where we use the symbol k to denote the quantum numbers p and σ of the previous section and the sign of the energy, E ( k ), and a < sub > k </ sub > denotes the corresponding annihilation operators.

where k < sub > B </ sub > is Boltzmann's constant, T is the temperature, R is the resistance, and is the bandwidth of the frequency.

This involves an auxiliary regression, wherein the residuals obtained from estimating the model of interest are regressed on ( a ) the original regressors and ( b ) k lags of the residuals, where k is the order of the test.

The fundamental theorem of arithmetic states that any positive integer n can be represented uniquely as a product of powers of primes: where p < sub > 1 </ sub > < p < sub > 2 </ sub > < ... < p < sub > k </ sub > are primes and the a < sub > j </ sub > are positive integers.

The properties of binomial coefficients have led to extending the meaning of the symbol beyond the basic case where n and k are nonnegative integers with ; such expressions are then still called binomial coefficients.

Another occurrence of this number is in combinatorics, where it gives the number of ways, disregarding order, that k objects can be chosen from among n objects ; more formally, the number of k-element subsets ( or k-combinations ) of an n-element set.

This shows in particular that is a natural number for any natural numbers n and k. There are many other combinatorial interpretations of binomial coefficients ( counting problems for which the answer is given by a binomial coefficient expression ), for instance the number of words formed of n bits ( digits 0 or 1 ) whose sum is k is given by, while the number of ways to write where every a < sub > i </ sub > is a nonnegative integer is given by.

where A, B, S and T are active masses and k < sub >+</ sub > and k < sub >−</ sub > are rate constants.

The same number however occurs in many other mathematical contexts, where it is denoted by ( often read as " n choose k "); notably it occurs as coefficient in the binomial formula, hence its name binomial coefficient.

where i, j, and k are the unit vectors for the x -, y -, and z-axes, respectively.

where e < sub > k </ sub > are the coordinate vector fields.

That is a non-deterministic Turing machine with a tape of only kn cells, where n is the size of the input and k is a constant associated with the machine.

where E < sub > a </ sub > is the activation energy and k < sub > B </ sub > is the Boltzmann constant.

where and h and k are the distances between the successive pentagons on the virus surface for each axis ( see figure on right ).

After completing high school Doppler studied philosophy in Salzburg and mathematics and physics at the k. k. Polytechnisches Institut ( now Vienna University of Technology ) where he worked as an assistant since 1829.

The term " discothèque " was coined in Europe to describe clubs where there was no live music played ( a. k. a. disk-only events ).

where m is the mass and k is the spring constant that represents a measure of spring stiffness.

where a is the radius of the circular aperture, k is equal to 2π / λ and J < sub > 1 </ sub > is a Bessel function.

It's bigger than it has to be, though I don't see where it's doing any harm.

Since 1944 he has also conducted regularly at the San Francisco Opera, where he made his debut with a memorable performance of Verdi's Falstaff.

He returned to Germany for the first time in 1953, where he has since conducted in Cologne, Frankfurt, and Berlin.

Even in domains where detailed and predictive understanding is still lacking, but where some explanations are possible, as with lightning and weather and earthquakes, the appropriate kind of human action has been more adequately indicated.

This is done for simplicity of commands and to bring the hidden redundancy up to where misunderstanding has almost zero possibility.

Ideally speaking, it should be allowed to operate only where the public has a great stake in the continuity of supply or services, and where the actions of a single proprietor are secondary to the needs of society.

The fact that he has cast over those materials the light of a skeptical mind does not make him any the less Southern, I rather think, for the South has been no more solid than other regions except in the political and related areas where patronage and force and intimidation and fear may produce a surface uniformity.

`` History has this in common with every other science: that the historian is not allowed to claim any single piece of knowledge, except where he can justify his claim by exhibiting to himself in the first place, and secondly to any one else who is both able and willing to follow his demonstration, the grounds upon which it is based.

Further, it has its work cut out stopping anarchy where it is now garrisoned.

A nuclear pacifier of these dimensions -- roughly some six and a half times bigger than anything the United States has triggered experimentally -- would certainly produce a bigger bang, and, just for kicks, Khrushchev might use it to propel the seminar of the house of delegates from St. Louis to the moon, where there wouldn't even be any beer to drink.

Carbondale is in the Herrin-Murphysboro-West Frankfort labor market, where unemployment has been substantially higher than the national average.

