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13.5
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AND CUT IT HERE THEN THE SMALL PORTION THAT WILL APPEAR IS MORE OR JUST LIKE VERY CLOSE
and cut it here then the small portion that will appear is more or just like very close
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AND WE ALSO MENTIONED THAT SUCH A LINEAR DISCRIMINANT CAN BE THOUGHT OF AS A SPECIAL CASE OF LINEAR
and we also mentioned that such a linear discriminant can be thought of as a special case of linear
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IS NON NEGATIVE OF COURSE WE DO NOT NEED ANY SIGN RESTRICTIONS ON MU STAR SO LET
is non negative of course we do not need any sign restrictions on mu star so let
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THE WATER TODAY AND THEN YOU CAN GO THROUGH THE ROUT SITUATION IN A BETTER MANNER SO BEING ABLE TO FORECAST ACCURATELY IS ALSO
the water today and then you can go through the rout situation in a better manner so being able to forecast accurately is also
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DO NOT OCCUR UNLESS THERE IS AN APPROPRIATE CATALYST NOW EVEN IN PRESENCE OF APPROPRIATE
do not occur unless there is an appropriate catalyst now even in presence of appropriate
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NOW ONE OHM BY FOUR OHMS WHICH IS YOUR BASE SO IT HAS A VALUE OF ZERO PER UNIT
now one ohm by four ohms which is your base so it has a value of zero per unit
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N PLUS L ELEMENTS IN THE Y IN THE RANGE SET THEN WE START WITH ANY N PLUS ONE ELEMENT IN
n plus l elements in the y in the range set then we start with any n plus one element in
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YOU HAVE ALREADY SEEN INDIANS ARE USING THE RADIUS TIMES THE SINE FUNCTION AS THE FL THAT
you have already seen indians are using the radius times the sine function as the fl that
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FORMALLY THEY ARE REFERRED TO AS BLOCK PLACEMENT WHICH IS THE DECISION REGARDING WHERE IN THE
formally they are referred to as block placement which is the decision regarding where in the
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HEAT OF HYDRATION WITH TIME LET US SEE HEAT OF BECAUSE WE HAVE SEEN OTHER CONTRIBUTION OF EACH COMPOUND OF CEMENT TO HEAT OF HYDRATION
heat of hydration with time let us see heat of because we have seen other contribution of each compound of cement to heat of hydration
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IT MOVES FURTHER AND FURTHER RIGHT BUT IT IS MULTIPLIED BY E TO THE NU T BECAUSE THIS
it moves further and further right but it is multiplied by e to the nu t because this
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IS ZERO V B R IS MINUS V D C BY TWO YOU CAN ACHIEVE THIS SAME THING IF FOR EXAMPLE WE
is zero v b r is minus v d c by two you can achieve this same thing if for example we
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HAVE TO CORRESPONDS TO THE ROWS AND THE RIGHT VERTICES JUST TO DISTINGUISH THEM I WILL
have to corresponds to the rows and the right vertices just to distinguish them i will
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T RIGHT NOW VS IS A ONE OF THE STATE VARIABLES SO THAT WE CAN WRITE DOWN THE EQUATION IN
t right now vs is a one of the state variables so that we can write down the equation in
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THREE N IT NOT GOING TO WORK NOT GOING TO BE ABLE TO DO THAT BUT STILL IT WILL BE EFFICIENT
three n it not going to work not going to be able to do that but still it will be efficient
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AS I HAVE SAID THAT DI SQUARE IS CHI SQUARE DISTRIBUTED SO THERE WILL BE RELATIONSHIP
as i have said that di square is chi square distributed so there will be relationship
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DIMENSIONAL LESS EQUATION BECOMES MINUS U X PRIME U Y PRIME BY U STAR SQUARE PLUS NU
dimensional less equation becomes minus u x prime u y prime by u star square plus nu
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EQUAL TO MINUS A OMEGA SQUARE SIN OMEGA T IS EQUAL TO MINUS OMEGA SQUARE X
equal to minus a omega square sin omega t is equal to minus omega square x
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TOWERS AND COMES DOWN TO ENGAGE WITH THE PROBLEMS OF THE REAL WORLD OUT THERE NOW THIS IS QUITE A PASSIONATE PLEA
towers and comes down to engage with the problems of the real world out there now this is quite a passionate plea
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THEN THE ANOTHER CATEGORY OF SIGNAL HERE IS THE CALLINGON SIGNAL AND THIS CALLINGON
