statistics of stable marriages in the stable marriage problem n men and n women have to be matched by pairs under the constraint that the resulting matching is stable we study the statistical properties of stable matchings in the large n limit using both numerical and analytical methods generalizations of the model including singles and unequal numbers of men and women are also investigated

a model for distribution of high tax payers we propose a model to show the power law application to high income against the ranking this model is very simple and easy to analyze mathematically the simulation result of our model shows a good fit with the data for japan and us ceo we could also obtain the stationary solution for this model the power index of the stationary solution also coincides satisfactorily with the estimated results

clone size distributions in networks of genetic similarity we build networks of genetic similarity in which the nodes are organisms sampled from biological populations the procedure is illustrated by constructing networks from genetic data of a marine clonal plant an important feature in the networks is the presence of clone subgraphs i e sets of organisms with identical genotype forming clones as a first step to understand the dynamics that has shaped these networks we point up a relationship between a particular degree distribution and the clone size distribution in the populations we construct a dynamical model for the population dynamics focussing on the dynamics of the clones and solve it for the required distributions scale free and exponentially decaying forms are obtained depending on parameter values the first type being obtained when clonal growth is the dominant process average distributions are dominated by the power law behavior presented by the fastest replicating populations

universality of zipf s law zipf s law is the most common statistical distribution displaying scaling behavior cities populations or firms are just examples of this seemingly universal law although many different models have been proposed no general theoretical explanation has been shown to exist for its universality here we show that zipf s law is in fact an inevitable outcome of a very general class of stochastic systems borrowing concepts from algorithmic information theory our derivation is based on the properties of the symbolic sequence obtained through successive observations over a system with an ubounded number of possible states specifically we assume that the complexity of the description of the system provided by the sequence of observations is the one expected for a system evolving to a stable state between order and disorder this result is obtained from a small set of mild physically relevant assumptions the general nature of our derivation and its model free basis would explain the ubiquity of such a law in real systems

monotonic continuous time random walks with drift and stochastic reset events in this paper we consider a stochastic process that may experience random reset events which suddenly bring the system to the starting value and analyze the relevant statistical magnitudes we focus our attention on monotonic continuous time random walks with a constant drift the process increases between the reset events either by the effect of the random jumps or by the action of the deterministic drift as a result of all these combined factors interesting properties emerge like the existence for any drift strength of a stationary transition probability density function or the faculty of the model to reproduce power law like behavior general formulas for two extreme statistics the survival probability and the mean exit time are also derived to corroborate in an independent way the results of the paper monte carlo methods were used these numerical estimations are in full agreement with the analytical predictions

complex dynamics in the distribution of players scoring performance in rugby union world cups abstract the evolution of the scoring performance of rugby union players is investigated over the seven rugby world cups rwc that took place from 1987 to 2011 and a specific attention is given to how they may have been impacted by the switch from amateurism to professionalism that occurred in 1995 the distribution of the points scored by individual players p s ranked in order of performance were well described by the simplified canonical law p s r where r is the rank and and are the parameters of the distribution the parameter did not significantly change from 1987 to 2007 0 92 0 03 indicating a negligible effect of professionalism on players scoring performance in contrast the parameter significantly increased from 1 32 for 1987 rwc 2 30 for 1999 to 2003 rwc and 5 60 for 2007 rwc suggesting a progressive decrease in the relative performance of the best players finally the sharp decreases observed in both 0 38 and 0 70 in the 2011 rwc indicate a more even distribution of the performance of individuals among scorers compared to the more heterogeneous distributions observed from 1987 to 2007 and suggest a sharp increase in the level of competition leading to an increase in the average quality of players and a decrease in the relative skills of the top players note that neither nor significantly correlate with traditional performance indicators such as the number of points scored by the best players the number of games played by the best players the number of points scored by the team of the best players or the total number of points scored over each rwc this indicates that the dynamics of the scoring performance of rugby union players is influenced by hidden processes hitherto inaccessible through standard performance metrics this suggests that players scoring performance is connected to ubiquitous phenomena such as anomalous diffusion

