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User:FleurDeOdile/sandbox

Draft:Tropical Storm Laura (2020)

Meteorological history
On August 16, the NHC began tracking a tropical wave over western Africa. The wave gradually organized amid favorable conditions as it crossed the Tropical Atlantic, and at 03:00 UTC on August 20, it was designated as Tropical Depression Thirteen. Later that day, the system seemed to weaken as multiple circulations were present, and convection faltered due to dry air intrusion. However, at 13:00 UTC on August 21, the depression strengthened into Tropical Storm Laura. This made it the earliest twelfth named Atlantic storm, beating Hurricane Luis of 1995 by 8 days.

Current storm information
As of 11:00 a.m. AST (15:00 UTC) August 21, Tropical Storm Laura is located within 40 nautical miles of 17°N, -60.2°W, about 210 miles (335 km) east-southeast of the northern Leeward Islands. Maximum sustained winds are 40 knots, with gusts up to 50 knots. The minimum barometric pressure is 1007 mbar, and the system is moving west at 16 knots.

For the latest official information, see:
 * The NHC's latest public advisory on Tropical Storm Laura
 * The NHC's latest forecast advisory on Tropical Storm Laura
 * The NHC's latest forecast discussion on Tropical Storm Laura

title: User:FleurDeOdile/sandbox


text:
User:Mustafa Ansari

Mustafa Ansari Is a Student,He studing in Isc 1st year in Annanda Collage Hazari bagh.

source: wikimedia

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

title: User:Mustafa Ansari


text:
suavitas

Etymology
From.

Noun

 * 1)  sweetness ; melodiousness, tunefulness ; attractiveness
 * 2)  pleasantness, agreeableness, charm, attractiveness, sweetness

title: suavitas


text:
User:Runnerupnj~enwikiversity

My name is Rob. I am a 23 year old male, raised in New Jersey and living in Philadelphia, PA. For any other information, please see my user page at Wikipedia.

title: User:Runnerupnj~enwikiversity


text:
Patrick Nolan (politician)

Patrick J. "Paddy" Nolan (March 17, 1881 – January 11, 1941) was mayor of Ottawa, Canada from 1934 to 1935.

He was born in Ottawa on St. Patrick's Day in 1881, the son of poor Irish parents. He worked as a clerk in a drug store, studied to become a pharmacist and opened his own drug store. He owned several movie theatres in the city.

Nolan was first elected to city council in 1922.

He died of influenza in 1941, aged 59.

title: Patrick Nolan (politician)


text:
Τρίτων

Etymology
etymology. Related to the second combining form of, his mother's name. Neither belongs to the etymological group. It has been connected to 🇨🇬, in reference to his trident, from. Also connected to 🇨🇬. Not related to.

Proper noun

 * 1)   god of the sea, son of Poseidon

Noun

 * 1)   god of the sea, son of Poseidon

title: Τρίτων


text:
Vievis

Vievis is a small city in Elektrėnai municipality, Lithuania. It is located 14 km east of Elektrėnai, on Lake Vievis.

History
Its alternate names include Anastasevskaya, Jewie (Polish), Vevis, Viyevis, V’yevis, and Yev’ye.

Vievis Manor was first mentioned in 1522. The town, which belonged to the Ogiński family, was mentioned in 1539. In the first half of the 16th century, the first Catholic church was built there. About 1600, the Ogiński family built a Uniate church and founded the abbey of the Holy Spirit (Lithuanian: Šventosios dvasios). At the beginning of the 17th century, a printing press was established near the abbey, notable for printing books by various Protestant Calvinist scholars. The printing press is featured on the modern coat of arms of the city, adopted in 1999.

In 1794 and 1812, the church burned down and was rebuilt in 1816. In 1837 an Orthodox church was built.

In the period between World War I and World War II, after the Polish–Lithuanian War, Vievis was near the dividing line between Lithuania and Poland. The town used to be among those with the largest Polish population, with roughly 77% inhabitants identifying themselves as Poles. In 2011 census, only 10.9% of inhabitants identified themselves as Poles as well as 3.74% Russians and 82.56% Lithuanians.

