Notation . When we write
is a martingale (submartingale,
supermartingale), we are asserting
X
N is integrable,
Z
N is a decision sequence,
, and
X
N is a MG (SMG, SRMG) relative to
Z
N .
Definition . If
Y
N is integrable and
Z
N is a decision sequence, then
Y
N is
absolutely fair relative to
Z
N iff
Y
N is
favorable relative to
Z
N iff
Y
N is
unfavorable relative to
Z
N iff
Notation . When we write
is absolutely fair (favorable,
unfavorable), we are asserting
Y
N is integrable,
Z
N is a decision sequence,
, and
Y
N is absolutely fair (favorable, unfavorable)
relative to
Z
N .
IXA2-2
Ixa2-1
If
X
N is a basic sequence and
Y
N is the corresponding incremental
sequence, then
is a martingale iff
is absolutely fair.
is a submartingale iff
is favorable.
is a supermartingale iff
is unfavorable.
Let * be any one of the symbols
, or
. Then by linearity and
(CE7)
Remarks
is a SMG iff
is a SRMG
We write (S)MG to indicate the same statement can be made for a MG or a SMG with
the appropriate choice of = or
We write
to indicate simultaneously two cases:
read as = in all places (for a MG)
read as
in all places (for a SMG)
Some basic patterns
Ixa3-1
If
is a (S)MG and
, with
, then
is a (S)MG.
Let
. By
(CE9) , the (S)MG definition,
monotonicity, and
(CE7)
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life