DubniumDubnium is a synthetic chemical element with the symbol Db and atomic number 105. It is highly radioactive: the most stable known isotope, dubnium-268, has a half-life of about 16 hours. This greatly limits extended research on the element. Dubnium does not occur naturally on Earth and is produced artificially. The Soviet Joint Institute for Nuclear Research (JINR) claimed the first discovery of the element in 1968, followed by the American Lawrence Berkeley Laboratory in 1970.
Solvable groupIn mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group is a group whose derived series terminates in the trivial subgroup. Historically, the word "solvable" arose from Galois theory and the proof of the general unsolvability of quintic equation. Specifically, a polynomial equation is solvable in radicals if and only if the corresponding Galois group is solvable (note this theorem holds only in characteristic 0).
Reductive groupIn mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a perfect field is reductive if it has a representation that has a finite kernel and is a direct sum of irreducible representations. Reductive groups include some of the most important groups in mathematics, such as the general linear group GL(n) of invertible matrices, the special orthogonal group SO(n), and the symplectic group Sp(2n).
Automorphism groupIn mathematics, the automorphism group of an object X is the group consisting of automorphisms of X under composition of morphisms. For example, if X is a finite-dimensional vector space, then the automorphism group of X is the group of invertible linear transformations from X to itself (the general linear group of X). If instead X is a group, then its automorphism group is the group consisting of all group automorphisms of X. Especially in geometric contexts, an automorphism group is also called a symmetry group.
Dihedral groupIn mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry. The notation for the dihedral group differs in geometry and abstract algebra. In geometry, D_n or Dih_n refers to the symmetries of the n-gon, a group of order 2n. In abstract algebra, D_2n refers to this same dihedral group.
Fula peopleThe Fula, Fulani, or Fulɓe people (Fulɓe, 𞤊𞤵𞤤𞤩𞤫; Peul; Fulani or Hilani; Kanuri: Fillata; Fula; Pël; Fulaw; A̱fa̱taa) is an ethnic group in Sahara, Sahel and West Africa, widely dispersed across the region. Inhabiting many countries, they live mainly in West Africa and northern parts of Central Africa, South Sudan, Darfur, and regions near the Red Sea coast in Sudan. The approximate number of Fula people is unknown, due to clashing definitions regarding Fula ethnicity. Various estimates put the figure between 25 and 30 million people worldwide.
X-ray astronomyX-ray astronomy is an observational branch of astronomy which deals with the study of X-ray observation and detection from astronomical objects. X-radiation is absorbed by the Earth's atmosphere, so instruments to detect X-rays must be taken to high altitude by balloons, sounding rockets, and satellites. X-ray astronomy uses a type of space telescope that can see x-ray radiation which standard optical telescopes, such as the Mauna Kea Observatories, cannot.
Identity elementIn mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied. For example, 0 is an identity element of the addition of real numbers. This concept is used in algebraic structures such as groups and rings. The term identity element is often shortened to identity (as in the case of additive identity and multiplicative identity) when there is no possibility of confusion, but the identity implicitly depends on the binary operation it is associated with.
MaliMali (ˈmɑːli; mali), officially the Republic of Mali, is a landlocked country in West Africa. Mali is the eighth-largest country in Africa, with an area of over . The country is bordered on the north by Algeria, on the east by Niger, on the northwest by Mauritania, on the south by Burkina Faso and Côte d'Ivoire, and on the west by Guinea and Senegal. The population of Mali is million. 67% of its population was estimated to be under the age of 25 in 2017. Its capital and largest city is Bamako.
SaharaThe Sahara (səˈhɑːrə, səˈhærə) is a desert on the African continent. With an area of , it is the largest hot desert in the world and the third-largest desert overall, smaller only than the deserts of Antarctica and the northern Arctic. The name "Sahara" is derived from the Arabic word for "desert" in the feminine irregular form, the singular (صحراء //ˈSaHra), plural (صَحَارَى //ˈSaHaaraa), (صَحَار), (صَحْرَاوَات), (صَحَارِي).
NigerNiger or the Niger (niːˈʒɛər,_ˈnaɪdʒər , niʒɛʁ), officially the Republic of the Niger (République du Niger; Jamhuriyar Nijar), is a landlocked country in West Africa. It is a unitary state bordered by Libya to the northeast, Chad to the east, Nigeria to the south, Benin and Burkina Faso to the southwest, Mali to the west, and Algeria to the northwest. It covers a land area of almost , making it the largest landlocked country in West Africa. Over 80% of its land area lies in the Sahara.
Set (mathematics)A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.
