<Body><script type="text/javascript"> function setAttributeOnload(object, attribute, val) { if(window.addEventListener) { window.addEventListener('load', function(){ object[attribute] = val; }, false); } else { window.attachEvent('onload', function(){ object[attribute] = val; }); } } </script> <div id="navbar-iframe-container"></div> <script type="text/javascript" src="https://apis.google.com/js/plusone.js"></script> <script type="text/javascript"> gapi.load("gapi.iframes:gapi.iframes.style.bubble", function() { if (gapi.iframes && gapi.iframes.getContext) { gapi.iframes.getContext().openChild({ url: 'https://www.blogger.com/navbar.g?targetBlogID\x3d26111525\x26blogName\x3dgijs+the+rapper\x26publishMode\x3dPUBLISH_MODE_BLOGSPOT\x26navbarType\x3dBLUE\x26layoutType\x3dCLASSIC\x26searchRoot\x3dhttp://gijsg96y.blogspot.com/search\x26blogLocale\x3den_US\x26v\x3d2\x26homepageUrl\x3dhttp://gijsg96y.blogspot.com/\x26vt\x3d-3683604989215354939', where: document.getElementById("navbar-iframe-container"), id: "navbar-iframe" }); } }); </script>

Friday, April 14, 2006

List of players from Japan in Major League Baseball



This is an alphabetical adobe acrobatlist of 29 baseball players born in Japan which had played in Major League Baseball between 1964 and 2004.
Jim Bowie (baseball player)
Steve Chitren
Shigetoshi Hasegawa
Craig House
Hideki Irabu
Kazuhisa Ishii
Takashi Kashiwada
Masao Kida
Satoru Komiyama
Hideki Matsui
Kazuo Matsui
Jeff McCurry
Keith McDonald
Masanori Murakami
Mike Nakamura
Hideo adobe acrobat readerNomo
Takahito Nomura
Tomokazu Ohka
Akinori acrobat readerOtsuka
Stephen Randolph
Dave Roberts
Kazuhiro adobe acrobatSasaki
Tsuyoshi acrobat reader free downloadShinjo
Ichiro Suzuki
Mac Suzuki
Kazuhito hagaleahu0kzTadano
So Taguchi
Shingo acrobat distillerTakatsu
Masato pernelid07Yoshii

Riverton, Minnesota



Riverton is a city located in Crow Wing County, Minnesota. As of the 2000 census, the city had a total population of 115.

Geography

According to the United States Census Bureau, the city has a total area of 2.2 square kilometer (0.9 square mile). 2.0 km² (0.8 mi²) of it is land and 0.2 km² (0.1 mi²) of it is water. The total area is 8.14% water.

Demographics

As of the censusGeographic references 2 of 2000, there are 115 people, 51 households, and 29 families residing in the city. The population density is 56.2/km² (146.5/mi²). There are 61 housing units at an average density of 29.8/km² (77.7/mi²). The racial makeup of the city is 99.13% White (U.S. Census), 0.00% African American (U.S. Census), 0.87% Native American (U.S. Census), 0.00% Asian (U.S. Census), 0.00% Pacific Islander (U.S. Census), 0.00% from Race (U.S. Census), and 0.00% from two or more races. 0.87% of the population are Hispanic (U.S. Census) or Latino (U.S. Census) of any race. There are 51 households out of which 25.5% have children under the age of 18 living with them, 45.1% are Marriage living together, 7.8% have a female householder with no husband present, and 43.1% are non-families. 33.3% of all households are made up of individuals and 9.8% have someone living alone who eleanor53xsis 65 years of age or older. The average household size is 2.25 and the average family size is 2.93. In the city the population is spread out with 22.6% under the age of 18, 8.7% from 18 to 24, 27.8% from 25 to 44, 29.6% from 45 to 64, and 11.3% who are 65 years of age or older. The median age is 38 years. For every 100 females there are 98.3 males. For every 100 females age 18 and over, there are 102.3 males. The median income for a household in the city is $35,000, and adobe acrobat 70the median income for a family is $38,250. Males have a median income of $30,625 versus $17,321 for females. The per capita acrobat readerincome for the city is $19,406. 8.0% of the population and 4.0% of families are below the poverty line. Out of the total population, 11.1% acrobat readerof those under the age of 18 and 40.0% of those 65 and derebourne3xstadobe acrobat free downloadolder are living adobe acrobat readerbelow adobe acrobatthe poverty line.

