|
LBOZ
LBOZ is a coefficient used in spectrophotometry to estimate selectivity (amount of overlapping of spectra) in a quantitative manner. It is named after its creators: Lorber, Bergmann, von Oepen, and Zinn. Definition Let \mathbf be a matrix of the spectra (absorbances), where the ''k'' rows correspond to the components in mixture and ''n'' columns correspond to the sequence of wavelengths. The LBOZ criterion for ''k''th component is calculated from the following formula: :\xi_k = \frac where \mathbf^ means a pseudoinverse of the matrix and \, \cdots \, means an euclidean length of a vector. Properties The image above show synthetic gaussian spectra. The LBOZ criteria are: 0.561 for black compound, 0.402 for red compound, 0.899 for green and 0.549 for blue. LBOZ always lie in range and has strong mathematical sense - it presents the amount of spectral signal which is not overlapped by the others. Hence, the uncertainty Uncertainty refers to epistemic situations inv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectrophotometry
Spectrophotometry is a branch of electromagnetic spectroscopy concerned with the quantitative measurement of the reflection or transmission properties of a material as a function of wavelength. Spectrophotometry uses photometers, known as spectrophotometers, that can measure the intensity of a light beam at different wavelengths. Although spectrophotometry is most commonly applied to ultraviolet, visible, and infrared radiation, modern spectrophotometers can interrogate wide swaths of the electromagnetic spectrum, including x-ray, ultraviolet, visible, infrared, and/or microwave wavelengths. Overview Spectrophotometry is a tool that hinges on the quantitative analysis of molecules depending on how much light is absorbed by colored compounds. Important features of spectrophotometers are spectral bandwidth (the range of colors it can transmit through the test sample), the percentage of sample-transmission, the logarithmic range of sample-absorption, and sometimes a percentage of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrimination
Discrimination is the act of making unjustified distinctions between people based on the groups, classes, or other categories to which they belong or are perceived to belong. People may be discriminated on the basis of race, gender, age, religion, disability, or sexual orientation, as well as other categories. Discrimination especially occurs when individuals or groups are unfairly treated in a way which is worse than other people are treated, on the basis of their actual or perceived membership in certain groups or social categories. It involves restricting members of one group from opportunities or privileges that are available to members of another group. Discriminatory traditions, policies, ideas, practices and laws exist in many countries and institutions in all parts of the world, including territories where discrimination is generally looked down upon. In some places, attempts such as quotas have been used to benefit those who are believed to be current or past victims ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectrum
A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors in visible light after passing through a prism. As scientific understanding of light advanced, it came to apply to the entire electromagnetic spectrum. It thereby became a mapping of a range of magnitudes (wavelengths) to a range of qualities, which are the perceived "colors of the rainbow" and other properties which correspond to wavelengths that lie outside of the visible light spectrum. Spectrum has since been applied by analogy to topics outside optics. Thus, one might talk about the " spectrum of political opinion", or the "spectrum of activity" of a drug, or the "autism spectrum". In these uses, values within a spectrum may not be associated with precisely quantifiable numbers or definitions. Such uses imply a broad range of condition ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudoinverse
In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element ''x'' is an element ''y'' that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of matrices than invertible matrices. Generalized inverses can be defined in any mathematical structure that involves associative multiplication, that is, in a semigroup. This article describes generalized inverses of a matrix A. A matrix A^\mathrm \in \mathbb^ is a generalized inverse of a matrix A \in \mathbb^ if AA^\mathrmA = A. A generalized inverse exists for an arbitrary matrix, and when a matrix has a regular inverse, this inverse is its unique generalized inverse. Motivation Consider the linear system :Ax = y where A is an n \times m matrix and y \in \mathcal R(A), the column space of A. If A is nonsingular (which implies n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, Euclid's ''Elements'', it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension (mathematics), dimension, including the three-dimensional space and the ''Euclidean plane'' (dimension two). The qualifier "Euclidean" is used to distinguish Euclidean spaces from other spaces that were later considered in physics and modern mathematics. Ancient History of geometry#Greek geometry, Greek geometers introduced Euclidean space for modeling the physical space. Their work was collected by the Greek mathematics, ancient Greek mathematician Euclid in his ''Elements'', with the great innovation of ''mathematical proof, proving'' all properties of the space as theorems, by starting from a few fundamental properties, called ''postulates'', which either were considered as eviden ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f(x) = \exp (-x^2) and with parametric extension f(x) = a \exp\left( -\frac \right) for arbitrary real constants , and non-zero . It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric " bell curve" shape. The parameter is the height of the curve's peak, is the position of the center of the peak, and (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell". Gaussian functions are often used to represent the probability density function of a normally distributed random variable with expected value and variance . In this case, the Gaussian is of the form g(x) = \frac \exp\left( -\frac \frac \right). Gaussian functions are widely used in statistics to describe the normal distributions, in signal processing to define Gaussian filters, in image processing where two-dimensio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uncertainty
Uncertainty refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or stochastic environments, as well as due to ignorance, indolence, or both. It arises in any number of fields, including insurance, philosophy, physics, statistics, economics, finance, medicine, psychology, sociology, engineering, metrology, meteorology, ecology and information science. Concepts Although the terms are used in various ways among the general public, many specialists in decision theory, statistics and other quantitative fields have defined uncertainty, risk, and their measurement as: Uncertainty The lack of certainty, a state of limited knowledge where it is impossible to exactly describe the existing state, a future outcome, or more than one possible outcome. ;Measurement of uncertainty: A set of possible states or outc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
