By Archer K.J., Dumur C.I., Joel S.E.
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Utilizing Discrete selection Experiments to price future health and future health Care takes a clean and contemporay examine the growing to be curiosity within the improvement and alertness of discrete selection experiments (DCEs) in the box of overall healthiness economics. The authors have written it with the aim of giving the reader a greater figuring out of matters raised within the layout and alertness of DCEs in healthiness economics.
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Frustrated double chain (Fig. 1e) Magnetic susceptibility NA g 2 µ2B A χ = 8kT B A = U 2 exp(K 1 ) exp(K 2 ) + 2 1 − exp(2K 1 ) U + exp(3K 1 ) exp(−K 2 ) + exp(−K 1 ) exp(−K 2 ) − 2 exp(K 1 ) exp(−K 2 ) B = ER with E = exp(−2K 1 ) + cosh(K 2 ) + exp(−K 1 )R R = exp(2K 1 ) sinh2 (K 2 ) + 2 cosh(K 2 ) + 2 1/2 U = exp(K 1 ) cosh(K 2 ) + exp(−K 1 ) + exp(2K 1 ) sinh2 (K 2 ) + 2 cosh(K 2 ) + 2 1/2 Specific heat C p /R = (B/Z − A2 /Z 2 ) Z = exp(−K 1 ) + exp(K 1 ) cosh(K 2 ) + U 1/2 A = V + P/U 1/2 B = W + (U Q − P 2 )/U 3/2 U = exp(2K 2 ) sinh2 (K 1 ) + 2 cosh(K 1 ) + 2 V = −K 1 exp(−K 1 ) + K 1 exp(K 1 ) cosh(K 2 ) + K 2 exp(K 1 ) sinh(K 2 ) W = K 22 exp(K 2 ) cosh(K 1 ) + exp(−K 2 ) + K 1 K 2 exp(K 1 + K 2 ) + K 1 exp(K 2 ) sinh(K 1 ) P = K 2 exp(2K 2 ) sinh2 (K 1 ) + (1/2)K 1 exp(2K 2 ) sinh(2K 1 ) + K 1 sinh(K 1 ) Q = 2K 22 exp(K 2 ) sinh(K 1 ) + 2K 1 K 2 exp(2K 2 ) sinh(2K 1 ) + K 12 exp(2K 2 ) cosh(2K 1 ) + K 12 cosh(K 1 ) with K i = Ji /2kT ; i = 1, 2 This problem has been encountered in the Cu(II) compounds A3 Cu3 (PO4 )4 (A = CaII and SrII ) and Cu2 OSO4 .
3. An example which illustrates this case is provided by the series of solid state compounds formulated as Sr3 CuPt1−x Irx O6 which exhibit a chain structure formed by two alternating sites A and B (Fig. 6a). Site A is occupied Table 4. F/AF alternating chain (s = 1/2) A–H parameters for the rational expression of the susceptibility given as a function of polynomials in α, (α = J2 /|J1 |): X i (α) = x0 + x1 α + x2 α 2 + x3 α 3 . 02686769 S2i S2i−1 j ATr3 + BTr2 + C Tr + D ; + E Tr3 + F Tr2 + GTr + H NA g 2 µ2B kT ; χM = χr |J1 | 4|J1 | 10 1 One-dimensional Magnetism: An Overview of the Models Table 5.
The general approach of the mathematics, which is now briefly described, remains unchanged when dealing with more complex classical-spin systems. The partition function is first calculated for a finite length chain containing N spin vectors. We have: Z N (B) = d 0 d N exp(−β H ) (7) where β is Boltzmann’s factor 1/kT , and d i means integrating over all the directions (defined by the usual spherical angles θi and φi ) available to each vector ui . In order to perform the integrations, the argument of the exponential is written as a sum of terms, each one involving a pair of neighboring sites, say ui and ui+1 .