markov chains of nonlinear markov processes and an application to a winner takes all model for social conformity we discuss nonlinear markov processes defined on discrete time points and discrete state spaces using markov chains in this context special attention is paid to the distinction between linear and nonlinear markov processes we illustrate that the chapman kolmogorov equation holds for nonlinear markov processes by a winner takes all model for social conformity

the inequality process as a wealth maximizing process abstract the one parameter inequality process opip long predates the saved wealth model swm to which it is isomorphic up to the different choice of stochastic driver of wealth exchange both are stochastic interacting particle systems intended to model wealth and income distribution the opip and other versions of the inequality process explain many aspects of wealth and income distribution but have gone undiscussed in econophysics the opip is a jump process with a discrete 0 1 uniform random variate driving the exchange of wealth between two particles while the swm as an extension of the stochastic version of the ideal gas model is driven by a continuous uniform random variate with support at 0 0 1 0 the opip s stationary distribution is a levy stable distribution attracted to the pareto pdf near the hot upper bound of the opip s parameter and attracted to the normal gaussian pdf toward the cool lower bound of a gamma pdf model approximating the opip s stationary distribution is heuristically derived from the solution of the opip the approximation works for 5 better as 0 the gamma pdf model has parameters in terms of the inequality process with distributed omega ipdo is a generalization of the opip in the ipdo each particle can have a unique value of its parameter i e particle i has i the meta model of the inequality process implies that smaller is associated with higher skill level among workers this hypothesis is confirmed in a test of the ipdo particle wealth gain or loss in the opip and ipdo is more clearly asymmetric than in the swm 0 time reversal asymmetry follows from asymmetry of gain and loss while the ipdo scatters wealth it also transfers wealth from particles with larger to those with smaller particles that according to the ipdo s meta model are more productive of wealth nourishing wealth production the smaller the harmonic mean of the i s in the ipdo population of particles the more wealth is concentrated in particles with smaller the less noise and the more signal there is in particle wealth and the deeper the time horizon of the process the ipdo wealth concentration mechanism is simpler than maxwell s demon

nonconvexity of the relative entropy for markov dynamics a fisher information approach we show via counterexamples that relative entropy between the solution of a markovian master equation and the steady state is not a convex function of time we thus disprove the hypotheses that a general evolution principle of thermodynamics based on the decrease of the nonadiabatic entropy production could hold however we argue that a large separation of typical decay times is necessary for nonconvex solutions to occur making concave transients extremely short lived with respect to the main relaxation modes we describe a general method based on the fisher information matrix to discriminate between generators that admit nonconvex solutions and those that do not while initial conditions leading to concave transients are shown to be extremely fine tuned by our method we are able to select nonconvex initial conditions that are arbitrarily close to the steady state convexity does occur when the system is close to satisfying detailed balance or more generally when certain normality conditions of the decay modes are satisfied our results circumscribe the range of validity of a conjecture by maes et al phys rev lett 107 010601 2011 regarding monotonicity of the large deviation rate functional for the occupation probability showing that while the conjecture might hold in the long time limit the conditions for lyapunov s second criterion for stability are not met

clausius inequality and h theorems for some models of random wealth exchange a b s t r a c t we discuss a possibility of deriving an h theorem for nonlinear discrete time evolution equation that describes random wealth exchanges in such kinetic models economical agents exchange wealth in pairwise collisions just as particles in a gas exchange their energy it appears useful to reformulate the problem and represent the dynamics as a combination of two processes the first is a linear transformation of a two particle distribution function during the act of exchange while the second one corresponds to new random pairing of agents and plays a role of some kind of feedback control this representation leads to a clausius type inequality which suggests a new interpretation of the exchange process as an irreversible relaxation due to a contact with a reservoir of a special type only in some special cases when equilibrium distribution is exactly a gamma distribution this inequality results in the h theorem with monotonically growing entropy functional which differs from the boltzmann entropy by an additional term but for arbitrary exchange rule the evolution has some features of relaxation to a non equilibrium steady state and it is still unclear if any general h theorem could exist

