Quasi-Exactly Solvable Potentials on the Line and Orthogonal Polynomials

In this paper we show that a quasi-exactly solvable (normalizable or periodic) one-dimensional Hamiltonian satisfying very mild conditions defines a family of weakly orthogonal polynomials which obey a three-term recursion relation. In particular, we prove that (normalizable) exactly-solvable one-dimensional systems are characterized by the fact that their associated polynomials satisfy a two-term recursion relation. We study the properties of the family of weakly orthogonal polynomials defined by an arbitrary one-dimensional quasi-exactly solvable Hamiltonian, showing in particular that its associated Stieltjes measure is supported on a finite set. From this we deduce that the corresponding moment problem is determined, and that the $k$-th moment grows like the $k$-th power of a constant as $k$ tends to infinity. We also show that the moments satisfy a constant coefficient linear difference equation, and that this property actually characterizes weakly orthogonal polynomial systems.Comment: 22 pages, plain TeX. Please typeset only the file orth.te

Critical behavior of su(1|1) supersymmetric spin chains with long-range interactions

We introduce a general class of su$(1|1)$ supersymmetric spin chains with long-range interactions which includes as particular cases the su$(1|1)$ Inozemtsev (elliptic) and Haldane-Shastry chains, as well as the XX model. We show that this class of models can be fermionized with the help of the algebraic properties of the su$(1|1)$ permutation operator, and take advantage of this fact to analyze their quantum criticality when a chemical potential term is present in the Hamiltonian. We first study the low energy excitations and the low temperature behavior of the free energy, which coincides with that of a $(1+1)$-dimensional conformal field theory (CFT) with central charge $c=1$ when the chemical potential lies in the critical interval $(0,\mathcal E(\pi))$, $\mathcal E(p)$ being the dispersion relation. We also analyze the von Neumann and R\'enyi ground state entanglement entropies, showing that they exhibit the logarithmic scaling with the size of the block of spins characteristic of a one-boson $(1+1)$-dimensional CFT. Our results thus show that the models under study are quantum critical when the chemical potential belongs to the critical interval, with central charge $c=1$. From the analysis of the fermion density at zero temperature, we also conclude that there is a quantum phase transition at both ends of the critical interval. This is further confirmed by the behavior of the fermion density at finite temperature, which is studied analytically (at low temperature), as well as numerically for the su$(1|1)$ elliptic chain.Comment: 13 pages, 6 figures, typeset in REVTe

Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies

We introduce a new class of generalized isotropic Lipkin-Meshkov-Glick models with su$(m+1)$ spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su$(m+1)$ type. We evaluate in closed form the reduced density matrix of a block of $L$ spins when the whole system is in its ground state, and study the corresponding von Neumann and R\'enyi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as $a\log L$ when $L$ tends to infinity, where the coefficient $a$ is equal to $(m-k)/2$ in the ground state phase with $k$ vanishing su$(m+1)$ magnon densities. In particular, our results show that none of these generalized Lipkin-Meshkov-Glick models are critical, since when $L\to\infty$ their R\'enyi entropy $R_q$ becomes independent of the parameter $q$. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su$(m+1)$ Lipkin-Meshkov-Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when $m-k\ge3$. Finally, in the su$(3)$ case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su$(3)$. This is also true in the su$(m+1)$ case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an $(m+1)$-simplex in $\mathbf R^m$ whose vertices are the weights of the fundamental representation of su$(m+1)$.Comment: Typeset with LaTeX, 32 pages, 3 figures. Final version with corrections and additional reference

Population Ageing and Future Demand for Old-Age and Disability Pensions in Germany – A Probabilistic Approach

