In other words, if F satisfies the differential equation Af, then F is uniquely expressible in the form Af where Af satisfies the differential equation Af.

In other words, solutions of the 1D wave equation are sums of a right traveling function and a left traveling function.

In other words, the first equation has distinct roots, while the second does not.

In words, the equation states:

In other words, the defining equation for W ( z ) is

This equation uses signed lengths of segments, in other words the length AB is taken to be positive or negative according to whether A is to the left or right of B in some fixed orientation of the line.

In other words, we wish to maximize the Shannon entropy equation:

This equation may be translated into words as follows:

In other words, an equation ( or virtual environment ) describing an admittance would have inputs of force and would have outputs such as position or velocity.

In other words, it is an equation of the form

In other words, the solution of equation ( 2 ), u ( x ), can be determined by the integration given in equation ( 3 ).

for every f in F. In other words take the smallest normal subgroup N of G ∗ H containing all elements on the left-hand side of the above equation, which are tacitly being considered in G ∗ H by means of the inclusions of G and H in their free product.

In other words, solving an equation does not solve social problems.

That is, given a number of functions on a moduli space, a modular equation is an equation holding between them, or in other words an identity for moduli.

A solution of the equation is an assignment of expressions to the unknowns that satisfies the equation ; in other words, expressions such that, when they are substituted for the unknowns, the equation becomes an identity.

In words, this equation says that: the ionic current ( I < sub > ion </ sub >) is equal to that ion's conductance ( g < sub > ion </ sub >) multiplied by the driving force, which is represented by the difference between the membrane potential and the ion's equilibrium potential ( i. e. V < sub > m </ sub >- E < sub > ion </ sub >).

In other words, every type of mean-field kinetic equation, and in fact every mean-field theory, involves a quasi-particle concept.

By construction, the distance from the origin to a point on the cissoid is equal the difference between the distances between the origin and the corresponding points on L and C. In other words, the polar equation of the cissoid is

The equation would apply equally to masses ( or other conserved quantities ), where the word mass is substituted for the words electric charge above.

Zoroastrianism states that for the righteous souls, a beautiful maiden, which is the personification of the soul's good thoughts, words and deeds, appears.

Anthony Heilbut, author of The Gospel Sound, states that the " dangers, toils, and snares " of Newton's words are a " universal testimony " of the African American experience.

In Gandhi ’ s thought, ahimsa precludes not only the act of inflicting a physical injury, but also mental states like evil thoughts and hatred, unkind behavior such as harsh words, dishonesty and lying, all of which he saw as manifestations of violence incompatible with ahimsa. Gandhi believed ahimsa to be a creative energy force, encompassing all interactions leading one's self to find satya, " Divine Truth ".

Since Lavoisier's knowledge of strong acids was mainly restricted to oxoacids, such as ( nitric acid ) and ( sulphuric acid ), which tend to contain central atoms in high oxidation states surrounded by oxygen, and since he was not aware of the true composition of the hydrohalic acids ( HF, HCl, HBr, and HI ), he defined acids in terms of their containing oxygen, which in fact he named from Greek words meaning " acid-former " ( from the Greek οξυς ( oxys ) meaning " acid " or " sharp " and γεινομαι ( geinomai ) meaning " engender ").

On his website, Brooks states that his potential followers must first prepare by combining the junk food diet with the meditative incantation of five magic " fifth-dimensional " words which appear on his website, some of which are words from Kundalini yoga.

Brooks states that he may be contacted on his fifth-dimensional phone in order to get the correct pronunciation of the five magic words.

* Morse code uses six digital states — dot, dash, intra-character gap ( between each dot or dash ), short gap ( between each letter ), medium gap ( between words ), and long gap ( between sentences )— to send messages via a variety of potential carriers such as electricity or light, for example using an electrical telegraph or a flashing light.

In other words, this theory states that a true belief counts as knowledge only if it is produced by a reliable belief-forming process.

The Court is quite permissive in accepting a state's derogations from the Convention but applies a higher degree of scrutiny in deciding whether measures taken by states under a derogation are, in the words of Article 15, " strictly required by the exigencies of the situation ".

In other words, in an antisymmetric state two identical particles cannot occupy the same single-particle states.

In other words, symmetric and antisymmetric states are essentially unchanged under the exchange of particle labels: they are only multiplied by a factor of + 1 or − 1, rather than being " rotated " somewhere else in the Hilbert space.

Louis Feldman, who believes the Josephus passage on John is authentic, states that Christian interpolators would have been very unlikely to have devoted almost twice as much space to John ( 163 words ) as to Jesus ( 89 words ).

In 1954 Nehru signed with China the Five Principles of Peaceful Coexistence, known in India as the Panchsheel ( from the Sanskrit words, panch: five, sheel: virtues ), a set of principles to govern relations between the two states.

Rather, Madison explained that " interposition " involved a collective action of the states, not a refusal by an individual state to enforce federal law, and that the deletion of the words " void, and of no force or effect " was intended to make clear that no individual state could nullify federal law.

In other words, matter is the only substance, and reality is identical with the actually occurring states of energy and matter.

In Van Buren's own words, " Without strong national political organizations, there would be nothing to moderate the prejudices between free and slaveholding states.

In other words, the energy states of each electron are described as if all the other electrons simply form a homogeneous background.

Senior Director of Search states that "... What changed with Yahoo's ranking algorithms is that while we still index the meta keyword tag, the ranking importance given to meta keyword tags receives the lowest ranking signal in our system .... it will actually have less effect than introducing those same words in the body of the document, or any other section.

In other words, physical states can be identified with equivalence classes of vectors of length 1 in H, where two vectors represent the same state if they differ only by a phase factor.

Some Newfoundland English differs from General Canadian English in vowel pronunciation ( e. g., in much of Newfoundland, the words fear and fair are homophones ), in morphology and syntax ( e. g., in Newfoundland the word bes is sometimes used in place of the normally conjugated forms of to be to describe continual actions or states of being, as in that rock usually bes under water instead of that rock is usually under water, but normal conjugation of to be is used in all other cases ; bes is likely a carryover of British Somerset usage with Irish grammar ) or Cornish, and in preservation of archaic adverbial-intensifiers ( e. g., in Newfoundland that play was right boring and that play was some boring both mean " that play was very boring ").

In other words, quantum states cannot be measured reliably.

In other words, the possible states are points in the projective space of a Hilbert space, usually called the complex projective space.