extremes of a class of nonhomogeneous gaussian random fields this contribution establishes exact tail asymptotics of sup s t e x s t for a large class of nonhomogeneous gaussian random fields x on a bounded convex set e r2 with variance function that attains its maximum on a segment on e these findings extend the classical results for homogeneous gaussian random fields and gaussian random fields with unique maximum point of the variance applications of our result include the derivation of the exact tail asymptotics of the shepp statistics for stationary gaussian processes brownian bridge and fractional brownian motion as well as the exact tail asymptotic expansion for the maximum loss and span of stationary gaussian processes

automorphism invariant modules satisfy the exchange property abstract warfield proved that every injective module has the exchange property this was generalized by fuchs who showed that quasi injective modules satisfy the exchange property we extend this further and prove that a module invariant under automorphisms of its injective hull satisfies the exchange property we also show that automorphism invariant modules are clean and that directly finite automorphism invariant modules satisfy the internal cancellation and hence the cancellation property

statistical model with a standard γ distribution we study a statistical model consisting of n basic units which interact with each other by exchanging a physical entity according to a given microscopic random law depending on a parameter ensuremath lambda we focus on the equilibrium or stationary distribution of the entity exchanged and verify through numerical fitting of the simulation data that the final form of the equilibrium distribution is that of a standard gamma distribution the model can be interpreted as a simple closed economy in which economic agents trade money and a saving criterion is fixed by the saving propensity ensuremath lambda alternatively from the nature of the equilibrium distribution we show that the model can also be interpreted as a perfect gas at an effective temperature t ensuremath lambda where particles exchange energy in a space with an effective dimension d ensuremath lambda

rings with internal cancellation in this paper we study the class of rings that satisfy internal direct sum cancellation with respect to their 1 sided ideals these are known to be precisely the rings in which regular elements are unitregular further characterizations for such ic rings are given in terms of suitable versions of stable range conditions and unique generator properties of idempotent generated right ideals this approach leads to a uniform treatment of many of the known characterizations for an exchange ring to have stable range 1 rings whose matrix rings are ic turn out to be precisely those rings whose finitely generated projective modules satisfy cancellation we also offer a couple of hidden characterizations of unit regular elements in rings that shed some new light on the relation between similarity and pseudo similarity in monoids as well as in rings the paper concludes with a treatment of ideals for which idempotents lift modulo all 1 sided subideals an appendix by r g swan 1 on the failure of cancellation for finitely generated projective modules over complex group algebras shows that such algebras are in general not ic

exponential wealth distribution in a random market a rigorous explanation abstract in simulations of some economic gas like models the asymptotic regime shows an exponential wealth distribution independently of the initial wealth distribution given to the system the appearance of this statistical equilibrium for this type of gas like models is explained in a rigorous analytical way

extreme values and high boundary crossings of locally stationary gaussian processes we consider the large values of a locally stationary gaussian process which satisfies berman s condition on the long range dependence we present some limit results on the exceedances of the process above a certain general smooth high boundary this allows deriving the limiting distribution of the maximum up to time t for example in the case of a standardized process with a constant boundary or in the case of a nonstandardized process with a smooth trend

inner inverses and inner annihilators in rings abstract for any ring element r we study the group of inner annihilators iann p r p 0 and the set i of inner inverses of for any jacobson pair 1 a b and 1 b a the groups a iann and b iann are shown to be equipotent and a c is shown to be group isomorphic to b c where c ann l ann r in the case where is von neumann regular we show further that a b as groups for any jacobson pair a new jacobson map i i is constructed that is a semigroup homomorphism with respect to the von neumann product and preserves units reflexive inverses and commuting inner inverses in particular for any abelian ring r is a semigroup isomorphism between i and i as a byproduct of our methods we also show that a ring r satisfies internal cancellation iff every jacobson pair of regular elements are equivalent over r in particular the latter property holds for many rings including semilocal rings unit regular rings strongly regular rings and finite von neumann algebras

