Window functionIn signal processing and statistics, a window function (also known as an apodization function or tapering function) is a mathematical function that is zero-valued outside of some chosen interval, normally symmetric around the middle of the interval, usually approaching a maximum in the middle, and usually tapering away from the middle. Mathematically, when another function or waveform/data-sequence is "multiplied" by a window function, the product is also zero-valued outside the interval: all that is left is the part where they overlap, the "view through the window".
Kaiser windowThe Kaiser window, also known as the Kaiser–Bessel window, was developed by James Kaiser at Bell Laboratories. It is a one-parameter family of window functions used in finite impulse response filter design and spectral analysis. The Kaiser window approximates the DPSS window which maximizes the energy concentration in the main lobe but which is difficult to compute. The Kaiser window and its Fourier transform are given by: where: I0 is the zeroth-order modified Bessel function of the first kind, L is the window duration, and α is a non-negative real number that determines the shape of the window.
Carboxylic acidIn organic chemistry, a carboxylic acid is an organic acid that contains a carboxyl group () attached to an R-group. The general formula of a carboxylic acid is or , with R referring to the alkyl, alkenyl, aryl, or other group. Carboxylic acids occur widely. Important examples include the amino acids and fatty acids. Deprotonation of a carboxylic acid gives a carboxylate anion. Carboxylic acids are commonly identified by their trivial names. They often have the suffix -ic acid.
Hamiltonian (quantum mechanics)In quantum mechanics, the Hamiltonian of a system is an operator corresponding to the total energy of that system, including both kinetic energy and potential energy. Its spectrum, the system's energy spectrum or its set of energy eigenvalues, is the set of possible outcomes obtainable from a measurement of the system's total energy. Due to its close relation to the energy spectrum and time-evolution of a system, it is of fundamental importance in most formulations of quantum theory.
Potassium hydroxidePotassium hydroxide is an inorganic compound with the formula KOH, and is commonly called caustic potash. Along with sodium hydroxide (NaOH), KOH is a prototypical strong base. It has many industrial and niche applications, most of which exploit its caustic nature and its reactivity toward acids. An estimated 700,000 to 800,000 tonnes were produced in 2005. KOH is noteworthy as the precursor to most soft and liquid soaps, as well as numerous potassium-containing chemicals. It is a white solid that is dangerously corrosive.
Enzyme kineticsEnzyme kinetics is the study of the rates of enzyme-catalysed chemical reactions. In enzyme kinetics, the reaction rate is measured and the effects of varying the conditions of the reaction are investigated. Studying an enzyme's kinetics in this way can reveal the catalytic mechanism of this enzyme, its role in metabolism, how its activity is controlled, and how a drug or a modifier (inhibitor or activator) might affect the rate. An enzyme (E) is typically a protein molecule that promotes a reaction of another molecule, its substrate (S).
Potassium permanganatePotassium permanganate is an inorganic compound with the chemical formula KMnO4. It is a purplish-black crystalline salt, that dissolves in water as K+ and MnO4-, an intensely pink to purple solution. Potassium permanganate is widely used in the chemical industry and laboratories as a strong oxidizing agent, and also as a medication for dermatitis, for cleaning wounds, and general disinfection. It is on the World Health Organization's List of Essential Medicines. In 2000, worldwide production was estimated at 30,000 tons.
Wittig reactionThe Wittig reaction or Wittig olefination is a chemical reaction of an aldehyde or ketone with a triphenyl phosphonium ylide called a Wittig reagent. Wittig reactions are most commonly used to convert aldehydes and ketones to alkenes. Most often, the Wittig reaction is used to introduce a methylene group using methylenetriphenylphosphorane (Ph3P=CH2). Using this reagent, even a sterically hindered ketone such as camphor can be converted to its methylene derivative.
MagnesiumMagnesium is a chemical element with the symbol Mg and atomic number 12. It is a shiny gray metal having a low density, low melting point and high chemical reactivity. Like the other alkaline earth metals (group 2 of the periodic table) it occurs naturally only in combination with other elements and it almost always has an oxidation state of +2. It reacts readily with air to form a thin passivation coating of magnesium oxide that inhibits further corrosion of the metal. The free metal burns with a brilliant-white light.
Potassium iodatePotassium iodate (KIO3) is an ionic chemical compound consisting of K+ ions and IO3− ions in a 1:1 ratio. Potassium iodate is an oxidizing agent and as such it can cause fires if in contact with combustible materials or reducing agents. It can be prepared by reacting a potassium-containing base such as potassium hydroxide with iodic acid, for example: HIO3 + KOH → KIO3 + H2O It can also be prepared by adding iodine to a hot, concentrated solution of potassium hydroxide.
