scaling in income inequalities and its dynamical origin abstract we provide an analytically treatable model that describes in a unified manner income distribution for all income categories the approach is based on a master equation with growth and reset terms the model assumptions on the growth and reset rates are tested on an exhaustive database with incomes on individual level spanning a nine year period in the cluj county romania in agreement with our theoretical predictions we find that income distributions computed for several years collapse on a master curve when a properly normalised income is considered the beta prime distribution is appropriate to fit the collapsed data and it is shown that distributions derived for other countries are following similar trends with different fit parameters the non universal feature of the fit parameters suggests that for a more realistic modelling the model parameters have to be linked with specific socio economic regulations

asymptotic behavior of densities of unimodal convolution semigroups we prove the asymptotic formulas for the transition densities of isotropic unimodal convolution semigroups of probability measures on r d under the assumption that its levy khintchine exponent is regularly varying of index between 0 and 2

growth and fluctuations of personal income pareto s law states that the distribution of personal income obeys a power law in high income range many researchers have proposed models over a century since its discovery but the dynamical understanding of hie phenomenon necessitates empirical study on growth of individual income here we uncovered several properties in the fluctuations of individual income growth derived from income tax data including all taxpayers more than 80 000 with high income iii japan for two consecutive years 1997 and 1998 in a relatively stable period of economics in this work 8 we show i that the dynamics has approximate time reversal symmetry in the period ii that the distribution of growth rate is independent of income tax in the past yearm and iii that the pareto s law breaks down in bubble collapse of japanese economy in 1990 it is shown in 3 how these phenomenological facts are consistent with pareto law these findings provide first direct observation of dynamical process of ruuirey flow in an economic network and its relation to risky assets price fluctuations of lands and stocks

asymptotic behaviour of densities of stable semigroups of measures we prove that densities of the measures in a strictly stable semigroup ht of symmetric measures on a homogeneous group if they exist have the following asymptotic behaviour mathop lim limits x to infty x q alpha cdot h 1 x k bar x where is the characteristic exponent bar x x 1 x andk is the density of the levy measure associated to the semigroup moreover if k bar x 0 a more precise description is given

fractional square functions and potential spaces abstract carlos segovia and richard wheeden defined fractional square functions involving fractional derivatives they obtained characterizations of potential spaces via square functions our aim in this paper is to reconsider the ideas of segovia and wheeden under the light of the semigroups of operators we develop a quite general theory of fractional square functions associated to certain classes of operators we present some examples of differential operators where our theory applies we recover in a more compact way the results of segovia and wheeden and we obtain new characterizations of the potential spaces associated to the harmonic oscillator and ornstein uhlenbeck operators

sobolev spaces related to schrodinger operators with polynomial potentials the aim of this note is to prove the following theorem let af x p d f x v x f x where p ix is a nonnegative homogeneous elliptic polynomial on r d and v is a nonnegative polynomial potential then for every 1 0 there exist constants c 1 c 2 0 such that p d alpha f l p v alpha f l p le c 1 a alpha f l p and a alpha f l p le c 2 left p d alpha v alpha right f l p for f in the schwartz class mathcal s bf r d we take advantage of the christ inversion theorem for singular integral operators with a small amount of smoothness on nilpotent lie groups the maximal subelliptic l 2 estimates for the generators of stable semi groups of measures and the principle of transference of coifman weiss

two dimensional iir filter design with magnitude and phase error criteria two dimensional iir filters are designed using an error criterion consisting of the weighted sum of magnitude phase and stability errors thereby extending the spectral factorization based method to complex approximation the weights are adjusted to effectively constrain stability while minimizing a weighted sum of frequency domain magnitude and phase errors we use a derivative free variant of the marquardt optimization algorithm augmented by a one dimensional search we present examples of approximation of both linear and nonlinear phase ideal transfer functions and conduct comparisons across a range of numerator and denominator orders from fir to all pole while keeping the total number of coefficients approximately constant we find that the designed iir filters offer better magnitude response in the case of linear phase ideal functions even considering coefficient reflection symmetry but of course the fir filter has the better zero phase error when the ideal transfer function has nonlinear phase and hence no coefficient reflection symmetry we find that the designed iir filter can perform better than the fir filter with regard to both magnitude and phase error when magnitude error is weighted more heavily than phase error

riesz transforms related to schrodinger operators acting on bmo type spaces abstract in this work we obtain boundedness on suitable weighted bmo type spaces of riesz transforms and their adjoints associated to the schrodinger operator v where v satisfies a reverse holder inequality our results are new even in the unweighted case