then the another category of signal here is the callingon signal and this callingon
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DIRECTION IN WHICH CRACK HAS PROPAGATED SO THIS THESE INFORMATION CANNOT BE OBSERVED
direction in which crack has propagated so this these information cannot be observed
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DEPENDING ON THE SIZE RANGE OF THE PARTICLES YOU MAY CHOOSE TO USE OPTICAL MICROSCOPY OR SCANNING ELECTRON MICROSCOPY OR TUNNELING ELECTRON MICROSCOPY YOU COUNT THE NUMBER
depending on the size range of the particles you may choose to use optical microscopy or scanning electron microscopy or tunneling electron microscopy you count the number
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OVER A DIAGRAM FOR EXAMPLE IF I TAKE THIS IS A SLAG METAL INTERFACE LET US SEE SULPHUR
over a diagram for example if i take this is a slag metal interface let us see sulphur
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DO IT BY THE METHOD WE DID IT IN THE LAST CLASS IS IT CLEAR NOW ARE YOU ABSOLUTELY
do it by the method we did it in the last class is it clear now are you absolutely
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WHICH CONDITIONS YOU GET MAXIMUM CONCENTRATE ETCETERA ETCETERA AND THEY HAVE BEEN FOUND
which conditions you get maximum concentrate etcetera etcetera and they have been found
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IS DISSIPATED THERE IS A LARGER ZONE WERE THE TOUGHENING OF OCCURS AND ENERGY IS DISSIPATED
is dissipated there is a larger zone were the toughening of occurs and energy is dissipated
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ERROR TERMS ARE WELL CONNECTED AND HOW IT CAN BE VERY POTENTIAL AND VERY INFLUENTIAL
error terms are well connected and how it can be very potential and very influential
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THAT IS ALL THE POWER THAT IS FED FROM PORT NUMBER ONE COMES BACK TO PORT NUMBER TWO NOW
that is all the power that is fed from port number one comes back to port number two now
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THAN OR EQUAL TO X J J SO SINCE THREE AND FIVE ARE MEDIANS X THREE THREE EQUAL TO ONE X FIVE FIVE EQUAL
than or equal to x j j so since three and five are medians x three three equal to one x five five equal
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BEING COVERED WHICH ARE COVERED BY THIS MAP SHEET IT IS HERE KANPUR AND UNNAO
being covered which are covered by this map sheet it is here kanpur and unnao
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EQUAL TO Z F INTO I ONE V ONE MINUS V TWO IS EQUAL TO Z F INTO I ONE CURRENT FLOWING HERE SO Z
equal to z f into i one v one minus v two is equal to z f into i one current flowing here so z
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CURVED DISLOCATION AND THIS ANGLE IS THETA AND IF THIS RADIUS OF CURVATURE IS LARGE
curved dislocation and this angle is theta and if this radius of curvature is large
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THE DEFECT FREE PURE METAL AT THE INLET
the defect free pure metal at the inlet
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FILM AND GO TO THE SURFACE AND THE REACT ON THE SURFACE IF IT IS ONLY NONPOROUS PARTICLE
film and go to the surface and the react on the surface if it is only nonporous particle
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A STATE THE GROUND STATE OF THE SIMPLE HARMONIC OSCILLATOR WHERE DELTA X DELTA P IS EQUAL
a state the ground state of the simple harmonic oscillator where delta x delta p is equal
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FOUR METERS HEIGHT OF SURCHARGE AND IT IS A CONSOLIDATION IS ONLY OCCURRING THERE
four meters height of surcharge and it is a consolidation is only occurring there
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WE KNOW X W WE CAN GET X W PERP AS X MINUS X W AND AN ALTERNATELY IF WE KNOW THE PROJECTION
we know x w we can get x w perp as x minus x w and an alternately if we know the projection
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IT IS R WE SAY THE REAL VECTOR SPACE OR A COMPLEX VECTOR SPACE SO WHAT WE SEE HERE
it is r we say the real vector space or a complex vector space so what we see here
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WILL TAKE TO MANUFACTURE OTHER PRODUCT SO METHOD STUDY IF CARRIED OUT PROPERLY TO
will take to manufacture other product so method study if carried out properly to
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SO BASICALLY YOUR ITS JUSTIFIED WHEN THIS SUMMATION CONVERGES TO ANALYTIC FUNCTION
so basically your its justified when this summation converges to analytic function
