Index of a subgroup

In mathematics, specifically group theory, the index of a subgroup H in a group G is the "relative size" of H in G: equivalently, the number of "copies" (cosets) of H that fill up G. For example, if H has index 2 in G, then intuitively "half" of the elements of G lie in H. The index of H in G is usually denoted |G : H| or [G : H] or (G:H).

Formally, the index of H in G is defined as the number of cosets of H in G. (The number of left cosets of H in G is always equal to the number of right cosets.) For example, let Z be the group of integers under addition, and let 2Z be the subgroup of Z consisting of the even integers. Then 2Z has two cosets in Z (namely the even integers and the odd integers), so the index of 2Z in Z is two. To generalize,

for any positive integer n.

If N is a normal subgroup of G, then the index of N in G is also equal to the order of the quotient group G / N, since this is defined in terms of a group structure on the set of cosets of N in G.

If G is infinite, the index of a subgroup H will in general be a non-zero cardinal number. It may be finite - that is, a positive integer - as the example above shows.

Jīva (Jainism)

The Jīva or Atman (/ˈɑːtmən/; Sanskrit: आत्मन्) is a philosophical term used within Jainism to identify the soul. It is one's true self (hence generally translated into English as 'Self') beyond identification with the phenomenal reality of worldly existence. As per the Jain cosmology, jīva or soul is also the principle of sentience and is one of the tattvas or one of the fundamental substances forming part of the universe. According to The Theosophist, "some religionists hold that Atman (Spirit) and Paramatman (God) are one, while others assert that they are distinct ; but a Jain will say that Atman and Paramatman are one as well as distinct." In Jainism, spiritual disciplines, such as abstinence, aid in freeing the jīva "from the body by diminishing and finally extinguishing the functions of the body." Jain philosophy is essentially dualistic. It differentiates two substances, the self and the non-self.

Real Self

According to the Jain text, Samayasāra (The Nature of the Self):-

Life (manga)

Life (Japanese: ライフ, Hepburn: Raifu) is a shōjo manga series created by Keiko Suenobu, a manga creator well known for her work on Vitamin and Happy Tomorrow. Life was serialized in Bessatsu Friend, a publication of Kodansha, and deals with many controversial topics such as self-mutilation, bullying, rape, suicide, and manipulation. In 2006, it won the Kodansha Manga Award for shōjo.

The English language version of the manga, published by Tokyopop, was originally rated OT (Older Teen; 16+), but starting with the release of Volume 6 and carrying back over to future reprintings of the previous five, the rating was changed to M (Mature; 18+) for extremely explicit content in that volume. As of June 2008, nine volumes have been released in the United States; Volume 10 was scheduled for a September 2008 release, but on August 31, 2009, Kodansha (original Japanese publisher of the series) announced that they would drop their manga licensing contract with Tokyopop, leaving Life and other well-known series such as Rave Master unfinished, whether permanently or until picked up by other manga publishing companies (Dark Horse Manga and Del Rey Manga have already picked up certain titles). Kodansha also did not offer an explanation for their decision. The future of the English version of the manga is unknown, as Tokyopop itself shut down in May 2011 after they were faced with bankruptcy.

Life (Sly and the Family Stone album)

Life is the third studio album by funk/soul band Sly and the Family Stone, released in September 1968 on Epic/CBS Records.

Music

Unlike its predecessor, Dance to the Music, Life was not a commercial success, although it has received mostly positive reviews from music critics over the years. Many of its songs, including "M'Lady", "Fun", "Love City", as well as the title track, became popular staples in the Family Stone's live show. A middle ground between the fiery A Whole New Thing and the more commercial Dance to the Music, Life features very little use of studio effects, and is instead more driven by frontman Sly Stone's compositions. Topics for the album's songs include the dating scene ("Dynamite!", "Chicken", "M'Lady"), groupies ("Jane is a Groupee"), and "plastic" (or "fake") people (the Beatlesque "Plastic Jim"). Of particular note is that the Family Stone's main themes of unity and integration are explored here in several songs ("Fun", "Harmony", "Life", and "Love City"). The next Family Stone LP, Stand!, would focus almost exclusively on these topics.

Medical Subject Headings

Medical Subject Headings (MeSH) is a comprehensive controlled vocabulary for the purpose of indexing journal articles and books in the life sciences; it serves as a thesaurus that facilitates searching. Created and updated by the United States National Library of Medicine (NLM), it is used by the MEDLINE/PubMed article database and by NLM's catalog of book holdings. MeSH is also used by ClinicalTrials.gov registry to classify which diseases are studied by trials registered in ClinicalTrials.gov.

MeSH was introduced in 1960, with the NLM's own index catalogue and the subject headings of the Quarterly Cumulative Index Medicus (1940 edition) as precursors. The yearly printed version of MeSH was discontinued in 2007 and MeSH is now available online only. It can be browsed and downloaded free of charge through PubMed. Originally in English, MeSH has been translated into numerous other languages and allows retrieval of documents from different languages.

Structure of MeSH

Mesh-29

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Mesh-29 were an English indie rock band from Whittlesey, Peterborough, United Kingdom. The band formed in 1999 and consisted of Adam Mezzatesta on lead vocals and guitar and Anthony Shiels on the piano.

Mesh-29 entered the UK top 40 chart with their single Over The Barricade, reaching number 35 in the singles chart on 8 July 2007; only the second unsigned band in history of the UK charts to achieve such a result.

The band played their last ever gig on October 9, 2010.

Biography

On 2 July 2007, Mesh-29 released their single Over The Barricade, which reached number 35 in the UK singles chart. The band supported Scouting for Girls and Air Traffic amongst others. On 30 August 2007, they were interviewed (and played three live tracks) on the Janice Long show on BBC Radio 2.

The album closer, Alone, was used on the soundtrack to the MTV series The Hills.

Their second album Secret Traffic was released in the UK in October 2008 after their promotion single White Light was released on 13 October.

World

World is a common name for the whole of human civilization, specifically human experience, history, or the human condition in general, worldwide, i.e. anywhere on Earth or pertaining to anywhere on Earth.

In a philosophical context it may refer to:

In a theological context, world usually refers to the material or the profane sphere, as opposed to the celestial, spiritual, transcendent or sacred. The "end of the world" refers to scenarios of the final end of human history, often in religious contexts.

World history is commonly understood as spanning the major geopolitical developments of about five millennia, from the first civilizations to the present.

World population is the sum of all human populations at any time; similarly, world economy is the sum of the economies of all societies (all countries), especially in the context of globalization. Terms like world championship, gross world product, world flags etc. also imply the sum or combination of all current-day sovereign states.