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Page "Logarithmic derivative" ¶ 6
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So and for
So we are faced with a vast network of amorphous entities perpetuating themselves in whatever manner they can, without regard to the needs of society, controlling society and forcing upon it a regime representing only the corporation's needs for survival.
Again omitting recent developments, E.T. Leeds' dictum of 1913 has stood unchallenged: `` So far as archaeology is concerned, there is not the least warrant for the second ( shore occupied by ) of these theories ''.
So far as I am concerned, the child is unmistakably father to the man, despite the obvious fact that child and father differ greatly -- sometimes for the better and sometimes for the worse.
So much for all that.
So be it -- then we must embark on a crash program for 200-megaton bombs of the common or hydrogen variety, and neutron bombs, which do not exist but are said to be the coming thing.
`` So, we have to protect the old man for his own good.
`` So that's sculpture '', commented Argiento wryly, when he had sluiced down the floor for a week, `` making mud pies ''.
So when the Big House filled up and ran over, the sisters-in-law found beds for everyone in their own homes.
So, I say, Mr. Speaker, God bless you and keep you for many years not only for this body but for the United States of America and the free world.
So many times I have wondered why veterinarians do not wipe the table clean before each new canine patient is placed on it for examination.
So much for the prototype.
So our innate generosity of spirit prompts us to share our trials, errors and solutions with any who are taking the pool plunge for the first time -- in the pious hope that some may profit from our experience.
So much for the tiresome facts, as familiar to you, I'm sure, as to the constables and state troopers who followed in your wake.
So far as I can see, there is only one way out for the positivist.
So strenuous it was physically, with its days of horseback riding over rough roads that it seems an amazing feat of endurance for both Miss Packard and Miss Upton.
`` So you're looking for a woman who married a man who might have lived here a year ago and might have been poisoned.
So it wouldn't be for days or even a week before you could do anything.
So in the name of justice the magistrate cleared the court of all except officials to allow the captain to elaborate for almost an hour.
So they go looking for mergers with other firms that have publicly quoted stock, and almost daily they pound on the doors of firms like Frito.
So junior's bedroom was usually tricked out with heavy, nondescript pieces that supposedly could take the `` hard knocks '', while the fine secretary was relegated to the parlor where it was for show only.
The biblical symbol for this affirmation is expressed in the words: `` So God created man in his own image ; ;
`` So that the man should not have thoughts of grandeur, and become lifted up, as if he had no lord, because of the dominion that had been given to him, and the freedom, fall into sin against God his Creator, overstepping his bounds, and take up an attitude of self-conceited arrogance towards God, a law was given him by God, that he might know that he had for lord the lord of all.

So and functions
So are many approximations to real-valued functions.
* So long as there are non-measurable sets in a measure space, there are non-measurable functions from that space.
So BBC engineers began talks with one or two television manufacturers, which led to early prototypes in around 1977 – 1978 that could control many more functions.
So, a collection of functions with given signatures generate a free algebra, the term algebra T. Given a set of equational identities ( the axioms ), one may consider their symmetric, transitive closure E. The quotient algebra T / E is then the algebraic structure or variety.
So in mathematical terms a curve is defined by four coordinate functions ( where usually denotes the time coordinate ) depending on one parameter.
So, different functions could indeed be ascribed to particular regions of the brain, but that a finer localization was lacking.
So long as the reaction functions have a slope of less than-1, this will converge to the Nash equilibrium.
So in particular the Gaussian functions with b = 0 and c = 1 are kept fixed by the Fourier transform ( they are eigenfunctions of the Fourier transform with eigenvalue 1 ).
So the Wronskian can be used to show that a set of differentiable functions is linearly independent on an interval by showing that it does not vanish identically.
So the derivative of cumulant generating functions is a generalization of the real constants.
So it is possible to have two different loss functions which lead to the same decision when the prior probability distributions associated with each compensate for the details of each loss function.
So we think of a noncommutative C *- algebra as the algebra of functions on a ' noncommutative space ' which does not exist classically.
So, in 1979, three companies and part of the HQ of the 1st Battalion were split and used to form the 2nd Battalion ; this mirrored the form and functions of the 1st Battalion.
So that a society functions adequately, their members must acquire a character structure which enables them to do what they need to do in order to prosper.
So far it has, however, not been made clear to the public what the powers and functions of these spokespersons are.
So understanding these central actions also became the province of neuroendocrinologists, sometimes even when these peptides cropped up in quite different parts of the brain that appeared to serve functions unrelated to endocrine regulation.
So for example you could mount a CompactPCI Network interface controller in a PXI rack to provide additional network interface functions to a test stand.

So and logarithmic
So we see that the mean flow in the surface layer has a logarithmic relationship with depth.

So and derivative
So the above product is always equal to the difference quotient, and to show that the derivative of at a exists and to determine its value, we need only show that the limit as x goes to a of the above product exists and determine its value.
So initially the whole function just gets rescaled, and it maintains the property that its time derivative is proportional to itself, so for all times t,
So F can be replaced by F-G and G by the constant function 0, making the goal to prove that an everywhere differentiable function whose derivative is always zero must be constant:
So, calculating the covariant derivative in terms of the new lift, one has
So if we choose a control volume that is moving at the same rate as the fluid ( i. e. ( dx / dt, dy / dt, dz / dt ) = v ), then this expression simplifies to the material derivative:
That is, the path follows the fluid current described by the fluid's velocity field v. So, the material derivative of the scalar φ is:
So, formally, it follows that the Fourier series for the derivative is simply in multiplied by the Fourier series for ƒ.
So, for the standard MACD filter time constants of 12 and 26 days, the MACD derivative estimate is filtered approximately by the equivalent of a low-pass EMA filter of 38 days.
So the derivative is
So, by the commutation between the pull-back and the exterior derivative,
So to change the hidden layer weights, we must first change the output layer weights according to the derivative of the activation function, and so this algorithm represents a backpropagation of the activation function.

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