Mean life time value

To summarize, in the present scenario pure hadronic stars having a central pressure larger than the static transition pressure for the formation of the Q -phase are metastable to the decay (conversion) to a more compact stellar configuration in which deconfined quark matter is present (i. e., HyS or SS). These metastable HS have a mean-life time which is related to the nucleation time to form the first critical-size drop of deconfined matter in their interior (the actual mean-life time of the HS will depend on the mass accretion or on the spin-down rate which modifies the nucleation time via an explicit time dependence of the stellar central pressure). We define as critical mass Mcr of the metastable HS, the value of the gravitational mass for which the nucleation time is equal to one year Mcr = Miis t = lyr). Pure hadronic stars with Mh > Mcr are very unlikely to be observed. Mcr plays the role of an effective maximum mass for the hadronic branch of compact stars. While the Oppenheimer-Volkov maximum mass Mhs,max (Oppenheimer Volkov 1939) is determined by the overall stiffness of the EOS for hadronic matter, the value of Mcr will depend in addition on the bulk properties of the EOS for quark matter and on the properties at the interface between the confined and deconfined phases of matter (e.g., the surface tension a). 

The possibility to have metastable hadronic stars, together with the feasible existence of two distinct families of compact stars, demands an extension of the concept of maximum mass of a neutron star with respect to the classical one introduced by Oppenheimer Volkoff (1939). Since metastable HS with a short mean-life time are very unlikely to be observed, the extended concept of maximum mass must be introduced in view of the comparison with the values of the mass of compact stars deduced from direct astrophysical observation. Having in mind this operational definition, we call limiting mass of a compact star, and denote it as Mum, the physical quantity defined in the following way ... 

There are various specific features and predictions of the present model, which we briefly mention in the following. The second explosion (QDN) take place in a baryon-clean environment due to the previous SN explosion. Is is possible to have different time delays between the two events since the mean-life time of the metastable hadronic star depends on the value of the stellar central pressure. Thus the model of Berezhiani et al. (2003) is able to interpret a time delay of a few years (as observed in GRB990705 (Amati et al. 2000 Lazzati et al. 2001)), of a few months (as in the case of GRB020813 (Butler et al. 2003)), of a few days (as deduced for GRB011211 (Reeves et al. 2002)), or the nearly simultaneity of the two events (as in the case of SN2003dh and GRB030329 (Hjorth et al. 2003). 

Fig. 1. Rate constants, for the exchange of water molecules from the first coordination sphere of a given metal ion and the corresponding mean life times, tm = l//zex, of a particular water molecule measured by " 0 NMR. The gray bars indicate values determined by NMR isotope exchange technique (except Cr + ).

Choosing for rAB of small molecules the probable value of 5 x 10-1°m, Ksr becomes about 0.3 mol dm3. Small molecules thus generate a collision pair at a rate characterized by a rate constant often reaching the value 109 to 1010 mol-1 dm3 s". For /c(u this gives a value of 1010 s-1. Thus the mean life time of the pair is about 10 10 s. Ion association si affected by strong electrostatic interactions. These forces are considered in association constant calculations they are usually included in the Boltzmann factor. 

According to Groh , the mean life-time of the state emitting fluorescence is less than 8 x 10 sec, while Okabe and Noyes reported a value of 2.5 x 10 sec. Fluorescence is not quenched by oxygen however, its efficiency decreases, to some extent, with increasing temperature. The fluorescence is much less dependent on temperature than the phosphorescence. 

Table. Values of individual components Xi and their relative amplitudes Ai as well as mean life times for the non-exponential decays of CdSe quantum dots for various molar ratios x=Couinonc/CQD.

Covering temperatures from -140 up to 200 C and chain lengths from one to six carbon atoms, the intracrystalline mean life times are found to coincide with the values oi rV 1 r calculated from the nmr self-diffusion coefficients. This clearly indicates that molecular exchange is controlled by intracrystalline self-diffusion, and that for the considered adsorbate-adsorbent systems there are no perceptible surface barriers. 

In the present case, the intracrystalline mean life times should be compared with a value of Ti lrou ,f = 0,007 ms, which results from inserting the mean crystallite radius and the intracrystalline self-diffusion coefficient (- 10 nrs ) at the given temperature and concentration (15) into Equation 10. Since in the nmr measurement is found to be much less than 0.2 ms,... 

Figure t gives a comparison of the intracrystalline mean life times of methane in ZSK-5 type monocrystais alter diiferent coxing times, and the values of t 1, calculated from the... 