Industrialised economies are experiencing a decline in mortality alongside low fertility rates – a situation that puts social security systems under severe pressure. Population ageing is associated not only with longer periods of pension claims but also smaller cohorts eventually entering the labour market. This threatens the sustainability of pay-as-you-go social security systems for implementing or further improving appropriate reform measures; adequate forecasts of the future population structure are needed. We propose a probabilistic approach to forecast the number of pensions in Germany up to 2040. Our model considers trends in population development, labour force participation, and early retirement, as well as the effects of pension reforms. Principal component analysis is used to manage the high degree of complexity involved in forecasting trends in old-age and disability pension claims, which arises because of cross-correlations between old-age and disability pension rates, different age groups, and gender. Time series methods enable the inclusion of autocorrelations of the pension rate time series in the model. Monte Carlo simulation is used to quantify future risk. The latter is an important feature of our model, as the future development of the population and, eventually, the pension claims and the financial burden resulting from those claims, are highly stochastic. The model predicts that, in the median trajectory, the number of old-age pensions will increase by almost 5 million between 2017 and 2036, alongside increases in the number of disability pensions by 2036. These numbers take account of the increase in legal retirement ages as part of the 2007 pension reform. After the mid-2030s, however, a moderate decrease can be expected. The results show a clear need for further reforms, especially in the medium term

The Effect of Silver Nanofibers on the Deformation Properties of Blood Vessels: Towards the Development of New Nanotechnologies to Prevent Rupture of Aneurysms

An aneurysm is the result of a widening or ballooning of a portion of a blood vessel. The rupture of an aneurysm occurs when the mechanical stress acting on the inner wall exceeds the failure strength of the blood vessel. We propose an innovative approach to prevent the rupture of an aneurysm based on the use of nanotechnology to improve the strength of the blood vessel. We present results on the effect of silver nanofibers on the resistance toward deformation of blood vessels. The silver nanofibers are grown on the surface of the blood vessels. The nanofibers are 120±30 nm in diameter and 2.7±0.8 μm in length. The deformation per applied force of blood vessels was found to decrease from 0.15 m/N in control blood vessels to 0.003 m/N in blood vessels treated with the nanofibers. This represents an increase in the resistance towards deformation of a factor of 50. The increase in the resistance towards deformation is clinically significant since blood pressure increases by factors slightly larger than one in the human body. Treatment of blood vessels with silver nanofibers is a potential translational clinical tool for preventing rupture of aneurysms in a clinical setting

Risikoprämien am europäischen Staatsanleihenmarkt: Neue empirische Erkenntnisse und Überlegungen aus der Sicht der Lebensversicherungsbranche

