In geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. Specifically, a k-simplex is a k-dimensional polytope which is the convex hull of its k + 1 vertices. More formally, suppose the k + 1 points are affinely independent, which means are linearly independent. Then, the simplex determined by them is the set of points
Linear programming is a method to achieve the best outcome in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming.
In mathematics, a simplicial complex is a set composed of points, line segments, triangles, and their n-dimensional counterparts. Simplicial complexes should not be confused with the more abstract notion of a simplicial set appearing in modern simplicial homotopy theory. The purely combinatorial counterpart to a simplicial complex is an abstract simplicial complex.
In mathematical optimization, Dantzig's simplex algorithm is a popular algorithm for linear programming.
The Nelder–Mead method is a commonly applied numerical method used to find the minimum or maximum of an objective function in a multidimensional space. It is a direct search method and is often applied to nonlinear optimization problems for which derivatives may not be known. However, the Nelder–Mead technique is a heuristic search method that can converge to non-stationary points on problems that can be solved by alternative methods.
Herpes simplex virus1 and 2, also known by their taxonomical names Human alphaherpesvirus 1 and Human alphaherpesvirus 2, are two members of the human Herpesviridae family, a set of viruses that produce viral infections in the majority of humans. Both HSV-1 and HSV-2 are common and contagious. They can be spread when an infected person begins shedding the virus. About 67% of the world population under the age of 50 has HSV-1. In the United States more than one in six people have HSV-2. Although it can be transmitted through any intimate contact, it is one of the most common sexually transmitted infections.
In geometry, a uniform k21 polytope is a polytope in k + 4 dimensions constructed from the En Coxeter group, and having only regular polytope facets. The family was named by their Coxeter symbol k21 by its bifurcating Coxeter–Dynkin diagram, with a single ring on the end of the k-node sequence.
Herpes simplex is a viral infection caused by the herpes simplex virus. Infections are categorized based on the part of the body infected. Oral herpes involves the face or mouth. It may result in small blisters in groups often called cold sores or fever blisters or may just cause a sore throat. Genital herpes, often simply known as herpes, may have minimal symptoms or form blisters that break open and result in small ulcers. These typically heal over two to four weeks. Tingling or shooting pains may occur before the blisters appear. Herpes cycles between periods of active disease followed by periods without symptoms. The first episode is often more severe and may be associated with fever, muscle pains, swollen lymph nodes and headaches. Over time, episodes of active disease decrease in frequency and severity. Other disorders caused by herpes simplex include: herpetic whitlow when it involves the fingers, herpes of the eye, herpes infection of the brain, and neonatal herpes when it affects a newborn, among others.
In six-dimensional Euclidean geometry, the 6-simplex honeycomb is a space-filling tessellation. The tessellation fills space by 6-simplex, rectified 6-simplex, and birectified 6-simplex facets. These facet types occur in proportions of 1:1:1 respectively in the whole honeycomb.
Herpetic simplex keratitis is a form of keratitis caused by recurrent herpes simplex virus (HSV) infection in the cornea.
Haplothrix is a genus of longhorn beetles of the subfamily Lamiinae, containing the following species:
Haplothrix amicator is a species of beetle in the family Cerambycidae. It was described by Charles Joseph Gahan in 1888.
Haplothrix andamanicus is a species of beetle in the family Cerambycidae. It was described by Stephan von Breuning in 1979. It is known from the Andaman Islands.
Haplothrix andrewesi is a species of beetle in the family Cerambycidae. It was described by Stephan von Breuning in 1935, originally misspelled as Hoplothrix andrewesi.
Haplothrix blairi is a species of beetle in the family Cerambycidae. It was described by Stephan von Breuning in 1935, originally misspelled as Hoplothrix blairi. It is known from Thailand, Myanmar, Laos, and Vietnam.
Haplothrix strandi is a species of beetle in the family Cerambycidae. It was described by Stephan von Breuning in 1935, originally misspelled as Hoplothrix strandi.
Haplothrix paramicator is a species of beetle in the family Cerambycidae. It was described by Stephan von Breuning in 1965. It is known from India.
Haplothrix fouqueti is a species of beetle in the family Cerambycidae. It was described by Maurice Pic in 1932.
Haplothrix pulcher is a species of beetle in the family Cerambycidae. It was described by Karl-Ernst Hüdepohl in 1998.
