However, it is essential that the various mathematical symbols used in the equations be understood so that the mathematical processes can be done properly and in their correct order.

; Analysis of variance ( ANOVA ): A mathematical process for separating the variability of a group of observations into assignable causes and setting up various significance tests.

The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts.

He held that the Absolute Infinite had various mathematical properties, including the reflection principle which says that every property of the Absolute Infinite is also held by some smaller object.

Constructed languages such as Esperanto, programming languages, and various mathematical formalisms are not necessarily restricted to the properties shared by human languages.

The study of condensed matter physics involves measuring various material properties via experimental probes along with using techniques of theoretical physics to develop mathematical models that help in understanding physical behavior.

The study of categories is an attempt to axiomatically capture what is commonly found in various classes of related mathematical structures by relating them to the structure-preserving functions between them.

By studying categories and functors, we are not just studying a class of mathematical structures and the morphisms between them ; we are studying the relationships between various classes of mathematical structures.

Chemical thermodynamics involves not only laboratory measurements of various thermodynamic properties, but also the application of mathematical methods to the study of chemical questions and the spontaneity of processes.

It seeks to understand physical systems, using mathematical modeling, in terms of inputs, outputs and various components with different behaviors ; use control systems design tools to develop controllers for those systems ; and implement controllers in physical systems employing available technology.

In short, virtual manipulatives are dynamic visual / pictorial replicas of physical mathematical manipulatives, which have long been used to demonstrate and teach various mathematical concepts.

The principles underlying intra-and inter-individual differences could be educationally useful, because knowing how students differ in regard to the various dimensions of cognitive development, such as processing and representational capacity, self-understanding and self-regulation, and the various domains of understanding, such as mathematical, scientific, or verbal abilities, would enable the teacher to cater for the needs of the different students so that no one is left behind.

Indeed, according to various historical accounts, after that point few mathematicians tackled the issues and the work of those who did remained obscured largely because of resistance to such unfamiliar emerging concepts, which were sometimes referred to as mathematical " monsters ".

Hedge fund managers can use various types of analysis to identify price discrepancies in securities, including mathematical, technical or fundamental techniques.

Kepler calculated and recalculated various approximations of Mars ' orbit using an equant ( the mathematical tool that Copernicus had eliminated with his system ), eventually creating a model that generally agreed with Tycho's observations to within two arcminutes ( the average measurement error ).

He discovered ways to express various logarithmic functions using power series, and he successfully defined logarithms for negative and complex numbers, thus greatly expanding the scope of mathematical applications of logarithms.

The ambition of geometric model theory is to provide a geography of mathematics by embarking on a detailed study of definable sets in various mathematical structures, aided by the substantial tools developed in the study of pure model theory.

The set has a number of important mathematical properties that are foundational to various branches of mathematics.

Further work continues to find mathematical constructs that join various surrounding theories.

Prime numbers give rise to various generalizations in other mathematical domains, mainly algebra, such as prime elements and prime ideals.

undertake economic studies and surveys to determine present and prospective costs of producing water for beneficial consumptive purposes in various parts of the United States by the leading saline water processes as compared with other standard methods.

* Targets in depth may also be ' acquired ' by intelligence processes using various sources and agencies such as HUMINT, SIGINT, ELINT and IMINT.

The Earth's natural processes, particularly sea level rises, waves and various weather phenomena, have resulted in the erosion, accretion and reshaping of coasts as well as flooding and creation of continental shelves and drowned river valleys ( rias ).

The following articles describe the various geologic processes that affect a coastal zone:

The chemical elements are thought to have been produced by various cosmic processes, including hydrogen, helium ( and smaller amounts of lithium, beryllium and boron ) created during the Big Bang and cosmic-ray spallation.

On Earth ( and elsewhere ), trace amounts of various elements continue to be produced from other elements as products of natural transmutation processes.

Caves are formed by various geologic processes.

In addition to the traditional compost pile, various approaches have been developed to handle different composting processes, ingredients, locations, and applications for the composted product.

Microfabrication processes widely use CVD to deposit materials in various forms, including: monocrystalline, polycrystalline, amorphous, and epitaxial.

There are various extremely important electrochemical processes in both nature and industry, like the coating of objects with metals or metal oxides through electrodeposition and the detection of alcohol in drunken drivers through the redox reaction of ethanol.

Ecosystem processes, such as primary production, pedogenesis, nutrient cycling, and various niche construction activities, regulate the flux of energy and matter through an environment.

A variety of definitions exist: F. Stuart Chapin and coauthors define it as " the application of ecological science to resource management to promote long-term sustainability of ecosystems and the delivery of essential ecosystem goods and services ", while Norman Christensen and coauthors defined it as " management driven by explicit goals, executed by policies, protocols, and practices, and made adaptable by monitoring and research based on our best understanding of the ecological interactions and processes necessary to sustain ecosystem structure and function " and Peter Brussard and colleagues defined it as " managing areas at various scales in such a way that ecosystem services and biological resources are preserved while appropriate human use and options for livelihood are sustained ".

The physiological processes of releasing the old exoskeleton from the tissues beneath typically cause various colour changes, such as darkening.

The differences in geometry between the various types of unsaturated fatty acids, as well as between saturated and unsaturated fatty acids, play an important role in biological processes, and in the construction of biological structures ( such as cell membranes ).

The achievements of the democratic period, such as the establishment, strengthening or expansion of the various governmental and civil society structures and integrative processes necessary for normal functioning of the reunited state and nation, were too easily overlooked.

Thanks to various processes overseen by capitalism, such as urbanisation, the working class, the proletariat, should grow in numbers and develop class consciousness, in time realising that they have to and can change the system.

Therefore, Weber was more interested in explaining how a certain outcome was the result of various historical processes rather than predicting an outcome of those processes in the future.

Silicon is machined using various etching processes.

Instead, one tends to think in terms of the various processes, tasks, and objects subject to management.

Past the optimum point for extraction, various processes in the plant produce codeine, thebaine, and in some cases negligible amounts of hydromorphone, dihydromorphine, dihydrocodeine, tetrahydro-thebaine, and hydrocodone ( these compounds are rather synthesized from thebaine and oripavine ).

Higher education is an imperfect meritocratic screening system for various reasons, such as lack of uniform standards worldwide, lack of scope ( not all occupations and processes are included ), and lack of access ( some talented people never have an opportunity to participate because of the expense, most especially in developing countries ).