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Wax jack | Wax jack | The wax jack was first introduced in 1700. Before that time a simple taper was used in a loose ball. Despite the resemblance to a candle, they were not used for illumination. Although common in England and Europe, they were not used much in North America.Most early wax jacks were worked by silversmiths, although later models also exist in other metals such as iron, brass or bell metal. |
Wax jack | Description | A wax jack was a vertical or horizontal shaft around which a thin beeswax taper was coiled. The top end protruded through a hole in a pan that had a pincer to hold the taper in place. This allowed the taper to be lit and the resulting puddle of wax easily controlled. Some models, called "bougie boxes" had a pierced enclosure around the shaft to protect the taper. They were often used when travelling, and to protect the taper from mice. Others included a snuffer. |
Cutaneous and Ocular Toxicology | Cutaneous and Ocular Toxicology | Cutaneous and Ocular Toxicology is an international, peer-reviewed medical journal that covers all types of harm to skin and eyes. It is published by Taylor and Francis Group. Topics covered include pharmaceutical and medical products; consumer, personal care, and household products; and issues in environmental and occupational exposures. The editor-in-chief is A. Wallace Hayes, Harvard School of Public Health.According to ISI it received an impact factor of 1.122 as reported in the 2014 Journal Citation Reports by Thomson Reuters, ranking it 43rd out of 57 journals in the category "Ophthalmology" and ranking it 75th out of 87 journals in the category "Toxicology". |
Linearly ordered group | Linearly ordered group | In mathematics, specifically abstract algebra, a linearly ordered or totally ordered group is a group G equipped with a total order "≤" that is translation-invariant. This may have different meanings. We say that (G, ≤) is a: left-ordered group if ≤ is left-invariant, that is a ≤ b implies ca ≤ cb for all a, b, c in G, right-ordered group if ≤ is right-invariant, that is a ≤ b implies ac ≤ bc for all a, b, c in G, bi-ordered group if ≤ is bi-invariant, that is it is both left- and right-invariant.A group G is said to be left-orderable (or right-orderable, or bi-orderable) if there exists a left- (or right-, or bi-) invariant order on G. A simple necessary condition for a group to be left-orderable is to have no elements of finite order; however this is not a sufficient condition. It is equivalent for a group to be left- or right-orderable; however there exist left-orderable groups which are not bi-orderable. |
Linearly ordered group | Further definitions | In this section ≤ is a left-invariant order on a group G with identity element e . All that is said applies to right-invariant orders with the obvious modifications. Note that ≤ being left-invariant is equivalent to the order ≤′ defined by g≤′h if and only if h−1≤g−1 being right-invariant. In particular a group being left-orderable is the same as it being right-orderable. In analogy with ordinary numbers we call an element g≠e of an ordered group positive if e≤g . The set of positive elements in an ordered group is called the positive cone, it is often denoted with G+ ; the slightly different notation G+ is used for the positive cone together with the identity element.The positive cone G+ characterises the order ≤ ; indeed, by left-invariance we see that g≤h if and only if g−1h∈G+ . In fact a left-ordered group can be defined as a group G together with a subset P satisfying the two conditions that: for g,h∈P we have also gh∈P let P−1={g−1,g∈P} , then G is the disjoint union of P,P−1 and {e} .The order ≤P associated with P is defined by g≤Ph⇔g−1h∈P ; the first condition amounts to left-invariance and the second to the order being well-defined and total. The positive cone of ≤P is P The left-invariant order ≤ is bi-invariant if and only if it is conjugacy invariant, that is if g≤h then for any x∈G we have xgx−1≤xhx−1 as well. This is equivalent to the positive cone being stable under inner automorphisms. If a∈G , then the absolute value of a , denoted by |a| , is defined to be: If in addition the group G is abelian, then for any a,b∈G a triangle inequality is satisfied: |a+b|≤|a|+|b| |
Linearly ordered group | Examples | Any left- or right-orderable group is torsion-free, that is it contains no elements of finite order besides the identity. Conversely, F. W. Levi showed that a torsion-free abelian group is bi-orderable; this is still true for nilpotent groups but there exist torsion-free, finitely presented groups which are not left-orderable.
Archimedean ordered groups Otto Hölder showed that every Archimedean group (a bi-ordered group satisfying an Archimedean property) is isomorphic to a subgroup of the additive group of real numbers, (Fuchs & Salce 2001, p. 61). |
Linearly ordered group | Examples | If we write the Archimedean l.o. group multiplicatively, this may be shown by considering the Dedekind completion, G^ of the closure of a l.o. group under n th roots. We endow this space with the usual topology of a linear order, and then it can be shown that for each g∈G^ the exponential maps lim lim igqi are well defined order preserving/reversing, topological group isomorphisms. Completing a l.o. group can be difficult in the non-Archimedean case. In these cases, one may classify a group by its rank: which is related to the order type of the largest sequence of convex subgroups. |
Linearly ordered group | Examples | Other examples Free groups are left-orderable. More generally this is also the case for right-angled Artin groups. Braid groups are also left-orderable.The group given by the presentation ⟨a,b|a2ba2b−1,b2ab2a−1⟩ is torsion-free but not left-orderable; note that it is a 3-dimensional crystallographic group (it can be realised as the group generated by two glided half-turns with orthogonal axes and the same translation length), and it is the same group that was proven to be a counterexample to the unit conjecture. More generally the topic of orderability of 3--manifold groups is interesting for its relation with various topological invariants. There exists a 3-manifold group which is left-orderable but not bi-orderable (in fact it does not satisfy the weaker property of being locally indicable). Left-orderable groups have also attracted interest from the perspective of dynamical systems cas it is known that a countable group is left-orderable if and only if it acts on the real line by homeomorphisms. Non-examples related to this paradigm are lattices in higher rank Lie groups; it is known that (for example) finite-index subgroups in SLn(Z) are not left-orderable; a wide generalisation of this has been recently announced. |
DIPS (Digital Image Processing with Sound) | DIPS (Digital Image Processing with Sound) | DIPS (Digital Image Processing with Sound) is a set of plug-in objects that handle real-time digital image processing in Max/MSP programming environment. Combining with the built-in objects of the environment, DIPS enables to program the interaction between audio and visual events with ease, and supports the realization of interactive multimedia art as well as interactive computer music. |
DIPS (Digital Image Processing with Sound) | Summary of Features | A plug-in software for Max/MSP (Max 5 and 6) More than 300 Max external objects and abstractions More than 90 OpenGL objects included More than 110 visual effect objects (Dfx library, Core Image Filters) A utility library for the easy of programming (prefix Dlib) A comprehensive set of sample patches, and a detailed tutorial Handling images & movie files (QuickTime, OpenGL) Render and move 3D models (OpenGL) Video signal input (QuickTime, video texture) Video input analysis: motion detect, face tracking (OpenCV, OpenGL) Importing 3D models (.obj file) Importing Quartz Composer files OpenGL Shading Language (GLSL) programming interface Easy integration of visual events using DIPSWindowMixer (OpenGL) |
DIPS (Digital Image Processing with Sound) | Description | DIPS is a free plug-in software (a set of external objects) for Max/MSP. It supports the designing of the interaction between sound and visual events in Max using Apple’s Core Image, OpenGL and OpenCV technologies, and consequently, provides a powerful and user-friendly programming environment for the creation of interactive multimedia art. |
DIPS (Digital Image Processing with Sound) | Description | DIPS can be used to detect a performer’s motions and to track positions of subtle details, such as the face, mouth, and eyes. It can also be used to measure the distance between objects and a Kinect sensor system, and offers powerful tools for realtime image processing of incoming video stream and stored movie files. In addition, it can be used to create complex images in a virtual three-dimensional space. |