pseudosimilarity and cancellation of modules abstract two square matrices a and b over a ring are pseudosimilar if there exist x y and z satisfying xay b zbx a and xyx xzx x hartwig and hall showed this is equivalent to similarity over a field this result is extended to rings where free modules satisfy a cancellation property these include rings r with r rad r artinian or more generally rings with one in the stable range and polynomial rings over dedekind domains furthermore it is shown for commutative rings that if a and b are pseudosimilar then diag a o m and diag b o m are similar for some m

consistent estimates of deformed isotropic gaussian random fields on the plane this paper proves fixed domain asymptotic results for estimating a smooth invertible transformation f r 2 r 2 when observing the deformed random field z o f on a dense grid in a bounded simply connected domain where z is assumed to be an isotropic gaussian random field on r 2 is constructed on a simply connected domain u such that and is defined using kernel smoothed quadratic variations bergman projections and results from quasiconformal theory we show under mild assumptions on the random field z and the deformation f that r f c uniformly on compact subsets of u with probability one as the grid spacing goes to zero where r is an unidentifiable rotation and c is an unidentifiable translation

the moore penrose inverse of von neumann regular matrices over a ring abstract necessary and sufficient conditions are given in order that a von neumann regular matrix a over an arbitrary ring and also the matrices arising in certain factorizations of a be moore penrose invertible

extremes of locally stationary gaussian random fields the main result of this contribution is the derivation of the exact asymptotic behavior of the supremum of a class of a t locally stationary gaussian random fields we present two applications of our result the first one deals with the extremes of aggregate multifractional brownian motions whereas the second one establishes the exact asymptotics of the supremum of the x process generated by multifractional brownian motions

nonequilibrium detailed fluctuation theorem for repeated discrete feedback we extend the framework of forward and reverse processes commonly utilized in the derivation and analysis of the nonequilibrium work relations to thermodynamic processes with repeated discrete feedback within this framework we derive a generalization of the detailed fluctuation theorem which is modified by the addition of a term that quantifies the change in uncertainty about the microscopic state of the system upon making measurements of physical observables during feedback as an application we extend two nonequilibrium work relations the nonequilibrium work fluctuation theorem and the relative entropy work relation

thermodynamics of genuine nonequilibrium states under feedback control for genuine nonequilibrium states that even at fixed external control parameter exhibit dissipation we extend the hatano sasa equality to processes with feedback control the resulting bound on the maximal extractable work is substantially sharper than what would follow from applying the sagawa ueda equality to transitions involving such states for repeated measurements at short enough intervals the power thus extracted can even exceed the average cost of driving as demonstrated explicitly with a simple analytically solvable example

dynamics of money and income distributions we formulate a model of personal income distributions within society our aim is to understand the origin of the natural law first proposed by pareto who suggested that the high end part of the income distribution follows a power law where f 1 w w 1 we generalise a model proposed the so called cc ccm model introducing the possibility of exchanges of money at random times unlike the cc ccm model this generalisation predicts tail exponents greater than unity in line with pareto s prediction and empirical observation

the moore penrose inverse of a factorization abstract in this paper we consider the product of matrices paq where a is von neumann regular and there exist p and q such that p pa a aqq we give necessary and sufficient conditions in order to paq be moore penrose invertible extending known characterizations finally an application is given to matrices over separative regular rings

generalized inverses uniqueness proofs and three new classes abstract given any ring r with 1 and any a b c r then generalizing ideas of j j koliha and p patricio in 2002 and of z wang and j chen in 2012 a is called b c pseudo polar if there exists an idempotent p r such that 1 p b r j r c j p b and c p j where j denotes the jacobson radical of r and p lies in the second commutant of a this p is shown to be unique whenever it exists a new outer generalized inverse y of a called the b c pseudo inverse of a is also defined and the existence of y is shown to imply that a is b c pseudo polar and hence that y is itself unique generalizing results of koliha patricio wang and chen further connections between the b c pseudo polar and b c pseudo invertible properties are found and the b c pseudo invertibility of a 1 a 2 is shown to imply a corresponding property for a 2 a 1 two further types of uniquely defined outer generalized inverses are also introduced

