Geometric transformationIn mathematics, a geometric transformation is any bijection of a set to itself (or to another such set) with some salient geometrical underpinning. More specifically, it is a function whose domain and range are sets of points — most often both or both — such that the function is bijective so that its inverse exists. The study of geometry may be approached by the study of these transformations. Geometric transformations can be classified by the dimension of their operand sets (thus distinguishing between, say, planar transformations and spatial transformations).
Cellulose fiberCellulose fibers (ˈsɛljʊloʊs,_-loʊz) are fibers made with ethers or esters of cellulose, which can be obtained from the bark, wood or leaves of plants, or from other plant-based material. In addition to cellulose, the fibers may also contain hemicellulose and lignin, with different percentages of these components altering the mechanical properties of the fibers. The main applications of cellulose fibers are in the textile industry, as chemical filters, and as fiber-reinforcement composites, due to their similar properties to engineered fibers, being another option for biocomposites and polymer composites.
Transformation matrixIn linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then for some matrix , called the transformation matrix of . Note that has rows and columns, whereas the transformation is from to . There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Matrices allow arbitrary linear transformations to be displayed in a consistent format, suitable for computation.
Fluid catalytic crackingFluid Catalytic Cracking (FCC) is the conversion process used in petroleum refineries to convert the high-boiling point, high-molecular weight hydrocarbon fractions of petroleum (crude oils) into gasoline, alkene gases, and other petroleum products. The cracking of petroleum hydrocarbons was originally done by thermal cracking, now virtually replaced by catalytic cracking, which yields greater volumes of high octane rating gasoline; and produces by-product gases, with more carbon-carbon double bonds (i.e.
Total derivativeIn mathematics, the total derivative of a function f at a point is the best linear approximation near this point of the function with respect to its arguments. Unlike partial derivatives, the total derivative approximates the function with respect to all of its arguments, not just a single one. In many situations, this is the same as considering all partial derivatives simultaneously. The term "total derivative" is primarily used when f is a function of several variables, because when f is a function of a single variable, the total derivative is the same as the ordinary derivative of the function.
Carboxymethyl celluloseCarboxymethyl cellulose (CMC) or cellulose gum is a cellulose derivative with carboxymethyl groups (-CH2-COOH) bound to some of the hydroxyl groups of the glucopyranose monomers that make up the cellulose backbone. It is often used as its sodium salt, sodium carboxymethyl cellulose. It used to be marketed under the name Tylose, a registered trademark of SE Tylose. Carboxymethyl cellulose is synthesized by the alkali-catalyzed reaction of cellulose with chloroacetic acid.
Religious conversionReligious conversion is the adoption of a set of beliefs identified with one particular religious denomination to the exclusion of others. Thus "religious conversion" would describe the abandoning of adherence to one denomination and affiliating with another. This might be from one to another denomination within the same religion, for example, from Protestant Christianity to Roman Catholicism or from Sunnī Islam to Shīʿa Islam. In some cases, religious conversion "marks a transformation of religious identity and is symbolized by special rituals".
Methyl celluloseMethyl cellulose (or methylcellulose) is a compound derived from cellulose. It is sold under a variety of trade names and is used as a thickener and emulsifier in various food and cosmetic products, and also as a bulk-forming laxative. Like cellulose, it is not digestible, non-toxic, and not an allergen. In 2020, it was the 422nd most commonly prescribed medication in the United States, with more than 100 thousand prescriptions. Methyl cellulose has a wide range of uses. Methyl cellulose is used to treat constipation.
Generalizations of the derivativeIn mathematics, the derivative is a fundamental construction of differential calculus and admits many possible generalizations within the fields of mathematical analysis, combinatorics, algebra, geometry, etc. The Fréchet derivative defines the derivative for general normed vector spaces . Briefly, a function , an open subset of , is called Fréchet differentiable at if there exists a bounded linear operator such that Functions are defined as being differentiable in some open neighbourhood of , rather than at individual points, as not doing so tends to lead to many pathological counterexamples.
Selective catalytic reductionSelective catalytic reduction (SCR) means of converting nitrogen oxides, also referred to as NOxNOx with the aid of a catalyst into diatomic nitrogen (N2), and water (H2O). A reductant, typically anhydrous ammonia (NH3), aqueous ammonia (NH4OH), or a urea (CO(NH2)2) solution, is added to a stream of flue or exhaust gas and is reacted onto a catalyst. As the reaction drives toward completion, nitrogen (N2), and carbon dioxide (CO2), in the case of urea use, are produced.