DIPS (Digital Image Processing with Sound) | Description | The DIPS consists of a library of more than 300 Max external objects and abstractions, a comprehensive set of sample patches, and a detailed tutorial. Some of its strong points, in comparison with other similar plug-ins and software, are its ease of programming, power, and efficiency. |
DIPS (Digital Image Processing with Sound) | Description | The sample patches and tutorial contained in the installation package allows composers and artists who are interested in the creation of interactive art to realize sophisticated realtime video effects on a live video signal at their first practice. And because of its ease of programming, it is likely that one will soon acquire skills needed to create state-of-the-art interactive performance works, multimedia installations, interactive multimedia artworks, and Max VJ applications using DIPS. |
DIPS (Digital Image Processing with Sound) | History | Initially developed by Shu Matsuda in 1997, DIPS was a plug-in software for Max/FTS running on SGI Octane and O2 computers. Since 2000, it has been developed by the DIPS Development Group supervised by Takayuki Rai. Current active group members are Shu Matsuda, Yota Morimoto, Takuto Fukuda, and Keitaro Takahashi. Previously, Chikashi Miyama, Daichi Ando and Takayuki Hamano also contributed to its development. |
DIPS (Digital Image Processing with Sound) | History | 2013 DIPS5 for Max (Mac OS X) 2009 DIPS4 for Max/MSP (Mac OS X) 2006 DIPS3 for Max/MSP (Mac OS X) 2003 DIPS2 for jMax4 (Mac OS X) 2002 DIPS for jMax2 (Mac OS X & Linux) 2000 DIPS for jMax (Linux) |
Evolutionary database design | Evolutionary database design | Evolutionary database design involves incremental improvements to the database schema so that it can be continuously updated with changes, reflecting the customer's requirements. People across the globe work on the same piece of software at the same time hence, there is a need for techniques that allow a smooth evolution of database as the design develops. Such methods utilize automated refactoring and continuous integration so that it supports agile methodologies for software development. These development techniques are applied on systems that are in pre-production stage as well on systems that have already been released. These techniques not only cover relevant changes in the database schema according to customer's changing needs, but also migration of modified data into the database and also customizing the database access code accordingly without changing the data semantics. |
Evolutionary database design | History | After using the waterfall model for a long time, the software industry has witnessed a rise in adoption of agile methods for software development. Agile methodologies don’t assume requirements to be permanent at any stage of the software life cycle. These methods are designed to support sporadic changes in contrast to waterfall design technique. An important part of this approach is iterative development, where the entire software life-cycle is run multiple times during the life of a project. Every iteration witnesses the complete software development life cycle despite the iterations being of short duration that can vary between weeks to a few months.Before the adoption of these methodologies, the entire system was designed before starting to develop the code. The same principle was applied to the database schema as well where it was considered to be derived out of the software requirements which were in turn developed by collaboration between the customer, end-users, business analysts, etc. and these requirements were not expected to change with the progress in the software development. This approach proved to be cumbersome because as time progressed, the redundancies in the existing database schema in the form of unused rows or columns were evident. This redundancy along with data quality problems went on to become a costly affair. It was concluded that the practice of not having design interleaved with construction and testing was highly inefficient. |
Evolutionary database design | Techniques | As mentioned in the previous section evolutionary methods are iterative in nature and these methods have become immensely popular over last two decades. Evolutionary database design aims to construct the database schema over the course of the project instead of building the entire database schema at the beginning of the project. This method of database design can capture and deal effectively with the changing requirements of projects. |
Evolutionary database design | Techniques | There are five evolutionary database design techniques that can aid developers in building their database in an iterative fashion. A brief overview about the five techniques are provided below. |
Evolutionary database design | Techniques | Database refactoring Refactoring is the process of making changes to the program without affecting the functionality of the program. Database refactoring is the technique of implementing small changes to the database schema without affecting the functionality and information stored in the database. The main purpose of database refactoring is to improve the database design so that the database is more in-sync with the changing requirements. The user can modify tables, views, stored procedures and triggers. Dependency between the database and external applications make database refactoring a challenge. |
Evolutionary database design | Techniques | Evolutionary data modeling Data modeling is the technique of identifying entities, associating attributes to the entities and deciding the data structure to represent the attributes. In the traditional database scenario, a logical data model is created at the beginning to represent the entities and their associated attributes. In evolutionary data modeling the technique of data modeling is performed in an iterative manner, that is multiple data models are developed, each model representing a different aspect of the database. This kind of data modeling technique is practiced in an agile environment and it is one of the main principles of agile development. |
Evolutionary database design | Techniques | Database regression testing Whenever a new functionality is added to a system, it is essential to verify that the update does not corrupt or render the system unusable. In a database, the business logic is implemented in stored procedures, data validation rules and referential integrity and they have to be tested thoroughly when any change is implemented in the system. Regression testing is the process of executing all the test cases whenever a new feature is added to the system. test-first development (TFD) is a form of regression testing followed in evolutionary database design. The steps involved in TFD approach are, Before adding a new function to the system, add a test to the test case suite such that the system fails the test Run the tests, either the entire set of test cases or just a subset and ensure that the newly added test does indeed fail Update the function such that the test passes Run the tests again to ensure that all they succeed and that the system is not broken Configuration management of database artifacts Configuration management is a detailed recording of versions and updates that have been applied to any system. Configuration management is useful in rolling back updates and changes which have impacted the system in a negative manner. To ensure that any updates made in database refactoring can be rolled back, it is important to maintain database artifacts like data definition language scripts, data model files, reference data, stored procedures, etc. in a configuration management system. |
Evolutionary database design | Techniques | Developer sandboxes A sandbox is a fully functional environment in which the system can be built, tested and executed. In order to make changes to the database schema in an evolutionary manner it is ideal for every developer to have his/her own physical sandbox, copy of source code and a copy of database. In a sandbox environment the developer can make changes to the database schema and run tests without affecting the work of other developers and other environments. Once the change has been implemented successfully, it is promoted to pre-production environment where in acceptance testing is performed and after the acceptance tests succeed it is deployed into production. |
Evolutionary database design | Advantages and disadvantages | Advantages High quality of database design: In evolutionary database design, the developer makes small changes to the database schema in an incremental manner and this achieves a highly optimized database schema.