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OF OSCILLATION IT IS GOING TO INTERACT WITH THE GUSTING WIND WHEREAS THE SHORT PERIOD
of oscillation it is going to interact with the gusting wind whereas the short period
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SO R C TRIPLE BOND C AND THIS WOULD GIVE YOU A CONJUGATED TRIPLE BOND C COUPLED PRODUCTS
so r c triple bond c and this would give you a conjugated triple bond c coupled products
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A TO X F T DT AS IF IT IS A DEFINITE INTEGRAL FIND OUT THE VALUE IN TERMS OF X AND THEN
a to x f t dt as if it is a definite integral find out the value in terms of x and then
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OF THE DETECTOR IN A RADIO RECEIVER CIRCUIT IT IS DERIVED OUT OF THE DETECTOR THE DC VOLTAGE
of the detector in a radio receiver circuit it is derived out of the detector the dc voltage
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THE POINT RATING METHOD IN THE RANKING METHOD WHAT IS DONE IS TO PULL ALL THE EXISTING DESIGNATIONS
the point rating method in the ranking method what is done is to pull all the existing designations
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OF THIS SO IF ANY SEQUENCE CONVERGES IN THIS METRIC THEN THAT SEQUENCE HAS TO CONVERGE
of this so if any sequence converges in this metric then that sequence has to converge
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KIND OF CONFIGURATIONS IN A BGA OR A CSP SO A BGA PACKAGE TODAY IS A WORK CROSS OF THE INDUSTRY
kind of configurations in a bga or a csp so a bga package today is a work cross of the industry
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SECOND WHICH SAYS THAT ITS RELATIVELY GRANULAR SOIL THE FLOW NET IS DRAWN LIKE THIS WITH
second which says that its relatively granular soil the flow net is drawn like this with
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SURFACE AREA IS ABOUT FIFTEEN METER SQUARE PER GRAM
surface area is about fifteen meter square per gram
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MORE HIGHER BUT QUICKLY ARE GOING DOWN GROUP ONE AND THE ND GROUP IT IS IN OPPOSITE
more higher but quickly are going down group one and the nd group it is in opposite
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DP AND ALSO WE NEED TO ACCOUNT FOR THE PARTICLES WHICH ARE ALREADY PRESENT IN THIS SMALL ELEMENT
dp and also we need to account for the particles which are already present in this small element
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TEND TO BUY EXACTLY WHAT IS DEMANDED OR THEY BUY FOR THE DEMAND OF A VERY SHORT PERIOD
tend to buy exactly what is demanded or they buy for the demand of a very short period
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IS LEFT AS ONE IN THIS STATE NOW IT IS SCANNING THIS PARTICULAR SYMBOL WHICH WILL BE CONVERTED
is left as one in this state now it is scanning this particular symbol which will be converted
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X MINUS A TO THE POWER N PLUS ONE THAT IS ZERO THAT IS FOR CHOOSING M IN THIS MANNER THIS
x minus a to the power n plus one that is zero that is for choosing m in this manner this
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WHEN YOU WANT TO DECODE CONVOLUTIONAL CODE OVER AN ADDITIVE WHITE GAUSSIAN CHANNEL SO
when you want to decode convolutional code over an additive white gaussian channel so
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WE HEAR SOME UNWANTED TALK GOING ON IN THE BACKGROUND
we hear some unwanted talk going on in the background
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MAY COME INTO PLAY IN HOW THE CACHE CONTROLLER HANDLES THE VARIOUS SCENARIOS THAT COULD ARISE WE WILL LOOK INTO THESE DETAILS ABOUT THE OPERATION OF THE CACHE IN THE FEW LECTURES
may come into play in how the cache controller handles the various scenarios that could arise we will look into these details about the operation of the cache in the few lectures
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WHY LATER OUT OF THIS FORTY NINE QUESTIONS A FEW OF THEM BECAME IMPORTANT SO THE FIRST THING IS
why later out of this forty nine questions a few of them became important so the first thing is
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LINK PLUS L SINE THETA HERE WHICH IS THE LENGTH OF THE THIRD LINK SINE THETA PLUS
link plus l sine theta here which is the length of the third link sine theta plus
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ALSO DOES THE SAME THING INSERTION TO SIGMA BOND BUT IT IS MUCH MORE SELECTIVE FOR EXAMPLE
also does the same thing insertion to sigma bond but it is much more selective for example
