Strength of materialsThe field of strength of materials (also called mechanics of materials) typically refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio.
Rearrangement reactionIn organic chemistry, a rearrangement reaction is a broad class of organic reactions where the carbon skeleton of a molecule is rearranged to give a structural isomer of the original molecule. Often a substituent moves from one atom to another atom in the same molecule, hence these reactions are usually intramolecular. In the example below, the substituent R moves from carbon atom 1 to carbon atom 2: Intermolecular rearrangements also take place.
Inner product spaceIn mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an inner product. The inner product of two vectors in the space is a scalar, often denoted with angle brackets such as in . Inner products allow formal definitions of intuitive geometric notions, such as lengths, angles, and orthogonality (zero inner product) of vectors. Inner product spaces generalize Euclidean vector spaces, in which the inner product is the dot product or scalar product of Cartesian coordinates.
Organoboron chemistryOrganoboron chemistry or organoborane chemistry is the chemistry of organoboron compounds or organoboranes, which are chemical compounds of boron and carbon that are organic derivatives of borane (BH3), for example trialkyl boranes. . Organoboron compounds are important reagents in organic chemistry enabling many chemical transformations, the most important ones being hydroboration and carboboration. Reactions of organoborates and boranes involve the transfer of a nucleophilic group attached to boron to an electrophilic center either inter- or intramolecularly.
Natural buildingA natural building involves a range of building systems and materials that place major emphasis on sustainability. Ways of achieving sustainability through natural building focus on durability and the use of minimally processed, plentiful or renewable resources, as well as those that, while recycled or salvaged, produce healthy living environments and maintain indoor air quality. Natural building tends to rely on human labor, more than technology. As Michael G.
Borel functional calculusIn functional analysis, a branch of mathematics, the Borel functional calculus is a functional calculus (that is, an assignment of operators from commutative algebras to functions defined on their spectra), which has particularly broad scope. Thus for instance if T is an operator, applying the squaring function s → s2 to T yields the operator T2. Using the functional calculus for larger classes of functions, we can for example define rigorously the "square root" of the (negative) Laplacian operator −Δ or the exponential The 'scope' here means the kind of function of an operator which is allowed.
Injective tensor productIn mathematics, the injective tensor product of two topological vector spaces (TVSs) was introduced by Alexander Grothendieck and was used by him to define nuclear spaces. An injective tensor product is in general not necessarily complete, so its completion is called the . Injective tensor products have applications outside of nuclear spaces.
Chiral auxiliaryIn stereochemistry, a chiral auxiliary is a stereogenic group or unit that is temporarily incorporated into an organic compound in order to control the stereochemical outcome of the synthesis. The chirality present in the auxiliary can bias the stereoselectivity of one or more subsequent reactions. The auxiliary can then be typically recovered for future use. Most biological molecules and pharmaceutical targets exist as one of two possible enantiomers; consequently, chemical syntheses of natural products and pharmaceutical agents are frequently designed to obtain the target in enantiomerically pure form.
Hermitian adjointIn mathematics, specifically in operator theory, each linear operator on an inner product space defines a Hermitian adjoint (or adjoint) operator on that space according to the rule where is the inner product on the vector space. The adjoint may also be called the Hermitian conjugate or simply the Hermitian after Charles Hermite. It is often denoted by A† in fields like physics, especially when used in conjunction with bra–ket notation in quantum mechanics.
Random accessRandom access (more precisely and more generally called direct access) is the ability to access an arbitrary element of a sequence in equal time or any datum from a population of addressable elements roughly as easily and efficiently as any other, no matter how many elements may be in the set. In computer science it is typically contrasted to sequential access which requires data to be retrieved in the order it was stored. For example, data might be stored notionally in a single sequence like a row, in two dimensions like rows and columns on a surface, or in multiple dimensions.