Handling change: In a traditional database approach, a lot of time is spent in remodeling and restructuring the database when the requirements change. In evolutionary database technique, the schema of the database is adjusted periodically to keep up with the changing requirements. Hence, evolutionary database design technique is better suited in handling the changing requirements.
Guaranteed working of system at all times: The evolutionary database design approach follows test-first development model, in which the complete working of a system is tested before and after implementing an update. Hence, it is guaranteed that the system always works.
Compatible with software development: The IT industry is progressing towards agile method of software development and evolutionary database design ensures that data development is in sync with software development.
Reduced overall effort: In an evolutionary environment only the functionality that is required at that moment is implemented and no more.
Disadvantages Cultural impediments: Evolutionary database design approach is relatively a newer concept and many well qualified data professionals still advocate the traditional approach. Therefore, most of the databases are still being designed in a serial fashion and evolutionary database design is yet to gain support and traction among experienced data professionals.
Requires a learning curve: Most of the developers are more familiar with the traditional approach and it takes time to learn evolutionary design as it is not intuitive.
Complex: When the database has many external dependencies, making changes to the schema becomes all the more complicated as the external dependencies should also be updated to cope up with the changes made in the database schema. With the increase in number of dependencies, Evolutionary Database Design approach becomes extremely complex. |
Evolutionary database design | Comparison with traditional database design | Traditional database design technique does not support changes like evolutionary database design technique.'Unfortunately, the traditional data community assumed that evolving database schema is a hard thing to do and as a result never thought through how to do it.' In a way, the evolutionary design is better for application developers and traditional design is better for data professionals. |
Evolutionary database design | Tools | Given below are a list of tools that provide the functionality of designing and developing a database in an evolutionary manner.
LiquiBase Red Gate Deployment Manager Ruby on Rails Active Record Migration Flyway (software) Autopatch |
Rice mill | Rice mill | A rice mill is a food-processing facility where paddy is processed to rice to be sold in the market.The entire product is procured from paddy fields, milled and processed hygienically in modern machinery and dust-free environment and cleaned through sorting machines. |
Rice mill | Paddy procurement | Paddy is collected from the fields to be processed. The paddy is again rechecked before the process begins. The procured paddy is checked bag by bag by a team and stored in Paddy Milling Plants. |
Rice mill | Manufacturing process | To start with the production process, paddy is cleaned by a paddy pre-cleaning machine and the cleaned paddy is stored in raw paddy storage bins. The stored paddy is moved to food-grade stainless steel soaking tanks. Water is drained from the tank and the wet paddy is ready for boiling.
Boiling is done by a steam boiler. The boiled paddy is then moved to the paddy dryer through a belt conveyor. |
Rice mill | Dryer | The boiled wet paddy is dried in a food-grade stainless steel paddy drier using hot air. The heat energy for the drier is generated using a heat exchanger that uses steam from the boiler. Using a steam heat exchanger will sustain the real aroma of the paddy. These are indirect heat exchangers so there is no chance of smoke air entering the drier. The dried paddy is ready for hulling. |
Rice mill | Hulling process | The paddy is pre-cleaned again and destoned by a pre-cleaning machine. After cleaning the paddy is moved to dehusker called sheller. The outer covering of the paddy, the husk is removed here and is used as a fuel for the boiler. The whole rice is collected from the Sheller and moved on to whitener. Here, The film coat on the rice which is called bran is removed from the rice and the bran is collected separately. The whitening process is done by a whitener . The whitened rice is polished by a silky polisher. The polished rice is destoned by a destoner and the broken rice is separated by a length grader. |
Rice mill | Color sorting | The polished full-grain rice is sorted in a colour sorter which removes black rice, yellow rice, and white belly. Then, the rice is moved to the packing section.
Packing The processed rice is then packed in woven sacks and is ready to be sold in the market |
Chondroplasty | Chondroplasty | Chondroplasty is surgery of the cartilage, the most common being corrective surgery of the cartilage of the knee.
Surgery known as thyroid chondroplasty (or tracheal shave) is used to reduce the visibility of the Adam's apple in transgender women. |
Projective vector field | Projective vector field | A projective vector field (projective) is a smooth vector field on a semi Riemannian manifold (p.ex. spacetime) M whose flow preserves the geodesic structure of M without necessarily preserving the affine parameter of any geodesic. More intuitively, the flow of the projective maps geodesics smoothly into geodesics without preserving the affine parameter. |
Projective vector field | Decomposition | In dealing with a vector field X on a semi Riemannian manifold (p.ex. in general relativity), it is often useful to decompose the covariant derivative into its symmetric and skew-symmetric parts: Xa;b=12hab+Fab where hab=(LXg)ab=Xa;b+Xb;a and Fab=12(Xa;b−Xb;a) Note that Xa are the covariant components of X Equivalent conditions Mathematically, the condition for a vector field X to be projective is equivalent to the existence of a one-form ψ satisfying Xa;bc=RabcdXd+2ga(bψc) which is equivalent to hab;c=2gabψc+gacψb+gbcψa The set of all global projective vector fields over a connected or compact manifold forms a finite-dimensional Lie algebra denoted by P(M) (the projective algebra) and satisfies for connected manifolds the condition: dim P(M)≤n(n+2) . Here a projective vector field is uniquely determined by specifying the values of X , ∇X and ∇∇X (equivalently, specifying X , h , F and ψ ) at any point of M . (For non-connected manifolds you need to specify these 3 in one point per connected component.) Projectives also satisfy the properties: LXRabcd=δadψb;c−δacψb;d LXRab=−3ψa;b |
Projective vector field | Subalgebras | Several important special cases of projective vector fields can occur and they form Lie subalgebras of P(M) . These subalgebras are useful, for example, in classifying spacetimes in general relativity. |
Projective vector field | Subalgebras | Affine algebra Affine vector fields (affines) satisfy ∇h=0 (equivalently, ψ=0 ) and hence every affine is a projective. Affines preserve the geodesic structure of the semi Riem. manifold (read spacetime) whilst also preserving the affine parameter. The set of all affines on M forms a Lie subalgebra of P(M) denoted by A(M) (the affine algebra) and satisfies for connected M, dim A(M)≤n(n+1) . An affine vector is uniquely determined by specifying the values of the vector field and its first covariant derivative (equivalently, specifying X , h and F ) at any point of M . Affines also preserve the Riemann, Ricci and Weyl tensors, i.e. LXRabcd=0 , LXRab=0 , LXCabcd=0 Homothetic algebra Homothetic vector fields (homotheties) preserve the metric up to a constant factor, i.e. h=LXg=2cg . As ∇h=0 , every homothety is an affine and the set of all homotheties on M forms a Lie subalgebra of A(M) denoted by H(M) (the homothetic algebra) and satisfies for connected M dim H(M)≤12n(n+1)+1 .A homothetic vector field is uniquely determined by specifying the values of the vector field and its first covariant derivative (equivalently, specifying X , F and c ) at any point of the manifold. |