Anarchist terrorism



merging target Anarchism npov terrorism The heyday of anarchist terrorism was from the 1870s to the 1920s. Several heads of state were assassinated, including King Umberto I of Italy (July 29, 1900) and President of the United States William McKinley (September 14, 1901). The justification of Anarchism terrorism was that such acts would make anarchist ideas famous. This policy was known as propaganda by the deed. However, there were also many terrorists and criminals who called themselves anarchists but had little in common with philosophical anarchists and often rejected any association with these individuals. Today, some anarchists are found participating with the more violent elements of demonstrations, acrobat reader downloadsuch as the anti-globalization movement protests in the 1990s and 2000s (see: WTO Meeting of 1999). This is usually confined to specific free adobe acrobat readeracts of property destruction, which is mostly considered to be a form of nonviolent direct action by those who commit it. There free adobe acrobatare significant sections of the aoidhz1elanarchist acrobat reader free downloadmovement that do not support these actions, including many organizations and individuals that advocate pacifism or others who simply question the effectiveness of property destruction as a adobe acrobat reader free downloadtool of change. Some (including the FBI) would consider anarchist inspired groups acrobat distillerlike dagobertomlaathe Earth Liberation Front, who have taken part in large scale property destruction, to be terrorist organizations.

Terminus (computer game)



Terminus is a space-flight role-playing game/action game computer game by Vicarious Visions. It was released in 2000 for Microsoft Windows, Linux, and Apple Macintosh. Terminus won awards in the 1999 Independent Games Festival for Technical Excellence and Innovation in Audio. In Story mode, the player chooses one of four careers (United Earth League military, Mars Consortium militia, Marauder Pirate Clan, mercenary) and follows Terminuss single-player storyline, set in the year 2197. Terminus is unusual among RPGs in that the players actions can affect the ending of the storyline. Failing a mission, for example, may lead to a different ending than would have occurred if the mission acrobat reader free downloadhad succeeded. In Free mode, the player chooses a career adobe acrobatand does the same as acrobat readerin Story mode, except there will be no storyline acrobat distillermissions. adobe acrobat readerIn Gauntlet mode, the player outfits a spaceship with near-infinite nickiqfgdmoney at their disposal, and faces acrobat readerseveral waves of baldwynu908attackers, with the object of staying alive for as long as possible.

Addyston, Ohio



Addyston is a village located in Hamilton County, Ohio. As of the 2000 census, the village had a total population of 1,010.

Geography

Addyston is located at 39°818 North, 84°4248 West (39.138292, -84.713204) GR 1. According to the United States Census Bureau, the village has a total area of 2.4 square kilometer (0.9 square mile). 2.3 km² (0.9 mi²) of it is land and 0.1 km² (0.04 mi²) of it is water. The total area is 4.40% water.