The Lithuanian Road Museum is in the city.

Twin towns

 * 🇭🇺 Óbuda-Békásmegyer – Hungary, since 2016

title: Vievis


text:
User:Jkoop

Hello world, I exist! (or existed; it can be hard to be perfectly sure)

17:41, 27 April 2021 (UTC)

title: User:Jkoop


text:
File:Ironbark SmokeView.jpg

Summary
This is an image of the smoke coming from the St Peters Lutheran College, Australia, Ironbark outdoor education. Sp0kk 13:33, 11 August 2006 (UTC)

title: File:Ironbark SmokeView.jpg


text:
Ranu Devi Adhikari

Ranu Devi Adhikari (रानुदेवी अधिकारी) (27 November 1936 – 30 April 2020) was a singer of Nepal. She was also one of the prominent leaders of the Nepali Congress party. She was the first female singer of Radio Nepal. She used to sing revolutionary songs like "Jaago Nepali" on radio Nepal, to ignite fire in the hearts of the Nepalese people during the times of oppression.

She was born on 27 November 1936 in Birgunj. She grew up in Benaras, India.

She was the younger sister of the late Nona Koirala. She, along with her sister, brother-in-law Yuvaraj Adhikari and other members of the Koirala family were part of the revolution that led to the ultimate downfall of the Rana regime.

Ranu Devi was also a history teacher at Ballika Vidyalaya in Biratnagar.

She married Tirtha Prasad Adhikari. She had three children, namely Archana Sharma, Alpana Regmi, and Avin Adhikari.

She died on 30 April 2020 at KMC Hospital, Sinamangal, Kathmandu.

title: Ranu Devi Adhikari


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erhu

Etymology
From, from +.

Noun

 * 1) A type of bowed spike fiddle having two strings, originating in China as part of the huqin family of string instruments.

Translations

 * Catalan:
 * Chinese:
 * Cantonese: 二胡
 * Hokkien: 二胡
 * Mandarin:, , 二弦
 * Esperanto: erhuo, nanhuo
 * French:
 * Japanese: 二胡
 * Korean: 얼후, 이호(二胡)
 * Russian:
 * Swedish:
 * Thai:
 * Vietnamese: nhị hồ (二胡)

title: erhu


text:
Van Dwelling/Conversion Diaries/1983 Chevy Diesel SuperVan (G20)

In this section, I'm going to describe how I converted my 1983 Chevy diesel SuperVan (G20) into a vandwelling. I bought the van for $800.00 from AAA Upholstery in Raleigh, NC.

To Do:
 * 1) Clean interior
 * 2) Replace tires
 * 3) Paint body
 * 4) Replace rear fender
 * 5) Repair air conditioning
 * 6) Paint interior
 * 7) Install Flooring
 * 8) Build cooking module
 * 9) Build bed
 * 10) Build bath module
 * 11) Install 4X4
 * 12) Install poptop
 * 13) Repair front driver's side window
 * 14) Repair rear door lock
 * 15) Repair window rollers
 * 16) Install window tinting
 * 17) Install shatterguard
 * 18) Install autogen generator
 * 19) Install water tanks
 * 20) Build toilet module


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Mladen Urem

Mladen Urem (born 16 April 1964) is a literary critic, author and editor.

Urem was born in Rijeka, Croatia, where he received his BSc in radiology from the Medical School in Rijeka and also a B. A. in the Croatian language and literature from the Faculty of Philosophy.

During 1980–82, he was a singer and a guitarist with a new-wave & punk rock group Istočni izlaz (The Eastern Exit). His name appears in The Little Encyclopaedia of Croatian Pop and Rock Music (1994). He was the literary editor of the Val journal (The Wave, 1985–1989), founder and editor-in-chief of the Rival literary magazine (1988–2000) and also of the Biblioteka Val — an original titles series (since 1987). He co-founded the philological magazine Fluminensia (1989), founded and served as the editor-in-chief in the Sušačka revija culture magazine (1993–1995) and as the editor-in-chief of the journal called Dometi (1996).

