Archive for February, 2008

« Previous Entries
Next Entries »

1976 world oil market chronology; prices

Saturday, February 23rd, 2008

Official price of Saudi Light remains at $12.37 per barrel throughout 1976.

  • February: EPCA 3-tier price regulation begins. Small changes in Entitlements Program.
  • April - May: Lebanese civil war causes a drop in Iraq exports through trans-Lebanon pipelines to the Mediterranean.
  • May: OPEC issues press release vowing to “take appropriate measures” to protect OPEC interests in light of protectionist actions by certain countries.
  • September 1: U.S. stripper well oil prices decontrolled.
  • December 14: 640 foot oil tanker Argo Merchant runs aground on the Nantucket Shoals, spilling 7.6 million gallons of No. 6 fuel oil.
  • December: Moderates and OPEC “hawks” disagree on how fast oil prices should rise. Saudi Arabia and United Arab Emirates increase prices by 5 percent, others by 10 percent.

|-
| width=”30%” align=”center” | previous year:
1975 world oil market chronology
| width=”40%” align=”center” | This article is part of the
Chronology of world oil market events (1970-2005)
| width=”30%” align=”center” | following year:
1977 world oil market chronology
|-

Posted in Uncategorized | No Comments »

Glossary of differential geometry and topology; bundle

Saturday, February 23rd, 2008

This is a glossary of terms specific to differential geometry and differential topology.
The following two glossaries are closely related:

  • Glossary of general topology
  • Glossary of Riemannian and metric geometry.

See also:

  • List of differential geometry topics

Words in italics denote a self-reference to this glossary.


A

Atlas


B

Bundle, see fiber bundle.


C

Chart

Cobordism

Codimension. The codimension of a submanifold is the dimension of the ambient space minus the dimension of the submanifold.

Connected sum

Connection

Cotangent bundle, the vector bundle of cotangent spaces on a manifold.

Cotangent space


D

Diffeomorphism. Given two differentiable manifolds
M and N, a bijective map <math>f</math> from M to N is called a diffeomorphism if both <math>f:M\to N</math> and its inverse <math>f^{-1}:N\to M</math> are smooth functions.

Doubling, given a manifold M with boundary, doubling is taking two copies of M and identifying their boundaries.
As the result we get a manifold without boundary.


E

Embedding


F

Fiber. In a fiber bundle, π: E → B the preimage π−1(x) of a point x in the base B is called the fiber over x, often denoted Ex.

Fiber bundle

Frame. A frame at a point of a differentiable manifold M is a basis of the tangent space at the point.

Frame bundle, the principal bundle of frames on a smooth manifold.

Flow


G

Genus


H

Hypersurface. A hypersurface is a submanifold of codimension one.


I

Immersion


L

Lens space. A lens space is a quotient of the 3-sphere (or (2n + 1)-sphere) by a free isometric action of Zk.


M

Manifold. A topological manifold is a locally Euclidean Hausdorff space. (In Wikipedia, a manifold need not be paracompact or second-countable.) A Ck manifold is a differentiable manifold whose chart overlap functions are k times continuously differentiable. A C∞ or smooth manifold is a differentiable manifold whose chart overlap functions are infinitely continuously differentiable.


P

Parallelizable. A smooth manifold is parallelizable if it admits a smooth global frame. This is equivalent to the tangent bundle being trivial.

Principal bundle. A principal bundle is a fiber bundle P → B together with right action on P by a Lie group G that preserves the fibers of P and acts simply transitively on those fibers.

Pullback


S

Section

Submanifold. A submanifold is the image of a smooth embedding of a manifold.

Submersion

Surface, a two-dimensional manifold or submanifold.


T

Tangent bundle, the vector bundle of tangent spaces on a differentiable manifold.

Tangent field, a section of the tangent bundle. Also called a vector field.

Tangent space

Torus

Transversality. Two submanifolds M and N intersect transversally if at each point of intersection p their tangent spaces <math>T_p(M)</math> and <math>T_p(N)</math> generate the whole tangent space at p of the total manifold.

Trivialization


V

Vector bundle, a fiber bundle whose fibers are vector spaces and whose transition functions are linear maps.

Vector field, a section of a vector bundle. More specifically, a vector field can mean a section of the tangent bundle.


W

Whitney sum. A Whitney sum is an analog of the direct product for vector bundles. Given two vector bundles α and β over the same base B their cartesian product is a vector bundle over B ×B. The diagonal map <math>B\to B\times B</math> induces a vector bundle over B called the Whitney sum of these vector bundles and denoted by α⊕β.

Utility maximization problem; utility

Saturday, February 23rd, 2008

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

<math>\textbf R^L_+</math>

has L commodities. If the prices of the L commodities are

<math>p \in \textbf R^L_+</math>

and the consumer’s wealth is w, then the set of all affordable packages, the budget set, is

<math>B(p, w) = \{x \in \textbf R^L_+ : p \cdot x \leq w\}</math>.

The consumer would like to buy the best package of commodities it can afford. If

<math>u : \textbf R^L_+ \rightarrow \textbf R</math>

is the consumer’s utility function, then the consumer’s optimal choices x(p, w) are

<math>x(p, w) = \arg \max_{x^* \in B(p, w)} u(x^*)</math>.

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.


See also

  • Utility function
  • Expenditure minimization problem
  • Profit maximization problem


References

  • Mas-Colell, Andreu; Whinston, Michael; & Green, Jerry (1995). Microeconomic Theory. Oxford: Oxford University Press. ISBN 0-19-507340-1
  • Consumer Theory: The Neoclassical Model and Its Opposite Alternative, by Valentino Piana.

Posted in Uncategorized | No Comments »

Public utility district; utility

Saturday, February 23rd, 2008

A Public Utility District (PUD) is an entity that provides, electricity, natural gas, sewer, waste collection, wholesale telecommunications, water, etc., to the residents of that district. The district is created by a geographical and political body such as a city, county, metropolitan service area (multiple communities joining together for efficiency), etc., for the sole purpose of promoting the development of a designated area by providing a service, such as water and sewer, electricity or gas, to the members, or consumers, of that district. The PUD operates in the same manner as a municipal utility district, but is created by a local government, not a private developer. Normally the districts are nonprofit entities. The general members usually elect a board to run the utility.

Posted in Uncategorized | No Comments »

NCR 53C9x; consume

Saturday, February 23rd, 2008

The NCR 53C9x is a chipset made by the former NCR Corporation for implementing the SCSI protocol. The 53C9x is a low-cost solution and was therefore widely adopted by OEMs in various motherboard and peripheral device designs; however, the chipset lacks many features commonly attributed as beneficial aspects of SCSI interfaces—for example, the 53C9x lacks Direct memory access (DMA) or bus-mastering capability, and therefore drivers for the chipset consume more processor cycles than those for chipsets which implement such features, due to the necessity of programmed IO.

QLogic FAS216 and Emulex ESP100 chips are a drop-in replacement for the NCR 53c94.

A list of systems which include the 53C9x chipset includes:

  • 53c94 - MIPS Magnum
  • 53c94 - DECstations and Turbochannel PMAZ-A card
  • 53c94 - Power Macintosh G3 (often used as a secondary SCSI controller with MESH (Macintosh Enhanced SCSI Hardware) as primary)


External links

  • Am53CF94/Am53CF96 specs

Posted in Uncategorized | No Comments »

Higher order derivative test; w </math>

Saturday, February 23rd, 2008

In mathematics, the higher-order derivative test is used to find maxima, minima, and points of inflexion in an nth degree polynomial’s curve.


The test

Let <math>f</math> be a differentiable function on the interval <math>I</math> and let <math>c</math> be a point on it such that

  1. <math>f’(c)=f(c)=f’(c)=\cdots=f^{(n-1)}(c)=0</math>;
  2. <math>f^{(n)}(c)</math> exists and is non-zero.

Then,

  1. if n is even

    1. <math>f^{(n)}(x)<0 \implies x=c</math> is a point of local maximum
    2. <math>f^{(n)}(x)>0 \implies x=c</math> is a point of local minimum
  2. if n is odd <math>\implies x=c</math> is a point of inflection


See also

  • Extremum
  • First derivative test
  • Second derivative test
  • Saddle point
  • Inflection point
  • Saddle-point method
  • Stationary point

Posted in Uncategorized | No Comments »

Consumer health informatics; consumer

Saturday, February 23rd, 2008

Consumer health informatics is a relatively new discipline and has been defined by Gunther Eysenbach as follows:

Consumer health informatics is the branch of medical informatics that analyses consumers’ needs for information; studies and implements methods of making information accessible to consumers; and models and integrates consumers’ preferences into medical information systems. (Eysenbach 2000)

Contents


Benefits

Consumer health informatics (CHI) provides patients and healthy consumers with the e-health tools, skills and support they need to better manage their health decisions. Examples for CHI tools are Web sites providing self-care information, Internet-based disease management tools, telemedicine, personal health records (PHRs), online support groups, etc. In the age of the Internet, almost any health information system or communication tool has an interface for consumers.

Healthcare providers are turning to consumer health informatics to provide patients not only with health advice but with an opportunity to manage certain aspects of their condition. One of the purposes of the aforementionned PHR is to involve patients in the management of their healthcare. Meanwhile, consumers are themselves looking for resources on the Internet or even starting their own.


References

  • Eysenbach G. Recent Advances: Consumer Health Informatics. BMJ 2000; 320: 1713–16
  • Lewis D, Eysenbach G et al. Consumer Health Informatics. Springer 2005 ISBN 0-387-23991-X)
  • National Library of Medicine.; National Institutes of Health. [WWW] 3RD July 2003. Consumer Health Informatics Research. http://lhncbc.nlm.nih.gov/cgsb/research/chr/ (30TH July 2003).
  • Simpson, Louise.; Robinson, Paul.; e-Clinical Governance. Radcliffe Medical Press (Oxford). 2002.


External links

  • Journal of Medical Internet Research (JMIR) www.jmir.org, publishes consumer health informatics articles related to health on the Internet
  • Biohealthmatics.com
  • Journal of Consumer Health on the Internet


See also

Posted in Uncategorized | No Comments »

Utility player (baseball); utility

Saturday, February 23rd, 2008

In baseball, a utility player is a player who can play several different positions.

In general, each major league baseball team has at least one player who can be described as a utility player. The most famous utility player is probably Pete Rose (though he was not described as such), because during his career, he played left field, right field, center field, third base, second base and finally, first base late in his career. Most professional teams have two types of utility players. There are “utility infielders”, who usually play all of the infield positions (plus occasionally catcher). Utility outfielders, or fourth outfielders, tend to play all three outfield positions as various times. Occasionally, there will be players who perform a combination of the two duties. Utility players tend to be players who come off of the bench, though this isn’t absolute. Often, players who don’t have high prospects to be a major league star will learn additional positions so they can look more attractive to major league clubs as bench talent.

José “The Utilityman” Oquendo is regarded as the most versatile utility player in the modern game, having played every position, including Pitcher.


See also

  • Ramon Santiago
  • Willie Bloomquist
  • Miguel Cairo
  • Chone Figgins
  • Rex Hudler
  • Aubrey Huff
  • Rob Mackowiak
  • Mark McLemore
  • Eli Marrero
  • Josh Phelps
  • Pete Rose
  • Honus Wagner 
Mark Derosa

Organic computer; computing

Friday, February 22nd, 2008

An organic computer may refer to:

  • a wetware computer, a computer made from biological materials
  • organic computing, an emerging computing paradigm where a system and its components and subsystems are well coordinated in a purposeful manner.

Posted in Uncategorized | No Comments »

Generic function; function

Friday, February 22nd, 2008

In certain systems for object-oriented programming such as the Common Lisp Object System and Dylan, a generic function is an entity made up of all methods having the same name.

Generic functions correspond roughly to what Smalltalk calls messages; but when a generic function is called, method dispatch occurs on the basis of all arguments, not just a single privileged one. See under multiple dispatch for more. This is also known as a multimethod.

Another, completely separate definition of generic function is a function that uses parametric polymorphism. This is the definition used when working with a language like OCaml. An example of a generic function is 

id: a->a
let id a = a

which takes an argument of any type and returns something of that same type.

Posted in Uncategorized | 109 Comments »

Working Conditions (Hotels and Restaurants) Convention, 1991; conditions. This

Friday, February 22nd, 2008

Working Conditions (Hotels and Restaurants) Convention, 1991 is an International Labour Organization Convention.

It was established in 1991, with the preamble stating:

Having decided upon the adoption of certain proposals with regard to working conditions in hotels, restaurants and similar establishments,,…


Ratifications

The following countries have ratified this Convention:
Country Date Notes


References

  1. - ILO Convention C172


External links

  • www.ilo.org/ official ILO site.

Posted in Uncategorized | 107 Comments »

Identity of indiscernibles; identical

Friday, February 22nd, 2008

The identity of indiscernibles is an ontological principle which states that two or more objects or entities are identical (are one and the same entity), if and only if they have all their properties in common. That is, entities x and y are identical if and only if any predicate possessed by x is also possessed by y and vice versa.

The principle is also known as Leibniz’s law since a form of it is attributed to the German philosopher Gottfried Wilhelm Leibniz. It is one of his two great metaphysical principles, the other being the principle of sufficient reason. Both are famously used in his arguments with Newton and Clarke in the Leibniz-Clarke correspondence.

Associated with this principle is also the question as to whether it is a logical principle, or merely an empirical principle.

Contents


Identity and indiscernibility

There are two principles here that must be distinguished (two equivalent versions of each are given in the language of the predicate calculus).

  1. The indiscernibility of identicals

    • For any x and y, if x is identical to y, then x and y have all the same properties.

      <math>\forall x \forall y[x=y \rightarrow \forall P(Px \leftrightarrow Py)]</math>
    • For any x and y, if x and y differ with respect to some property, then x is non-identical to y.
      <math>\forall x \forall y[\neg \forall P(Px \leftrightarrow Py) \rightarrow x \neq y]</math>
  2. The identity of indiscernibles
    • For any x and y, if x and y have all the same properties, then x is identical to y.

      <math>\forall x \forall y[\forall P(Px \leftrightarrow Py) \rightarrow x=y]</math>
    • For any x and y, if x is non-identical to y, then x and y differ with respect to some property.
      <math>\forall x \forall y [x \neq y \rightarrow \neg \forall P(Px \leftrightarrow Py)]</math>

Principle 1. is taken to be a logical truth and (for the most part) uncontroversial. Principle 2. is controversial. Max Black famously argued against 2. (see Critique, below).

Note that these are all second-order expressions. Neither of these principles can be expressed in first-order logic.


Controversial applications

One famous application of the identity of indiscernibles was by René Descartes in his Meditations on First Philosophy. Descartes concluded that he could not doubt the existence of himself (the famous cogito ergo sum argument), but that he could doubt the existence of his body. From this he inferred that the person Descartes must not be identical to his body, since one possessed a characteristic that the other did not: namely, it could be known to exist.

This argument is normally rejected by modern philosophers on the grounds that it derives a conclusion about what is true from a premise about what people know. What people know or believe about an entity, they argue, is not really a characteristic of that entity. Numerous counterexamples are given to debunk Descartes’ reasoning via reductio ad absurdum, such as the following argument based on a secret identity:

  1. Entities x and y are identical if and only if any predicate possessed by x is also possessed by y and vice versa.
  2. Clark Kent is Superman’s secret identity; that is, they’re the same person (identical) but people don’t know this fact.
  3. Lois Lane thinks that Clark Kent cannot fly.
  4. Lois Lane thinks that Superman can fly.
  5. Therefore Superman has a property that Clark Kent does not have, namely that Lois Lane thinks that he can fly.
  6. Therefore, Superman is not identical to Clark Kent.
  7. Since in proposition 6 we come to a contradiction with proposition 2, we conclude that at least one of the premises is wrong. Either:
    • Leibniz’s law is wrong; or else
    • A person’s knowledge about x is not a predicate of x, thus undermining Descartes’ argument.


Critique

Max Black has argued against the identity of indiscernibles by counterexample. Notice that to show that the identity of indiscernibles is false, it is sufficient that one provide a model in which there are two distinct (non-identical) things that have all the same properties. He claimed that in the symmetric universe where only two symmetrical spheres exist, the two spheres are two distinct objects, even though they have all the properties in common.


Notes and references

  • Metaphysics an Anthology. eds. J. Kim and E. Sosa, Blackwell Publishing, 1999
  • Lecture notes of Kevin Falvey / UCSB


See also

  • Duck test
  • Elephant test


External links

  • http://www.consciousentities.com/tactics.htm
  • Stanford Encyclopedia of Philosophy entry

Posted in Uncategorized | 110 Comments »

Lamella (zoology); increase in

Friday, February 22nd, 2008

A lamella is a thin plate-like structure, often one amongst many lamellae very close to one another, with open space between. Aside from respiratory organs, they appear in other biological roles including filter feeding, the traction surfaces of geckos, and chloroplast membranes where high permeability is important.

In humans, the precursors of the prepuce during the development of the urinary and reproductive organs are called lamellae.

The microscopic lamellae in bone and nacre are lamellar structures in the materials science sense of the word.

In fish gills there are two types of lamellae, primary and secondary. The primary gill lamellae come out of the interbranchial septum to increase the contact area between the water and the blood capillaries. The secondary gill lamellae are small lamellae that come out of the primary ones and are used to further increase the contact area. Both types of lamellae are used to increase the amount of oxygen intake of the blood.

In birds, the water-feeding ducks and water birds have lamellae in their bills which are miniature ridges, like the ‘teeth of a comb’. They act as a filter when feeding for organisms or plant matter.

Posted in Uncategorized | No Comments »

Blok M; prices

Friday, February 22nd, 2008

Blok M is a business and shopping quarter located in Kebayoran Baru, South Jakarta, Indonesia. The development is less modern than some of the developments near Kota, Central Jakarta and many of the buildings are run down. Still, the area becomes quite crowded daily, and even more so nightly. Much of the popularity of the quarter is due to the prices of goods (which are often low due to the relatively inexpensive property costs for vendors), the night life, and the accessibility of the center, considering it contains one of the largest bus stations in Jakarta.

In the main shopping portion of the quarter (called Blok M mall) one can purchase any variety of goods. The mall is notorious for having low prices but bartering is considered a requirement. Outside of the Blok M mall, there are a couple of western standard malls, Plaza Blok M, and Pasaraya Grande. The Plaza is a standard mall, while Pasaraya Grande is a giant department store run by the government. Its two contiguous buildings include a big food court in the basement and an international standard (with corresponding prices) movie theatre at the top.

Arguably the most popular portion of blok M, and certainly what has given it most of its notoriety is the Pelatehan Road, which is the portion of the quarter that contains the bars and clubs. Many of the bars become extremely crowded at night and are known to stay open extremely late.


External links

  • Blok M homepage

Posted in Uncategorized | No Comments »

Robbie Ribspreader; consume

Friday, February 22nd, 2008


Robbie Ribspreader is the reclusive b-movie screenwriter of such films as Doomed to Consume, She-Demons of the Black Sun, Tender Flesh For Zombie Goddess, and others. His film Purple Glow (directed by Sv Bell) was screened in 2005 at the Fantasia Festival and took first place in the science-fiction category at the 2005 Wreck-Beach Film Festival. He is known throughout the industry as the fastest screenwriter on the underground scene, and has worked with a variety of filmmakers on many different projects simultaneously.

Robbie Ribspreader currently resides at either of his two homes, in Germany and New Orleans.


Films

  • Purple Glow (2005)
  • “The Locksmith” (2005 short film)
  • She-Demons of the Black Sun (2006)
  • Doomed to Consume (2006)
  • Tender Flesh for Zombie Goddess (2006)
  • “Inbred and Undead” (2006, segment from Graveyard Picture Show)
  • Rise of the Ghosts (2007)

Posted in Uncategorized | No Comments »

Service à la française; consume

Friday, February 22nd, 2008

Service à la française is the practice of serving all the dishes of a meal at the same moment.

This style prevailed in the courts of French royalty, for it made the greatest impression for all the delicacies of the kitchen to emerge simultaneously. However, unless the kitchen and staff are enormous in relation to the persons being served, it is impossible for all dishes to be perfectly hot and ready to consume. Furthermore, it is impossible for the diners to consume each dish when it is at its peak. Thus all modern restaurants provide the dishes sequentially, so that they may be enjoyed individually: a style called Service à la russe.

Posted in Uncategorized | No Comments »

Rich Mountain Electric Cooperative; utility

Friday, February 22nd, 2008

Rich Mountain Electric Cooperative is a non-profit rural electric utility cooperative headquartered in Mena, Arkansas, with a district office in Dierks, Arkansas.

The Cooperative serves portions of six counties in the states of Arkansas and Oklahoma, in a territory generally surrounding Mena.

As of September 2005, the Cooperative had more than 1,512 miles of power lines, and serves over 7,600 customers.


External links

  • Rich Mountain Electric Cooperative

Posted in Uncategorized | No Comments »

Esther Peterson; because consumers

Friday, February 22nd, 2008

Esther Eggertsen Peterson (December 9, 1906 - December 20, 1997) was a lifelong consumer and women’s advocate.

She was Assistant Secretary of Labor and Director of the United States Women’s Bureau for President John F. Kennedy, Special Assistant for Consumer Affairs under Presidents Lyndon B. Johnson and Jimmy Carter, Vice President for Consumer Affairs at Giant Food Corporation, and president of the National Consumers League.

She received the Presidential Medal of Freedom in 1981 and was named a delegate the UN as a UNESCO representative in 1993.


External links

  • Consumers Union bio


See also

  • Great Society

Subbundle; bundle

Friday, February 22nd, 2008

In mathematics, a subbundle U of a vector bundle V on a topological space X is a collection of linear subspaces Ux of the fibers Vx of V at x in X, that make up a vector bundle in their own right.

In connection with foliation theory, a subbundle of the tangent bundle of a smooth manifold may be called a distribution (of tangent vectors).

If a set of vector fields Yk span the vector space U, and all Lie commutators [Yi,Yj] are linear combinations of the Yk, then one says that U is an involutive distribution.


See also

  • Frobenius theorem (differential topology)
  • Sub-Riemannian manifold


References

Posted in Uncategorized | No Comments »

Bundle gerbe; bundle

Friday, February 22nd, 2008

In mathematics, a bundle gerbe is a geometrical model of certain 1-gerbes with connection, or equivalently of a 2-class in Deligne cohomology.

Contents


Topology

U(1)-principal bundles over a space M (see circle bundle) are geometrical realizations of 1-classes in Deligne cohomology which consist of 1-form connections) and 2-form curvatures. The topology of a U(1) bundle is classified by its Chern class, which is an arbitrary element of H2(M), the second integral cohomology of M.

Gerbes, or more precisely 1-gerbes, are abstract descriptions of Deligne 2-classes, which each define an element of H3(M), the third integral cohomology of M.


History

Historically the most popular construction of a gerbe is a category-theoretic model featured in Giraud’s theory of gerbes, which are roughly sheaves of groupoids over M.

In 1994 Murray introduced bundle gerbes, which are geometric realizations of 1-gerbes.
For many purposes these are more suitable for calculations than Giraud’s realization, because their construction is entirely within the framework of classical geometry. In fact, as their name suggests, they are fiber bundles. This notion was extended to higher gerbes the following year.in Higher Bundle Gerbes and Cohomology Classes In Gauge Theories by Alan Carey, Michael Murray and Bai-Ling Wang


Relationship with twisted K-theory

In Twisted K-theory and the K-theory of Bundle Gerbes by Peter Bouwknegt, Alan Carey, Varghese Mathai, Michael Murray and Danny Stevenson the authors defined modules of bundle gerbes and used this to define a K-theory for bundle gerbes. They then showed that this K-theory is isomorphic to Rosenberg’s twisted K-theory, and provides an analysis-free construction.

In addition they defined a notion of twisted Chern character which is a characteristic class for an element of twisted K-theory. The twisted Chern character is a differential form that represents a class in the twisted cohomology with respect to the nilpotent operator

d + H,

where d is the ordinary exterior derivative and the twist H is a 3-form. This construction was extended to equivariant K-theory and to holomorphic K-theory by Mathai and Stevenson. in Chern Character in Twisted K-theory: Equivariant and Holomorphic Cases


Relationship with field theory

Bundle gerbes have also appeared in the context of conformal field theories. Gawedzki and Reis have interpreted the Wess-Zumino term in the Wess-Zumino-Witten model (WZW) of string propagation on a group manifold as the connection of a bundle gerbe. Urs Schreiber, Christoph Schweigert and Konrad Waldorf have used this construction to extend WZW models to unoriented surfaces and, more generally, the global Kalb-Ramond coupling to unoriented strings.

More details can be found at the n-Category Café:

  • Bundle Gerbes: General Idea and Definition
  • Bundle Gerbes: Connections and Surface Transport


References

  • Bundle gerbes, by Michael Murray.
  • Nonabelian Bundle Gerbes, their Differential Geometry and Gauge Theory, by Paolo Aschieri, Luigi Cantini and Branislav Jurco.


Notes

Almost flat manifold; preferred bundle

Friday, February 22nd, 2008

In mathematics, a smooth compact manifold M is called almost flat if for any <math>\epsilon>0 </math> there is a Riemannian metric <math>g_\epsilon </math> on M such that <math> \mbox{diam}(M,g_\epsilon)\le 1 </math> and
<math> g_\epsilon </math> is <math>\epsilon</math>-flat, i.e. for sectional curvature of <math> K_{g_\epsilon} </math> we have <math> |K_{g_\epsilon}| < \epsilon</math>.

In fact, given n, there is a positive number <math>\epsilon_n>0 </math> such that if a n-dimensional manifold admits an <math>\epsilon_n</math>-flat metric with diameter <math>\le 1 </math> then it is almost flat.

According to the Gromov—Ruh theorem, M is almost flat if and only if it is infranil. In particular, it is a finite factor of a nilmanifold, i.e. a total space of an oriented circle bundle over an oriented circle bundle over … over a circle.


References

  • M. Gromov, Almost flat manifolds, J. Differential Geom. 13, 231-241, 1978
  • E. A. Ruh, Almost flat manifolds, J. Differential Geom. 17, 1-14, 1982

Posted in Uncategorized | No Comments »

Matthew Walker knot; bundle

Friday, February 22nd, 2008

A Matthew Walker knot is a decorative knot that is used to keep the end of a rope from fraying. It is tied by unraveling the strands of a twisted rope, knotting the strands together, then laying up the strands together again. It may also be tied using several separate cords, in which case it keeps the cords together in a bundle.

It is not specifically known who Matthew Walker was, nor why this knot was named for him. However, early references from the 19th century suggest he may have been a ship’s rigger in the Royal Navy.


How to tie

A Matthew Walker knot is tied in a circular bundle of any number of strands. To tie the knot, the tier takes each strand and forms a loop around the rest of the bundle, then passes the end through the newly-formed loop to form an overhand knot. He then moves to the next strand over, moving around the bundle in the direction he passes the loops. Tying the first strand around the bundle is straightforward, but each subsequent end must be passed through the previously-formed loops in order to contain all of the other strands in its loop. When tightening, it may help to roll the knot along the bundle, especially when using only two strands. The final effect is a spiral knot vaguely resembling a section of a barber’s pole.


External link

  • Matthew Walker knot at Bead & Button Magazine

Posted in Uncategorized | No Comments »

PR (complexity); function

Thursday, February 21st, 2008

PR is the complexity class of all primitive recursive functions – or, equivalently, the set of all formal languages that can be decided by such a function. This includes addition, multiplication, exponentiation, tetration, etc.

The Ackermann function is an example of a function that is not primitive recursive, showing that PR is strictly contained in R.

PR functions can be explicitly enumerated, whereas functions in R cannot be (since otherwise the halting problem would be decidable). That is, PR is a “syntactic” class whereas R is “semantic.”

On the other hand, we can “enumerate” any recursively enumerable set (see also its complexity class RE) by a primitive-recursive function in the following sense: given an input (M, k), where M is a Turing machine and k is an integer, if M halts within k steps then output M; otherwise output nothing. Then the union of the outputs, over all possible inputs (M, k), is exactly the set of M that halt.

PR strictly contains ELEMENTARY.


See also

  • Primitive recursive function

Posted in Uncategorized | No Comments »

Activity-based costing; indirect

Thursday, February 21st, 2008

In a business organization, Activity-based costing (ABC) is a method of allocating costs to products and services. It is generally used as a tool for planning and control. This is a necessary tool for doing value chain analysis.

Contents


Historical development

Traditionally cost accountants had arbitrarily added a broad percentage of expenses onto the direct costs to allow for the indirect costs.

However as the percentages of indirect or overhead costs had risen, this technique became increasingly inaccurate because the indirect costs were not caused equally by all the products. For example, one product might take more time in one expensive machine than another product, but since the amount of direct labor and materials might be the same, the additional cost for the use of the machine would not be recognised when the same broad ‘on-cost’ percentage is added to all products. Consequently, when multiple products share common costs, there is a danger of one product subsidising another.

The concepts of ABC were developed in the manufacturing sector of the United States during the 1970s and 1980s. During this time, the Consortium for Advanced Manufacturing-International, now known simply as CAM-I, provided a formative role for studying and formalizing the principles that have become more formally known as Activity-Based Costing.Consortium for Advanced Manufacturing-International

Robin Cooper and Robert Kaplan, proponent of the Balanced Scorecard, brought notice to these concepts in a number of articles published in Harvard Business Review beginning in 1988. Cooper and Kaplan described ABC as an approach to solve the problems of traditional cost management systems. These traditional costing systems are often unable to determine accurately the actual costs of production and of the costs of related services. Consequently managers were making decisions based on inaccurate data especially where there are multiple products.

Instead of using broad arbitrary percentages to allocate costs, ABC seeks to identify cause and effect relationships to objectively assign costs. Once costs of the activities have been identified, the cost of each activity is attributed to each product to the extent that the product uses the activity. In this way ABC often identifies areas of high overhead costs per unit and so directs attention to finding ways to reduce the costs or to charge more for costly products.

Activity-based costing was first clearly defined in 1987 by Robert S. Kaplan and W. Bruns as a chapter in their book Accounting and Management: A Field Study Perspective.Kaplan, Robert S. and Bruns, W. Accounting and Management: A Field Study Perspective (Harvard Business School Press, 1987) ISBN 0-87584-186-4 They initially focused on manufacturing industry where increasing technology and productivity improvements have reduced the relative proportion of the direct costs of labor and materials, but have increased relative proportion of indirect costs. For example, increased automation has reduced labor, which is a direct cost, but has increased depreciation, which is an indirect cost.

