Newspapers, taxpayer-funded entities with some religious affiliation, and political parties can obtain fairly clear guidance on the boundaries within which their freedom of expression rights apply.

Then, using the periodic Bernoulli function P < sub > n </ sub > defined above and repeating the argument on the interval, one can obtain an expression of ƒ ( 1 ).

We can factor this expression to obtain

By using the streamwise vector i parallel to the freestream in place of k in the integral, we obtain an expression for the pressure drag D < sub > p </ sub > ( which includes induced drag in a 3D wing ).

In modern language, what Diophantus does is to find rational parametrisations of many varieties ; in other words, he shows how to obtain infinitely many rational numbers satisfying a system of equations by giving a procedure that can be made into an algebraic expression

When the Zeeman effect is small compared to zero-field state separations, line width, and kT and when the line shape is independent of H, it could be obtain to first order in H for the expression of Δk, assuming j to be sufficiently high in energy that N < sub > j </ sub > = 0, and it is given by:

This is the classical method used by Ricci and Levi-Civita to obtain an expression for the Riemann curvature tensor.

To obtain the CHSH test statistic S ( expression ( 2 )), all that is needed is to multiply the inequalities for which j is different from k by − 1 and add these to the inequalities for which j and k are the same.

If we call v < sub > mon </ sub > the STP volume of adsorbate required to form a monolayer on the adsorbent ( per gram of adsorbent ), and we obtain an expression for a straight line:

This expression should be substituted into the expression for projectile momentum in order to obtain more a more accurate description of the recoil process.

To obtain an approximate expression for the average magnetic field on a railgun armature, we assume that the rail radius is small compared with the rail separation and, by assuming that the railgun rails can be modelled as a pair of semi-infinite conductors, we compute the following integral:

The chief aim of the association in France also was political, namely, to obtain a constitution in which the conception of the sovereignty of the people could find expression.

We may integrate the expression for to obtain the Helmholtz energy:

This constraint can be used to rearrange the expression for the total energy fluctuation and obtain:

and after some elementary manipulation, we obtain an elegant expression for the Ricci flow:

To obtain the first-order correction to the energy eigenstate, we insert our expression for the first-order energy correction back into the result shown above of equating the first-order coefficients of λ.

Choosing local coordinates we obtain the local expression for the Hessian as

" Whatever the twists and turns of a system of threads in space, one can always obtain an expression for the calculation of its dimensions, but this expression will be of little use in practice.

This recursive relation can be successively substituted into itself and expanded to obtain expression for total amount of work done.

Substituting the explicit expression for U we obtain:

Taking in above expression outside the integral sign and expanding the integrand with the help of the Hadamard lemma one can obtain the following useful expression for the derivative of matrix exponent:

Carbohydrates are not necessary building blocks of other molecules, and the body can obtain all its energy from protein and fats .< ref >

For natural proteins, a series of purification steps may be necessary to obtain protein sufficiently pure for laboratory applications.

Younger turtles tend to be more carnivorous ( to obtain more animal protein ) than adults.

In the first use of electron crystallography to obtain an atomic-level protein structure, the structure of bacteriorhodopsin was resolved in 1990.

in cell culture to obtain a Islets of Langerhans | pancreatic lineage from mesoderm al stem cells the retinoic acid signalling pathway must be activated while the sonic hedgehog pathway inhibited, which can be done by adding to the Growth medium | media anti-shh antibodies, HHIP | Hedgehog interacting protein or cyclopamine, the first two are protein and the last a small molecule.

As the merozoites are released, they invade erythrocytes and initiate the erythrocytic cycle, where the parasite digests hemoglobin to obtain amino acids for protein synthesis.

Enteropeptidase's specificity makes it an ideal tool in biochemical applications ; a fusion protein containing a C-terminal tag ( such as poly-His ) linked by this sequence can be cleaved by enteropeptidase to obtain the target protein following protein purification.

Cultured cells expressing the aequorin gene can effectively synthesize aequorin: however, recombinant expression yields only the apoprotein, therefore it is necessary to add coelenterazine into the culture medium of the cells to obtain a functional protein and thus use its blue light emission to measure Ca < sup > 2 +</ sup > concentration.

Similar to those of Staphylococcus aureus, the cell walls of S. epidermidis have a transferrin binding protein that helps the organism obtain iron from transferrin.

If every frame was encoded using this technique, there would be no way for a decoder to synchronize to a video stream because it would be impossible to obtain the reference images.

On the way out Mr. Sakellariadis detoured up a special hill from which one may obtain a matchless view of the Acropolis lighted by night.

Thus we obtain g{t} by introducing an oblique g{t}-axis in the Aj.

