CushionTheBlow (구 BluemoonSoft)

A polyhedron (plural polyhedra or polyhedrons) is often defined as a geometric object with flat faces and straight edges (the word polyhedron comes from the Classical Greek πολυεδρον, from poly-, stem of πολυς, "many," + -edron, form of εδρον, "base", "seat", or "face").

This definition of a polyhedron is not very precise, and to a modern mathematician is quite unsatisfactory. Grünbaum (1994, p.43) observed that:

The Original Sin in the theory of polyhedra goes back to Euclid, and through Kepler, Poinsot, Cauchy and many others ... [in that] at each stage ... the writers failed to define what are the 'polyhedra' ...

Modern mathematicians do not even agree as to exactly what makes something a polyhedron.

Reference:
http://en.wikipedia.org/wiki/Polyhedron

In computer science, in particular networking, a session is a semi-permanent interactive information exchange, i.e. a dialogue, a conversation or a meeting, between two or more communicating devices, or between a computer and user (see Login session). A session is set up or established at a certain point in time, and torn down at a later point in time. An established communication session may involve more than one message in each direction. A session is typically, but not always, stateful, meaning that at least one of the communicating parts need to save information about the session history in order to be able to communicate, as opposed to stateless communication, where the communication consists of independent requests with responses.

Communication sessions may be implemented as part of protocols and services at the application layer, at the session layer or at the transport layer in the OSI model.

Application layer examples:
- HTTP sessions, which may allow dynamic web pages, i.e. interactive web pages, as opposed to static web pages.
- A telnet remote login session

Session layer example:
- A Session Initiation Protocol (SIP) based Internet phone call

Transport layer example:
- A TCP session, which is synonymous to a TCP virtual circuit, a TCP connection, or an established TCP socket.

In the case of transport protocols which do not implement a formal session layer (e.g., UDP) or where sessions at the session layer are generally very short-lived (e.g., HTTP), sessions are maintained by a higher level program using a method defined in the data being exchanged. For example, an HTTP exchange between a browser and a remote host may include an HTTP cookie which identifies state, such as a unique session ID, information about the user's preferences or authorization level.

Protocol version HTTP/1.1 makes it possible to reuse the same TCP session for a sequence of service requests and responses (a sequence of file transfers) in view to reduce the session establishment time, while HTTP/1.0 only allows a single request and response during one TCP session. However, this transport layer session mechanism should not be confused with a so called HTTP session, since it is not lasting sufficiently long time, and does not provide application level interactive services such as dynamic web pages.

Communication sessions, especially stateful communication, are often implemented in software using multithreading, where a new thread is created when the computer establishes or joins a session. The advantage over a single-thread approach is relaxed complexity of the software, since each thread is an instance with its own history and variables. The disadvantage is large overhead in terms of system resources.

When a client may connect to any in a cluster of servers, a special problem is encountered in maintaining consistency when the servers must maintain session state. The client must either be directed to the same server for the duration of the session, or the servers must transmit server-side session information via a shared file system or database. Otherwise, the client may reconnect to a different server than the one it started the session with, which will cause problems when the new server does not have access to the stored state of the old one.

Reference:
http://en.wikipedia.org/wiki/Session_%28computer_science%29

A database transaction is a unit of work performed against a database management system or similar system that is treated in a coherent and reliable way independent of other transactions. A database transaction, by definition, must be atomic, consistent, isolated and durable. These properties of database transactions are often referred to by the acronym ACID.

Transactions provide an "all-or-nothing" proposition stating that work units performed in a database must be completed in their entirety or take no effect whatsoever. Further, transactions must be isolated from other transactions, results must conform to existing constraints in the database and transactions that complete successfully must be committed to durable storage.

In some systems, transactions are also called LUWs for Logical Units of Work.

Reference:
http://en.wikipedia.org/wiki/Database_transaction

In computer science, ACID (Atomicity, Consistency, Isolation, Durability) is a set of properties that guarantee that database transactions are processed reliably. In the context of databases, a single logical operation on the data is called a transaction.

An example of a transaction is a transfer of funds from one account to another, even though it might consist of multiple individual operations (such as debiting one account and crediting another).

Reference:
http://en.wikipedia.org/wiki/ACID

In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined.

The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space. In fact, the notion of "metric" is a generalization of the Euclidean metric arising from the four long known properties of the Euclidean distance. The Euclidean metric defines the distance between two points as the length of the straight line connecting them.

The geometric properties of the space depends on the metric chosen, and by using a different metric we can construct interesting non-Euclidean geometries such as those used in the theory of general relativity.

A metric space also induces topological properties like open and closed sets which leads to the study of even more abstract topological spaces.

Reference:
http://en.wikipedia.org/wiki/Metric_space

In computational complexity theory, big O notation is often used to describe how the size of the input data affects an algorithm's usage of computational resources (usually running time or memory). It is also called Big Oh notation, Landau notation, Bachmann-Landau notation, and asymptotic notation. Big O notation is also used in many other scientific and mathematical fields to provide similar estimations.

The symbol O is used to describe an asymptotic upper bound for the magnitude of a function in terms of another, usually simpler, function. There are also other symbols o, Ω, ω, and Θ for various other upper, lower, and tight bounds. Informally, the O notation is commonly employed to describe an asymptotic tight bound, but tight bounds are more formally and precisely denoted by the Θ (capital theta) symbol as described below. This distinction between upper and tight bounds is useful, and sometimes critical; most computer scientists would urge distinguishing the usage of O and Θ. In some other fields, however, the Θ notation is not commonly known.

Reference:
http://en.wikipedia.org/wiki/Big_o_notation

A comparison sort is a type of sorting algorithm that only reads the list elements through a single abstract comparison operation (often a "less than or equal to" operator) that determines which of two elements should occur first in the final sorted list. The only requirement is that the operator obey the three defining properties of a total order:

1. if a ≤ b and b ≤ a then a = b (antisymmetry)
2. if a ≤ b and b ≤ c then a ≤ c (transitivity)
3. a ≤ b or b ≤ a (totalness or trichotomy)

A metaphor for thinking about comparison sorts is that you have a set of unlabelled weights and a balance scale. The goal is to line up the weights in order by their weight without any information except that obtained by placing two weights on the scale and seeing which one is heavier (or if they weigh the same).

Reference:
http://en.wikipedia.org/wiki/Comparison_sort

Generally, a trichotomy is a splitting into three disjoint parts. In mathematics, the law (or axiom) of trichotomy is most commonly the statement that for any (real) numbers x and y, exactly one of the following relations holds:

x < y,
x = y,
x > y.

If applied to cardinal numbers, the law of trichotomy is equivalent to the axiom of choice.

More generally, a binary relation R on X is trichotomous if for all x and y in X exactly one of xRy, yRx or x = y holds. If such a relation is also transitive it is a strict total order; this is a special case of a strict weak order. For example, in the case of three elements the relation R given by aRb, aRc, bRc is a strict total order, while the relation R given by the cyclic aRb, bRc, cRa is a non-transitive trichotomous relation.

In the definition of an ordered integral domain or ordered field, the law of trichotomy is usually taken as more foundational than the law of total order, with y = 0, where 0 is the zero of the integral domain or field.

In set theory, trichotomy is most commonly defined as a property that a binary relation < has when all its members <x,y> satisfy exactly one of the relations listed above. Strict inequality is an example of a trichotomous relation in this sense. Trichotomous relations in this sense are irreflexive and antisymmetric.

Reference:
http://en.wikipedia.org/wiki/Trichotomy_%28mathematics%29