boundary regularity and the dirichlet problem for harmonic maps in a previous paper 10 we developed an interior regularity theory for energy minimizing harmonic maps into riemannian manifolds in the first two sections of this paper we prove boundary regularity for energy minimizing maps with prescribed dirichlet boundary condition we show that such maps are regular in a full neighborhood of the boundary assuming appropriate regularity on the manifolds the boundary and the data the reader may refer to theorem 2 7 for a statement of the precise result it is not surprising that the boundary regularity is actually stronger than the partial regularity we obtained for the interior this is due to the fact that there are no nontrivial smooth harmonic maps from hemispheres s which map the boundary s 9s to a point i j n 2 and is analogous to the fact that in certain cases we were able to obtain complete regularity in the interior many authors have worked on boundary regularity for this general type of problem we mention hildebrandt and widman 5 and hamilton 4 as having obtained important results specifically for harmonic maps morrey had obtained the boundary regularity for domain dimension n 2 in conjunction with his investigation of the plateau problem in riemannian manifolds 8 in 3 of this paper we observe that the direct method gives solvability of the dirichlet problem under reasonable hypotheses on the manifolds we give as an application an amusing proof of a theorem of sacks and uhlenbeck 9 on the existence of minimal 2 spheres representing the second homotopy group of a manifold the same method gives smooth harmonic representations for k n for a certain class of manifolds n these are characterized by the nonexistence of lower dimensional harmonic spheres whose homogeneous extensions are minimal see proposition 3 4 in the last section of the paper we discuss approximation of l maps by smooth maps we give a simple example of an l map from the three dimensional ball to the two sphere which is not an l limit of continuous maps we

income dynamics with a stationary double pareto distribution once controlled for the trend the distribution of personal income appears to be double pareto a distribution that obeys the power law exactly in both the upper and the lower tails i propose a model of income dynamics with a stationary distribution that is consistent with this fact using us male wage data for 1970 1993 i estimate the power law exponent in two ways i from each cross section assuming that the distribution has converged to the stationary distribution and ii from a panel directly estimating the parameters of the income dynamics model and obtain the same value of 8 4

two results on the equivariant ginzburg landau vortex in arbitrary dimension we characterize the o n equivariant vortex solution for ginzburg landau type equations in the n dimensional euclidean space and we prove its local energy minimality for the corresponding energy functional

scale free networks from self organization we show how scale free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment this result holds for several variants of the walk algorithm and for a wide range of parameters the growth mechanism is based on using local graph information only so this is a process of self organisation the standard mean field equations are an excellent approximation for network growth using these rules we discuss the effects of finite size on the degree distribution and compare analytical results to simulated networks finally we generalise the random walk algorithm to produce weighted networks with power law distributions of both weight and degree

dynamics and bifurcations of nonsmooth systems a survey abstract in this survey we discuss current directions of research in the dynamics of nonsmooth systems with emphasis on bifurcation theory an introduction to the state of the art also for non specialists is complemented by a presentation of the main open problems we illustrate the theory by means of elementary examples the main focus is on piecewise smooth systems which have recently attracted a lot of attention but we also briefly discuss other important classes of nonsmooth systems such as nowhere differentiable ones and differential variational inequalities this extended framework allows us to put the diverse range of papers and surveys in this special issue in a common context a dedicated section is devoted to concrete applications that stimulate the development of the field this survey is concluded by an extensive bibliography

rotationally symmetric biharmonic maps between models abstract the main aim of this paper is to study existence and stability properties of rotationally symmetric proper biharmonic maps between two m dimensional models in the sense of greene and wu we obtain a complete classification of rotationally symmetric proper biharmonic conformal diffeomorphisms in the special case that m 4 and the models have constant sectional curvature then by introducing the hamiltonian associated to this problem we also obtain a complete description of conformal proper biharmonic solutions in the case that the domain model is r 4 in the second part of the paper we carry out a stability study with respect to equivariant variations equivariant stability in particular we prove that i the inverse of the stereographic projection from the open 4 dimensional euclidean ball to the hyperbolic space is equivariant stable ii the inverse of the stereographic projection from the closed 4 dimensional euclidean ball to the sphere is equivariant stable with respect to variations which preserve the boundary data

finiteness and fluctuations in growing networks we study the role of finiteness and fluctuations about average quantities for basic structural properties of growing networks we first determine the exact degree distribution of finite networks by generating function approaches the resulting distributions exhibit an unusual finite size scaling behaviour and they are also sensitive to the initial conditions we argue that fluctuations in the number of nodes of degree k become gaussian for fixed degree as the size of the network diverges we also characterize the fluctuations between different realizations of the network in terms of higher moments of the degree distribution