Nevertheless, with a reading public that longs for the `` good old days '' and with an awareness of our expanding international interests, it is easy for the Benets to obtain a magnified position in literature by use of all sorts of Americana, real or fake, and it is easy for the Steinbecks and Sandburgs to support their messages of reform by reading messages of reform into the minds of the folk.

`` I would expect the proposed committee to hold public hearings '', Mr. Notte said, `` to obtain the views of the general public and religious, labor and special-interest groups affected by these laws ''.

Any needy family living in San Francisco can obtain toys by writing to Christmas Toys, 676 Howard street, San Francisco 5, and listing the parent's name and address and the age and sex of each child in the family between the ages of 1 and 12.

An appeal " by leave " or " permission " requires the appellant to obtain leave to appeal ; in such a situation either or both of the lower court and the appellate court may have the discretion to grant or refuse the appellant's demand to appeal the lower court's decision.

* To obtain a declaration on a legal document, such as an application for voter registration, that the information provided by the applicant is truthful to the best of the applicant's knowledge.

For example for any ( even infinite ) collection of pairs of shoes, one can pick out the left shoe from each pair to obtain an appropriate selection, but for an infinite collection of pairs of socks ( assumed to have no distinguishing features ), such a selection can be obtained only by invoking the axiom of choice.

A consequence of using waveforms to describe particles is that it is mathematically impossible to obtain precise values for both the position and momentum of a particle at the same time ; this became known as the uncertainty principle, formulated by Werner Heisenberg in 1926.

In order to obtain better results, possible coexisting motor deficits need to be addressed in addition to those induced by ataxia.

But whereas professionals obtain licenses as their “ measurability of the excellence of service provided ” ( Stebbins, 1992, p. 21 ), amateurs break taboos by loving their work and not passing standardized tests.

But all of them seemed to agree that, " There is some body or other that is of its own nature supremely cold and by participation of which all other bodies obtain that quality.

After the indecisive < ref name =" British historian Townsend Miller "> British historian Townsend Miller: “ But, if the outcome of < nowiki > battle of </ nowiki > Toro, militarily, is debatable, there is no doubt whatsoever as to its enormous psychological and political effects ” in The battle of Toro, 1476, in History Today, volume 14, 1964, p. 270 </ ref > Battle of Toro in 1476 against King Ferdinand II of Aragon, the husband of Isabella I of Castile, he went to France to obtain the assistance of Louis XI, but finding himself deceived by the French monarch, he returned to Portugal in 1477 in very low spirits.

One of the tasks imposed upon Heracles by Eurystheus was to obtain possession of the girdle of the Amazonian queen Hippolyta.

Andrew went to Constantinople to obtain the Crown of Thorns bought by Louis IX of France | Louis IX to Baldwin II of Constantinople | Baldwin II.

Andrew's first mission to the East was when he was asked by the French king Louis IX to go and fetch the Crown of Thorns which had been sold to him by the Latin Emperor of Constantinople Baldwin II in 1238, who was anxious to obtain support for his tottering empire.

Anthemius assumes a property of an ellipse not found in Apollonius's work, that the equality of the angles subtended at a focus by two tangents drawn from a point, and having given the focus and a double ordinate he goes on to use the focus and directrix to obtain any number of points on a parabola — the first instance on record of the practical use of the directrix.

The RAND Corporation's Memorandum 5446-ISA / ARPA states: " the fact that the VC obtain most of their food from the neutral rural population dictates the destruction of civilian crops ... if they ( the VC ) are to be hampered by the crop destruction program, it will be necessary to destroy large portions of the rural economy – probably 50 % or more ".

*# The second basic thesis is that intellectual freedom is essential to human society — freedom to obtain and distribute information, freedom for open-minded and unfearing debate and freedom from pressure by officialdom and prejudices.

Manufacturers specify much higher drain efficiencies, and designers are able to obtain higher efficiencies by providing current to the drain of the transistor through an inductor or a transformer winding.

Originally, poorly organised Lions teams regularly suffered defeat at the hands of their hosts, but by 1955 the tourists took the matches seriously enough to obtain a 2 – 2 draw in South Africa.

Now, plants are considered to be organisms that obtain their energy from sunlight by means of photosynthesis and some closely related, chlorophyll-free parasitic plants.

According to this view, the story of Jacob's visit to Laban to obtain a wife originated as a metaphor for this migration, with the property and family which were gained from Laban representing the gains of the Joseph tribes by the time they returned from Egypt ; according to textual scholars, the Jahwist version of the Laban narrative only mentions the Joseph tribes, and Rachel, and does not mention the other tribal matriarchs whatsoever.