This overlaps with the issue of scientific reduction. Philosophy of space and time The existence and nature of space and time (or space-time) are central topics in the philosophy of physics. Time Time is often thought ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Train Of Thought
The train of thought or track of thought refers to the interconnection in the sequence of ideas expressed during a connected discourse or thought, as well as the sequence itself, especially in discussion how this sequence leads from one idea to another. When a reader or listener "loses the train of thought" (i.e., loses the relation between consecutive sentences or phrases, or the relation between non-verbal concepts in an argument or presentation), comprehension is lost of the expressed or unexpressed thought.Edward Parmelee Morris, "On Principles and Methods in Latin Syntax" (1901), Chapter VI: ''Parataxis'' The term "train of thoughts" was introduced and elaborated as early as in 1651 by Thomas Hobbes in his '' Leviathan'', though with a somewhat different meaning (similar to the meaning used by the British associationists): See also * Absent-mindedness * Association of Ideas * Associationism * Derailment (thought disorder) * Internal monologue * Mind-wandering Mind- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trial And Error
Trial and error is a fundamental method of problem-solving characterized by repeated, varied attempts which are continued until success, or until the practicer stops trying. According to W.H. Thorpe, the term was devised by C. Lloyd Morgan (1852–1936) after trying out similar phrases "trial and failure" and "trial and practice". Under Morgan's Canon, animal behaviour should be explained in the simplest possible way. Where behavior seems to imply higher mental processes, it might be explained by trial-and-error learning. An example is a skillful way in which his terrier Tony opened the garden gate, easily misunderstood as an insightful act by someone seeing the final behavior. Lloyd Morgan, however, had watched and recorded the series of approximations by which the dog had gradually learned the response, and could demonstrate that no insight was required to explain it. Edward Lee Thorndike was the initiator of the theory of trial and error learning based on the findings he sho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypothesis
A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can test it. Scientists generally base scientific hypotheses on previous observations that cannot satisfactorily be explained with the available scientific theories. Even though the words "hypothesis" and "theory" are often used interchangeably, a scientific hypothesis is not the same as a scientific theory. A working hypothesis is a provisionally accepted hypothesis proposed for further research in a process beginning with an educated guess or thought. A different meaning of the term ''hypothesis'' is used in formal logic, to denote the antecedent of a proposition; thus in the proposition "If ''P'', then ''Q''", ''P'' denotes the hypothesis (or antecedent); ''Q'' can be called a consequent. ''P'' is the assumption in a (possibly counterfactual) ''What If'' question. The adjective ''hypothetical'', meaning ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Guesstimate
''Guesstimate'' is an informal English portmanteau of ''guess'' and ''estimate'', first used by American statisticians in 1934 or 1935.''guesstimate'' Dictionary.com Unabridged (v 1.1) It is defined as an estimate made without using adequate or complete information, or, more strongly, as an estimate arrived at by work or .''guesstimate'' American Heritage Dictionary Like the words estimate and guess, guesstimate may be used as a verb or a no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Demarcation Problem
In philosophy of science and epistemology, the demarcation problem is the question of how to distinguish between science and non-science. It examines the boundaries between science, pseudoscience, and other products of human activity, like art and literature, and beliefs.. Alternative source/ref> The debate continues after over two millennia of dialogue among philosophers of science and scientists in various fields. The debate has consequences for what can be called "scientific" in fields such as education and public policy. The ancient world An early attempt at demarcation can be seen in the efforts of Greek natural philosophers and medical practitioners to distinguish their methods and their accounts of nature from the mythological or mystical accounts of their predecessors and contemporaries. G. E. R. Lloyd noted that there was a sense in which the groups engaged in various forms of inquiry into nature set out to "legitimate their own positions", laying "claim to a new k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