the stress energy tensor for biharmonic maps using hilbert s criterion we consider the stress energy tensor associated to the bienergy functional we show that it derives from a variational problem on metrics and exhibit the peculiarity of dimension four first we use this tensor to construct new examples of biharmonic maps then classify maps with vanishing or parallel stress energy tensor and riemannian immersions whose stress energy tensor is proportional to the metric thus obtaining a weaker but high dimensional version of the hopf theorem on compact constant mean curvature immersions we also relate the stress energy tensor of the inclusion of a submanifold in euclidean space with the harmonic stress energy tensor of its gauss map

proper r harmonic submanifolds into ellipsoids and rotation hypersurfaces abstract the study of r harmonic maps was proposed by eells sampson in 1965 and by eells lemaire in 1983 these maps are a natural generalization of harmonic maps and are defined as the critical points of the r energy functional e r 1 2 m d d r 2 d v m where m n denotes a smooth map between two riemannian manifolds if an r harmonic map m n is an isometric immersion and it is not minimal then we say that m is a proper r harmonic submanifold of n in this paper we prove the existence of several new proper r harmonic submanifolds into ellipsoids and rotation hypersurfaces

on the asymptotic behavior of rotationally symmetrical harmonic maps abstract we study a second order ordinary differential equation which is the euler lagrange equation of the energy functional for maps with prescribed rotational symmetry we obtain liouville s type theorems for symmetric harmonic maps into ellipsoids euclidean and hyperbolic spaces and existence results as well

the geometric triharmonic heat flow of immersed surfaces near spheres abstract we consider closed immersed surfaces in r 3 evolving by the geometric triharmonic heat flow using local energy estimates we prove interior estimates and a positive absolute lower bound on the lifespan of solutions depending solely on the local concentration of curvature of the initial immersion in l 2 we further use an e regularity type result to prove a gap lemma for stationary solutions using a monotonicity argument we then prove that a blowup of the flow approaching a singular time is asymptotic to a non umbilic embedded stationary surface this allows us to conclude that any solution with initial l 2 norm of the tracefree curvature tensor smaller than an absolute positive constant converges exponentially fast to a round sphere with radius equal to 3 v 0 4 3 where v 0 denotes the signed enclosed volume of the initial data

the marriage problem from the bar of appointments to the agency abstract we study the stable marriage problem from different points of view we proposed a microscopic dynamic that led the system to a stationary state that we are able to characterize analytically then we derive a thermodynamical description of the nash equilibrium states of the system that agree very well with the results of monte carlo simulations finally through large scale numerical simulations we compare the global optimum of the society with the stable marriage of lower energy we showed that both states are strongly correlated and that the selfish attitude results in a benefit for most of the practitioners belonging to blocking pairs in the global optimum of the society

q exponential fitting for distributions of family names abstract we study the applicability of the q exponential function for the distribution of family names we mainly focus on the rank size distribution of japanese family names the result supports the fact that the q exponential distribution is relevant to the distribution of family names that is understood until now to obey power law distribution zipf law

power law distributions in empirical data power law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man made phenomena unfortunately the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power law behavior holds commonly used methods for analyzing power law data such as least squares fitting can produce substantially inaccurate estimates of parameters for power law distributions and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all here we present a principled statistical framework for discerning and quantifying power law behavior in empirical data our approach combines maximum likelihood fitting methods with goodness of fit tests based on the kolmogorov smirnov ks statistic and likelihood ratios we evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches we also apply the proposed methods to twenty four real world data sets from a range of different disciplines each of which has been conjectured to follow a power law distribution in some cases we find these conjectures to be consistent with the data while in others the power law is ruled out

family name distributions master equation approach although cumulative family name distributions in many countries exhibit power law forms there also exist counterexamples the origin of different family name distributions across countries is discussed analytically in the framework of a population dynamics model combined with empirical observations made it is suggested that those differences in distributions are closely related to the rate of appearance of new family names

border collision bifurcations an explanation for observed bifurcation phenomena recently physical and computer experiments involving systems describable by continuous maps that are nondifferentiable on some surface in phase space have revealed novel bifurcation phenomena these phenomena are part of a rich new class of bifurcations which we call border collision bifurcations a general criterion for the occurrence of border collision bifurcations is given illustrative numerical results including transitions to chaotic attractors are presented these border collision bifurcations are found in a variety of physical experiments

