Traces of functions in Fock spaces on lattices of critical density

Following a scheme of Levin we describe the values that functions in Fock spaces take on lattices of critical density in terms of both the size of the values and a cancelation condition that involves discrete versions of the Cauchy and Beurling-Ahlfors transforms.

Uniform estimates in the Poincare-Aronszajn theorem on the separation of singularities of analytic functions

We study the possibility of splitting any bounded analytic function $f$ with singularities in a closed set $E\cup F$ as a sum of two bounded analytic functions with singularities in $E$ and $F$ respectively. We obtain some results under geometric restrictions on the sets $E$ and $F$ and we provide some examples showing the sharpness of the positive results.

Endogenous growth with capital in R&D production functions

[eng] In this paper we claim that capital is as important in the production of ideas as in the production of final goods. Hence, we introduce capital in the production of knowledge and discuss the associated problems arising from the public good nature of knowledge. We show that although population growth can affect economic growth, it is not necessary for growth to arise. We derive both the social planner and the decentralized economy growth rates and show the optimal subsidy that decentralizes it. We also show numerically that the effects of population growth on the market growth rate, the optimal growth rate and the optimal subsidy are small. Besides, we find that physical capital is more important for the production of knowledge than for the production of goods.

Endogenous growth with capital in R&D production functions

[eng] In this paper we claim that capital is as important in the production of ideas as in the production of final goods. Hence, we introduce capital in the production of knowledge and discuss the associated problems arising from the public good nature of knowledge. We show that although population growth can affect economic growth, it is not necessary for growth to arise. We derive both the social planner and the decentralized economy growth rates and show the optimal subsidy that decentralizes it. We also show numerically that the effects of population growth on the market growth rate, the optimal growth rate and the optimal subsidy are small. Besides, we find that physical capital is more important for the production of knowledge than for the production of goods.

Characterization of Reward Functions in Networks with Costs

In this paper we study network structures in which the possibilities for cooperation are restricted and can not be described by a cooperative game. The benefits of a group of players depend on how these players are internally connected. One way to represent this type of situations is the so-called reward function, which represents the profits obtainable by the total coalition if links can be used to coordinate agents' actions. The starting point of this paper is the work of Vilaseca et al. where they characterized the reward function. We concentrate on those situations where there exist costs for establishing communication links. Given a reward function and a costs function, our aim is to analyze under what conditions it is possible to associate a cooperative game to it. We characterize the reward function in networks structures with costs for establishing links by means of two conditions, component permanence and component additivity. Finally, an economic application is developed to illustrate the main theoretical result.

Are figures accessible in mathematics academic journals?

Are figures accessible in mathematics academic journals? An analysis of current image accessibility in highly cited mathematics journals.

Are figures accessible in mathematics academic journals?

Are figures accessible in mathematics academic journals? An analysis of current image accessibility in highly cited mathematics journals.

Bandlimited Lipschitz functions

We study the space of bandlimited Lipschitz functions in one variable. In particular we provide a geometrical description of interpolating and sampling sequences for this space. We also give a description of the trace of such functions to sequences of critical density in terms of a cancellation condition.

Estimation of age- and stage-specific Catalan breast cancer survival functions using US and Catalan survival data

Background: During the last part of the 1990s the chance of surviving breast cancer increased. Changes in survival functions reflect a mixture of effects. Both, the introduction of adjuvant treatments and early screening with mammography played a role in the decline in mortality. Evaluating the contribution of these interventions using mathematical models requires survival functions before and after their introduction. Furthermore, required survival functions may be different by age groups and are related to disease stage at diagnosis. Sometimes detailed information is not available, as was the case for the region of Catalonia (Spain). Then one may derive the functions using information from other geographical areas. This work presents the methodology used to estimate age- and stage-specific Catalan breast cancer survival functions from scarce Catalan survival data by adapting the age- and stage-specific US functions. Methods: Cubic splines were used to smooth data and obtain continuous hazard rate functions. After, we fitted a Poisson model to derive hazard ratios. The model included time as a covariate. Then the hazard ratios were applied to US survival functions detailed by age and stage to obtain Catalan estimations. Results: We started estimating the hazard ratios for Catalonia versus the USA before and after the introduction of screening. The hazard ratios were then multiplied by the age- and stage-specific breast cancer hazard rates from the USA to obtain the Catalan hazard rates. We also compared breast cancer survival in Catalonia and the USA in two time periods, before cancer control interventions (USA 1975–79, Catalonia 1980–89) and after (USA and Catalonia 1990–2001). Survival in Catalonia in the 1980–89 period was worse than in the USA during 1975–79, but the differences disappeared in 1990–2001. Conclusion: Our results suggest that access to better treatments and quality of care contributed to large improvements in survival in Catalonia. On the other hand, we obtained detailed breast cancer survival functions that will be used for modeling the effect of screening and adjuvant treatments in Catalonia.

Weierstrass integrability of differential equations

The integrability problem consists in finding the class of functions a first integral of a given planar polynomial differential system must belong to. We recall the characterization of systems which admit an elementary or Liouvillian first integral. We define {\it Weierstrass integrability} and we determine which Weierstrass integrable systems are Liouvillian integrable. Inside this new class of integrable systems there are non--Liouvillian integrable systems.

Affinity distribution functions in multicomponent heterogeneous adsorption. Analytical inversion of isotherms to obtain affinity spectra

An analytical approach for the interpretation of multicomponent heterogeneous adsorption or complexation isotherms in terms of multidimensional affinity spectra is presented. Fourier transform, applied to analyze the corresponding integral equation, leads to an inversion formula which allows the computation of the multicomponent affinity spectrum underlying a given competitive isotherm. Although a different mathematical methodology is used, this procedure can be seen as the extension to multicomponent systems of the classical Sips’s work devoted to monocomponent systems. Furthermore, a methodology which yields analytical expressions for the main statistical properties (mean free energies of binding and covariance matrix) of multidimensional affinity spectra is reported. Thus, the level of binding correlation between the different components can be quantified. It has to be highlighted that the reported methodology does not require the knowledge of the affinity spectrum to calculate the means, variances, and covariance of the binding energies of the different components. Nonideal competitive consistent adsorption isotherm, widely used in metal/proton competitive complexation to environmental macromolecules, and Frumkin competitive isotherms are selected to illustrate the application of the reported results. Explicit analytical expressions for the affinity spectrum as well as for the matrix correlation are obtained for the NICCA case. © 2004 American Institute of Physics.

New insights into cellular prion protein (PrPc) functions: the 'ying and yang' of a relevant protein.

The conversion of cellular prion protein (PrPc), a GPI-anchored protein, into a protease-K-resistant and infective form (generally termed PrPsc) is mainly responsible for Transmissible Spongiform Encephalopathies (TSEs), characterized by neuronal degeneration and progressive loss of basic brain functions. Although PrPc is expressed by a wide range of tissues throughout the body, the complete repertoire of its functions has not been fully determined. Recent studies have confirmed its participation in basic physiological processes such as cell proliferation and the regulation of cellular homeostasis. Other studies indicate that PrPc interacts with several molecules to activate signaling cascades with a high number of cellular effects. To determine PrPc functions, transgenic mouse models have been generated in the last decade. In particular, mice lacking specific domains of the PrPc protein have revealed the contribution of these domains to neurodegenerative processes. A dual role of PrPc has been shown, since most authors report protective roles for this protein while others describe pro-apoptotic functions. In this review, we summarize new findings on PrPc functions, especially those related to neural degeneration and cell signaling.

N=1 SQCD-like theories with N_f massive flavors from AdS/CFT and beta functions

We study new supergravity solutions related to large-N c N=1 supersymmetric gauge field theories with a large number N f of massive flavors. We use a recently proposed framework based on configurations with N c color D5 branes and a distribution of N f flavor D5 branes, governed by a function N f S(r). Although the system admits many solutions, under plausible physical assumptions the relevant solution is uniquely determined for each value of x ≡ N f /N c . In the IR region, the solution smoothly approaches the deformed Maldacena-Núñez solution. In the UV region it approaches a linear dilaton solution. For x < 2 the gauge coupling β g function computed holographically is negative definite, in the UV approaching the NSVZ β function with anomalous dimension γ 0 = −1/2 (approaching − 3/(32π 2)(2N c  − N f )g 3)), and with β g  → −∞ in the IR. For x = 2, β g has a UV fixed point at strong coupling, suggesting the existence of an IR fixed point at a lower value of the coupling. We argue that the solutions with x > 2 describe a"Seiberg dual" picture where N f  − 2N c flips sign.

Why Mathematics is essential in Biomedical Sciences degree?

Improvement of mathematical education and motivation of students in the mathematics" area is needed. What can be done? We introduce some ideas to generate the student"s interest for mathematics, because they often present difficulties in appreciating the relevance of mathematics and its role in the health sciences. We consider that a cornerstone in the strategy to attract the students" interest is linking the mathematics with real biomedical situations. We proceed in the following manner: We first present a real biomedical situation to produce interest and to generate curiosity. Second, we ask thought-provoking questions to students as: Which is the biomedical problem presented? Which is my knowledge on this situation? What could I do to solve this biomedical situation? Do I need some new mathematical concepts and procedures? Thereupon, the teacher explains the mathematical concepts necessary to solve the case presented, providing definitions, properties and tools for graphical display and/or mathematical calculations. In this learning methodology, ICTs were cornerstones for reaching the proposed competences. Furthermore, ICTs can also be used in the evaluative task in its two possible aspects: formative and for obtaining a qualification. Comments from students about this new mathematics teaching method indicate that the use of real biomedical case studies kept the lessons in mathematics interesting.

A Database of >20 keV Electron Green's Functions of Interplanetary Transport at 1 AU

We use interplanetary transport simulations to compute a database of electron Green's functions, i.e., differential intensities resulting at the spacecraft position from an impulsive injection of energetic (>20 keV) electrons close to the Sun, for a large number of values of two standard interplanetary transport parameters: the scattering mean free path and the solar wind speed. The nominal energy channels of the ACE, STEREO, and Wind spacecraft have been used in the interplanetary transport simulations to conceive a unique tool for the study of near-relativistic electron events observed at 1 AU. In this paper, we quantify the characteristic times of the Green's functions (onset and peak time, rise and decay phase duration) as a function of the interplanetary transport conditions. We use the database to calculate the FWHM of the pitch-angle distributions at different times of the event and under different scattering conditions. This allows us to provide a first quantitative result that can be compared with observations, and to assess the validity of the frequently used term beam-like pitch-angle distribution.