text:
Wikipedia:WikiProject Spam/Local/mbtilounge.com

Links

 * mbtilounge.com resolves to [//<IP_ADDRESS> <IP_ADDRESS>]
 * Link is not on the blacklist.
 * Link is not on the domainredlist.
 * Link is not on the Monitorlist.
 * None of the mentioned users is on the blacklist.
 * Link is not on the whitelist.
 * Link is not on the monitor list.
 * Link is blacklisted by \bmbtilounge\.com\b on [//en.wikipedia.org/wiki/Mediawiki:Spam-blacklist en.wikipedia.org]
 * Link is not on the monitor list.
 * Link is blacklisted by \bmbtilounge\.com\b on [//en.wikipedia.org/wiki/Mediawiki:Spam-blacklist en.wikipedia.org]

Selected additions

 * Displayed 5 additions out of 5 total.	 For more info see WikiProject_Spam/LinkReports/mbtilounge.com

Entry
Log entry for the MediaWiki:Spam-blacklist:

\bmbtilounge\.com\b         # ADMINNAME # see  [[Wikipedia:WikiProject_Spam/Local/mbtilounge.com ]]

Discussion
See COIBot report for more details.

New data reported. --COIBot (talk) 20:10, 17 August 2020 (UTC)

 * to MediaWiki:Spam-blacklist. --GeneralNotability (talk) 20:48, 17 August 2020 (UTC)

Link is locally blacklisted by \bmbtilounge\.com\b. --COIBot (talk) 23:08, 17 August 2020 (UTC)

source: wikimedia

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Talk:James Hagerty

Quotes belong in Wikiquote
Should the content of the “Quotes” section be moved to Wikiquote instead? The James Hagerty article at that wiki currently does not exist.

Random mention of Hagerty's name in a single Peanuts comic strip
- Please stop reposting your mention of Hagerty's name appearing in a random comic strip without addressing the concerns I raised. As per WP:BRD, you need to discuss this on the talk page first. As I mentioned in my edit summary, this page is about James Hagerty, not the "Peanuts" comic strip. Your factoid does not tell us anything substantive about James Hagerty himself and thus does not belong here. Just because "Peanuts" is a famous comic strip, it does not follow that we need to talk about "Peanuts" on the page of anyone ever mentioned one time in a "Peanuts" comic strip. James Hagerty was the White House Press Secretary for the entire eight years of Eisenhower's presidency and thus was a prominent public figure mentioned in the media thousands of times on a near daily basis. It does not rise to notability that he was merely mentioned by name in some aspect of the media, unless that tells us something substantive about his life and career. Lastly, I'll note that you made no effort to integrate your addition into the existing article, simply dropping your "Peanuts" reference under the "Political career" subheading where it is not at all relevant. Please stop reverting without any changes or discussion, or I'll have to report you for edit warring. --Ash-Gaar (talk) 18:12, 15 May 2023 (UTC)

 * You're the one "edit-warring", not me. Get a life. Dr Clyde Crashcup (talk) 20:07, 15 May 2023 (UTC)

title: Talk:James Hagerty


text:
Wikipedia:WikiProject X/Newsletter/Past issues

 * Issue 1 – February 2015
 * Issue 2 – March 2015
 * Issue 3 – April 2015
 * Issue 4 – June 2015
 * Issue 5 – October 2015
 * Issue 6 – January 2016
 * Issue 7 – February 2016
 * Issue 8 – March/April 2016
 * Issue 9 – May/June 2016
 * Issue 10 – March 2017
 * Issue 11 – February 2018
 * Issue 12 – August 2018
 * Issue 13 – December 2018
 * Issue 14 – June 2019
 * Issue 15 – September 2019


text:
User:Sereneta123456789/sandbox

James is a man who is fun and goes to a school, he is a age, and has a certain amount of siblings who have a gender that i am not going to say.

title: User:Sereneta123456789/sandbox


text:
Classic Mac OS

Introduction
Property of: Apple Latest Version: 9.2.2 Status: Ceased Development

The Apple Macintosh platform uses its own operating system known as Mac OS. Subsequent releases of the operating system have been denoted by appending the version number, such as Mac OS 9. With the advent of Mac OS X based on FreeBSD, previous versions have become known as Classic Mac OS and are no longer supported by Apple. Despite the lack of support, many systems running the Classic Mac OS are still in use today.

Graphical User Interface
Mac OS featured the first graphical user interface (GUI) on a mass produced computer. (Xerox produced the first GUI, but it did not enter production.) Many of the features of the original release of Mac OS are still implemented in modern operating systems, including:

 * Icons
 * Shortcuts
 * Mouse usage
 * Visual interactions (e.g. drag and drop)
 * Windows, buttons and dialog boxes
 * Boot directly into visual interface
 * Cut-and-paste

The ability to interact graphically with the operating system significantly reduced the learning curve. Initially many doubted the viability of the Macintosh for business applications, as the GUI was a significant departure from console based terminals. This preconception was dispelled largely through the passage of time and the adoption of GUIs in several other operating systems.

Table of Contents
The Macintosh Interface
 * /Menus and Windows/
 * The  Menu
 * /Application Menu/

title: Classic Mac OS


text:
Talk:Kingston Frontenacs

Bruce Cassidy
Here is the source for the possible hiring of Bruce Cassidy as the new coach. Kingston Whig Standard Flibirigit 18:41, 11 July 2006 (UTC)

Kingston Canadians alumni
Stop removing valid alumni from the Kingston Canadians and the [Kingston Frontenacs]] articles. Flibirigit 19:48, 16 November 2006 (UTC)
 * 1) Scott Arniel played 3 games for the Kingston Canadiens in the 1978-79 playoffs. See Here
 * 2) Darren Lowe played 1 game for the Kingston Canadiens in the 1977-78 season. See Here

Kingston Frontenacs (disambiguation)
Please see St. Marys Lincolns. In 1963 they beat the Kingston Frontenacs to win the Sutherland Cup. The Lincolns are Jr. B. —Preceding unsigned comment added by <IP_ADDRESS> (talk • contribs)
 * Section moved to Kingston Frontenacs (disambiguation). Flibirigit 03:53, 8 February 2007 (UTC)

New Logo?
Is it confirmed that they have changed their logo to just the K with Kinston Frontenacs below it? — Preceding unsigned comment added by <IP_ADDRESS> (talk) 12:55, 11 September 2013 (UTC)

title: Talk:Kingston Frontenacs


text:
Zimri D. Thomas

Zimri Dinsmore Thomas (born September 16, 1809) was a Michigan politician.

Early life
Thomas was born in Rowe, Massachusetts on September 16, 1809. In 1820, Thomas moved to central New York.

Career
Thomas served as postmaster at Hamburg, New York for six years. In 1835, Thomas moved to Michigan. From 1857 to 1858, Thomas served as supervisor of Allen Township, Michigan. On November 8, 1864, Thomas was elected to the Michigan House of Representatives where he represented the Hillsdale County 1st district from January 4, 1865 to December 31, 1866. In 1866, Thomas served as justice of the peace for Hillsdale Township, Michigan alongside George W. Burchard. They were filling the vacancy left by justice Henry T. Kellogg. In 1873, Thomas served as a justice of the peace in the city of Hillsdale with C. B. Dresser. In 1877, Thomas again served as a justice of the peace for the city of Hillsdale. Thomas served as a Hillsdale County coroner from 1873 to at least 1881.

title: Zimri D. Thomas


text:
Talk:Hailes Castle

There are two separate sets of coordinates given for this site. Oscar Wilde notwithstanding, it seems that there should be some standard set for establishing geographical coordinates. Perhaps from the main entrance or form the centre of the property, if the main entrance cannot be determined? Kibi78704 (talk) 14:13, 11 July 2009 (UTC)

title: Talk:Hailes Castle


text:
Talk:Dean Watkins

Source
The source of this Wikipedia entry is "Temperance movement Groups and Leaders in the U.S., " from which the material in bold was taken. Omission of this source reference has now been corrected.David Justin 18:54, 28 March 2007 (UTC)

'''Dean Watkins, a retired aeronautical engineer, was the Prohibition Party candidate for vice-president of the United States in 2000. Watkins' family has had a long association with the temperance movement. His grandfather, Aaron Watkins, was the Prohibition Party candidate for vice-president in 1908 and 1912 and its candidate for president in 1920.'''