surname complex network for brazil and portugal abstract we present a study of social networks based on the analysis of brazilian and portuguese family names surnames we construct networks whose nodes are names of families and whose edges represent parental relations between two families from these networks we extract the connectivity distribution clustering coefficient shortest path and centrality we find that the connectivity distribution follows an approximate power law we associate the number of hubs centrality and entropy to the degree of miscegenation in the societies in both countries our results show that portuguese society has a higher miscegenation degree than brazilian society all networks analyzed lead to approximate inverse square power laws in the degree distribution we conclude that the thermodynamic limit is reached for small networks 3 or 4 thousand nodes the assortative mixing of all networks is negative showing that the more connected vertices are connected to vertices with lower connectivity finally the network of surnames presents some small world characteristics

on the emergence of a power law in the distribution of covid 19 cases the first confirmed case of coronavirus disease 2019 covid 19 in the us was reported on january 21 2020 by the end of march 2020 there were more than 180 000 confirmed cases in the us distributed across more than 2000 counties we find that the right tail of this distribution exhibits a power law with pareto exponent close to one we investigate whether a simple model of the growth of covid 19 cases involving gibrat s law can explain the emergence of this power law the model is calibrated to match i the growth rates of confirmed cases and ii the varying lengths of time during which covid 19 had been present within each county thus calibrated the model generates a power law with pareto exponent nearly exactly equal to the exponent estimated directly from the distribution of confirmed cases across counties at the end of march

matching games with partial information abstract we analyze different ways of pairing agents in a bipartite matching problem with regard to its scaling properties and to the distribution of individual satisfactions then we explore the role of partial information and bounded rationality in a generalized marriage problem comparing the benefits obtained by self searching and by a matchmaker finally we propose a modified matching game intended to mimic the way consumers information makes firms to enhance the quality of their products in a competitive market

the marriage problem and the fate of bachelors abstract in the marriage problem a variant of the bi parted matching problem each member has a wish list expressing his her preference for all possible partners this list consists of random positive real numbers drawn from a certain distribution one searches the lowest cost for the society at the risk of breaking up pairs in the course of time minimization of a global cost function hamiltonian is performed with statistical mechanics techniques at a finite fictitious temperature the problem is generalized to include bachelors needed in particular when the groups have different size and polygamy exact solutions are found for the optimal solution t 0 the entropy is found to vanish quadratically in t also other evidence is found that the replica symmetric solution is exact implying at most a polynomial degeneracy of the optimal solution whether bachelors occur or not depends not only on their intrinsic qualities or lack thereof but also on global aspects of the chance for pair formation in society

chinese family name distributions in multiple scales abstract the distribution of chinese family names is investigated based on data of the fifth national census of china in 2000 including 7329 chinese family names and 1 28 billion people the cumulative distribution function cdf of family name in multiple scales is presented and the correlation between distribution and scale is discussed the fitting results show that cdfs at the scales of country province city and county all follow stretched exponential truncated power law while the fitting parameters vary greatly a characteristic index is proposed to measure the extent the distribution is stretched exponential like the index increases as the scale goes down indicating that the distribution at lower scale is more stretched exponential like and the distribution at higher scale is more power law like such correlation between distribution and scale is verified by investigating how the distribution changes as the scale is expanded county by county furthermore the correlation is qualitatively explained by artificially constructing multiple scales with a partition process

power law distribution of family names in japanese societies abstract we study the frequency distribution of family names from a common data base we count the number of people who share the same family name this is the size of the family we find that i the total number of different family names in a society scales as a power law of the population ii the total number of family names of the same size decreases as the size increases with a power law and iii the relation between size and rank of a family name also shows a power law these scaling properties are found to be consistent for five different regional communities in japan

the pareto positive stable distribution a new descriptive model for city size data abstract the pareto positive stable pps distribution is introduced as a new model for describing city size data in a country the pps distribution provides a flexible model for fitting the entire range of a set of city size data where zero and unimodality are possible and the classical pareto and zipf distributions are included as a particular case expressions for the shape moments and other descriptive probabilistic measures are given estimation methods are discussed and a simple graphical method for studying the adequacy of the data to model is given finally we consider city size data for spain for several different years the new distribution is compared with three classical models pareto lognormal and tsallis distributions in all the data sets considered the pps distribution outperforms the fits of these three previous distributions

