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Improvements in nutritional value for forage crops from the use of analytical chemistry and rumen fermentation technology have been recorded since 1960; this science and technology gave breeders the ability to screen thousands of samples within a small amount of time, meaning breeders could identify a high performing h...
Plant breeding
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Cereal Genomics. Methods in Molecular Biology. Vol.
Plant breeding
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(ISBN 9781439802427), CRC Press, Boca Raton, FL, USA, pp 584 Schlegel, Rolf (2007) Concise Encyclopedia of Crop Improvement: Institutions, Persons, Theories, Methods, and Histories (ISBN 9781560221463), CRC Press, Boca Raton, FL, USA, pp 423 Schlegel, Rolf (2014) Dictionary of Plant Breeding, 2nd ed., (ISBN 978-1439802...
Plant breeding
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Plant breeding is the science of changing the traits of plants in order to produce desired characteristics. It has been used to improve the quality of nutrition in products for humans and animals. The goals of plant breeding are to produce crop varieties that boast unique and superior traits for a variety of applicatio...
Plant breeding
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In molecular biology, an actomyosin contractile ring is a prominent structure during cytokinesis. It forms perpendicular to the axis of the spindle apparatus towards the end of telophase, in which sister chromatids are identically separated at the opposite sides of the spindle forming nuclei (Figure 1). The actomyosin ...
Actomyosin ring
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In mathematics, a quadratic-linear algebra is an algebra over a field with a presentation such that all relations are sums of monomials of degrees 1 or 2 in the generators. They were introduced by Polishchuk and Positselski (2005, p.101). An example is the universal enveloping algebra of a Lie algebra, with generators ...
Quadratic-linear algebra
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106
In computer science, a search algorithm is an algorithm designed to solve a search problem. Search algorithms work to retrieve information stored within particular data structure, or calculated in the search space of a problem domain, with either discrete or continuous values. Although search engines use search algorit...
Search algorithms
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Specific applications of search algorithms include: Problems in combinatorial optimization, such as: The vehicle routing problem, a form of shortest path problem The knapsack problem: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total wei...
Search algorithms
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Molecular biophysics typically addresses biological questions similar to those in biochemistry and molecular biology, seeking to find the physical underpinnings of biomolecular phenomena. Scientists in this field conduct research concerned with understanding the interactions between the various systems of a cell, inclu...
Protein chemistry
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Molecular biophysics is a rapidly evolving interdisciplinary area of research that combines concepts in physics, chemistry, engineering, mathematics and biology. It seeks to understand biomolecular systems and explain biological function in terms of molecular structure, structural organization, and dynamic behaviour at...
Protein chemistry
0.85758
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Computational biology involves the development and application of data-analytical and theoretical methods, mathematical modeling and computational simulation techniques to the study of biological, ecological, behavioral, and social systems. The field is broadly defined and includes foundations in biology, applied mathe...
Protein chemistry
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Protein structure prediction is the inference of the three-dimensional structure of a protein from its amino acid sequence—that is, the prediction of its folding and its secondary and tertiary structure from its primary structure. Structure prediction is fundamentally different from the inverse problem of protein desig...
Protein chemistry
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For example, they could be used to identify and destroy cancer cells. Molecular nanotechnology is a speculative subfield of nanotechnology regarding the possibility of engineering molecular assemblers, biological machines which could re-order matter at a molecular or atomic scale. Nanomedicine would make use of these n...
Protein chemistry
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113
The table below summarizes how algebraic expressions compare with several other types of mathematical expressions by the type of elements they may contain, according to common but not universal conventions. A rational algebraic expression (or rational expression) is an algebraic expression that can be written as a quot...
Algebraic expression
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Usually, π is constructed as a geometric relationship, and the definition of e requires an infinite number of algebraic operations. A rational expression is an expression that may be rewritten to a rational fraction by using the properties of the arithmetic operations (commutative properties and associative properties ...
Algebraic expression
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In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3x2 − 2xy + c is an algebraic expression. Since taking th...
Algebraic expression
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In 1658, in the first edition of The New World of English Words, it says: Algorithme, (a word compounded of Arabick and Spanish,) the art of reckoning by Cyphers. In 1706, in the sixth edition of The New World of English Words, it says: Algorithm, the Art of computing or reckoning by numbers, which contains the five pr...
Algorithmic problem
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Total weight that can be carried is no more than some fixed number X. So, the solution must consider weights of items as well as their value. Quantum algorithm They run on a realistic model of quantum computation. The term is usually used for those algorithms which seem inherently quantum, or use some essential feature...
