text stringlengths 2 4.67k | source dict |
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, 1 ] {\displaystyle [0,1]} but does not converges (in R {\displaystyle \mathbb {R} } ) to it. The free prefilter ( R , β ) := { ( r , β ) : r β R } {\displaystyle (\mathbb {R} ,\infty ):=\{(r,\infty ):r\in \mathbb {R} \}} of intervals does not converge (in R {\displaystyle \mathbb {R} } ) to any point. The same is als... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
any family finer than B . {\displaystyle {\mathcal {B}}.} This has many important consequences. One consequence is that the limit points of a family B {\displaystyle {\mathcal {B}}} are the same as the limit points of its upward closure: lim X β‘ B = lim X β‘ ( B β X ) . {\displaystyle \operatorname {lim} _{X}{\mathcal {... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
lim X B β lim X C {\displaystyle {\mathcal {B}}\leq {\mathcal {C}}{\text{ then }}\lim {}_{X}{\mathcal {B}}\subseteq \lim {}_{X}{\mathcal {C}}} and moreover, for every x β X , {\displaystyle x\in X,} both { x } {\displaystyle \{x\}} and the maximal/ultrafilter { x } β X {\displaystyle \{x\}^{\uparrow X}} converge to x .... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
{\text{ for every }}B\in {\mathcal {B}}} and every neighborhood N {\displaystyle N} of x . {\displaystyle x.} In particular, a point x β X {\displaystyle x\in X} is a cluster point or an accumulation point of a family B {\displaystyle {\mathcal {B}}} if B {\displaystyle {\mathcal {B}}} meshes with the neighborhood filt... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
cluster points of a prefilter are the same as the cluster points of the filter that it generates. Given x β X , {\displaystyle x\in X,} the following are equivalent for a prefilter B on X {\displaystyle {\mathcal {B}}{\text{ on }}X} : B {\displaystyle {\mathcal {B}}} clusters at x . {\displaystyle x.} The family B β X ... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
The set cl X β‘ B {\displaystyle \operatorname {cl} _{X}{\mathcal {B}}} of all cluster points of a prefilter B {\displaystyle {\mathcal {B}}} satisfies cl X β‘ B = β B β B cl X β‘ B . {\displaystyle \operatorname {cl} _{X}{\mathcal {B}}=\bigcap _{B\in {\mathcal {B}}}\operatorname {cl} _{X}B.} Consequently, the set cl X β‘ ... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
than B {\displaystyle {\mathcal {B}}} (that is, if N ( x ) and B {\displaystyle {\mathcal {N}}(x){\text{ and }}{\mathcal {B}}} mesh and C β€ B {\displaystyle {\mathcal {C}}\leq {\mathcal {B}}} then N ( x ) and C {\displaystyle {\mathcal {N}}(x){\text{ and }}{\mathcal {C}}} mesh). Equivalent families and subordination An... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
point. For instance, every point in any given non-empty subset K β X {\displaystyle K\subseteq X} is a cluster point of the principle prefilter B := { K } {\displaystyle {\mathcal {B}}:=\{K\}} (no matter what topology is on X {\displaystyle X} ) but if X {\displaystyle X} is Hausdorff and K {\displaystyle K} has more t... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
{\displaystyle x\in \operatorname {cl} _{X}{\mathcal {B}}.} In particular, any limit point of a filter subbase subordinate to B β β
{\displaystyle {\mathcal {B}}\neq \varnothing } is necessarily also a cluster point of B . {\displaystyle {\mathcal {B}}.} If x {\displaystyle x} is a cluster point of a prefilter B {\disp... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
continuous map f : X β Y {\displaystyle f:X\to Y} is contained in a primitive subset of Y . {\displaystyle Y.} Assume that P , Q β X {\displaystyle P,Q\subseteq X} are two primitive subset of X . {\displaystyle X.} If U {\displaystyle U} is an open subset of X {\displaystyle X} that intersects P {\displaystyle P} then ... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
( X ) , {\displaystyle {\mathcal {B}}\subseteq \wp (X),} and y β Y . {\displaystyle y\in Y.} If y {\displaystyle y} is a limit point (respectively, a cluster point) of f ( B ) in Y {\displaystyle f({\mathcal {B}}){\text{ in }}Y} then y {\displaystyle y} is called a limit point or limit (respectively, a cluster point) o... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
{Tails} (I,\leq ))\to x{\text{ in }}X,} where the left hand side states that x {\displaystyle x} is a limit of the net Ο {\displaystyle \chi } while the right hand side states that x {\displaystyle x} is a limit of the function Ο {\displaystyle \chi } with respect to B := Tails β‘ ( I , β€ ) {\displaystyle {\mathcal {B}}... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
