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Indeed and <
Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.
If φ is C < sup > k </ sup >, then the inhomogeneous equation is explicitly solvable in any bounded domain D, provided φ is continuous on the closure of D. Indeed, by the Cauchy integral formula,
Another way to describe G-sets is the functor category, where is the groupoid ( category ) with one element and isomorphic to the group G. Indeed, every functor F of this category defines a set X = F and for every g in G ( i. e. for every morphism in ) induces a bijection F < sub > g </ sub >: X → X.
) Indeed, if a space is Hausdorff then it is T < sub > 0 </ sub >, and each T < sub > 0 </ sub > regular space is Hausdorff: given two distinct points, at least one of them misses the closure of the other one, so ( by regularity ) there exist disjoint neighborhoods separating one point from ( the closure of ) the other.
Observe first the following: if a is a limit point of S, then any finite collection C of open sets, such that each open set U ∈ C is disjoint from some neighborhood V < sub > U </ sub > of a, fails to be a cover of S. Indeed, the intersection of the finite family of sets V < sub > U </ sub > is a neighborhood W of a in R < sup > n </ sup >.
Indeed, the center consists solely of the identity element and x < sup > 2 </ sup >.
An important consequence of the domain invariance theorem is that R < sup > n </ sup > cannot be homeomorphic to R < sup > m </ sup > if m ≠ n. Indeed, no non-empty open subset of R < sup > n </ sup > can be homeomorphic to any open subset of R < sup > m </ sup > in this case.
Indeed, in the example given above any jet where θ < 35 ° will be observed on Earth as less luminous than it would be from the rest frame of the jet.
Indeed, if the interval were sequentially compact in constructive analysis, then the classical IVT would follow from the first constructive version in the example ; one could find c as a cluster point of the infinite sequence ( c < sub > n </ sub >)< sub > n </ sub >.
Indeed, the area of a disk of radius R is πR < sup > 2 </ sup > and the circumference of the circle is 2πR, so both sides of the inequality are equal to< sup > 2 </ sup > R < sup > 2 </ sup > in this case.
Indeed, any " point " p < sub > x </ sub >: 1 → X in Top is mapped to a morphism Ω ( p < sub > x </ sub >): Ω ( X ) → Ω ( 1 ).

Indeed and >
Indeed, Japan accepts a steady flow of 15, 000 new Japanese citizens by naturalization ( 帰化 ) per year .< ref >
Indeed, it is difficult to imagine that the Priestly Writer could have turned Ezekiel's land of exile (< big > ארץ מגוריהם </ big >) into Israel's land of promise, Israel's enemies (< big > קהל עמים </ big >) in to a sign of fecundity, or Israel's abundant sin (< big > במאד מאד </ big >) into a sign of YHWH's covenant.

Indeed and 2
Indeed television sets sold throughout the 1970s and early 1980s had a spare channel called ' ITV / IBA 2 '.
Indeed, in the U. S. estimates of the environmental regulation's total costs reach 2 % of GDP, and any new regulation will arguably contribute in some way to that burden.
Indeed, Emperor Louis Napoleon III surrendered himself and 100, 000 French troops to the German troops at Sedan on 1 – 2 September 1870.
Indeed, if x and y are integers satisfying this equation, then x / y is an approximation of2.
Indeed, 2, 4-D is not a poison, but classified as " harmful " ( EU ).
Indeed 78. 2 ° C is the minimum temperature at which any ethanol / water solution can boil at atmospheric pressure.
Indeed, phosphorylation replaces neutral hydroxyl groups on serines, threonines, or tyrosines with negatively-charged phosphates with pKs near 1. 2 and 6. 5.
Indeed, it was under his orders that Lt. Francisco de Castañeda went to Gonzales, Texas, to secure a cannon from the hands of the Texans, leading to the battle on October 2 that initiated hostilities in the Texas Revolution.
Indeed, nearly 67 % of the haplogroups resulting from are Euro – Eurasian ( R1a ( 2. 76 %), R1b ( 50. 62 %), I ( 9. 66 %) and G ( 3. 99 %)).
Indeed, in 1969 a " Birding Glossary " appeared in Birding Volume 1, No. 2, which stated the following:
Indeed no communication was ever established and Beagle 2 was declared lost on 6 February 2004.
Indeed, on the evidence, I find that the public want to be able to buy tea and coffee served hot, that is to say at a temperature of at least 65 ° C, even though they know ( as I think they must be taken to do for the purposes of answering issues ( 1 ) and ( 2 )) that there is a risk of a scalding injury if the drink is spilled.
Indeed, the inland and coastal populations of A. californica seem to constitute 2 distinct species too, as might different populations of the Mexican Jay.
Indeed, the full Bible has been translated into over 450 languages, and some sections of the Bible have been translated into over 2, 000 languages.
Indeed, our whole knowledge of God is limited to two certainties, ( 1 ) that He exists and ( 2 ) that His essence is incomprehensible ( ib.
Indeed, God " desires all men to be saved and to come to the knowledge of the truth " ( 1 Timothy 2: 4 ); that is, God wills the salvation of everyone through the knowledge of the truth.
Indeed, C has one eigenvalue ( namely zero ) and this eigenvalue has algebraic multiplicity 2 and geometric multiplicity 1.
Indeed, the UN declaration of partition, though it was generally met with by peaceful protests in Arab countries, provided the pretext for a pogrom in Aden soon after, on 2 December 1947, in which 82 Jews were killed.
Indeed each incidence structure gives a spherical building of rank 2 ( see ); and Ballmann and Brin proved that every 2-dimensional simplicial complex in which the links of vertices are isomorphic to the flag complex of a finite projective plane has the structure of a building, not necessarily classical.
Indeed, he obtained 49. 2 % of votes in the second round.
Indeed, in the case of Kirmani v Captain Cook Cruises Pty Ltd ( No 2 ) ( 1985 ), the court said that it would never again grant a certificate of appeal.

Indeed and +</
Indeed, the first great discovery in the field was in 1986 by T. Story and co-workers where they demonstrated that the ferromagnetic Curie temperature of Mn < sup > 2 +</ sup >- doped Pb < sub > 1-x </ sub > Sn < sub > x </ sub > Te can be controlled by the carrier concentration.

Indeed and >-
Indeed, let f ( x )= x < sup > 2 </ sup >- a.

Indeed and dependent
Indeed, from the standpoint of Attachment theory or Object relations theory, " to risk becoming dependent " may be for the compulsively self-reliant a psychological advance, and " depending on a source outside oneself ... successful, or tolerable, dependence " may be valorized accordingly.
Indeed, many modern day amniotes are dependent on moisture to keep their eggs from desiccating.
Indeed, " typically for those close personal relations there is a certain degree in ' interdependence ' - which means that the partners are alternately mutually dependent on each other.
Indeed, JUSTICE itself gave birth to a number of subordinate branches in what were then still British colonies and dependent territories.

Indeed and enzymes
Indeed, the bromodomain — a protein segment ( domain ) that specifically binds acetyl-lysine — is found in many enzymes that help activate transcription, including the SWI / SNF complex ( on the protein polybromo ).

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