Algorithmic problem
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In mathematics and computer science, an algorithm ( ) is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use conditionals to d...
Algorithmic problem
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The most common type of equation is a polynomial equation (commonly called also an algebraic equation) in which the two sides are polynomials. The sides of a polynomial equation contain one or more terms.
Mathematical equations
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An algebraic number is a number that is a solution of a non-zero polynomial equation in one variable with rational coefficients (or equivalently — by clearing denominators — with integer coefficients). Numbers such as π that are not algebraic are said to be transcendental. Almost all real and complex numbers are transc...
Mathematical equations
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A parametric equation for a curve expresses the coordinates of the points of the curve as functions of a variable, called a parameter. For example, x = cos ⁡ t y = sin ⁡ t {\displaystyle {\begin{aligned}x&=\cos t\\y&=\sin t\end{aligned}}} are parametric equations for the unit circle, where t is the parameter. Together,...
Mathematical equations
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In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutions — the set of functions that satisfy the equation. Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential e...
Mathematical equations
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A differential equation is a mathematical equation that relates some function with its derivatives. In applications, the functions usually represent physical quantities, the derivatives represent their rates of change, and the equation defines a relationship between the two. They are solved by finding an expression for...
Mathematical equations
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In the United Kingdom, the original boxes (prior to the introduction of the Happy Meal-sized nugget boxes) were of 6, 9, and 20 nuggets. According to Schur's theorem, since 6, 9, and 20 are (setwise) relatively prime, any sufficiently large integer can be expressed as a (non-negative, integer) linear combination of the...
Coin problem
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One special case of the coin problem is sometimes also referred to as the McNugget numbers. The McNuggets version of the coin problem was introduced by Henri Picciotto, who placed it as a puzzle in Games Magazine in 1987, and included it in his algebra textbook co-authored with Anita Wah. Picciotto thought of the appli...
Coin problem
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Reasons for this may be that silicon is less versatile than carbon in forming compounds, that the compounds formed by silicon are unstable, and that it blocks the flow of heat.Even so, biogenic silica is used by some Earth life, such as the silicate skeletal structure of diatoms. According to the clay hypothesis of A. ...
Hypothetical types of biochemistry
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This may suggest a greater variety of complex carbon compounds throughout the cosmos, providing less of a foundation on which to build silicon-based biologies, at least under the conditions prevalent on the surface of planets. Also, even though Earth and other terrestrial planets are exceptionally silicon-rich and carb...
Hypothetical types of biochemistry
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Silicon, on the other hand, interacts with very few other types of atoms. Moreover, where it does interact with other atoms, silicon creates molecules that have been described as "monotonous compared with the combinatorial universe of organic macromolecules". This is because silicon atoms are much bigger, having a larg...
Hypothetical types of biochemistry
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Silicon dioxide, also known as silica and quartz, is very abundant in the universe and has a large temperature range where it is liquid. However, its melting point is 1,600 to 1,725 °C (2,912 to 3,137 °F), so it would be impossible to make organic compounds in that temperature, because all of them would decompose. Sili...
Hypothetical types of biochemistry
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Plant physiology is a subdiscipline of botany concerned with the functioning, or physiology, of plants. Closely related fields include plant morphology (structure of plants), plant ecology (interactions with the environment), phytochemistry (biochemistry of plants), cell biology, genetics, biophysics and molecular biol...
Plant Physiology
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The ripening of fruit and loss of leaves in the winter are controlled in part by the production of the gas ethylene by the plant. Finally, plant physiology includes the study of plant response to environmental conditions and their variation, a field known as environmental physiology. Stress from water loss, changes in ...
Plant Physiology
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Major subdisciplines of plant physiology include phytochemistry (the study of the biochemistry of plants) and phytopathology (the study of disease in plants). The scope of plant physiology as a discipline may be divided into several major areas of research. First, the study of phytochemistry (plant chemistry) is includ...
Plant Physiology
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Whatever name is applied, it deals with the ways in which plants respond to their environment and so overlaps with the field of ecology. Environmental physiologists examine plant response to physical factors such as radiation (including light and ultraviolet radiation), temperature, fire, and wind.
Plant Physiology
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Paradoxically, the subdiscipline of environmental physiology is on the one hand a recent field of study in plant ecology and on the other hand one of the oldest. Environmental physiology is the preferred name of the subdiscipline among plant physiologists, but it goes by a number of other names in the applied sciences....
