Since the change to better nutrition, he feels he can report on improvements in health, though he considers the following statements observations and not scientific proof.

The proof of this fact relies on an algorithm which, given the first n digits of Ω, solves Turing's halting problem for programs of length up to n. Since the halting problem is undecidable, Ω can not be computed.

Since then the proof has gained wider acceptance, although doubts remain.

' In the second case, he cites an example that demonstrates ignorance of statistical principles in the lay press: ' Since no such proof is possible genetically modified food is harmless, the article in The New York Times was what is called a " bad rap " against the U. S. Department of Agriculture-a bad rap based on a junk-science belief that it's possible to prove a null hypothesis.

Since he was eleven years her elder, already married, and a Buddhist, May-ling's mother vehemently opposed the marriage between the two, but finally agreed after Chiang showed proof of his divorce and promised to convert to Christianity.

Since the proof Evans produces relies on the assumption that terms precisely denote vague objects, the implication is that the assumption is false, and so the vague-objects view is wrong.

: proof: Since the algebra is closed under squaring, and it has but two dimensions, the non-real basis element u squares to an arbitrary linear combination of 1 and u:

Since that date, proof of unbroken possession or use of any right made it unnecessary to establish the original grant under certain circumstances.

However, the more difficult proof of the converse ( see below ) makes use of the vector space structure: Since both of the factors are vector spaces over Q, the tensor product can be taken over Q.

Since God is absolutely self-sufficient ( a result from the cosmological " proof " of His existence ), all-knowing, and all-powerful, He is categorically free from any type of need and, consequently, He never does anything that is ridiculous, unwise, ugly, or evil.

Since the leaks, Statoil has stated that the oil has mostly dissolved, and there is not much proof of ecological harm.

Since the only known way to solve that problem is to factor the modulus, it is generally regarded that the difficulty of integer factorization provides a conditional security proof for the Blum Blum Shub algorithm.

Since this probability is an increasing function of p ( proof via coupling argument ), there must be a critical p ( denoted by p < sub > c </ sub >) below which the probability is always 0 and above which the probability is always 1.

Since, further, according to him the fulfilment of prophecy is the only valid proof of Christianity, he thus secretly aims a blow at Christianity as a revelation.

Since the prosecution at her trial did not meet their burden of proof, by today ’ s standards, it is impossible to know for sure whether she was guilty.

Since even a free person could not possibly have knowledge of their own freedom, we cannot use our failure to find a proof for freedom as evidence for a lack of it.

Since a defense is raised by the defendant in a direct attempt to avoid what would otherwise result in liability, the defendant typically holds the burden of proof.

Since God needs faith to exist, and this proof dispels the need for faith, this therefore causes God to vanish " in a puff of logic ".

Since this early work, sequent calculi ( also called Gentzen systems ) and the general concepts relating to them have been widely applied in the fields of proof theory, mathematical logic, and automated deduction.

Since formal proofs in proof theory are purely syntactic, the meaning of ( the derivation of ) a sequent is only given by the properties of the calculus that provides the actual rules of inference.

Since no such computer to fully evolve Autoverse life exists, Durham has to try to convince Maria that he is a wealthy Autoverse enthusiast interested in her evolvability results and looking for a proof of concept for a much larger system.

Since the Chinese troops at Mukden had put up such a poor resistance, he told Manchukuo Emperor Puyi that this was proof that the Chinese remained loyal to him.

Since proof of the writer's malicious intentions is hard to provide, proof that the writer knowingly published a falsehood was generally accepted as proof of malice, under the assumption that only a malicious person would knowingly publish a falsehood.

Since the Lagrangian ( eq ( 1 )) contains second derivatives, the Euler – Lagrange equation of motion for this field is

Since only a few atoms must be excited into the upper laser level to form a population inversion, a four-level laser is much more efficient than a three-level one, and most practical lasers are of this type.

Since 1986 the stagnation in employment has led to a new inversion of the trend, caused not so much by an increase in the number of people leaving but by a fall in the number coming to live in the region, but in the 2000s ( decade ) net immigration has been positive again.

Since inversion in the unit sphere leaves the spheres orthogonal to it invariant, the inversion maps the points inside the unit sphere to the outside and vice-versa.

