Product

Product may refer to:

Business

Sciences

Mathematics

In linear algebra:

In abstract algebra:

Product breakdown structure

In project management, a product breakdown structure (PBS) is a tool for analysing, documenting and communicating the outcomes of a project, and forms part of the product based planning technique.

The PBS provides ''an exhaustive, hierarchical tree structure of deliverables (physical, functional or conceptual) that make up the project, arranged in whole-part relationship'' (Duncan, 2015).

This diagrammatic representation of project outputs provides a clear and unambiguous statement of what the project is to deliver.

The PBS is identical in format to the work breakdown structure (WBS), but is a separate entity and is used at a different step in the planning process. The PBS precedes the WBS and focuses on cataloguing all the desired outputs (products) needed to achieve the goal of the project. This feeds into creation of the WBS, which identifies the tasks and activities required to deliver those outputs. Supporters of product based planning suggest that this overcomes difficulties that arise from assumptions about what to do and how to do it by focusing instead on the goals and objectives of the project - an oft-quoted analogy is that PBS defines where you want to go, the WBS tells you how to get there.

Product (category theory)

In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the cartesian product of sets, the direct product of groups, the direct product of rings and the product of topological spaces. Essentially, the product of a family of objects is the "most general" object which admits a morphism to each of the given objects.

Definition

Let C be a category with some objects X₁ and X₂. An object X is a product of X₁ and X₂, denoted X₁ × X₂, if it satisfies this universal property:

The unique morphism f is called the product of morphisms f₁ and f₂ and is denoted < f₁, f₂ >. The morphisms π₁ and π₂ are called the canonical projections or projection morphisms.

Above we defined the binary product. Instead of two objects we can take an arbitrary family of objects indexed by some set I. Then we obtain the definition of a product.

An object X is the product of a family (X_i)_i∈I of objects iff there exist morphisms π_i : X → X_i, such that for every object Y and a I-indexed family of morphisms f_i : Y → X_i there exists a unique morphism f : Y → X such that the following diagrams commute for all i∈I:

Bosh (band)

Bosh, stylized BOSH, were a British Christian rock band based in Bournemouth on England's South Coast. The band formed in 1996 around brothers David and Michael Griffiths. BOSH are noted as one bands that started the Nth Degree Community and Risen Records in the early 2000s.

BOSH released four CD's on Risen Records, the EP 'VII' in 2005, the live album 'Middle of Somewhere' in 2007. 'Sound the Alarms' was released in 2008 produced by a team that included Grammy Nominated producer Steve Ennever (formally of Bournemouth band Denzil) and Paul Burton. The Gloaming Hour EP was released in 2009. They were also a regular feature in the Christian music scene in the UK, playing at Nth Fest, Creation Fest, Greenbelt festival, Grace Festivals and The Big Church Day Out Festival. They also played outside the Christian music scene, and opened for bands such as Frightened Rabbit

The band's final line-up consisted of David Griffiths, Mike Griffiths, Steve Coates, James Grant and touring keys player Dave Evans. According to the band's Facebook page, former keyboard player Grant Howard left the band in March 2010 to move to Ontario, Canada . He was followed in July 2010 by guitarist Matt Gainsford who left to continue studying in Wisconsin.

BOSH

Bidirectional-streams Over Synchronous HTTP (BOSH) is a transport protocol that emulates a bidirectional stream between two entities (such as a client and a server) by using multiple synchronous HTTP request/response pairs without requiring the use of polling or asynchronous chunking.

For applications that require both "push" and "pull" communications, BOSH is significantly more bandwidth-efficient and responsive than most other bidirectional HTTP-based transport protocols and AJAX. BOSH achieves this by avoiding HTTP polling, yet it does so without resorting to chunked HTTP responses as is done in the technique known as Comet. To date, BOSH has been used mainly as a transport for traffic exchanged between Jabber/XMPP clients and servers (e.g., to facilitate connections from web clients and from mobile clients on intermittent networks).

For "push", a BOSH client starts an HTTP request, but the server postpones sending a reply until it has data to send. After receiving a reply, the client immediately makes another request on the same HTTP connection, so the server can always send data to the client without waiting for the client to poll. If, while waiting for a reply, the client needs to send data to the server, it opens a second HTTP connection. There are at most two HTTP connections open at a time, one on which the server can send data as a reply and one on which the client can send data as a POST.