Heavy metalsHeavy metals are generally defined as metals with relatively high densities, atomic weights, or atomic numbers. The criteria used, and whether metalloids are included, vary depending on the author and context. In metallurgy, for example, a heavy metal may be defined on the basis of density, whereas in physics the distinguishing criterion might be atomic number, while a chemist would likely be more concerned with chemical behaviour. More specific definitions have been published, none of which have been widely accepted.
Transition metalIn chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. The lanthanide and actinide elements (the f-block) are called inner transition metals and are sometimes considered to be transition metals as well. Since they are metals, they are lustrous and have good electrical and thermal conductivity.
Complex numberIn mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit and satisfying the equation ; every complex number can be expressed in the form , where a and b are real numbers. Because no real number satisfies the above equation, i was called an imaginary number by René Descartes. For the complex number , a is called the , and b is called the . The set of complex numbers is denoted by either of the symbols or C.
Transition metal dioxygen complexDioxygen complexes are coordination compounds that contain O2 as a ligand. The study of these compounds is inspired by oxygen-carrying proteins such as myoglobin, hemoglobin, hemerythrin, and hemocyanin. Several transition metals form complexes with O2, and many of these complexes form reversibly. The binding of O2 is the first step in many important phenomena, such as cellular respiration, corrosion, and industrial chemistry. The first synthetic oxygen complex was demonstrated in 1938 with cobalt(II) complex reversibly bound O2.
Tetradentate ligandIn chemistry, tetradentate ligands are ligands that bind four donor atoms to a central atom to form a coordination complex. This number of donor atoms that bind is called denticity and is a method of classifying ligands. Tetradentate ligands are common in nature in the form of chlorophyll, which has a core ligand called chlorin, and heme, which has a core ligand called porphyrin. They are responsible for the colour observed in plants and humans. Phthalocyanine is an artificial macrocyclic tetradentate ligand that is used to make blue and green pigments.
Stability theoryIn mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.
Transition metal alkene complexIn organometallic chemistry, a transition metal alkene complex is a coordination compound containing one or more alkene ligands. The inventory is large. Such compounds are intermediates in many catalytic reactions that convert alkenes to other organic products. The simplest monoalkene is ethene. Many complexes of ethene are known, including Zeise's salt (see figure), Rh2Cl2(C2H4)4, Cp*2Ti(C2H4), and the homoleptic Ni(C2H4)3. Substituted monoalkene include the cyclic cyclooctene, as found in chlorobis(cyclooctene)rhodium dimer.
Complex analysisComplex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic geometry, number theory, analytic combinatorics, applied mathematics; as well as in physics, including the branches of hydrodynamics, thermodynamics, quantum mechanics, and twistor theory. By extension, use of complex analysis also has applications in engineering fields such as nuclear, aerospace, mechanical and electrical engineering.
Lyapunov stabilityVarious types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis).
Cline (biology)In biology, a cline (from the Greek κλίνειν klinein, meaning "to lean") is a measurable gradient in a single characteristic (or biological trait) of a species across its geographical range. First coined by Julian Huxley in 1938, the cline usually has a genetic (e.g. allele frequency, blood type), or phenotypic (e.g. body size, skin pigmentation) character. Clines can show smooth, continuous gradation in a character, or they may show more abrupt changes in the trait from one geographic region to the next.
PHIn chemistry, pH (piːˈeɪtʃ ), also referred to as acidity, historically denotes "potential of hydrogen" (or "power of hydrogen"). It is a scale used to specify the acidity or basicity of an aqueous solution. Acidic solutions (solutions with higher concentrations of hydrogen () ions) are measured to have lower pH values than basic or alkaline solutions. The pH scale is logarithmic and inversely indicates the activity of hydrogen ions in the solution. where [H+] is the equilibrium molar concentration (mol/L) of H+ in the solution.
Acid dissociation constantIn chemistry, an acid dissociation constant (also known as acidity constant, or acid-ionization constant; denoted K_a) is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction HA A^- + H^+ known as dissociation in the context of acid–base reactions. The chemical species HA is an acid that dissociates into , the conjugate base of the acid and a hydrogen ion, .