External link
 *  Dean Watkins

title: Talk:Dean Watkins


text:
Wikipedia:Articles for deletion/Wartburg College Concert Bands

The result was redirect to Wartburg College. Tone 08:33, 25 August 2020 (UTC)

Wartburg College Concert Bands

 * – ( View AfD View log  Stats )

Guesswork, promo, and unverifiable material are hallmarks of the page. What little information is sourced is sourced back to self-published sources. Doesn’t pass WP:GNG.  Willsome 4 29  (say hey or see my edits!) 17:34, 17 August 2020 (UTC)
 * Note: This discussion has been included in the list of Bands and musicians-related deletion discussions.  Willsome 4 29  (say hey or see my edits!) 17:34, 17 August 2020 (UTC)
 * Note: This discussion has been included in the list of Iowa-related deletion discussions.  Willsome 4 29  (say hey or see my edits!) 17:34, 17 August 2020 (UTC)

 * Delete This is not a musical group per se, it is the history of the band program at a small liberal arts college, and nothing shows this is worth having a stand alone article on.John Pack Lambert (talk) 00:19, 18 August 2020 (UTC)
 * Merge or Redirect to Wartburg_College. Since this seems like a non-notable fork that is just as well mentioned in the article about the college instead of having a standalone article. --Adamant1 (talk) 12:04, 18 August 2020 (UTC)
 * Merge to Wartburg College as not enough sources for a standalone article but it can be covered there in a reduced fashion, imv Atlantic306 (talk) 22:27, 21 August 2020 (UTC)


text:
User:Kimsanders

Kimberley Sanders (born August 19, 1979) holds a Bachelor of Arts degree in English from Campbellsville University and a Master of Arts degree in Literature from the University of Louisville. She also holds minors in Political Science and History. She recently taught English 101 and English 102 as a graduate teaching assistant at the University of Louisville while completing her graduate studies. She is currently living in Louisville, Kentucky.

Areas of Interest
Works listed are ones I am on most familiar terms with. Listing every book I like would take forever.

 * British/Irish Literature
 * Jane Austen
 * Pride and Prejudice
 * Persuasion
 * Sense and Sensibility
 * William Shakespeare
 * Hamlet
 * Macbeth
 * King Lear
 * Much Ado About Nothing
 * J.R.R. Tolkien
 * The Silmarillion
 * The Lord of the Rings trilogy
 * Farmer Giles of Ham
 * Alfred Lord Tennyson
 * John Keats
 * Beowulf
 * Oscar Wilde
 * The Importance of Being Earnest
 * The Canterville Ghost
 * William Butler Yeats
 * Sir Arthur Conan Doyle
 * Sherlock Holmes series

 * European Literature
 * Rainer Maria Rilke
 * Letters to a Young Poet
 * Duino Elegies

 * American Literature
 * Edgar Allan Poe
 * Henry James

 * European History
 * Pictish Scotland
 * Celtic Britain
 * Arthurian (Romano-British) Britain
 * World War I
 * Edwardian Britain
 * Black Death
 * Georgian Britain
 * Plantagenet Britain
 * Crusade Era
 * Medieval Italy
 * Revolutionary France

title: User:Kimsanders


text:
Talk:Algebra/Function Graphing

When I first wrote this module, Function graphing, I had just two fundamental general linear equation forms, Ax + By = C and the slope-intercept form y = m x + b.  That, along with the formula for slope of a line, seemed sufficient to me to solve all linear equation problems. Later, I looked in several algebra books which also had the point-slope form and the intercept form of a line. I added these two extra forms to the Function graphing module for completeness and to meet educational standards, since all the algebra books I looked at had them. After further comparison and contemplation about the two additional line forms, it seems to me they are redundant and not really necessary, but I left them in there to meet any educational textbook standards that might call for them. Is anyone familiar with the educational standards on these items? I now think that these two extra line forms are a redundant and unnecessary complications which could boggle the student's mind (Ya think?!!! This is the chapter that has ultimately forced me to give up on algerbra!) more than they might help a math student accomplish anything useful. Maybe educational standards should be changed to delete the point-slope and intercept forms of a line in modern algebra courses to reduce the number of equations that have to be learned. H Padleckas 00:59, 23 Jul 2004 (UTC)

I'm finished with the theory in this module.[[Image:75%.png]]
This module has become quite long and I'm pretty much finished covering the graphing theory of linear functions. I've decided to end work on the theory in this module and continue in subsequent modules. I'm basically finished with this module except for problems or exercises. Graphing multiple systems of equations with multiple unknowns will continue in the next module, which I've just started. In the following three modules after that, math equation theory on quadratics and inequality theory have been written up in modules that are not really long, but the graphing of quadratics and inequalities has not yet been covered. Time and energy permitting, I may add some graphics on quadratics and inequalities to these modules. After that, I've just started another module, Algebra/Additional function and relation graphing, which will provide further examples of graphs, discuss other aspects of graphing, and cover circles and ellipses. In still further parts of the Algebra book, polynomials, exponential functions, and logarithms will be covered and graphs on those subjects can then be added to those modules.

Of course, if someone wants to work on this stuff, go ahead. I would like to know your plans so there's not a duplication of effort. You can use my graphs as "templates" to make your own or you can tell me what you want and I will try to make the graphs for you, my time and energy permitting. I have gained a bit of experience making these graphs now. H Padleckas 18:35, 24 Jul 2004 (UTC)

Slope vs. gradient
I'm assuming slope is the American term for the gradient of a straight line (the m in $$y=mx+c$$). I'm a Brit, and we refer to it as the gradient. Which is more widely used in mathematical circles, and would it make more sense to use gradient as it will be referred to once a student reaches a level where differentiation is becoming involved? I'm happy to be shot down, I just thought I'd bring this up. Odd bloke 15:20, 28 November 2005 (UTC)
 * Also, on a related note, I've always referred to the y-intercept constant as c, as opposed to b... Odd bloke 15:25, 28 November 2005 (UTC)

title: Talk:Algebra/Function Graphing


text:
Coluber constrictor flaviventris

Coluber constrictor flaviventris, commonly known as the eastern yellow-bellied racer, is a subspecies of the eastern racer, non-venomous  colubrid snake. It is endemic to North America.

Description
The eastern yellow-bellied racer is a thin-bodied snake, capable of attaining a total length of 1.5 metres (60 inches). As an adult, its color is an olive grey-green with a yellow underside. As a juvenile it is remarkably different, having a tan or cream-colored body with brown or grey blotches. The color gradually changes as the snake ages, becoming solid olive grey-green. Authors disagree as to when this transformation is complete, from 1½ to three years old, and from 18 to 30 inches (46–76 cm) in total length.

Geographic Range
The eastern yellow-bellied racer is found in the United States, from the states of Montana, North Dakota, South Dakota, east to Iowa, south to Texas and southeast to Louisiana. It is also found in isolated populations in Canada.

Conservation status
Coluber constrictor flaviventris is listed as an endangered species in the province of Saskatchewan.

Behavior
Racers are diurnal, active predators. They are fast moving and are often quick to bite if handled. They generally eat rodents, lizards and frogs, but as juveniles they will also consume various kinds of soft-bodied insects. They are fairly nervous snakes, and as such, do not typically fare well in captivity.

title: Coluber constrictor flaviventris


text:
Polyamine

A polyamine is an organic compound having more than two amino groups. Alkyl polyamines occur naturally, but some are synthetic. Alkylpolyamines are colorless, hygroscopic, and water soluble. Near neutral pH, they exist as the ammonium derivatives. Most aromatic polyamines are crystalline solids at room temperature.

Natural polyamines
Low-molecular-weight linear polyamines are found in all forms of life. The principal examples are the triamine spermidine and the tetraamine spermine. They are structurally and biosynthetically related to the diamines putrescine and cadaverine. Polyamine metabolism is regulated by the activity of the enzyme ornithine decarboxylase (ODC). Polyamines are found in high concentrations in the mammalian brain.

