Abstraction in mathematics is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.

He pointed out that implicit in the early Buddhist concept of dependent origination is the lack of any substantial being ( anatta ) underlying the participants in origination, so that they have no independent existence, a state identified as emptiness ( śūnyatā ), or emptiness of a nature or essence ( svabhāva ).

The underlying concept can be traced back to 1864 in the published work of George Perkins Marsh (" Man and Nature ").

Hypertext is the underlying concept defining the structure of the World Wide Web.

The philosophy of human rights attempts to examine the underlying basis of the concept of human rights and critically looks at its content and justification.

: The knowledge base underlying the INTERNIST system is composed of two basic types of elements: disease entities and manifestations .... also contains a ... hierarchy of disease categories, organized primarily around the concept of organ systems, having at the top level such categories as " liver disease ," " kidney disease ," etc.

The original surface micromachining concept was based on thin polycrystalline silicon layers patterned as movable mechanical structures and released by sacrificial etching of the underlying oxide layer.

The underlying concept of the poet as creator is not uncommon, and some modernist poets essentially do not distinguish between the creation of a poem with words, and creative acts in other media.

The underlying concept is that their head height may never be equal to that of their superior.

In the related concept of overfitting, excessively complex models are affected by statistical noise ( a problem also known as the bias-variance trade-off ), whereas simpler models may capture the underlying structure better and may thus have better predictive performance.

The underlying concept is that such students need specific guidance to be able to analyze case studies.

The underlying concept is that with enough practice ( hundreds of case analyses ) students develop intuitive skills for analyzing and resolving complex business situations.

There is no real difference in the genetic processes underlying artificial and natural selection, and the concept of artificial selection was used by Charles Darwin as an illustration of the wider process of natural selection.

The concept that insulin resistance may be the underlying cause of diabetes mellitus type 2 was first advanced by Prof. Wilhelm Falta and published in Vienna in 1931, and confirmed as contributary by Sir Harold Percival Himsworth of the University College Hospital Medical Centre in London in 1936.

This concept is largely fuzzy and unclear in earlier stories depicting very rudimentary robots who are only programmed to comprehend basic physical tasks, where the Three Laws act as an overarching safeguard, but by the era of The Caves of Steel featuring robots with human or beyond-human intelligence the Three Laws have become the underlying basic ethical worldview that determines the actions of all robots.

The tool's underlying concept and data were published in various scientific publications.

The primary concept underlying Dōgen's Zen practice is " oneness of practice-enlightenment " ( 修證一如 shushō-ittō / shushō-ichinyo ).

Because it was the first major typesetting program to incorporate the concept of an implicit " underlying page " frame, and one of the first to incorporate a strong " style sheet " concept, Ventura Publisher produces documents with a high degree of internal consistency, unless specifically overridden by the user.

The underlying concept is that early intervention through play with adapted toys and technology can teach disabled children to deal with the " normal " world.

If the concept of belief is incoherent, then any attempt to find the underlying neural processes that support it will fail.

The concept of ki underlying Reiki is speculative and there is no scientific evidence that it exists ; a 2008 systematic review of randomised clinical trials concluded that " the evidence is insufficient to suggest that reiki is an effective treatment for any condition.

This concept provided scholarly substance for explaining the underlying Indian-ness of apparently divergent cultural and linguistic patterns.

In his autobiographical work Ecce Homo, Nietzsche states that the book's underlying concept is discussed within " the penultimate section of the fourth book " of ' The Gay Science ' ( Ecce Homo, Kaufmann ).

The underlying concept behind the Unplugged series has been attributed to the popularity among musicians of a variety of informal musical performances on stage, film, television and record in earlier decades.

According to the theory underlying odd-lot indices, the trader who trades odd lots is most likely a small trader, one who can't afford to trade round lots.

The Mathematical Appendix presents the rigorous argument, but is best read after Part 1, in order that the assumptions underlying the equations may be explicit.

The underlying assumption, of course, is that only sight and touch enable us, in any precise and fully dependable way, to locate objects in space beyond us, the other senses being decidedly inferior, if not totally inadequate, in this regard.

To speak of this underlying view of the world is to embark upon matters of subjective judgment.

It is really as though the Russians have seen in this character the oftentimes underlying vitality and courage of supposed buffoons.

An appeal " as of right " is one that is guaranteed by statute or some underlying constitutional or legal principle.

In Heidegger's phenomenology, Dasein is always in a meaningful world, but there is always an underlying background for every instance of signification.

Although single genes have little effect on complex traits and interact heavily both between themselves and with the external factors, research is underway to unravel possible molecular mechanisms underlying anxiety and comorbid conditions.

Central to his behaviour in the later novels is the underlying assumption that particular crimes are only committed by particular types of people.

It receives its name from its soil ( weathered from the weak underlying limestone ), which is black in colour, almost destitute of sand and loam, and rich in limestone and marl formations, especially adapted to the production of cotton ; hence the region is also called the Cotton Belt.

29 .</ ref > This tendency to identify one specific underlying reality made up of a material thing constitutes the bulk of the contributions for which Anaximenes is most famed.

Is there some underlying unity to aesthetic judgment and is there some way to articulate the similarities of a beautiful house, beautiful proof, and beautiful sunset?

Specifically, at speeds of OC-3 and above, the cost of segmentation and reassembly ( SAR ) hardware makes ATM less competitive for IP than Packet Over SONET ( POS ); because of its fixed 48-byte cell payload, ATM is not suitable as a data link layer directly underlying IP ( without the need for SAR at the data link level ) since the OSI layer on which IP operates must provide a maximum transmission unit ( MTU ) of at least 576 bytes.

Eventually what he'd be left with is something similar to a call option on the underlying stock, acquired at a very low price.

The correspondence between these values and the physical states of the underlying storage or device is a matter of convention, and different assignments may be used even within the same device or program.

If X is a Banach space and K is the underlying field ( either the real or the complex numbers ), then K is itself a Banach space ( using the absolute value as norm ) and we can define the continuous dual space as X ′ = B ( X, K ), the space of continuous linear maps into K.

Typically bronze only oxidizes superficially ; once a copper oxide ( eventually becoming copper carbonate ) layer is formed, the underlying metal is protected from further corrosion.

Most scholars hold that the Hebrew text underlying the Septuagint version is older than the Masoretic text and that either the Masoretic evolved either from this vorlage or from a closely related version.