In mathematics, more specifically in functional analysis, a Banach space ( pronounced ) is a complete normed vector space.

Most general purpose functional programming languages allow unrestricted recursion and are Turing complete, which makes the halting problem undecidable, can cause unsoundness of equational reasoning, and generally requires the introduction of inconsistency into the logic expressed by the language's type system.

The basic and historically first class of spaces studied in functional analysis are complete normed vector spaces over the real or complex numbers.

Banach's dissertation, completed in 1920 and published in 1922, formally axiomatized the concept of a complete normed vector space and laid the foundations for the area of functional analysis.

Increasingly, however, XSLT processors use optimization techniques found in functional programming languages and database query languages, such as static rewriting of an expression tree ( e. g., to move calculations out of loops ), and lazy pipelined evaluation to reduce the memory footprint of intermediate results ( and allow " early exit " when the processor can evaluate an expression such as without a complete evaluation of all subexpressions ).

OS / 390 was introduced in late 1995 in an effort, led by the late Randy Stelman, to simplify the packaging and ordering for the key, entitled elements needed to complete a fully functional MVS operating system package.

It provides tools to complete product definition, including functional tolerances, as well as kinematics definition.

By 1875, the Territory had 10 schools ; a remarkable development in light of the complete absence of functional schools after the insurrection of 1853.

Although he made many contributions that were crucial to the early development of all-electronic television, he is perhaps best known for inventing the first fully functional all-electronic image pickup device ( video camera tube ), the " image dissector ", the first fully functional and complete all-electronic television system, and for being the first person to demonstrate such a system to the public.

This, however, delays testing of the ultimate functional units of a system until significant design is complete.

This " inclusive " approach contrasted with the typical modernist effort to resolve and unify all factors in a complete and rigidly structured — and possibly less functional and more simplistic — work of art.

* In functional analysis, a subset S of a topological vector space V is complete if its span is dense in V. In the particular case of Hilbert spaces ( or more generally, inner product spaces ), an orthonormal basis is a set that is both complete and orthonormal.

Inflation-adjusting the total money supply ( excluding bank notes and coins of the fiat functional currency created by means of fractional reserve banking within an economy ) in terms of a daily index or rate under complete co-ordination would result in zero cost of inflation ( not zero inflation ) in only the entire money supply ( as qualified ) in an economy.

Further adaptations to the cold include a thick layer of subcutaneous fat, and an almost complete lack of functional sweat glands.

It is the process by which strangers resocialized into a new culture so as to attain an increasing functional fitness ... complete adaptation is a lifetime goal.

In functional analysis, it is often convenient to define a linear transformation on a complete, normed vector space by first defining a linear transformation on a dense subset of and then extending to the whole space via the theorem below.

In this case the longer instructions are " stalled " in their functional units, and then re-inserted into the instruction stream when they can complete.

There is little functional plasticity observed in partial and complete callosotomies ; however, much more plasticity can be seen in infant patients receiving a hemispherectomy, which suggests the opposite hemisphere can adapt some functions typically performed by its opposite pair.

There is little functional plasticity observed in partial and complete callosotomies on adults ; however, much more plasticity can be seen in infant patients.

Combining the two sources of information to yield a complete functional understanding of the human brain is an ongoing challenge for neuroscience.

Advocates of the promotion of Low German have expressed considerable hope that this political development will at once lend legitimacy to their claim that Low German is a separate language and help mitigate the functional limits of the language that may still be cited as objective criteria for a mere dialect ( such as the virtually complete absence from legal and administrative contexts, schools, the media, etc.

Design elements describe the desired software features in detail, and generally include functional hierarchy diagrams, screen layout diagrams, tables of business rules, business process diagrams, pseudo-code, and a complete entity-relationship diagram with a full data dictionary.

In reality, however, Jiang's era saw the return to complete, centralized leadership by 1998, after ousting rival party leader Qiao Shi and firmly taking the positions of the CPC General secretary, the President, and the Chairman of the Central Military Commission, becoming paramount leader of China's tripartite Party-State-Military functional structure.

One of my virtues or vices is a sort of three-dimensional imagination complete with sound effects and glorious living color.

Its massive contours are rooted in the simple need of man, since he is always incomplete, to complete himself.

The second reason for his popularity is his complete spontaneity with the guitar.

A tragedy, by his definition, is an imitation of an action that is serious, of a certain magnitude, and complete in itself.

Much criticism has been leveled at this rather forced analogy, but what is equally significant is Adams' complete acceptance of the Biblical record as `` good and trustworthy history ''.

My last gift to him is complete silence until the book is out and the first heated discussion dies down.

One matter of concern to the complete effectiveness of pool operations is the lack of adequate central garage facilities.

Since the validity of all subsequent planning depends on the accuracy of the basic inventory information, great care is being taken that the inventory is as complete as possible.

Another recent achievement was the successful development of a method for the complete combustion in a bomb calorimeter of a metal in fluorine when the product is relatively non-volatile.

Mortar is poured between this bracing and the 4-inch blocks on edge to complete the wall thickness for radiation shielding.

The structure is complete.

Because the bobbin-to-cone winding process is a relatively high-cost operation for the mill, the almost complete automation provided by the Uniconer can mean important economies in textile production, at the same time upgrading quality.

As you can see, in this Push-Pull Super Set the entire chest-back-shoulder area is vigorously exercised in alternate sectors by alternate exercises so the complete torso remains pumped-up all the time!!

The first substantially complete stereo Giselle ( and the only one of its scope since Feyer's four-sided LP edition of 1958 for Angel ), this set is, I'm afraid, likely to provide more horrid fascination than enjoyment.

The jig is erected after the frames and transom are complete.

It is a full scale, small, but efficient house that can become a year 'round retreat complete in every detail.

It is doubtful that the complete solution to the over-all problem can result entirely from company efforts.

Although we are still far from a complete understanding of these problems, as a first approximation, it is suggested that alterations in the hypothalamic balance with consequent changes in the hypothalamic-cortical discharges account for major changes in behavior seen in various moods and states of emotions in man and beast under physiological circumstances, in experimental and clinical neurosis, and as the result of psychopharmacological agents.

It is proposed that in the future complete sampling censuses be carried out at five-year intervals.

The dictionary is a form dictionary, at least in the sense that complete forms are used as the basis for matching text occurrences with dictionary entries.

When irregularity and variation prevent summarizing, information is written in complete detail.