In the war-edition of the Rival (1-4/1991), Urem published the first retrospection of the Croatian literary works written on the frontlines at the beginning of the Croatian War of Independence (1991–1995).

During its thirteen years of existence, the Rival featured 800 authors and their works from the fields of Croatian and world literature and arts. During that period, the magazine presented many of the phenomena in the 90s world culture, as well as the authors that would later receive important awards and honours (the Nobel Prize for V. S. Naipaul and many other authors and prizes) and was considered one of the most significant Croatian journals. The Rival magazine also published the English translations of the Croatian literary texts and developed a substantial collaboration with various world magazines and journals published in English.

He has authored the following titles: Riječki krug redom (1987), Pogledom u riječ (1987), Janko Polić Kamov – Selected Short Stories and Poems (1997), Dan velikih valova (prose and poetry by the Rival-generation, with the complete Rival bibliography 1988–2000, as well as the 1987–2001 series, co-authored with Goran Ušljebrka and Milan Zagorac, 2001), Pavica Julija Kaftanić (co-authored with Boris Zakošek, Lovorka Ruck and Igor Žic, 2005), Southerly Thoughts and Other Stories (An Anthology of Croatian Short Stories by Ksaver Šandor Gjalski, Janko Polić Kamov, Miroslav Krleža, Vladan Desnica, Ranko Marinković, Slobodan Novak, Ivan Aralica, Ivan Slamnig, Antun Šoljan and Nedjeljko Fabrio — selection by Mladen Urem, Damir Biličić and Želimir Galjanić, 2005) and Janko Polić Kamov, Dora Maar i hrvatska avangarda (Janko Polić Kamov, Dora Maar and Croatian Avantgarde, 2006).

Many of his essays and studies concerning the topics from the contemporary Croatian literature, especially studies of writer Janko Polić Kamov (Rijeka 1886 – Barcelona 1910), his life and work, have appeared in various American and Croatian periodicals. In collaboration with Dolores Čikić and Boris Zakošek, he explored Dora Maar's genealogy for the Parisian Andriveau, also publishing the findings in the Croatian daily Večernji list, as well as in the book Dora Maar - zatočenica pogleda (Dora Maar: Prisonniere du regard) by Alicia Dujovne Ortiz (Zagreb, 2004).

Urem is frequent a contributor to the US literary journals Grand Street (New York City), Partisan Review (Boston), World Literature Today (Norman, Oklahoma) and Corner (Oakland, California), in which he has also published various works by the Croatian writers Janko Polić Kamov, Miroslav Krleža, Ivo Andrić and Ivan Goran Kovačić. He has collaborated with the famous US authors and editors Deborah Treisman (1971), William Phillips (1907–2002), Robert Bingham (1966–1999) and others, as well as with the British historian Lucy Hughes-Hallett (1953).

Urem has published almost 200 texts concerning the field of Croatian literature, and edited as many books. On more than one occasion has he been a member of the jury for the literary awards Drago Gervais and Nagrada grada Rijeke (The City of Rijeka Award). He is a member of the Croatian PEN Center in Zagreb and works at the Rijeka State Archives, managing its Library and Publishing Department.

title: Mladen Urem


text:
User:Laraburke0806

Hello my name is Lara I am 19 years old and am studying social science in UCD. I love to hang out with my friends and my main hobbies would be to play hockey which I also play in ucd.

I live in Ireland.

title: User:Laraburke0806


text:
General Relativity/Einstein's equation

<General Relativity

 * Main article: Einstein's field equation

The Einstein field equation or Einstein equation is a dynamical equation which describes how matter and energy change the geometry of spacetime, this curved geometry being interpreted as the gravitational field of the matter source. The motion of objects (with a mass much smaller than the matter source) in this gravitational field is described very accurately by the geodesic equation.