Synthetic polyamines
Ethyleneamines are a commercially-important class of synthetic polyamines with ethylene (\sCH2CH2\s linkages); global production capacity was estimated at 385,000 tonnes in 2001. They are chemical intermediates often used to make surfactants and as crosslinkers for epoxy resins. Some interesting members of this class include:
 * Ethylenediamine, first member of this series. It is a chelating ligand by itself, and it is a precursor to the popular metal sequestrant, EDTA (ethylenediaminetetraacetic acid). Permethylated, ethylenediamine yields tetramethylethylenediamine (TMEDA) that has a very high affinity for lithium ions.
 * Macrocyclic polyamines analogous to crown ethers: 1,4,7-triazacyclononane ((NHCH2CH2)3) and cyclen ((NHCH2CH2)4). A related tetraaza macrocycle is cyclam.
 * Tris(2-aminoethyl)amine (N(CH2CH2NH2)3) is a branched polyamine that is a minor side product of the polyethyleneamine process. A related tripodal polyamine is 1,1,1-tris(aminomethyl)ethane. These are interesting chelating ligands.
 * Polyethylenimine is a polymer derived from aziridine.

Other synthetic polyamines include 1,3,5-triazinane (not to be confused with 1,3,5-triazine) and N-substituted analogs. The methylene (\sCH2) linkages are derived from formaldehyde. The reaction product of monoethanolamine and formaldehyde is known industrially as "MEA triazine" (it is actually a triazinane), and it serves as a water-soluble hydrogen sulfide scavenger. Hexamethylenetetramine (hexamine) is another product of formaldehyde and ammonia that has various uses in industry. Domestically, it is used as a solid camping fuel. In the laboratory, it reacts with alkyl halides to selectively prepare primary amines in the Delépine reaction.

Biological function
Although it is known that the biosynthesis of polyamines is highly regulated, the biological function of polyamines is only partly understood. In their cationic ammonium form, they bind to DNA, and, in structure, they represent compounds with cations that are found at regularly spaced intervals (in contrast to or, which are point charges). They have also been found to act as promoters of programmed ribosomal frameshifting during translation.

Inhibition of polyamine biosynthesis retards or stops cell growth. The provision of exogenous polyamines restores the growth of these cells. Most eukaryotic cells express a polyamine-transporting ATPase on their cell membrane that facilitates the internalization of exogenous polyamines. This system is highly active in rapidly proliferating cells and is the target of some chemotherapeutics currently under development.

Polyamines are also modulators of a variety of ion channels, including NMDA receptors and AMPA receptors. They block inward-rectifier potassium channels so that the currents of the channels are inwardly rectified, thereby the cellular energy, i.e. ion gradient across the cell membrane, is conserved. In addition, polyamine participate in initiating the expression of SOS response of Colicin E7 operon and down-regulate proteins that are essential for colicin E7 uptake, thus conferring a survival advantage on colicin-producing E. coli under stress conditions.

Polyamines can enhance the permeability of the blood–brain barrier.

They are involved in modulating senescence of organs in plants and are therefore considered as a plant hormone. In addition, they are directly involved in regulation of programmed cell death.

Homology-directed DNA repair
Polyamines promote homologous recombination (HR)-mediated double-strand break (DSB) repair. Polyamines enhance the DNA strand exchange activity of RAD51 recombinase. Depletion of polyamines sensitizes cells to genotoxic substances such as ionizing radiation and ultraviolet radiation. The effect of polyamines on RAD51 arises from their ability to enhance the capture of homologous duplex DNA and promote RAD-51-mediated homologous DNA pairing and exchange activity. Polyamines appear to have an evolutionarily conserved role in regulating recombinase activity.

Biosynthesis of spermidine, spermine, thermospermine
Spermidine is synthesized from putrescine, using an aminopropyl group from decarboxylated S-adenosyl-L-methionine (SAM), S-Adenosylmethioninamine. The reaction is catalyzed by spermidine synthase.

Spermine is synthesized from the reaction of spermidine with SAM in the presence of the enzyme spermine synthase.

The polyamines undergo rapid interconversion in the polyamine cycle, in which putrescine leads to synthesis of spermidine and spermine, with degradation of these polyamines to form putrescine, which can begin the cycle again.

Thermospermine (NH2\s(CH2)3\sNH\s(CH2)3\sNH\s(CH2)4\sNH2) is a structural isomer of spermine and a novel type of plant growth regulator. It is produced from spermidine by the action of thermospermine synthase, which is encoded by a gene named ACAULIS5 (ACL5).

Polyamine analogues
The critical role of polyamines in cell growth has led to the development of a number of agents that interfere with polyamine metabolism. These agents are used in cancer therapy. Polyamine analogues upregulate p53 in a cell leading to restriction of proliferation and apoptosis. It also decreases the expression of estrogen receptor alpha in ER-positive breast cancer.

title: Polyamine


text:
User:Duffman~enwikiversity

Duffman is mostly active on the Norwegian Wikipedia.

 * /Sandbox
 * /monobook.css
 * Special:Prefixindex/User:Duffman

title: User:Duffman~enwikiversity


text:
Achyut Charan Choudhury

Achyut Charan Choudhury (অচ্যুৎচরণ চৌধুরী; 5 February 1866 – 25 September 1953) was a Bengali writer and historian. Though he wrote several books regarding Vaishnav Hinduism, Choudhury is most well known for his monumental work on the history of the Sylhet region, the Srihatter Itibritta.

Life
Born in the village of Moina in Karimganj (then part of the District of Sylhet), he was the son of Aditya Charan Choudhury and his wife Kotimoni. Through his father, Choudhury was a descendant of the Zamindars of Jafargarh.

As a child, while he received some primary education, Choudhury also taught himself history and religion, with a special focus on literature and Vaishnav theory. The latter proved of particular importance in adulthood when he converted to the faith, performing pilgrimages to holy sites in places such as Puri, Vrindavan and Dhakadakkhin. In the last of these, he established a temple out of his own expenses.

In 1897, he began his career as a teacher in Girish Middle English School in Sylhet, before later being appointed treasurer of the landed estate in Patharkandi. In 1897, Choudhury establish a monthly newspaper called Srihatter Durpun, though this ceased publication after only two years.

A decade later, he began his magnum opus, an extensive work on the history of Sylhet, termed the Srihatter Itibritta. The text was published in two volumes. The first, released in 1910, focused its early chapters on the geography of Sylhet before chronicling the development of the region. This continued on in the second volume, published six years later, which also included the genealogies of prominent Sylheti families, as well as over a hundred short biographies of notable personages. The work was widely praised at the time of its release, with the contemporary historian Jadunath Sarkar applauding its "ideal technique" in chronicling regional history. The Srihatter Itibritta remains a lauded and popular work to the present-day.

Choudhury maintained an extensive personal library composed of three thousand books and manuscripts regarding history and religion. He also wrote a series of books on Vaishnav theology, with his devotion to the faith leading him to be regarded by local people as a guru. He died on 25 September 1953, aged eighty-seven.

title: Achyut Charan Choudhury


text:
Ancient Greek philosophy

Welcome to the Ancient Greek Philosophy learning project, part of the School of Philosophy.

Description
I will illustrate my meaning, Theodorus, by the jest which the clever witty Thracian handmaid is said to have made about Thales, when he fell into a well as he was looking up at the stars. She said, that he was so eager to know what was going on in heaven, that he could not see what was before his feet. This is a jest which is equally applicable to all philosophers. For the philosopher is wholly unacquainted with his next-door neighbour; he is ignorant, not only of what he is doing, but he hardly knows whether he is a man or an animal; he is searching into the essence of man, and busy in enquiring what belongs to such a nature to do or suffer different from any other. (Plato: Theatetus, 174 A, translated by Benjamin Jowett)

Philosophy may be seen as one of the products of a vital human impulse that has probably given rise to religion and science as well. From as far back as history can take us, we have strived for ultimate truths about life and existence.

Philosophy is usually described vaguely as the study of fundamental questions. Therefore, other great general fields of inquiry, like Science ("How did that happen? Can we change it?") and Theology ("What is God like? How can we change His mind?") can be seen as offshoots of the same source.