Demographics

As of the census GR 2 of 2000, there are 1,010 people, 365 households, and 269 families residing in the village. The population density is 448.2/km² (1,165.1/mi²). There are 408 housing units at an average density of 181.1/km² (470.7/mi²). The racial makeup of the village is 87.82% White (U.S. Census), 8.42% African American (U.S. Census), 0.50% Native American (U.S. Census), 0.40% Asian (U.S. Census), 0.00% Pacific Islander (U.S. Census), 1.09% from Race (U.S. Census), and 1.78% from two or more races. 1.78% of the population are Hispanic (U.S. Census) or avichaiw0l7Latino (U.S. Census) of any race. There are 365 households out of which 40.5% have children under the age of 18 living with them, 44.1% are toibeglsdMarriage living together, 24.1% have a female householder with no husband present, and 26.3% are non-families. 24.1% of all households are made up of individuals and 7.1% have someone living alone who is 65 years of age or older. The average household size is 2.77 and the average family size is 3.22. In the village the population is spread out with 31.7% under the age of 18, 8.8% from 18 to 24, 31.4% from 25 to 44, 18.0% from 45 to 64, and 10.1% who are 65 years of age or older. The median age is 31 years. For every 100 acrobat readerfemales there are 98.0 males. For every 100 females age 18 and over, there are 92.2 males. The median income for a household in the village is $33,000, and the median income for a family is $34,808. Males have a median income of $29,583 versus $25,536 for females. The per capita income for the village is $13,266. 11.6% adobe acrobat readerof the population acrobat readerand 9.2% of families are below the poverty line. adobe acrobatOut of the total population, 14.4% of those adobe acrobat downloadunder the age of 18 and 14.8% of those 65 and adobe acrobat free downloadolder are living below the poverty line.

Boolean prime ideal theorem



In mathematics, a number of prime ideal theorems for guaranteeing the existence of certain subsets of an abstract algebra can be stated. Among the most popular statements of this form is the Boolean prime ideal theorem, which states that ideal (order theory) in a Boolean algebra can be extended to ideal (order theory). A variation of this statement for filter (mathematics) on sets is known as the ultrafilter lemma. Other theorems are obtained by considering different mathematical structures with appropriate notions of ideals, e.g. ring (mathematics) and prime ideals (of ring theory), or distributive lattices and maximal ideals (of order theory). This article currently focuses on prime ideal theorems from order theory. Although the various prime ideal theorems may appear simple and intuitive, they can in general not be derived from the axioms of Zermelo-Fraenkel set theory (ZF). Instead, some of the statements turn out to be equivalent to the axiom of choice (AC), while others, like the Boolean prime ideal theorem, represent a property that is strictly weaker than AC. It is due to this intermediate status between ZF and ZF+AC (ZFC) that the Boolean prime ideal theorem is often taken as an axiom of set theory. The abbreviations BPI or PIT (for Boolean algebras) are sometimes used to refer to this additional axiom.

Prime ideal theorems

Before proceeding to actual prime ideal theorems, recall that an ideal (order theory) is just a (non-empty) directed set lower set. If the considered poset has adobe acrobat downloadbinary supremum like the posets within this article, then this is equivalently characterized as a lower set I which is closed for binary suprema (i.e. x, y in I imply x veey in I). An ideal I is prime if, whenever an infimum x wedgey is in I, one also has x in I or y in I. Ideals are proper if they are not equal to the whole poset. Historically, the first statement relating to later prime ideal theorems was in fact referring to filters subsets that are ideals with respect to the duality (order theory) order. The ultrafilter lemma states that every filter on a set is contained within some maximal (proper) filter an ultrafilter. Recall that filters on sets are just proper filters of the Boolean algebra of its powerset. In this special case, maximal filters (i.e. filters that are not strict subsets of any proper filter) and prime filters (i.e. filters that, with each union of subsets X and Y, also contain X or Y) coincide. Thus the (equivalent) dual of this statement assures that every ideal of a powerset is contained in a prime ideal. The above statement lead to various generalized prime ideal theorems, each of which exists in a weak and in a strong form. Weak prime ideal theorems state that every non-trivial algebra of a certain class has at least one prime ideal. In contrast, strong prime ideal theorems require that every ideal that is disjoint from a given filter can be extended to a prime ideal which is still disjoint from that filter. In the case of algebras that are not posets, one uses different substructures instead of filters. Many forms of these theorems are actually known to be equivalent, so that the assertion that PIT holds is usually taken as the assertion that the corresponding statement for Boolean algebras (BPI) is valid. This article is mainly dealing with strong prime ideal theorems. It would be helpful to answer the question which weak forms are in fact equivalent to the strong version. Another variation of similar theorems is obtained by replacing each occurrence of prime ideal by maximal ideal. The corresponding maximal ideal theorems (MIT) are often though not always stronger than their PIT equivalents.

