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Writhe
In knot theory, there are several competing notions of the quantity writhe, or \operatorname. In one sense, it is purely a property of an oriented link diagram and assumes integer values. In another sense, it is a quantity that describes the amount of "coiling" of a mathematical knot (or any closed simple curve) in three-dimensional space and assumes real numbers as values. In both cases, writhe is a geometric quantity, meaning that while deforming a curve (or diagram) in such a way that does not change its topology, one may still change its writhe. Writhe of link diagrams In knot theory, the writhe is a property of an oriented link diagram. The writhe is the total number of positive crossings minus the total number of negative crossings. A direction is assigned to the link at a point in each component and this direction is followed all the way around each component. For each crossing one comes across while traveling in this direction, if the strand underneath goes from ri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gheorghe Călugăreanu
Gheorghe Călugăreanu (16 June 1902 – 15 November 1976) was a Romanian mathematician, professor at Babeș-Bolyai University, and full member of the Romanian Academy. He was born in Iași, the son of physician, naturalist, and physiologist Dimitrie Călugăreanu. From 1913 to 1921 he studied at the Gheorghe Lazăr High School in Bucharest, after which he attended University of Cluj, graduating in 1924. In 1926 he went to Paris to pursue his studies at the Sorbonne, supported by a scholarship from the Romanian government. He obtained his Ph.D. in mathematics in 1929, with thesis ''Sur les fonctions polygènes d'une variable complexe'' written under the direction of Émile Picard and defended before a jury that also included Édouard Goursat and Gaston Julia. After returning to Romania, he was appointed assistant the University of Cluj in 1930; he was promoted to lecturer in 1934 and named professor in 1942. From 1953 to 1957 he served as Dean of the Faculty of Mathematics. Hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Winding Number
In mathematics, the winding number or winding index of a closed curve in the plane around a given point is an integer representing the total number of times that curve travels counterclockwise around the point, i.e., the curve's number of turns. The winding number depends on the orientation of the curve, and it is negative if the curve travels around the point clockwise. Winding numbers are fundamental objects of study in algebraic topology, and they play an important role in vector calculus, complex analysis, geometric topology, differential geometry, and physics (such as in string theory). Intuitive description Suppose we are given a closed, oriented curve in the ''xy'' plane. We can imagine the curve as the path of motion of some object, with the orientation indicating the direction in which the object moves. Then the winding number of the curve is equal to the total number of counterclockwise turns that the object makes around the origin. When counting the total nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linking Number
In mathematics, the linking number is a numerical invariant that describes the linking of two closed curves in three-dimensional space. Intuitively, the linking number represents the number of times that each curve winds around the other. In Euclidean space, the linking number is always an integer, but may be positive or negative depending on the orientation of the two curves (this is not true for curves in most 3-manifolds, where linking numbers can also be fractions or just not exist at all). The linking number was introduced by Gauss in the form of the linking integral. It is an important object of study in knot theory, algebraic topology, and differential geometry, and has numerous applications in mathematics and science, including quantum mechanics, electromagnetism, and the study of DNA supercoiling. Definition Any two closed curves in space, if allowed to pass through themselves but not each other, can be moved into exactly one of the following standard positions. Thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linking Number
In mathematics, the linking number is a numerical invariant that describes the linking of two closed curves in three-dimensional space. Intuitively, the linking number represents the number of times that each curve winds around the other. In Euclidean space, the linking number is always an integer, but may be positive or negative depending on the orientation of the two curves (this is not true for curves in most 3-manifolds, where linking numbers can also be fractions or just not exist at all). The linking number was introduced by Gauss in the form of the linking integral. It is an important object of study in knot theory, algebraic topology, and differential geometry, and has numerous applications in mathematics and science, including quantum mechanics, electromagnetism, and the study of DNA supercoiling. Definition Any two closed curves in space, if allowed to pass through themselves but not each other, can be moved into exactly one of the following standard positions. Thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ribbon (mathematics)
In differential geometry, a ribbon (or strip) is the combination of a smooth space curve and its corresponding normal vector. More formally, a ribbon denoted by (X,U) includes a curve X given by a three-dimensional vector X(s), depending continuously on the curve arc-length s (a\leq s \leq b), and a unit vector U(s) perpendicular to X at each point. Ribbons have seen particular application as regards DNA. Properties and implications The ribbon (X,U) is called ''simple'' if X is a simple curve (i.e. without self-intersections) and ''closed'' and if U and all its derivatives agree at a and b. For any simple closed ribbon the curves X+\varepsilon U given parametrically by X(s)+\varepsilon U(s) are, for all sufficiently small positive \varepsilon, simple closed curves disjoint from X. The ribbon concept plays an important role in the Călugăreanu-White-Fuller formula, that states that :Lk = Wr + Tw , where Lk is the asymptotic (Gauss) ''linking number'', the integer number of tu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biopolymers (journal)