In Western culture (Occidental, as opposed to Oriental) we generally study the history of Western philosophy, which we trace back to the Greeks, who first used the word philosophy, and who first began to organize such an inquiry in a systematic way in our culture. One of the problems with this method is that it tends to minimize the effects of other ancient civilizations on Western thought, which was greatly influenced by the cultures in Egypt and Mesopotamia. It also walls off an entire parallel development of Eastern philosophy which, though dealing with similar questions, made use of profoundly different methods. Ironically, the civilizations of Egypt and Mesopotamia can probably be considered closer to Eastern than to Western thought.

But we have to start somewhere, and that will be the traditional approach. The reader can find an overview of Eastern thought in the Eastern Philosophy course.

Resources

 * The origins of philosophy
 * The Presocratic philosophers
 * Socrates, Plato and Aristotle

title: Ancient Greek philosophy


text:
Mel O'Callaghan

Mel O'Callaghan (born 1975) is an Australian-born contemporary artist who works in video, performance, sculpture, installation, and painting. Her work has been exhibited in solo and group exhibitions around the world and received a number of awards for her artistic practice, and her work is held in a various collections in Australia and France.

Early life and education
O'Callaghan was born in Sydney, Australia in 1975. She attained a Bachelor of Visual Arts with Honours from the Sydney College of Arts, University of Sydney, and a Masters of Fine Arts in Research from the College of Fine Arts (COFA), University of New South Wales, and a Bachelor of Science Architecture from the University of Sydney.

Practice
She is interested in human behaviour, psychology, and transformative states. Her work is experiential and looks at the human condition and ritual.

O'Callaghan lives and works in Paris, France and Sydney, Australia. She and her husband, Clemens Habicht, founded the Parisian art gallery Galerie Allen in 2013.

Exhibitions
O'Callaghan has been in solo and group exhibitions around the world and received a number of awards for her artistic practice.

Centre of the Centre
Centre of the Centre was O'Callaghan's first large scale exhibition in an Australian public institution. Combining a large-scale video, sculptural installations, and regular performances, the show explored the origins of life and regeneration

The video was a result of multiple cross-disciplinary collaborations, including one with Daniel Fornari from the Woods Hole Oceanographic Institution in Massachusetts. It is 20 minutes long, was projected 7 metres wide, and includes underwater shots of thermal vents in the Pacific Ocean as well as the coco worm. The performances involved breath-induced trances and took place around the exhibition's glass and metal sculptures.

Centre of the Centre was commissioned by Le Confort Moderne, Poitiers; Artspace, Sydney; and UQ Art Museum, Brisbane. It premiered at the former in June 2019 and will be on show at the latter until January 2021, after which it will tour various other Australian venues.

Major solo exhibitions
O'Callaghan has had solo exhibitions in many parts of the world, including Australia, France, The Netherlands, Portugal, Spain, and the USA.

 * 2019: Centre of the Centre, Artspace, Sydney, Australia
 * 2018: Primary/Secondary Score, Barangaroo et Carriageworks, Sydney, Australia
 * 2017: Mel O'Callaghan: Ensemble, National Gallery of Victoria (NGV) Melbourne, Australia, Kronenberg Wright, Sydney, Australia
 * 2017: Dangerous on-the-way, Palais de Tokyo, Paris, France
 * 2004: The Fall, Salles E.M. Sandoz M. David Weill, Cité internationale des arts, Paris, France
 * 2003: In the Half Light, 4A Centre for Contemporary Asian Art, Sydney, Australia
 * 2002: The Fly and the Mountain, Art Gallery of New South Wales (AGNSW), Sydney, Australia

Major group exhibitions
O'Callaghan has been involved in group exhibitions in Australia, Brazil, France, Germany, Italy, the Netherlands, Norway, the Philippines, Portugal, Singapore, Spain, Taiwan, and the UK.

 * 2019: Yo-Chang Art Museum, National Taiwan University of Arts
 * 2018: 200 Videos, Museo D'Art Contemporanea di Roma, Italy
 * 2018: International Film Festival Rotterdam, The Netherlands
 * 2016: L'art de la re'volte (The Art of Revolt), Hors-Pistes, Centre Pompidou, Malaga, Spain
 * 2015: Nature/Revelation, The Ian Potter Museum, National Gallery of Victoria (NGV), Melbourne, Australia
 * 2014: 19th Biennale of Sydney, You Imagine What You Desire, Sydney, Australia
 * 2010: Dying in Spite of the Miraculous, Gurtrude Contemporary art Space and Melbourne International Arts Festival, Melbourne, Australia
 * 2010: La Main Numerique, National Taiwan Museum of Fine Arts, Taipei, Taiwan
 * 2006: Videoformes, Prix de la Creation Video, Clermont Ferrand, France
 * 2005: National Sculpture Prize, National Gallery of Australia (NGA), Canberra, Australia
 * 2005 Videobrasil 05 15º, Internacional Video Art Biennale, São Paulo, Brazil
 * 2003: Printroom, Gertrude Centre for Contemporary Art, Melbourne, Australia
 * 2001: Helen Lempriere Travelling Art Award, Artspace, Sydney, Australia

Major grants, awards, residencies

 * 2019: Aide de Projet, Fondation National des Arts Graphiques et Plastiques (FNAGP)
 * 2017: Finalist, Prix Meurice pour l'art contemporain, France
 * 2017: Fondation National des Arts Graphiques et Plastiques (FNAGP), Artist Studio, Nogent-sur-Marne, France
 * 2017: Cité internationale des arts, Artist Residency, Paris, France
 * 2016: Cité internationale des arts, Artist Residency, Paris, France
 * 2015: Recipient, Prix SAM pour l'Art Contemporain, France
 * 2014: Nominated for the Bernd Lohaus Prize, Belgium
 * 2014: Finalist, Kaldor Public Arts Projects, Sydney, Australia
 * 2011: Cité Internationale des Arts, Artist Residency, Paris, France
 * 2007: Cité Internationale des Arts, Artist Residency, Paris, France
 * 2005: Cité Internationale des Arts, Artist Residency, Paris, France
 * 2005: National Sculpture Prize, Finalist, National Gallery of Australia (NGA), Australia
 * 2005: Australian Film Commission, Australia
 * 2004: Cité International des Arts, Artist Residency, Paris, France
 * 2001: Centre for Contemporary Art, Artist Residency, Prague, Czech Republic
 * 2001: Finalist, Helen Lempriere Travelling Art Award

Collections
O'Callaghan's work is held in a various collections in Australia and France.
 * Ensemble (2013) at the National Gallery of Victoria, Melbourne, Australia
 * Framework (2014) at FRAC Bretagne, Rennes, France
 * Monash University Museum of Modern Art (MUMA), Australia
 * Artbank, Australian Government Art Collection, Australia
 * Attorney General's Department, Australian Government
 * Musee National d'Art Moderne/Centre Pompidou, Paris, France

title: Mel O'Callaghan


text:
Talk:Data Networking/Fall 2016/Sanket Jabade

 * Start a Wikiversity Project - a more comprehensive approach for larger projects (may not be appropriate here). Ktucker 00:30, 21 January 2009 (UTC)


text:
Talk:Dennys Reyes

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title: Talk:Dennys Reyes


text:
Follow Me Home (song)

"Follow Me Home" is a song by British girl group the Sugababes, released as the fourth single from their fourth studio album, Taller in More Ways (2005). The pop and R&B ballad was written by band members Keisha Buchanan, Mutya Buena and Heidi Range, with Jony Rockstar, Karen Poole and Jeremy Shaw. The producer, Rockstar, developed the idea of a close person as its inspiration. Buena wrote a verse about her daughter, while Buchanan wrote a verse based on her close friend. The song was released as the album's fourth single on 5 June 2006 and contains vocals from Amelle Berrabah in replacement of Buena's, who left the band in December 2005.

"Follow Me Home" received mixed reviews from critics. Although its instrumentation and the group's vocals were praised, the song was criticised as tedious and uninspiring. The single reached the top forty in Ireland and the United Kingdom, and also charted in Romania, Slovakia, and on the European Hot 100 singles chart. The music video for "Follow Me Home" was directed by Tony Tremlett and filmed in Prague, the Czech Republic. It features the Sugababes in a winter environment and contains various scenes of the group in a large house. The Sugababes performed "Follow Me Home" at the O2 ABC Glasgow, the NIA Academy and on Top of the Pops.