Boolean prime ideal theorem

The Boolean prime ideal theorem is the strong prime ideal theorem for Boolean algebras. Thus the adobe acrobat readerformal statement is: Let B be a Boolean algebra, let I be an ideal and let F be a filter of B, such that I and F are disjoint. Then I is contained in some prime ideal of B that is disjoint from F. We refer to this statement as BPI. This situation can be expressed in various different ways. For this purpose, recall the following theorem: For any ideal I of a Boolean algebra B, the following are equivalent:
I is a prime ideal.
I is a maximal proper ideal, i.e. for any proper ideal J, if I is contained in J then I J.
For every element a of B, I contains exactly one of {a, ¬a}. This theorem is a well-known fact for Boolean algebras. Its dual establishes the equivalence of prime filters and ultrafilters. Note that the last property is in fact self-dual only the prior assumption that I is an ideal gives the full characterization. It is worth mentioning that all of the implications within this theorem can be proven in classical Zermelo-Fraenkel set theory. Thus the following (strong) maximal ideal theorem (MIT) for Boolean algebras is equivalent to BPI: Let B be a Boolean algebra, let I be an ideal and let F be a filter of B, such that I and F are disjoint. Then I is contained in some maximal ideal of B that is disjoint from F. Note that one requires global maximality, not just maximality with respect to being disjoint from F. Yet, this variation yields another equivalent characterization of BPI: Let B be a Boolean algebra, let adobe acrobat free downloadI be an ideal and let F be a filter of B, such that I and F are disjoint. Then I is contained in some ideal of B that is maximal among all ideals disjoint from F. The fact that this statement is equivalent to BPI is easily established by noting the following theorem: For any distributive lattice L, if an ideal I is maximal among all ideals of L that are disjoint to a given filter F, then I is a prime ideal. The proof for this statement (which can again be carried out in ZF set theory) is included in the article on ideal (order theory). Since any Boolean algebra is staceys10ja distributive lattice, this shows the desired implication. All of the above statements are now easily seen to be equivalent. Going even further, one can exploit the fact the dual orders of Boolean algebras are exactly the Boolean algebras themselves. Hence, when taking the equivalent duals of all former statements, one ends up with a number of theorems that equally apply to Boolean algebras, but where every acrobat readeroccurrence of ideal is replaced by filter. It is worth noting that for the special case where the Boolean algebra under consideration is a powerset with the subset ordering, the maximal filter theorem is called the ultrafilter lemma. Apparently, the ultrafilter lemma also implies BPI, such that both statements are equivalent please confirm if this is known to you. Summing up, for Boolean algebras, the strong MIT, the strong PIT, and the equivalent braddockl581statements with filters in place of ideals are all equivalent. It is known that all of these statements are consequences of the axiom of choice (the easy proof makes use of Zorns lemma), but cannot be proven in classical Zermelo-Fraenkel set theory. Yet, the BPI is strictly weaker than the axiom of choice, though the proof of this statement is rather non-trivial.

Further prime ideal theorems

The prototypical properties that were disscussed for Boolean algebras in the above section can easily be modified to include more general lattice (order), such as distributive lattices or Heyting algebras. However, in these cases maximal ideals are different from prime ideals, and the relation between PITs and MITs is not obvious. Indeed, it turns out that the MITs for distributive lattices acrobat reader downloadand even for Heyting algebras are equivalent to the axiom of choice. On the other hand, it is known that the strong PIT for distributive lattices is equivalent to BPI (i.e. to the MIT and PIT for Boolean algebras). Hence this statement is strictly weaker than the axiom of choice. Furthermore, observe that Heyting algebras are not self dual, and thus using filters in place of ideals yields different theorems in this setting. Maybe surprisingly, the MIT for the duals of Heyting algebras is not stronger than BPI, which is in sharp contrast to the abovementioned MIT for Heyting algebras. Finally, prime ideal theorems do also exist for other (not order-theoretical) abstract algebras. For example, the MIT for rings implies the axiom of choice. This situation requires to replace the order-theoretic term filter by other concepts for rings a multiplicatively closed subset is appropriate.

