Heap (mathematics)

In abstract algebra, a heap (sometimes also called a groud) is a mathematical generalization of a group. Informally speaking, a heap is obtained from a group by "forgetting" which element is the unit, in the same way that an affine space can be viewed as a vector space in which the 0 element has been "forgotten". A heap is essentially the same thing as a torsor, and the category of heaps is equivalent to the category of torsors, with morphisms given by transport of structure under group homomorphisms, but the theory of heaps emphasizes the intrinsic composition law, rather than global structures such as the geometry of bundles.

Formally, a heap is an algebraic structure consisting of a non-empty set H with a ternary operation denoted that satisfies

A group can be regarded as a heap under the operation . Conversely, let H be a heap, and choose an element e ∈ H. The binary operation makes H into a group with identity e and inverse . A heap can thus be regarded as a group in which the identity has yet to be decided.

Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers),structure,space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.

Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert (1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.

! (disambiguation)

! is a punctuation mark called an exclamation mark (33 in ASCII), exclamation point, ecphoneme, or bang.

! may also refer to:

Mathematics and computers

Music

Other

See also

Junior Certificate

The Junior Certificate (Irish: Teastas Sóisearach) is an educational qualification awarded in Ireland by the Department of Education and Skills to students who have successfully completed the junior cycle of secondary education, and achieved a minimum standard in their Junior Certification examinations. These exams, like those for the Leaving Certificate, are supervised by the State Examinations Commission. A "recognised pupil"<ref name"">Definitions, Rules and Programme for Secondary Education, Department of Education, Ireland, 2004</ref> who commences the Junior Cycle must reach at least 12 years of age on 1 January of the school year of admission and must have completed primary education; the examination is normally taken after three years' study in a secondary school. Typically a student takes 9 to 13 subjects – including English, Irish and Mathematics – as part of the Junior Cycle. The examination does not reach the standards for college or university entrance; instead a school leaver in Ireland will typically take the Leaving Certificate Examination two or three years after completion of the Junior Certificate to reach that standard.

Heap

Heap may refer to:

Computer science

Mathematics

Industry

Comics

Names

Place

Acronyms

See also

Heap (comics)

The Heap is the name of several fictional comic book muck-monsters, the original of which first appeared in Hillman Periodicals' Air Fighters Comics #3 (Dec. 1942), during the period fans and historians call the Golden Age of Comic Books. The character was created by writer Harry Stein and artist Mort Leav, and revived in the 1980s by Eclipse Comics.

Similar but unrelated characters appeared in comics stories published by Skywald in the 1970s and Image Comics in the 1990s.

Publication history

Hillman

Following its debut Air Fighters Comics #3 (cover-dated Dec. 1942), the Heap reappeared as a guest character sporadically in that title. With its fourth appearance, in the by-then re-titled Airboy Comics vol. 3, #9 (Oct. 1946), it became the star of a backup feature. That feature continued until the final issue, vol. 10, #4 (May 1953). Other artists associated with Hillman's Heap include Jack Abel, Paul Reinman, and Ernie Schroeder.

In 1986, Eclipse Comics, having acquired rights to some Hillman characters, began publishing a new Airboy comic with the Heap as a supporting character. The Heap also appeared in the Eclipse title The New Wave, where the creature was considered by some members of that group to be a member. Eclipse Comics went bankrupt and ceased operations in the 1990s. Image Comics purchased the Eclipse assets, including the Heap.

Memory management

Memory management is the act of managing computer memory at the system level. The essential requirement of memory management is to provide ways to dynamically allocate portions of memory to programs at their request, and free it for reuse when no longer needed. This is critical to any advanced computer system where more than a single process might be underway at any time.

Several methods have been devised that increase the effectiveness of memory management. Virtual memory systems separate the memory addresses used by a process from actual physical addresses, allowing separation of processes and increasing the effectively available amount of RAM using paging or swapping to secondary storage. The quality of the virtual memory manager can have an extensive effect on overall system performance.

Dynamic memory allocation

Details

The task of fulfilling an allocation request consists of locating a block of unused memory of sufficient size. Memory requests are satisfied by allocating portions from a large pool of memory called the heap or free store. At any given time, some parts of the heap are in use, while some are "free" (unused) and thus available for future allocations.