The Office of the Parliamentary Counsel to Government is a constituent department of the Office of the Attorney General of Ireland. Parliamentary Counsel to Government draft government Bills (including Bills to amend the Constitution of Ireland, revision Bills, amendments to Bills, consolidation and restatement Bills).
“Wide Right” is a term in American football used to denote an extra point or field goal attempt that the kicker misses to the right of the field goal posts. In the history of both NCAA and NFL football, the term is often associated with these two separate teams/events:
The Read the Bills Act is legislation written by Downsize DC, a non-profit organization focused on decreasing the size of the federal government. The intention of the Read the Bills Act is to require Congress to read the legislation that they pass. The proposed act is a response to the passing of bills like the Patriot Act that are thousands of pages long and are passed without copies being made available to the members of Congress who vote on the bill. The bill is aimed at decreasing the size of government and the speed at which it grows.
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The Read the Bills Act would require each house of Congress, in the presence of a quorum, to read any bill that they vote on. If a member is not present at the reading, s/he will be required to sign a sworn affidavit saying that s/he has read the bill. If a bill is amended at the last moment, Congress will be required to read, again in full, the bill before a quorum in front of Congress. The same rules applying to absent members will apply to all readings of last minute amendments to the legislation.
Congress will also be required to post the newest version of the bill on their website at least seven days prior to a publicly-announced vote. Any amendments to the bill will yield a new posting on the Internet of the bill and another seven-day waiting period.
It will also require that all bills coming up for renewal in Congress under sunset provisions will be subject to all rules of the Read the Bills Act.
The Read the Bills Act is intended to slow down Congress. Instead of passing many large bills in a short amount of time, Congress will have to either pass shorter bills or pass fewer bills than they currently do.(2/2006)
Theoretically, legislation will become shorter and less complex. In order to be able to read the bills, Congress will have to tackle fewer issues and have fewer projects in each bill. Due to the seven day waiting period, Congress will not be able to pass as many “pork” projects because the public will have a chance to voice their objection. Old legislation coming up under sunset provisions will probably become shorter because Congress will have to reread the bills.
Congress will not be able to insert last-minute secret clauses because they will have to reread the entire bill with the new additions and wait another seven days before passing the legislation.
Larry Tripplett (born January 18, 1979 in Los Angeles, California) is an American football defensive tackle who currently plays for the Buffalo Bills of the National Football League. He was originally drafted by the Indianapolis Colts in the second round (42nd overall) of the 2002 NFL Draft. He played collegiately at Washington.
On March 12, 2006 Tripplett signed as a free agent with the Bills.
Edward “Abe” Abramoski served as Head Athletic Trainer for the Buffalo Bills for 37 years. Prior to his stint in Buffalo, he was an athletic trainer at the University of Detroit, the Detroit Lions, and the United States Military Academy, and has long been recognized as a pioneer athletic trainer in professional football. His service to the Bills and the City of Buffalo is set to be formally recognized with the inclusion of his name on the Wall of Fame at Ralph Wilson Stadium, home of the Bills. He is a member of the Greater Buffalo Sports Hall of Fame (1996), a recipient of the Buffalo Bills Alumni Association Appreciation Award (1990,1994), and a member of the Niagara Frontier for Distinguished Achievements in Sports. Abe was inducted into the NATA Hall of Fame in 1986. A frequent volunteer for the New York State Special Olympics, Abe was instrumental in establishing a means for all athletes in Western New York High Schools receiving services from athletic trainers.
In microeconomics, the utility maximization problem is the problem consumers face: “how should I spend my money in order to maximize my utility?”
Suppose their consumption set
has L commodities. If the prices of the L commodities are
and the consumer’s wealth is w, then the set of all affordable packages, the budget set, is
The consumer would like to buy the best package of commodities it can afford. If
is the consumer’s utility function, then the consumer’s optimal choices x(p, w) are
Finding x(p, w) is the utility maximization problem.
The solution x(p, w) need not be unique. If u is continuous and no commodities are free of charge, then x(p, w) is nonempty. Proof: B(p, w) is a compact space. So if u is continuous, then the Weierstrass theorem implies that u(B(p, w)) is a compact subset of <math>\textbf R</math>. By the Heine-Borel theorem, every compact set contains its maximum, so we can conclude that u(B(p, w)) has a maximum and hence there must be a package in B(p, w) that maps to this maximum.
If a consumer always picks an optimal package as defined above, then x(p, w) is called the Marshallian demand correspondence. If there is always a unique maximizer, then it is called the Marshallian demand function. The relationship between the utility function and Marshallian demand in the Utility Maximization Problem mirrors the relationship between the expenditure function and Hicksian demand in the Expenditure Minimization Problem.
In practice, a consumer may not always pick an optimal package. For example, it may require too much thought. Bounded rationality is a theory that explains this behaviour with satisficing - picking packages that are suboptimal but good enough.
Egodystonic is a psychological term referring to behaviors, (e.g., dreams,
impulses, compulsions, desires, etc.), that are in conflict, or dissonant, with the needs and goals of the ego, or, further, in conflict with a person’s ideal self-image.
The concept is studied in detail in abnormal psychology, and is the opposite of egosyntonic. Obessive compulsive disorder is considered to be an ego-dystonic disorder, as the thoughts and compulsions experienced or expressed are often not consistent with the individual’s self-perception, causing extreme distress.
In economics, marginal concepts refer to the effect of producing or consuming one more of a good, i.e. at the edge, or margin, of the total produced/consumed.
For example, marginal cost refers to the cost of producing one more unit of some good. In general this will be lower than the average cost because the average cost includes fixed costs. (See economies of scale). Marginal benefit is the extra utility accrued from one additional unit of a good.
Similarly marginal utility is the additional utility (satisfaction or benefit) that a consumer derives from an additional unit of a commodity or service. It is assumed that marginal utility generally falls as consumption increases, so that one’s 10th doughnut in a day is less satisfying than the first or second.
Other marginal concepts include:
The related concept of elasticity is the ratio of the incremental percentage change in one variable with respect to an incremental percentage change in another variable.
In science fiction stories involving time travel, an alternate future or alternative future is a possible future which never comes to pass, typically because someone travels back into the past and alters it so that the events of the alternate future cannot occur.
An alternate future differs from alternate history in that alternate history usually speculates on what might have happened in the past if some events in the past had occurred differently, while an alternative future usually speculates on what might happen in the future. Also, alternative histories commonly forgo time travel, while alternate futures do not.
An alternate future should not be confused with a possible future. Many science fiction stories are set in the future and treat it as if it were the only future within the context of the story; an alternate future story is specifically set in an alternate one, that is, one that, within the context of the story, does not come about to pass.
Examples of fictional works which show alternate futures include:
In the theory of cybernetics, teleogenesis (from the Greek teleos = ‘purpose’ and genesis = ‘creation’) is the creation of goal-creating processes.
According to Peter Corning:
“A cybernetic system is by definition a dynamic purposive system; it is ‘designed’ to pursue or maintain one or more goals or end-states”.
Teleogenesis refers from an extension of classical cybernetics, as proposed by Norbert Wiener, Ashby and others in late 1950s.
This is the main article on Utilities of Seattle. In Seattle, Washington, USA, water is furnished by Seattle Public Utilities (SPU), an agency of the city, which owns two water collection facilities–one in the Cedar River watershed, which primarily serves the city south of the Lake Washington Ship Canal, and the other in the Tolt River watershed, which primarily serves the city north of the canal.
Natural gas is furnished by privately owned Puget Sound Energy, which began its existence in 1886, generating electrical power as the Seattle Electric Light Company. Nowadays, the city’s electricity is furnished by Seattle City Light, an agency of the city, which owns numerous hydroelectric dams on the Cedar and Skagit Rivers. Seattle first decided to invest in public power generation in 1902, initially handling this as part of the water department; the resulting Cedar Falls hydroelectric facility (1905) is now the oldest continually operating, publicly owned hydro plant in the U.S. City Light became a separate city agency in 1910, and, in 1951, bought out the last of their privately owned competitors. [1], [2]
The privately owned Seattle Steam Company, founded 1893, generates steam by burning natural gas and wood, and provides it to over 200 business in downtown Seattle — where hotels figure prominently among its customers — and on First Hill, where it serves several of the city’s largest hospitals.
Most landline telephone service is provided by Qwest.
Cable television is dominated by Comcast, with Millennium Digital Media providing service in some neighborhoods.
New Jersey Monthly is a monthly glossy publication featuring issues of interest to residents of the United States state of New Jersey.
In addition to articles of general interest, occasional special subject issues covering and ranking high schools, lawyers and municipalities (among other topics), have been popular sources of bragging rights for those selected and especially for those featured in the rankings, the higher the better.
Emulex is a California based manufacturer of storage networking infrastructure solutions. Products include host bus adapters (HBAs), embedded storage switches, storage I/O controller and SAN storage switch products.
The term quasilinear has several meanings, usually meaning something close to almost linear.
The following meanings are related to the field of mathematics and its applications in computer science and economics.
Westcoast Pipeline is a natural gas pipeline in British Columbia that brings natural gas to the United States and to TransCanada pipeline. It is owned by Duke Energy.
In mathematics, integral polytopes have associated Ehrhart polynomials which encode relations between the volume of a polytope, number of integer points the polytope contains, and other related geometric quantities. The theory of Ehrhart polynomials can be seen as a higher dimensional generalization of Pick’s theorem in the Euclidean plane.
Specifically, consider a lattice L in Euclidean space Rn and an n-dimensional polytope P in Rn, and assume that all vertices of the polytope are points of the lattice. (A common example is L = Zn and a polytope with all its vertex coordinates being integers.) For any positive integer t, let tP be the t-fold dilation of P and let L(P, t) be the number of lattice points contained in tP. Ehrhart showed in 1962 that L is a rational polynomial of degree n in t, i.e. there exist rational numbers a0,…,an such that:
Furthermore, if P is closed (i.e. the boundary faces belong to P), some of the coefficients of L(P, t) have an easy interpretation:
The case n=2 and t=1 of these statements yields Pick’s theorem. Formulas for the other coefficients are much harder to get; Todd classes of toric varieties, the Riemann–Roch theorem as well as Fourier analysis have been used for this purpose.
The Ehrhart polynomial of the interior of a closed convex polytope P can be computed as:
As a solution to the Bertrand paradox in economics, it has been suggested that each firm produces a somewhat differentiated product, and consequently faces a demand curve that is downward-sloping for all levels of the firm’s price.
An increase in a competitor’s price is represented as an increase (for example, an upward shift) of the firm’s demand curve.
As a result, when a competitor raises price, generally a firm can also raise its own price and increase its profits.
Merger simulation models ordinarily assume differentiated Bertrand competition within a market that includes the merging firms.
In computer science, left recursion is a special case of recursion.
A formal grammar that contains left recursion cannot be parsed by a recursive descent parser. In contrast, left recursion is preferred for LALR parsers because it results in lower stack usage than right recursion.
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“A grammar is left-recursive if we can find some non-terminal A which will eventually derive a sentential form with itself as the left-symbol.”Notes on Formal Language Theory and Parsing, James Power, Department of Computer Science National University of Ireland, Maynooth Maynooth, Co. Kildare, Ireland.JPR02
Immediate left recursion occurs in rules of the form
<math>A \rightarrow A\alpha\,|\,\beta</math>
Where <math>\alpha</math> and <math>\beta</math> are sequences of nonterminals and terminals, and <math>\beta</math> doesn’t start with A.
Example :
The rule
<math>Expr \rightarrow Expr\,+\,Term</math>
is immediately left-recursive. The recursive descent parser for this rule might look like :
and a recursive descent parser would fall into infinite recursion when trying to parse a grammar which contains this rule.
Indirect left recursion in its simplest form could be defined as :
<math>A \rightarrow B\alpha\,|\,C</math>
<math>B \rightarrow A\beta\,|\,D</math>
Possibly giving the derivation <math>A \Rightarrow B\alpha \Rightarrow A\beta\alpha \Rightarrow … </math>
More generally, for the non-terminals <math>A_0, A_1, …, A_n</math>, indirect left recursion can be defined as being of the form :
<math>A_0 \rightarrow A_1\alpha_1\,|…</math>
<math>A_1 \rightarrow A_2\alpha_2\,|…</math>
<math>…</math>
<math>A_n \rightarrow A_0\alpha_{(n+1)}\,|…</math>
Where <math>\alpha_1, \alpha_2, …, \alpha_n</math> are sequences of nonterminals and terminals.
The general algorithm to remove immediate left recursion follows. Several improvements to this method have been made, including the ones described in “Removing Left Recursion from Context-Free Grammars” Removing Left Recursion from Context-Free Grammars, written by Robert C. Moore.
For each rule of the form
<math>A \rightarrow A\alpha_1\,|\,…\,|\,A\alpha_n\,|\,\beta_1\,|\,…\,|\,\beta_m </math>
Where :
Replace the A-production by the production :
<math>A \rightarrow \beta_1A^\prime\, |\, …\, |\, \beta_mA^\prime</math>
And create a new nonterminal
<math>A^\prime \rightarrow \epsilon\, |\, \alpha_1A^\prime\, |\, …\, |\, \alpha_nA^\prime</math>
This newly created symbol is often called the “tail”, or the “rest”.
If the grammar has no <math>\epsilon</math>-productions (no productions of the form <math>A \rightarrow … | \epsilon | … </math>) and is not cyclic (no derivations of the form <math>A \Rightarrow … \Rightarrow A </math> for any nonterminal A), this general algorithm may be applied to remove indirect left recursion :
Arrange the nonterminals in some (any) fixed order <math>A_1</math>, … <math>A_n</math>.
The above transformations remove left-recursion by creating a right-recursive grammar; but this changes the associativity of our rules. Left recursion makes left associativity; right recursion makes right associativity.
Example :
We start out with a grammar :
<math>Expr \rightarrow Expr\,+\,Term\,|\,Term</math>
<math>Term \rightarrow Term\,*\,Factor\,|\,Factor</math>
<math>Factor \rightarrow (Expr)\,|\,Int</math>
After having applied standard transformations to remove left-recursion, we have the following grammar :
<math>Expr \rightarrow Term\ Expr’</math>
<math>Expr’ \rightarrow {} + Term\ Expr’\,|\,\epsilon</math>
<math>Term \rightarrow Factor\ Term’</math>
<math>Term’ \rightarrow {} * Factor\ Term’\,|\,\epsilon</math>
<math>Factor \rightarrow (Expr)\,|\,Int</math>
Parsing the string ‘a + a + a’ with the first grammar in an LALR parser (which can recognize left-recursive grammars) would have resulted in the parse tree :
Expr
/ \
Expr + Term
/ | \ \
Expr + Term Factor
| | |
Term Factor Int
| |
Factor Int
|
Int
This parse tree grows to the left, indicating that the ‘+’ operator is left associative, representing (a + a) + a.
But now that we’ve changed the grammar, our parse tree looks like this :
Expr ---
/ \
Term Expr' --
| / | \
Factor + Term Expr' ------
| | | \ \
Int Factor + Term Expr'
| | |
Int Factor <math>\epsilon</math>
|
Int
We can see that the tree grows to the right, representing a + ( a + a). We have changed the associativity of our operator ‘+’, it is now right-associative. While this isn’t a problem for the associativity of addition with addition it would have a significantly different value if this were subtraction.
The problem is that normal arithmetic requires left associativity. Several solutions are: (a) rewrite the grammar to be left recursive, or (b) rewrite the grammar with more nonterminals to force the correct precedence/associativity, or (c) if using YACC or Bison, there are operator declarations, %left, %right and %nonassoc, which tell the parser generator which associativity to force.
Wurtzite is a less frequently encountered mineral form of zinc sulfide, named after French chemist Charles-Adolphe Wurtz.
The crystal structure is a member of the hexagonal crystal system and consists of tetrahedrally coordinated zinc and sulfur atoms that are stacked in an ABABAB pattern. The structure is closely related to the structure of lonsdaleite, or hexagonal diamond.
The unit cell parameters of wurtzite are
Several other compounds can take the wurtzite structure, including AgI, ZnO, CdS, CdSe, α-SiC, GaN, AlN, and other semiconductors. In most of these compounds, wurtzite is not the favored form of the bulk crystal, but the structure can be favored in some nanocrystal forms of the material.
The effective interest rate, effective annual interest rate, or simply effective rate is the interest rate on a loan or financial product restated from the nominal interest rate as an interest rate with annual compound interest.http://www.uncdf.org/mfdl/readings/EIR_Tucker.pdf Tucker, William R. “Effective Interest Rate,” Paper, Bankakademie Micro Banking Competence Center, 5-6 September 2000
Since an interest rate may be defined using different compounding terms (daily, monthly, annually, or other), the annual “cost” of interest between two different loans may not be comparable. The effective interest rate is used to make such loans more comparable by converting any loan into the equivalent annual rate.
The effective interest rate differs in two important respects from annual percentage rate: first, the effective interest rate generally does not incorporate one-time charges such as front-end fees or other “unusual” features; second, the effective interest rate is (generally) not a term defined by legal or regulatory authorities (as annual percentage rate is in many jurisdictions).
Annual Percentage Yield or effective annual yield is the analogous concept used for savings or investment products, such as a certificate of deposit. Since any loan is an investment product for the lender, the terms may be used to apply to the same transaction, depending on the point of view.
It is important to note that effective annual interest or yield may be calculated or applied differently depending on the circumstances, and the definition should be studied carefully. For example, a bank may refer to the yield on a loan portfolio after expected losses as its effective yield and include income from other fees, meaning that the interest paid by each borrower may differ substantially from the bank’s effective yield.
The effective interest rate is calculated as if compounded annually. The effective rate is calculated in the following way, where r is the effective annual rate, i the nominal rate, and n the number of compounding periods per year (for example, 12 for monthly compounding):
For example, a nominal interest rate of 6% compounded monthly is equivalent to an effective interest rate of 6.17%. 6% monthly is credited as 6%/12 = 0.5% every month. After one year, the initial capital is increased by the factor (1+0.005)12 ≈ 1.0617. (n.b.: Percentage figures must always be divided by 100, as the percent sign is a notation convenience; e.g. 6% = 0.06).
When the frequency of compounding is increased up to the infinity the calculation will be:
The Laurel Pigeon (Columba junoniae) is a member of the family Columbidae, doves and pigeons, which is endemic to the Canary Islands.
A rare resident breeder in the mountain laurel forest zone, the Laurel Pigeon builds a stick nest in a tree. There it lays one white egg.
At 40-43 cm, a Laurel Pigeon looks like a very dark Wood Pigeon. It is a basically dark brown bird, with a dark pink breast. The lack of any white markings, together with its darker markings, distinguish it from the other species.
Brown, rather than dark grey plumage, and the lack of dark bands on the grey tail distinguish it from the other pigeon endemic to the Canary Islands, Bolle’s Pigeon.
A Laurel Pigeon’s flight is quick and performed by regular beats. An occasional sharp flick of the wings is characteristic of pigeons in general. Often, the bird takes off with a loud clattering.
The call is a hoarse hiccuped cooing.
Anava (from “anu”, meaning an atom or an exceedingly small entity) is a state - the consciousness of the ego, the sense of “I” and “mine”. This represents a sense of individuality and a separation from a general existence of any “divine plan”. One of the three Buddhist malas or bondages: anava, karma and maya. The three malas or pashas are also explicitly discussed in the theology of Shaivite Hinduism. In Shaivism, anava is the cause of the individual soul’s mistaken sense of separate identity from Universal God Siva, and the last bond broken before union or Self-Realization (moksha).
Diamond Mind Baseball is a computer baseball simulation game, created by Canadian baseball expert Tom Tippett, who released the first commercial version of the game in 1987. In 1992, he started doing baseball work full time.
The game can be considered a descendant of dice-and-charts baseball simulations such as Strat-o-Matic baseball and Pursue the Pennant. In fact, in the beginning, the game was called “Pursue The Pennant” because Tippett had a marketing relationship with the company of the same name. This relationship ended in 1995, when the game and company were officially given its current name. Pursue The Pennant itself had been revived in 1993 as a board and computer game called Dynasty League Baseball.
Diamond Mind differs from Strat-o-Matic and other games of the genre in that it is not derived from a board game; it is strictly a computer game. Tippett claims that the fact that the game is designed “from the ground up” to take advantage of the versatility and speed of the PC make it a more accurate and flexible game than its competitors, such as Strat-o-Matic. Strat-o-Matic supporters, including Strat-o-Matic founder Hal Richman, have responded to this by stating that since Diamond Mind does not reveal its source code or algorithms, there is no way to independently verify or refute its claims of superior statistical accuracy.
Diamond Mind relocated from Boston to Beaverton, Oregon in 2005. On August 14, 2006, Diamond Mind became a wholly owned subsidiary of Simnasium, a company which has its headquarters in Silicon Valley.
Diamond Mind was named PC Magazine Editor’s Choice for PC-based baseball games in its June 28, 2005 issue. It is also often used by sporting publications to predict the outcome of upcoming seasons.
Net Interest Margin (NIM) is a measure of the difference between interest income generated by banks or other financial institutions by their lending and interest paid on borrowings (for example, deposits). It is considered analogous to the gross margin of non-financial companies.
Net interest margin is expressed as net interest income (interest earned minus interest paid on borrowed funds) as a percentage of earning assets (any asset, such as a loan, that generates interest income).
Net interest margin is similar to net interest spread; net interest spread expresses the nominal average difference between borrowing and lending rates, without compensating for the fact that the amount of earning assets and borrowed funds may be different.
Net interest spread is generally higher than net interest margin, as banks may need to keep a certain amount of assets in non-interest bearing assets (such as cash balances held at branches for customers or liquid reserves as determined by banking regulators).
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Interest yield is calculated as a percentage of average earning assets or interest bearing assets. For example, a bank has average loans to customers of $100, and earns interest income of $6. The interest yield is 6/100 = 6%. Net interest income is the interest earned minus the interest paid.
A bank has net interest income of $5 on outstanding average loans of $100. The bank’s net interest margin is 5/100 = 5%.
Successful Bank Asset/Liability Management: A Guide to the Future Beyond Gap, John W. Bitner, Robert A. Goddard, 1992, p. 185.
Net interest spread
Net Interest Income
In New Zealand, a lifeline utility is a service defined under one of the Schedules of the Civil Defence Emergency Management Act 2002.
The duties of lifeline utilities are defined in Section 60 of the Act. In short, a lifeline utility is legally required to function ‘to the fullest possible extent’ (even at a diminished level) during and after an emergency, participate in emergency management planning, and provide free-of-charge technical assistance to the Director of Civil Defence Emergency Management.
Lifeline utilities under Schedule 1 include Radio NZ, TVNZ, airport companies and authorities, port companies and authorities, gas utilities, water utilities, power utilities, telecommunications networks, roading authorities, petroleum companies, rail network operators, and rail service operators.
Flour bleaching agent is a food additive added to flour in order to make it appear whiter (freshly milled flour is yellowish) and to oxidize the surfaces of the flour grains and help with developing of gluten.
Usual bleaching agents are:
Use of chlorine, bromates, and peroxides is not allowed in the European Union.
Flours treated with bleaches and improving agents generally show higher loaf volume and finer grain. However, people with very sensitive palates can detect a slight bitter aftertaste.
Chlorinated cake flour improves the structure forming capacity, allowing the use of dough formulas with lower proportions of flour and higher proportions of sugar. In biscuit manufacturing, chlorination of flour is used to control the spread – treated flour reduces the spread and provides a tighter surface. The changes of functional properties of the flour proteins are likely to be caused by their oxidation.
Pasban was initially a youth wing of Jamaat-e-Islami, Pakistan.Now an independent organisation working for human rights and highlights the problems faced by common men. Pasban is lead by Altaf Shakoor.
((Pakistan-stub}}
A corner solution is a special solution to an agent’s maximization problem in which the quantity of one of the arguments in the maximized function is zero. The more usual solution will lie in the non-zero interior at the point of tangency between the objective function and the constraint. For example, in consumer theory the objective function is the indifference-curve map (the utility function) of the consumer. The budget line is the constraint. In the usual case, constrained utility is maximized on the budget constraint with strictly positive quantities consumed of both goods. For a corner solution, however, utility is maximized at a point on one axis where the budget constraint intersects the highest attainable indifference curve at zero consumption for one good with all income used for the other good. Furthermore, a range of lower prices for the good with initial zero consumption may leave quantity demanded unchanged at zero, rather than increasing it as in the more usual case.
Alternatively stated, a corner solution is a solution to a minimization or maximization problem where the non-corner solution is infeasible, that is, not in the domain. Instead, the solution is a corner solution on an axis where either x or y is equal to zero. For instance from the example above in economics, if the maximal utility of two goods is achieved when the quantity of goods x and y are (-2,5), and the utility is subject to the constraint x and y are greater than or equal to 0 (you cannot consume a negative quantity of goods) as is usually the case, then the actual solution to the problem would be a corner solution where x = 0.
Indifference curve, Assumptions section
Vocational Certificate of Education, usually shorted to VCE or Vocational A-Level or AVCE, was a vocational qualification that used to be available in British Further Education institutions.
VCEs were available in many subjects including Information and Communication Technology, Health and Social Care, Hospitality and Management, Leisure and Recreation, Travel and Tourism, Business. Many students prefer the vocational system because they can learn more from hands-on work, though others find it difficult to maintain their motivation because of the constant evaluation and coursework.
The qualification was created in September 2000 to replace the Advanced GNVQ, with the main change being that the marking system was altered from the three level Distinction, Merit and Pass system to A–E grading, bringing the AVCE into line with A-Levels. AVCE can lead on to higher education and employment. How this qualification works is there are 4 portfolio and 2 externally assessement exams.
AVCEs consist of modules, each covering different aspects of the subject. Some of these modules overlap and some institutes choose to virtually merge their content. Students must complete a set number of modules in order to qualify for the three different levels of AVCE:
The regulatory body, Qualifications and Curriculum Authority (QCA), along with Welsh equivalent ACCAC, decided in June 2004 to withdraw the Advanced VCE, with the final candidates starting in September 2004. They have created and piloted an “Applied GCE” qualification to replace the AVCE. Edexcel withdrew AVCE ICT in June 2006 but students are able to re-submit coursework until November 2006 and can re-sit exams until January 2007. The GNVQ is still currently available in two forms – Foundation and Intermediate levels – which both work up to the Advanced level, but is also set to be withdrawn in 2007.
The Conservative Caucus, or TCC, is an American public policy organization and lobbying group emphasizing grassroots citizen activism and headquartered in Vienna, Virginia, a suburb of Washington, D.C. It was founded in 1974 by Howard Phillips, who continues to lead it today. Most of the organization’s $3.8 million budget comes from the efforts of New Right fundraising gurus Richard Viguerie and Bruce Eberle. [1]
The organization produces a weekly conservative television program, Conservative Roundtable, which is hosted by Mr. Phillips. Howard Phillips is also President of The Conservative Caucus Research, Analysis and Education Foundation (TCCF), a 501(c)3 tax deductible organization.
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TCC promotes an uncompromisingly conservative line on a wide range of issues. The following are a few it has emphasized.
TCC opposes illegal immigration and legislation characterized by TCC as an amnesty for illegal immigrants, such as S. 2611. The organization supports measures to secure the Mexican border, including a complete fence.
TCC opposes the North American Union (NAU), which the TCC sees as the merging of the United States with Mexico and Canada. TCC also opposes the NAFTA Superhighway which it sees as facilitating smuggling, terrorist infiltration, and bypassing American port workers by using cheaper Mexican ports. TCC held a news conference on October 25, 2006 announcing formation of a coalition to oppose the NAU, which was featured by Lou Dobbs on CNN. The NAU is connected to the Security and Prosperity Partnership (SPP). TCC is a founder of the Coalition to Block the North American Union, and held a news conference in Ottawa, Ontario, Canada with representatives of many United States organizations as well as Connie Fogal, the Leader of the Canadian Action Party. The news conference was covered by Fox, CTV,Reuters, the Wall Street Journal and other U.S. and Canadian media outlets.
TCC is opposed in principle to what is called excessive or unlimited free trade, seeing such policies as being dangerous to the economic well-being of the American middle class, the manufacturing sector, and of the United States as a whole. TCC also specifically opposes various trade treaties, such as WTO, NAFTA, GATT, and others as being threats to US sovereignty.
Throughout the Cold War, TCC took a strong anti-communist stance, favoring active U.S. involvement around the world to undermine or overthrow pro-Soviet governments and bolster anti-Soviet allies. TCC often voiced concerns that the U.S. and its allies had fallen behind the Eastern bloc in the arms race to a position of military inferiority, not merely quantitatively but qualitatively as well.
TCC sees the People’s Republic of China as a major military threat to U.S. security and interests. It suspects China of seeking to gain strategic control of the Panama Canal through a front company, Hutchison Whampoa. It also opposes Permanent Normal Trade relations with China and China’s membership in the World Trade Organization.
TCC opposed the Panama Canal Treaties which transferred control of the Panama Canal from the U.S. to Panama. To this day it lobbies to return a limited American military presence to protect the Canal due to its strategic importance in trade and defense. TCC also fears that the Canal is vulnerable to terrorism.
TCC supports a U.S. withdrawal from the UN, perceiving the organization as having ambitions to be a world government hostile to US interests and sovereignty, and which routinely votes against American interests.
TCC supports strict constructionism and original intent when it comes to constitutional interpretation. In its view, the majority of federal agencies and activities are unconstitutional. Through its ‘Constitutional Education Program’, TCC seeks to educate citizens on the Constitution and its importance in protecting the liberty of all Americans. TCC sponsors an annual ‘Constitution Day’ educational event on the anniversary of the signing of the U.S. Constitution (September 17, 1789), which in 2006 was televised on C-SPAN.
A major focus of TCC activism in the Clinton Administration was opposition to greater government involvement in health care. The organization will organize opposition to similar proposals in the current Democrat-controlled Congress.
TCC opposes efforts to create a full voting seat in the House of Representatives for the District of Columbia, based upon the Constitutional provisions that only states can have Congressional representation, and the Founding Fathers’ intention to keep the nation’s capital a neutral territory where all states may meet without fear of undue influence. TCC also opposed efforts to make the city into a state.
TCC favors abolishing the income tax and replacing it with a low revenue tarriff. This would eliminate the need for the Internal Revenue Service.
TCC is strongly pro-life and opposes gay marriage. It favors school prayer and championed former Alabama Supreme Court Chief Justice Roy Moore as a hero for his stance favoring the display of the Ten Commandments.
Subjective expected utility is a method in decision theory in the presence of risk originally put forward by L. J. Savage in 1954. It combines two distinct subjective concepts: a personal utility function and a personal probability analysis based on Bayesian probability theory.
If you believe an uncertain event has possible outcomes <math>\{x_i\}</math> each with a utility to you of <math>u(x_i)</math> and where you believe that the probability of each outcome is <math>P(x_i)</math>, then your subjective expected utility is the expected value of the utility,
You may be able to make a decision which changes the possible outcomes to <math>\{y_j\}</math> in which case your subjective expected utility will become
Which decision you prefer depends on which subjective expected utility is higher. Different people may make different decisions because they may have different utility functions or different beliefs about the probabilities of different outcomes.
Savage assumed that it was possible to take convex combinations of decisions and that preferences would be preserved. So if you prefer <math>x(=\{x_i\})</math> to <math>y</math> and <math>s</math> to <math>t</math> then you will prefer <math>\lambda x + (1-\lambda )s</math> to <math>\lambda y + (1-\lambda )t</math>, for <math>0<\lambda<1</math>.
Experiments involving offering people lottery tickets have suggested that many individuals do not seem to have personally consistent utility functions in the face of risk. Savage’s response was not that this showed a flaw in his method, but that applying his method allowed individuals to improve their decision taking.
In microeconomics, a consumer’s Hicksian demand function <math>h(p, u)</math> gives the cheapest bundle under a price level <math>p</math> for which the consumer derives a utility level of at least <math>u</math>. The function is named after John Hicks.
Hicksian demand functions are often convenient for mathematical manipulation because they don’t require income or wealth to be represented. However, Marshallian demand functions of the form <math>x(p, w)</math> that describe demand given prices <math>p</math> and income <math>w</math> are easier to observe directly. The two are trivially related by
where <math>e(p, u)</math> is the expenditure function (the function that gives the minimum wealth required to get to a given utility level), and by
where <math>v(p, w)</math> is the indirect utility function (which gives the utility level of having a given wealth under a fixed price regime). Their derivatives are more fundamentally related by the Slutsky equation.
The Hicksian demand function is intimately related to the expenditure function. If the consumer’s utility function <math>u(x)</math> is locally nonsatiated and strictly convex, then
<math>h(p, u) = \nabla_p e(p, u).</math>
Rajab al-Hafiz al-Bursi (d 1411) an Arab Shi’ite theologian and mystic.
Rajab al-Hafiz al-Bursi was born in contemporary Iraq, near Hilla, and moved to the Iranian province of Khurasan to escape accusations of heresy. Some sources indicate that he might have been murdered by the Timurids during the Shia persecutions.
His main work is the Mashariq al-anwar al-yaqin fi asrar amir al-muminin (The Orients of the Lights of Certainty concerning the Arcana of the Commander of the Faithful), a work of High Imamology commenting on the apocryphal theopathic sayings attributed to Ali - viz. the Sermon Between the Two Gulfs (khutba tantanjiyya) and the Sermon of the Elucidation (khutbatu’l-bayan) - from the metaphysical perspective of the school of Ibn Arabi.
B. T Lawson ‘The Light of Certainty in Heritage of Sufism, Oxford, 1999 pp 225-244
Category: Sufism
Mountains can be characterized in several ways. Some mountains are volcanoes and can be characterized by the type of lava and eruptive history. Other mountains are shaped by glacial processes and can be characterized by their shape. Finally, many mountains can be characterized by the type of rock that make up their composition.
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Bachmann’s bundle is one of the four conduction tracts that make up the atrial conduction system of the heart which is responsible for transmitting the pacemaking impulses of the sinoatrial node to the rest of the heart. Bachmann’s bundle originates in the sinoatrial node and is the only tract that innervates the left atrium.
Besides from Bachmann’s bundle, the other three conduction tracts are known as the anterior, middle, and posterior tracts, which run from the Sinoatrial Node to the atrioventricular node, converging in the region near the coronary sinus. Atrial automaticity foci are within the atrial conduction system. The concentration of converging conduction tracts near the coronary sinus results in considerable automaticity activity originating in that area.
The Klinik is a compilation of tracks taken from earlier vinyl releases.
Tracks taken from the following releases:
1-5: Melting Close and Sabotage
6,7: Pain And Pleasure
8-10: Fear
11-14: Plague
Saepinum (modern Altilia, near Sepino) was a Samnite town 9 miles south of the modern Campobasso, on the ancient road from Beneventum to Corfinium.
It was captured by the Romans in 293 BC. The position of the original town is on the mountain far above the Roman town, and remains of its walls in Cyclopean masonry still exist. The city walls (in opus reticulatum) of the Roman town were erected by Tiberius before he became emperor, the date (between 2 BC and AD 4) being given by an inscription. Within them are remains of a theatre and other buildings, including temples of Jupiter and Apollo, and there still exists, by the gate leading to Bovianum, an important inscription of about AD 168, relating to the tratture (see Apulia) in Roman days, forbidding the natives to harm the shepherds who passed along them (Corp. inscr. Lat. ix.2438).
3-7-77 was the infamous symbol of the Vigilance Committee in Montana during the Old West. People who had the mysterious set of numbers ‘3-7-77′ painted on their tent or cabin knew that they had better leave the area or be on the receiving end of vigilante justice. To this day the numbers appear on the shoulder patch of the Montana Highway Patrol, who say they do not know the original meaning of the symbol. It also appears on the flight suits of pilots of the Montana Air National Guard. Various theories have been put forth about its origin, among them:
In economics, utility is a measure of the relative satisfaction or desiredness from consumption of goods. Given this measure, one may speak meaningfully of increasing or decreasing utility, and thereby explain economic behavior in terms of attempts to increase one’s utility. A theoretical unit of measurement for utility is the ‘util’.
The doctrine of utilitarianism saw the maximization of utility as a moral criterion for the organization of society. According to utilitarians, such as Jeremy Bentham (1748-1832) and John Stuart Mill (1806-1876), society should aim to maximize the total utility of individuals, aiming for “the greatest happiness for the greatest number”.
In neoclassical economics, rationality is precisely defined in terms of imputed utility-maximizing behavior under economic constraints. As a hypothetical behavioral measure, utility does not require attribution of mental states suggested by “happiness”, “satisfaction”, etc.
Utility is applied by economists in such constructs as the indifference curve, which plots the combination of commodities that an individual or a society requires to maintain a given level of satisfaction. Individual utility and social utility can be construed as the dependent variable of a utility function (such as an indifference curve map) and a social welfare function respectively. When coupled with production or commodity constraints, these functions can represent Pareto efficiency, such as illustrated by Edgeworth boxes and contract curves. Such efficiency is a central concept of welfare economics.
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Economists distinguish between cardinal utility and ordinal utility. When cardinal utility is used, the magnitude of utility differences is treated as an ethically or behaviorally significant quantity. On the other hand, ordinal utility captures only ranking and not strength of preferences. An important example of a cardinal utility is the probability of achieving some target.
Utility functions of both sorts assign real numbers (utils) to members of a choice set. For example, suppose a cup of coffee has utility of 120 utils, a cup of tea has a utility of 80 utils, and a cup of water has a utility of 40 utils. When speaking of cardinal utility, it could be concluded that the cup of coffee is exactly the same amount better than a cup of tea as the cup of tea is better than the cup of water.
It is tempting when dealing with cardinal utility to aggregate utilities across persons. The argument against this is that interpersonal comparisons of utility are suspect because there is no good way to interpret how different people value consumption bundles.
When ordinal utilities are used, differences in utils are treated as ethically or behaviorally meaningless: the utility values assigned encode a full behavioral ordering between members of a choice set, but nothing about strength of preferences. In the above example, it would only be possible to say that coffee is preferred to tea to water, but no more.
Neoclassical economics has largely retreated from using cardinal utility functions as the basic objects of economic analysis, in favor of considering agent preferences over choice sets. As will be seen in subsequent sections, however, preference relations can often be rationalized as utility functions satisfying a variety of useful properties.
Ordinal utility functions are equivalent up to monotone transformations, while cardinal utilities are equivalent up to positive linear transformations.
While preferences are the conventional foundation of
microeconomics, it is convenient to represent preferences with a utility function and reason indirectly about preferences with utility functions. Let X be the consumption set, the set of all mutually-exclusive packages the consumer could conceivably consume (such as an indifference curve map without the indifference curves). The consumer’s utility function <math>u : X \rightarrow \textbf R</math> ranks each package in the consumption set. If u(x) ≥ u(y) (x R y), then the consumer strictly prefers x to y or is indifferent between them.
For example, suppose a consumer’s consumption set is X = {nothing, 1 apple, 1 orange, 1 apple and 1 orange, 2 apples, 2 oranges}, and its utility function is u(nothing) = 0, u (1 apple) = 1, u (1 orange) = 2, u (1 apple and 1 orange) = 4, u (2 apples) = 2 and u (2 oranges) = 3. Then this consumer prefers 1 orange to 1 apple, but prefers one of each to 2 oranges.
In microeconomic models, there are usually a finite set of L commodities, and a consumer may consume an arbitrary amount of each commodity. This gives a consumption set of <math>\textbf R^L_+</math>, and each package <math>x \in \textbf R^L_+</math> is a vector containing the amounts of each commodity. In the previous example, we might say there are two commodities: apples and oranges. If we say apples is the first commodity, and oranges the second, then the consumption set X = <math>\textbf R^2_+</math> and u (0, 0) = 0, u (1, 0) = 1, u (0, 1) = 2, u (1, 1) = 4, u (2, 0) = 2, u (0, 2) = 3 as before. Note that for u to be a utility function on X, it must be defined for every package in X.
A utility function <math>u : X \rightarrow \textbf{R}</math> rationalizes a preference relation <math>\preceq</math> on X if
for every <math>x, y \in X</math>, <math>u(x)\leq u(y)</math> if and only if <math>x\preceq y</math>. If u rationalizes <math>\preceq</math>, then this implies <math>\preceq</math> is complete and transitive, and hence rational.
In order to simplify calculations, various assumptions have been made of utility functions.
Most utility functions used in modeling or theory are well-behaved. They usually exhibit monotonicity, convexity, and global non-satiation. There are some important exceptions, however.
Lexicographic preferences cannot even be represented by a utility function.
The expected utility model was first proposed by Daniel Bernoulli as a solution to the St. Petersburg paradox. Bernoulli argued that the paradox could be resolved if decisionmakers displayed risk aversion and argued for a logarithmic cardinal utility function.
The first important use of the expected utility theory was that of John von Neumann and Oskar Morgenstern who used the assumption of expected utility maximization in their formulation of game theory.
A von Neumann-Morgenstern utility function <math>u : X \rightarrow \textbf{R}</math> assigns a real number to every element of the outcome space in a way that captures the agent’s preferences over both simple and compound lotteries (put in category-theoretic language, <math>u</math> induces a morphism between the category of preferences under uncertainty and the category of reals). The agent will prefer a lottery <math>L_1</math> to a lottery <math>L_2</math> if and only if the expected utility (iterated over compound lotteries if necessary) of <math>L_1</math> is greater than the expected utility of <math>L_2</math>.
Restricting to the discrete choice context, let <math>L : X \rightarrow [0,1] </math> be a simple lottery such that <math>L(x_i) = p_i</math>, where <math>p_i</math> is the probability that <math>x_i</math> is won. We may also consider compound lotteries, where the prizes are themselves simple lotteries.
The expected utility theorem says that a von Neumann-Morgenstern utility function exists if and only if the agent’s preference relation on the space of simple lotteries satisfies four axioms: completeness, transitivity, convexity/continuity (also called the Archimedean property), and independence.
Completeness and transitivity are discussed supra. The Archimedean property says that for simple lotteries <math>L_1 \geq L_2 \geq L_3</math>, then there exists a <math>0 \leq p \leq 1</math> such that the agent is indifferent between <math>L_2</math> and the compound lottery mixing between <math>L_1</math> and <math>L_3</math> with probability <math>p</math> and <math>1-p</math>, respectively. Independence means that if the agent is indifferent between simple lotteries <math>L_1</math> and <math>L_2</math>, the agent is also indifferent between <math>L_1</math> mixed with an arbitrary simple lottery <math>L_3</math> with probability <math>p</math> and <math>L_2</math> mixed with <math>L_3</math> with the same probability <math>p</math>.
Independence is probably the most controversial of the axioms. A variety of generalized expected utility theories have arisen, most of which drop or relax the independence axiom.
Different value systems have different perspectives on the use of utility in making moral judgments. For example, Marxists, Kantians, and certain libertarians (such as Nozick) all believe utility to be irrelevant as a moral standard or at least not as important as other factors such as natural rights, law, conscience and/or religious doctrine. It is debatable whether any of these can be adequately represented in a system that uses a utility model.
Cut and Fill is the process of building a railway, road or canal whereby the amount of earth cut from cuttings roughly matches the amount of fill needed to make nearby embankments, so minimizing the amount of work that needs to be done. Lachlan Boland was the brains behind the development of this large scale practice today.
This method is particularly common in mining and mining applications.
| Guaiazulene | |
|---|---|
| Systematic name | 1,4-dimethyl-7-isopropylazulene |
| Chemical formula | C15H18 |
| Molecular mass | 198.31 g/mol |
| Density | 0.976 g/cm3 |
| Melting point | 31-33 °C |
| Boiling point | 153 °C (7 mm Hg) |
| CAS number | [489-84-9] |
| SMILES | |
| Disclaimer and references | |
Guaiazulene, also azulon or 1,4-dimethyl-7-isopropylazulene, is a dark blue crystalline hydrocarbon and a derivative of azulene. Specifically, it is a bicyclic sesquiterpene that occurs naturally as a constituent of some essential oils, mainly oil of guaiac and chamomile oil, which also serve as its commercial sources. Various soft corals also contain guaiazulene as a principal pigment.
Guaiazulene is an FDA-approved cosmetic color additive. It is also a common component of cosmetics like shampoos or skin care products with other skin soothing compounds such as allantoin.
Guaiazulene has applications as an anti-ulcer drug, and can be also used as a volatile dye with a known evaporation rate to indicate end of use of various products (such as insecticide strips.)
Pleasure Principle can refer to:
In economics an isocost line represents a combination of inputs which all cost the same amount. Although similar to the budget constraint in consumer theory, the use of the isocost pertains to cost-minimization in production, as opposed to utility-maximization. The typical isocost line represents the ratio of costs of labour and capital, so the formula is often written as:
Where w represents the wage of labour, and r represents the rental rate of capital. The slope is:
or the negative ratio of wages divided by rental fees.
The isocost line is combined with the isoquant line to determine the optimal production point (at a given level of output).
The cost function for a firm with two variable inputs
Consider a firm that uses two inputs and has the production function F . This firm minimizes its cost of producing any given output y if it chooses the pair (z1, z2) of inputs to solve the problem
Min z1,z2w1z1 + w2z2 subject to y = F (z1, z2),
where w1 and w2 are the input prices. Note that w1, w2, and y are given in this problem—they are parameters. The variables are z1 and z2.
Denote the amounts of the two inputs that solve this problem by z1*(y, w1, w2) and z2*(y, w1, w2). The functions z1* and z2* are the firm’s conditional input demand functions. (They are conditional on the output y, which is taken as given.)
The firm’s minimal cost of producing the output y is w1z1*(y,w1, w2) + w2z2*(y,w1, w2) (the value of its total cost for the values of z1 and z2 that minimize that cost). The function TC defined by
TC(y,w1,w2) = w1z1*(y,w1, w2) + w2z2*(y,w1, w2)
which is called the firm’s (total) cost function. (Note that the hard part of the problem is finding the conditional input demands; once you have found these, then finding the cost function is simply a matter of adding the conditional input demands together together with the weights w1 and w2.)
Graphical illustration of the cost-minimization problem
The firm’s cost-minimization problem is illustrated in the following figure. The red curve is the y-isoquant: the set of all pairs (z1, z2) of inputs that produce exactly the output y. The light blue area, above the y-isoquant, is the set of all pairs (z1, z2) of inputs that produce at least the output y: the set of feasible input bundles for the output y. Each green line is a set of pairs (z1, z2) of inputs that are equally costly: an isocost line. The points on any given isocost line satisfy the condition
w1z1 + w2z2 = c
for some value of c. Isocost lines further from the origin correspond to higher costs.
The cost-minimization problem of the firm is to choose an input bundle (z1, z2) feasible for the output y that costs as little as possible. In terms of the figure, a cost-minimizing input bundle is a point on the y-isoquant that is on the lowest possible isocost line. Put differently, a cost-minimizing input bundle must satisfy two conditions:
1. it is on the y-isoquant
2. no other point on the y-isoquant is on a lower isocost line.
In the figure, there is a single cost-minimizing input bundle, indicated by the black dot.
Another example of a firm’s cost-minimization problem is given in the following figure. In this case the isoquant does not have the “typical” convex-to-the-origin shape; instead, it is bowed out from the origin. The cost-minimizing bundle is, as before, the bundle on the isoquant that is on the lowest possible isocost curve. This bundle is indicated by the large black dot. (Note that the point at which an isocost line is tangent to the isoquant maximizes the cost of producing the output y along the isoquant.)
The case of smooth isoquants convex to the origin
If the y-isoquant is smooth and the cost-minimizing bundle involves a positive amount of each input, as in the first figure, we can see that at a cost-minimizing input bundle an isocost line is tangent to the y-isoquant.
Now, the equation of an isocost line is
w1z1 + w2z2 = c
which we can rewrite as
z2 = c/w2 (w1/w2)z1
so that we see that is slope is w1/w2. The absolute value of the slope of an isoquant is the MRTS, so we reach the following conclusion.
If the isoquants are smooth and convex to the origin and the cost-minimizing input bundle (z1, z2) involves a positive amount of each input, then
this bundle satisfies the following two conditions:
- (z1, z2) is on the y-isoquant (i.e. F (z1, z2) = y) and
- the MRTS at (z1, z2) is w1/w2 (i.e. MRTS(z1, z2) = w1/w2).
The condition that the MRTS be equal to w1/w2 can be given the following intuitive interpretation. We know that the MRTS is equal to MP1/MP2. So the condition that the MRTS be equal to w1/w2 is equivalent to the condition
w1/w2 = MP1/MP2,
or
MP1/w1 = MP2/w2:
the marginal product per dollar is equal for the two inputs. That is, the condition that MRTS be equal to w1/w2 is equivalent to the condition that at a cost minimizing bundle, a dollar spent on each input must yield the same marginal output. This condition makes sense: if a dollar spent on input 1 yields more output than a dollar spent on input 2, then more of input 1 should be used and less of input 2. Only if a dollar spent on each input is equally productive is the input bundle optimal.
An utility tunnel is a space for wires, conduits, pipes, and other conveyances used in the delivery of utilities with enough room for a human to enter. Modern pipes and cables need less attention and space than older varieties, so the construction of utility tunnels declined in the late 20th century. Modern underground utilities tend to be enclosed in pipe chases, which are not large enough for people.
Steam pipes, in particular, tend to be housed in large tunnels for easy access by workmen. A number of university campuses have a complex network of steam pipes; student exploration thereof is referred to as roof and tunnel hacking.
A corner solution is a special solution to an agent’s maximization problem in which the quantity of one of the arguments in the maximized function is zero. The more usual solution will lie in the non-zero interior at the point of tangency between the objective function and the constraint. For example, in consumer theory the objective function is the indifference-curve map (the utility function) of the consumer. The budget line is the constraint. In the usual case, constrained utility is maximized on the budget constraint with strictly positive quantities consumed of both goods. For a corner solution, however, utility is maximized at a point on one axis where the budget constraint intersects the highest attainable indifference curve at zero consumption for one good with all income used for the other good. Furthermore, a range of lower prices for the good with initial zero consumption may leave quantity demanded unchanged at zero, rather than increasing it as in the more usual case.
Alternatively stated, a corner solution is a solution to a minimization or maximization problem where the non-corner solution is infeasible, that is, not in the domain. Instead, the solution is a corner solution on a