Tlie first hypothesis can be sustained witli the values of the activation energies of the CH3OH + O2 reaction, calculated for CoM and CuM. For the first catalyst E = 48.3 kcal/mol was obtained, and for CuM, E = 29.6 kcal/mol. Tliese values indicate a greater stability of methanol over CoM. It seems reasonable tlien that in the case of tlie CoM catalyst, an oxygenated intennediate may acquire a mean life time enougli to reduce nitric oxide, whereas in CuM this possibility is smaller. 

The quantitative information provided by PPG NMR about the existence of additional transport resistances on the external surface of the zeolite crystallites (surface barriers) results from a comparison of the values for the intracrystalline mean life time determined directly (viz. Tintra) by an analysis of the time dependence of the spin-echo attenuation (and, hence, of the propagator), and determined indirectly (viz. tP ) from the intracrystalline diffusivity on the assumption that molecular exchange between different crystallites is controlled by intracrystalhne diffusion. On the additional assumption that the shape of the crystallites may be approximated by spheres with a mean square radius (R ) one has in the latter case [87,103]... 

A representation of the values for the intracrystalline mean life time in parallelepipeds with varying edge lengths may be found in [104]. 

Fig. 8 Values for the intracrystalline mean life time tintra ( M) and the quantity (A,A) for methane in H-ZSM5 which has been coked by n-hexane (filled symbols) and mesitylene (open symbols) as a function of the coking time (methane concentration 12 molecules per unit cell measuring temperature 296 K). From [116] with permission...

The termination rate constants can be estimated in two ways. If conductivity measurements are available plus a reasonable value for then k. =X Ri l. Where X is the mean life time for the charge carriers and may be rigorously determined from the conductivity measurements. Alternatively kt can be calculated from the simplified Debye equation. 

The half-time (or half-life) of the reaction is independent of [A]o. The reciprocal of the rate constant, t = l/k, is referred to as the lifetime or the mean reaction time. In that time [A] falls to l/e of its initial value. The pharmaceutical industry refers to the shelf life or t90, the time at which [A]/[A]o reaches 0.90. Both t and t90 are also independent of [A]o. 

Mean serum clearance values ranged from 9.4 to 28.9 mL/min/kg and were independent of dose. Mean terminal elimination half-life values ranged from 8 minutes to 4.3 hours and mean steady-state volume of distribution values ranged from 0.25 to 2.88 L/kg. IV dosing 3 times/week for 2 weeks resulted in no accumulation of interferon beta-la or beta-lb in the serum of patients. 

For the kinetics of a reaction, it is critical to know the rough time to reach equilibrium. Often the term "mean reaction time," or "reaction timescale," or "relaxation timescale" is used. These terms all mean the same, the time it takes for the reactant concentration to change from the initial value to 1/e toward the final (equilibrium) value. For unidirectional reactions, half-life is often used to characterize the time to reach the final state, and it means the time for the reactant concentration to decrease to half of the initial value. For some reactions or processes, these times are short, meaning that the equilibrium state is easy to reach. Examples of rapid reactions include H2O + OH (timescale < 67 /is at... 

On the other hand, the slope of the lines plotted in Fig, 38, from the value of which the mean life of the chains is calculated, may be greatly effected even by small errors in the determination of the intrinsic viscosity of polymers obtained by shorter time tests. The resulting data are mostly concerned by eventual errors. 

Apparently monochromatic resonance radiation of mercury which passes through mercury vapor at the saturated pressure at 25 °C is about half absorbed in four millimeters distance. Beer s law is not obeyed at all because the incident radiation cannot be considered to be actually monochromatic, and absorption coefficients of mercury vapor vary many times between zero and very high values in the very short space of one or two hundredths of an Angstrom unit. Moreover, absorption of mercury resonance radiation by mercury vapor is sufficiently great even at room temperature to make radiation imprisonment a very important phenomenon. If the reaction vessel has any dimension greater than a few millimeters the apparent mean life of Hg(63P ) may be several fold the true radiative life of 1.1 x 10"7 sec, reaction (27), because of multiple absorption and re-emission. 

The distinction between these concepts is illustrated by the population of a country the average age of the population might be 40 years while the mean residence time, or life expectancy, might be twice that value. Human populations are not, however, a simple case for illustrating the concept of turnover time as we described it above, because they are not homogeneous in that all members do not have an equal probability of leaving at any time. If this population were homogeneous with respect to mortality and at steady state, turnover time would be the population divided by the number of members who die each year (the stock divided by the flux out). 

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