application of tauberian theorem to the exponential decay of the tail probability of a random variable in this correspondence we give a sufficient condition for the exponential decay of the tail probability of a nonnegative random variable we consider the laplace stieltjes transform of the probability distribution function of the random variable we present a theorem according to which if the abscissa of convergence of the ls transform is negative finite and the real point on the axis of convergence is a pole of the ls transform then the tail probability decays exponentially for the proof of the theorem we extend and apply so called a finite form of ikehara s complex tauberian theorem by graham vaaler

discontinuity mappings for stochastic nonsmooth systems abstract for stability and bifurcation analysis involving recurrent behaviour such as periodic orbits it is important to be able to quantify how nearby trajectories behave by means of a local mapping in smooth systems these mappings can be computed using the system s variational equations for piecewise smooth or hybrid systems the same technique cannot be used without some corrections this is due to the fact that nearby trajectories can be topologically distinct because they can undergo different sequences of events associated with the system s discontinuity boundaries to account for this one can derive zero time discontinuity mappings associated with boundary interactions in this paper we derive zero time discontinuity mappings for piecewise smooth vector fields and hybrid dynamical systems in which the position of the discontinuity boundary has a stochastic component in particular we consider systems with stochastically oscillating boundaries and systems with stochastic imperfections on the discontinuity boundary

kinetic theory of random graphs from paths to cycles the structural properties of evolving random graphs are investigated treating linking as a dynamic aggregation process rate equations for the distribution of node to node distances paths and of cycles are formulated and solved analytically at the gelation point the typical length of paths and cycles l scales with the component size k as l approximately k 1 2 dynamic and finite size scaling laws for the behavior at and near the gelation point are obtained finite size scaling laws are verified using numerical simulations

vertical transmission of culture and the distribution of family names abstract a stochastic model for the evolution of a growing population is proposed in order to explain empirical power law distributions in the frequency of family names as a function of the family size preliminary results show that the predicted exponents are in good agreement with real data the evolution of family name distributions is discussed in the frame of vertical transmission of cultural features

statistical properties and network structure of the marriage problem abstract we study the statistical properties of the distribution of total energies or costs over the set of n configurations for the marriage problem with n men and n women analytical results and exhaustive numerical calculations for the whole configuration space are presented taking into account several definitions of the individual energies the distribution of the minimal energy is evaluated approximately moreover we point out a natural association between the configuration space of the marriage problem and a network we study the topological and metric properties of this network as well as the distribution of local energy minima on it

stochastic multiplicative processes with reset events we study a stochastic multiplicative process with reset events it is shown that the model develops a stationary power law probability distribution for the relevant variable whose exponent depends on the model parameters two qualitatively different regimes are observed corresponding to intermittent and regular behavior in the boundary between them the mean value of the relevant variable is time independent and the exponent of the stationary distribution equals ensuremath 2 the addition of diffusion to the system modifies in a nontrivial way the profile of the stationary distribution numerical and analytical results are presented

exact solution for the time evolution of network rewiring models we consider the rewiring of a bipartite graph using a mixture of random and preferential attachment the full mean field equations for the degree distribution and its generating function are given the exact solution of these equations for all finite parameter values at any time is found in terms of standard functions it is demonstrated that these solutions are an excellent fit to numerical simulations of the model we discuss the relationship between our model and several others in the literature including examples of urn backgammon and balls in boxes models the watts and strogatz rewiring problem and some models of zero range processes our model is also equivalent to those used in various applications including cultural transmission family name and gene frequencies glasses and wealth distributions finally some voter models and an example of a minority game also show features described by our model

the stress energy tensor for polyharmonic maps abstract we derive the stress energy tensor for polyharmonic maps between riemannian manifolds moreover we employ the stress energy tensor to characterize polyharmonic maps where we pay special attention to triharmonic maps

a growth model of community graph with a degree distribution consisting of two distinct parts abstract many complex systems can be represented as complex networks among them there has been much interest on community structure recently and many studies focus attention on it in particular community detection while community detection can provide us much information the community structure implies another feature hierarchy of the system coarse graining of complex networks can lead us to the definition of community graph the empirical degree distribution of community graph has a unique nature where it consists of two distinct parts exponential and power law distribution in this paper we propose a modified model of community graph pollner et al europhys lett 73 2006 478 that mimics the empirical features of it the growth mechanism of the model is a combination of preferential and non preferential attachment in a higher level we show that the model can reproduce the unique degree distribution by theoretical and numerical analysis while such features might stem from some other reasons we would expect to provide a unique aspect of community graph