, β ) := { ( r , β ) : r β R } and ( β β , R ) := { ( β β , r ) : r β R } , {\displaystyle (\mathbb {R} ,\infty ):=\{(r,\infty ):r\in \mathbb {R} \}~~{\text{ and }}~~(-\infty ,\mathbb {R} ):=\{(-\infty ,r):r\in \mathbb {R} \},} where f β β {\displaystyle f\to \infty } along B {\displaystyle {\mathcal {B}}} if and only ... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
) β β β {\displaystyle \lim _{x\to x_{0}}f(x)\to -\infty } if and only if ( β β , R ) β€ f ( N ( x 0 ) ) , {\displaystyle (-\infty ,\mathbb {R} )\leq f\left({\mathcal {N}}\left(x_{0}\right)\right),} or equivalently, if and only if ( β β , R ] β€ f ( N ( x 0 ) ) . {\displaystyle (-\infty ,\mathbb {R} ]\leq f\left({\mathca... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
in X {\displaystyle X} then Tails β‘ ( f ( x β ) ) = f ( Tails β‘ ( x β ) ) . {\displaystyle \operatorname {Tails} \left(f\left(x_{\bullet }\right)\right)=f\left(\operatorname {Tails} \left(x_{\bullet }\right)\right).} === Prefilters to nets === A pointed set is a pair ( S , s ) {\displaystyle (S,s)} consisting of a non-... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
it is a directed set if (and only if) B {\displaystyle {\mathcal {B}}} is a prefilter. So the most immediate choice for the definition of "the net in X {\displaystyle X} induced by a prefilter B {\displaystyle {\mathcal {B}}} " is the assignment ( B , b ) β¦ b {\displaystyle (B,b)\mapsto b} from PointedSets β‘ ( B ) {\di... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
in 1955 Bruns and Schmidt discovered a construction (detailed here: Filter (set theory)#Partially ordered net) that allows for the canonical net to have a domain that is both partially ordered and directed; this was independently rediscovered by Albert Wilansky in 1970. Because the tails of this partially ordered net a... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
\right\}} ) then Tails β‘ ( x n β ) β’ Tails β‘ ( x β ) {\displaystyle \operatorname {Tails} \left(x_{n_{\bullet }}\right)~\vdash ~\operatorname {Tails} \left(x_{\bullet }\right)} (which by definition means Tails β‘ ( x β ) β€ Tails β‘ ( x n β ) {\displaystyle \operatorname {Tails} \left(x_{\bullet }\right)\leq \operatorname... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
written C β’ B , {\displaystyle {\mathcal {C}}\vdash {\mathcal {B}},} is the analog of " C {\displaystyle {\mathcal {C}}} is a subsequence of B . {\displaystyle {\mathcal {B}}.} " So "finer than" and "subordinate to" is the prefilter analog of "subsequence of." Some people prefer saying "subordinate to" instead of "fine... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
A β I {\displaystyle h:A\to I} between two preordered sets is order-preserving if whenever a , b β A {\displaystyle a,b\in A} satisfy a β€ b , {\displaystyle a\leq b,} then h ( a ) β€ h ( b ) . {\displaystyle h(a)\leq h(b).} Kelley did not require the map h {\displaystyle h} to be order preserving while the definition of... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
an AA-subnet of Net B . {\displaystyle \operatorname {Net} _{\mathcal {B}}.} If "AA-subnet" is replaced by "Willard-subnet" or "Kelley-subnet" then the above statement becomes false. In particular, as this counter-example demonstrates, the problem is that the following statement is in general false: False statement: If... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
a base for some topology can be immediately reworded as: B {\displaystyle {\mathcal {B}}} is a base for some topology on X {\displaystyle X} if and only if B x {\displaystyle {\mathcal {B}}_{x}} is a filter base for every x β X . {\displaystyle x\in X.} If Ο {\displaystyle \tau } is a topology on X {\displaystyle X} an... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
. {\displaystyle \{x\}\not \in {\mathcal {B}}.} In contrast, a topological space has the discrete topology if and only if the neighborhood filter of every point is a principal filter generated by exactly one point. This shows that a non-principal filter on an infinite set is not necessarily free. The neighborhood filte... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
converse is in general false. This shows that in a sense, filters are almost topologies. Topologies of the form { β
} βͺ B {\displaystyle \{\varnothing \}\cup {\mathcal {B}}} where B {\displaystyle {\mathcal {B}}} is an ultrafilter on X {\displaystyle X} are an even more specialized subclass of such topologies; they hav... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
β Ο {\displaystyle {\mathcal {B}}\subseteq \tau } will be a basis for Ο {\displaystyle \tau } if and only if B β { β
} {\displaystyle {\mathcal {B}}\setminus \{\varnothing \}} is equivalent to Ο β { β
} , {\displaystyle \tau \setminus \{\varnothing \},} in which case B β { β