a novel dynamic model of pseudo random number generator an interesting hierarchy of random number generators is introduced in this paper based on the review of random numbers characteristics and chaotic functions theory the main objective of this paper is to produce an ergodic dynamical system which can be implemented in random number generators in order to check the efficacy of pseudo random number generators based on this map we have carried out certain statistical tests on a series of numbers obtained from the introduced hierarchy the results of the tests were promising as the hierarchy passed the tests satisfactorily and offers a great capability to be employed in a pseudo random number generator

generalized potlatch and smoothing processes we consider simple generalizations of the potlatch and smoothing processes which were introduced in 8 and studied in 5 these generalizations provide relatively simple examples of infinite interacting systems which exhibit phase transition the original potlatch and smoothing processes do not exhibit phase transition our results show that for the generalized processes phase transition does not usually occur in one or two dimensions but usually does occur in higher dimensions upper and lower bounds for the relevant critical values are obtained as one application of our results we obtain the limiting behavior of the critical values for the linear contact process in d dimensions as d thus answering a question we raised in 3 this is done by comparing the contact process with an appropriate generalized smoothing process

on a kinetic model for a simple market economy in this paper we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading we show that the kinetic model admits non trivial quasi stationary states with power law tails of pareto type in order to do this we consider a suitable asymptotic limit of the model yielding a fokker planck equation for the distribution of wealth among individuals for this equation the stationary state can be easily derived and shows a pareto power law tail numerical results confirm the previous analysis

on similarity of matrices over commutative rings the paper studies the problem on matrix similarity over a commutative rings the conditions are determined under which the matrix is similar to a companion or diagonal matrices

a nonequilibrium extension of the clausius heat theorem we generalize the clausius in equality to overdamped mesoscopic and macro scopic diffusions in the presence of nonconservative forces in contrast to previous frame works we use a decomposition scheme for heat which is based on an exact variant of the minimum entropy production principle as obtained from dynamical fluctuation theory this new extended heat theorem holds true for arbitrary driving and does not require assumptions of local or close to equilibrium the argument remains exactly intact for diffusing fields where the fields correspond to macroscopic profiles of interacting particles under hydro dynamic fluctuations we also show that the change of shannon entropy is related to the antisymmetric part under a modified time reversal of the time integrated entropy flux

extremes of α t locally stationary gaussian processes with non constant variances abstract with motivation from 9 in this paper we derive the exact tail asymptotics of t locally stationary gaussian processes with non constant variance functions we show that some certain variance functions lead to qualitatively new results

extremes of randomly scaled gumbel risks we investigate the product y1y2 of two independent positive risks y1 and y2 if y1 has distribution in the gumbel max domain of attraction with some auxiliary function which is regularly varying at infinity and y2 is bounded then we show that y1y2 has also distribution in the gumbel max domain of attraction if both y1 y2 have log weibullian or weibullian tail behaviour we prove that y1y2 has log weibullian or weibullian asymptotic tail behaviour respectively we present here three theoretical applications concerned with a the limit of point wise maxima of randomly scaled gaussian processes b extremes of gaussian processes over random intervals and c the tail of supremum of iterated processes

on products of three triangular matrices over associative rings abstract in this paper we characterize an associative ring over which any n n n 2 square matrix a can be written as lum where l m are lower triangular u is upper triangular and l and u have all their diagonal entries 1

rings of square stable range one abstract a ring s is said to have square stable range one written ssr s 1 if a s b s s implies that a 2 b x is a unit for some x s in the commutative case this extends the class of rings of stable range 1 and allows many new examples such as rings of real valued continuous functions and real holomorphy rings on the other hand ssr s 1 sometimes forces s to have stable range 1 for instance this is the case for exchange rings s for which ssr s 1 is characterized by s rad s being reduced or abelian or right quasi duo we also characterize rings s whose von neumann regular elements are strongly regular by using an element wise notion of square stable range one extending a result of estes and ohm we show that a possibly noncommutative infinite domain with stable range one or square stable range one must have a non artinian group of units

