Linear algebra is the branch of mathematics concerning linear equations such as:
In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix that generalizes the eigendecomposition of a square normal matrix to any matrix via an extension of the polar decomposition.
Proof theory is a major branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as inductively-defined data structures such as plain lists, boxed lists, or trees, which are constructed according to the axioms and rules of inference of the logical system. As such, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature.
Six Sigma (6σ) is a set of techniques and tools for process improvement. It was introduced by American engineer Bill Smith while working at Motorola in 1986. Jack Welch made it central to his business strategy at General Electric in 1995. A six sigma process is one in which 99.99966% of all opportunities to produce some feature of a part are statistically expected to be free of defects.
Rapid-application development (RAD), also called rapid-application building (RAB), is both a general term for adaptive software development approaches, and the name for James Martin's method of rapid development. In general, RAD approaches to software development put less emphasis on planning and more emphasis on an adaptive process. Prototypes are often used in addition to or sometimes even instead of design specifications.
H∞methods are used in control theory to synthesize controllers to achieve stabilization with guaranteed performance. To use H∞ methods, a control designer expresses the control problem as a mathematical optimization problem and then finds the controller that solves this optimization. H∞ techniques have the advantage over classical control techniques in that H∞ techniques are readily applicable to problems involving multivariate systems with cross-coupling between channels; disadvantages of H∞ techniques include the level of mathematical understanding needed to apply them successfully and the need for a reasonably good model of the system to be controlled. It is important to keep in mind that the resulting controller is only optimal with respect to the prescribed cost function and does not necessarily represent the best controller in terms of the usual performance measures used to evaluate controllers such as settling time, energy expended, etc. Also, non-linear constraints such as saturation are generally not well-handled. These methods were introduced into control theory in the late 1970s-early 1980s by George Zames, J. William Helton , and Allen Tannenbaum.
In mathematical statistics, the Fisher information is a way of measuring the amount of information that an observable random variable X carries about an unknown parameter θ of a distribution that models X. Formally, it is the variance of the score, or the expected value of the observed information. In Bayesian statistics, the asymptotic distribution of the posterior mode depends on the Fisher information and not on the prior. The role of the Fisher information in the asymptotic theory of maximum-likelihood estimation was emphasized by the statistician Ronald Fisher. The Fisher information is also used in the calculation of the Jeffreys prior, which is used in Bayesian statistics.
Latent semantic analysis (LSA) is a technique in natural language processing, in particular distributional semantics, of analyzing relationships between a set of documents and the terms they contain by producing a set of concepts related to the documents and terms. LSA assumes that words that are close in meaning will occur in similar pieces of text. A matrix containing word counts per document is constructed from a large piece of text and a mathematical technique called singular value decomposition (SVD) is used to reduce the number of rows while preserving the similarity structure among columns. Documents are then compared by taking the cosine of the angle between the two vectors formed by any two columns. Values close to 1 represent very similar documents while values close to 0 represent very dissimilar documents.
Design for Six Sigma (DFSS) is an Engineering design process, business process management method related to traditional Six Sigma. It is used in many industries, like finance, marketing, basic engineering, process industries, waste management, and electronics. It is based on the use of statistical tools like linear regression and enables empirical research similar to that performed in other fields, such as social science. While the tools and order used in Six Sigma require a process to be in place and functioning, DFSS has the objective of determining the needs of customers and the business, and driving those needs into the product solution so created. DFSS is relevant for relatively simple items / systems. It is used for product or process design in contrast with process improvement. Measurement is the most important part of most Six Sigma or DFSS tools, but whereas in Six Sigma measurements are made from an existing process, DFSS focuses on gaining a deep insight into customer needs and using these to inform every design decision and trade-off.
The World Wide Web has become a major delivery platform for a variety of complex and sophisticated enterprise applications in several domains. In addition to their inherent multifaceted functionality, these Web applications exhibit complex behaviour and place some unique demands on their usability, performance, security, and ability to grow and evolve. However, a vast majority of these applications continue to be developed in an ad hoc way, contributing to problems of usability, maintainability, quality and reliability. While Web development can benefit from established practices from other related disciplines, it has certain distinguishing characteristics that demand special considerations. In recent years, there have been developments towards addressing these considerations.
A concept of design science was introduced in 1957 by R. Buckminster Fuller who defined it as a systematic form of designing. He expanded on this concept in his World Design Science Decade proposal to the International Union of Architects in 1961. The term was later used by S. A. Gregory in the 1965 'The Design Method' Conference where he drew the distinction between scientific method and design method. Gregory was clear in his view that design was not a science and that design science referred to the scientific study of design. Herbert Simon in his 1968 Karl Taylor Compton lectures used and popularized these terms in his argument for the scientific study of the artificial. Over the intervening period the two uses of the term have co-mingled to the point where design science may have both meanings: a science of design and design as a science.
Structured analysis and design technique (SADT) is a systems engineering and software engineering methodology for describing systems as a hierarchy of functions. SADT is a structured analysis modelling language, which uses two types of diagrams: activity models and data models. It was developed in the late 1960s by Douglas T. Ross, and was formalized and published as IDEF0 in 1981.
Axiomatic Product Development Lifecycle (APDL) is a systems engineering product development model proposed by Bulent Gumus that extends the Axiomatic design (AD) method. APDL covers the whole product lifecycle including early factors that affect the entire cycle such as development testing, input constraints and system components.
In systems engineering, software engineering, and computer science, a function model or functional model is a structured representation of the functions within the modeled system or subject area.
In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. For example, the dimension of the matrix below is 2 × 3, because there are two rows and three columns:
Software testability is the degree to which a software artifact supports testing in a given test context. If the testability of the software artifact is high, then finding faults in the system by means of testing is easier.
Lisa Seeman is an inventor and an entrepreneur and has been instrumental in creating standards for interoperability and accessibility.
SDI Tools is a set of commercial software add-in tools for Microsoft Excel developed and distributed by Statistical Design Institute, LLC., a privately owned company located in Texas, United States.
Dynamic Substructuring (DS) is an engineering tool used to model and analyse the dynamics of mechanical systems by means of its components or substructures. Using the dynamic substructuring approach one is able to analyse the dynamic behaviour of substructures separately and to later on calculate the assembled dynamics using coupling procedures. Dynamic substructuring has several advantages over the analysis of the fully assembled system:
The Surveillance of Partially Observable Systems is a research method done for the first time by S. Amir Mir M. and Daniel Lane from 2005 to 2008 at the University of Ottawa, Canada.