} {\displaystyle {\mathcal {B}}\setminus \{\... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
, Ο ) {\displaystyle x\in X,{\mathcal {B}}\to x{\text{ in }}(X,\sigma )} if and only if B β x in ( X , Ο ) . {\displaystyle {\mathcal {B}}\to x{\text{ in }}(X,\tau ).} However, it is possible that Ο β Ο {\displaystyle \sigma \neq \tau } while also for every filter B on X , B {\displaystyle {\mathcal {B}}{\text{ on }}X,... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
x {\displaystyle x} is a cluster point of the prefilter { S } . {\displaystyle \{S\}.} The prefilter { S } {\displaystyle \{S\}} meshes with some (or equivalently, with every) filter base for N ( x ) {\displaystyle {\mathcal {N}}(x)} (that is, with every neighborhood basis at x {\displaystyle x} ). The following are eq... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
in X . {\displaystyle X.} The above statement but with the word "prefilter" replaced by any one of the following: filter, ultra prefilter, ultrafilter. Compactness As discussed in this article, the Ultrafilter Lemma is closely related to many important theorems involving compactness. The following are equivalent: ( X ,... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
{\displaystyle {\mathcal {F}}} is a filter on X {\displaystyle X} if and only if X {\displaystyle X} is not compact. Continuity Let f : X β Y {\displaystyle f:X\to Y} be a map between topological spaces ( X , Ο ) and ( Y , Ο
) . {\displaystyle (X,\tau ){\text{ and }}(Y,\upsilon ).} Given x β X , {\displaystyle x\in X,}... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
of f ( B ) in Y . {\displaystyle f({\mathcal {B}}){\text{ in }}Y.} Any one of the above two statements but with the word "prefilter" replaced by "filter". If B {\displaystyle {\mathcal {B}}} is a prefilter on X , x β X {\displaystyle X,x\in X} is a cluster point of B , and f : X β Y {\displaystyle {\mathcal {B}},{\text... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
that is a family of prefilters where each B i {\displaystyle {\mathcal {B}}_{i}} is a prefilter on X i . {\displaystyle X_{i}.} Then the product B β {\displaystyle {\mathcal {B}}_{\bullet }} of these prefilters (defined above) is a prefilter on the product space β X β , {\displaystyle {\textstyle \prod }X_{\bullet },} ... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
{\displaystyle \left(x_{i},y_{i}\right)_{i=1}^{\infty }\subseteq X\times Y} does not have a cluster point in X Γ Y . {\displaystyle X\times Y.} Example application: The ultrafilter lemma along with the axioms of ZF imply Tychonoff's theorem for compact Hausdorff spaces: == Examples of applications of prefilters == === ... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
compact uniform space is complete because any Cauchy filter has a cluster point (by compactness), which is necessarily also a limit point (since the filter is Cauchy). Uniform spaces were the result of attempts to generalize notions such as "uniform continuity" and "uniform convergence" that are present in metric space... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
x {\displaystyle x} is an element of C . {\displaystyle {\mathfrak {C}}.} If F β C {\displaystyle F\in {\mathfrak {C}}} is a subset of a proper filter G , {\displaystyle G,} then G β C . {\displaystyle G\in {\mathfrak {C}}.} If F , G β C {\displaystyle F,G\in {\mathfrak {C}}} and if each member of F {\displaystyle F} i... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
for subsets P β β ( β ( X ) ) . {\displaystyle \mathbb {P} \subseteq \wp (\wp (X)).} For every S β X , {\displaystyle S\subseteq X,} let O ( S ) := { B β P : S β B β X } {\displaystyle \mathbb {O} (S):=\left\{{\mathcal {B}}\in \mathbb {P} ~:~S\in {\mathcal {B}}^{\uparrow X}\right\}} where O ( X ) = P and O ( β
) = β
. ... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
{O} (S)} shows that the family { O ( S ) : S β X } {\displaystyle \{\mathbb {O} (S)~:~S\subseteq X\}} is a Ο {\displaystyle \pi } -system that forms a basis for a topology on P {\displaystyle \mathbb {P} } called the Stone topology. It is henceforth assumed that P {\displaystyle \mathbb {P} } carries this topology and ... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
{\mathcal {B}}^{\uparrow X}\right\}\subseteq \mathbb {B} } (that is, such that for all B β P , if F β B β X then B β B {\displaystyle {\mathcal {B}}\in \mathbb {P} ,{\text{ if }}F\in {\mathcal {B}}^{\uparrow X}{\text{ then }}{\mathcal {B}}\in \mathbb {B} } ). It will be henceforth assumed that X β β
{\displaystyle X\ne... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