Plant Physiology
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There may be uncertainty about the shape of a probability distribution because the sample size of the empirical data characterizing it is small. Several methods in traditional statistics have been proposed to account for this sampling uncertainty about the distribution shape, including Kolmogorov–Smirnov and similar co...
Probability box
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Baudrit, C., and D. Dubois (2006). Practical representations of incomplete probabilistic knowledge. Computational Statistics & Data Analysis 51: 86–108. Baudrit, C., D. Dubois, D. Guyonnet (2006).
Probability box
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P-boxes and probability bounds analysis have been used in many applications spanning many disciplines in engineering and environmental science, including: Engineering design Expert elicitation Analysis of species sensitivity distributions Sensitivity analysis in aerospace engineering of the buckling load of the frontsk...
Probability box
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The hidden subgroup problem (HSP) is a topic of research in mathematics and theoretical computer science. The framework captures problems such as factoring, discrete logarithm, graph isomorphism, and the shortest vector problem. This makes it especially important in the theory of quantum computing because Shor's quantu...
Hidden subgroup problem
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The hidden subgroup problem is especially important in the theory of quantum computing for the following reasons. Shor's quantum algorithm for factoring and discrete logarithm (as well as several of its extensions) relies on the ability of quantum computers to solve the HSP for finite Abelian groups. The existence of e...
Hidden subgroup problem
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Many algorithms where quantum speedups occur in quantum computing are instances of the hidden subgroup problem. The following list outlines important instances of the HSP, and whether or not they are solvable.
Hidden subgroup problem
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Discrete probability theory deals with events that occur in countable sample spaces. Examples: Throwing dice, experiments with decks of cards, random walk, and tossing coins. Classical definition: Initially the probability of an event to occur was defined as the number of cases favorable for the event, over the number ...
Mathematical probability
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Common intuition suggests that if a fair coin is tossed many times, then roughly half of the time it will turn up heads, and the other half it will turn up tails. Furthermore, the more often the coin is tossed, the more likely it should be that the ratio of the number of heads to the number of tails will approach unity...
Mathematical probability
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{\displaystyle \sigma ^{2}>0.\,} Then the sequence of random variables Z n = ∑ i = 1 n ( X i − μ ) σ n {\displaystyle Z_{n}={\frac {\sum _{i=1}^{n}(X_{i}-\mu )}{\sigma {\sqrt {n}}}}\,} converges in distribution to a standard normal random variable. For some classes of random variables, the classic central limit theorem...
Mathematical probability
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The central limit theorem (CLT) explains the ubiquitous occurrence of the normal distribution in nature, and this theorem, according to David Williams, "is one of the great results of mathematics. "The theorem states that the average of many independent and identically distributed random variables with finite variance ...
Mathematical probability
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In probability theory, there are several notions of convergence for random variables. They are listed below in the order of strength, i.e., any subsequent notion of convergence in the list implies convergence according to all of the preceding notions. Weak convergence A sequence of random variables X 1 , X 2 , … , {\di...
Mathematical probability
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Most introductions to probability theory treat discrete probability distributions and continuous probability distributions separately. The measure theory-based treatment of probability covers the discrete, continuous, a mix of the two, and more.
Mathematical probability
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147
Beckmann's version of this story has been widely copied in several books and internet sites, usually without his reservations and sometimes with fanciful embellishments. Several attempts to find corroborating evidence for this story, or even for the existence of Valmes, have failed.The proof that four is the highest de...
Fourth-degree equation
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Lodovico Ferrari is credited with the discovery of the solution to the quartic in 1540, but since this solution, like all algebraic solutions of the quartic, requires the solution of a cubic to be found, it could not be published immediately. The solution of the quartic was published together with that of the cubic by ...
Fourth-degree equation
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Though it is now regarded as pseudoscience, belief in a mystical significance of numbers, known as numerology, permeated ancient and medieval thought. Numerology heavily influenced the development of Greek mathematics, stimulating the investigation of many problems in number theory which are still of interest today.Dur...
Numerical value
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Their study or usage is called arithmetic, a term which may also refer to number theory, the study of the properties of numbers. Besides their practical uses, numbers have cultural significance throughout the world. For example, in Western society, the number 13 is often regarded as unlucky, and "a million" may signify...