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FEATURES FEATURES COULD BE THESE LIKE THE MEAN RMS STANDARD DEVIATION VARIANCE KURTOSIS
features features could be these like the mean rms standard deviation variance kurtosis
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ALREADY OBTAINED THE VELOCITY SOLUTION AS GIVEN BY C ONE C TWO FOR DIFFERENT VALUES OF
already obtained the velocity solution as given by c one c two for different values of
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SO IF WE LOOK AT THIS MASS BALANCE EQUATION FOR I AM GOING TO ASSUME A PLUCK FLOW REACTOR
so if we look at this mass balance equation for i am going to assume a pluck flow reactor
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IS GOING TO SATURATION AND OUTPUT OF THE DIFFERENTIAL AMPLIFIER IS GOING TO BE NOTHING BUT A FAIRLY
is going to saturation and output of the differential amplifier is going to be nothing but a fairly
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SO FORTH IT IS AN INFINITE SERIES THAT WE ARE GOING WE ARE GOING TO LOOK AT SO WHAT
so forth it is an infinite series that we are going we are going to look at so what
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I THINK MANY OF YOU HAVE STUDIED THE BOOK BY N N LEBEDEV SO HE HAS WRITTEN A BOOK
i think many of you have studied the book by n n lebedev so he has written a book
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THE DISTANCE BETWEEN THE DEPOT AND CITY TWO AND SO ON THEREFORE TWENTY FOURTEEN TWELVE AND NINETEEN
the distance between the depot and city two and so on therefore twenty fourteen twelve and nineteen
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BE A DISCRETE PRODUCT IT WOULD BE EXACT DUPLICATE OF THE SHAPE OF THE MOLD THAT IS USED IN THE
be a discrete product it would be exact duplicate of the shape of the mold that is used in the
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TWENTY FOUR HOURS DATA AND BEYOND WHICH IT REMAINS TWENTY FOUR HOURS BUT IT CANNOT BE SINCE IT CANNOT
twenty four hours data and beyond which it remains twenty four hours but it cannot be since it cannot
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ZOOMED IMAGES OF OPEN CHANNELS AND HERE YOU SEE THE CLOSED CHANNELS OKAY AFTER THIS COC
zoomed images of open channels and here you see the closed channels okay after this coc
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MODEL OF THE FLOW AND THAT WAY WE ARE GETTING DIFFERENT FORMS OF THE EQUATION AND THEN
model of the flow and that way we are getting different forms of the equation and then
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AND THEREFORE THIS IS HOW THE COMPONENTS OF ANGULAR MOMENTUM ALONG THE THREE AXIS CHANGE
and therefore this is how the components of angular momentum along the three axis change
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EIGHT NOW HAVING CONSTRUCTED THE TENSOR PRODUCTS OF EACH ONE OF THESE EIGEN VECTORS WE MULTIPLIED
eight now having constructed the tensor products of each one of these eigen vectors we multiplied
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BE INCREASING IN TERMS OF MAGNITUDE WHEN WE ARE DEALING WITH STREAM FUNCTION VELOCITY
be increasing in terms of magnitude when we are dealing with stream function velocity
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THAT CAN BE A LIMITATION THAT CAN BE INDIFFERENT OR THAT CAN BE INDEPENDENT OF WHAT IS THE MOST LOVING THING TO DO OR
that can be a limitation that can be indifferent or that can be independent of what is the most loving thing to do or
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SO WH IS THE HOMOGENOUS COORDINATE CORRESPONDING TO WORLD COORDINATE W AND CH IS THE HOMOGENOUS
so wh is the homogenous coordinate corresponding to world coordinate w and ch is the homogenous
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SEE THIS SLUDGE THAT WOULD BE PRODUCED HERE SELECTIVELY SELECTIVELY IT WOULD BE BROUGHT
see this sludge that would be produced here selectively selectively it would be brought
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OFFERED NEXT SEMESTER THAT IS HAVE THE PROCESS ABOUT THIS PRISON PROCESS THAT IS JUST F Y
offered next semester that is have the process about this prison process that is just f y
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DEVIATION OF THE ROTOR SPEED RIGHT NOW IT HAS PRIMARILY THREE BLOCKS THE FIRST BLOCK WE
deviation of the rotor speed right now it has primarily three blocks the first block we
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WENT ON FOR SOME TIME TILL YOU HAD THE LIBERALIZED ERA COMING IN AND THAT BROUGHT WITH IT A GREAT
