Estate Administrator of an estate
The Administrator of an estate is a legal term referring to a person appointed by a court to administer the estate of a deceased person who left no will. Where a person dies intestate the court may appoint a person to settle their debts, pay any necessary taxes and funeral expenses, and distribute the remainder according to the procedure set down at law. Such a person is known as the administrator of the estate and will enjoy similar powers to those of an executor under a will.
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Potential buyers think Threshold price-point
In economics, a threshold price point is the psychological fixing of prices to entice a buyer. The most common example in the United States is the $??.99 phenomenon — e.g. setting the price for a good at $9.99. Though it is effectively ten dollars — especially when you add sales tax — it still appears to the potential buyer to be significantly cheaper than if the good was sold $10.00.
Economists and advertising analysts note that should a company need to increase the price of a product beyond the threshold price-point, it should not be done in small amounts. If a candy bar originally cost $1.99, then there is apparently little difference in making the new price $2.05 or even $2.25. Instead, companies are encouraged to raise the price to the next threshold price-point, which in this case may be as high as $2.99. The logic behind the move is that while some potential buyers will be lost by the increase in price beyond the threshold, those that stay will not notice the difference in prices between thresholds. Buyers do not make judgement calls on a per-cent basis, so will not differentiate between $2.05 and $2.06. However, they do differentiate at thresholds. So while you wouldn’t necessarily lose a buyer jumping from $2.05 and $2.06, you could lose one going from $1.99 to $2.00. Therefore companies can actually increase overall profit despite losing customers by increasing the revenue per buyer significantly.
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An independent Algebraic independence
In abstract algebra, a subset S of a field L is algebraically independent over a subfield K if the elements of S do not satisfy any non-trivial polynomial equation with coefficients in K. This means that for every finite sequence α1, …, αn of elements of S, no two the same, and every non-zero polynomial P(x1, …, xn) with coefficients in K, we have
- P(α1,…,αn) ≠ 0.
In particular, a one element set {α} is algebraically independent over K if and only if α is transcendental over K. In general, all the elements of an algebraically independent set over K are by necessity transcendental over K, but that is far from being a sufficient condition.
For example, the subset {√π, 2π+1} of the real numbers R is not algebraically independent over the rationals Q, since the non-zero polynomial
- <math>P(x_1,x_2)=2x^2_1-x_2+1</math>
yields zero when √π is substituted for x1 and 2π+1 is substituted for x2.
The Lindemann-Weierstrass theorem can often be used to prove that some sets are algebraically independent over Q. It states that whenever α1,…,αn are algebraic numbers that are linearly independent over Q, then eα1,…,eαn are algebraically independent over Q.
It is not known whether the set {π, e} is algebraically independent over Q. Nesterenko proved in 1996 that {π, eπ, Γ(1/4)} is algebraically independent over Q.
Given a field extension L/K, we can use Zorn’s lemma to show that there always exists a maximal algebraically independent subset of L over K. Further, all the maximal algebraically independent subsets have the same cardinality, known as the transcendence degree of the extension.
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Real estate Abstract of title
An abstract of title is the condensed history of title to a particular parcel of real estate, consisting of a summary of the original grant and all subsequent conveyances and encumbrances affecting the property and a certification by the abstractor that the history is complete and accurate. In the United States, the abstract of title furnishes the raw data for the preparation of a policy of title insurance for the parcel of land in question.
An abstract of title should be distinguished from an opinion of title. While an abstract states that all of the public record documents concerning the property in question are contained therein, an opinion states the professional judgment of the person giving the opinion as to the vesting of the title and other matters concerning the status of the chain of title. Many jurisdictions define the giving of an opinion of title as the practice of law, thus making it unlawful for a non-attorney to do so.
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Specific segment Acentric fragment
An acentric fragment is a segment of a chromosome that lacks a centromere.
Because it is the centromere is the point of attachment for the mitotic apparatus, such fragments are not evenly distributed to the daughter cells in cell division (mitosis and meiosis). As a result one of the daughters will lack the acentric fragment.
Lack of the acentric fragment in one of the daughter cells may have deleterious or consequences, depending on the function of the DNA in this region of the chromosome. In the case of a haploid organism or a gamete, it will be fatal if essential DNA is contained in that DNA segment. In the case of a diploid organism, the daughter cell lacking the acetric fragment will show expression of any recessive genes found in the homologous chromosome. Developmental geneticists look to cells and cell lineages lacking unpaired chromosome segments produced this way as a means of identifying essential genes for specific functions.
Acentric fragments are commonly generated by chromosome-breaking events, such as irradiation. Acentric fragments can also be produced when an inverted segment is present in one member of a chromosome pair. In that case, a crossover event will result in one chromosome with two centromeres and an acentric fragment. The acentric fragment will be lost as explained above, and chromosomes with two centromeres will break unevenly during mitosis, resulting in one daughter lacking essential genes.