on the biharmonic and harmonic indices of the hopf map biharmonic maps are the critical points of the bienergy functional and from this point of view generalize harmonic maps we consider the hopf map and modify it into a nonharmonic biharmonic map we show to be unstable and estimate its biharmonic index and nullity resolving the spectrum of the vertical laplacian associated to the hopf map we recover urakawa s determination of its harmonic index and nullity

exact analytical solutions of the susceptible infected recovered sir epidemic model and of the sir model with equal death and birth rates abstract in this paper the exact analytical solution of the susceptible infected recovered sir epidemic model is obtained in a parametric form by using the exact solution we investigate some explicit models corresponding to fixed values of the parameters and show that the numerical solution reproduces exactly the analytical solution we also show that the generalization of the sir model including births and deaths described by a nonlinear system of differential equations can be reduced to an abel type equation the reduction of the complex sir model with vital dynamics to an abel type equation can greatly simplify the analysis of its properties the general solution of the abel equation is obtained by using a perturbative approach in a power series form and it is shown that the general solution of the sir model with vital dynamics can be represented in an exact parametric form

noise and multistability in the square root map abstract in this paper we describe the complex structure of the basins of attraction of stable periodic orbits of the one dimensional square root map and how this produces sensitivity to the addition of small amplitude noise in particular we focus on how noise of varying amplitudes affects the system in parameter regions of attractor coexistence and also how trajectories jump between different periodic behaviours we show that there is a non monotonic relationship between the noise amplitude and the proportion of time spent in each periodic behaviour these relationships are explained by examining approximations of steady state distributions of trajectory deviations due to noise and the complicated deterministic structures of the map we also show how the effect of noise scales on consecutive intervals of multistability

new examples of r harmonic immersions into the sphere abstract polyharmonic or r harmonic maps are a natural generalization of harmonic maps whose study was proposed by eells lemaire in 1983 the main aim of this paper is to construct new examples of proper r harmonic immersions into spheres in particular we shall prove that the canonical inclusion i s n 1 r s n is a proper r harmonic submanifold of s n if and only if the radius r is equal to 1 r we shall also prove the existence of proper r harmonic generalized clifford s tori into the sphere

renormalization group evaluation of exponents in family name distributions abstract according to many phenomenological and theoretical studies the distribution of family name frequencies in a population can be asymptotically described by a power law we show that the galton watson process corresponding to the dynamics of a growing population can be represented in hilbert space and its time evolution may be analyzed by renormalization group techniques thus explaining the origin of the power law and establishing the connection between its exponent and the ratio between the population growth and the name production rates

bifurcations in nonsmooth dynamical systems a review is presented of the one parameter nonsmooth bifurcations that occur in a variety of continuous time piecewise smooth dynamical systems motivated by applications a pragmatic approach is taken to defining a discontinuity induced bifurcation dib as a nontrivial interaction of a limit set with respect to a codimension one discontinuity boundary in phase space only dibs that are local are considered that is bifurcations involving equilibria or a single point of boundary interaction along a limit cycle for flows three classes of systems are considered involving either state jumps jumps in the vector field or jumps in some derivative of the vector field a rich array of dynamics are revealed involving the sudden creation or disappearance of attractors jumps to chaos bifurcation diagrams with sharp corners and cascades of period adding for each kind of bifurcation identified where possible a kind of normal form or discontinuity mapping dm is given together with a canonical example and an application the goal is always to explain dynamics that may be observed in simulations of systems which include friction oscillators impact oscillators dc dc converters and problems in control theory

stability of axisymmetric chiral skyrmions abstract we examine topological solitons in a minimal variational model for a chiral magnet so called chiral skyrmions in the regime of large background fields we prove linear stability of axisymmetric chiral skyrmions under arbitrary perturbations in the energy space a long standing open question in physics literature moreover we show strict local minimality of axisymmetric chiral skyrmions and nearby existence of moving soliton solutions for the landau lifshitz gilbert equation driven by small spin transfer torques

self organized critical forest fire model a forest fire model is introduced which contains a lightning probability f this leads to a self organized critical state in the limit f ensuremath rightarrow 0 provided that the time scales of tree growth and burning down of forest clusters are separated we derive scaling laws and calculate all critical exponents the values of the critical exponents are confirmed by computer simulations for a two dimensional system we show that the forest density in the critical state assumes its minimum possible value i e that energy dissipation is maximum

