Currently, Amaranthus includes three recognized subgenera and 70 species, although species numbers are questionable due to hybridization and species concepts.

One of the more popular concepts of dahlia history, and the basis for many different interpretations and confusion, is that all the original discoveries were single flowered types, which, through hybridization and selective breeding, produced double forms.

Later, Linus Pauling used the pair bonding ideas of Lewis together with Heitler – London theory to develop two other key concepts in VB theory: resonance ( 1928 ) and orbital hybridization ( 1930 ).

However, the hybridization of folk and rock has been seen as having a major influence on the development of rock music, bringing in elements of psychedelia, and helping to develop the ideas of the singer-songwriter, the protest song and concepts of " authenticity ".

Both concepts are undergoing alteration ; ;

Such modifications are all for the best but it takes something as different as a Deerstalker or a Jet to change arms-making concepts.

in working with these patients the therapist eventually gets to do some at least private mulling over of the possible meaning of a belch, or the passage of flatus, not only because he is reduced to this for lack of anything else to analyze, but also because he learns that even these animal-like sounds constitute forms of communication in which, from time to time, quite different things are being said, long before the patient can become sufficiently aware of these, as distinct feelings and concepts, to say them in words.

After they have developed concepts, they are free from the necessity of manipulating objects ; ;

Mythological concepts may by all means still be used, but they can be used responsibly only as `` symbols '' or `` ciphers '', that is, only if they are also constantly interpreted in nonmythological ( or existential ) terms.

Biological anthropologists are interested in both human variation and in the possibility of human universals ( behaviors, ideas or concepts shared by virtually all human cultures ) They use many different methods of study, but modern population genetics, participant observation and other techniques often take anthropologists " into the field ," which means traveling to a community in its own setting, to do something called " fieldwork.

More problematic are words whose senses express closely related concepts.

Other continental philosophers suggest that concepts such as life, nature, and sex are ambiguous.

Crucial to this definition are the ancient Greek concepts of honor ( timē ) and shame.

The overlapping concepts of immunogenicity and antigenicity are, therefore, subtly different.

Arrays are analogous to the mathematical concepts of vectors, matrices, and tensors.

Therefore rings and Z-algebras are equivalent concepts, in the same way that abelian groups and Z-modules are equivalent.

Abstraction is a process by which higher concepts are derived from the usage and classification of literal (" real " or " concrete ") concepts, first principles, or other methods.

The oldest known physical representations identified as symbols for abstract concepts are abstract engravings found on two pieces of ochre in Blombos Cave, South Africa, in 2001.

The main disadvantage of abstraction is that highly abstract concepts are more difficult to learn, and require a degree of mathematical maturity and experience before they can be assimilated.

But these are physical representations of the corresponding mathematical entities ; the line and the curve are idealized concepts whose width is 0 ( see Line ).

" Educators are now adjusting their curricula to focus on more quantitative concepts and tools.

Binary relations are used in many branches of mathematics to model concepts like " is greater than ", " is equal to ", and " divides " in arithmetic, " is congruent to " in geometry, " is adjacent to " in graph theory, " is orthogonal to " in linear algebra and many more.

Dependent origination posits that certain specific events, concepts, or realities are always dependent on other specific things.

All concepts in biology are subject to the same laws that other branches of science obey, such as the laws of thermodynamics and conservation of energy.

Conversely, modern biological sciences ( including even concepts such as molecular ecology ) are intimately entwined and dependent on the methods developed through biotechnology and what is commonly thought of as the life sciences industry.

Abstraction allows program designers to separate categories and concepts from instances of implementation, so that they do not depend on software or hardware.

Either approach is adequate for most uses, provided that one attends to the necessary changes in language, notation, and the definitions of concepts like restrictions, composition, inverse relation, and so on.

Some, like René Descartes, have thought that this is so ( this view is known as dualism, and functionalism also considers the mind as distinct from the body ), while others have thought that concepts of the mental can be reduced to physical concepts ( this is the view of physicalism or materialism ).

However, concepts of regional geography has altered and so have regional varieties of Indian dances.

Some researchers have taken up speculative views, such as Jerzy Strzelczyk, who assumed that in the light of contemporary concepts and habits of marriage of that time ( when as a rule marriages were contracted with teenage girls ) is assumed that Dobrawa had passed her early youth, so, it's probable that she was in her late teens or twenties.

Eliminative materialists believe " folk psychology " is so unscientific that, ultimately, it will be better to eliminate primitive concepts such as mind, desire and belief, in favor of a future neuro-scientific account.

Diffeomorphism does not respect distance and angle, so these key concepts of Euclidean geometry are lost on a smooth manifold.

The declaration also permits new concepts to be expressed as the speaker sees fit, but it recommends doing so in accordance with the original style.

However, programming languages are often hybrids of several programming paradigms, so programmers using " mostly imperative " languages may have utilized some of these concepts.

In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry.

Yet they appear in different contexts for application ( plane mapping and kinematics ) so the isomorphism is insufficient to merge the concepts.

Rousseau ’ s philosophy of education is not concerned with particular techniques of imparting information and concepts, but rather with developing the pupil ’ s character and moral sense, so that he may learn to practice self-mastery and remain virtuous even in the unnatural and imperfect society in which he will have to live.

Maintainers and developers of MUSH servers have traditionally shared ideas with one another, so most MUSH servers include concepts or code developed originally in other servers.

That is, how can an entity design and bring all the following listed objects or concepts into existence if they are so central to our, or any conscious entity's existence?

" Saussure believed that dismantling signs was a real science, for in doing so we come to an empirical understanding of how humans synthesize physical stimuli into words and other abstract concepts.

Information retrieval thesauri are formally organized so that existing relationships between concepts are made explicit.

Energy and torque are entirely different concepts, so the practice of using different unit names ( i. e., reserving newton metres for torque and using only joules for energy ) helps avoid mistakes and misunderstandings.

These words and terms were used because of their familiarity, but more so because in most cases there were no equivalent terms in the vernacular which could express the Jewish concepts or describe the objects of cultural significance.

) The concepts of the Boehm system have been applied across the range of flutes available, including piccolos, alto flutes, bass flutes, and so on, as well as other wind instruments.

This distinction between online and offline is sometimes inverted, with online concepts being used to define and to explain offline activities, rather than ( as per the conventions of the desktop metaphor with its desktops, trash cans, folders, and so forth ) the other way around.

Mary Shaw and David Garlan of Carnegie Mellon wrote a book titled Software Architecture: Perspectives on an Emerging Discipline in 1996, which brought forward the concepts in Software Architecture, such as components, connectors, styles and so on.

In doing so, he reversed a Pythagorean emphasis on number and arithmetic, focusing instead on geometrical concepts as the basis of rigorous mathematics.