A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.

Local volatility changes in the black-scholes model

In this paper we address a problem arising in risk management; namely the study of price variations of different contingent claims in the Black-Scholes model due to anticipating future events. The method we propose to use is an extension of the classical Vega index, i.e. the price derivative with respect to the constant volatility, in thesense that we perturb the volatility in different directions. Thisdirectional derivative, which we denote the local Vega index, will serve as the main object in the paper and one of the purposes is to relate it to the classical Vega index. We show that for all contingent claims studied in this paper the local Vega index can be expressed as a weighted average of the perturbation in volatility. In the particular case where the interest rate and the volatility are constant and the perturbation is deterministic, the local Vega index is an average of this perturbation multiplied by the classical Vega index. We also study the well-known goal problem of maximizing the probability of a perfect hedge and show that the speed of convergence is in fact dependent of the local Vega index.

Riesz-Nágy singular functions revisited

In 1952 F. Riesz and Sz.Nágy published an example of a monotonic continuous function whose derivative is zero almost everywhere, that is to say, a singular function. Besides, the function was strictly increasing. Their example was built as the limit of a sequence of deformations of the identity function. As an easy consequence of the definition, the derivative, when it existed and was finite, was found to be zero. In this paper we revisit the Riesz-N´agy family of functions and we relate it to a system for real numberrepresentation which we call (t, t-1) expansions. With the help of these real number expansions we generalize the family. The singularity of the functions is proved through some metrical properties of the expansions used in their definition which also allows us to give a more precise way of determining when the derivative is 0 or infinity.

The use of derivatives in the Spanish mutual fund industry

We study the use of derivatives in the Spanish mutual fund industry. The picture that emerges from our analysis is rather negative. In general, the use of derivatives does not improve the performance of the funds. In only one out of eight categories we find some (very weak and not robust) evidence of superior performance. In most of the cases users significantly underperform non users. Furthermore, users do not seem to exhibit superior timing or selectivity skills either, but rather the contrary. This bad performance is only partially explained by the larger fees funds using derivatives charge. Moreover,we do not find evidence of derivatives being used for hedging purposes. We do find evidence of derivatives being used for speculation. But users in only one category exhibit skills as speculators. Finally, we find evidence of derivatives being used to manage the funds cash inflows and outflows more efficiently.

On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.

A note on the Malliavin differentiability of the Heston volatility

We show that the Heston volatility or equivalently the Cox-Ingersoll-Ross process is Malliavin differentiable and give an explicit expression for the derivative. This result assures the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model and the Cox-Ingersoll-Ross model for interest rates.

Projecte executiu d'una instal·lació de climatització i control d'un habitatge unifamiliar