Numerical value
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The fundamental theorem of algebra asserts that the complex numbers form an algebraically closed field, meaning that every polynomial with complex coefficients has a root in the complex numbers. Like the reals, the complex numbers form a field, which is complete, but unlike the real numbers, it is not ordered. That is,...
Numerical value
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These methods use rotamer libraries, which are collections of favorable conformations for each residue type in proteins. Rotamer libraries may contain information about the conformation, its frequency, and the standard deviations about mean dihedral angles, which can be used in sampling. Rotamer libraries are derived f...
Protein folding problem
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Accurate packing of the amino acid side chains represents a separate problem in protein structure prediction. Methods that specifically address the problem of predicting side-chain geometry include dead-end elimination and the self-consistent mean field methods. The side chain conformations with low energy are usually ...
Protein folding problem
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Ab initio- or de novo- protein modelling methods seek to build three-dimensional protein models "from scratch", i.e., based on physical principles rather than (directly) on previously solved structures. There are many possible procedures that either attempt to mimic protein folding or apply some stochastic method to se...
Protein folding problem
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Secondary structure prediction is a set of techniques in bioinformatics that aim to predict the local secondary structures of proteins based only on knowledge of their amino acid sequence. For proteins, a prediction consists of assigning regions of the amino acid sequence as likely alpha helices, beta strands (often no...
Protein folding problem
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These groups can therefore interact in the protein structure. Proteins consist mostly of 20 different types of L-α-amino acids (the proteinogenic amino acids). These can be classified according to the chemistry of the side chain, which also plays an important structural role.
Protein folding problem
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157
It follows from the first five pairs of axioms that any complement is unique. The set of axioms is self-dual in the sense that if one exchanges ∨ with ∧ and 0 with 1 in an axiom, the result is again an axiom. Therefore, by applying this operation to a Boolean algebra (or Boolean lattice), one obtains another Boolean al...
Boolean algebra (structure)
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158
A Boolean algebra is a set A, equipped with two binary operations ∧ (called "meet" or "and"), ∨ (called "join" or "or"), a unary operation ¬ (called "complement" or "not") and two elements 0 and 1 in A (called "bottom" and "top", or "least" and "greatest" element, also denoted by the symbols ⊥ and ⊤, respectively), suc...
Boolean algebra (structure)
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As a counter-example, considering the non-square-free n=60, the greatest common divisor of 30 and its complement 2 would be 2, while it should be the bottom element 1. Other examples of Boolean algebras arise from topological spaces: if X is a topological space, then the collection of all subsets of X which are both op...
Boolean algebra (structure)
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160
This lattice is a Boolean algebra if and only if n is square-free. The bottom and the top element of this Boolean algebra is the natural number 1 and n, respectively. The complement of a is given by n/a.
Boolean algebra (structure)
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161
A truth assignment in propositional calculus is then a Boolean algebra homomorphism from this algebra to the two-element Boolean algebra. Given any linearly ordered set L with a least element, the interval algebra is the smallest algebra of subsets of L containing all of the half-open intervals [a, b) such that a is in...
Boolean algebra (structure)
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Starting with the propositional calculus with κ sentence symbols, form the Lindenbaum algebra (that is, the set of sentences in the propositional calculus modulo logical equivalence). This construction yields a Boolean algebra. It is in fact the free Boolean algebra on κ generators.
Boolean algebra (structure)
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This can for example be used to show that the following laws (Consensus theorems) are generally valid in all Boolean algebras: (a ∨ b) ∧ (¬a ∨ c) ∧ (b ∨ c) ≡ (a ∨ b) ∧ (¬a ∨ c) (a ∧ b) ∨ (¬a ∧ c) ∨ (b ∧ c) ≡ (a ∧ b) ∨ (¬a ∧ c)The power set (set of all subsets) of any given nonempty set S forms a Boolean algebra, an alg...
Boolean algebra (structure)
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164
The simplest non-trivial Boolean algebra, the two-element Boolean algebra, has only two elements, 0 and 1, and is defined by the rules:It has applications in logic, interpreting 0 as false, 1 as true, ∧ as and, ∨ as or, and ¬ as not. Expressions involving variables and the Boolean operations represent statement forms, ...
Boolean algebra (structure)
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165
A filter of the Boolean algebra A is a subset p such that for all x, y in p we have x ∧ y in p and for all a in A we have a ∨ x in p. The dual of a maximal (or prime) ideal in a Boolean algebra is ultrafilter. Ultrafilters can alternatively be described as 2-valued morphisms from A to the two-element Boolean algebra. T...