explicit equilibria in a kinetic model of gambling we introduce and discuss a nonlinear kinetic equation of boltzmann type which describes the evolution of wealth in a pure gambling process where the entire sum of wealths of two agents is up for gambling and randomly shared between the agents for this equation the analytical form of the steady states is found for various realizations of the random fraction of the sum which is shared to the agents among others the exponential distribution appears as steady state in case of a uniformly distributed random fraction while gamma distribution appears for a random fraction which is beta distributed the case in which the gambling game is only conservative in the mean is shown to lead to an explicit heavy tailed distribution

stable range one for rings with many idempotents an associative ring r is said to have stable range 1 if for any a b e r satisfying ar br r there exists y e r such that a by is a unit the purpose of this note is to prove the following facts theorem 3 an exchange ring r has stable range 1 if and only if every regular element of r is unit regular theorem 5 if r is a strongly 7r regular ring with the property that all powers of every regular element are regular then r has stable range 1 the latter generalizes a recent result of goodearl and menal 5 let r be an associative ring with identity r is said to have stable range 1 if for any a b e r satisfying ar br r there exists y e r such that a by is a unit this definition is left right symmetric by vaserstein 9 theorem 2 furthermore by a theorem of kaplansky all one sided units are two sided in rings having stable range 1 cf vaserstein 10 theorem 2 6 it is well known that a von neumann regular ring r has stable range 1 if and only if r is unit regular see for example goodearl 4 proposition 4 12 call a ring r strongly 7 regular if for every element a e r there exist a number n depending on a and an element x e r such that an an lx this is in fact a two sided condition 3 it is an open question whether all strongly 7r regular rings have stable range 1 goodearl and menal 5 proved that strongly 7r regular rings are unit regular and hence have stable range 1 theorem 5 8 p 278 in this note we first extend the above result for von neumann regular rings to a larger class of rings which includes all strongly 7r regular rings 7r regular rings von neumann regular rings and algebraic algebras as an application of this we prove that a strongly 7r regular ring r has stable range 1 if powers of every regular element are regular the latter is a generalization of the abovementioned result of goodearl and menal for strongly 7r regular regular rings as one can see from our proofs rings in these classes have a large supply of idempotents throughout r stands for an associative ring with identity and j r for the jacobson radical of r modules are unitary right r modules except otherwise specified for other undefined terms readers are referred to 4 let mr be a right r module following crawley and jonsson 2 mr is said to have the exchange property if for every module ar and any two received by the editors january 24 1994 and in revised form may 3 1994 originally communicated to the proceedings of the ams by k a goodearl 1991 mathematics subject classification primary 1 6d70 1 6p70

extremes of vector valued gaussian processes with trend abstract let x t x 1 t x n t t t r be a centered vector valued gaussian process with independent components and continuous trajectories and h t h 1 t h n t t t be a vector valued continuous function we investigate the asymptotics of p sup t t min 1 i n x i t h i t u as u as an illustration to the derived results we analyze two important classes of x t with locally stationary structure and with varying variances of the coordinates and calculate exact asymptotics of simultaneous ruin probability and ruin time in a gaussian risk model

nonequilibrium thermodynamics of feedback control we establish a general theory of feedback control on classical stochastic thermodynamic systems and generalize nonequilibrium equalities such as the fluctuation theorem and the jarzynski equality in the presence of feedback control with multiple measurements our results are generalizations of the previous relevant works to the situations with general measurements and multiple heat baths the obtained equalities involve additional terms that characterize the information obtained by measurements or the efficacy of feedback control a generalized szilard engine and a feedback controlled ratchet are shown to satisfy the derived equalities