if and only if N Ο = N Ο . {\displaystyle {\mathcal {N}}_{\tau }={\mathcal {N}}_{\sigma }.} Thus every topology Ο β Top β‘ ( X ) {\displaystyle \tau \in \operatorname {Top} (X)} can be identified with the canonical map N Ο β Func β‘ ( X ; P ) , {\displaystyle {\mathcal {N}}_{\tau }\in \operatorname {Func} (X;\mathbb {P} ... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
\operatorname {Filters} (X)} is a map such that x β ker β‘ F ( x ) := β F β F ( x ) F for every x β X {\displaystyle x\in \ker {\mathfrak {F}}(x):={\textstyle \bigcap \limits _{F\in {\mathfrak {F}}(x)}}F{\text{ for every }}x\in X} (which is true of F := N Ο , {\displaystyle {\mathfrak {F}}:={\mathcal {N}}_{\tau },} for ... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
and Exercises. Mathematics and Its Applications. Vol. 13. Dordrecht Boston: D. Reidel. ISBN 978-90-277-1355-1. OCLC 9944489. Berberian, Sterling K. (1974). Lectures in Functional Analysis and Operator Theory. Graduate Texts in Mathematics. Vol. 15. New York: Springer. ISBN 978-0-387-90081-0. OCLC 878109401. Bourbaki, N... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
Publications. ISBN 978-0-486-68143-6. OCLC 30593138. Howes, Norman R. (23 June 1995). Modern Analysis and Topology. Graduate Texts in Mathematics. New York: Springer-Verlag Science & Business Media. ISBN 978-0-387-97986-1. OCLC 31969970. OL 1272666M. Jarchow, Hans (1981). Locally convex spaces. Stuttgart: B.G. Teubner.... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
in Topological Vector Spaces. Mineola, New York: Dover Publications, Inc. ISBN 978-0-486-49353-4. OCLC 849801114. Wilansky, Albert (17 October 2008) [1970]. Topology for Analysis. Mineola, New York: Dover Publications, Inc. ISBN 978-0-486-46903-4. OCLC 227923899. Willard, Stephen (2004) [1970]. General Topology. Mineol... | {
"page_id": 47516955,
"title": "Filters in topology"
} |
Transcription activator-like effector nucleases (TALEN) are restriction enzymes that can be engineered to cut specific sequences of DNA. They are made by fusing a TAL effector DNA-binding domain to a DNA cleavage domain (a nuclease which cuts DNA strands). Transcription activator-like effectors (TALEs) can be engineere... | {
"page_id": 31001884,
"title": "Transcription activator-like effector nuclease"
} |
The FokI domain functions as a dimer, requiring two constructs with unique DNA binding domains for sites in the target genome with proper orientation and spacing. Both the number of amino acid residues between the TALE DNA binding domain and the FokI cleavage domain and the number of bases between the two individual TA... | {
"page_id": 31001884,
"title": "Transcription activator-like effector nuclease"
} |
joining (NHEJ) directly ligates DNA from either side of a double-strand break where there is very little or no sequence overlap for annealing. This repair mechanism induces errors in the genome via indels (insertion or deletion), or chromosomal rearrangement; any such errors may render the gene products coded at that l... | {
"page_id": 31001884,
"title": "Transcription activator-like effector nuclease"
} |
pigmentosum, and epidermolysis bullosa. Recently, it was shown that TALEN can be used as tools to harness the immune system to fight cancers; TALEN-mediated targeting can generate T cells that are resistant to chemotherapeutic drugs and show anti-tumor activity. In theory, the genome-wide specificity of engineered TALE... | {
"page_id": 31001884,
"title": "Transcription activator-like effector nuclease"
} |
and may consequently yield chromosomal rearrangements and/or cell death. Studies have been carried out to compare the relative nuclease-associated toxicity of available technologies. Based on these studies and the maximal theoretical distance between DNA binding and nuclease activity, TALEN constructs are believed to h... | {
"page_id": 31001884,
"title": "Transcription activator-like effector nuclease"
} |
In generalized blockmodeling, the blockmodeling is done by "the translation of an equivalence type into a set of permitted block types", which differs from the conventional blockmodeling, which is using the indirect approach. It's a special instance of the direct blockmodeling approach. Generalized blockmodeling was in... | {
"page_id": 68488477,
"title": "Generalized blockmodeling"
} |
results to in-built measure of fit, which is integral to the establishment of the blockmodels (in conventional blockmodeling, there is no compelling and coherent measures of fit); partitions, based on generalized blockmodeling, regularly outperform and never perform less well than the partitions, based on conventional ... | {
"page_id": 68488477,
"title": "Generalized blockmodeling"
} |
(Series Editor), Generalized Blockmodeling (Structural Analysis in the Social Sciences), Cambridge University Press 2004 (ISBN 0-521-84085-6) | {