Development and composition
"Follow Me Home" was written by the Sugababes—Keisha Buchanan, Mutya Buena, and Heidi Range—in collaboration with Jonathan Lipsey, Karen Poole, and Jeremy Shaw, for the group's fourth studio album, Taller in More Ways (2005). Lipsey developed the idea of a close person as the song's inspiration. Buena wrote the first verse based upon her daughter Tahlia, who was born in March 2005. While writing the verse, she pondered questions such as 'What would you say to her if she was ever in trouble?', and 'How would you say, I'll always be there for you?'. Buena wanted people to interpret the verse in different ways, and stated that the lyrics came naturally. Buchanan drew inspiration from her close friend when she wrote the other verse. Lipsey produced the song under his production name Jony Rockstar. "Follow Me Home" was mixed and engineered at Metropolis Studios by Tom Elmhirst and Richard Wilkinson, respectively.

"Follow Me Home" is an electropop and R&B ballad. Stuart Heritage of the website HecklerSpray described it as an "R&B-tinged ballad". Instrumentation consists of keyboards, a guitar, beats and bass, which were provided by Shaw, Rockstar and Cameron McVey. According to Alex Roginski of Sydney Morning Herald, the song is "fleshed out with the string grandeur" of Welsh producers Hybrid, and channels European electropop music. The main concept of "Follow Me Home" is romance, and the song's lyrical content is about protecting your loved one. During the chorus, the Sugababes sing: "I won't walk away / I'll stand by your side / I'm here for you / For the rest of our lives".

Release and reception
In December 2005, Buena left the Sugababes due to "personal reasons", and was replaced by Amelle Berrabah in the same month. Some tracks on Taller in More Ways were subsequently re-recorded to feature Berrabah's vocals in replacement of Buena's; these included "Gotta Be You", "Follow Me Home" and "Red Dress". Buena expressed her disappointment with the re-recording of "Follow Me Home", saying: "My verse was talking about my daughter, it was personal." The song was announced as the fourth and final single from Taller in More Ways, and was released as a CD single and digital download on 5 June 2006. The CD single contains the radio edit of the song in addition to two remixes. The digital release features a cover of English band Hard-Fi's single "Living for the Weekend".

Critical response
"Follow Me Home" received mixed reviews from critics. K. Ross Hoffman of AllMusic described it as an "aptly pitched inspirational mini-epic", while Stylus Magazine's Nick Southall complimented the song's "luscious, romantic strings." Talia Kraines of BBC noted the song as having a near-level standard of the group's 2003 single, "Too Lost in You". QX gave the song seven out of ten stars, writing: "With this film themed track they’re staying true to their roots and retain their position as leaders amidst the all-girl band rankings". Stuart Heritage of Hecklerspray wrote that the song "benefits from some lovely strings and gorgeous, sultry vocals", although admitted that the single is not as exciting as the album's previous ones. Daily Record's Rick Fulton described the song as one of the group's more thoughtful tracks, but admitted that it lacks "bite". He applauded the Soul Seekerz Vocal Mix version as "breathing life" into it. Alexis Petridis of The Guardian criticised the song as tedious and stated that it "is every bit as gripping as new parents foisting their baby photos on you". Linda McGee of RTÉ.ie considered it "nothing special".

Commercial performance
"Follow Me Home" debuted and peaked at number 32 on the UK Singles Chart in the issue dated 17 June 2006. The following week, the song dropped ten places to number 42, and in its third and last week on the chart, it fell to number 72. It is the group's lowest-charting single in the UK, and one of their lowest-selling singles. The song achieved more success on the Irish Singles Chart, where it peaked at number 25 and spent four weeks on the chart. The song debuted at number 88 on the Romanian Top 100 singles chart, and peaked at number 64 the following week. "Follow Me Home" achieved minor success on the Slovakian Singles Chart, where it peaked at number 93. The single's performance throughout Europe allowed it to chart on the European Hot 100 singles chart, peaking at number 91.

Music video
The music video for "Follow Me Home" was directed by Toby Tremlett, who collaborated with the group on the video for their single "Ugly". Filming of the video took place in Prague, the Czech Republic, and most scenes were filmed in a large house. It is set in winter time and features the Sugababes wearing winter clothing such as thick coats and scarves. The video was released onto the iTunes Store on 23 May 2006 and is featured on the song's CD release. The video opens with a scene of an alcohol bottle and a glass next to it. It then cuts to a scene of Berrabah on a couch, while follow-up scenes show Buchanan against a wall and Range on a bed.

An elderly man is shown by a pool located in the house, while a young girl in a swimsuit is on the other side of it. Another elderly man enters a room in the house where there is another girl. Throughout the video, various scenes of older men and younger women appear. Towards the end of the video, Berrabah, Buchanan and Range are shown standing outside in the dark. A car stops next to the trio and they enter it. In the last scene, an elderly man watches by as the car drives off. Avril Cadden from the Sunday Mail praised the video as "great". Former group member Buena expressed her dissatisfaction with it, saying: "I just saw a bunch of perverted men and paedophile guys". The video reached number eight on the UK TV airplay chart.

Live performances
The Sugababes performed "Follow Me Home" in October 2005 at the O2 ABC Glasgow, where they played to a crowd of 300 competition winners to promote the release of Taller in More Ways. The song was included in the set list for the group's Taller in More Ways tour. Gurdip Thandi from the Birmingham Mail described their performance at Birmingham's NIA Academy as "polished". In June 2006, following its release as a single, the group performed "Follow Me Home" on Top of the Pops.

Track listings and formats

 * CD1 single
 * 1) "Follow Me Home" (Radio Edit) – 3.23
 * 2) "Red Dress" (Kardinal Beats Remix) – 3.48
 * 3) "Follow Me Home" (Soul Seekerz Vocal Mix) – 6.53
 * 4) "Follow Me Home" (Video) – 3.23

 * CD2 single / digital download
 * 1) "Follow Me Home" (Amelle Mix) – 3:59
 * 2) "Living for the Weekend" (Live Radio 1 Session) – 3:12

Credits and personnel
Credits are adapted from the liner notes of Taller in More Ways.

Recording
 * Recorded and mixed at Metropolis Studios, London

Personnel
 * Songwriting – Keisha Buchanan, Mutya Buena, Heidi Range, Jonathan Lipsey, Karen Poole, Jeremy Shaw
 * Production – Jony Rockstar
 * Mixing – Tom Elmhirst
 * Engineering – Richard Wilkinson
 * Keyboards and guitar – Jeremy Shaw
 * Beats – Jony Rockstar
 * Bass – Cameron McVey

title: Follow Me Home (song)


text:
List of The Millionaire's Wife episodes

The Millionaire's Wife is a 2016 Philippine television drama romance series broadcast by GMA Network. It premiered on the network's Afternoon Prime line up from March 14, 2016 to June 24, 2016, replacing Destiny Rose.

Mega Manila ratings are provided by AGB Nielsen Philippines.

June 2016

 * Episodes notes

title: List of The Millionaire's Wife episodes


text:
List of cities in the Americas by population

The following is a list of the 100 largest cities in the Americas by city proper population using the most recent official estimate.

List
Italics represents capital city

Bold represents largest city in country


text:
King Juan Carlos University

Rey Juan Carlos University (Universidad Rey Juan Carlos, URJC) is a Spanish public research university located in the southern area of the Community of Madrid (Spain), with five campuses at Móstoles, Alcorcón, Vicálvaro, Aranjuez and Fuenlabrada.

It is named after former king Juan Carlos I of Spain and has the Latin motto Non nova, sed nove ("Not new things, but in a new way"). It was established in 1996 by the government of the Community of Madrid.

With 44.916 students, it is the second-biggest public university in the Community of Madrid, behind the historical Universidad Complutense. URJC is one of eight universities in the Community of Madrid, and it is the second-newest university in the autonomous community.

