Diamond-like carbonDiamond-like carbon (DLC) is a class of amorphous carbon material that displays some of the typical properties of diamond. DLC is usually applied as coatings to other materials that could benefit from such properties. DLC exists in seven different forms. All seven contain significant amounts of sp3 hybridized carbon atoms. The reason that there are different types is that even diamond can be found in two crystalline polytypes. The more common one uses a cubic lattice, while the less common one, lonsdaleite, has a hexagonal lattice.
Linear acetylenic carbonLinear acetylenic carbon (LAC), also known as carbyne or Linear Carbon Chain (LCC), is an allotrope of carbon that has the chemical structure as a repeat unit, with alternating single and triple bonds. It would thus be the ultimate member of the polyyne family. This polymeric carbyne is of considerable interest to nanotechnology as its Young's modulus is 32.7TPa – forty times that of diamond; this extraordinary number is, however, based on a novel definition of cross-sectional area that does not correspond to the space occupied by the structure.
Organometallic chemistryOrganometallic chemistry is the study of organometallic compounds, chemical compounds containing at least one chemical bond between a carbon atom of an organic molecule and a metal, including alkali, alkaline earth, and transition metals, and sometimes broadened to include metalloids like boron, silicon, and selenium, as well. Aside from bonds to organyl fragments or molecules, bonds to 'inorganic' carbon, like carbon monoxide (metal carbonyls), cyanide, or carbide, are generally considered to be organometallic as well.
CombinatoricsCombinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas.
Inclusion–exclusion principleIn combinatorics, a branch of mathematics, the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as where A and B are two finite sets and |S | indicates the cardinality of a set S (which may be considered as the number of elements of the set, if the set is finite). The formula expresses the fact that the sum of the sizes of the two sets may be too large since some elements may be counted twice.
CisplatinCisplatin is a chemotherapy medication used to treat a number of cancers. These include testicular cancer, ovarian cancer, cervical cancer, bladder cancer, head and neck cancer, esophageal cancer, lung cancer, mesothelioma, brain tumors and neuroblastoma. It is given by injection into a vein. Common side effects include bone marrow suppression, hearing problems, including total irreversible hearing loss, usually restricted to one ear, kidney damage, and vomiting.