"page_id": 68488477,
"title": "Generalized blockmodeling"
} |
Fluctuating asymmetry (FA), is a form of biological asymmetry, along with anti-symmetry and direction asymmetry. Fluctuating asymmetry refers to small, random deviations away from perfect bilateral symmetry. This deviation from perfection is thought to reflect the genetic and environmental pressures experienced through... | {
"page_id": 1969440,
"title": "Fluctuating asymmetry"
} |
ideal. Directional asymmetry of traits can be distinguished by showing significantly biased measurements towards traits being larger on either the left or right sides, for example, human testicles (where the right is more commonly larger), or handedness (85% are right handed, 15% are left handed). Anti-symmetry can be ... | {
"page_id": 1969440,
"title": "Fluctuating asymmetry"
} |
individuals show more asymmetry in observed bilateral traits, the differences were not significant. Furthermore, ant colonies created by an inbreeding queen do not show significantly higher FA than those produced by a non-inbreeding queen. === Environmental factors === Multiple sources provide information on environmen... | {
"page_id": 1969440,
"title": "Fluctuating asymmetry"
} |
russula) from more polluted areas show higher levels of asymmetry. Radioactive contamination may also increase FA levels, as mice (Apodemus flavicollis) living closer to the failed Chernobyl reactor show greater asymmetry. == Developmental stability == Developmental stability is achieved when an organism is able to wit... | {
"page_id": 1969440,
"title": "Fluctuating asymmetry"
} |
of medical conditions than those with lower levels of FA. However, they did not experience worse outcomes in areas such as systolic blood pressure or cholesterol levels. Higher levels of FA have also been linked to higher body mass index (BMI) in women, and lower BMI in men. Research has shown that both men and women w... | {
"page_id": 1969440,
"title": "Fluctuating asymmetry"
} |
an organism's genetic quality. The relationship between FA and behaviours with high health risks has received mixed support. Individuals with body piercings and tattoos (which increase risk of blood-borne infections) have been shown to have lower levels of FA, but individuals with lower FA do not engage in any more rec... | {
"page_id": 1969440,
"title": "Fluctuating asymmetry"
} |
in patients experiencing lower back pain, and higher levels of FA have also been linked to congenital spinal problems. Studies have also shown increased levels of FA of ear length in individuals with cleft lip and/or non-syndromic cleft palate syndrome. === Physical fitness in humans === In addition to general health a... | {
"page_id": 1969440,
"title": "Fluctuating asymmetry"
} |
and antler asymmetry at reproductive age was lower than in development or at post-reproductive age. FA and health outcomes have been examined within insect populations. For instance, it has been found that Mediterranean field crickets (Gryllus bimaculatus) with higher levels of FA in three hind-limb traits have lower e... | {
"page_id": 1969440,
"title": "Fluctuating asymmetry"
} |
appears limited to the most fertile phases of the menstrual cycle. However, research has failed to find changes in women's preferences for low FA across the menstrual cycle when assessing pictures of faces, as opposed to scents. Facial symmetry has been positively correlated with higher occurrences of mating. Also, one... | {
"page_id": 1969440,
"title": "Fluctuating asymmetry"
} |
dark-winged damselfly (Calopteryx maculate), successfully mating male flies showed significantly lower levels of FA in their forewings than unsuccessful males, while for Japanese scorpionflies, FA levels are a good predictor for the outcome of fights between males in that more symmetrical males won significantly more f... | {
"page_id": 1969440,
"title": "Fluctuating asymmetry"
} |
FA and intelligence. A meta-analysis of the research covering this topic demonstrated that whilst published studies largely report negative correlations, unpublished studies often find no association between FA and intelligence. === Personality === Research into FA suggests that there may be some correlation to specifi... | {
"page_id": 1969440,
"title": "Fluctuating asymmetry"
} |
animals. In Japanese scorpionflies (Panorpa nipponensis and Panorpa ochraceopennis), FA differences between members of the same sex competing for food determines the outcome of interspecific contests and aggression better than body size or ownership of food. Furthermore, cannibalistic laying hens (Gallus gallus domesti... | {
"page_id": 1969440,
"title": "Fluctuating asymmetry"
} |
