DeterminantIn mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism. The determinant of a product of matrices is the product of their determinants (the preceding property is a corollary of this one). The determinant of a matrix A is denoted det(A), det A, or .
Del in cylindrical and spherical coordinatesThis is a list of some vector calculus formulae for working with common curvilinear coordinate systems. This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): The polar angle is denoted by : it is the angle between the z-axis and the radial vector connecting the origin to the point in question. The azimuthal angle is denoted by : it is the angle between the x-axis and the projection of the radial vector onto the xy-plane.
Multiplicative inverseIn mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the function f(x) that maps x to 1/x, is one of the simplest examples of a function which is its own inverse (an involution).
Entire functionIn complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane. Typical examples of entire functions are polynomials and the exponential function, and any finite sums, products and compositions of these, such as the trigonometric functions sine and cosine and their hyperbolic counterparts sinh and cosh, as well as derivatives and integrals of entire functions such as the error function.
Cas9Cas9 (CRISPR associated protein 9, formerly called Cas5, Csn1, or Csx12) is a 160 kilodalton protein which plays a vital role in the immunological defense of certain bacteria against DNA viruses and plasmids, and is heavily utilized in genetic engineering applications. Its main function is to cut DNA and thereby alter a cell's genome. The CRISPR-Cas9 genome editing technique was a significant contributor to the Nobel Prize in Chemistry in 2020 being awarded to Emmanuelle Charpentier and Jennifer Doudna.
CRISPRCRISPR (ˈkrɪspər) (an acronym for clustered regularly interspaced short palindromic repeats) is a family of DNA sequences found in the genomes of prokaryotic organisms such as bacteria and archaea. These sequences are derived from DNA fragments of bacteriophages that had previously infected the prokaryote. They are used to detect and destroy DNA from similar bacteriophages during subsequent infections. Hence these sequences play a key role in the antiviral (i.e. anti-phage) defense system of prokaryotes and provide a form of acquired immunity.
Douglas firThe Douglas fir (Pseudotsuga menziesii) is an evergreen conifer species in the pine family, Pinaceae. It is native to western North America and is also known as Douglas-fir, Douglas spruce, Oregon pine, and Columbian pine. There are three varieties: coast Douglas-fir (P. menziesii var. menziesii), Rocky Mountain Douglas-fir (P. menziesii var. glauca) and Mexican Douglas-fir (P. menziesii var. lindleyana). Despite its common names, it is not a true fir (genus Abies), spruce (genus Picea), or pine (genus Pinus).
Original sin'Original sin' is the Christian doctrine that holds that humans, through the fact of birth, inherit a tainted nature with a proclivity to sinful conduct in need of regeneration. The biblical basis for the belief is generally found in Genesis 3 (the story of the expulsion of Adam and Eve from the Garden of Eden), in a line in Psalm 51:5 ("I was brought forth in iniquity, and in sin did my mother conceive me"), and in Paul's Epistle to the Romans, 5:12-21 ("Therefore, just as sin entered the world through one man, and death through sin, and in this way death came to all people, because all sinned").
FirFirs are evergreen coniferous trees belonging to the genus Abies ('eIbi%iz) in the family Pinaceae. There are approximately 48–56 extant species, found on mountains throughout much of North and Central America, Europe, Asia, and North Africa. The genus is most closely related to Cedrus (cedar). The genus name is derived from the Latin "to rise" in reference to the height of its species. The common English name originates with the Old Norse, fyri, or the Old Danish, fyr.
RiceRice is the seed of the grass species Oryza sativa (Asian rice) or, less commonly, O. glaberrima (African rice). The name wild rice is usually used for species of the genera Zizania and Porteresia, both wild and domesticated, although the term may also be used for primitive or uncultivated varieties of Oryza. As a cereal grain, domesticated rice is the most widely consumed staple food for over half of the world's human population, particularly in Asia and Africa.
DichromacyDichromacy (from Greek di, meaning "two" and chromo, meaning "color") is the state of having two types of functioning photoreceptors, called cone cells, in the eyes. Organisms with dichromacy are called dichromats. Dichromats require only two primary colors to be able to represent their visible gamut. By comparison, trichromats need three primary colors, and tetrachromats need four. Likewise, every color in a dichromat's gamut can be evoked with monochromatic light.
Rice hullsRice hulls (or rice husks) are the hard protecting coverings of grains of rice. In addition to protecting rice during the growing season, rice hulls can be put to use as building material, fertilizer, insulation material, or fuel. Rice hulls are part of the chaff of the rice. Rice hulls are part of the rice seed. The hull protects the grain during the growing season from pests. The hull is formed from hard materials, including opaline silica and lignin.