Like manufacturing industries, financial institutions also have diverse products which can cause cross-product subsidies. Since personnel expenses represent the largest single component of non-interest expense in financial institutions, these costs must also be attributed more accurately to products and customers. Activity based costing, even though developed for manufacturing, can therefore be a useful tool for doing this.Sapp, Richard, David Crawford and Steven Rebishcke “Article title?” Journal of Bank Cost and Management Accounting (Volume 3, Number 2), 1990.Author(s)? “Article title?” Journal of Bank Cost and Management Accounting (Volume 4, Number 1), 1991.


Methodology

  • Cost center
  • Cost allocation
  • Fixed cost
  • Variable cost
  • Cost driver

Direct labor and materials are relatively easy to trace directly to products, but it is more difficult to directly allocate indirect costs to products. Where products use common resources differently, some sort of weighting is needed in the cost allocation process. The measure of the use of a shared activity by each of the products is known as the cost driver. For example, the cost of the activity of bank tellers can be ascribed to each product by measuring how long each product’s transactions takes at the counter and then by measuring the number of each type of transaction.


Limitations

Even in activity-based costing, some overhead costs are difficult to assign to products and customers, for example the chief executive’s salary. These costs are termed ‘business sustaining’ and are not assigned to products and customers because there is no meaningful method. This lump of unallocated overhead costs must nevertheless be met by contributions from each of the products, but it is not as large as the overhead costs before ABC is employed.

Although some may argue that costs untraceable to activities should be “arbitrarily allocated” to products, it is important to realize that the only purpose of ABC is to provide information to management. Therefore, there is no reason to assign any cost in an arbitrary manner.


References


External links

  • Who Wins in a Dynamic World: Theory of Constraints Vs. Activity-Based Costing? article on SSRN

Posted in Uncategorized | No Comments »

Yugoslavia national under-21 football team; A qualification introduced

Thursday, February 21st, 2008

The Yugoslavia national under-21 football team existed in the Socialist Federal Republic of Yugoslavia. (For the team under the Federal Republic of Yugoslavia (from 1992-2003) see Serbia and Montenegro national football team.)

Following the realignment of UEFA’s youth competitions in 1976, Yugoslavia’s Under-21 team was formed. The team had a varied record, reaching the last four in four tournaments and failing to qualify for four. Yugoslavia won the inaugural competition in 1978. Since the under-21 competition rules insist that players must be 21 or under at the start ot a two year competition, technically it is an U-23 competition. Yugoslavia’s record in U-23 competitions is also shown.

Contents


UEFA U-23 Championship Record

Yugoslavia were randomly chosen to play holders Bulgaria for the title, which they won. They then faced (and beat) other randomly-chosen teams until the competition was abandoned in summer 1970 for a larger competition.

  • October 26, 1968: Bulgaria 1-2 Yugoslavia
  • June 6, 1969: Yugoslavia 3-0 Spain
  • November 6, 1969: Yugoslavia 2-0 Sweden
  • March 24, 1970: Greece 1-5 Yugoslavia
  • 1972: Did not qualify. Finished 2nd of 3 in qualification group.
  • 1974: Did not qualify. Finished 2nd of 3 in qualification group.
  • 1976: Losing semi-finalists.


UEFA U-21 Championship Record

  • 1978: Winners.
  • 1980: Losing semi-finalists.
  • 1982: Did not qualify. Finished 2nd of 3 in qualification group.
  • 1984: Losing semi-finalists.
  • 1986: Did not qualify. Finished 4th of 4 in qualification group.
  • 1988: Did not qualify. Finished 3rd of 3 in qualification group.
  • 1990: Runners-up.
  • 1992: Did not qualify. Finished 2nd of 4 in qualification group.


See also

  • European Under-21 Football Championship


External links

  • UEFA Under-21 website Contains full results archive
  • The Rec.Sport.Soccer Statistics Foundation Contains full record of U-21/U-23 Championships.

Posted in Uncategorized | No Comments »

Compensated demand curve; consumer

Thursday, February 21st, 2008

In economics, the compensated demand curve shows how the substitution effect influences the number of units of a good the consumer will purchase.

A Compensated Demand Curve shows how the number of units of a good purchased changes as the price changes, assuming the consumer’s income is increased enough to offset the income effect and thus, maintain constant utility.

Also see:

  • Uncompensated Demand Curve
  • Federal Consumer Information Center Federal Citizen Information Center - answers to your questions about the Federal government and common consumer issues. The citizen's help desk for everyday