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Because the Möbius function only takes the values − 1, 0, and + 1, the Mertens function moves slowly and there is no n such that | M ( n )| > n. The Mertens conjecture went further, stating that there would be no n where the absolute value of the Mertens function exceeds the square root of n. The Mertens conjecture was proven false in 1985 by Andrew Odlyzko and Herman te Riele.
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Because and Möbius
Because of Wittmann's actions " the bulk of the 2nd Company and Rolf Möbius 1st Company came up against an enemy who had gone onto the defensive ".
Because the twist can be left-handed or right-handed, the resulting Möbius aromatics are dissymmetric or chiral.
Because and function
Because the object is illuminated by the Sun, absolute magnitude is a function of phase angle and this relationship is referred to as the phase curve.
Because of this, each of the infinitely many antiderivatives of a given function f is sometimes called the " general integral " or " indefinite integral " of f and is written using the integral symbol with no bounds:
Because the volatility of a comet's material decreases as it gets further from the Sun, the comet becomes increasingly difficult to observe as a function of not only distance, but the progressive shrinking and eventual disappearance of its tail and the reflective elements it carries.
Because the RDOS < tt >. systm </ tt > call macro implements a < tt > jsr </ tt >, AC3 is overwritten by the return address for the < tt >. pchar </ tt > function.
Because intermediates only function to maintain the image information accurately across duplication, each manufacturer tends to only produce one or two different intermediate stocks.
Because of its emphasis on usage, communicative function, and the social context of language, functional grammar differs significantly from other linguistic theories which stress purely formal approaches to grammar, notably Chomskyan generative grammar.
Because the males have a stronger odor than the females, it is suspected that it also has a sexual function.
Because of this function, radioisotopes of iodine are concentrated in the thyroid gland along with nonradioactive iodine.
Because the high peaks function as moisture catchers, Kyrgyzstan is relatively well watered by the streams that descend from them.
Because they function as an energy store, these lipids comprise the bulk of storage fat in animal tissues.
Because mania and hypomania have also been associated with creativity and artistic talent, it is not always the case that the clearly manic bipolar person needs or wants medical help ; such persons often either retain sufficient self-control to function normally or are unaware that they have " gone manic " severely enough to be committed or to commit themselves.
Because of the connection between the Riemann zeta function and π ( x ), the Riemann hypothesis has considerable importance in number theory: if established, it would yield a far better estimate of the error involved in the prime number theorem than is available today.
Because the stars were all born at roughly the same time, the different properties of all the stars in a cluster are a function only of mass, and so stellar evolution theories rely on observations of open and globular clusters.
Because the continental crust is so much thicker than the oceanic crust, it conducts heat less efficiently, making it function like an insulating blanket.
Because the units of throughput are the reciprocal of the unit for propagation delay, which is ' seconds per message ' or ' seconds per output ', throughput can be used to relate a computational device performing a dedicated function such as an ASIC or embedded processor to a communications channel, simplifying system analysis.
Because FCB compatibility has not been maintained, WordStar 3. x will not function properly on modern versions of Windows.
Because the check value has a fixed length, the function that generates it is occasionally used as a hash function.
Because the equation is second order in the time derivative, then by the nature of solving differential equations, one must specify both the initial values of the wave function itself and of its first time derivative, in order to solve definite problems.
Because both may be specified more or less arbitrarily, the wave function cannot maintain its former role of determining the probability density of finding the electron in a given state of motion.
Because group delay is, as defined in ( 1 ), it therefore follows that a constant group delay can be achieved if the transfer function of the device or medium has a linear phase response ( i. e., where the group delay is a constant ).
Because the logarithm is a monotonically increasing function, the logarithm of a function achieves its maximum value at the same points as the function itself, and hence the log-likelihood can be used in place of the likelihood in maximum likelihood estimation and related techniques.
Because there are 26 letters in the English alphabet and 26 = 2 × 13, the ROT13 function is its own inverse:
Because and only
Because of this, only those with truly fine equipment will be able to appreciate the exact degree of the engineers' triumph.
Because Christianity teaches not only salvation in history, but salvation by the history of Christ, such an interpretation of death would require a drastic revision of the Christian understanding of the work of Christ.
Because the urn itself is so delicate, it has been allowed to travel to Australia only twice.
Because of the first proposition, God himself is thought as invisible and only recognizable in his creation.
In fact, Fitzmyer believes that the preface of Luke should only be “ the starting point in the discussion of the aim of Luke-Acts .” Because the author ’ s intended purpose for the Book of Acts is not that straightforward, scholars have put forth four main claims to address this.
Because it is a Sacred Mystery of the Church, only Orthodox Christians may receive it.
Because the English language has 40 sounds and only 26 letters, children and beginning readers also need to learn the different sounds ( phonemes ) associated with each letter.
Because the differences between the prices are likely to be small ( and not to last very long ), this can be done profitably only with computers examining a large number of prices and automatically exercising a trade when the prices are far enough out of balance.
Because grocery stores are not permitted to carry wine or liquor, the older law essentially meant that only beer and alcoholic malt beverages could be purchased at all on Sundays.
Because of this, the United States Air Force XB-70 Valkyrie program was cancelled in the early 1960s ; the later B-1B Lancer and B-2 Spirit aircraft entered service only after protracted political and development problems.
Because Justice John Paul Stevens had recused himself, only eight Justices heard the case, and it ended in a 4 – 4 tie.
Because the FLRW metric assumes a uniform distribution of mass and energy, it applies to our Universe only on large scales — local concentrations of matter such as our galaxy are gravitationally bound and as such do not experience the large-scale expansion of space.
Because a black hole eventually achieves a stable state with only three parameters, there is no way to avoid losing information about the initial conditions: the gravitational and electric fields of a black hole give very little information about what went in.
Because the fossil record of chordates is poor, only molecular phylogenetics offers a reasonable prospect of dating their emergence.
Because society needs people to do computing well, we must think of computing not only as a profession but also as a discipline.
Because Berlin was located within the Soviet-occupied zone of Germany and the other occupying powers had previously relied on Soviet good will for access to Berlin, the only available methods of supplying the city were three limited air corridors.
Because the de facto administration is recognized only by Turkey, it has had much difficulty arranging foreign financing, and foreign firms have hesitated to invest there.
Because of the specific transport mechanisms, only limited amounts of chromium ( III ) enter the cells.
Because the earthworms grind and uniformly mix minerals in simple forms, plants need only minimal effort to obtain them.
Because each governor held equal imperium to the equivalent magistrate, they were escorted by the same number of lictors ( 12 ) and could only be vetoed by a reigning Consul or Praetor.
Because they lack this key defence, only 0. 5 % of cane toads are estimated to reach adulthood.
Because of the switch to Portland cement, by the end of the 1920s of the 15 Rosendale cement companies, only one had survived.
Because of that the vehicle with the bridge on board is only 11. 6 m long, but the over all span length is 20 m. This is an increase of about 62 % over that of the older MTU-1.
Because only a fraction of the cells in a tumor die with each treatment ( fractional kill ), repeated doses must be administered to continue to reduce the size of the tumor.
0.616 seconds.