Boolean algebra (structure)
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An ideal of the Boolean algebra A is a subset I such that for all x, y in I we have x ∨ y in I and for all a in A we have a ∧ x in I. This notion of ideal coincides with the notion of ring ideal in the Boolean ring A. An ideal I of A is called prime if I ≠ A and if a ∧ b in I always implies a in I or b in I. Furthermor...
Boolean algebra (structure)
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As well as discrete metric spaces, there are more general discrete topological spaces, finite metric spaces, finite topological spaces. The time scale calculus is a unification of the theory of difference equations with that of differential equations, which has applications to fields requiring simultaneous modelling of...
Discrete math
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Many questions and methods concerning differential equations have counterparts for difference equations. For instance, where there are integral transforms in harmonic analysis for studying continuous functions or analogue signals, there are discrete transforms for discrete functions or digital signals.
Discrete math
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169
In discrete calculus and the calculus of finite differences, a function defined on an interval of the integers is usually called a sequence. A sequence could be a finite sequence from a data source or an infinite sequence from a discrete dynamical system. Such a discrete function could be defined explicitly by a list (...
Discrete math
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170
Graph theory, the study of graphs and networks, is often considered part of combinatorics, but has grown large enough and distinct enough, with its own kind of problems, to be regarded as a subject in its own right. Graphs are one of the prime objects of study in discrete mathematics. They are among the most ubiquitous...
Discrete math
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They can model many types of relations and process dynamics in physical, biological and social systems. In computer science, they can represent networks of communication, data organization, computational devices, the flow of computation, etc. In mathematics, they are useful in geometry and certain parts of topology, e....
Discrete math
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172
In university curricula, discrete mathematics appeared in the 1980s, initially as a computer science support course; its contents were somewhat haphazard at the time. The curriculum has thereafter developed in conjunction with efforts by ACM and MAA into a course that is basically intended to develop mathematical matur...
Discrete math
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Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are significant in appl...
Discrete math
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However, there is no exact definition of the term "discrete mathematics".The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business...
Discrete math
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Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continuous functions). Objects studied in discrete mathematics include integers, graphs, ...
Discrete math
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Number theory is concerned with the properties of numbers in general, particularly integers. It has applications to cryptography and cryptanalysis, particularly with regard to modular arithmetic, diophantine equations, linear and quadratic congruences, prime numbers and primality testing. Other discrete aspects of numb...
Discrete math
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177
Modern Molecular phylogenetics largely ignores morphological characters, relying on DNA sequences as data. Molecular analysis of DNA sequences from most families of flowering plants enabled the Angiosperm Phylogeny Group to publish in 1998 a phylogeny of flowering plants, answering many of the questions about relations...
Plant biology
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20th century developments in plant biochemistry have been driven by modern techniques of organic chemical analysis, such as spectroscopy, chromatography and electrophoresis. With the rise of the related molecular-scale biological approaches of molecular biology, genomics, proteomics and metabolomics, the relationship b...
Plant biology
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Building on the extensive earlier work of Alphonse de Candolle, Nikolai Vavilov (1887–1943) produced accounts of the biogeography, centres of origin, and evolutionary history of economic plants.Particularly since the mid-1960s there have been advances in understanding of the physics of plant physiological processes suc...
Plant biology
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The discipline of plant ecology was pioneered in the late 19th century by botanists such as Eugenius Warming, who produced the hypothesis that plants form communities, and his mentor and successor Christen C. Raunkiær whose system for describing plant life forms is still in use today. The concept that the composition o...
Plant biology
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Building upon the gene-chromosome theory of heredity that originated with Gregor Mendel (1822–1884), August Weismann (1834–1914) proved that inheritance only takes place through gametes. No other cells can pass on inherited characters. The work of Katherine Esau (1898–1997) on plant anatomy is still a major foundation ...
Plant biology
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The single celled green alga Chlamydomonas reinhardtii, while not an embryophyte itself, contains a green-pigmented chloroplast related to that of land plants, making it useful for study. A red alga Cyanidioschyzon merolae has also been used to study some basic chloroplast functions. Spinach, peas, soybeans and a moss ...
Plant biology
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183
Model plants such as Arabidopsis thaliana are used for studying the molecular biology of plant cells and the chloroplast. Ideally, these organisms have small genomes that are well known or completely sequenced, small stature and short generation times. Corn has been used to study mechanisms of photosynthesis and phloem...
