✸ 2. 1 ~ p ∨ p " This is the Law of excluded middle " ( PM, p. 101 ).

✸ 2. 11 p ∨ ~ p ( Permutation of the assertions is allowed by axiom 1. 4 )

✸ 2. 13 p ∨ ~

Observationally, the linear polarization fraction p ~ 0. 015 from a single scattering ; circular polarization from multiple scattering goes as, so we expect a circularly polarized fraction of.

A Consistency proof requires ( i ) an axiomatic system ( ii ) a demonstration that it is not the case that both the formula p and its negation ~ p can derived in the system.

De Sacy, p. 126 ) speaks instead of the ` anl ~ a.

For example, if the base cases have constant-bounded size, the work of splitting the problem and combining the partial solutions is proportional to the problem's size n, and there are a bounded number p of subproblems of size ~ n / p at each stage, then the cost of the divide-and-conquer algorithm will be O ( n log n ).

For example instead of showing directly p ⇒ q, one proves its contrapositive ~ q ⇒ ~ p ( one assumes ~ q and shows that it leads to ~ p ).

If negation is cyclic and "∨" is a " max operator ", then the law can be expressed in the object language by ( P ∨ ~ P ∨ ~~ P ∨ ... ∨ ~...~ P ), where "~...~" represents n − 1 negation signs and "∨ ... ∨" n − 1 disjunction signs.

( T → P ) ∨ ( T → ~ R ).

: φ ≡ ( P ∨ ~ R ) ∧ Q.

Thus, if φ holds, then ( P ∨ ~ R ) holds.

In turn, ( P ∨ ~ R ) tautologically implies ψ.

Because the two propositional variables occurring in ( P ∨ ~ R ) occur in both φ and ψ, this means that ( P ∨ ~ R ) is an interpolant for the implication φ → ψ.

This also represents the equivalent nature of the six carbon-carbon bonds all of bond order ~ 1. 5.

Furthermore, a number of ~ omics based on analytical chemistry have become important areas in modern biology.

This in turn results in the slowing down of the rotation rate of Earth ( at about 42 nsec / day ), and in gradual increase of the radius of Moon's orbit ( at ~ 4. 5 cm / year rate ).

( 1990 ) carried out a radial velocity ( Doppler shift of spectral lines ) study of the star in April and May 1988, which showed variability with a frequency of the order of a few microhertz, the highest peak corresponding to 4. 3 μHz ( 2. 7 days ) with an amplitude of 60 ms < sup >− 1 </ sup >, with a frequency separation of ~ 5 μHz.

" Jesus that I know as my Redeemer cannot be less than God " ~ at the Council of Nicæa ( c. 325 )

~ describing the canon in his 39th Festal Letter ( c. 367 )

The largest documented single crystal of amblygonite measured 7. 62x2. 44x1. 83 m < sup > 3 </ sup > and weighed ~ 102 tons.

Beryllium has a large scattering cross section for high-energy neutrons, about 6 barns for energies above ~ 0. 01 MeV.

* Latvian (~ 2 – 2. 5 million speakers, whereof ~ 1. 39 million native speakers, 0. 5 – 1 million ethnic Russian speakers, 0. 15 million others )

File: BM, Main Floor Main Entrance Hall ~ South Stairs. 6. JPG | Main Staircase, Discobolus of Myron ( the Discus-Thrower )

File: BM ; RM8-ANE, Nimrud Palace Reliefs 75 South + East Wall ( S ) ~ Central Palace of Tiglath-pileser III ( 744-727 B. C ) + Full Elevation & Viewing South. 1. JPG | Room 8-Pair of Lamassu from Nimrud & reliefs from the palace of Tiglath-Pileser III

File: BM ; RM7-ANE, Nimrud Palace Reliefs 1 Northwest Palace of Ashurnasirpal II ( 883-859 B. C ) ~ Full Elevation & Viewing South. JPG | Room 7-Reliefs from the North-west palace of Ashurnasirpal II, Nimrud

Since both the crystal and the beam are often very small, the crystal must be centered within the beam to within ~ 25 micrometers accuracy, which is aided by a camera focused on the crystal.

Since that beginning, they planted a variety of vines including ... Chardonnay, Vidal Blanc, Cabernet Franc, and Norton ~ a grape native to Virginia this makes an excellent stopping off place between Williamsburg and Richmond at I-64 Exit 211.

Since p ⇒ q and ~ q ⇒ ~ p are equivalent by the principle of transposition ( see law of excluded middle ), p ⇒ q is indirectly proved.

Since the power of the laser is constant when sampling over frequencies much shorter than the frequency of the laser's light ~ 10 < sup > 14 </ sup > Hz, the derivative of this term averages to zero and the force can be written as

Since 2000, their old bikes have been shipped to Africa by Re ~ Cycle ( 10, 000 ).

Since the basic physical phenomenon is based on diffraction, the periodicity of the photonic crystal structure has to be of the same length-scale as half the wavelength of the EM waves i. e. ~ 200 nm ( blue ) to 350 nm ( red ) for photonic crystals operating in the visible part of the spectrum-the repeating regions of high and low dielectric constants have to be of this dimension.

Since galactic redshift is proportional to distance, NGC 7320 is only a foreground projection and is ~ 39 million ly from Earth versus the 210-340 million ly of the other five.

Since the DF in a good capacitor is usually small, δ ~ DF, and DF is often expressed as a percentage.

Since the middle of 2010 PALPlus was dropped in favor of regular 16: 9 letterbox, because the system caused considerable image degradation ( with an effective horizontal resolution of only about ~ 400px compared to 720px of a digital SDTV image ) when used on digital transmissions.

Since then two more occultations have been observed, which give an estimated mean diameter of ~ 150 km for diameter.

Since Q2 is dissipating very little power compared to Q1 ( since all the load current goes through Q1, not Q2 ), Q2 will not heat up any significant amount and the reference ( current setting ) voltage across Re will remain rock steady at ~ 0. 6V, or one diode drop above ground, regardless of the thermal changes in the Vbe drop of Q1.

*' Song Book ~ Since 1997-2001 ~' ( 23 January 2002 )

Since the tunneling current in a scanning tunneling microscope only flows in a region with diameter ~ 5 Å, STS is unusual in comparison with other surface spectroscopy techniques, which average over a larger surface region.

Since the mid-1980s most 3D traps ( Paul traps ) have used ~ 1 mtorr of helium.

Since October 2006, the grant provides additional funding for the Emergency School Construction and Rehabilitation Project to construct ~ 33 new schools in the Marshland areas of Iraq.

Since transitorized amplifiers had become more common by this time, it was rated at a more contemporary 4 ~ 8 Ohms, with power handling of 12 watts.