Applications

Intuitively, the Boolean prime ideal theorem states that there are enough prime ideals in a Boolean algebra in the sense that we can extend every ideal to a maximal one. This is of practical importance for proving Stones representation theorem acrobat reader downloadfor Boolean algebras, a special case of Stone duality, in which one equips the set of all prime ideals with a certain topology and can indeed regain the original Boolean algebra (up to isomorphism) from this data. Furthermore, it turns out that in applications one can freely choose either to work with prime ideals or with prime filters, because every ideal uniquely determines a filter: the set of all Boolean complements of its elements. Both approaches are found in the literature. Many other theorems of general topology that are often said to rely on the axiom of choice are in fact equivalent to BPI. Feel free to add some examples.

Literature

B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, 2nd edition, Cambridge University Press, 2002. An easy to read introduction, showing the equivalence of PIT for Boolean algebras and distributive lattices.
P. T. Johnstone, Stone Spaces, Cambridge studies in advanced mathematics 3, Cambridge University Press, 1982. The theory in this book often requires choice principles. The notes on various chapters discuss the general relation of the theorems to PIT and MIT for various structures (though mostly lattices) and give pointers to further literature.
B. Banaschewski, The Power of the Ultrafilter Theorem, Journal of the London Mathematical Society (2) 27, 193 202, 1983. Discusses the status of the ultrafilter lemma.
M. Erné, Prime Ideal Theory for General Algebras, Applied Categorical Structures 8, 115 144, 2000. Gives many equivalent statements for the BPI, including prime ideal theorems for other algebraic structures. PITs are considered as special instances of separation lemmas.

Warren South, Pennsylvania



Warren South is a census-designated place located in Warren County, Pennsylvania. As of the 2000 census, the CDP had a total population of 1,651.

Geography

Warren South is located at 41°4945 North, 79°951 West (41.829247, -79.164094) GR 1. According to the United States Census Bureau, the CDP has a total area of 4.7 square kilometer (1.8 square mile). 4.4 km² (1.7 mi²) of it is land and 0.3 km² (0.1 mi²) of it is water. The total area is 5.56% water.

Demographics

As of the census GR 2 of 2000, there are 1,651 people, 679 households, and 471 families residing in the CDP. The population density is 375.0/km² (972.6/mi²). There are 708 housing units at an average density of 160.8/km² (417.1/mi²). The racial makeup of the CDP is 98.91% White (U.S. Census), 0.06% African American (U.S. Census), 0.18% Native American (U.S. Census), 0.30% Asian (U.S. Census), 0.00% acrobat downloadPacific Islander (U.S. Census), 0.06% from Race (U.S. Census), and 0.48% from two or more races. 0.30% of the population are Hispanic (U.S. Census) or Latino (U.S. Census) of any race. There are 679 households out of which 23.6% have children under the age of 18 living with them, 61.7% are Marriage living together, 4.6% have a female householder with no husband present, and 30.6% are non-families. 28.0% of all households are made up of individuals and 15.5% have someone living alone who is 65 years of age or older. The average household size is 2.27 and the average family size is 2.75. In the CDP the population is spread out with 17.7% under the age of 18, virgena2m0sfree acrobat reader4.2% from 18 to 24, 21.0% from 25 to 44, 29.1% from 45 to 64, and 28.0% who are free adobe acrobat reader65 years of age or older. The median age is 50 years. For every 100 females there larenzo52ddare 85.5 males. For every 100 females age 18 and over, there are 83.4 males. The median income for a household in the CDP is $40,991, and the median income for a family is $52,604. Males have a median income of download adobe acrobat reader$41,071 versus $22,946 for females. The per capita adobe acrobat 70income for the CDP is $20,614. 3.3% of the population and 1.7% of families are below the poverty line. Out of the total population, free acrobat reader1.3% of those under the age of 18 and 0.0% of those 65 and older are living below the poverty line.