''Biopolymers'' is a biweekly peer-reviewed scientific journal covering the study of biopolymers from a biochemical and biophysical perspective. It was established in 1963 and is published by John Wiley & Sons. The editor-in-chief is Hilary J. Crichton. The journal has three sections: ''Peptide Science'' (established in 1995, published bimonthly), ''Nucleic Acid Sciences'' (established in 1997, published four times per year), and ''Biospectroscopy'' (merged with ''Biopolymers'' in 2004). ''Peptide Science'' is the affiliate journal of the American Peptide Society. According to the ''Journal Citation Reports'', the journal has a 2015 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as ... of 2.248, ranking it 39th out of 72 journals in the category "Biophysics" and 186th out ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Molecular Biology
The ''Journal of Molecular Biology'' is a biweekly peer-reviewed scientific journal covering all aspects of molecular biology. It was established in 1959 and is published by Elsevier. The editor-in-chief is Peter Wright ( The Scripps Research Institute). Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 5.469. Notable articles Some of the most highly cited articles that have appeared in the journal are: *, in which Jacques Monod, Jeffries Wyman, and Jean-Pierre Changeux presented the MWC model, that explained the cooperativity exhibited by allosteric proteins, such as hemoglobin. *, in which Edwin Southern presented the first description of nucleic acid blotting, a technique that revolutionized the field of molecular biology. *, in which the Smith–Waterman algorithm for determining the degree of homology of DNA, RNA, or protein sequences was first described. *, in which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oxford University Press
Oxford University Press (OUP) is the university press of the University of Oxford. It is the largest university press in the world, and its printing history dates back to the 1480s. Having been officially granted the legal right to print books by decree in 1586, it is the second oldest university press after Cambridge University Press. It is a department of the University of Oxford and is governed by a group of 15 academics known as the Delegates of the Press, who are appointed by the vice-chancellor of the University of Oxford. The Delegates of the Press are led by the Secretary to the Delegates, who serves as OUP's chief executive and as its major representative on other university bodies. Oxford University Press has had a similar governance structure since the 17th century. The press is located on Walton Street, Oxford, opposite Somerville College, in the inner suburb of Jericho. For the last 500 years, OUP has primarily focused on the publication of pedagogical texts and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twist (mathematics)
In differential geometry Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ..., the twist of a ''Ribbon (mathematics), ribbon'' is its rate of change (mathematics), rate of axial rotation. Let a ribbon (X,U) be composted of space curve X=X(s), where s is the arc length of X, and U=U(s) the a unit normal vector, perpendicular at each point to X. Since the ribbon (X,U) has edges X and X'=X+\varepsilon U, the twist (or ''total twist number'') Tw measures the average winding number, winding of the edge curve X' around and along the axial curve X. According to Love (1944) twist is defined by : Tw = \dfrac \int \left( U \times \dfrac \right) \cdot \dfrac ds \; , where dX/ds is the unit tangent vector to X. The total twist number Tw can be decomposed (Moffatt & Ricca 1992) into ''normalized ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DNA Supercoil
DNA supercoiling refers to the amount of twist in a particular DNA strand, which determines the amount of strain on it. A given strand may be "positively supercoiled" or "negatively supercoiled" (more or less tightly wound). The amount of a strand’s supercoiling affects a number of biological processes, such as compacting DNA and regulating access to the genetic code (which strongly affects DNA metabolism and possibly gene expression). Certain enzymes, such as topoisomerases, change the amount of DNA supercoiling to facilitate functions such as DNA replication and transcription. The amount of supercoiling in a given strand is described by a mathematical formula that compares it to a reference state known as "relaxed B-form" DNA. Overview In a "relaxed" double-helical segment of B-DNA, the two strands twist around the helical axis once every 10.4–10.5 base pairs of sequence. Adding or subtracting twists, as some enzymes do, imposes strain. If a DNA segment under twist s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
DNA Supercoiling
DNA supercoiling refers to the amount of twist in a particular DNA strand, which determines the amount of strain on it. A given strand may be "positively supercoiled" or "negatively supercoiled" (more or less tightly wound). The amount of a strand’s supercoiling affects a number of biological processes, such as compacting DNA and regulating access to the genetic code (which strongly affects DNA metabolism and possibly gene expression). Certain enzymes, such as topoisomerases, change the amount of DNA supercoiling to facilitate functions such as DNA replication and transcription. The amount of supercoiling in a given strand is described by a mathematical formula that compares it to a reference state known as "relaxed B-form" DNA. Overview In a "relaxed" double-helical segment of B-DNA, the two strands twist around the helical axis once every 10.4–10.5 base pairs of sequence. Adding or subtracting twists, as some enzymes do, imposes strain. If a DNA segment under twist s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simulation Of An Elastic Rod Relieving Torsional Stress By Forming Coils
A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of Conceptual model, models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the computer simulation, simulation. Simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games. Simulation is also used with scientific modelling of natural systems or human systems to gain insight into their functioning, as in economics. Simulation can be used to show the eventual real effects of alternative conditions and courses of action. Simulation is also used when the real system cannot be engaged, because it may not be accessible, or it may be dangerous or unacceptable to engage, or it is being designed bu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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