Studies
King Juan Carlos University offers a range of degrees, all adapted to the European Higher Education Area. This includes 64 undergraduate degrees, 44 dual degrees, 6 English-medium degrees, 6 university degrees on-line, 18 diplomas, and 8 engineering degrees, as well as a wide range of official master's (81) and doctoral programs involving both degrees and training (34) in health sciences, experimental sciences and technology, communication sciences, and law and social sciences. King Juan Carlos University has five campuses in Madrid, Fuenlabrada, Móstoles, Aranjuez and Vicálvaro, as well as a foundation whose headquarters are on Madrid's Plaza de Manuel Becerra.

Campus
The URJC is divided into four campuses. Each campus is composed of one or more schools:

 * Móstoles Campus is, since 1998, the headquarters of the School of Experimental Sciences and Technology (ESCET) and since 2007 the School of Computer Engineering (ETSII). It also houses the University Senate and the office of the President (Rector).
 * Alcorcón Campus houses the Faculty of Health Sciences since 1997 and the University Hospital URJC.
 * Vicálvaro Campus (Madrid) is the seat of the Faculty of Juridical and Social Sciences (FCJS) since 1998.
 * Fuenlabrada Campus houses since 2000, the Faculty of Communication Sciences and School of Tourism, which since November 2009 was renamed the Faculty of Tourism, and since 2005 the School of Telecommunications Engineering (ETSIT), renamed in 2023 as Fuenlabrada School of Engineering (EIF).

Each school or college is governed by a Dean or School Director, and is divided into academic departments.

Affiliated centres:
 * Institute of Commercial Management and Marketing in Somosaguas (Madrid).
 * ESERP School (Madrid).

Colleges:
 * Higher Institute of Dance Alicia Alonso (Fuenlabrada).
 * Institute of Humanities (Vicálvaro).
 * Institute of International Legal Studies (Vicálvaro).

University Centres:
 * University Language Centre (Vicálvaro), which regularly gives courses in English, French, German, Italian, Chinese and Spanish for foreigners.
 * Emile Noël Research and Documentation Centre of the European Union (Vicálvaro).
 * Volunteering and Cooperation Centre (Alcorcón).
 * University Centre for Applied Social Studies (Vicálvaro).
 * Economics Study Centre in Madrid (Vicálvaro).
 * Centre for Latin American Studies (Móstoles).
 * Centre for the Study of the Olympic Movement (Vicálvaro).
 * Centre for Intelligent Information Technologies and Applications (CETINIA).
 * Business Incubator (Vicálvaro).
 * Legal Office (Vicálvaro).
 * Technology Support Centre (Móstoles).
 * Centre for Innovation, Technology Transfer and Knowledge (Móstoles).
 * Laboratory Network URJC (REDLABU).
 * Centre of Research and Teaching, located in the so-called Nuncio's Palace in Aranjuez.

King Juan Carlos University organizes its summer courses in Aranjuez.

Academic programs
Studies include computer science, telecommunications engineering, chemical engineering, environmental science, odontology, medicine, nursing, physiotherapy, audiovisual communication, telecommunications, tourism, journalism, law, economics, applied economics including Austrian economics, business administration and management, sociology, history, accounting and finance, marketing, food science and technology, biology, psychology, preschool education, international relations, visual arts and dance, and criminology, among others.

Honorary doctorates
In 2007 Juan Velarde Fuertes, Iñaki Gabilondo, Luis del Olmo and Antonio Mingote were awarded honorary doctorates from King Juan Carlos University. In January 2008, Bernardo Kliksberg became the first foreigner to receive an honorary doctorate degree from the university along with Jaime Gil Aluja, José Antonio Pastor Ridruejo and Fernando Sánchez Calero. In 2011, honorary doctorates were awarded to Harald zur Hausen, Ramón Tamames and Peter Waldmann.

In 2014 James A. Yorke, distinguished University Professor of Mathematics and Physics at the University of Maryland and recipient of the 2003 Japan Prize in Science and Technology, was awarded an honorary doctorate from King Juan Carlos University. Prof. Yorke is known worldwide for the definition of the mathematical term "chaos" in 1975. Rodrigo Rato, former Managing Director of the IMF and Spanish Deputy Prime Minister, previously held an honorary doctorate from King Juan Carlos University, which was not immediately canceled when he was later sentenced to 4½ years' imprisonment for bank fraud in his role as chairman of bank Bankia.

title: King Juan Carlos University


text:
vedersi

Verb

 * 1)  to see or look at oneself
 * 2)  to see or look at each other
 * 3)  to think oneself a certain quality; to see oneself as
 * 4) to see
 * 5)  to watch
 * 6)  to see to meet, visit
 * 7)  to see to date frequently
 * 1)  to watch
 * 2)  to see to meet, visit
 * 3)  to see to date frequently
 * 1)  to see to meet, visit
 * 2)  to see to date frequently
 * 1)  to see to date frequently
 * 1)  to see to date frequently

title: vedersi


text:
aduno

Etymology
From. Compare the similarly formed.

Verb

 * 1) to unite, make one

Etymology
From 🇰🇲.

Verb

 * 1) to reunite, to rejoin

title: aduno


text:
High School Mathematics Extensions/Logic

Introduction
Logic is the study of the way we reason. In this chapter, we focus on the methods of logical reasoning, i.e. digital logic, predicate calculus, application to proofs and the (insanely) fun logical puzzles.

Boolean algebra
In the black and white world of ideals, there is absolute truth. That is to say everything is either true or false. With this philosophical backdrop, we consider the following examples:
 * "One plus one equals two." True or false?

That is (without a doubt) true!

 * "1 + 1 = 2 AND 2 + 2 = 4." True or false?

That is also true.

But what about:
 * "1 + 1 = 3 OR Sydney is in Australia" True or false?

It is true! Although 1 + 1 = 3 is not true, the OR in the statement made the whole statement to be true if at least one of the statements is true.

Now let's consider a more puzzling example
 * "2 + 2 = 4 OR 1 + 1 = 3 AND 1 - 3 = -1" True or false?

The truth or falsity of the statements depends on the order in which you evaluate the statement. If you evaluate "2 + 2 = 4 OR 1 + 1 = 3" first, the statement is false, and otherwise true. As in ordinary algebra, it is necessary that we define some rules to govern the order of evaluation, so we don't have to deal with ambiguity.

Before we decide which order to evaluate the statements in, we do what most mathematician love to do -- replace sentences with symbols. Let x represent the truth or falsity of the statement 2 + 2 = 4. Let y represent the truth or falsity of the statement 1 + 1 = 3. Let z represent the truth or falsity of the statement 1 - 3 = -1.

Then the above example can be rewritten in a more compact way:
 * x OR y AND z

To go one step further, mathematicians also replace OR by + and AND by ×, the statement becomes:
 * $$x + y \times z$$

Now that the order of precedence is clear. We evaluate (y AND z) first and then OR it with x. The statement "x + yz" is true, or symbolically
 * $$x+yz=1$$

where the number 1 represents "true".

There is a good reason why we choose the multiplicative sign for the AND operation. As we shall see later, we can draw some parallels between the AND operation and multiplication.

The Boolean algebra we are about to investigate is named after the British mathematician George Boole. Boolean algebra is about two things -- "true" or "false" which are often represented by the numbers 1 and 0 respectively. Alternative, T and F are also used.

Boolean algebra has operations (AND and OR) analogous to the ordinary algebra that we know and love.

Basic Truth tables
We have all had to memorize the 9 by 9 multiplication table and now we know it all by heart. In Boolean algebra, the idea of a truth table is somewhat similar.

Let's consider the AND operation which is analogous to the multiplication. We want to consider:
 * x AND y

where and x and y each represent a true or false statement (e.g. It is raining today). It is true if and only if both x and y are true, in table form:

We shall use 1 instead of T and 0 instead of F from now on.

Now you should be able to see why we say AND is analogous to multiplication, we shall replace the AND by ×, so x AND y becomes x×y (or just xy). From the AND truth table, we have:
 * 0 × 0 = 0
 * 0 × 1 = 0
 * 1 × 0 = 0
 * 1 × 1 = 1

To the OR operation.  x OR y  is FALSE if and only if both x and y are false. In table form:

We say OR is almost analogous to addition. We shall illustrate this by replacing OR with +:
 * 0 + 0 = 0
 * 0 + 1 = 1
 * 1 + 0 = 1
 * 1 + 1 = 1 (like 1 OR 1 is 1)

The NOT operation is not a binary operation like AND and OR, but a unary operation, meaning it works with one argument. NOT x  is true if x is false and false if x is true. In table form:

In symbolic form, NOT x is denoted x' or ~x (or by a bar over the top of x).

