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Yes. If I understand your question correctly (I cleaned up the wording slightly). Activators are proteins that bind to enhancer regions of DNA. This facilitates the binding of transcription factors and the RNA Polymerase to read the DNA of the gene.
In Prokaryotic Cells transcription and translation can occur simultaneously, but transcription happens after a transcription initiation complex has been formed.
Most eukaryotic genes are controlled individually and have regulatory sequences that are much more complex than those of the lac operon. (this answer above was found in my Biology text book too so it is correct) :)
diarrhea
co-enzymes
No, Eukayotic transcription begins after promoter clearance. Promoter clearance just prepares the transcription initiation complex to begin elongation. Promoter clearance does not produce any functional gene.
template for RNA transcription. RNA is spliced (in eukaryotes) and moves out of the nucleus into the cytosol where it associates with a ribosome (can also have ribosomes on ER membrane). various factors form a complex that initiates translation of the mRNA message from the chromosome.
If you have a complex function in the form "a+ib", the (complex) conjugate is "a-ib". "Conjugate" is usually a function that the original function must be multiplied by to achieve a real number.
In it's very earliest phase; that of the synthesis of messenger Rna.
No, Transcription does not require Replication to take place first. Transcription is simply the process of making mRNA from DNA so that the ribosomes have directions to make proteins. Replication is the complete copy of the genetic material in the host chromosome which would occur before the cell divides.
Motility
Liouville's theorem, which is also known as the Complex Analysis was developed by Joseph Liouville. It states that a bounded function is considered a constant function.