On harmonic Bloch-type mappings

Let $f$ be a complex-valued harmonic mapping defined in the unit disk $\mathbb D$. We introduce the following notion: we say that $f$ is a Bloch-type function if its Jacobian satisfies $$\sup_{z\in\mathbb D}(1-|z|^2)\sqrt{|J_f(z)|}<\infty.$$ This gives rise to a new class of functions which generalizes and contains the well-known analytic Bloch space. We give estimates for the schlicht radius, the growth and the coefficients of functions in this class. We establish an analogue of the theorem which states that an analytic $\varphi$ is Bloch if and only if there exists $c>0$ and a univalent $\psi$ such that $\varphi = c \log \psi'$.Comment: 11 pages, LaTeX; corrected typos in version 2; to appear in Complex Variables and Elliptic Equation

The Valuation of Mortgage Backed Securities with Stochastic Probabilities of Default and Prepayment

The aim of this paper is to provide a new approach to project the Mortgage Backed Securities (MBS) cash flows in emerging markets where collateral information is limited, wrong or scarce. Under this framework, we use the Cox Process to model stochastic probabilities of prepayment and default. The model deals with general intensity dynamics and is applied to the starting MBS Mexican market.Mortgage valuation, MBS prepayment, MBS default, MBS curtailment, Cox Process.

Quantum Walks with Entangled Coins

We present a mathematical formalism for the description of unrestricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, two different coin operators, two different shift operators, and one walker. We compare and contrast the performance of these quantum walks with that of a classical random walk consisting of one walker and two maximally correlated coins as well as quantum walks with coins sharing different degrees of entanglement. We illustrate that the behaviour of our walk with entangled coins can be very different in comparison to the usual quantum walk with a single coin. We also demonstrate that simply by changing the shift operator, we can generate widely different distributions. We also compare the behaviour of quantum walks with maximally entangled coins with that of quantum walks with non-entangled coins. Finally, we show that the use of different shift operators on 2 and 3 qubit coins leads to different position probability distributions in 1 and 2 dimensional graphs.Comment: Two new sections and several changes from referees' comments. 12 pages and 12 (colour) figure

Oils and fats on food: is it possible to have a healthy diet?

Oils and fats are an important part of our diet as components of many food formulations. Thus, they are retailed for domestic or hostelry uses and broadly used by food industry for the elaboration of margarines, ice cream, canned food, pre-cooked dishes, bakery, confectionary, chocolates, etc. Chemically, the main component of oils and fats are triacylglycerols (TAGs), which account for up to 95% of their total weight. They consisted of a molecule of glycerol esterified with three fatty acids, usually the saturated, palmitic and stearic, the monounsatu�rated oleic, and the polyunsaturated, linoleic or linolenic, all with 18 carbons excepting the palmitic which has 16 carbons. Out of those most common fatty acids, we can found other fatty acids present only in certain oils such as saturated medium chained fatty acids like lauric and myristic, which contain 12 and 14 carbons respectively

Oils and fats on food: is it possible to have a healthy diet?

Oils and fats are an important part of our diet as components of many food formulations. Thus, they are retailed for domestic or hostelry uses and broadly used by food industry for the elaboration of margarines, ice cream, canned food, pre-cooked dishes, bakery, confectionary, chocolates, etc. Chemically, the main component of oils and fats are triacylglycerols (TAGs), which account for up to 95% of their total weight. They consisted of a molecule of glycerol esterified with three fatty acids, usually the saturated, palmitic and stearic, the monounsatu�rated oleic, and the polyunsaturated, linoleic or linolenic, all with 18 carbons excepting the palmitic which has 16 carbons. Out of those most common fatty acids, we can found other fatty acids present only in certain oils such as saturated medium chained fatty acids like lauric and myristic, which contain 12 and 14 carbons respectively

New Insights Into Sunflower (Helianthus annuus L.) FatA and FatB Thioesterases, Their Regulation, Structure and Distribution

Sunflower seeds (Helianthus annuus L.) accumulate large quantities of triacylglycerols (TAG) between 12 and 28 days after flowering (DAF). This is the period of maximal acyl-acyl carrier protein (acyl-ACP) thioesterase activity in vitro, the enzymes that terminate the process of de novo fatty acid synthesis by catalyzing the hydrolysis of the acyl-ACPs synthesized by fatty acid synthase. Fatty acid thioesterases can be classified into two families with distinct substrate specificities, namely FatA and FatB. Here, some new aspects of these enzymes have been studied, assessing how both enzymes contribute to the acyl composition of sunflower oil, not least through the changes in their expression during the process of seed filling. Moreover, the binding pockets of these enzymes were modeled based on new data from plant thioesterases, revealing important differences in their volume and geometry. Finally, the subcellular location of the two enzymes was evaluated and while both possess an N-terminal plastid transit peptide, only in FatB contains a hydrophobic sequence that could potentially serve as a transmembrane domain. Indeed, using in vivo imaging and organelle fractionation, H. annuus thioesterases, HaFatA and HaFatB, appear to be differentially localized in the plastid stroma and membrane envelope, respectively. The divergent roles fulfilled by HaFatA and HaFatB in oil biosynthesis are discussed in the light of our data.España MINECO y FEDER Projects AGL2014- 53537-R y AGL2017-83449-

Exchange Narrowing Effects in the EPR Linewidth of Gd Diluted in Ce Compounds

Anomalous thermal behavior on the EPR linewidths of Gd impurities diluted in Ce compounds has been observed. In metals, the local magnetic moment EPR linewidth, \Delta H, is expected to increase linearly with the temperature. In contrast, in Ce_{x}La_{1-x}Os_{2} the Gd EPR spectra show a nonlinear increase. In this work, the mechanisms that are responsible for the thermal behavior of the EPR lines in Ce_{x}La_{1-x}Os_{2} are examined. We show that the exchange interaction between the local magnetic moments and the conduction electrons are responsible for the narrowing of the spectra at low temperatures. At high temperatures, the contribution to the linewidth of the exchange interaction between the local magnetic moments and the $Ce$ ions has an exponential dependence on the excitation energy of the intermediate valent ions. A complete fitting of the EPR spectra for powdered samples is obtained.Comment: 11 pages, 1 figur