The iliococcygeal raphe is a raphe representing the midline location where the levatores ani converge. == See also == Anococcygeal body == References == | {
"page_id": 24644898,
"title": "Iliococcygeal raphe"
} |
Vat Green 1 is an organic compound that is used as a vat dye. It is a derivative of benzanthrone. It is a dark green solid. Vat Green 1 can dye viscose, silk, wool, paper, and soap. == References == | {
"page_id": 42208547,
"title": "Vat Green 1"
} |
This list of sequenced animal genomes contains animal species for which complete genome sequences have been assembled, annotated and published. Substantially complete draft genomes are included, but not partial genome sequences or organelle-only sequences. For all kingdoms, see the list of sequenced genomes. == Porifer... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
compressa, Finger coral (2022) == Hemichordata == === Order Enteropneusta (Acorn Worms) === == Echinodermata == Acanthaster planci, starfish (2014) Apostichopus japonicus, sea cucumber (2017) Arbacia lixula, black sea urchin (2024) Astropecten irregularis, sand sea star (2024) Australostichopus mollis, Australian sea c... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
Anguilla anguilla, European Eel (2012) Anguilla japonica, Japanese Eel (2022) Order Atheriniformes Atherinopsis californiensis, Jack silverside (2023) Order Beloniformes Oryzias latipes, medaka (2007) Order Callionymiformes Callionymus lyra, common dragonet (2020) Order Carangiformes Caranx ignobilis, Giant trevally (2... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
bicolor, bicolor angelfish (2021) Chaetodon trifasciatus, melon butterflyfish (2020) Channa argus, northern snakehead (2017) Channa maculata, blotched snakehead (2021) Chelmon rostratus, copperband butterflyfish (2020) Dissostichus mawsoni, Antarctic toothfish (2019) Eleginops maclovinus, Patagonian robalo (2019) Epine... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
(2018) ==== Caecillians ==== Family Dermophiidae Geotrypetes seraphini, Gaboon caecillian, (2023) Family Siphonopidae Microcaecilia unicolor, a caecillian, (2023) === Birds === ==== Ratites (Palaeognathae) ==== ===== Order Struthioniformes ===== ===== Order Rheiformes (Rheas) ===== ===== β Order Dinornithiformes (Moas)... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
mendiculus, GalΓ‘pagos penguin (2019) ====== Order Ciconiiformes (Storks) ====== ====== Order Suliformes ====== ====== Order Pelecaniformes ====== ===== Afroaves ===== ====== Order Strigiformes (Owls) ====== ====== Order Accipitriformes ====== Add 87 hawk genomes found here: https://pmc.ncbi.nlm.nih.gov/articles/PMC9851... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
(2019) Charina bottae, Rubber boa, (2022) Clade Caenophidia Family Viperidae Azemiops feae, Fea's viper (2022) Bothrops jararaca, Jararaca lancehead, (2021) Crotalus adamanteus, Eastern diamondback rattlesnake (2021) Crotalus mitchellii pyrrhus, southwestern speckled rattlesnake (2014) Crotalus oreganus helleri, southe... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
Order Notoryctemorphia, Family Notoryctidae Notoryctes typhlops, southern marsupial mole (ongoing) Order Diprotodontia Family Macropodidae Macropus eugenii, tammar wallaby (2011) Petrogale penicillata, brush-tailed rock-wallaby (ongoing) Family Potoroidae Bettongia gaimardi, eastern bettong (ongoing) Bettongia penicill... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
(2004) ===== Laurasiatheria ===== Order Artiodactyla (even-toed ungulates) Family Antilocapridae Antilocapra americana, pronghorn (2019) Family Balaenidae Balaena mysticetus, bowhead whale (2015) Eubalaena glacialis, North Atlantic right whale (2018) Family Balaenopteridae Balaenoptera acutorostrata, common minke whale... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
(2015) Sousa chinensis, Indo-Pacific humpback dolphin (2019) Family Eschrichtiidae Eschrichtius robustus, gray whale (2018) Family Giraffidae Giraffa camelopardalis, Giraffe (2019) Giraffa camelopardalis tippelskirchi, Masai giraffe (2019) Okapia johnstoni, Okapi (2019) Family Monodontidae Delphinapterus, beluga whale ... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
(2009 2018) == Arthropods == === Insects === Order Blattodea Blattella germanica, German cockroach (2018) Periplaneta americana, American cockroach (2018) Zootermopsis nevadensis, a dampwood termite (2014 Cryptotermes secundus, a drywood termite(2018) Macrotermes natalensis, a higher termite (2014 Order Coleoptera Dend... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