Since the dual of the pseudoscalar is the product of two " pseudo-quantities " it can be seen that the resulting tensor is a true tensor, and does not change sign upon an inversion of axes.

Since multiplication and inversion are continuous functions on C < sup >×</ sup >, the circle group has the structure of a topological group.

Since the sides of the cavity did not need to be reflective, the gain medium could easily be optically pumped to achieve the necessary population inversion.

Since a Static Reduction requires several inversion steps it is an expensive matrix operation and is prone to some error in the solution.

Since a molecule can form two enantiomers around a chiral center, the Walden inversion converts the configuration of the molecule from one enantiomeric form to the other.

Since the backwave is already in opposite polarity with the front wave, this inversion brings the two emissions in phase ( although the vent emission is lagging byFHDHDFX one wave period ) and therefore they reinforce each other.

Since the term " fanny " had obscene implications in the 18th century, Joseph's longings for " my Fanny " survive as satirical blows, and the inversion of sexual predation strips bare the essentials of Richardson's valuation of virginity.

Since is not necessary a bijection, one may find more than one solution to this inversion ( there exist at most d different solutions since is a polynomial of degree d ).

Since the complex of singular lines is of order K and since there is no complex of invariant lines, it follows from the formula Af that the order of the involution is Af.

Since the entries of the Jacobian matrix are partial derivatives, we may simplify the above formula to get:

Since then, the tariff is calculated by a formula based on various factors such as the number of twist and somersaults, the height, the group etc., and divers are free to submit new combinations.

Since mathematics is related to logic, he cites an example from mathematics: If we have a formula like ( a + b )( a-b )= a²-b² it does not tell us how to think mathematically.

Since biconditionality is an equivalence relation, any instance of ¬¬ A in a well-formed formula can be replaced by A, leaving unchanged the truth-value of the well-formed formula.

Since the harmonic series, obtained when s = 1, diverges, Euler's formula ( which becomes ) implies that there are infinitely many primes.

Since 1990 most new Australian serials have been based on the successful Neighbours formula of foregrounding youthful attractive casts in appealing locations.

Since Euler's formula states that e < sup > ix </ sup >

Since Pupin's patent contained a ( less accurate ) formula, AT & T was open to claims of incomplete disclosure.

Since every element of C < sub > n </ sub > generates a cyclic subgroup and the subgroups of C < sub > n </ sub > are of the form C < sub > d </ sub > where d | n, the formula follows.

Since the same argument works for any number, not just 20, the formula is established.

Since, an analog to De Moivre's formula also applies to the hypberbolic trigonometry.

Since all logical formulae can be converted into an equivalent formula in conjunctive normal form, proofs are often based on the assumption that all formulae are CNF.

Since that time, The Sentencing Project has become a leader in the effort to bring national attention to disturbing trends and inequities in the criminal justice system with a successful formula that includes the publication of groundbreaking research, aggressive media campaigns strategic advocacy for policy reform.

Since the derivative of ln x is 1 / x, we make ( ln x ) part of u ; since the antiderivative of 1 / x < sup > 2 </ sup > is − 1 / x, we make ( 1 / x < sup > 2 </ sup >) part of v. The formula now yields:

Since the meaning and the words never vary, except for the spelling and inflection of populus in literature, Latin dictionaries classify it as a formula.

Since the cardinality of R ( n ) is n, and that of P ( n ) is φ ( n ), this demonstrates the classical formula

Applying both sides to e < sub > j </ sub >, the result on each side is the jth partial derivative of f at p. Since p and j were arbitrary, this proves the formula (*).

Since every formula in the antecedent ( the left side ) must be true to conclude the truth of at least one formula in the succedent ( the right side ), adding formulas to either side results in a weaker sequent, while removing them from either side gives a stronger one.

Since Pythagoras calculated the formula for the musical cycle of fourths and fifths, Steel Pans are the only instruments made to follow this configuration.

Since the inception of Grand Prix racing, competitions had been run in accordance with a strict formula based on engine size and vehicle weight.

The New York Times stated, " Since its debut in the late 1980 ’ s, the magazine has surpassed traditional men ’ s books like Esquire and GQ by following the formula of best-selling women ’ s magazines — by catering to men ’ s anxieties about their bodies and sexual performance.