Projective vector field | Subalgebras | Killing algebra Killing vector fields (Killings) preserve the metric, i.e. h=LXg=0 . Taking c=0 in the defining property of a homothety, it is seen that every Killing is a homothety (and hence an affine) and the set of all Killing vector fields on M forms a Lie subalgebra of H(M) denoted by K(M) (the Killing algebra) and satisfies for connected M dim K(M)≤12n(n+1) .A Killing vector field is uniquely determined by specifying the values of the vector field and its first covariant derivative (equivalently, specifying X and F ) at any point (for every connected component) of M |
Projective vector field | Applications | In general relativity, many spacetimes possess certain symmetries that can be characterised by vector fields on the spacetime. For example, Minkowski space M admits the maximal projective algebra, i.e. dim 24 . Many other applications of symmetry vector fields in general relativity may be found in Hall (2004) which also contains an extensive bibliography including many research papers in the field of symmetries in general relativity. |
29-Norlanosterol | 29-Norlanosterol | 29-Norlanosterol, or 4-demethyllanosterol, also called 4α,14α-dimethylzymosterol, is a Metabolic intermediate of plant sterol biosynthesis. In the pathway, it is transformed from ring-opening reactions of Norcycloartenol and then demethylation by CYP51 into 4α-methyl-5α-cholesta-8,14,24-trien-3β-ol. |
Asperity (geotechnical engineering) | Asperity (geotechnical engineering) | In geotechnical engineering and contact mechanics the term asperity is used to refer to individual features of unevenness (roughness) of the surface of a discontinuity, grain, or particle with heights in the range from approximately 0.1 mm to the order of metres. Below the asperity level, surface interactions are normally considered to be a material property, arising from mechanisms of adhesion and repulsion at the atomic scale (often accounted for by material friction, atomic friction or molecular friction). |
Asperity (geotechnical engineering) | Dilation | An often used definition for asperities in geotechnical engineering: Unevenness of a surface are asperities if these cause dilation if two blocks with in between a discontinuity with matching asperities on the two opposing surfaces (i.e. a fitting discontinuity) move relative to each other, under low stress levels that do not cause breaking of the asperities. |
Asperity (geotechnical engineering) | Contrast with asperity in materials science | Materials science recognizes asperities ranging from the sub-visual (normally less than 0.1 mm) to the atomic scale. |
Tetrahedral bipyramid | Tetrahedral bipyramid | In 4-dimensional geometry, the tetrahedral bipyramid is the direct sum of a tetrahedron and a segment, {3,3} + { }. Each face of a central tetrahedron is attached with two tetrahedra, creating 8 tetrahedral cells, 16 triangular faces, 14 edges, and 6 vertices,. A tetrahedral bipyramid can be seen as two tetrahedral pyramids augmented together at their base.
It is the dual of a tetrahedral prism, , so it can also be given a Coxeter-Dynkin diagram, , and both have Coxeter notation symmetry [2,3,3], order 48.
Being convex with all regular cells (tetrahedra) means that it is a Blind polytope.
This bipyramid exists as the cells of the dual of the uniform rectified 5-simplex, and rectified 5-cube or the dual of any uniform 5-polytope with a tetrahedral prism vertex figure. And, as well, it exists as the cells of the dual to the rectified 24-cell honeycomb. |
Guerrilla ontology | Guerrilla ontology | Guerilla ontology is a practice described by author Robert Anton Wilson in his 1980 book The Illuminati Papers as "the basic technique of all my books. Ontology is the study of being; the guerrilla approach is to so mix the elements of each book that the reader must decide on each page 'How much of this is real and how much is a put-on?'" |
Guerrilla ontology | Practice | The goal of guerrilla ontology is to expose an individual or individuals to radically unique ideas, thoughts, and words, in order to invoke cognitive dissonance, which can cause a degree of discomfort in some individuals as they find their belief systems challenged by new concepts. The ultimate goal of guerrilla ontology is to promote positive brain change and new ways of experiencing and adapting to reality. |
Admissible set | Admissible set | In set theory, a discipline within mathematics, an admissible set is a transitive set A such that ⟨A,∈⟩ is a model of Kripke–Platek set theory (Barwise 1975).
The smallest example of an admissible set is the set of hereditarily finite sets. Another example is the set of hereditarily countable sets. |
Vanillin synthase | Vanillin synthase | In enzymology, a vanillin synthase (EC 4.1.2.41) is an enzyme that catalyzes the chemical reaction 3-hydroxy-3-(4-hydroxy-3-methoxyphenyl)propanoyl-CoA ⇌ vanillin + acetyl-CoAHence, this enzyme has one substrate, 3-hydroxy-3-(4-hydroxy-3-methoxyphenyl)propanoyl-CoA, and two products, vanillin and acetyl-CoA.
This enzyme belongs to the family of lyases, specifically the aldehyde-lyases, which cleave carbon-carbon bonds. The systematic name of this enzyme class is 3-hydroxy-3-(4-hydroxy-3-methoxyphenyl)propanoyl-CoA vanillin-lyase (acetyl-CoA-forming). Other names in common use include 3-hydroxy-3-(4-hydroxy-3-methoxyphenyl)propionyl-CoA:vanillin lyase, and (acetyl-CoA-forming). |
ISC High Performance | ISC High Performance | The ISC High Performance, formerly known as the International Supercomputing Conference, is a yearly conference on supercomputing which has been held in Europe since 1986. It stands as the oldest supercomputing conference in the world. |
ISC High Performance | History | In 1986 Professor Dr. Hans Werner Meuer, director of the computer centre and professor for computer science at the University of Mannheim (Germany) co-founded and organized the "Mannheim Supercomputer Seminar" which had 81 participants. This was held yearly and became the annual International Supercomputing Conference and Exhibition (ISC). In 2015, the name was officially changed to ISC High Performance. The conference is attended by speakers, vendors, and researchers from all over the world. Since 1993 the conference has been the venue for one of the twice yearly TOP500 announcements where the fastest 500 supercomputers in the world are named. The other annual announcement is in November at the SC Conference (The International Conference for High Performance Computing, Networking, Storage and Analysis) in the USA. |
ISC High Performance | History | The conference celebrated 30 years with the 19 June 2016 meeting in Frankfurt, Germany. Its 33rd edition in 2019 attracted a record number of participants – 164 exhibitors, and 3,573 visitors from 64 countries. |
Brahmagupta matrix | Brahmagupta matrix | In mathematics, the following matrix was given by Indian mathematician Brahmagupta: B(x,y)=[xy±ty±x].
It satisfies B(x1,y1)B(x2,y2)=B(x1x2±ty1y2,x1y2±y1x2).
Powers of the matrix are defined by Bn=[xytyx]n=[xnyntynxn]≡Bn.