do wealth distributions follow power laws evidence from rich lists abstract we use data on the wealth of the richest persons taken from the rich lists provided by business magazines like forbes to verify if the upper tails of wealth distributions follow as often claimed a power law behaviour the data sets used cover the world s richest persons over 1996 2012 the richest americans over 1988 2012 the richest chinese over 2006 2012 and the richest russians over 2004 2011 using a recently introduced comprehensive empirical methodology for detecting power laws which allows for testing the goodness of fit as well as for comparing the power law model with rival distributions we find that a power law model is consistent with data only in 35 of the analysed data sets moreover even if wealth data are consistent with the power law model they are usually also consistent with some rivals like the log normal or stretched exponential distributions

on the maximal bochner riesz conjecture in the plane for p 2 we give a new estimate on the maximal bochner riesz operator in the plane for p 2 as a corollary we obtain an almost everywhere convergence result for certain bochner riesz means this work was inspired by discussions with michael christ and chris sogge

an efficient approach for the synthesis of 2 d recursive fan filters using 1 d prototypes an elliptic approximation based design approach is proposed for obtaining 2 d recursive fan filters the 1 d elliptic filter is reduced to a cascade parallel combination of all pass sections and is then used as a prototype for fan filter synthesis resulting in final realization of 2 d transfer functions using allpass filters it is shown that the synthesis procedure not only gives a filter that has far fewer coefficients but also enjoys a very low computational complexity

class formation in a social network with asset exchange abstract we study two kinds of economic exchanges additive and multiplicative in a system of n agents the work is divided into two parts in the first one the agents are free to interact with each other the system evolves to a boltzmann gibbs distribution with additive exchange and condenses with a multiplicative one if bankruptcy is introduced both types of exchange lead to condensation condensation times have been studied in the second part the agents are placed in a social network we analyze the behavior of wealth distributions in time and the formation of economic classes is observed for certain values of network connectivity

two weight norm inequalities for the cesaro means of hermite expansions an accurate estimate is obtained of the cesaro kernel for hermite expansions this is used to prove two weight norm inequalities for cesaro means of hermite polynomial series and for the supremum of these means these extend known norm inequalities even in the single power weight and unweighted cases an almost everywhere convergence result is obtained as a corollary it is also shown that the conditions used to prove norm boundedness of the means and most of the conditions used to prove the boundedness of the cesaro supremum of the means are necessary

wealth dynamics on complex networks abstract we study a model of wealth dynamics physica a 282 2000 536 which mimics transactions among economic agents the outcomes of the model are shown to depend strongly on the topological properties of the underlying transaction network the extreme cases of a fully connected and a fully disconnected network yield power law and log normal forms of the wealth distribution respectively we perform numerical simulations in order to test the model on more complex network topologies we show that the mixed form of most empirical distributions displaying a non smooth transition from a log normal to a power law form can be traced back to a heterogeneous topology with varying link density which on the other hand is a recently observed property of real networks

conical square functions associated with bessel laguerre and schrodinger operators in umd banach spaces abstract in this paper we consider conical square functions in the bessel laguerre and schrodinger settings where the functions take values in umd banach spaces following a recent paper of hytonen van neerven and portal 36 in order to define our conical square functions we use radonifying operators we obtain new equivalent norms in the lebesgue bochner spaces l p 0 b and l p r n b 1 p in terms of our square functions provided that b is a umd banach space our results can be seen as banach valued versions of known scalar results for square functions

algebraic approach to two dimensional recursive digital filter synthesis an effective algorithm is developed for synthesizing two dimensional recursive digital filters which approximate prescribed ideal frequency response specifications the algorithm is based on an algebraic approach that uses the eigenvalue eigenvector decomposition of the ideal filter s excitation response matrix in conjunction with a recently developed signal enhancement method this results in a recursive filter which has a unit impulse that closely approximates the ideal filter s unit impulse response illustrative examples and comparisons to an existing technique are included

on the regularity of inverses of singular integral operators sur r d on considere un operateur de convolution sf f k ou k est une distribution homogene de degre d on suppose que s s etend a un operateur borne et inversible sur l 2 r d l inverse de s est donne par convolution avec une distribution l aussi homogene de degre d on montre qu une regularite possedee par k est partagee par l

self organization of collaboration networks we study collaboration networks in terms of evolving self organizing bipartite graph models we propose a model of a growing network which combines preferential edge attachment with the bipartite structure generic for collaboration networks the model depends exclusively on basic properties of the network such as the total number of collaborators and acts of collaboration the mean size of collaborations etc the simplest model defined within this framework already allows us to describe many of the main topological characteristics degree distribution clustering coefficient etc of one mode projections of several real collaboration networks without parameter fitting we explain the observed dependence of the local clustering on degree and the degree degree correlations in terms of the aging of collaborators and their physical impossibility to participate in an unlimited number of collaborations