Mathematical form of Einstein's field equation
Einstein's field equation (EFE) is usually written in the form:

 * $$R_{\mu\nu} - {1 \over 2} {R g_{\mu\nu}} + \Lambda g_{\mu\nu} = 8 \pi {G \over c^4} T_{\mu\nu}$$

Where

 * $$R_{\mu\nu}$$ is the Ricci curvature tensor
 * $$R$$ is the Ricci scalar (the tensor contraction of the Ricci tensor)
 * $$g_{\mu\nu}$$ is a (symmetric 4 x 4) metric tensor
 * $$\Lambda$$ is the Cosmological constant
 * $$\pi$$ is pi=3.1415..., the ratio between a circle's circumference and diameter
 * $$G$$ is the Gravitational constant
 * $$c$$ is the speed of light in free space
 * $$T_{\mu\nu}$$ is the energy-momentum stress tensor of matter

The EFE equation is a tensor equation relating a set of symmetric 4 x 4 tensors. It is written here in terms of components. Each tensor has 10 independent components. Given the freedom of choice of the four spacetime coordinates, the independent equations reduce to 6 in number.

The EFE is understood to be an equation for the metric tensor $$g_{\mu\nu}$$ (given a specified distribution of matter and energy in the form of a stress-energy tensor). Despite the simple appearance of the equation it is, in fact, quite complicated. This is because both the Ricci tensor and Ricci scalar depend on the metric in a complicated nonlinear manner.

One can write the EFE in a more compact form by defining the Einstein tensor
 * $$G_{\mu\nu} = R_{\mu\nu} + (\Lambda - {1 \over 2}R) g_{\mu\nu}$$

which is a symmetric second-rank tensor that is a function of the metric. Working in geometrized units where G = c = 1, the EFE can then be written as

 * $$G_{\mu\nu} = 8\pi T_{\mu\nu}\,$$

The expression on the left represents the curvature of spacetime as determined by the metric and the expression on the right represents the matter/energy content of spacetime. The EFE can then be interpreted as a set of equations dictating how the curvature of spacetime is related to the matter/energy content of the universe.

These equations, together with the geodesic equation, form the core of the mathematical formulation of General Relativity.

Conservation of energy and momentum
An important consequence of the EFE is the local conservation of energy and momentum; this result arises by using the differential Bianchi identity to obtain

 * $$\nabla_b G^{\mu\nu}=G^{\mu\nu}{}_{;b}=0$$

which, by using the EFE, results in

 * $$\nabla_b T^{\mu\nu}= T^{\mu\nu}{}_{;b}=0$$

which expresses the local conservation law referred to above.

Nonlinearity of the field equations
The EFE are a set of 10 coupled elliptic-hyperbolic nonlinear partial differential equations for the metric components. This nonlinear feature of the dynamical equations distinguishes general relativity from other physical theories.

For example, Maxwell's equations of electromagnetism are linear in the electric and magnetic fields (i.e. the sum of two solutions is also a solution).

Another example is Schrodinger's equation of quantum mechanics where the equation is linear in the wavefunction.

The correspondence principle
Einstein's equation reduces to Newton's law of gravity by using both the weak-field approximation and the slow-motion approximation. In fact, the gravitational constant $$G$$ appearing in the EFE's is determined by making these two approximations.

The cosmological constant
The cosmological constant term $$\Lambda g_{\mu\nu}$$ was originally introduced by Einstein to allow for a static universe (i.e., one that is not expanding or contracting). This effort was unsuccessful for two reasons: the static universe described by this theory was unstable, and observations of distant galaxies by Hubble a decade later confirmed that our universe is in fact not static but expanding. So $$\Lambda$$ was abandoned (set to 0), with Einstein calling it the "biggest blunder he ever made".