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Edit External List of asteroids/103001–104000
! colspan=”5″ style=”background-color:silver;text-align:center;” id=”001″| 103001–103100 [ edit]
! colspan=”5″ style=”background-color:silver;text-align:center;” id=”101″| 103101–103200 [ edit]
! colspan=”5″ style=”background-color:silver;text-align:center;” id=”201″| 103201–103300 [ edit]
! colspan=”5″ style=”background-color:silver;text-align:center;” id=”301″| 103301–103400 [ edit]
! colspan=”5″ style=”background-color:silver;text-align:center;” id=”401″| 103401–103500 [ edit]
! colspan=”5″ style=”background-color:silver;text-align:center;” id=”501″| 103501–103600 [ edit]
! colspan=”5″ style=”background-color:silver;text-align:center;” id=”601″| 103601–103700 [ edit]
! colspan=”5″ style=”background-color:silver;text-align:center;” id=”701″| 103701–103800 [ edit]
! colspan=”5″ style=”background-color:silver;text-align:center;” id=”801″| 103801–103900 [ edit]
! colspan=”5″ style=”background-color:silver;text-align:center;” id=”901″| 103901–104000 [ edit]
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Property Quasi in rem
Quasi in rem (Latin, “as if against a thing”) is a legal term referring to a legal action based on property rights of a person absent from the jurisdiction.
A quasi in rem action is commonly used when jurisdiction over the defendant is unobtainable due to his/her absence from the state. Any judgment will affect only the property seized, as in personam jurisdiction is unobtainable.
Of note, in a quasi in rem case the court may lack personal jurisdiction over the defendant, but it has jurisdiction over the defendant’s property. The property could be seized to obtain a claim against the defendant. A judgment based on quasi in rem jurisdiction generally affects rights to the property only between the persons involved and does not “bind the entire world” as does a judgment based on “jurisdiction in rem“.
The claim does not have to be related to the property seized, but the person must have minimum contacts with the forum state in order for jurisdiction to be proper.
For example, see Pennoyer v. Neff, 95 U.S. 714 (1877)
See also
- in rem
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Real Real representation
There are some small but confusing differences in terminology between mathematicians and physicists when discussing real and complex representations.
In mathematics a real representation is usually a group representation on a real vector space, while in physics a real representation is usually a group representation on a complex vector space that allows the matrices representing the group elements to be real. These two definitions are essentially equivalent, because if U is a real vector space acted on by a group G, then V = U⊗C is a representation on a complex vector space that can be represented by real matrices. The difference in viewpoints is in whether one thinks of the real representation as the action of G on the real vector space U or the action of G on the complex vector space V.
A real representation is equivalent to its complex conjugate but the converse is not true: representations equivalent to their complex conjugate but that are not real are called pseudoreal representations (symplectic representations).
Another formulation of the (physics) definition is that there exists an antilinear map on the complex vector space V
- <math>j:V\to V\,</math>
that commutes with the elements of the group, and that satisfies
- <math>j^2=+1.\,</math>
The fixed points of j form a real vector space U with V = U⊗C.
In physics, a group representation on a complex vector space that is neither real nor pseudoreal is called a
complex representation. (In mathematics, any representation on a complex vector space is called a complex representation.)
Frobenius-Schur indicator
A criterion (for compact groups G) for reality of irreducible representations in terms of character theory is based on the Frobenius-Schur indicator.
If a representation of a compact group G has character χ its Schur indicator is defined to be
- <math>\int_{g\in G}\chi(g^2)\,d\mu</math>
which when G is finite is given by
- <math>{1\over |G|}\sum_{g\in G}\chi(g^2)</math>
which may take the values 1, 0 or −1, for Haar measure μ with μ(G) = 1. If the indicator is 1, then the representation is real (for the physics definition of real). If the indicator is zero, the representation is complex (for the physics definition of complex), and if the indicator is −1, the representation is pseudoreal.
Examples
Examples of real representations are the spinors in 8k−1, 8k, and 1 + 8k dimensions for k = 1, 2, 3 … . This periodicity modulo 8 is known in mathematics not only in the theory of Clifford algebras, but also in algebraic topology, in KO-theory.
See Representations of Clifford algebras.
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Estate Grange Industrial Estate
The Grange Industrial Estate is an area of warehousing and employment in Warrington, England. The largest of these was the Safeway warehouse until it was taken over by Morrisons in January 2006 and the large bank vault of the former Midland Bank (ie HSBC ?}.
The Estate borders the civil parish of Woolston.
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Division of property, also known as equitable distribution, is a judicial division of property rights and obligations between spouses during divorce. It may be done by agreement, through a property settlement, or by judicial decree.
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Pagliowska v Pagliowski refers to runaway costs.
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Real Luciana, Ciudad Real
Luciana is a small village and municipality in the province of Ciudad Real (Spain), near the confluence of the Bullaque and Guadiana Rivers.
See also
- List of municipalities in Ciudad Real
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