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Introduction, Important Definitions and Related Concepts:
In mathematical logic, a formula is said to be absolute if it has the same truth value in each of some class of structures. Theorems about absoluteness typically show that each of a large syntactic class of formulas is absolute. Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions". Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. In mathematics and in the sciences, a formula (plural: formulae, formulæ or formulas) is a concise way of expressing information symbolically (as in a mathematical or chemical formula), or a general relationship between quantities. One of many famous formulae is Albert Einstein's E = mc² (see special relativity). Structure is a fundamental and sometimes intangible notion covering the recognition, observation, nature, and stability of patterns and relationships of entities. From a child's verbal description of a snowflake, to the detailed scientific analysis of the properties of magnetic fields, the concept of structure is an essential foundation of nearly every mode of inquiry and discovery in science, philosophy, and art. Quantity is a kind of property which exists as magnitude or multitude. It is among the basic classes of things along with quality, substance, change, and relation. Science considers space to be a fundamental quantity (a quantity which can not be defined via other quantities because other quantities — like force and energy — are already defined via space). Thus an operational definition is used in which the procedure of measurement of space intervals (distances) and the units of measurement are defined. Change denotes the transition that occurs between one state to another. Ovid produced a classic thematic handling of change as metamorphosis in his Metamorphoses. Benjamin Peirce (pronounced /ˈpɜrs/ purse), April 4, 1809 – October 6, 1880) was an American mathematician who taught at Harvard University for forty years. He made contributions to celestial mechanics, number theory, algebra, and the philosophy of mathematics.Classical antiquity and the study of "the classics", refers to the culture of Ancient Greece or Rome.
"High classical" refers to Greek art associated mainly with Athens and the works atop the Acropolis. The Greeks (Greek: Έλληνες, IPA: [ˈelines]) are a nation and ethnic group who have populated Greece and the area of the Aegean Sea for over 3,500 years. Today they are primarily found in the Balkan peninsula of southeastern Europe, the Greek islands, Cyprus, and throughout the world as part of the Greek diaspora. Logos (Greek λόγος) is an important term in philosophy, analytical psychology, rhetoric and religion. It derives from the verb λέγω legō: to count, tell, say, or speak. Inference is the act or process of deriving a conclusion based solely on what one already knows. Inference is studied within several different fields. In mathematics, a proof is a convincing demonstration that some mathematical statement is necessarily true, within the accepted standards of the field. A proof is a logical argument, not an empirical one. In mathematical logic, a formal calculation is sometimes defined as a calculation which is systematic, but without a rigorous justification. This means that we are manipulating the symbols in an expression using a generic substitution, without proving that the necessary conditions hold. Science (from the Latin scientia, 'knowledge'), in the broadest sense, refers to any systematic knowledge or practice. In a more restricted sense, science refers to a system of acquiring knowledge based on the scientific method, as well as to the organized body of knowledge gained through such research. System (from Latin systēma, in turn from Greek σύστημα systēma) is a set of interacting or interdependent entities, real or abstract, forming an integrated whole. The concept of an 'integrated whole' can also be stated in terms of a system embodying a set of relationships which are differentiated from relationships of the set to other elements, and from relationships between an element of the set and elements not a part of the relational regime. A chemical formula is a concise way of expressing information about the atoms that constitute a particular chemical compound. A chemical formula is also a short way of showing how a chemical reaction occurs. Albert Einstein (German: IPA: [ˈalbɐt ˈaɪ̯nʃtaɪ̯n] ; English: IPA: /ˈælbɝt ˈaɪnstaɪn/) (March 14, 1879 – April 18, 1955) was a German-born theoretical physicist. He is best known for his theory of relativity and specifically mass-energy equivalence, E = mc2. Example:
Shape Transition and Propulsive Force of an Elastic Rod Rotating in a Viscous Fluid Bian Qian, Thomas R. Powers, and Kenneth S. Breuer
Division of Engineering, Box D, Brown University, Providence, Rhode Island 02912, USA
(Received 2 December 2007; published 19 February 2008) The deformation of an elastic rod rotating in a viscous fluid is considered, with applications related to flagellar motility. The rod is tilted relative to the rotation axis, and experiments and theory are used to study the shape transition when driven either at constant torque or at constant speed. At low applied torque, the rod bends gently and generates small propulsive force. At a critical torque, the rotation speed increases abruptly, and the rod forms a helical shape with increased propulsive force. We find good agreement between theory and experiment. A simple physical model is presented to capture and explain the essential behavior. (Ref. Physical Review Letters). Mass is a fundamental concept in physics, roughly corresponding to the intuitive idea of "how much matter there is in an object". Mass is a central concept of classical mechanics and related subjects, and there are several definitions of mass within the framework of relativistic kinematics (see mass in special relativity and mass in General Relativity). Another Example:
Flow, Ordering, and Jamming of Sheared Granular Suspensions Denis S. Grebenkov,2,3 Massimo Pica Ciamarra,1,2 Mario Nicodemi,2,4 and Antonio Coniglio2
1CNISM and Department of Information Engineering, Second University of Naples, 81031 Aversa (CE), Italy 2Dip.to di Scienze Fisiche, Universitá di Napoli “Federico II” and INFN, Naples, Italy 3LPMC, C.N.R.S.-Ecole Polytechnique, F-91128 Palaiseau, France 4Complexity Science and Department of Physics, University of Warwick, United Kingdom
(Received 16 July 2007; published 19 February 2008) We study the rheological properties of a granular suspension subject to constant shear stress by constant volume molecular dynamics simulations. We derive the system “flow diagram” in the volume fraction or stress plane (, F): at low the flow is disordered, with the viscosity obeying a Bagnold-like scaling only at small F and diverging as the jamming point is approached; if the shear stress is strong enough, at higher an ordered flow regime is found, the order-disorder transition being marked by a sharp drop of the viscosity. A broad jamming region is also observed where, in analogy with the glassy region of thermal systems, slow dynamics followed by kinetic arrest occurs when the ordering transition is prevented. (Ref. Physical Review Letters). Special relativity (SR) (aka the special theory of relativity (STR)) is the physical theory of measurement in inertial frames of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies". It generalizes Galileo's principle of relativity — that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames) — from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be. Snowflake is A particle of snow, an aggregate of ice crystals that forms while falling in and below a cloud. A magnetized bar has its power concentrated at two ends, its poles; they are known as its north (N) and south (S) poles, because if the bar is hung by its middle from a string, its N end tends to point northwards and its S end southwards. The N end will repel the N end of another magnet, S will repel S, but N and S attract each other. Philosophy is the discipline concerned with questions of how one should live (ethics); what sorts of things exist and what are their essential natures (metaphysics); what counts as genuine knowledge (epistemology); and what are the correct principles of reasoning (logic). The word is of Greek origin: φιλοσοφία (philosophía), meaning love of wisdom. Art refers to a diverse range of human activities and artifacts, and may be used to cover all or any of the arts, including music, literature and other forms. It is most often used to refer specifically to the visual arts, including media such as painting, sculpture, and printmaking. Quality in everyday life and business, engineering and manufacturing has a pragmatic interpretation as the non-inferiority, superiority or usefulness of something. This is the most common interpretation of the term. The word originates from Latin substantia, literally meaning "standing under". The word was used to translate the Greek philosophical term ousia.
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