went on for some time till you had the liberalized era coming in and that brought with it a great
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AND THIS BENDING IS CAUSED BY THE ROTATION THAT IS THE MOMENT THAT IS APPLIED AT THE
and this bending is caused by the rotation that is the moment that is applied at the
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NO AVERAGE RATE THAT IS THE ACTUAL RATE YOU WILL GET AND THEN OFCOURSE YOU HAVE THAT AS
no average rate that is the actual rate you will get and then ofcourse you have that as
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THIS EQUATION IS BASICALLY A SIN OMEGAN T PLUS B COS OMEGAN T THE CONSTANTS A AND B
this equation is basically a sin omegan t plus b cos omegan t the constants a and b
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WITH AN AXIS SYMMETRIC RIM NOW YOU WILL HAVE IMAGINE THIS IS AXIS SYMMETRIC SO NOW THESE
with an axis symmetric rim now you will have imagine this is axis symmetric so now these
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THE PHYSICAL PROPERTIES FOR EXAMPLE ELECTRICAL CONDUCTIVITY RELATIVE TO SOME FIXED AXIS IN
the physical properties for example electrical conductivity relative to some fixed axis in
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STAR MUST BE IS EQUAL TO F N MINUS TWO DIVIDED BY F N L ZERO WHAT IS MY F N MINUS TWO HERE MY
star must be is equal to f n minus two divided by f n l zero what is my f n minus two here my
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NINETY FIVE PERCENT OF AREA CONTAINING THAT SO THIS AREA BETWEEN Z IS EQUAL TO MINUS TWO TO Z IS
ninety five percent of area containing that so this area between z is equal to minus two to z is
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IN THIS CASE IT IS THE SAME AS U TRANSPOSE A U BECAUSE U STAR IS U TRANSPOSE BECAUSE
in this case it is the same as u transpose a u because u star is u transpose because
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THIS PARTICULAR Z VECTOR IS ROTATING IN ANTICLOCKWISE DIRECTION INSIDE THE CIRCLE AND A IS THE
this particular z vector is rotating in anticlockwise direction inside the circle and a is the
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IS GIVING SEE YOU YOU KNOW SOMETHING IS REQUIRED LIKE YOU KNOW THE EARTH PRESSURE
is giving see you you know something is required like you know the earth pressure
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STRESS TO ATTEND THE SAME AMOUNT OF STRAIN WHEREAS CERAMICS WHICH IS KNOWN TO BE A BRITTLE
stress to attend the same amount of strain whereas ceramics which is known to be a brittle
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WATERCEMENT RATIO OUTER PRODUCT REQUIRED WILL BE LOW AND FILLER AFFECT WITH THIS
watercement ratio outer product required will be low and filler affect with this
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OF PLUS N Z SQUARE F Z AND MINUS N Z SQUARE F Z
of plus n z square f z and minus n z square f z
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ALSO IT WILL BECOME V PLUS V W AND THEN VELOCITY OF THIS IN THIS DIRECTION WILL BECOME
also it will become v plus v w and then velocity of this in this direction will become
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X BAR K PLUS ONE THIS IS M OF X K M OF X K PLUS X BAR K NOW PLEASE REMEMBER X K TO A
x bar k plus one this is m of x k m of x k plus x bar k now please remember x k to a
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BOUNDED LINEAR FUNCTIONAL ON X NOW THIS LEADS THE CONCEPT OF THE ADJOINT OPERATOR
bounded linear functional on x now this leads the concept of the adjoint operator
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LAYER OF OXYGEN FOLLOWED BY FIRST LAYER OF IRON FOLLOWED BY B LAYER OF OXYGEN FOLLOWED
layer of oxygen followed by first layer of iron followed by b layer of oxygen followed
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CALL IT C S H THAT IS WHY THERE IS A REASON YOU KNOW THERE IS A REASON WE SAID THAT IT HAS GOT GENERAL LIKE STRUCTURE
call it c s h that is why there is a reason you know there is a reason we said that it has got general like structure
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SQUARE BY C SQUARE N SQUARE OF X AND THEREFORE THIS IS EQUAL TO FOUR PI SQUARE BY LAMBDA SQUARE
square by c square n square of x and therefore this is equal to four pi square by lambda square
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US CALL IT THIRD TYPE THIRD TYPE OF CONSONANTS ARE CALLED WHAT ARE THEY CALLED PLEASE GIVE
us call it third type third type of consonants are called what are they called please give
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