Following the rules: Integrating asset allocation and annuitization in retirement portfolios

Financial advisers have developed standardized payout strategies to help Baby Boomers manage their money in their golden years. Prominent among these are phased withdrawal plans offered by mutual funds including the “self-annuitization” or default rules encouraged under US tax law, and fixed payout annuities offered by insurers. Using a utility-based framework, and taking account of stochastic capital markets and uncertain lifetimes, we first evaluate these rules on a stand-alone basis for a wide range of risk aversion. Next, we permit the consumer to integrate these standardized payout strategies at retirement and compare the results. We show that integrated strategies can enhance retirees’ well-being by 25%-50% for low/moderate levels of risk aversion when compared to full annuitization at retirement. Finally, we examine how welfare changes if the consumer is permitted to switch to a fixed annuity at an optimal point after retirement. This affords the retiree the chance to benefit from the equity premium when younger, and exploit the mortality credit in later life. For moderately risk-averse retirees, the optimal switching age lies between 80 and 85.     

Fraïssé’s Construction from a Topos-Theoretic Perspective

We present a topos-theoretic interpretation of (a categorical generalization of) Fraïssé’s construction in Model Theory, with applications to homogeneous models and countably categorical theories.     

A General Method for Building Reflections

We establish a general method for generating reflections between categories. We then apply our technique to generate adjunctions starting from geometric morphisms between Grothendieck toposes; as particular cases, we recover various well-known Stone-type adjunctions and establish several new ones.     

Formic acid oxidation on Pd/RuO2: does the RuO2 support enhance the electrocatalytic activity of Pd nanoparticles?

Journal of Solid State Electrochemistry - The aim of this work was to study the effect of a RuO2 support on the activity of Pd nanoparticles for formic acid oxidation, comparing the results with...     

Newman’s identity and infinite families of congruences modulo 7 for broken 3-diamond partitions

In 2007, Andrews and Paule introduced the notion of broken k-diamond partitions. Let \(\Delta _k(n)\) denote the number of broken k-diamond partitions of n for a fixed positive integer k. Recently, Paule and Radu presented some conjectures on congruences modulo 7 for \(\Delta _3(n)\) which were proved by Jameson and Xiong based on the theory of modular forms. Very recently, Xia proved several infinite families of congruences modulo 7 for \(\Delta _3(n)\) using theta function identities. In this paper, many new infinite families of congruences modulo 7 for \(\Delta _3(n)\) are derived based on an identity of Newman and the (p; k)-parametrization of theta functions due to Alaca, Alaca and Williams. In particular, some non-standard congruences modulo 7 for \(\Delta _3(n)\) are deduced. For example, we prove that for \(\alpha \ge 0\), \(\Delta _3\left( \frac{14\times 757^{\alpha }+1}{3}\right) \equiv 6 -\alpha \ (\mathrm{mod}\ 7)\).     

Thermodynamics and Spectroscopy of Halogen- and Hydrogen-Bonded Complexes of Haloforms with Aromatic and Aliphatic Amines

Similarities and differences of halogen and hydrogen bonding were explored via UV–Vis and ¹H NMR measurements, X-ray crystallography and computational analysis of the associations of CHX₃ (X=I, Br, Cl) with aromatic (tetramethyl-p-phenylenediamine) and aliphatic (4-diazabicyclo[2,2,2]octane) amines. When the polarization of haloforms was taken into account, the strengths of these complexes followed the same correlation with the electrostatic potentials on the surfaces of the interacting atoms. However, their spectral properties were quite distinct. While the halogen-bonded complexes showed new intense absorption bands in the UV–Vis spectra, the absorptions of their hydrogen-bonded analogues were close to the superposition of the absorption of reactants. Additionally, halogen bonding led to a shift in the NMR signal of haloform protons to lower ppm values compared with the individual haloforms, whereas hydrogen bonding of CHX₃ with aliphatic amines resulted in a shift in the opposite direction. The effects of hydrogen bonding with aromatic amines on the NMR spectra of haloforms were ambivalent. Titration of all CHX₃ with these nucleophiles produced consistent shifts in their protons’ signals to lower ppm values, whereas calculations of these pairs produced multiple hydrogen-bonded minima with similar structures and energies, but opposite directions of the NMR signals’ shifts. Experimental and computational data were used for the evaluation of formation constants of some halogen- and hydrogen-bonded complexes between haloforms and amines co-existing in solutions.     

An inequality concerning the growth bound of an evolution family and the norm of a convolution operator

Let \(\mathcal {U}=\{U(t,s)\}_{t\ge s\ge 0}\) be a strongly continuous and exponentially bounded evolution family acting on a complex Banach space X and let \(\mathcal {X}\) be a certain Banach function space of X-valued functions. We prove that the growth bound of the family \(\mathcal {U}\) is less than or equal to \(-\frac{1}{c(\mathcal {U}, \mathcal {X})}\) provided that the convolution operator \(f\mapsto \mathcal {U}*f\) acts on \(\mathcal {X}.\) It is well known that under the latter assumption, the convolution operator is bounded and then \(c(\mathcal {U}, \mathcal {X})\) denotes (ad-hoc) its norm in \(\mathcal {L}(\mathcal {X}).\) As a consequence, we prove that if \(\sup \nolimits _{s\ge 0}\int \nolimits _{s}^\infty \Vert U(t,s)\Vert dt=u_1(\mathcal {U})<\infty ,\) then \(\omega _0(\mathcal {U})u_1(\mathcal {U})\le -1.\) Finally, we give an example showing that the accuracy of the estimates may be quite accurate.     

Scientific investigations of the Imperial Gates from the Petrindu wooden church,Salaj County,Romania

In order to preserve and restore the Imperial Gates from the Petrindu wooden church, Salaj County, Romania, (map location—latitude, longitude: 46.97, 23.19), the scientific investigation of the wooden support and painting materials (ground and pigments) was performed, employing Fourier‐transform infrared spectroscopy (FTIR), X‐ray fluorescence spectroscopy, and 3D scanning. FTIR spectroscopy offered information about the wooden degradation stage, whereas X‐ray fluorescence and FTIR spectroscopic methods were employed for structural painting materials characterization. The structural data can be correlated with the artistic, theological, and historical analysis of this religious patrimony object. After obtaining information about the wooden support and painting materials, the Imperial Gates were 3D digitized using state of the art laser scanning technology. The digital 3D model obtained was restored in a virtual environment and converted into an interactive 3D model that can be used for Romanian cultural heritage digital dissemination.     

The strong perfect graph conjecture holds for diamonded odd cycle-free graphs

In this paper, we show that the strong perfect graph conjecture holds for a new class of graphs which we call diamonded odd cycle-free graphs. The class of diamonded odd cycle-free graphs contains the classes of threshold graphs and K₄\e-free graphs.