On variable discounting in dynamic programming: applications to resource extraction and other economic models

This paper generalizes the classical discounted utility model introduced in Samuelson (Rev. Econ. Stud. 4:155–161, 1937) by replacing a constant discount rate with a function. The existence of recursive utilities and their constructions are based on Matkowski’s extension of the Banach Contraction Principle. The derived utilities go beyond the class of recursive utilities studied in the literature and enable a discussion on subtle issues concerning time preferences in the theory of finance, economics or psychology. Moreover, our main results are applied to the theory of optimal economic growth related with resource extraction models with unbounded utility function of consumption.     

On homogeneous Lagrange means

Let \(f\) be a real differentiable function in an open interval \(I\) with one-to-one derivative. We observe that if the Lagrange mean \(L^{[f]}\) of a generator \(f\) is conditionally positively homogeneous, then \(f\) must be of the class \(C^{\infty }\) and the function $$\begin{aligned} g(x):=xf^{\prime }\left( x\right) -f\left( x\right) ,\quad \quad x\in I, \end{aligned}$$ is also a generator of \(L^{[f]}\) i.e. that \(L^{[g]}=L^{[f]}.\) We show that this fact and a result on equality of two Lagrange means allow easily to determine all positively homogeneous Lagrange means.     

The hydrogen‐bonding network in deacetyl­cephalothin

The structural analysis of deacetyl­cephalothin [systematic name: (6R,7R)‐3‐hydroxy­methyl‐8‐oxo‐7‐(2‐thio­phen‐2‐yl­acetyl­amino)‐5‐thia‐1‐aza­bicyclo­[4.2.0]oct‐2‐ene‐2‐carboxylic acid], C₁₄H₁₄N₂O₅S₂, shows that the geometry of the central bicyclic moiety is close to the geometry exhibited by other biologically active cephalosporin antibiotics. The mol­ecules are arranged in a helical chain running parallel to the 2₁ axis via a strong O—H⋯O hydrogen bond. The main helices are zipped together via N—H⋯O inter­actions, forming infinite layers. The supramolecular architecture is stabilized by O—H⋯S and C—H⋯O hydrogen bonds.     

l-Seryl-l-leucine

The structure of l -seryl-l -leucine, C₉H₁₈N₂O₄, has been determined and analysed in relation to the geometries of its amino acid constituents. The most important feature is the different conformational behaviour of the side chains at the C^β atoms; a less pronounced discrepancy concerns the orientation of the C=O bond with respect to the C^α—N bond. The conformational preferences of these torsion angles are also established for related structures stored in the Cambridge Structural Database [Allen & Kennard (1993). Chem.Des.Autom. News, 8 , 1, 31–37]; the title structure compares well with these data. The mol­ecules are organized in double layers, with the hydro­philic faces linked by an extensive hydrogen-bonding network, as in l -leucine.     

Functionalization of some benzylthioarylboronic acids by benzylic lithiation of their N‐butyldiethanolamine esters or lithium (triisopropoxy)borates

The reaction of benzylthioarylboronic acids protected as N‐butyldiethanolamine esters or as triisopropoxyborates with organolithium bases or lithium diisopropylamide (LDA) has been investigated. The benzylic lithiation occurs selectively using LDA at − 68 °C. The stability of the resultant borio‐lithio intermediates is strongly influenced by the position of the boron atom in the phenyl ring. The reaction with various electrophiles affords new arylboronic acids substituted in the benzylic position. Copyright © 2011 John Wiley & Sons, Ltd.     

5‐Carboxymethyl‐2‐(4‐methylthiophenyl)‐1,3,2‐dioxaborolan‐4‐one: synthesis,characterization and application in enantioselective reduction of ketones

The reaction of arylboronic acids with L ‐O‐benzoyl‐tartaric acid and D ,L ‐malic acid has been studied. The obtained (acyloxy)boranes are moderately stable in solution and decompose to give boroxines. 5‐Carboxymethyl‐2‐(4‐methylthiophenyl)‐1,3,2‐dioxaborolan‐4‐one was obtained in the reaction of 4‐methylthiophenylboronic acid with D ,L ‐malic acid and characterized by X‐ray structural analysis. The use of L ‐(−)‐malic acid afforded the optically pure product which can be used as the powerful chiral reagent in the enantioselective reduction of ketones. Copyright © 2011 John Wiley & Sons, Ltd.     

Speciation of functional groups formed on the surface of ammoxidised carbonaceous materials by XPS method

X-ray photoelectron spectroscopy (XPS) has been used to investigate the fate of nitrogen functional groups present in carbonaceous materials obtained from European plum (Prunus domestica) stones and modified by ammonia-air mixture at 250 or 300 °C. Peaks have been found in the XPS patterns, corresponding to different nitrogen functional forms i.e. pyrrolic, pyridinic, pyridone, amine and chemisorbed nitrogen oxides. It has been found that the distribution of nitrogen functional forms changes as a result of the modification processes.     

On subadditive functions and ψ-additive mappings

In [4], assuming among others subadditivity and submultiplicavity of a function ψ: [0, ∞)→[0, ∞), the authors proved a Hyers-Ulam type stability theorem for “ψ-additive” mappings of a normed space into a normed space. In this note we show that the assumed conditions of the function ψ imply that ψ=0 and, consequently, every “ψ-additive” mapping must be additive