We study yield spreads between government bonds in the European Monetary Union. This segment of the global fixed income market is of particular importance for insurance companies in Europe. Our empirical research strategy is inspired by Gunay (2020) who has analyzed the relationship between credit and liquidity risk in the United States using Granger causality tests. More specifically, we employ the procedure developed by Toda and Yamamoto (1995) to test for Granger causality among yield spreads in five different member countries of the European Monetary Union (namely Austria, Belgium, France, Italy and Ireland) relative to Germany. We examine interest rate data from bonds with three different maturities (5, 10 and 30 years). Given the importance of long-term bonds as asset class for European life insurers and pension funds, the empirical results from the often ignored market for government bonds with a maturity of 30 years should be of interest. With regard to long-term sovereign debt, there is no evidence for Granger causality among the time series examined here. Consequently, the risk premia required by investors to hold government bonds of one specific member country of the EMU do not help to forecast the risk premia that have to be paid by other countries. Given the structure of their liabilities, this empirical finding should be of high relevance for portfolio and risk managers in the European life insurance industry and in pension funds. With regard to the yield spreads to be observed in the market for 10-year government bonds, there seems to be no clear picture. Focusing on fixed income securities with a maturity of 5 years, there is one very interesting empirical finding. The test results reported here seem to imply that there is unidirectional Granger causality running from the yield spreads in all other four countries to Austria. Given that Austria is a comparably small country which is assumed to be in a fiscally stable position, this result could be interpreted as evidence for credit risk premia as being helpful to forecast liquidity risk premia in the market for medium-term government bonds issued by member states of the European Monetary Union.Diese Studie untersucht Zinsdifferenzen am Markt von Staatsanleihen der Mitgliedsländer der Europäischen Währungsunion. Dieses Segment des globalen Rentenmarktes hat eine besondere Bedeutung für europäische Versicherungsunternehmen. Unsere empirische Studie ist von Gunay (2000) inspiriert, der den Zusammenhang zwischen Kredit- und Liquiditätsrisiko in den Vereinigten Staaten mittels Grangerkausalitätstests untersucht. Genauer gesagt findet hier der Ansatz von Toda und Yamamoto (1995) Anwendung. Untersucht werden die Zinsdifferenzen von fünf Ländern (Österreich, Belgien, Frankreich, Italien und Irland) zu Deutschland. Dabei wird auf drei Laufzeiten (5, 10 und 30 Jahre) geblickt. Der häufig in empirischen Studien ignorierte Markt für Staatsanleihen mit einer Restlaufzeit von 30 Jahren dürfte aufgrund der Struktur der Verbindlichkeiten von besonderem Interesse für Lebensversicherer und Pensionsfonds sein. In diesem Segment des europäischen Staatsanleihemarktes konnten wir keine Hinweise auf Grangerkausalität zwischen den Zinsdifferenzen finden. Die von den hier betrachteten Ländern für ihre Schulden zu zahlenden Risikoprämien helfen somit nicht, die Risikoprämien in den jeweils anderen untersuchten Nationen vorherzusagen. Dieses Ergebnis sollte von hoher Bedeutung für Kapitalanleger und Risikomanager bei europäischen Lebensversicherungen und Pensionsfonds sein. Im Laufzeitsegment 10 Jahre ergibt sich kein klares Bild. Bei den Zinsdifferenzen der Papiere mit einer Laufzeit von 5 Jahren zeigt sich dagegen klar, dass die Risikoprämien in allen anderen Ländern helfen, die Zinsdifferenz von Österreich zu Deutschland vorherzusagen. Da Österreich eher ein kleines Land mit relativ soliden Staatsfinanzen ist, mag dieses Ergebnis ein Hinweis darauf sein, dass das Kreditrisiko in diesem Segment des europäischen Rentenmarktes zur Prognose des Liquiditätsrisikos verwendet werden kann

Leading indicators for US house prices: New evidence and implications for EU financial risk managers

This study draws on machine learning as a means to causal inference for econometric investigation. We utilize the concept of transfer entropy to examine the relationship between the US National Association of Home Builders Index and the S&P CoreLogic Case-Shiller 20 City Composite Home Price Index (SPCS20). The empirical evidence implies that the survey data can help to predict US house prices. This finding extends the results of Granger causality tests performed by Rodriguez Gonzalez et al. in 2018 using a new machine learning approach that methodologically differs from traditional methods in empirical financial research. © 2021 The Authors. European Financial Management published by John Wiley & Sons Ltd

Atractividad del mercado japones para la exportacion de arandanos chilenos

111 p.El propósito de la investigación es entregar información oportuna a quienes se encuentren evaluando la posibilidad de exportar arándanos congelados al mercado japonés. Se realizó una investigación que determinó la atractividad del mercado japonés para la exportación de arándanos congelados chilenos. Para ello se describieron las características de la industria del arándano congelado en Chile, así como también las del macroentorno e industria del arándano en el mercado japonés, junto con esto, se detalla claramente el proceso de logística que debe recorrer el fruto para llegar a dicho destino. Como una forma de incitar futuras inversiones en el rubro, se analizó el impacto que tendrá la reciente firma del Tratado de Libre Comercio con el país nipón. La aplicación de los tres modelos detectó la baja participación de Chile en Japón y el sostenido crecimiento de las ventas chilenas en el país nipón, por lo que la investigación concluyó que el mercado japonés es atractivo dependiendo de las variables que considere más relevantes el interesado. Junto con esto, se entregan recomendaciones que permiten aprovechar las actuales condiciones en las que compite Chile, así como también estrategias que permitan potenciar las fortalezas como país productor de arándano