Despite Einstein's misguided motivation for introducting the cosmological constant term, there is nothing wrong (i.e. inconsistent) with the presence of such a term in the equations. Indeed, quite recently, improved astronomical techniques have found that a non-zero value of $$\Lambda$$ is needed to explain some observations.

Einstein thought of the cosmological constant as an independent parameter, but its term in the field equation can also be moved algebraically to the other side, written as part of the stress-energy tensor:
 * $$T_{\mu\nu}^{\mathrm{(vac)}} = -\frac{\Lambda}{8\pi}g_{\mu\nu}$$

The constant
 * $$\rho_{\mathrm{vac}} = \frac{\Lambda}{8\pi}$$

is called the vacuum energy. The existence of a cosmological constant is equivalent to the existence of a non-zero vacuum energy. The terms are now used interchangeably in general relativity.

Solutions of the field equations
The solutions of the Einstein field equations are metrics of spacetime. The solutions are hence often called 'metrics'. These metrics describe the structure of the spacetime including the inertial motion of objects in the spacetime. As the field equations are non-linear, they cannot always be completely solved (i.e. without making approximations). For example, there is no known complete solution for a spacetime with two massive bodies in it (which is a theoretical model of a binary star system, for example). However, approximations are usually made in these cases. These are commonly referred to as post Newtonian approximations. Even so, there are numerous cases where the field equations have been solved completely, and those are called exact solutions.

The study of exact solutions of Einstein's field equations is one of the activities of cosmology. It leads to the prediction of black holes and to different models of evolution of the universe.

Vacuum field equations
If the energy-momentum tensor $$T_{\mu\nu}$$ is zero in the region under consideration, then the field equations are also referred to as the vacuum field equations, which can be written as:

 * $$R_{ab} = 0\,$$

The solutions to the vacuum field equations are called vacuum solutions. Flat Minkowski space is the simplest example of a vacuum solution. Nontrivial examples include the Schwarzschild solution and the Kerr solution.

The above vacuum equation assumes that the cosmological constant is zero. If it is taken to be nonzero then the vacuum equation becomes:
 * $$R_{\mu\nu} = \Lambda g_{\mu\nu}\,$$

Mathematicians usually refer to manifolds with a vanishing Ricci tensor as Ricci-flat manifolds and manifolds with a Ricci tensor proportional to the metric as Einstein manifolds.

title: General Relativity/Einstein's equation


text:
J Award of 2006

The J Award of 2006 is the second annual J Awards, established by the Australian Broadcasting Corporation's youth-focused radio station Triple J. The announcement comes at the culmination of Ausmusic Month (November). For the second and final year, there was only one category, Australian Album of the Year.

Who's eligible?
Any Australian album released independently or through a record company, or sent to Triple J in consideration for airplay, is eligible for the J Award. The 2006 nominations were selected from albums received by triple j between December 2005 and November 2006.

The criteria
The J Award is for an album of outstanding achievement as an Australian musical work of art - for its creativity, innovation, musicianship and contribution to Australian music. Fifteen nominations were announced throughout the year.

Award
Australian Album of the Year

title: J Award of 2006


text:
User:Scercrow2

The legend of the world is the way we live we love the world for who it was before they came a ZAYLEES is the religion that's in 3 different categories is the first also called the 1st pendent is the fact that you believe in a god also know as the creator and you aren't afraid to show it you worship the life and death trees and there is the god tree its the eye of the world respect it when in its present. The second is also called 2nd pendent also named after the name moss its the way you believe when the world is called a disses also life is the moss that's over the planet and since DNA is indestructible that means it will forever exists destroying the planets before man is more intelligent than the planet itself it will grow tell its destroyed for eternity it will be the fault of the humans that we will all die a fate that was set from the beginning. The third and last is called 3red pendent also the true law of this religion/colt never kill for the pleasure only for survival,never hurt someone that dose not deserve it but defend your self if needed,never forget the oath is what brings us together as brothers and sisters. Never forget your own way of the world its your way never change for anyone live free with no regret.

title: User:Scercrow2


text:
User:MssKitt/Books/DemoralisationMyWikiCreations

 * Demoralization (warfare)
 * Force concentration
 * Incapacitating agent
 * Non-lethal weapon
 * Propaganda
 * Psychological warfare
 * Siege
 * Strategic bombing


text:
OPS 5118

OPS 5118, also known as Navstar 6, GPS I-6 and GPS SVN-6, was an American navigation satellite launched in 1980 as part of the Global Positioning System development programme. It was the sixth of eleven Block I GPS satellites to be launched.