The xn and yn are called Brahmagupta polynomials. The Brahmagupta matrices can be extended to negative integers: B−n=[xytyx]−n=[x−ny−nty−nx−n]≡B−n. |
Dock plate | Dock plate | In a loading dock, one problem to overcome is the problem of bridging the gap between a truck and the dock or warehouse floor. Not all trucks are the same height, and the height of the trailer floor within a truck can vary according to how heavily the truck is laden. Thus there is not only a gap to bridge but a height difference to overcome. Various devices are employed in order to achieve this: dock plates, dock levelers, dock boards, and various forms of lift. These devices vary in construction, suitability to dock conditions, cost of installation, and loading capacity.Dock levelers and lifts are generally permanent fixtures at each door of a dock. Dock plates and dock boards are generally, by contrast, portable, and not fixed either to dock or truck.Dock plates and dock boards are simply metal ramps, bridging the gaps between dock and truck. Dock plates are generally made out of aluminium whilst dock boards are generally made out of steel. Aluminium dock plates are thus more suitable for lighter loads, such as handcarts and dollies, whereas steel dock boards are more suitable for heavier motorized equipment such as fork lift trucks and electric pallet trucks. Another difference between dock plates and dock boards, in addition to their load-bearing capabilities, is their construction. Dock plates are simple flat plates, whereas dock boards have curbs, bolted or welded to the edge of the board. Run-off is prevented by a simple painted yellow strip along the edge of a dock plate, whereas it is the curbs (also generally painted yellow) that prevent run-off on dock boards; these curbs are also where the higher weight capacities of dock boards come from. Run-off is thus a significant risk on dock plates, since the yellow strip is not a particularly effective mechanism for preventing it.Both dock plates and dock boards have a diamond pattern embossed onto their upper surfaces, to prevent wheel slip as carts and vehicles travel up and down the incline. Similarly, they both have locking T-bar legs that extend down into the gap between truck and dock, to secure them. They are both portable. But dock boards are heavier than dock plates. The latter may be carried by hand, and are generally fitted with handles for doing so. The former usually require a fork lift in order to place and remove them, and are generally fitted with either loops or chains, used for attaching the dock board to the forks of the fork lift. |
Dock plate | Dock plate | Dock levelers are, as mentioned, fixed to the dock. They comprise a simple metal plate, called a lip, that is raised from a stowed position and then lowered onto the back of the truck. Lip can be hinged or telescopic type. They are operated either manually, via a simple pull chain, or hydraulically, (most common) with an electric pump driving a piston to lift the plate and another one to move the lip.Dock levelers are more expensive devices than the comparatively light-weight dock plates and dock boards. The most common form of dock leveler is the recessed, or pit, dock leveler. As the name suggests, this type of leveler is contained in a recess, or pit, beneath the dock door and floor surface. Dock levelers are stronger than dock plates and have similar ranges to dock boards, making them suitable not only for motorized fork lift trucks but also for master conveyors (for which neither dock plates or dock boards are suitable). Safety, also, is very high for this kind of product: Safety rules as EN1398 (European Standard) specifies the safety requirements for design, construction, installation, maintenance and testing of dock levelers and for safety components on dock levelers. NOTE: edge of dock levelers have fixed positions which have restricted ranges making them unsuitable for nonstandard dock heights. Because they carry heavy motorized equipment, the grade of the incline has to be shallow. The greater the height differential between truck and dock that a dock leveler can compensate for, the longer the leveler itself has to be. Moreover, the grade of the incline must not be so great that the vehicles cannot climb it. A height differential of between 7 and 8 inches generally requires a 6-foot-long (1.8 m) leveler for an electric palette carrier. A height differential of between 17 and 18 inches generally requires a 12-foot-long (3.7 m) leveler for a petrol-engined fork lift truck. Anyway, the lip has to be considered in the length of the leveler, as it is part of it. A telescopic lip (20 or 40 inches) can help to reduce the length of the leveler to 10 feet. |
Dock plate | Dock plate | Dock levelers (and indeed dock plates and dock boards) are used where a building has a truck-level door, i.e. a door with a floor level roughly at the same height as the floor of the truck's trailer. Some buildings only have drive-in doors, i.e. doors at the same level as the ground outside of the building, suitable for driving directly into the building.For loading docks with drive-in doors, and also (albeit rarely) for loading docks with truck-level doors, a lift is sometimes employed.Other, less common, devices employed when bridging the gap between truck and dock are truck levelers. These are hydraulic lifts positioned beneath the rear wheels of the truck, that are used to raise and lower the truck so that it is level with the loading dock edge. The problems with truck levelers, that make them rarely employed, are twofold. First: They cause the truck interior to be at an incline, which causes loading and unloading difficulties. Second: They are expensive to maintain, since they require (being below ground level and open to the air) proper drainage and protection against the weather.Recessed dock levelers also have problems of exposure to the weather. However, because they are recessed into the dock, which is above ground level, they do not have as great a problem with drainage. Equally, because they are recessed into the dock, they extend partially back from the dock edge. A dock leveler can be installed so that it extends inside the loading dock door, and thus inside the building, protecting it from the weather. |
Extended reality | Extended reality | Extended reality (XR) is a catch-all term to refer to augmented reality (AR), virtual reality (VR), and mixed reality (MR). The technology is intended to combine or mirror the physical world with a "digital twin world" able to interact with it.The fields of virtual reality and augmented reality are rapidly growing and being applied in a wide range of areas such as entertainment, marketing, real estate, training, maintenance and remote work. |
Windows Ultimate Extras | Windows Ultimate Extras | Windows Ultimate Extras were optional features offered by Microsoft to users of the Ultimate edition of Windows Vista and are accessible via Windows Update. Ultimate Extras replaced the market role of Microsoft Plus!, a product sold for prior consumer releases of Microsoft Windows. According to Microsoft's Barry Goffe, the company's goal with Ultimate Extras was to delight customers who purchased the Ultimate edition of Windows Vista, the most expensive retail edition of the operating system.Windows Ultimate Extras have been discontinued as of Windows 7 and the operating system also removes all installed extras during an upgrade from Windows Vista Ultimate. |
Windows Ultimate Extras | Contents | Microsoft released a total of nine Ultimate Extras for users of Windows Vista Ultimate. |
Windows Ultimate Extras | Contents | BitLocker and EFS enhancements The BitLocker Drive Preparation Tool utility and the Secure Online Key Backup utility were among the first Ultimate Extras to be made available, and were released to coincide with the general retail availability of Windows Vista. BitLocker Drive Preparation Tool prepares the hard drive to be encrypted with BitLocker, whereas Secure Online Key Backup enabled users to create an off-site backup of their BitLocker recovery password and Encrypting File System recovery certificates at Digital Locker, as part of the Windows Marketplace digital distribution platform. Secure Online Key Backup was rendered inoperable after Digital Locker shut down in August 2009. |
Windows Ultimate Extras | Contents | Multilingual User Interface language packs Unlike previous versions of Windows, Windows Vista is language-independent; the language architecture separates the language resources for the user interface from the binary code of the operating system. Support for installing additional languages is included in the Enterprise and Ultimate editions of Windows Vista. In the Ultimate edition, the functionality is made available through Windows Update as Ultimate Extras.Microsoft stated that 16 languages were made available on January 30, 2007. The company released the remaining language packs on October 23, 2007 for a total of 35 language packs. An additional 36th language pack version is available for Windows Vista that supports traditional Chinese characters with the Hong Kong Supplementary Character Set. |
