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Übersetzung für 'G&F' von Englisch nach Deutsch
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• obengenannt <o. g.> = aforementioned
• Gramm {n} <g> = gram <g>
• Gramm {n} <g> = gramme <g> [Br.] [spv.]
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Anwendungsbeispiele Englisch
• Given a group "G" and a field "F", the elements of its representation ring "R'F"("G") are the formal differences of isomorphism classes of finite dimensional linear "F"-representations of "G". For the ring structure, addition is given by the direct sum of representations, and multiplication by their tensor product over "F". When "F" is omitted from the notation, as in "R"("G"), then "F" is implicitly taken to be the field of complex numbers.
• The lower Fitting series of a finite group "G" is the sequence of characteristic subgroups "F'n"("G") defined by "F"0("G") = "G", and "F'n"+1("G") = "γ"∞("F'n"("G")). It is a descending nilpotent series, at each step taking the "minimal" possible subgroup.
• In a treatment of predicate logic that allows one to introduce new predicate symbols, one will also want to be able to introduce new function symbols. Given the function symbols "F" and "G", one can introduce a new function symbol "F" ∘ "G", the "composition" of "F" and "G", satisfying ("F" ∘ "G")("X") = "F"("G"("X")), for all "X".
• "G"/"F", for "F" an open subgroup of "G".
• "Face the Change" is written in the key of G-sharp minor, has a tempo of 124 beats per minute, and the chorus follows a chord progression of E–F#–G#m–E–F#–B–D#–E–F#–G#m–E–F#–G#m.

• Since a morphism of sheaves φ: "F" → "G" on "X" gives rise to a morphism of sheaves "f"∗(φ): "f"∗("F") → "f"∗("G") on "Y" in an obvious way, we indeed have that "f"∗ is a functor.
• Finally, in an operation too simple to really be called a fourth stage, the results of the second and third stages can be rearranged by simple algebraic manipulation to work out the desired discrete logarithm "x" = "f"0log"g"(−1) + "f"1log"g"2 + "f"2log"g"3 + ··· + "f'r"log"g'pr" − "s".
• "g" : "B" → "A" such that "e" = "g" "f" and 1"B" = "f" "g".
• Seven Senior Eagles graduated in May: Assistant Captain Michael Sit – F, Assistant Captain Quinn Smith – F, Destry Straight – F, Cam Spiro – F. Danny Linell – F, Brian Billett – G, and Brad Barone – G.
• Suppose that "F" is an endomorphism of an algebraic group "G". The Lang map is the map from "G" to "G" taking "g" to "g"−1"F"("g").

• We now show that if "f" and "g" are homotopically equivalent, then "f"* = "g"*. From this follows that if "f" is a homotopy equivalence, then "f"* is an isomorphism.
• A morphism "f": "X" → "Y" is called a monomorphism if "f" ∘ "g"1 = "f" ∘ "g"2 implies "g"1 = "g"2 for all morphisms "g"1, "g"2: "Z" → "X". A monomorphism can be called a "mono" for short, and we can use "monic" as an adjective.
• A function "f" : "M" → "N" is called a morphism of "G"-modules (or a "G"-linear map, or a "G"-homomorphism) if "f" is both a group homomorphism and "G"-equivariant.
• For such "g", one can write "f" as a sum of positive linear functionals: "f" = "g" + "g' ". So π is unitarily equivalent to a subrepresentation of π"g" ⊕ π"g' ". This shows that π is irreducible if and only if any such π"g" is unitarily equivalent to π, i.e. "g" is a scalar multiple of "f", which proves the theorem.
• The corresponding normalised solutions "f'n" of the Beltrami equations and their inverses "g'n" satisfy uniform Hölder estimates. They are therefore equicontinuous on any compact subset of C; they are even holomorphic for |"z"| > "R". So by the Arzelà–Ascoli theorem, passing to a subsequence if necessary, it can be assumed that both "f'n" and "g'n" converge uniformly on compacta to "f" and "g". The limits will satisfy the same Hölder estimates and be holomorphic for |"z"| > "R". The relations "f'n"∘"g'n" = id = "g'n"∘"f'n" imply that in the limit "f"∘"g" = id = "g"∘"f", so that "f" and "g" are homeomorphisms.

• Every functor "F" : "C" → "D" determines a congruence on "C" by saying "f" ~ "g" iff "F"("f") = "F"("g"). The functor "F" then factors through the quotient functor "C" &rarr; "C"/~ in a unique manner. This may be regarded as the "first isomorphism theorem" for categories.
• Incident faces of different ranks, for example, a vertex F of an edge G, are ordered by the relation F < G. F is said to be a "subface" of G.
• Suppose that "g" is a completely solvable Lie algebra, and "f" is an element of the dual "g"*. A polarization of "g" at "f" is a subspace "h" of maximal dimension subject to the condition that "f" vanishes on [...], that is also a subalgebra. The Dixmier map "I" is defined by letting "I"("f") be the kernel of the twisted induced representation Ind~("f"|"h","g") for a polarization "h".
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