Log R2 Research Articles

Economic Valuation of Lippia adoensis, implication for Access and Benefit Sharing agreement in Sidama and WestArsi Zones, SNNPR and Oromia Regions, Ethiopia

Biodiversity has major economic value. Most of these values are often not captured by the market. Hence, the potential of biodiversity is often underestimated. Such an underestimation is considered as one of the factors for rapid depletion of biodiversity and loss of habitats and species. Valuation of bio-resources would facilitate in identifying the real value of genetic resources and obtaining a reasonably better share of the overall benefits of genetic materials to the local communities, who are involved in its management. Accordingly, the Economic Valuation of Lippia adoensis was conducted implication for ABS. The result of this study identified the direct and indirect use values of Lippia adoensis. Majority of the respondents (98.33%) were willing to pay for use values of Lippia adoensis. Moreover, (80.8%) of the respondents were willingness to pay for Conservation of Lippia adoensis. Furthermore, 95(79.2%) of the respondents were willingness to pay for non-use value of Lippia adoensis in the study areas. The cumulative estimates of willingness to pay for use of values Lippia adoensis were 30,437.50 birr with an average annual willingness to pay of 253.64±275.63 birr for Lippia adoensis. The maximum willingness to pay was 1000 birr while the minimum WTP was 125 birr with range 875 birr. The value of R2 for linear function (model) was 0.541, semi log R2=0.452 and double log R2=0.291.From the given result the linear regression function (R2=0.541) the one with the best performance. The R2=0.541or 54.1%, this means that the dependent variable can be explained by the independent variable. In this study, household size (Sig.0.000), income level (Sig.0.000), number of Lippia adoensis (Sig.0.044) and distance of the market (Sig. 0.051) of the respondents made a unique and statistically significant, contribution to the prediction of willingness to pay for Lippia adoensis. Of the nine variables, household size of the responders makes the largest unique contribution (beta=0.490), followed by income level of the respondents (beta -0.396). Therefore, because of its prospect for the production of many preservative, spices, aromatherapy, medicine and pharmaceuticals industry, bio prospecting companies require to access the genetic resources following the Ethiopian legislation of Access and Benefit Sharing.

Series wave functions for the helium atom

Series methods for solving differential equations have been applied to the Schrodinger equation for helium. Formally exact solutions have been obtained for singlet S states. The solutions are expressed as multipole expansions in the angle between the electron position vectors r1 and r2 at the nucleus. The radial functions cannot be expressed as power series in r1 and r2, but as series involving powers of r1, r2, log r1, and log r2. Recurrence relations, together with conditions for smoothness at r1 = r2 and proper behavior at the nucleus, determine most of the expansion coefficients. Simple, exact expressions for infinitely many of the coefficients, namely those for terms involving ri1rj2 with i + j = 0, 1, and 2, have been determined. Coefficients not determined in the recursion process (of which there are infinitely many for each multipole component) can have arbitrary values in the formal solution. They are determined by the additional requirement that the wave function should have a finite square integral. An observation that the eigenfunction should be asymptotically separable in r1 and r2 for large values of these variables leads to approximate relations among the arbitrary coefficients, reducing the number of undetermined parameters to one per multipole component. Estimates for these remaining coefficients can be made easily. All approximations can be improved systematically to obtain arbitrarily high accuracy. The possibility of obtaining the exact solutions is considered.

Effect of Solvent on the Radical Copolymerizability of Styrene with Acrylonitrile

Abstract Radical copolymerization of styrene (St, M1) with acrylonitrile (AN, M2) has been carried out using azobisisobutylonitrile as an initiator in benzene, dimethylsulfoxide, acetonitrile, and ethanol at 60 and 80°C. Good linear correlationships were obtained by plotting the values of log r1, log r2, Q2, and e2 against those of vC[dbnd]N and vC[dbnd]C determined in the solvents: the increase in the interaction between AN and the solvent was found to decrease the values of log r1 and e2 but to increase those of log r2 and Q2. The results are discussed in terms of the solvation both in the ground state and in the transition state.