generic emergence of power law distributions and levy stable intermittent fluctuations in discrete logistic systems the dynamics of generic stochastic lotka volterra discrete logistic systems of the form w i t 1 ensuremath lambda t w i t a overline w t ensuremath mathrm bw i t overline w t is studied by computer simulations the variables w i i 1 dots n are the individual system components and overline w t 1 n ensuremath sum i w i t is their average the parameters a and b are constants while ensuremath lambda t is randomly chosen at each time step from a given distribution models of this type describe the temporal evolution of a large variety of systems such as stock markets and city populations these systems are characterized by a large number of interacting objects and the dynamics is dominated by multiplicative processes the instantaneous probability distribution p w t of the system components w i turns out to fulfill a pareto power law p w t ensuremath sim w ensuremath 1 ensuremath ensuremath alpha the time evolution of overline w t presents intermittent fluctuations parametrized by a l evy stable distribution with the same index ensuremath alpha showing an intricate relation between the distribution of the w i mathrm s at a given time and the temporal fluctuations of their average

riesz transforms for multi dimensional laguerre function expansions abstract riesz transforms and conjugate poisson integrals for multi dimensional laguerre function expansions of type are defined and investigated it is proved that for any multi index 1 d such that i 1 2 the appropriately defined riesz laguerre transforms r j j 1 2 d are calderon zygmund operators in the sense of the associated space of homogeneous type hence their mapping properties follow from the general theory similar results are obtained for all higher order riesz laguerre transforms the conjugate poisson integrals are shown to satisfy a system of equations of cauchy riemann type and to recover the riesz laguerre transforms on the boundary

degree and wealth distribution in a network induced by wealth abstract a network induced by wealth is a social network model in which wealth induces individuals to participate as nodes and every node in the network produces and accumulates wealth utilizing its links more specifically at every time step a new node is added to the network and a link is created between one of the existing nodes and the new node innate wealth producing ability is randomly assigned to every new node and the node to be connected to the new node is chosen randomly with odds proportional to the accumulated wealth of each existing node analyzing this network using the mean value and continuous flow approaches we derive a relation between the conditional expectations of the degree and the accumulated wealth of each node from this relation we show that the degree distribution of the network induced by wealth is scale free we also show that the wealth distribution has a power law tail and satisfies the 80 20 rule we also show that over the whole range the cumulative wealth distribution exhibits the same topological characteristics as the wealth distributions of several networks based on the bouchaud mezard model even though the mechanism for producing wealth is quite different in our model further we show that the cumulative wealth distribution for the poor and middle class seems likely to follow by a log normal distribution while for the richest the cumulative wealth distribution has a power law behavior

a family network model for wealth distribution in societies a model based on first degree family relations network is used to describe the wealth distribution in societies the network structure is not a priori introduced in the model it is generated in parallel with the wealth values through simple and realistic dynamical rules the model has two main parameters governing the wealth exchange in the network choosing their values realistically leads to wealth distributions in good agreement with measured data the cumulative wealth distribution function has an exponential behavior in the low and medium wealth limit and shows the pareto like power law tail for the upper 5 of the society the obtained pareto indexes are in good agreement with the measured ones the generated family networks also converge to a statistically stable topology with a simple poissonian degree distribution on this family network many interesting correlations are studied and the main factors leading to wealth diversification and the formation of the pareto law are identified

wealth condensation in a simple model of economy abstract we introduce a simple model of economy where the time evolution is described by an equation capturing both exchange between individuals and random speculative trading in such a way that the fundamental symmetry of the economy under an arbitrary change of monetary units is insured we investigate a mean field limit of this equation and show that the distribution of wealth is of the pareto power law type the pareto behaviour of the tails of this distribution appears to be robust for finite range models as shown using both a mapping to the random directed polymer problem as well as numerical simulations in this context a phase transition between an economy dominated by a few individuals and a situation where the wealth is more evenly spread out is found an interesting outcome is that the distribution of wealth tends to be very broadly distributed when exchanges are limited either in amplitude or topologically favouring exchanges and less surprisingly increasing taxes seems to be an efficient way to reduce inequalities

transference between laguerre and hermite settings in this paper we present a new method in order to transfer boundedness results for operators associated with hermite functions to boundedness results for operators associated with laguerre functions the technique relies on an exact point wise identity relating the heat kernels of both systems the method that we present here has the novelty that can be used backwards that is boundedness results for laguerre systems can be also transfered to boundedness results for hermite systems we apply our method in order to get new properties of some operators in the laguerre setting among others we mention the description of riesz transforms as principal value operators as an application of the reversibility of the method we characterize the class of banach spaces b for which the riesz transforms in the laguerre setting are bounded from lbp into itself it is shown that this class coincides with the umd class

why social networks are different from other types of networks we argue that social networks differ from most other types of networks including technological and biological networks in two important ways first they have nontrivial clustering or network transitivity and second they show positive correlations also called assortative mixing between the degrees of adjacent vertices social networks are often divided into groups or communities and it has recently been suggested that this division could account for the observed clustering we demonstrate that group structure in networks can also account for degree correlations we show using a simple model that we should expect assortative mixing in such networks whenever there is variation in the sizes of the groups and that the predicted level of assortative mixing compares well with that observed in real world networks