Related results - meaning

It will be seen that each method for surface area determination involves the measurement of some property that is observed qualitatively to depend on the extent of surface development and that can be related by means of theory to the actual surface area. It is important to realize that the results obtained by different methods differ, and that one should in general expect them to differ. The problem is that the concept of surface area turns out to be a rather elusive one as soon as it is examined in detail. 

Precision The closeness of agreement between independent test results obtained under stipulated conditions. NOTES (i) Precision depends only on the distribution of random errors and does not relate to the true value or the specified value, (ii) The measure of precision is usually expressed in terms of imprecision and computed as a standard deviation of the test results. Less precision is reflected by a larger standard deviation, (iii) Independent test results means results obtained in a manner not influenced by any previous results on the same or similar test object, (iv) Quantitative measures of precision depend critically on the stipulated conditions. Repeatability and reproducibility conditions are particular sets of extreme stipulated conditions. 

Input of required significant figures for results of single related substance, mean value of related substances, related substances calculated with respect to label claim... 

For acyclic graphs only, if in the above formula only distances between endpoints are taken into account, the related endpoint mean square topological index Df1 results. 

The original theory of Brownian motion by Einstein was based on the diffusion equation and was valid for long times. Later, a more general formulism including short times also, has been developed. Instead of the diffusion equation, the telegrapher s equation enters. Again, an indeterminacy relation results, which, for short times, gives determinacy as a limit. Physically, this simply means that a Brownian particle s... 

This result means that nitrogen molecules are zooming about your head at about 1140 miles per hour. Note the values chosen first, we expressed the temperature in kelvins second, we have used R in its fundamental SI form. Third, we have expressed the molar mass in SI base units to be consistent with the choice for R. Fourth, the conversion of the units has made use of the relation 1 J = 1 kg-m 2-s-2. 

Metrological traceability of chemical measurement results means the establishment of a relation to a stated metrological reference (a trace). This can be the de nition of a measurement unit which, of necessity, must go through a practical realization or (better an embodiment) of that... 

We obtain the mean value confidence according to relation Result I = (19.307 21.013)... 

The optimum exploitation of physical mixtues of effective monofunctional stabilizers results in the ultimate complex protective effect having a favourable cost/performance relation. By means of a proper alteration of the molecular architecture of the stabilizer molecule, bifunctional stabilizers were synthesized e.g. intramolecularly cooperating systems having in one molecule CB-AO and HD-AO functions or AO and LS functions [22]. However, one of these functionalities is mostly dominant in these systems, the second functionality supports inherently the dominant function in a more or less concerted mechanism. 

Surgeons are concerned with brain blood flow to patients undergoing cardiopulmonary bypass surgery. An intensive study by Chow et al. was conducted where blood flows were restricted to patients from age 2 weeks to over 20 years [48]. Near-IR was used to correlate blood flow rate with NIR spectra of the brain. Flows of 0.6, 1.2, and 2.4 L/mVmin-1 were used. Their results showed that flow was related to mean arterial pressure, but did not correspond to pulsatility. This was interesting in that pulse rate is often used as a diagnostic to assure sufficient blood flow to the brain during surgery. 

This defines a set of equations for the mean field Hamiltonians HPF. These equations have to be solved self-consistently since the thermodynamic values within the angle brackets in (109) involve the mean field Hamiltonians // F. In principle, all // F can be different in practice, we impose symmetry relations. Therefore, we choose a unit cell, compatible with the symmetry of the lattice introduced in Section II,D, and we put Hpf equal to // F whenever P and P belong to the same sublattice. Moreover, we apply unit cell symmetry that relates the mean field Hamiltonians on different sublattices. By using the symmetry-adapted functions introduced in Section II,B, the latter symmetry can be imposed as follows. We select a set of molecules constituting the asymmetric part of the unit cell. Then we assign to all other molecules P Euler angles tip-through which the mean field. Hamiltonian of some molecule P in the asymmetric part has to be rotated in order to obtain HrF. As a result, we... 