mojavensis, fruit fly (2007) Drosophila neotestacea, fruit fly (transcriptome 2014) Drosophila persimilis, fruit fly (2007) Drosophila pseudoobscura, fruit fly (2005) Drosophila rhopaloa, fruit fly (2011) Drosophila santomea, fruit fly () Drosophila sechellia, fruit fly (2007) Drosophila simulans, fruit fly (2007) Dros... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
pomonella, codling moth (2019) Danaus plexippus, monarch butterfly) (2011) Heliconius melpomene, butterfly (2012) Keiferia lycopersicella, Tomato pinworm (2024) Melitaea cinxia, Glanville fritillary butterfly (2014) Megathymus ursus violae, bear giant skipper butterfly (2018) Morpho helenor, Common blue morpho (2023) M... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
widow spider (2022) Nephila clavipes, (golden silk orb-weaver) (2017) Parasteatoda tepidariorum, (common house spider) (2017) Stegodyphus mimosarum, African social velvet spider (2014) Uloborus diversus, Cribellate orb-weaving spider, (2023) === Myriapods === Strigamia maritima, centipede Trigoniulus corallinus, millip... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
Bivalves === Argopecten purpuratus, peruvian scallop (2018) Bathymodiolus platifrons, seep mussel (2017) Chlamys farreri, Zhikong scallop (2017) Crassostrea angulata, Portuguese oyster (2023) Crassostrea gigas, Pacific oyster (2012) Dreissena rostriformis, Quagga mussel (2019) Limnoperna fortunei, invasive golden musse... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
brachiopod (2015,) == Rotifera == Adineta vaga, rotifer (2013,) == See also == List of sequenced bacterial genomes List of sequenced archaeal genomes List of sequenced eukaryotic genomes List of sequenced fungi genomes List of sequenced plant genomes List of sequenced protist genomes List of sequenced plastomes == Refe... | {
"page_id": 35917093,
"title": "List of sequenced animal genomes"
} |
In statistical mechanics, the random-subcube model (RSM) is an exactly solvable model that reproduces key properties of hard constraint satisfaction problems (CSPs) and optimization problems, such as geometrical organization of solutions, the effects of frozen variables, and the limitations of various algorithms like d... | {
"page_id": 77073703,
"title": "Random subcube model"
} |
1 } {\displaystyle \{-1\},\{+1\},\{-1,+1\}} . The available states is the union of these subsets: S = βͺ i A i {\displaystyle S=\cup _{i}A_{i}} === Random subcube model === Each random subcube model is defined by two parameters Ξ± , p β ( 0 , 1 ) {\displaystyle \alpha ,p\in (0,1)} . To generate a random subcube A i {\dis... | {
"page_id": 77073703,
"title": "Random subcube model"
} |
( s ) ] 2 β 2 β N Ξ£ ( s ) {\displaystyle {\begin{aligned}E[n(s)]&=2^{(1-\alpha )N}P\to 2^{N\Sigma (s)+o(N)}\\Var[n(s)]&=2^{(1-\alpha )N}P(1-P)\\{\frac {Var[n(s)]}{E[n(s)]^{2}}}&\to 2^{-N\Sigma (s)}\end{aligned}}} where P := ( N s N ) p ( 1 β s ) N ( 1 β p ) s N , Ξ£ ( s ) := 1 β Ξ± β D K L ( s β 1 β p ) D K L ( s β 1 β p... | {
"page_id": 77073703,
"title": "Random subcube model"
} |
) N = 2 N ( log 2 β‘ ( 2 β p ) β Ξ± ) {\displaystyle 2^{(1-\alpha )N}(1-p/2)^{N}=2^{N(\log _{2}(2-p)-\alpha )}} So if Ξ± < log 2 β‘ ( 2 β p ) {\displaystyle \alpha <\log _{2}(2-p)} , then it concentrates to 2 N ( log 2 β‘ ( 2 β p ) β Ξ± ) {\displaystyle 2^{N(\log _{2}(2-p)-\alpha )}} , and so each state is in an exponential ... | {
"page_id": 77073703,
"title": "Random subcube model"
} |
) + s ) {\displaystyle s^{*}=\arg \max _{s}(\Sigma (s)+s)} . Thus, in the clustered phase, the state space is almost entirely partitioned among 2 N Ξ£ ( s β ) {\displaystyle 2^{N\Sigma (s^{*})}} clusters of size 2 N s β {\displaystyle 2^{Ns^{*}}} each. Roughly, the state space looks like exponentially many equally-sized... | {
"page_id": 77073703,
"title": "Random subcube model"
} |
c 2 β ( 1 + Ξ£ β² ( s c ) ) , 2 N s c 2 β 2 ( 1 + Ξ£ β² ( s c ) ) , β¦ {\displaystyle 2^{Ns_{c}},2^{Ns_{c}}2^{-(1+\Sigma '(s_{c}))},2^{Ns_{c}}2^{-2(1+\Sigma '(s_{c}))},\dots } We can tabulate them as follows: Thus, we see that for any Ο΅ > 0 {\displaystyle \epsilon >0} , at N β β {\displaystyle N\to \infty } limit, over 1 β ... | {
"page_id": 77073703,
"title": "Random subcube model"
} |
Tire-derived fuel (TDF) is composed of shredded scrap tires. Tires may be mixed with coal or other fuels, such as wood or chemical wastes, to be burned in concrete kilns, power plants, or paper mills. An EPA test program concluded that, with the exception of zinc emissions, potential emissions from TDF are not expected... | {
"page_id": 18877738,
"title": "Tire-derived fuel"
} |
this refined material are published in TDF Produced From Scrap Tires with 96+% Wire Removed. Tires are typically composed of about 1 to 1.5% Zinc oxide, which is a well known component used in the manufacture of tires and is also toxic to aquatic and plant life. The chlorine content in tires is due primarily to the chl... | {