And then there is St. Louis county, where the Democratic leadership has shown little appreciation of the need for sound zoning, of the important relationship between proper land use and economic growth.

They enlisted the help of the New Jersey congressman, who has been able to trace the letters to the national archives, where they are available on microfilm.

After all, when one has asked whatever became of old Joe and Charlie when one has inquired who it was Sue Brown married and where it is they now live when questions are asked and answered about families and children, and old professors when the game and its probable outcome has been exhausted that does it.

By making inroads in the name of law enforcement into the protection which Congress has afforded to the marriage relationship, the Court today continues in the path charted by the recent decision in Wyatt v. United States, 362 U.S. 525, where the Court held that, under the circumstances of that case, a wife could be compelled to testify against her husband over her objection.

In other instances where there is no automatic block signaling, the distant has only green and yellow aspects.

Menfolk can ride in the forward cockpit where the helmsman has a clear view.

The next step is to remove it and spread glue where it has been marked at the contact points.

Now, the machine has been improved to a point where it is generally more economical than oil heat at temperatures down to 15 degrees.

But now many of these same builders are finding they can cut their costs more by teaming up with a dealer who has volume enough to afford the most efficient specialized equipment to deliver everything just where it is needed -- drywall inside the house, siding along the sides, trusses on the walls, roofing on the roof, etc..

She was sitting on the edge of the bed again, back in the same position where the snake had found her.

I asked the same questions inside the launch-control rooms of an Atlas missile base in Wyoming, where officers who wear sidearms are manning the `` commit buttons '' that could start a war -- accidentally or by design -- and in the command centers where other pistol-packing men could give orders to push such buttons.

Robert Penn Warren puts it this way in `` Brother To Dragons '': `` The recognition of complicity is the beginning of innocence '', where innocence, I think, means about the same thing as redemption.

We were almost the same age, she was fifteen, I was twelve, and where I felt there was a life to look forward to Lilly felt she had had as much of it as was necessary.

We don't 'low nigras to walk on the same sidewalk with white men where I come from.

By this standard, it is determined that where two stations operating on the same frequency are involved, objectionable interference from station A exists at any point within the service area of station B where station A's signal is of an intensity one-twentieth or more of the strength of station B's signal at that point.

during the same period around sunrise, skywave transmission is declining, until at about 2 hours after sunrise it reaches a point where it becomes of little practical significance.

First, is the circulating form of the hormone the same as that found in the gland where it is synthesised and stored??

In even greater degree the same rule applied to the remainder of Eastern Europe, where the upper classes had generally collaborated with the Nazis, even to the extent of sending millions of their peasants into Russia as a part of Hitler's armies.

I think we were very tired, for we awoke at the same moment, deeply rested, surprised to see the late morning sun on the windows, which were wet where the rime had melted.

; Balanced design: An experimental design where all cells ( i. e. treatment combinations ) have the same number of observations.

Simone de Beauvoir tries to base an ethics on Heidegger's and Sartre's writings ( The Ethics of Ambiguity ), where she highlights the need to grapple with ambiguity: " as long as philosophers and they have thought, most of them have tried to mask it ... And the ethics which they have proposed to their disciples has always pursued thre same goal.

This is not the most general situation of a Cartesian product of a family of sets, where a same set can occur more than once as a factor ; however, one can focus on elements of such a product that select the same element every time a given set appears as factor, and such elements correspond to an element of the Cartesian product of all distinct sets in the family.

Although it had at first been somewhat established in many colonies, in 1861 it was ruled that, except where specifically established, the Church of England had just the same legal position as any other church.

The same definition holds in any unital ring or algebra where a is any invertible element.

The top of the building is a crown, like a huge gable, which is at the same level as the roof and helps to conceal the room where there used to be water tanks.

Around the same time, on the North slope, in a cave next to the one dedicated to Pan since the classical period, a sanctuary was founded where the archons dedicated to Apollo on taking office.

Writing about AD 94, Clement of Rome states that the apostles appointed successors to continue their work where they had planted churches and for these in their turn to do the same because they foresaw the risk of discord.

Consequently, Abba Mari removed first to Arles, and, within the same year, to Perpignan, where he finally settled and disappeared from public view.

She is thought to bear the name of the deity who was derived from Libya, where known as Neith, the same source sometimes identified as the parallel for Athene.