If a series of m arithmetic mean values /i, is determined each from n individual measurements, the following relation results for the estimator of the standard deviation of the arithmetic mean values ... 

Comparing this result with Eq. (2.18), we obtain the classic Debye result relating the mean-square radius of gyration and the mean-square end-to-end distance of an ideal linear chain ... 

That is, instead of determining the transport properties from the rather theoretical Enskog solution of the Boltzmann equation, for practical applications we may often resort to the much simpler but still fairly accurate mean free path approach (e.g., [12], section 5.1 [87], chap. 20 [34], section 9.6). Actually, the form of the relations resulting from the mean free path concept are about the same as those obtained from the much more complex theories, and even the values of the prefactors are considered sufficiently accurate for many reactor modeling applications. 

Precision Refers to the closeness of the agreement between independent test results obtained under stated and closely controlled conditions. Note that precision depends only on the distribution of random errors and does not relate to the actual true value. Independent test result means that each result is obtained in a manner that is not influenced by any previous result. 

Relaxation rates of nuclear spins can also be related to aspects of molecular structure and behaviour in favourable circumstances, in particular internal molecular motions. It is true to say, however, that the relationship between relaxation rates and structural features are not as well defined as those of the chemical shift and spin-spin coupling constants, and are not used on a routine basis. The problem of reliable interpretation of relaxation data arises largely from the numerous extraneous effects that influence experimental results, meaning empirical correlations for using such data are not generally available and this aspect of NMR will not be pursued further in this book. 

PH Value. An operational use of the pH term should occure naturally after students have tested various household solutions with universal indicator paper with pH scale - they don t have to deal with any logarithm (see Fig. 7.9). It is more difficult to teach the quantitative meaning of pH value one has to work with concentrations, the logarithm and the mol term. In this case, it is advantageous to relate the meaning of 1 mol to a specific amount of small particles and to decide the type of particles, which are to be counted 18 g water do not contain 1 mol of water , but rather 1 mol of H20 molecules . A liter of 1 M hydrochloric acid contains 1 mol of H30 + (aq) ions and 1 mol of Cl (aq) ions the concentration is equal to 1 mol/1 for both kinds of ions. Dilution in the volume ratio 1 10 results in a solution with the H + (aq) ion concentration of 0.1 mol/1, the dilution 1 100 leads to the 0.01 M or 10 2 M solution. 

We identify cl) — 4>Naa) with M.P/s specific adsorption potential < Na which they calculated to be independent of A (or a0) at given n and T. This implies that the left side of Equation 21 vanishes, whereas the right side is the sum of three positive terms. Thus M.P/s result means that there is no maximum in 0. If cl) is practically independent of o-0, one necessary condition that the original relation (Equation 19) has a solution is that d /dvo > 0. 

Ruch showed in his seminal 1975 paper (Ruch 1975) that a partial order relation for partitions already well known to mathematicians - namely the majorization partial order - is precisely the same partial order that corresponds to mixing. This fundamental result means that the mathematics of the Young Diagram Lattice applies to the physics of mixing. 

These results mean that tubulin is capable of two different modes of aggregation, leading to oligomers (e.g., at low temperature, without nucleotides) or polymers (e.g., at high temperature and with GTP). The two types of reaction have distinct physico-chemical characteristics and are thus not directly related to one another. However, they draw on the same pool of subunits, i.e., tubulin dimers. This is summarized in the scheme of Fig. 5. 

Fig. 2.10. Relation between mean system frequency v and driving frequency i/ (top) and number of locked cycles Ni ck (bottom) of the excitable model as a function of driving frequency v. Lines show dependence as solutions of eqs. (2.36) and (2.37). The + symbols present results from simulations of the discrete system and circles correspond to data from simulations of the FHN system. Parameters for the FHN system eq. (2.11) ao = 0.405, ai = 0.5, = 0.001, D = 10 , Sx(t) = 0, Sy t) = A with A = 0.015. Parameters for the two state model (theory and simulations) from simulations of the interspike interval distribution density (cf. Fig. 2.6) T ss 2620, ro 0.0087 and n 8.3 10- . [15]...

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