"page_id": 18877738,
"title": "Tire-derived fuel"
} |
and furan emissions increases of only as much as 58%. Still other facilities used as much as 8% TDF and experienced a decrease of as much as 83% of dioxin and furan emissions. One facility conducted four tests with two tests resulting in decreased emissions and two resulting in increased emissions. Another facility als... | {
"page_id": 18877738,
"title": "Tire-derived fuel"
} |
A hair dryer (the handheld type also referred to as a blow dryer) is an electromechanical device that blows ambient air in hot or warm settings for styling or drying hair. Hair dryers enable better control over the shape and style of hair, by accelerating and controlling the formation of temporary hydrogen bonds within... | {
"page_id": 986413,
"title": "Hair dryer"
} |
in at approximately 2 pounds (0.9 kg), and were difficult to use. They also had many instances of overheating and electrocution. Hair dryers were only capable of using 100 watts, which increased the amount of time needed to dry hair (the average dryer today can use up to 2000 watts of heat). Since the 1920s, developmen... | {
"page_id": 986413,
"title": "Hair dryer"
} |
so that it cannot electrocute a person if it gets wet. By 2000, deaths by blowdryers had dropped to fewer than four people a year, a stark difference to the hundreds of cases of electrocution accidents during the mid-20th century. == Function == Most hair dryers consist of electric heating coils and a fan that blows th... | {
"page_id": 986413,
"title": "Hair dryer"
} |
airflow concentrator does the opposite of a diffuser. It makes the end of the hair dryer narrower and thus helps to concentrate the heat into one spot to make it dry rapidly. The comb nozzle attachment is the same as the airflow concentrator, but it ends with comb-like teeth so that the user can dry the hair using the ... | {
"page_id": 986413,
"title": "Hair dryer"
} |
Sven Anders FlodstrΓΆm (born 1 October 1944) is a Swedish professor of materials physics at the Royal Institute of Technology. FlodstrΓΆm was born in SΓΆderhamn, Sweden. He studied engineering physics and electrical engineering in LinkΓΆping. In 1975, he was awarded a Ph.D. in physics in LinkΓΆping with the thesis "Electron... | {
"page_id": 22875437,
"title": "Anders FlodstrΓΆm"
} |
Zeta potential is the electrical potential at the slipping plane. This plane is the interface which separates mobile fluid from fluid that remains attached to the surface. Zeta potential is a scientific term for electrokinetic potential in colloidal dispersions. In the colloidal chemistry literature, it is usually deno... | {
"page_id": 1183025,
"title": "Zeta potential"
} |
or positive) are electrically stabilized while colloids with low zeta potentials tend to coagulate or flocculate as outlined in the table. Zeta potential can also be used for the pKa estimation of complex polymers that is otherwise difficult to measure accurately using conventional methods. This can help studying the i... | {
"page_id": 1183025,
"title": "Zeta potential"
} |
potential by inputting the dispersant viscosity and dielectric permittivity, and the application of the Smoluchowski theories. ==== Electrophoresis ==== Electrophoretic mobility is proportional to electrophoretic velocity, which is the measurable parameter. There are several theories that link electrophoretic mobility ... | {
"page_id": 1183025,
"title": "Zeta potential"
} |
only one justified way to perform this dilution β by using equilibrium supernatant. In this case, the interfacial equilibrium between the surface and the bulk liquid would be maintained and zeta potential would be the same for all volume fractions of particles in the suspension. When the diluent is known (as is the cas... | {
"page_id": 1183025,
"title": "Zeta potential"
} |
to convert streaming potential or streaming current results into the surface zeta potential. Applications of the streaming potential and streaming current method for the surface zeta potential determination consist of the characterization of surface charge of polymer membranes, biomaterials and medical devices, and min... | {
"page_id": 1183025,
"title": "Zeta potential"
} |
typically only a few nanometers in water. The model breaks only for nano-colloids in a solution with ionic strength approaching that of pure water. Smoluchowski's theory neglects the contribution of surface conductivity. This is expressed in modern theories as the condition of a small Dukhin number: D u βͺ 1 {\displayst... | {
"page_id": 1183025,
"title": "Zeta potential"
} |
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