Plant biology
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A considerable amount of new knowledge about plant function comes from studies of the molecular genetics of model plants such as the Thale cress, Arabidopsis thaliana, a weedy species in the mustard family (Brassicaceae). The genome or hereditary information contained in the genes of this species is encoded by about 13...
Plant biology
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The finding in 1939 that plant callus could be maintained in culture containing IAA, followed by the observation in 1947 that it could be induced to form roots and shoots by controlling the concentration of growth hormones were key steps in the development of plant biotechnology and genetic modification. Cytokinins are...
Plant biology
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Plant biochemistry is the study of the chemical processes used by plants. Some of these processes are used in their primary metabolism like the photosynthetic Calvin cycle and crassulacean acid metabolism. Others make specialised materials like the cellulose and lignin used to build their bodies, and secondary products...
Plant biology
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Plant responses to climate and other environmental changes can inform our understanding of how these changes affect ecosystem function and productivity. For example, plant phenology can be a useful proxy for temperature in historical climatology, and the biological impact of climate change and global warming. Palynolog...
Plant biology
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These techniques allowed for the discovery and detailed analysis of many molecules and metabolic pathways of the cell, such as glycolysis and the Krebs cycle (citric acid cycle), and led to an understanding of biochemistry on a molecular level. Another significant historic event in biochemistry is the discovery of the ...
Biochemistry
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189
In 1828, Friedrich Wöhler published a paper on his serendipitous urea synthesis from potassium cyanate and ammonium sulfate; some regarded that as a direct overthrow of vitalism and the establishment of organic chemistry. However, the Wöhler synthesis has sparked controversy as some reject the death of vitalism at his ...
Biochemistry
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In 1877, Felix Hoppe-Seyler used the term (biochemie in German) as a synonym for physiological chemistry in the foreword to the first issue of Zeitschrift für Physiologische Chemie (Journal of Physiological Chemistry) where he argued for the setting up of institutes dedicated to this field of study. The German chemist ...
Biochemistry
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Some might also point as its beginning to the influential 1842 work by Justus von Liebig, Animal chemistry, or, Organic chemistry in its applications to physiology and pathology, which presented a chemical theory of metabolism, or even earlier to the 18th century studies on fermentation and respiration by Antoine Lavoi...
Biochemistry
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At its most comprehensive definition, biochemistry can be seen as a study of the components and composition of living things and how they come together to become life. In this sense, the history of biochemistry may therefore go back as far as the ancient Greeks. However, biochemistry as a specific scientific discipline...
Biochemistry
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The 4 main classes of molecules in biochemistry (often called biomolecules) are carbohydrates, lipids, proteins, and nucleic acids. Many biological molecules are polymers: in this terminology, monomers are relatively small macromolecules that are linked together to create large macromolecules known as polymers. When mo...
Biochemistry
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However, NMR experiments are able to provide information from which a subset of distances between pairs of atoms can be estimated, and the final possible conformations for a protein are determined by solving a distance geometry problem. Dual polarisation interferometry is a quantitative analytical method for measuring ...
Structural proteins
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195
A key question in molecular biology is how proteins evolve, i.e. how can mutations (or rather changes in amino acid sequence) lead to new structures and functions? Most amino acids in a protein can be changed without disrupting activity or function, as can be seen from numerous homologous proteins across species (as co...
Structural proteins
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Circuit theory deals with electrical networks where the fields are largely confined around current carrying conductors. In such circuits, even Maxwell's equations can be dispensed with and simpler formulations used. On the other hand, a quantum treatment of electromagnetism is important in chemistry. Chemical reactions...
Introduction to electromagnetism
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Classical physics is still an accurate approximation in most situations involving macroscopic objects. With few exceptions, quantum theory is only necessary at the atomic scale and a simpler classical treatment can be applied. Further simplifications of treatment are possible in limited situations.
Introduction to electromagnetism
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Albert Einstein showed that the magnetic field arises through the relativistic motion of the electric field and thus magnetism is merely a side effect of electricity. The modern theoretical treatment of electromagnetism is as a quantum field in quantum electrodynamics. In many situations of interest to electrical engin...
Introduction to electromagnetism
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The fundamental law that describes the gravitational force on a massive object in classical physics is Newton's law of gravity. Analogously, Coulomb's law is the fundamental law that describes the force that charged objects exert on one another. It is given by the formula F = k e q 1 q 2 r 2 {\displaystyle F=k_{\text{e...
Introduction to electromagnetism
0.854357