Alternative notations:
 * $$x \times y = x \wedge y$$

and
 * $$x + y = x \vee y$$

Compound truth tables
The three truth tables presented above are the most basic of truth tables and they serve as the building blocks for more complex ones. Suppose we want to construct a truth table for xy + z (i.e. x AND y OR z). Notice this table involves three variables (x, y and z), so we would expect it to be bigger than the previous ones.

To construct a truth table, firstly we write down all the possible combinations of the three variables:

There is a pattern to the way the combinations are written down. We always start with 000 and end with 111. As to the middle part, it is up to the reader to figure out.

We then complete the table by hand computing what value each combination is going to produce using the expression xy + z. For example:
 * 000
 * x = 0, y = 0 and z = 0
 * xy + z = 0

 * 001
 * x = 0, y = 0 and z = 1
 * xy + z = 1

We continue in this way until we fill up the whole table

The procedure we follow to produce truth tables are now clear. Here are a few more examples of truth tables.

Example 1 -- x + y + z

 Example 2 -- (x + yz)'

When an expression is hard to compute, we can first compute intermediate results and then the final result.

 Example 3 -- (x + yz')w

Exercise
Produce the truth tables for the following operations:
 * 1) NAND: x NAND y = NOT (x AND y)
 * 2) NOR: x NOR y = NOT (x OR y)
 * 3) XOR: x XOR y is true if and ONLY if one of x or y is true.

Produce truth tables for:
 * 1) xyz
 * 2) x'y'z'
 * 3) xyz + xy'z
 * xz
 * 1) (x + y)'
 * 2) x'y'
 * 3) (xy)'
 * 4) x' + y'

Laws of Boolean algebra
In ordinary algebra, two expressions may be equivalent to each other, e.g. xz + yz = (x + y)z. The same can be said of Boolean algebra. Let's construct truth tables for:
 * xz + yz
 * (x + y)z

xz + yz

(x + y)z

By comparing the two tables, you will have noticed that the outputs (i.e. the last column) of the two tables are the same!

Definition
 * We say two Boolean expressions are equivalent if the output of their truth tables are the same.

We list a few expressions that are equivalent to each other
 * x + 0 = x
 * x × 1 = x
 * xz + yz = (x + y)z
 * x + x' = 1
 * x × x' = 0
 * x × x = x
 * x + yz = (x + y)(x + z)

Take a few moments to think about why each of those laws might be true.

The last law is not obvious but we can prove that it's true using the other laws:

\begin{matrix} (x + y)(x + z) &=& x(x + z) + y(x + z)\\ &=& xx + xz + xy + yz\\ &=& x + xz + xy + yz\\ &=& x(1 + z + y) + yz\\ &=& x + yz \end{matrix} $$

It has been said: "the only thing to remember in mathematics is that there is nothing to remember. Remember that!". You should not try to commit to memory the laws as they are stated, because some of them are so deadly obvious once you are familiar with the AND, OR and NOT operations. You should only try to remember those things that are most basic, once a high level of familiarity is developed, you will agree there really isn't anything to remember.

Simplification
Once we have those laws, we will want to simplify Boolean expressions just like we do in ordinary algebra. We can all simplify the following example with ease:

\begin{matrix} xyzw' + xyzw &=& xyz(w + w')\\ &=& xyz \end{matrix} $$

the same can be said about:

\begin{matrix} (x + y)(x' + y') &=& x(x' + y') + y(x' + y')\\ &=& xx' + xy' + yx' + yy'\\ &=& 0 + xy' + yx' + 0\\ &=& xy' + yx' \end{matrix} $$

From those two examples we can see that complex-looking expressions can be reduced very significantly. Of particular interest are expressions of the form of a sum-of-product, for example:
 * xyz + xyz' + xy'z + x'yz + x'y'z' + x'y'z

We can factorise and simplify the expression as follows

xyz + xyz' + xy'z + x'yz + x'y'z' + x'y'z $$

=\ xy(z + z') + xy'z + x'yz + x'y'(z' + z) $$

=\  xy + xy'z + x'yz + x'y' $$

=\ x(y + y'z) + x'(yz + y') $$

It is only hard to go any further, although we can. We use the identity:
 * x + yz = (x + y)(x + z)

If the next step is unclear, try constructing truth tables as an aid to understanding.

\begin{matrix} &=&\ x(y + z) + x'(z + y')\\ &=&\ xy + xz + x'z + x'y'\\ &=&\ xy + (x + x')z + x'y'\\ &=&\ xy + z + x'y'\\ \end{matrix} $$

And this is as far as we can go using the algebraic approach (or any other approach). The algebraic approach to simplification relies on the principle of elimination. Consider, in ordinary algebra:
 * x + y - x

We simplify by rearranging the expression as follows
 * (x - x) + y = y

Although we only go through the process in our head, the idea is clear: we bring together terms that cancel themselves out and so the expression is simplified.

De Morgan's theorems
So far we have only dealt with expressions in the form of a sum of products e.g. xyz + x'z + y'z'. De Morgan's theorems help us to deal with another type of Boolean expressions. We revisit the AND and OR truth tables:

{

You would be correct to suspect that the two operations are connected somehow due to the similarities between the two tables. In fact, if you invert the AND operation, i.e. you perform the NOT operations on x AND y. The outputs of the two operations are almost the same: {

The connection between AND, OR and NOT is revealed by reversing the output of x + y by replacing it with x' + y'. {

Now the two outputs match and so we can equate them:
 * (xy)' = x' + y'

this is one of de Morgan's laws. The other which can be derived using a similar process is:
 * (x + y)' = x'y'

We can apply those two laws to simplify equations:

Example 1 Express x in sum of product form

\begin{matrix} x &=& (ab' + c)'\\ &=& (ab')'c'\\ &=& (a' + b)c'\\ &=& a'c' + bc' \end{matrix} $$

Example 2 Express x in sum of product form

\begin{matrix} x &=& (a + b + c)'\\ &=& (a + b)'c'\\ &=& a'b'c'\\ \end{matrix} $$This points to a possible extension of De Morgan's laws to 3 or more variables.

Example 3 Express x in sum of product form

\begin{matrix} x &=& [(a' + c)\cdot (b + d')]'\\ &=& (a' + c)' + (b + d')'\\ &=& ac' + b'd\\ \end{matrix} $$

Example 4 Express x in sum of product form

\begin{matrix} x &=& [(a + bc)\cdot (d + ef)]'\\ &=& (a + bc)' + (d + ef)'\\ &=& a'(bc)' + d'(ef)'\\ &=& a'(b' + c') + d'(e' + f')\\ &=& a'b' + a'c' + d'e' + d'f'\\ \end{matrix} $$

Another thing of interest we learnt is that we can reverse the truth table of any expression by replacing each of its variables by their opposites, i.e. replace x by x' and y' by y etc. This result shouldn't have been a surprise at all, try a few examples yourself.

De Morgan's laws
 * $$(x + y)' = x'y'$$
 * $$(xy)' = x' + y'$$

Exercise

 * 1) Express in simplified sum-of-product form:
 * 2) z = ab'c' + ab'c + abc
 * 3) z = ab(c + d)
 * 4) z = (a + b)(c + d + f)
 * 5) z = a'c(a'bd)' + a'bc'd' + ab'c
 * 6) z = (a' + b)(a + b + d)d'
 * 7) Show that x + yz is equivalent to (x + y)(x + z)

Propositions
We have been dealing with propositions since the start of this chapter, although we are not told they are propositions. A proposition is simply a statement (or sentence) that is either TRUE or FALSE. Hence, we can use Boolean algebra to handle propositions.

There are two special types of propositions -- tautology and contradiction. A tautology is a proposition that is always TRUE, e.g. "1 + 1 = 2". A contradiction is the opposite of a tautology, it is a proposition that is always FALSE, e.g. 1 + 1 = 3. As usual, we use 1 to represent TRUE and 0 to represent FALSE. Please note that opinions are not propositions, e.g. "42 is an awesome number" is just an opinion, its truth or falsity is not universal, meaning some think it's true, some do not.

Examples

 * "It is raining today" is a proposition.
 * "Sydney is in Australia" is a proposition.
 * "1 + 2 + 3 + 4 + 5 = 16" is a proposition.
 * "Earth is a perfect sphere" is a proposition.
 * "How do you do?" is not a proposition - it's a question.
 * "Go clean your room!" is not a proposition - it's a command.
 * "Martians exist" is a proposition.

Since each proposition can only take two values (TRUE or FALSE), we can represent each by a variable and decide whether compound propositions are true by using Boolean algebra, just like we have been doing. For example "It is always hot in Antarctica OR 1 + 1 = 2" will be evaluated as true.

Implications
Propositions of the type if something something then something something are called implications. The logic of implications are widely applicable in mathematics, computer science and general everyday common sense reasoning! Let's start with a simple example
 * "If 1 + 1 = 2 then 2 - 1 = 1"

is an example of implication, it simply says that 2 - 1 = 1 is a consequence of 1 + 1 = 2. It's like a cause and effect relationship. Consider this example:
 * John says: "If I become a millionaire, then I will donate $500,000 to the Red Cross."

There are four situations:
 * John becomes a millionaire and donates $500,000 to the Red Cross
 * John becomes a millionaire and does not donate $500,000 to the Red Cross
 * John does not become a millionaire and donates $500,000 to the Red Cross
 * John does not become a millionaire and does not donate $500,000 to the Red Cross

In which of the four situations did John NOT fulfill his promise? Clearly, if and only if the second situation occurred. So, we say the proposition is FALSE if and only if John becomes a millionaire and does not donate. If John did not become a millionaire then he can't break his promise, because his promise is now claiming nothing, therefore it must be evaluated TRUE.

If x and y are two propositions, x implies y (if x then y), or symbolically
 * $$x \Rightarrow y$$

has the following truth table:

For emphasis, $$x \Rightarrow y$$ is FALSE if and only if x is true and y false. If x is FALSE, it does not matter what value y takes, the proposition is automatically TRUE. On a side note, the two propositions x and y need not have anything to do with each other, e.g. "1 + 1 = 2 implies Australia is in the southern hemisphere" evaluates to TRUE!

If
 * $$(x \Rightarrow y) \ \mbox{AND} \ (y \Rightarrow x)$$

then we express it symbolically as
 * $$x \Leftrightarrow y$$.

It is a two way implication which translates to x is TRUE if and only if y is true. The if and only if operation has the following truth table:

The two new operations we have introduced are not really new, they are just combinations of AND, OR and NOT. For example:
 * $$x \Rightarrow y = x' + y$$

Check it with a truth table. Because we can express the implication operations in terms of AND, OR and NOT, we have open them to manipulation by Boolean algebra and de Morgan's laws.

Example 1 Is the following proposition a tautology (a proposition that's always true)
 * $$[(x \Rightarrow y)(y \Rightarrow z)] \Rightarrow (x \Rightarrow z)$$

Solution 1
 * $$=\ [(x \Rightarrow y)(y \Rightarrow z)] \Rightarrow (x \Rightarrow z)$$
 * $$=\ [(x' + y)(y' + z)]' + (x' + z)$$
 * $$=\ (x' + y)' + (y' + z)' + x' + z$$
 * $$=\ xy' + yz' + x' + z$$
 * $$=\ y' + y + x' + z$$
 * $$=\ 1$$

Therefore it's a tautology.

Solution 2 A somewhat easier solution is to draw up a truth table of the proposition, and note that the output column are all 1s. Therefore the proposition is a tautology, because the output is 1 regardless of the inputs (i.e. x, y and z).

Example 2 Show that the proposition z is a contradiction (a proposition that is always false):
 * z = xy(x + y)'

Solution

\begin{matrix} z &=& xy(x + y)'\\ &=& xy(x'y')\\ &=& 0\\ \end{matrix} $$ Therefore it's a contradiction.

Back to Example 1, :$$[(x \Rightarrow y)(y \Rightarrow z)] \Rightarrow (x \Rightarrow z)$$. This isn't just a slab of symbols, you should be able translate it into everyday language and understand intuitively why it's true.

Exercises

 * 1) Decide whether the following propositions are true or false:
 * 2) If 1 + 2 = 3, then 2 + 2 = 5
 * 3) If 1 + 1 = 3, then boys don't like mud
 * 4) Show that the following pair of propositions are equivalent
 * 5) $$x \Rightarrow y$$ : $$y' \Rightarrow x'$$

Logic Puzzles
Puzzle is an all-encompassing word, it refers to anything trivial that requires solving. Here is a collection of logic puzzles that we can solve using Boolean algebra.

Example 1

We have two type of people -- knights or knaves. A knight always tell the truth but the knaves always lie.

Two people, Alex and Barbara, are chatting. Alex says :"We are both knaves"

Who is who?

We can probably work out that Alex is a knave in our heads, but the algebraic approach to determine Alex 's identity is as follows:
 * Let A be TRUE if Alex is a knight
 * Let B be TRUE if Barbara is a knight
 * There are two situations, either:
 * Alex is a knight and what he says is TRUE, OR
 * he is NOT a knight and what he says is FALSE.
 * There we have it, we only need to translate it into symbols:
 * A(A'B') + A'[(A'B')'] = 1

we simplify:
 * (AA')B' + A'[A + B] = 1
 * A'A + A'B = 1
 * A'B = 1

Therefore A is FALSE and B is TRUE. Therefore Alex is a knave and Barbara a knight.

Example 2

There are three businessmen, conveniently named Archie, Billy and Charley, who order martinis together every weekend according to the following rules:

 * 1) If A orders a martini, so does B.
 * 2) Either B or C always order a martini, but never at the same lunch.
 * 3) Either A or C always order a martini (or both)
 * 4) If C orders a martini, so does A.

 * 1) $$A \Rightarrow B$$ or $$A' + B = 1$$ (simplified from: $$AB + A'B' + A'B = 1$$
 * 2) $$B'C + BC' = 1$$
 * 3) $$A + C = 1$$
 * 4) $$C \Rightarrow A$$ or $$C' + A = 1$$ (simplified from: $$CA + C'A' + C'A = 1$$

Putting all these into one formula and simplifying:

$$ \begin{matrix} 1 &=& (A' + B) (B'C + BC') (A + C) (C' + A) \\ &=& (A' + B) (B'C + BC') (AC' + AA + CC' + AC) \\ &=& (A' + B) (B'C + BC') (AC' + A + 0 + AC) \\ &=& (A' + B) (B'C + BC') (AC' + A + AC) \\ &=& (A' + B) (B'C + BC') (C' + 1 + C)A \\ &=& (A' + B) (B'C + BC') (1)A \\ &=& (A' + B) (B'C + BC') A \\ &&\mbox{Now that we know that }A = 1\mbox{ we can substitute that in:} \\ &=& (0 + B) (B'C + BC') 1 \\ &=& (B) (B'C + BC') \\ &&\mbox{Now that we know that }B = 1\mbox{ we can substitute that in:} \\ &=& (1) (0C + 1C') \\ &=& C' \\ &&\mbox{If }1 = C'\mbox{ then }C = 0 \\ &&ABC' = 1 \end{matrix} $$

Exercises
Please go to Puzzles/Logic puzzles.

Problem Set
1. Decide whether the following propositions are equivalent:
 * $$x'\Rightarrow y'$$
 * $$y\Rightarrow x$$

2. Express in simplest sum-of-product form the following proposition:
 * $$(x \Leftrightarrow y) \Rightarrow z$$

3. Translate the following sentences into symbolic form and decide if it's true:
 * a. For all x, if x2 = 9 then x2 - 6x - 3 = 0
 * b. We can find a x, such that x2 = 9 and x2 - 6x - 3 = 0 are both true.

4. NAND is a binary operation:
 * x NAND y = (xy)'

Find a proposition that consists of only NAND operators, equivalent to:
 * (x + y)w + z

5. Do the same with NOR operators. Recall that x NOR y = (x + y)'