Moltes vegades l’usuari d’una instal•lació de climatització o calefacció, no dóna la suficient importància al sistema que l’hi ha de proporcionar un millor confort amb el màxim rendiment. Aquest confort és un factor determinant, entre molts d’altres, de la “qualitat de vida”. Mentre que el rendiment és un factor important a nivell econòmic i ecològic. Tot i tenir prevalença els aspectes d’estalvi energètic, aquests no impliquen haver de renunciar a un confort tèrmic i a un estalvi econòmic. Un dels aspectes que es centra el projecte és promoure l’ús racional de les fonts energètiques (solar, biomassa) per a la correcta climatització dels habitatges. El projecte es desenvolupa en l’àmbit domèstic, concretament correspon a un habitatge unifamiliar. Aquest està situat a la població de Roda de Ter, província de Barcelona. L’objectiu principal del projecte és l’elecció del sistema de climatització i el seu dimensionament, per tal de donar el màxim confort als usuaris que habitin a la vivenda. Criteris ambientals i eficients han estat objecte a considerar pel disseny constructiu de l’habitatge. Una de les mesures importants presses en el projecte, ha estat l’elecció de les diferents parts que formen la instal•lació de climatització. Es fa referència als aïllaments dels tancaments, el sistema solar de recolzament, equips de producció de fred i calor, entre d’altres. En el projecte, s’ha dut a terme un estudi dels diferents tancaments de l’habitatge, tot determinat per a cada un d’ells, el seu coeficient de transmissió tèrmica. Per seleccionar l’equipament més adequat s’ha partit de les condicions climatològiques del municipi de Roda de Ter i s’ha realitzat el càlcul de les necessitats tèrmiques de l’edifici. L’habitatge incorpora una instal•lació de captació solar tèrmica. Aquesta aportarà un suport energètic a tot el sistema de producció de calor, ja sigui per la producció d’aigua calenta sanitària com per el calefactat de la vivenda. La col•locació dels panells a la façana sud tindrà una doble funció: a més de proporcionar energia solar tèrmica, serviran d’elements de protecció solar en la temporada d’estiu. La caldera usada per donar recolzament tèrmic utilitzarà com a combustible el “pellet”. El “pellet” és un tipus de biomassa llenyosa que consta d’un derivat de la fusta en format granulat. Es defineix i es detalla el consum energètic en biomassa, electricitat i cost econòmic anual que ocasionarà la instal.lació dissenyada. El sistema de terra radiant adoptat permetrà el refrescament en èpoques estivals i el calefactat en èpoques hivernals. Aquest donarà el confort tèrmic necessari a cada estança de l’habitatge. En el projecte també es marquen les pautes bàsiques pel control de la instal•lació solar així com el control dels grups de bombament i la mescla d’aigua del terra radiant.

Frequency resolved admittance spectroscopy measurements on In0.52Al0.48As/InxGa1¿xAs/In0.52Al0.48As single quantum well structures

In this work a new admittance spectroscopy technique is proposed to determine the conduction band offset in single quantum well structures (SQW). The proposed technique is based on the study of the capacitance derivative versus the frequency logarithm. This method is found to be less sensitive to parasitic effects, such as leakage current and series resistance, than the classical conductance analysis. Using this technique, we have determined the conduction band offset in In0.52Al0.48As/InxGa1¿xAs/In0.52Al0.48As SQW structures. Two different well compositions, x=0.53, which corresponds to the lattice¿matched case and x=0.60, which corresponds to a strained case, and two well widths (5 and 25 nm) have been considered. The average results are ¿Ec=0.49±0.04 eV for x=0.53 and ¿Ec =0.51±0.04 eV for x=0.6, which are in good agreement with previous reported data.

Origin of the neutron skin thickness of 208Pb in nuclear mean-field models

We study whether the neutron skin thickness Δrnp of 208Pb originates from the bulk or from the surface of the nucleon density distributions, according to the mean-field models of nuclear structure, and find that it depends on the stiffness of the nuclear symmetry energy. The bulk contribution to Δrnp arises from an extended sharp radius of neutrons, whereas the surface contribution arises from different widths of the neutron and proton surfaces. Nuclear models where the symmetry energy is stiff, as typical of relativistic models, predict a bulk contribution in Δrnp of 208Pb about twice as large as the surface contribution. In contrast, models with a soft symmetry energy like common nonrelativistic models predict that Δrnp of 208Pb is divided similarly into bulk and surface parts. Indeed, if the symmetry energy is supersoft, the surface contribution becomes dominant. We note that the linear correlation of Δrnp of 208Pb with the density derivative of the nuclear symmetry energy arises from the bulk part of Δrnp. We also note that most models predict a mixed-type (between halo and skin) neutron distribution for 208Pb. Although the halo-type limit is actually found in the models with a supersoft symmetry energy, the skin-type limit is not supported by any mean-field model. Finally, we compute parity-violating electron scattering in the conditions of the 208Pb parity radius experiment (PREX) and obtain a pocket formula for the parity-violating asymmetry in terms of the parameters that characterize the shape of the 208Pb nucleon densities.

Brownian motion of multidimensional systems in nonpotential velocity-dependent fields of force

We study the Brownian motion in velocity-dependent fields of force. Our main result is a Smoluchowski equation valid for moderate to high damping constants. We derive that equation by perturbative solution of the Langevin equation and using functional derivative techniques.

Electronic structure and properties of AlN

The electronic structure of the wurtzite-type phase of aluminum nitride has been investigated by means of periodic ab initio Hartree-Fock calculations. The binding energy, lattice parameters (a,c), and the internal coordinate (u) have been calculated. All structural parameters are in excellent agreement with the experimental data. The electronic structure and bonding in AlN are analyzed by means of density-of-states projections and electron-density maps. The calculated values of the bulk modulus, its pressure derivative, the optical-phonon frequencies at the center of the Brillouin zone, and the full set of elastic constants are in good agreement with the experimental data.

Electronic structure and properties of AlN

The electronic structure of the wurtzite-type phase of aluminum nitride has been investigated by means of periodic ab initio Hartree-Fock calculations. The binding energy, lattice parameters (a,c), and the internal coordinate (u) have been calculated. All structural parameters are in excellent agreement with the experimental data. The electronic structure and bonding in AlN are analyzed by means of density-of-states projections and electron-density maps. The calculated values of the bulk modulus, its pressure derivative, the optical-phonon frequencies at the center of the Brillouin zone, and the full set of elastic constants are in good agreement with the experimental data.

Convenient synthesis of C75, an inhibitor of FAS and CPT1

C75 is a synthetic racemic α-methylene-γ-butyrolactone exhibiting anti-tumoral properties in vitro and in vivo as well as inducing hypophagia and weight loss in rodents. These interesting properties are thought to be a consequence of the inhibition of the key enzymes FAS and CPT1 involved in lipid metabolism. The need for larger amounts of this compound for biological evaluation prompted us to develop a convenient and reliable route to multigram quantities of C75 from easily available ethyl penta-3,4-dienoate 6. A recently described protocol for the addition of 6 to a mixture of dicyclohexylborane and nonanal followed by acidic treatment of the crude afforded lactone 8, as a mixture of cis and trans isomers, in good yield. The DBU-catalyzed isomerization of the methyl esters 9 arising from 8 gave a 10:1 trans/cis mixture from which the trans isomer was isolated and easily transformed into C75. The temporary transformation of C75 into a phenylseleno ether derivative makes its purification, manipulation and storage easier.

On Ito's formula for elliptic diffusion processes

Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83-109] prove an extension of Ito's formula for F(Xt, t), where F(x, t) has a locally square-integrable derivative in x that satisfies a mild continuity condition in t and X is a one-dimensional diffusion process such that the law of Xt has a density satisfying certain properties. This formula was expressed using quadratic covariation. Following the ideas of Eisenbaum [Potential Anal. 13 (2000) 303-328] concerning Brownian motion, we show that one can re-express this formula using integration over space and time with respect to local times in place of quadratic covariation. We also show that when the function F has a locally integrable derivative in t, we can avoid the mild continuity condition in t for the derivative of F in x.

ABS: a database of Annotated regulatory Binding Sites from orthologous promoters

Information about the genomic coordinates and the sequence of experimentally identified transcription factor binding sites is found scattered under a variety of diverse formats. The availability of standard collections of such high-quality data is important to design, evaluate and improve novel computational approaches to identify binding motifs on promoter sequences from related genes. ABS (http://genome.imim.es/datasets/abs2005/index.html) is a public database of known binding sites identified in promoters of orthologous vertebrate genes that have been manually curated from bibliography. We have annotated 650 experimental binding sites from 68 transcription factors and 100 orthologous target genes in human, mouse, rat or chicken genome sequences. Computational predictions and promoter alignment information are also provided for each entry. A simple and easy-to-use web interface facilitates data retrieval allowing different views of the information. In addition, the release 1.0 of ABS includes a customizable generator of artificial datasets based on the known sites contained in the collection and an evaluation tool to aid during the training and the assessment of motif-finding programs.