Greedy algorithm for Egyptian fractionsIn mathematics, the greedy algorithm for Egyptian fractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptian fractions. An Egyptian fraction is a representation of an irreducible fraction as a sum of distinct unit fractions, such as 5/6 = 1/2 + 1/3. As the name indicates, these representations have been used as long ago as ancient Egypt, but the first published systematic method for constructing such expansions was described in 1202 in the Liber Abaci of Leonardo of Pisa (Fibonacci).
Hyperpolarization (physics)Hyperpolarization is the nuclear spin polarization of a material in a magnetic field far beyond thermal equilibrium conditions determined by the Boltzmann distribution. It can be applied to gases such as 129Xe and 3He, and small molecules where the polarization levels can be enhanced by a factor of 104-105 above thermal equilibrium levels. Hyperpolarized noble gases are typically used in magnetic resonance imaging (MRI) of the lungs. Hyperpolarized small molecules are typically used for in vivo metabolic imaging.
Alkali metalThe alkali metals consist of the chemical elements lithium (Li), sodium (Na), potassium (K), rubidium (Rb), caesium (Cs), and francium (Fr). Together with hydrogen they constitute group 1, which lies in the s-block of the periodic table. All alkali metals have their outermost electron in an s-orbital: this shared electron configuration results in their having very similar characteristic properties. Indeed, the alkali metals provide the best example of group trends in properties in the periodic table, with elements exhibiting well-characterised homologous behaviour.
Spin–spin relaxationIn physics, the spin–spin relaxation is the mechanism by which Mxy, the transverse component of the magnetization vector, exponentially decays towards its equilibrium value in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). It is characterized by the spin–spin relaxation time, known as T2, a time constant characterizing the signal decay. It is named in contrast to T1, the spin–lattice relaxation time.
Physics of magnetic resonance imagingThe physics of magnetic resonance imaging (MRI) concerns fundamental physical considerations of MRI techniques and technological aspects of MRI devices. MRI is a medical imaging technique mostly used in radiology and nuclear medicine in order to investigate the anatomy and physiology of the body, and to detect pathologies including tumors, inflammation, neurological conditions such as stroke, disorders of muscles and joints, and abnormalities in the heart and blood vessels among others.
Chemical bondA chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules, crystals, and other structures. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of electrons as in covalent bonds. The strength of chemical bonds varies considerably; there are "strong bonds" or "primary bonds" such as covalent, ionic and metallic bonds, and "weak bonds" or "secondary bonds" such as dipole–dipole interactions, the London dispersion force, and hydrogen bonding.
NanoclusterNanoclusters are atomically precise, crystalline materials most often existing on the 0-2 nanometer scale. They are often considered kinetically stable intermediates that form during the synthesis of comparatively larger materials such as semiconductor and metallic nanocrystals. The majority of research conducted to study nanoclusters has focused on characterizing their crystal structures and understanding their role in the nucleation and growth mechanisms of larger materials.
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.
Generalized continued fractionIn complex analysis, a branch of mathematics, a generalized continued fraction is a generalization of regular continued fractions in canonical form, in which the partial numerators and partial denominators can assume arbitrary complex values. A generalized continued fraction is an expression of the form where the an (n > 0) are the partial numerators, the bn are the partial denominators, and the leading term b0 is called the integer part of the continued fraction.
Resonance (chemistry)In chemistry, resonance, also called mesomerism, is a way of describing bonding in certain molecules or polyatomic ions by the combination of several contributing structures (or forms, also variously known as resonance structures or canonical structures) into a resonance hybrid (or hybrid structure) in valence bond theory. It has particular value for analyzing delocalized electrons where the bonding cannot be expressed by one single Lewis structure.