on the distribution of family names abstract we present a model for the distribution of family names that explains the power law decay of the probability distribution for the number of people with a given family name the model includes a description of the process of generation or importation of new names and a description of the growth of the number of individuals with a name and corresponds for a long enduring culture to a galton watson branching process killed at a random time the exponent that characterizes the decay of the resulting distribution is determined by the characteristic rates for the creation of new names and for the growth of the population the power law decay is modulated by small amplitude log periodic oscillations this is rigorously established for a particular form of the offspring distribution in the branching process but arguments are presented to show that the phenomenon will occur under wide circumstances

higher order energy functionals abstract the study of higher order energy functionals was first proposed by eells and sampson in 1965 and later by eells and lemaire in 1983 these functionals provide a natural generalization of the classical energy functional more precisely eells and sampson suggested the investigation of the so called e s r energy functionals e r e s 1 2 m d d r 2 d v where m n is a map between two riemannian manifolds in the initial part of this paper we shall clarify some relevant issues about the definition of an e s r harmonic map i e a critical point of e r e s that seems important to us because in the literature other higher order energy functionals have been studied by several authors and consequently some recent examples need to be discussed and extended this shall be done in the first two sections of this work where we obtain the first examples of proper critical points of e r e s when n s m r 4 m 3 and we also prove some general facts which should be useful for future developments of this subject next we shall compute the euler lagrange system of equations for e r e s for r 4 we shall apply this result to the study of maps into space forms and to rotationally symmetric maps in particular we shall focus on the study of various family of conformal maps in section 4 we shall also show that even if 2 r dim m the functionals e r e s may not satisfy the classical palais smale condition c in the final part of the paper we shall study the second variation and compute index and nullity of some significant examples

controlling of chaotic motion by chaos and noise signals in a logistic map and a bonhoeffer van der pol oscillator the possibility of the conversion of a chaotic attractor to a strange but nonchaotic attractor is investigated numerically in both a discrete system the logistic map and in a continuous dynamical system the bonhoeffer van der pol oscillator a suppression of the chaotic property namely the sensitive dependence on initial states is found when an appropriate i chaotic signal and ii gaussian white noise are added a strange but nonchaotic attractor is shown to occur for some ranges of amplitude of the external perturbation the controlled orbit is characterized by the lyapunov exponent correlation dimension power spectrum and return map

the pareto law of incomes an explanation and an extension abstract a stochastic model for the generation of observed income distributions is used to provide an explanation for the pareto law of incomes analysis of the model also yields a prediction of paretian power law behaviour in the lower tail of the distribution and this is shown to occur in a number of empirical distributions a tractable four parameter distribution is derived and shown to fit extremely well to a number of different empirical income distributions

a note on equivariant biharmonic maps and stable biharmonic maps abstract in this note we generalize biharmonic equation for rotationally symmetric maps 4 20 12 to equivariant maps between model spaces and use it to give a complete classification of rotationally symmetric conformal biharmonic maps from a 4 dimensional space form into a 4 dimensional model space we also give an improved second variation formula for biharmonic maps into a space form and use it to prove that there exists no stable proper biharmonic map with constant square norm of tension field from a compact riemannian manifold without boundary into a space form of positive sectional curvature

from gene families and genera to incomes and internet file sizes why power laws are so common in nature we present a simple explanation for the occurrence of power law tails in statistical distributions by showing that if stochastic processes with exponential growth in expectation are killed or observed randomly the distribution of the killed or observed state exhibits power law behavior in one or both tails this simple mechanism can explain power law tails in the distributions of the sizes of incomes cities internet files biological taxa and in gene family and protein family frequencies

distribution of chinese names abstract we present a statistical model for the distribution of chinese names both family names and given names are studied on the same basis with naive expectation the distribution of family names can be very different from that of given names one is affected mostly by genealogy while the other can be dominated by cultural effects however we find that both distributions can be well described by the same model various scaling behaviors can be understood as a result of stochastic processes the exponents of different power law distributions are controlled by a single parameter we also comment on the significance of full name repetition in chinese population

stability and singularities of harmonic maps into 3 spheres the behavior of harmonic maps from a domain in r4 into s3 is discussed in this paper we show that if u is a strictly stable stationary harmonic map b4 s3 such that the singular set sing u of u consists of 0 then the degree deg u 0 of u at 0 is zero and that if u is a weakly stable harmonic map b4 s3 with sing u 0 then deg u 0 0 or 1 furthermore the characterization of homogeneous stable stationary harmonic maps from b4 into s3 is given

