Exotic sphereIn an area of mathematics called differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean n-sphere. That is, M is a sphere from the point of view of all its topological properties, but carrying a smooth structure that is not the familiar one (hence the name "exotic"). The first exotic spheres were constructed by in dimension as -bundles over . He showed that there are at least 7 differentiable structures on the 7-sphere.
Knudsen diffusionIn physics, Knudsen diffusion, named after Martin Knudsen, is a means of diffusion that occurs when the scale length of a system is comparable to or smaller than the mean free path of the particles involved. An example of this is in a long pore with a narrow diameter (2–50 nm) because molecules frequently collide with the pore wall. As another example, consider the diffusion of gas molecules through very small capillary pores.
Validity (statistics)Validity is the main extent to which a concept, conclusion or measurement is well-founded and likely corresponds accurately to the real world. The word "valid" is derived from the Latin validus, meaning strong. The validity of a measurement tool (for example, a test in education) is the degree to which the tool measures what it claims to measure. Validity is based on the strength of a collection of different types of evidence (e.g. face validity, construct validity, etc.) described in greater detail below.
Chemical kineticsChemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is different from chemical thermodynamics, which deals with the direction in which a reaction occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction.
Chemical engineeringChemical engineering is an engineering field which deals with the study of operation and design of chemical plants as well as methods of improving production. Chemical engineers develop economical commercial processes to convert raw materials into useful products. Chemical engineering uses principles of chemistry, physics, mathematics, biology, and economics to efficiently use, produce, design, transport and transform energy and materials.
IntegralIn mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, the other being differentiation. Integration started as a method to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Today integration is used in a wide variety of scientific fields.
Finite setIn mathematics, particularly set theory, a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example, is a finite set with five elements. The number of elements of a finite set is a natural number (possibly zero) and is called the cardinality (or the cardinal number) of the set. A set that is not a finite set is called an infinite set.
External validityExternal validity is the validity of applying the conclusions of a scientific study outside the context of that study. In other words, it is the extent to which the results of a study can be generalized to and across other situations, people, stimuli, and times. In contrast, internal validity is the validity of conclusions drawn within the context of a particular study. Because general conclusions are almost always a goal in research, external validity is an important property of any study.
Cas9Cas9 (CRISPR associated protein 9, formerly called Cas5, Csn1, or Csx12) is a 160 kilodalton protein which plays a vital role in the immunological defense of certain bacteria against DNA viruses and plasmids, and is heavily utilized in genetic engineering applications. Its main function is to cut DNA and thereby alter a cell's genome. The CRISPR-Cas9 genome editing technique was a significant contributor to the Nobel Prize in Chemistry in 2020 being awarded to Emmanuelle Charpentier and Jennifer Doudna.
Homology sphereIn algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer . That is, and for all other i. Therefore X is a connected space, with one non-zero higher Betti number, namely, . It does not follow that X is simply connected, only that its fundamental group is perfect (see Hurewicz theorem). A rational homology sphere is defined similarly but using homology with rational coefficients.
Chemical reactionA chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the nuclei (no change to the elements present), and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive elements where both electronic and nuclear changes can occur.
CatalysisCatalysis (kəˈtæləsɪs) is the process of change in rate of a chemical reaction by adding a substance known as a catalyst (ˈkætəlɪst). Catalysts are not consumed by the reaction and remain unchanged after it. If the reaction is rapid and the catalyst recycles quickly, very small amounts of catalyst often suffice; mixing, surface area, and temperature are important factors in reaction rate. Catalysts generally react with one or more reactants to form intermediates that subsequently give the final reaction product, in the process of regenerating the catalyst.
