Weak equivalence principle

First, and as already noted, the model universe is populated exclusively by primitive particles that possess solely the property of enumeration, and hence quantification. Consequently, all motions in the model universe are effectively gravitational, and we model this circumstance by constraining all such motions to satisfy the weak equivalence principle, by which we mean that the trajectory of a body is independent of its internal constitution. This constraint can be expressed as follows ... 

The recent advances in producing, trapping and cooling antiprotons and positrons opened the possibility of antihydrogen formation in laboratory. This may allow the studies of antimatter and tests of fundamental physical principles such as charge - parity - time ( CPT ) invariance or the weak equivalence principle (WEP) for antiparticles. Such experiments are planned at the newly built CERN AD (Antiproton Decelerator) within ASACUSA, ATRAP and ATHENA projects, which have just started their operations. 

In applying the same treatment to various sulfur vulcanization systems Wolff found that the assumption of equal cross-link densities in filled and unfilled vulcanizates was not violated. This is in complete agreement with the authors conclusion based on an analysis of swelling data (130) by use of Eq. (10). Wolffs aF values are not only independent of the vulcanization system, but depend only very weakly on the polymer. Wolffs treatment also is consistent with the structure-loading equivalence principle stated in Section V-3 The structure dependent parameter ap enters Eq. (13) in the product with the black concentration. 

Equivalence principles have always been and remain a hot topic. In typical disputes, one usually considers the so-called Einstein Equivalence Principle essentially stating that free fall and inertial motion are physically equivalent. In a more detailed argument, one distinguishes between weak, Einstein and strong equivalence principles, incorporating all effects from free fall to universal features of the theory of... 

In principle, any type of titration can be carried out conductometrically provided that during the titration a substantial change in conductance takes place before and/or after the equivalence point. This condition can be easily fulfilled in acid-base, precipitation and complex-formation titrations and also the corresponding displacement titrations, e.g., a salt of a weak acid reacting with a strong acid or a metal in a fairly stable complex reacting with an anion to yield a very stable complex. However, for redox titrations such a condition is rarely met. 

Words that can be used as topics in essays 5% rale buffer common ion effect equilibrium expression equivalence point Henderson-Hasselbalch equation heterogeneous equilibria homogeneous equilibria indicator ion product, P Ka Kb Kc Keq KP Ksp Kw law of mass action Le Chatelier s principle limiting reactant method of successive approximation net ionic equation percent dissociation pH P Ka P Kb pOH reaction quotient, Q reciprocal rule rule of multiple equilibria solubility spectator ions strong acid strong base van t Hoff equation weak acid weak base... 

We can calculate pH titration curves using the principles of aqueous solution equilibria. To understand why titration curves have certain characteristic shapes, let s calculate these curves for four important types of titration (1) strong acid-strong base, (2) weak acid-strong base, (3) weak base-strong acid, and (4) polyprotic acid-strong base. For convenience, we ll express amounts of solute in millimoles (mmol) and solution volumes in milliliters (mL). Molar concentration can thus be expressed in mmol/mL, a unit that is equivalent to mol/L ... 

The magnitude of the dissociation constant A plays an important role in the response characteristics of the sensor. For a weakly dissociated gas (e.g., CO2, K = 4.4 x 10-7), the sensor can reach its equilibrium value in less than 100 s and no accumulation of CO2 takes place in the interior layer. On the other hand, SO2, which is a much stronger acid (K = 1.3 x 10-2), accumulates inside the sensor and its rep-sonse time is in minutes. The detection limit and sensitivity of the conductometric gas sensors also depend on the value of the dissociation constant, on the solubility of the gas in the internal filling solution, and, to some extent, on the equivalent ionic conductances of the ions involved. Although an aqueous filling solution has been used in all conductometric gas sensors described to date, it is possible, in principle, to use any liquid for that purpose. The choice of the dielectric constant and solubility would then provide additional experimental parameters that could be optimized in order to obtain higher selectivity and/or a lower detection limit. 

It is known that, because of spin forbidding, molecular oxygen is weakly active in the normal state. However, when possible, it enters oxidation reactions much more easily by the one-electron rather than by the two-electron mechanism [71]. In this connection, it is believed that not so much molecular oxygen is toxic as reactive intermediates 02, H02 and OH, occurring in the course of its reduction to water. The radicals O and H02 are equivalent therefore, in the redox medium 02 possess the same unique properties, i.e. can be the oxidant and the reducer simultaneously. Thus, in principle, molecular oxygen is incapable of two-electron oxidation (because of spin forbidding), whereas H202 has this ability. This is the principal difference in the oxidation mechanisms of these radicals. 

Molecules with Several Atomic Cores.—From the above discussion it is seen that, in principle, the effective hamiltonian for atomic valence electrons is dependent on the valence state of the atom, this dependence arising from the valence contribution to the all-electron Fock operator F. In practice this dependence is very weak unless the atom is multiply ionized, and can usually be safely neglected, so that a single effective hamiltonian can suffice for many valence states. However, for a molecular system in which there is more than one core region additional approximations must be introduced to maintain a simple form of the effective hamiltonian. For two atomic cores defined in terms of orbital sets and and a valence set < F) the equation equivalent to (21) is... 

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