Background
Global Positioning System (GPS) was developed by the U.S. Department of Defense to provide all-weather round-the-clock navigation capabilities for military ground, sea, and air forces. Since its implementation, GPS has also become an integral asset in numerous civilian applications and industries around the globe, including recreational used (e.g., boating, aircraft, hiking), corporate vehicle fleet tracking, and surveying. GPS employs 24 spacecraft in 20,200 km circular orbits inclined at 55°. These vehicles are placed in 6 orbit planes with four operational satellites in each plane.

Spacecraft
The first eleven spacecraft (GPS Block 1) were used to demonstrate the feasibility of the GPS system. They were 3-axis stabilized, nadir pointing using reaction wheels. Dual solar arrays supplied over 400 watts. They had S-band communications for control and telemetry and Ultra high frequency (UHF) cross-link between spacecraft. They were manufactured by Rockwell Space Systems, were 5.3 meters across with solar panels deployed, and had a design life expectancy of 5 years. Unlike the later operational satellites, GPS Block 1 spacecraft were inclined at 63°.

Launch
OPS 5118 was launched at 22:00 UTC on 26 April 1980, atop an Atlas F launch vehicle with an SGS-1 upper stage. The Atlas used had the serial number 34F, and was originally built as an Atlas F. The launch took place from Space Launch Complex 3E at Vandenberg Air Force Base, and placed OPS 5118 into a transfer orbit. The satellite raised itself into medium Earth orbit using a Star-27 apogee motor.

Mission
By 16 May 1980, OPS 5118 had been raised to an orbit with a perigee of 20006 km, an apogee of 20357 km, a period of 717.94 minutes, and 62.8° of inclination to the equator. The satellite had a design life of 5 years and a mass of 758 kg. It broadcast the PRN 09 signal in the GPS demonstration constellation, and was retired from service on 6 March 1991.

title: OPS 5118


text:
Shamsiyeh

Shamsiyeh (, also Romanized as Shamsīyeh; also known as Shamīyeh) is a village in Rivand Rural District, in the Central District of Nishapur County, Razavi Khorasan Province, Iran. At the 2006 census, its population was 153, in 37 families.

title: Shamsiyeh


text:
Microeconomics/Indifference Curves and Budget Lines

Introduction A basic tool in economics is the mathematical representation of consumer behaviour. It is an abstract (i.e. theoretical) model, based on assumptions. Here, the model is presented in its simplest version, based on simplifying assumptions about the behaviour of an individual who wants to spend his/her money on a variety of goods available on the market. Needless to say, the simplified model is not always suitable for the analysis of complex situations. Advanced versions of the model, based on more realistic assumptions, have been designed to cope with non-standard real world situations.

The simplified model ultimately aims at representing the consumer's choice as the solution of an optimisation problem (so that algebra can be used to analyse his/her behaviour). In few words, the theory describes in mathematical language the behaviour of a consumer who selects the best available bundle on the market. The context should be taken as given and is made up of three 'exogenous' pieces of information: (i) an amount of money y (usually, but somehow improperly, called 'income') that can be entirely spent on consumption goods; (ii) the prices of all consumption goods; (iii) the consumer's preferences. The term 'exogenous' means that income, prices and preferences are not explained within (i.e. by) the model and are taken as given, preliminar information. The model in fact explains what amount of each good is bought by a consumer, given her/his income, the market prices and his/her preferences.

