Arbitrary transferability

Transactions to transfer authenticated messages from one recipient to another in the sense that the certainty that one can win disputes in court is transferred. Such transfers can work arbitrarily often (arbitrary transferability) or a fixed, finite number of times (finite tranrferability). 

Arbitrary transferability is the special case where the second recipient is in exactly the same position with respect to the authenticated message as the first recipient, and therefore, an arbitrary number of transfers can take place. 

In [PfWa92, Waid91], signature schemes with finite transferability were called pseudosignature schemes, to distinguish them from ordinary ones with arbitrary transferability. 

Arbitrary transferability among those users who are possible recipients according to initialization. 

Arbitrary transferability is easy to achieve as a consequence of the existence of public keys and non-interactive authentication The entity of the former recipient of a signed message can simply pass the signature on, and the entity of the new recipient tests it with the normal algorithm test. (Signatures had to be stored anyway in case of disputes.) The effectiveness of transfers, i.e., the requirement that the new recipient should accept the signature, is guaranteed information-theoretically without error probability because both entities have the same public key. 

It may also be observed that the coset factorization of Eq. (229) is valid for any orbital pair regardless of the CSF space. However, the completely arbitrary transfer of parameters from the orbital variation space to the CSF space may not result in a CSF partitioning as in the above examples. For example, consider the n -I- l)-term expansion case considered previously in which Cl2 is allowed to be non-zero. The transfer of the orbital rotation parameter from the orbital space into this CSF space requires the introduction of two new CSF expansion terms, C13 and C23. However, these two terms may not be varied independently one of the terms may be written as a function of the other terms in the expansion. Although the analysis of this transfer is straightforward in the two-electron case through Eq. (230), it is more difficult in the general case and this type of constrained CSF coefficient optimization will not be considered/further. 

Though the case of constant matrix elements and the example investigated by Hite are the only situations for which Che stoichiometric relations have been fully established in pellets of arbitrary shape, it is worth mentioning situations in which these relations are known not to hold. When the composition and pressure at the surface of the pellet may vary in an arbitrary way from point to point it seems unlikely on intuitive grounds that equations (11.3) will be satisfied, and Hite and Jackson [77] confirmed by direct computation that there are, indeed, simple situations in which they are violated. Less obviously, direct computation [75] has also shown them to be violated even when the pressure and composition of the environment are the same everywhere, in the case where finite resistances to mass transfer exist at the surface of Che pellet. 

Published Cost Correla.tions. Purchased cost of an equipment item, ie, fob at seller s site or other base point, is correlated as a function of one or more equipment—size parameters. A size parameter is some elementary measure of the size or capacity, such as the heat-transfer area for a heat exchanger (see HeaT-EXCHANGETECHNOLOGy). Historically the cost—size correlations were graphical log—log plots, but the use of arbitrary equation forms for correlation has become quite common. If cost—size equations are used in computer databases, some limit logic must be included so that the equation is not used outside of the appHcable size range. 

The definition of the heat-transfer coefficient is arbitrary, depending on whether bulk-fluid temperature, centerline temperature, or some other reference temperature is used for ti or t-. Equation (5-24) is an expression of Newtons law of cooling and incorporates all the complexities involved in the solution of Eq. (5-23). The temperature gradients in both the fluid and the adjacent solid at the fluid-solid interface may also be related to the heat-transfer coefficient ... 

Gebhart B. Surface temperature calculations in radiant surroundings of arbitrary complexity—for gray, Diffuse Radiation. Int.. Heat Mitss Transfer, vol. 3, no. 4, 19iil. 

Wetting and capillarity can be expressed in terms of dielectric polarisabilities when van der Waals forces dominate the interface interaction (no chemical bond or charge transfer) [37]. For an arbitrary material, polarisabilities can be derived from the dielectric constants (e) using the Clausius-Mossotti expression [38]. Within this approximation, the contact angle can be expressed as ... 

Furthermore, since in Sec. 121 we found the value J = 0.36 electron-volt for the proton transfer (211), this gives the occupied proton level of the (HCOOII2)+ ion a position at (0.52 — 0.36) = 0.16 electron-volt above that of the (H30)+ ion in formic acid as solvent. This is shown in Fig. 65, where, for comparison, a diagram for proton levels in aqueous solution has been included, the level of the (H30)+ ion in aqueous solution being drawn opposite to the level of the same ion in formic acid solution. This choice is quite arbitrary, but was made in order to show more clearly that we may expect that one or more acids that are strong... 

If the system undergoes a virtual change of composition, 8, at constant temperature and pressure, it is transferred to another state, which need not however be an equilibrium state, since the changes of the masses are quite arbitrary. They must, however, satisfy the equations ... 

Recent studies on heat- and mass-transfer to and from bubbles in liquid media have primarily been limited to studies of the transfer mechanism for single moving bubbles. Transfer to or from swarms of bubbles moving in an arbitrary liquid field is very complex and has been analyzed theoretically in certain simple cases only (G3, G5, G6, G8, M3, R9, Wl). 

Most studies on heat- and mass-transfer to or from bubbles in continuous media have primarily been limited to the transfer mechanism for a single moving bubble. Transfer to or from swarms of bubbles moving in an arbitrary fluid field is complex and has only been analyzed theoretically for certain simple cases. To achieve a useful analysis, the assumption is commonly made that the bubbles are of uniform size. This permits calculation of the total interfacial area of the dispersion, the contact time of the bubble, and the transfer coefficient based on the average size. However, it is well known that the bubble-size distribution is not uniform, and the assumption of uniformity may lead to error. Of particular importance is the effect of the coalescence and breakup of bubbles and the effect of these phenomena on the bubble-size distribution. In addition, the interaction between adjacent bubbles in the dispersion should be taken into account in the estimation of the transfer rates... 

The original semiclassical version of the centrifugal sudden approximation (SCS) developed by Strekalov [198, 199] consistently takes into account adiabatic corrections to IOS. Since the orbital angular momentum transfer is supposed to be small, scattering occurs in the collision plane. The body-fixed correspondence principle method (BFCP) [200] was used to write the S-matrix for f — jf Massey parameter a>xc. At low quantum numbers, when 0)zc —> 0, it reduces to the usual non-adiabatic expression, which is valid for any Though more complicated, this method is the necessary extension of the previous one adapted to account for adiabatic corrections at higher excitation... 

Reaction, diffusion, and catalyst deactivation in a porous catalyst layer are considered. A general model for mass transfer and reaction in a porous particle with an arbitrary geometry can be written as follows ... 

DNA is ideally suited as a structural material in supramolecular chemistry. It has sticky ends and simple rules of assembly, arbitrary sequences can be obtained, and there is a profusion of enzymes for modification. The molecule is stiff and stable and encodes information. Chapter 10 surveys its varied applications in nanobiotechnology. The emphasis of Chapter 11 is on DNA nanoensembles, condensed by polymer interactions and electrostatic forces for gene transfer. Chapter 12 focuses on proteins as building blocks for nanostructures. 

A number of authors have considered channel cross-sections other than rectangular [102-104]. Figure 2.17 shows some examples of cross-sections for which friction factors and Nusselt numbers were computed. In general, an analytical solution of the Navier-Stokes and the enthalpy equations in such channel geometries would be involved owing to the implementation of the wall boundary condition. For this reason, usually numerical methods are employed to study laminar flow and heat transfer in channels with arbitrary cross-sectional geometry. 

Shah, R. K., Laminar flow friction and forced convection heat transfer in ducts of arbitrary geometry, Int. ). Heat Mass Transfer 18 (1975) 849-842. 

---