Windows Ultimate Extras | Contents | Microsoft Tinker Microsoft Tinker is a puzzle game where players must navigate a robot through mazes and obstacles. A total of 60 levels are included, and players can create their own levels with a level editor. |
Windows Ultimate Extras | Contents | Hold 'Em Hold 'Em (formerly Windows Poker as in build 5284) is a poker card game released on January 29, 2007 that is fundamentally similar to Texas hold 'em. Hold 'Em allows users to play against up to five computer players and up to three levels of difficulty, and also allows users to customize aspects of the game's appearance; the game relies on DirectX to produce hardware-accelerated 3D animations and effects. For optimal performance, Hold 'Em requires a computer with a Windows Experience Index rating of 2.0 or higher.According to Paul Thurrott, Hold 'Em was originally intended to be bundled alongside the premium games—Chess Titans, Mahjong Titans, and InkBall—included by default with the Home Premium and Ultimate editions of Windows Vista, but was instead made an Ultimate Extra because of its gambling themes. |
Windows Ultimate Extras | Contents | Windows sound schemes A total of three sound schemes for Windows Vista were released: Ultimate Extras Glass, Ultimate Extras Pearl, and Microsoft Tinker. The first two were made available on April 22, 2008, while the latter was made available on the same day as Microsoft Tinker. The Glass and Pearl sound schemes are similar to the Default sound scheme included in Windows Vista as they were also developed in accordance with the design language and principles of the Windows Aero graphical user interface. |
Windows Ultimate Extras | Contents | Windows DreamScene Windows DreamScene is a utility that enables MPEG and WMV videos to be displayed as desktop backgrounds. DreamScene requires that the Windows Aero graphical user interface be enabled in order to function as the feature relies on the Desktop Window Manager to display videos on the desktop. |
Windows Ultimate Extras | Contents | Proposed extras Additional extras were also proposed but not released, including a podcast creation application, a game performance optimization utility, custom themes, exclusive access to online content and services, Windows Movie Maker effects and transitions, templates for Windows DVD Maker, digital publications, and the Group Shot photo manipulation application developed by Microsoft Research and shown by Bill Gates at the Consumer Electronics Show in 2007.Although not considered to be Ultimate Extras by the company, the Ultimate Extras team also released two wallpapers for users of Windows Vista Ultimate. Titled Start and Strands, the wallpapers were based on the design of the Windows Vista Ultimate retail packaging and were made available in three different display resolutions. |
Windows Ultimate Extras | Critical reception | Reaction to Windows Ultimate Extras was mixed. While Microsoft was praised for creating a value proposition for users who purchased the most expensive edition of Windows Vista, the company was criticized for its delays during delivery of updates, perceived lack of quality of delivered updates, and a lack of transparency regarding their development. Early on, there were concerns that the features would not live up to users' expectations. The company announced several Ultimate Extras in January 2007, but only a fraction of these were released five months later. After months without an official update since January, Microsoft released an apology for the delays, stating that it intended to ship the remaining features before the end of summer of 2007. The delays between consecutive updates and months of silence had led to speculation that the development team within the company responsible for the features had been quietly disbanded.When Microsoft announced its intentions to release the remaining Ultimate Extras and released an apology for delays, Paul Thurrott stated that the company had "dropped the ball" with the features. Ed Bott wrote that Ultimate Extras were "probably the biggest mistake Microsoft made with Vista," and that the company would downplay the Ultimate edition of Windows 7 as a result. Bott would later list them among his "decade's worth of Windows mistakes."Microsoft was also criticized for changing the description for Ultimate Extras within the operating system. The offerings slated to be made available were initially described as "cutting-edge programs," "innovative services," and "unique publications," but the description for the features within the Control Panel applet was later modified in Windows Vista Service Pack 1 to be more modest; this was interpreted as an attempt made by the company to avoid fulfilling prior expectations.Emil Protalinski of Ars Technica wrote that the Ultimate edition of Windows Vista "would have looked just fine without the joke that is 'Ultimate Extras'" and that the features were supposed to provide an incentive for consumers to purchase that edition, "not give critics something to point and laugh at." In the second part of his review of Windows 7, Peter Bright of Ars Technica wrote that "the value proposition of the Ultimate Extras was nothing short of piss-poor." Bright would later criticize Microsoft's decision not to release Internet Explorer 10 for Windows Vista, but would go on to state that this was still "not as bad as the Ultimate Extras farce." |
Indinavir | Indinavir | Indinavir (IDV; trade name Crixivan, made by Merck) is a protease inhibitor used as a component of highly active antiretroviral therapy to treat HIV/AIDS. It is soluble white powder administered orally in combination with other antiviral drugs. The drug prevents protease from functioning normally. Consequently, HIV viruses cannot reproduce, causing a decrease in the viral load. Commercially sold indinavir is indinavir anhydrous, which is indinavir with an additional amine in the hydroxyethylene backbone. This enhances its solubility and oral bioavailability, making it easier for users to intake. It was synthetically produced for the purpose of inhibiting the protease in the HIV virus.Currently, it is not recommended for use in HIV/AIDS treatment due to its side effects. Furthermore, it is controversial for many reasons starting from its development to its usage. |
Indinavir | Indinavir | It was patented in 1991 and approved for medical use in 1996. |
Indinavir | Medical uses | Indinavir does not cure HIV/AIDS, but it can extend the length of a person's life for several years by slowing the progression of the disease. The type that is widely used and created by Merck is indinavir sulfate. The pills are created from sulfate salts and are sold in dosages of 100, 200, 333, and 400 mg of indinavir. It is normally used as one of the three drugs in a triple-combination therapy for the HIV virus.Commercially available capsules should be stored at 15 - 30 °C. It should be kept in a tight container so that it is kept away from moisture. Therefore, it is advised that users should keep the pills in the manufacturer-provided bottle and do not remove the desiccant. |
Indinavir | Medical uses | Indinavir wears off quickly after dosing. Unboosted indinavir requires a very precise dosing of 400 mg every eight hours to thwart HIV from forming drug-resistant mutations, including resistances to other protease inhibitors. Boosted indinavir requires two 400-mg indinavir capsules with 1 to 2 100-mg ritonavir capsules twice a day. In both cases, the drugs must be taken with plenty of water one or two hours after a meal. It is recommended that users drink at least 1.5 liters a day when intaking the drug. Drug users must significantly increase their water intake due to indinavir's low solubility that can cause it to crystallize. There are restrictions on what sorts of food may be eaten concurrently with the unboosted indinavir treatment. Furthermore, it is no longer recommended to use in the United States for initial treatments due to pill burden and risk of kidney stones. |
Indinavir | Medical uses | Viral resistance Many people were skeptical of being too hopeful with indinavir due to previous events that occurred with AZT. Viral resistance to the drug leads to the drug becoming useless since the virus evolves to have cells that are able to resist the protease inhibitor. In order to avoid this as much as possible, it is important for users to consistently take the exact amount of the drug at the allocated times. This fear of viral resistance caused a lot of users to be wary of the drug. |
Indinavir | Side effects | The most common side effects of indinavir include: Gastrointestinal disturbances (abdominal pain, diarrhea, nausea, vomiting) General malaise and fatigue Nephrolithiasis/urolithiasis (the formation of kidney stones), which sometimes may lead to more severe condition including kidney failure Metabolic alterations including hyperlipidemia (cholesterol or triglyceride elevations) and hyperglycemia Alterations in body shape (lipodystrophy), colloquially known as "Crix belly" Increased levels of Bilirubin, causing skin and white parts of the eyes to turn yellow Inhibits urinary nitrous oxide production and may inhibit nitric oxide production. |
Indinavir | Side effects | Renal abnormalities, sterile leukocyturia, and reduced creatinine clearance.
Impairs endothelial function in healthy HIV-negative men and may accelerate atherosclerotic disease. |
Indinavir | Chemical properties | Indinavir is a white crystalline powder. It is very soluble in water and methanol. Each capsule contains sulfate salt in addition to anhydrous lactose and magnesium stearate. The capsule shell is made of gelatin and titanium dioxide. Its melting point or its temperature of decomposition is 150 - 153 °C at which it starts to emit toxic vapors such as nitrogen oxides and sulfur oxides. |
Indinavir | Chemical properties | The drug fits inside the protease, stopping it from functioning normally. As a result, structural proteins, resulting from polypeptide products of gag and gag-pol genes, that are necessary for the HIV virions cannot form. Eventually, the viral load decreases because of the lack of reproduction. |
Indinavir | History | The official start to its development started in December 1986 when Merck's president, Edward Scolnick, announced that they would start a comprehensive AIDS research program. They started a laboratory dedicated to AIDS research in West Point, Pennsylvania and placed Emilio Emini in charge of the laboratory. A couple months later on January, 1987, a team of researchers consisting of Emilio Emini, Joel Huff, and Irving Sigal, kickstarted their studies by basing their project off of earlier research on the protease enzyme, renin. They were the ones who started the process of research and development into protease inhibitors and its relation to the virus. Over a year later, in July 1988, Nancy Kohl, Emilio Emini, et al., published in the Proceedings of the National Academy of the Science about the idea of inhibiting the protease. On February, 1989, Manuela Navia, Paula Fitzgerald, et al., published a paper that showed the three-dimensional structure of HIV's protease enzyme. Other researchers claim that this study helped determine the future trajectory of the development of the inhibitor. After much research, in March, 1990, researchers under Reider received a patent to synthesize part of L-689, 502 compound. These were similar to existing inhibitors. However, it failed safety assessments because of its toxicity.Seeing that the research on their drug was heading in the direction of eventually getting it on the market, Merck decided to formulate a community advisory board composed of AIDS activists who would help with the development effort of the drug in March 1991. Later on, Merck faced serious backlash from community members who though did not like the pricing and distribution of the drug.In January 1992, researchers synthesized indinavir sulfate (Crixivan), which was assigned compound number L-735,524. They started to test L-735,524 on animals a couple months later and found that it was safe for animals. Consequently, the company decided that it was safe to start human trials on September of the same year.The Food and Drug Administration (FDA) approved indinavir on March, 1996, making it the eighth antiretroviral drug approved. It was first given its blessing by the FDA on March 1 then approved merely 42 days after the company filed the drug to the FDA. A major reason for this fast approval was the presentation Merck gave to the committee with results from Study 035 (see below). The fact that they had fast approval ran into trouble with groups like Treatment Action Group who thought that accelerated drug approval was not beneficial for people infected with HIV/AIDS.From then on, indinavir used with dual NRTIs set a new standard for treatment of HIV/AIDS. Protease inhibitors changed the nature of AIDS from a terminal illness to a somewhat manageable one. It significantly increased life expectancies and decreased noticeable symptoms from infectious diseases that were the result of a weakened immune system from the virus. Currently, it is being replaced by newer drugs that are more convenient to take, less likely to promote virus resistance, and less toxic, such as darunavir or atazanavir. |
Indinavir | Clinical trials | In January 1996, Merck & Co. proved that indinavir was a clinically efficient drug based on data from human trials. They were able to show that indinavir, when used with two other anti-HIV drugs, could significantly reduce the HIV viral load. |
Indinavir | Clinical trials | Study 035 The study's goal was to show the different effects of different antiviral treatments. 97 patients were randomly assigned to one of the three groups: indinavir monotherapy, AZT and lamivudine, or all three agents. Eligible patients were those who received AZT for at least 6 months and have CD4 cell counts between 50 and 400, viral loads of at least 200,000 copies/mL, and had no prior antiretroviral therapy with protease inhibitor or lamivudine.The results of the study showed that the most effective treatment was the three drug treatment. After 24 weeks of treatment, 24 patients of the 28 patients who were treated with the three drugs were able to have viral load levels have less than 500 copies/ml. 12 out of 28 patients under indinavir monotherapy reached 500 copies/ml, and none of the thirty patients in AZT and lamivudine group got below 500 copies. |
Indinavir | Clinical trials | ACTG 320 This study took a look at clinical efficiency of the different treatments. Patients had to have CD4 cell counts less than 200 and at least 3 months of AZT therapy before the trials. 1156 patients with a mean of 87 CD4 cell counts and mean viral load of 100,000 copies/ml were randomized to one of the two groups: AZT plus lamivudine or AZT plus lamivudine plus indinavir. Just like Study 035, patients couldn't be in the study if they had prior protease inhibitor treatment or lamivudine for more than one week. The end point of the study was death or development of opportunistic infections.After 38 weeks, 6% of the people in the three-drug group died while 11% of the people died in the two-drug group. There were higher CD4 cell counts and less viral load in patients assigned to the three-drug group, proving that a three-drug treatment is more efficient than a two-drug one. |
Indinavir | Controversy | Supply Merck did not have enough time to prepare enough drugs to distribute for all those who were infected. 650,000 to 900,000 people were infected with the virus, and Merck could only provide drugs for about 25,000 to 30,000 people. Furthermore, the drug has to be taken consistently or else users face dangers, meaning that the company has to take into account refills for users who take the drugs. This situation of limited supply caused a lot of activists to be angry at the fact that they were selling in such limited quantities. |
Indinavir | Controversy | Distribution Because of its limited supply, Merck decided to adopt a single distributor system in which they would send indinavir to only one pharmaceutical retail company. They sold it to Stadtalnder's Pharmacy and limited quantities to Veteran Administration's hospitals and some managed-care organizations. This caused prices to be raised and limited the number of people who could have access to this possibly life-saving drug. |
Indinavir | Controversy | Price Indinavir cost about $12 for a daily dose, which is 24% less than Invirase and 33% less than Norvir. Because the company used a single distributor system to sell their drugs, the retail price was marked up 37% by the pharmacy that sold it. In response to this hefty price, Merck stated that it cost a lot to research and develop the drug, and they did not have enough supplies to sell it through a normal distributor system. Activists protested against this price because it made it harder for people to have access to the drug. |
Brick Breaker | Brick Breaker | Brick Breaker is a video game developed by Canadian Developer Ali Asaria, that came preloaded on certain BlackBerry devices and is now available on the iOS App Store. |
Brick Breaker | Gameplay | Brick Breaker (platformer) is a Breakout clone in which the player must smash a wall of bricks by deflecting a bouncing ball with a paddle. The paddle may move horizontally and is controlled with the BlackBerry's trackwheel, the computer's mouse or the touch of a finger (in the case of touchscreen). The player gets three lives to start with; a life is lost if the ball hits the bottom of the screen. When all the bricks have been destroyed, the player advances to a new, harder level. There are 34 levels. Many levels have unbreakable silver bricks. If all lives are lost, the game is over. There are many versions of brick breaker, some in which you can shoot flaming fireballs or play with more than one ball if the player gets a power up. |
Brick Breaker | Reception | Brick Breaker has a cult following of professional players trying to achieve high scores. The game's addictiveness was highlighted by The Vancouver Sun: There are "dozens of forums, support groups and yes, a Brick Breaker Addiction Facebook page, with spouses complaining of addicted mates." |
Pseudotensor | Pseudotensor | In physics and mathematics, a pseudotensor is usually a quantity that transforms like a tensor under an orientation-preserving coordinate transformation (e.g. a proper rotation) but additionally changes sign under an orientation-reversing coordinate transformation (e.g., an improper rotation), which is a transformation that can be expressed as a proper rotation followed by reflection. This is a generalization of a pseudovector. To evaluate a tensor or pseudotensor sign, it has to be contracted with some vectors, as many as its rank is, belonging to the space where the rotation is made while keeping the tensor coordinates unaffected (differently from what one does in the case of a base change). Under improper rotation a pseudotensor and a proper tensor of the same rank will have different sign which depends on the rank being even or odd. Sometimes inversion of the axes is used as an example of an improper rotation to see the behaviour of a pseudotensor, but it works only if vector space dimensions is odd otherwise inversion is a proper rotation without an additional reflection. |
Pseudotensor | Pseudotensor | There is a second meaning for pseudotensor (and likewise for pseudovector), restricted to general relativity. Tensors obey strict transformation laws, but pseudotensors in this sense are not so constrained. Consequently, the form of a pseudotensor will, in general, change as the frame of reference is altered. An equation containing pseudotensors which holds in one frame will not necessarily hold in a different frame. This makes pseudotensors of limited relevance because equations in which they appear are not invariant in form. |
Pseudotensor | Definition | Two quite different mathematical objects are called a pseudotensor in different contexts. |
Pseudotensor | Definition | The first context is essentially a tensor multiplied by an extra sign factor, such that the pseudotensor changes sign under reflections when a normal tensor does not. According to one definition, a pseudotensor P of the type (p,q) is a geometric object whose components in an arbitrary basis are enumerated by (p+q) indices and obey the transformation rule under a change of basis.Here P^j1…jpi1…iq,Pl1…lpk1…kq are the components of the pseudotensor in the new and old bases, respectively, Aiqkq is the transition matrix for the contravariant indices, Blpjp is the transition matrix for the covariant indices, and det (Aiqkq))=±1. |
Pseudotensor | Definition | This transformation rule differs from the rule for an ordinary tensor only by the presence of the factor (−1)A. |
Pseudotensor | Definition | The second context where the word "pseudotensor" is used is general relativity. In that theory, one cannot describe the energy and momentum of the gravitational field by an energy–momentum tensor. Instead, one introduces objects that behave as tensors only with respect to restricted coordinate transformations. Strictly speaking, such objects are not tensors at all. A famous example of such a pseudotensor is the Landau–Lifshitz pseudotensor. |
Pseudotensor | Examples | On non-orientable manifolds, one cannot define a volume form globally due to the non-orientability, but one can define a volume element, which is formally a density, and may also be called a pseudo-volume form, due to the additional sign twist (tensoring with the sign bundle). The volume element is a pseudotensor density according to the first definition. |
Pseudotensor | Examples | A change of variables in multi-dimensional integration may be achieved through the incorporation of a factor of the absolute value of the determinant of the Jacobian matrix. The use of the absolute value introduces a sign change for improper coordinate transformations to compensate for the convention of keeping integration (volume) element positive; as such, an integrand is an example of a pseudotensor density according to the first definition. |
Pseudotensor | Examples | The Christoffel symbols of an affine connection on a manifold can be thought of as the correction terms to the partial derivatives of a coordinate expression of a vector field with respect to the coordinates to render it the vector field's covariant derivative. While the affine connection itself doesn't depend on the choice of coordinates, its Christoffel symbols do, making them a pseudotensor quantity according to the second definition. |
Quantificational variability effect | Quantificational variability effect | Quantificational variability effect (QVE) is the intuitive equivalence of certain sentences with quantificational adverbs (Q-adverbs) and sentences without these, but with quantificational determiner phrases (DP) in argument position instead. |
Quantificational variability effect | Quantificational variability effect | 1. (a) A cat is usually smart. (Q-adverb) 1. (b) Most cats are smart. (DP) 2. (a) A dog is always smart. (Q-adverb) 2. (b) All dogs are smart. (DP)Analysis of QVE is widely cited as entering the literature with David Lewis' "Adverbs of Quantification" (1975), where he proposes QVE as a solution to Peter Geach's donkey sentence (1962). Terminology, and comprehensive analysis, is normally attributed to Stephen Berman's "Situation-Based Semantics for Adverbs of Quantification" (1987). |
Quantificational variability effect | Literature | Core textsBerman, Stephen. The Semantics of Open Sentences. PhD thesis. University of Massachusetts Amherst, 1991.
Berman, Stephen. 'An Analysis of Quantifier Variability in Indirect Questions'. In MIT Working Papers in Linguistics 11. Edited by Phil Branigan and others. Cambridge: MIT Press, 1989. Pages 1–16.
Berman, Stephen. 'Situation-Based Semantics for Adverbs of Quantification'. In University of Massachusetts Occasional Papers 12. Edited by J. Blevins and Anne Vainikka. Graduate Linguistic Student Association (GLSA), University of Massachusetts Amherst, 1987. Pages 45–68.Select bibliography |
Torus | Torus | In geometry, a torus (PL: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle. The main types of toruses include ring toruses, horn toruses, and spindle toruses. A ring torus is sometimes colloquially referred to as a donut or doughnut. |
Torus | Torus | If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution, also known as a ring torus. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis of revolution passes twice through the circle, the surface is a spindle torus (or self-crossing torus or self-intersecting torus). If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a toroid, as in a square toroid. |