Indifference Curves is the curve that represents the bundle of goods which give consumer the same level of satisfaction, hence the word 'indifference' because consumer do not gain or lose utility or satisfaction if they move along the curve from one point to another. In simple model this is usually represented by two goods. However, it is possible to have more than two goods by writing it in vector and indifference curve will be all the combination of goods that give the same satisfaction to consumer.

Budget Lines Whilst the indifference curves are the mathematical representation of preferences, the budget set is the mathematical representation of all the bundles available to the consumer (because their cost does not exceed her/his income). It will turn out that, if a group of simplifying assumptions are met, the best choice for the consumer can be represented as a bundle in the budget set that also belongs to the highest attainable indifference curve. At this stage, this sounds obscure: in what follows, the attention will be focused at lenght on the definition and meaning of budget sets, lines and of indifference curves. Before, however, it is better to point out that, even at this very preliminar stage, some simplifying assumptions have indeed been introduced.

Optimizing behaviour The first assumption is that every consumer makes optimal choices, in other words she/he never selects intentionally a bundle A when a better bundle B is also available at the same (or lower) cost. This sounds quite reasonable and realistic. However, it is not entirely without problems. The main drawback concerns empirical research: if one assumes a priori that the consumer always makes optimal choices, then any bundle actually purchased should necessarily be considered by the researcher as the best available to her/him. This implies that the model does not permit any empirical test on the quality of consumption choices: mistakes are simply ruled out and, by assumption, the consumer never regrets about his/her choices. This may not be a severe limitation for the model: one has only to remind that it is not very well suited to analyse, for instance, those changes in the consumer's behavior that occur after a sequence of trials and errors (in real world situations a consumer may find the most preferred bundle after having proved and discarded some alternative choices).

Price-taking The second assumption underlying the simplified model maintains that a single consumer takes prices 'as they are' and does not bargain for a better price. Of course, price-makers will take account of the possible changes in the aggregate demand for their good when fixing the price. However, by assumption, a single consumer ignores this and acts accordingly 'as if' his/her consumption choices have no effect on market prices. Thus, the simplified model is not suited to analyze those situations when an individual buyer has in fact market power (and knows it).

Useful assumptions (conventions) Some ancillary assumptions are made just to ease the mathematical representation and to focus on the choice of the best available bundle. First of all, in the simplified model the number of goods available on the market is not infinite. Goods are distinguished according to their characteristics: for example, red apples are different from yellow apples. As in common language, a bundle is a list of quantities (one for each available good, including the zero-amount case). Only non-negative amounts of goods are considered (a more refined analysis would represent the goods possibly sold on the market by an individual as negative quantities, a possibility that is ruled out in the simplified model). Second, quantities are measured on a continuous scale: even the smallest amount of good can be further divided into smaller pieces (i.e. the goods are infinitely divisible). Such a convention permits to avoid 'kinks and holes' in the mathematical functions that represent the consumers' preferences and budget: a very nice property that allows the beginners to focus on economics and forget for a while about complex algebra. Obviously, it is a departure from many real world situations: one cannot easily buy a little bit of a car, nor it is customary to purchase two seconds of a movie... Third, in the simplified model the consumer is assumed to manage her/his budget in a sequence: at a preliminary stage, he/she has already decided how much work to sell on the labour market (that is, how much to earn) and also how much to save. In a last stage, he/she decides about consumption: the amount of money y left from the previous stages is thus given and can be spent entirely.

Mathematical symbols To save ink (digits), words are often replaced by mathematical symbols. A bundle is usually represented as a N-dimensional vector q, where N is the number of goods. Two bundles are distinguished by using superscripts:

$$ \mathbf{q^A}          \mathbf{q^B}$$

The budget set All the bundles that can be purchased with the given level of income y are elements of the 'budget set', the set of bundles available to the consumer (when his/her income is y). The obvious common property of the bundles in the budget set is that their cost is not greater than y. In mathematical terms, being p the N-vector of given market prices, a bundle q belongs to the budget set if: