Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

Two-dimensional relaxation-diffusion analysis to study water compartmentalization in cells by a single-sided NMR device

In questo lavoro di tesi è presentato un metodo per lo studio della compartimentalizzazione dell’acqua in cellule biologiche, mediante lo studio dell’autodiffusione delle molecole d’acqua tramite uno strumento NMR single-sided. Le misure sono state eseguite nel laboratorio NMR all’interno del DIFA di Bologna. Sono stati misurati i coefficienti di autodiffusione di tre campioni in condizione bulk, ottenendo risultati consistenti con la letteratura. È stato poi analizzato un sistema cellulare modello, Saccharomyces cerevisiae, allo stato solido, ottimizzando le procedure per l’ottenimento di mappe di correlazione 2D, aventi come assi il coefficiente di autodiffusione D e il tempo di rilassamento trasversale T2. In questo sistema l’acqua è confinata e l’autodiffusione è ristretta dalle pareti cellulari, si parla quindi di coefficiente di autodiffusione apparente, Dapp. Mediante le mappe sono state individuate due famiglie di nuclei 1H. Il campione è stato poi analizzato in diluizione in acqua distillata, confermando la separazione del segnale in due distinte famiglie. L’utilizzo di un composto chelato, il CuEDTA, ha permesso di affermare che la famiglia con il Dapp maggiore corrisponde all’acqua esterna alle cellule. L’analisi dei dati ottenuti sulle due famiglie al variare del tempo lasciato alle molecole d’acqua per la diffusione hanno portato alla stima del raggio dei due compartimenti: r=2.3±0.2µm per l’acqua extracellulare, r=0.9±0.1µm per quella intracellulare, che è probabilmente acqua scambiata tra gli organelli e il citoplasma. L’incertezza associata a tali stime tiene conto soltanto dell’errore nel calcolo dei parametri liberi del fit dei dati, è pertanto una sottostima, dovuta alle approssimazioni connesse all’utilizzo di equazioni valide per un sistema poroso costituito da pori sferici connessi non permeabili. Gli ordini di grandezza dei raggi calcolati sono invece consistenti con quelli osservabili dalle immagini ottenute con il microscopio ottico.

Numerical Solution of Fractional Diffusion-Wave Equation with two Space Variables by Matrix Method

Mathematics Subject Classi¯cation 2010: 26A33, 65D25, 65M06, 65Z05.

Both Sides of the Story: Skill-biased Technological Change, Labour Market Frictions, and Endogenous Two-Sided Heterogeneity

This paper presents a stylised framework to examine how skill-biased technological change and labour market frictions affect the relationship between economic expansion and unskilled unemployment. The first part of the analysis focuses on the investment decisions in skill-acquisition and technology adoption activities faced by workers and firms in response to the introduction of an innovative technology. The second part examines how endogenous two-sided heterogeneity in the labour market affects the macroeconomic outcomes in terms of unemployment, technological diffusion, and economic expansion. To conclude, the framework is used to discuss the effects of alternative forms of policy intervention on agents' investment decisions and on the macroeconomic outcomes.

One-sided and two-sided Green's functions

We discuss the one-sided Green's function, associated with an initial value problem and the two-sided Green's function related to a boundary value problem. We present a specific calculation associated with a differential equation with constant coefficients. For both problems, we also present the Laplace integral transform as another methodology to calculate these Green's functions and conclude which is the most convenient one. An incursion in the so-called fractional Green's function is also presented. As an example, we discuss the isotropic harmonic oscillator.

Alzheimer random walk model: Two previously overlooked diffusion regimes

A non-Markovian one-dimensional random walk model is studied with emphasis on the phase-diagram, showing all the diffusion regimes, along with the exactly determined critical lines. The model, known as the Alzheimer walk, is endowed with memory-controlled diffusion, responsible for the model's long-range correlations, and is characterized by a rich variety of diffusive regimes. The importance of this model is that superdiffusion arises due not to memory per se, but rather also due to loss of memory. The recently reported numerically and analytically estimated values for the Hurst exponent are hereby reviewed. We report the finding of two, previously overlooked, phases, namely, evanescent log-periodic diffusion and log-periodic diffusion with escape, both with Hurst exponent H = 1/2. In the former, the log-periodicity gets damped, whereas in the latter the first moment diverges. These phases further enrich the already intricate phase diagram. The results are discussed in the context of phase transitions, aging phenomena, and symmetry breaking.

Inverse Problem for Fractional Diffusion Equation

MSC 2010: 26A33, 33E12, 34K29, 34L15, 35K57, 35R30

The new economy: Essays in network economics and two-sided markets

Following the Introduction, which surveys existing literature on the technology advances and regulation in telecommunications and on two-sided markets, we address specific issues on the industries of the New Economy, featured by the existence of network effects. We seek to explore how each one of these industries work, identify potential market failures and find new solutions at the economic regulation level promoting social welfare. In Chapter 1 we analyze a regulatory issue on access prices and investments in the telecommunications market. The existing literature on access prices and investment has pointed out that networks underinvest under a regime of mandatory access provision with a fixed access price per end-user. We propose a new access pricing rule, the indexation approach, i.e., the access price, per end-user, that network i pays to network j is function of the investment levels set by both networks. We show that the indexation can enhance economic efficiency beyond what is achieved with a fixed access price. In particular, access price indexation can simultaneously induce lower retail prices and higher investment and social welfare as compared to a fixed access pricing or a regulatory holidays regime. Furthermore, we provide sufficient conditions under which the indexation can implement the socially optimal investment or the Ramsey solution, which would be impossible to obtain under fixed access pricing. Our results contradict the notion that investment efficiency must be sacrificed for gains in pricing efficiency. In Chapter 2 we investigate the effect of regulations that limit advertising airtime on advertising quality and on social welfare. We show, first, that advertising time regulation may reduce the average quality of advertising broadcast on TV networks. Second, an advertising cap may reduce media platforms and firms' profits, while the net effect on viewers (subscribers) welfare is ambiguous because the ad quality reduction resulting from a regulatory cap o¤sets the subscribers direct gain from watching fewer ads. We find that if subscribers are sufficiently sensitive to ad quality, i.e., the ad quality reduction outweighs the direct effect of the cap, a cap may reduce social welfare. The welfare results suggest that a regulatory authority that is trying to increase welfare via regulation of the volume of advertising on TV might necessitate to also regulate advertising quality or, if regulating quality proves impractical, take the effect of advertising quality into consideration. 3 In Chapter 3 we investigate the rules that govern Electronic Payment Networks (EPNs). In EPNs the No-Surcharge Rule (NSR) requires that merchants charge at most the same amount for a payment card transaction as for cash. In this chapter, we analyze a three- party model (consumers, merchants, and a proprietary EPN) with endogenous transaction volumes and heterogenous merchants' transactional benefits of accepting cards to assess the welfare impacts of the NSR. We show that, if merchants are local monopolists and the network externalities from merchants to cardholders are sufficiently strong, with the exception of the EPN, all agents will be worse o¤ with the NSR, and therefore the NSR is socially undesirable. The positive role of the NSR in terms of improvement of retail price efficiency for cardholders is also highlighted.

Moduli of smoothness and growth properties of Fourier transforms: two-sided estimates

We prove two-sided inequalities between the integral moduli of smoothness of a function on R d[superscript] / T d[superscript] and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is given by the equivalence results for functions satisfying certain regular conditions. Applications include a quantitative form of the Riemann-Lebesgue lemma as well as several other questions in approximation theory and the theory of function spaces.

Two-sided learning in new keynesian models: dynamics, (lack of) convergence and the value of information

This paper investigates the role of learning by private agents and the central bank (two-sided learning) in a New Keynesian framework in which both sides of the economy have asymmetric and imperfect knowledge about the true data generating process. We assume that all agents employ the data that they observe (which may be distinct for different sets of agents) to form beliefs about unknown aspects of the true model of the economy, use their beliefs to decide on actions, and revise these beliefs through a statistical learning algorithm as new information becomes available. We study the short-run dynamics of our model and derive its policy recommendations, particularly with respect to central bank communications. We demonstrate that two-sided learning can generate substantial increases in volatility and persistence, and alter the behavior of the variables in the model in a signifficant way. Our simulations do not converge to a symmetric rational expectations equilibrium and we highlight one source that invalidates the convergence results of Marcet and Sargent (1989). Finally, we identify a novel aspect of central bank communication in models of learning: communication can be harmful if the central bank's model is substantially mis-specified

Two-sided learning in New Keynesian models: Dynamics, (lack of) convergence and the value of information

This paper investigates the role of learning by private agents and the central bank(two-sided learning) in a New Keynesian framework in which both sides of the economyhave asymmetric and imperfect knowledge about the true data generating process. Weassume that all agents employ the data that they observe (which may be distinct fordifferent sets of agents) to form beliefs about unknown aspects of the true model ofthe economy, use their beliefs to decide on actions, and revise these beliefs througha statistical learning algorithm as new information becomes available. We study theshort-run dynamics of our model and derive its policy recommendations, particularlywith respect to central bank communications. We demonstrate that two-sided learningcan generate substantial increases in volatility and persistence, and alter the behaviorof the variables in the model in a significant way. Our simulations do not convergeto a symmetric rational expectations equilibrium and we highlight one source thatinvalidates the convergence results of Marcet and Sargent (1989). Finally, we identifya novel aspect of central bank communication in models of learning: communicationcan be harmful if the central bank's model is substantially mis-specified.

The pricing of academic journals: A two-sided market perspective

More and more academic journals adopt an open-access policy, by which articlesare accessible free of charge, while publication costs are recovered through authorfees. We study the consequences of this open access policy on a journal s qualitystandard. If the journal s objective was to maximize social welfare, open accesswould be optimal as long as the positive externalities generated by its diffusionexceed the marginal cost of distribution. However, we show that if an open accessjournal has a different objective (such as maximizing readers payoffs, the impactof the journal or its profit), it tends to choose a quality standard below the sociallyefficient level.

Threading dislocation lines in two-sided flux-array decorations

Two-sided flux decoration experiments indicate that threading dislocation lines (TDLs), which cross the entire film, are sometimes trapped in metastable states. We calculate the elastic energy associated with the meanderings of a TDL. The TDL behaves as an anisotropic and dispersive string with thermal fluctuations largely along its Burgers vector. These fluctuations also modify the structure factor of the vortex solid. Both effects can, in principle, be used to estimate the elastic moduli of the material.

The role of network externalities in value creating process of the commercial web service for two-sided international markets

Network externalities and two-sided markets in the context of web services and value creation is not very well discussed topic in academic literature. The explosive rise of the Internet users has created a strong base for many successful web services and pushed many firms towards e-business and online service based business models. Thus the subject of this thesis, the role of network externalities in value creating process of the commer-cial web service for two-sided international markets is very current and interesting topic to examine. The objective of this Master’s Thesis is to advance the study of network externalities from the viewpoint of two-sided markets and network effects as well as describe the value creation & value co-creation process in commercial web service business models. The main proposition suggests that the larger network of customers and the bigger number of users the web service is able to attract, the more value and stronger positive net-work externalities the service is able to create for each customer group. The empirical research of this study was implemented for commercial web service, targeted to Russian consumers and Finnish business users. The findings suggest that the size of the network is highly related to the experi-enced value of the customers and the whole value creation process of commercial web targeted for two-sided international markets varies from the value creation for one-sided or pure domestic markets.