Solvent Effects in Radical Copolymerization of Styrene with N, N-Dimethylacrylamide

Abstract The radical copolymerization of N, N-dimethylacrylamide (I) with styrene (St) (M1) was carried out in several solvents at 60 and 80°C. The monomer reactivity ratios were considerably affected by the reaction conditions. Linear correlationships were observed by plots of the values of both νC=0 and νC=C stretching frequencies of I obtained in the solvents against those of log r1, log r2, ΔΔE‡ (= ΔE11‡ - ΔE12‡), and ΔΔS‡ (= ΔS11‡ - ΔS12‡). The values of both ΔE12‡ and ΔS12‡ were also determined.

Calculation of the copolymerization parameters in the ternary copolymerization system of styrene/m‐divinyl‐benzene/p‐divinylbenzene

AbstractThe r‐values of styrene with p‐divinylbenzene or m‐divinylbenzene (DVB), respectively, as determined by several authors, deviate strongly from the ideal straight line in the binary polymerization diagram. In an attempt to convert the various r‐values into coincident e‐and q‐values according to the equations of Schwan and Price. log r1 = (1 T) [6.79 (q1 ‐ q2) ‐ 3.63 1( 1 – 2)] and log r2 = (‐ 1 T) [6.79 (q1 ‐ q2) + 3.63 2 ( 1 ‐ 2)] good agreement was found for several r‐values, while others gave results that could not be evaluated. From a couple of ‐ and q‐values of p‐divinylbenzene and m‐divinylbenzene, the unmeasured r‐values between p‐divinylbenzene and m‐divinylbenzene were computed according to Schwan and Price. Using these r‐values, the ternary, copolymerization system of styrene m‐divinylbenzene/p‐divinylbenzene was computed approximately for various molar ratios of p‐divinylbenzene to m‐divinylbenzene (2:1 1:4) according to Alfrey and Goldfinger. It was shown that p‐divinylbenzene has an essential influence on heterogeneity in a ternary system, too.

Location of Energy Barriers. II. Correlation with Barrier Height

In Paper I of this series a hypothetical potential-energy surface was used in order to examine the effect on the dynamics of exchange reactions A + BC→AB + C of moving the energy barrier from an “early” to a “late” position along the reaction coordinate (i.e., from the entry valley to the exit valley of the energy surface). In the present work an attempt has been made to correlate barrier location with other properties of the energy surface, as a step toward the application of the generalizations of Paper I to real cases. Related families of reactions have been examined in the London–Eyring–Polanyi–Sato (LEPS) and bond-energy bond-order (BEBO) approximations. The principal generalizations may be summarized as follows: (1) For substantially exothermic reactions the barrier is in the entry valley, and for substantially endothermic reactions the barrier is in the exit valley. In the light of Paper I this implies that the cross sections for these exothermic reactions will rise most steeply with increasing translational energy in the reagents, whereas the cross sections for the endothermic reactions will rise most steeply with increasing vibrational energy in the bond under attack. (2) For decreasing barrier height in related exothermic reactions the barrier moves to successively earlier positions along the entry valley, with increasing percentage “attractive energy release.” (3) In general [i.e., if (4), below, is obeyed even qualitatively], for increasing barrier height in related endothermic reactions the barrier moves to successively later positions along the exit valley. (4) The correlation between the classical barrier height EC and reaction energy qc, written ΔEC = −α Δqc by Ogg and Polanyi (OP) was found to be a weaker correlation than (2), above. For families where barrier height did decrease with increasing reaction energy, a logarithmic relationship, Δ logEC = −αl Δqc, was preferable for the exothermic reactions. The same relationship encompassed members of the family with qc < 0 (endothermic reactions). With the proviso that (4) shall be applicable, (1)–(3) are summarized in the proposition that the barrier moves to successively later positions along the reaction coordinate with increasing barrier height. This progressive shift of the barrier is embodied in the following approximate relationships: Δ logEC = −β1lΔr1‡,0, Δ log r2‡,0 = −aΔr1‡,0 + cΔ[(r1‡,0)−1], where r1‡,0 and r2‡,0 are the extensions of AB and BC, from their equilibrium separation, at the crest of the barrier. In view of (4), Δqc = (β1l / αl)Δr1‡,0, a relationship which encompasses both exothermic and endothermic reactions. The fraction of attractive energy release alters from one exothermic reaction to the next by approximately Δ(α⊥) = γ1Δr1‡,0; hence, Δ logEC = −(β1l / γ1) Δ (α⊥).