Other " miscellaneous " research areas in theoretical chemistry include the mathematical characterization of bulk chemistry in various phases ( e. g. the study of chemical kinetics ) and the study of the applicability of more recent math developments to the basic areas of study ( e. g. for instance the possible application of principles of topology to the study of elaborate electronic structure ).

On the other hand this type of application is also handled more simply by the use of covering morphisms of groupoids, and that technique has yielded subgroup theorems not yet proved by methods of algebraic topology.

However, large-scale application is problematic because of the problem of matching the correct neural topology to the market being studied.

On the one hand, the data entity creates and manages network layer data units from the payload of the application layer and performs routing according to the current topology.

This family of designs remains the dominant high power amplifier topology to this day for music application.

It was a non-trivial application of topology that first led to the discovery of peculiar hydrodynamic behavior in the A-phase of superfluid Helium-3.

Vector features can be made to respect spatial integrity through the application of topology rules such as ' polygons must not overlap '.

Major areas of research in mathematical chemistry include chemical graph theory, which deals with topology such as the mathematical study of isomerism and the development of topological descriptors or indices which find application in quantitative structure-property relationships ; and chemical aspects of group theory, which finds applications in stereochemistry and quantum chemistry.

In this application, the most typical frequency converter topology is the three-phase two-level voltage source inverter.

The main application of fibred categories is in descent theory, concerned with a vast generalisation of " glueing " techniques used in topology.

For an advanced application of this analysis to topology of manifolds, see Morse theory.

Diophantine geometry, which is the application of techniques from algebraic geometry in this field, has continued to grow as a result ; since treating arbitrary equations is a dead end, attention turns to equations that also have a geometric meaning.

: Why is there no formula for the roots of a fifth ( or higher ) degree polynomial equation in terms of the coefficients of the polynomial, using only the usual algebraic operations ( addition, subtraction, multiplication, division ) and application of radicals ( square roots, cube roots, etc )?

Formal methods are best described as the application of a fairly broad variety of theoretical computer science fundamentals, in particular logic calculi, formal languages, automata theory, and program semantics, but also type systems and algebraic data types to problems in software and hardware specification and verification.

This application was one of the beginnings of algebraic K-theory.

An important application of the cycle space are Whitney's planarity criterion and Mac Lane's planarity criterion, which give an algebraic characterization of the planar graphs.

Some striking applications of ultraproducts include very elegant proofs of the compactness theorem and the completeness theorem, Keisler's ultrapower theorem, which gives an algebraic characterization of the semantic notion of elementary equivalence, and the Robinson-Zakon presentation of the use of superstructures and their monomorphisms to construct nonstandard models of analysis, leading to the growth of the area of non-standard analysis, which was pioneered ( as an application of the compactness theorem ) by Abraham Robinson.

The importance of the concept, however, stems from its application to representations of Lie algebras and hence also to representations of algebraic and Lie groups.

One concludes that knowledge on the ' structure ' is bound up with what we can say about the representable functors on C. Characterisations of them, in interesting cases, were sought in the 1960s, for application in particular in the moduli problems of algebraic geometry ; showing in fact that these are very subtle matters.

The classification of algebraic varieties, i. e. application of this idea in the case of algebraic varieties, is very difficult due to the highly non-linear structure of the objects.

It has also turned out to be a central theme in algebraic number theory, allowing some features of the theory of cyclotomic fields to be carried over to wider areas of application.

The most common application of the plus construction is in algebraic K-theory.

Topics include polynomials, algebraic equations, separation of roots including Sturm's theorem, approximation of roots, and the application of matrices and determinants to the solving of equations.

This was put on a firm basis by foundational work of Kunihiko Kodaira and D. C. Spencer, after deformation techniques had received a great deal of more tentative application in the Italian school of algebraic geometry.

Helmut Hasse (; 25 August 1898 – 26 December 1979 ) was a German mathematician working in algebraic number theory, known for fundamental contributions to class field theory, the application of p-adic numbers to local classfield theory and diophantine geometry ( Hasse principle ), and to local zeta functions.

Arithmetic dynamics is the study of the number-theoretic properties of integer, rational ,-adic, and / or algebraic points under repeated application of a polynomial or rational function.

For thermodynamics and for the application of Kirchhoff's law, it is necessary that the total absorption be expressed as the algebraic sum of two components, described respectively by and, which may be regarded as positive and negative absorption, which are, respectively, the direct photon absorption, and what is commonly called stimulated or induced emission.

The algebraic classification of bivectors given above has an important application in relativistic physics: the electromagnetic field is represented by a skew-symmetric second rank tensor ( the electromagnetic field tensor ) so we immediately obtain an algebraic classification of electromagnetic fields.

Algebraic geometry now finds application in statistics, control theory, robotics, error-correcting codes, phylogenetics and geometric modelling.

Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.

An application of Euclidean solid geometry is the determination of packing arrangements, such as the problem of finding the most efficient packing of spheres in n dimensions.

Others claim that in some cases the geometric algebra approach is able to sidestep a " proliferation of manifolds " that arises during the standard application of differential geometry.

Other recent studies of Bruno have focused on his qualitative approach to mathematics and his application of the spatial paradigms of geometry to language.

The design of a successful solid-fuel motor requires application of continuum mechanics, combustion chemistry, materials science, fluid dynamics ( including compressible flow ), heat transfer, geometry ( particle spectrum packing ), and machining.

Composed of three books, it deals with the geometry of the sphere and its application in astronomical measurements and calculations.

* Geometric analysis involves the use of geometrical methods in the study of partial differential equations and the application of the theory of partial differential equations to geometry.

* Differential geometry, the application of calculus to specific mathematical spaces known as manifolds that possess a complicated internal structure but behave in a simple manner locally.

In ancient Egypt, when the Nile River overflowed its banks and washed out farm boundaries, boundaries were re-established by a rope stretcher, or surveyor, through the application of simple geometry.

The same inflexibility of the grid leads to disregarding environmentally sensitive areas such as small streams and creeks or mature woodlots in preference for the application of the immutable geometry.

* Median ( geometry )-an application

* Experimentally finding the centroid of a triangle with different weights at the vertices: a practical application of Ceva's theorem at Dynamic Geometry Sketches, an interactive dynamic geometry sketch using the gravity simulator of Cinderella.

For example, a Building feature in a particular GML application schema might have a position given by the primitive GML geometry object type Point.

See a blog article referring to an article and a book on this subject, also to a talk Dirac gave to a general audience in 1972 in Boston about projective geometry, without specifics as to its application in his physics.

Synthetic differential geometry is an application of topos theory to the foundations of differentiable manifold theory.

** Use of tap with improper tap geometry for a particular application.

Through some steps of application of the circle inversion map, a student of transformation geometry soon appreciates the significance of Felix Klein ’ s Erlangen program, an outgrowth of certain models of hyperbolic geometry

Thus, all of Vasquez ' work leads directly to the application of physical technology to directly access superspace geometry.

* the Radon transform, in integral geometry, based on integration over hyperplanes — with application to tomography for scanners ( see tomographic reconstruction );

We can therefore say that integral geometry in this sense is the application of probability theory ( as axiomatized by Kolmogorov ) in the context of the Erlangen programme of Klein.