non periodic motion caused by grazing incidence in an impact oscillator the motion of a single degree of freedom periodically forced oscillator subjected to a rigid amplitude constraint is considered using analytical methods the singularities caused by grazing impact are studied it is shown that as a stable periodic orbit comes to grazing impact under the control of a single parameter a special type of bifurcation occurs the motion after the bifurcation may be non periodic and a criterion for this based on orientation and eigenvalues is given

directed random walk with random restarts the sisyphus random walk in this paper we consider a particular version of the random walk with restarts random reset events which suddenly bring the system to the starting value we analyze its relevant statistical properties like the transition probability and show how an equilibrium state appears formulas for the first passage time high water marks and other extreme statistics are also derived we consider counting problems naturally associated with the system finally we indicate feasible generalizations useful for interpreting different physical effects

universal limit mapping in grazing bifurcations grazing bifurcations are nonsmooth bifurcations that occur in impacting mechanical oscillators a sign of the lack of smoothness is a square root expression that arises in mappings describing the dynamics certain types of grazing bifurcations involve chaotic bands or period adding cascades with or without chaotic bands there is also a characteristic scaling behavior present here this type of bifurcation is investigated and the self similarity under scaling is used to derive a renormalized limit mapping a study of the dynamics of the limit mapping identifying all attractors for all parameter values is also presented

on the existence of smooth self similar blowup profiles for the wave map equation consider the equivariant wave map equation from minkowski space to a rotationally symmetric manifold n that has an equator e g the sphere in dimension 3 this paper presents a necessary and sufficient condition on n for the existence of a smooth self similar blowup profile more generally we study the relation between the minimizing properties of the equator map for the dirichlet energy corresponding to the elliptic harmonic map problem and the existence of a smooth blowup profile for the hyperbolic wave map problem this has several applications to questions of regularity and uniqueness for the wave map equation 2008 wiley periodicals inc

monotonicity formulas for extrinsic triharmonic maps and the triharmonic lane emden equation abstract we derive monotonicity formulas and e regularity results for extrinsic triharmonic maps and triharmonic lane emden equations as an application we prove partial regularity results for both types of equations in the supercritical regime

bifurcations caused by grazing incidence in many degrees of freedom impact oscillators the transition from stable periodic non impacting motion to impacting motion is analysed for a mechanical oscillator by using local methods it is shown that a grazing impact leads to an almost one dimensional stretching in state space a condition can then be formulated such that a grazing trajectory will be stable if the condition is fulfilled if this is the case the bifurcation will be continuous and the motion after the bifurcation can be understood by a one dimensional mapping this mapping is known to exhibit chaotic solutions as well as arbitrary long stable cycles depending on parameters

universal features in the growth dynamics of complex organizations we analyze the fluctuations in the gross domestic product gdp of 152 countries for the period 1950 1992 we find that i the distribution of annual growth rates for countries of a given gdp decays with fatter tails than for a gaussian and ii the width of the distribution scales as a power law of gdp with a scaling exponent b 0 15 both findings are in surprising agreement with results on firm growth these results are consistent with the hypothesis that the evolution of organizations with complex structure is governed by similar growth mechanisms s0031 9007 98 07339 6 pacs numbers 02 50 ey 01 75 m 05 40 j 05 45 b in the study of physical systems the analysis of the scaling properties of the fluctuations has been shown to give important information regarding the underlying processes responsible for the observed macroscopic behavior in contrast most studies on the time evolution of economic time series have concentrated on average growth rates 1 18 here we investigate the possibility that the study of fluctuations in economics may also lead to a better understanding of the mechanisms responsible for the observed dynamics 19 23 we therefore analyze the fluctuations in the growth rate of the gross domestic product gdp of 152 countries during the period 1950 1992 24 we will show that i the distribution of annual growth rates for countries of a given gdp is consistent for a certain range with an exponential decay and ii the width of the distribution scales as a power law of gdp with a scaling exponent b 0 15 both findings are in surprising agreement with

sex oriented stable matchings of the marriage problem with correlated and incomplete information in the stable marriage problem two sets of agents must be paired according to mutual preferences which may happen to conflict we present two generalizations of its sex oriented version aiming to take into account correlations between the preferences of agents and costly information their effects are investigated both numerically and analytically