Two additions to Lucas's "inflation and welfare"

This work adds to Lucas (2000) by providing analytical solutions to two problems that are solved only numerically by the author. The first part uses a theorem in control theory (Arrow' s sufficiency theorem) to provide sufficiency conditions to characterize the optimum in a shopping-time problem where the value function need not be concave. In the original paper the optimality of the first-order condition is characterized only by means of a numerical analysis. The second part of the paper provides a closed-form solution to the general-equilibrium expression of the welfare costs of inflation when the money demand is double logarithmic. This closed-form solution allows for the precise calculation of the difference between the general-equilibrium and Bailey's partial-equilibrium estimates of the welfare losses due to inflation. Again, in Lucas's original paper, the solution to the general-equilibrium-case underlying nonlinear differential equation is done only numerically, and the posterior assertion that the general-equilibrium welfare figures cannot be distinguished from those derived using Bailey's formula rely only on numerical simulations as well.

Additions to the known distribution of Epipompilus aztecus (Cresson, 1869) and E. excelsus (Bradley, 1944) (Hymenoptera: Pompilidae)

Knowledge about the species distribution of Epipompilus Kohl, 1884, is largely based on the records from the species description. Recent efforts in South American bodiversity studies indicate that knowledge about the distribution of Epipompilus species in the region is in an early stage. Two new records of E. aztecus were obtained for the semideciduous Atlantic Forest, in central Brazil, and one record for the Amazonian Forest in northern Brazil, indicating that its distribution extends between Central and South America. The new records of E. excelsus were obtained mainly from the Atlantic Forest highlands, indicating that this species is commonly found in the southeastern South American Central Plateau and restricted to forest ecosystem of this region. © 2010 Eduardo Fernando dos Santos and Fernando Barbosa Noll.

Stereoselectivity of Additions to N-Methyl Acetonitrilium Fluorosulfonate

Alkoxy-N-methyl-acetiminium salts were prepared by addition of CH3OH and C2H5OH to N-methyl acetonitrilium fluorosulfonate at low temperature. Analysis of the (5)J(HH) and (3)J(13)C-H coupling constants in the NMR spectra showed an anti addition with a diastereoselectivity of >9596. Deprotonation of these salts with (Z)-configuration gave the corresponding N-methyl-alkoxyacetimines with very high (E)-configuration. Upon protonation at -78 degrees C, these iminoesters gave the corresponding alkoxy-N-methyl-acetirninium salts with (E)-configuration. Computational analyses of the iminoesters and the corresponding iminium cations including the conformations give insight into the relative stability. Nitrilium salts can be used as reagents, exemplified by some esterifications between simple acids and alcohols.

Iron-Promoted Nucleophilic Additions to Diimine-Type Ligands: A Synthetic and Structural Study

We report here three examples of the reactivity of protic nucleophiles with diimine-type ligands in the presence of FeII salts. In the first case, the iron-promoted alcoholysis reaction of one nitrile group of the ligand 2,3-dicyano-5,6-bis(2-pyridyl)-pyrazine (L1) permitted the isolation of an stable E-imido−ester, [Fe(L1‘)2](CF3SO3)2 (1), which has been characterized by spectroscopic studies (IR, ES-MS, Mössbauer), elemental analysis, and crystallographically. Compound 1 consists of mononuclear octahedrally coordinated FeII complexes where the FeII ion is in its low-spin state. The iron-mediated nucleophilic attack of water to the asymmetric ligand 2,3-bis(2-pyridyl)pyrido[3,4-b]pyrazine (L2) has also been studied. In this context, the crystal structures of two hydration−oxidation FeIII products, [Fe(L2‘)2](ClO4)3·3CH3CN (2) and trans-[FeL2‘‘Cl2] (3), are described. Compounds 2 and 3 are both mononuclear FeIII complexes where the metals occupy octahedral positions. In principle, L2 is expected to coordinate to metal ions through its bipyridine-type units to form a five-membered ring; however, this is not the case in compounds 2 and 3. In 2, the ligand coordinates through its pyridines and through the hydroxyl group attached to the pyrazine imino carbon after hydration, that is, in an N,O,N tridentate manner. In compound 3, the ligand has suffered further transformations leading to a very stable diamido complex. In this case, the metal ion achieves its octahedral geometry by means of two pyridines, two amido N atoms, and two axial chlorine atoms. Magnetic susceptibility measurements confirmed the spin state of these two FeIII species:  compounds 2 and 3 are low-spin and high-spin, respectively.

Our weakened Constitution : an historical and analytical study of the Constitution of the United States and of the additions to the original text undertaken to place the facts before the American people, and to emphasize the present necessity for a movement in behalf of an unvolated Constitution, state integrity and the rights and immunities established by the founders of this republic /

Mode of access: Internet.

Cadmium additions to agricultural lands via commercial phosphate fertilizers : a preliminary assessment.

Issued Sept. 1978.

List of additions to the natural history, antiquities, and prints of the British Museum in the years MDCCCXXXVI-MDCCCXXXIX.

Mode of access: Internet.

Generic names applied to birds during the years 1901 to 1905, inclusive, with further additions to Waterhouse's "Index generum avium" /

Issued December 16, 1908.

Lectures on slavery : from the London ed., with additions to the Amer. ed.

Mode of access: Internet.

Report to Congress, Coastal Barrier Resources System : recommendations for additions to or deletions from the Coastal Barrier Resources System /

Maps have title: Report to Congress on the Coastal Barrier Resources System.

Catalogue of additions to the manuscripts /

Mode of access: Internet.

The birds of Ireland; an account of the distribution, migrations and habits of birds as observed in Ireland, with all additions to the Irish list,

Mode of access: Internet.

Ten years of the world's progress : being a supplement to the work of that title, 1850-1861 : with some corrections and additions to the former pages /

Mode of access: Internet.

Additions to the Geological Samples Library.

Mode of access: Internet.