monotonic entropy growth for a nonlinear model of random exchanges we present a proof of the monotonic entropy growth for a nonlinear discrete time model of a random market this model based on binary collisions also may be viewed as a particular case of ulam s redistribution of energy problem we represent each step of this dynamics as a combination of two processes the first one is a linear energy conserving evolution of the two particle distribution for which the entropy growth can be easily verified the original nonlinear process is actually a result of a specific coarse graining of this linear evolution when after the collision one variable is integrated away this coarse graining is of the same type as the real space renormalization group transformation and leads to an additional entropy growth the combination of these two factors produces the required result which is obtained only by means of information theory inequalities

on the existence of paths between points in high level excursion sets of gaussian random fields research supported in part by us israel binational science foundation 2008262 by aro grant w911nf 07 1 0078 nsf grant dms 1005903 and nsa grant h98230 11 1 0154 at cornell university by israel science foundation 853 10 by afosr fa8655 11 1 3039 by office for absorption of new scientists and erc grant rcmt152

algorithm for normal random numbers we propose a simple algorithm for generating normally distributed pseudorandom numbers the algorithm simulates n molecules that exchange energy among themselves following a simple stochastic rule we prove that the system is ergodic and that a maxwell like distribution that may be used as a source of normally distributed random deviates follows in the n limit the algorithm passes various performance tests including monte carlo simulation of a finite two dimensional ising model using wolff s algorithm it only requires four simple lines of computer code and is approximately ten times faster than the box muller algorithm s1063 651x 99 04409 8 pacs number s 02 70 lq 02 90 1p

on rings whose projective modules have the exchange property it is well known that all projective modules over a perfect ring have the exchange property this was shown by yamagata 32 and independently by harada and ishii lo provided that the identity of the ring can be expressed as a sum of orthogonal primitive idempotents the converse is also true 32 that it fails in general was demonstrated by kutami and oshiro ls who constructed a nonartinian boolean ring whose projective modules nevertheless have the exchange property as it turned out this outsider example is representative of an extensive class of rings in fact both perfect and regular rings are subsumed in the hypotheses of the following

roth s theorems and decomposition of modules it is shown that there is a connection between roth s theorems on similarity and equivalence of block triangular matrices and decomposition of modules the module property is that if m n mn then n is a summand of m this holds for any commutative ring if m is finitely presented new proofs of roth s theorems are given for commutative rings some results are established in the noncommutative case

the pyramid decomposition and rank minimization it is shown that every m x n matrix m over a regular ring with 1 can be decomposed as m m m m m where m q m m d m m m m and q is the minus order this horizontal pyramid decomposition can be used to obtain firstly a pyramid decomposition for 2 x 2 block matrices which over a division ring immediately yields the classical rank formula for block matrices secondly it also yields a horizontal version of this block rank formula these rank formulae are then respectively used to solve the horizontal and vertical rank minimization problems which are involved in the computation of the shorted matrix of m relative to subspaces w and w

completion of diagrams by automorphisms and bass first stable range condition abstract let p be a quasi projective module and let e be its endomorphism ring the condition that e has one in the stable range is shown to be equivalent to a number of conditions involving mappings of modules and completions of diagrams by automorphisms the dual problems for quasi injective modules are also considered the condition that principal right ideals of e are uniquely generated is also characterized by diagram completion properties as consequences of these results several sufficient conditions are given for the equivalence of a pair of endomorphisms of p

entropy of continuous mixtures and the measure problem in its continuous version the entropy functional measuring the information content of a given probability density may be plagued by a measure problem that results from improper weighting of phase space this issue is addressed considering a generic collision process whereby a large number of particles or agents randomly and repeatedly interact in pairs with prescribed conservation law s we find a sufficient condition under which the stationary single particle distribution function maximizes an entropylike functional that is free of the measure problem this condition amounts to a factorization property of the jacobian associated with the binary collision law from which the proper weighting of phase space directly follows

aleph nought continuous regular rings abstract let r be a right 0 continuous regular ring we show that there exists a two sided ideal i of r such that r i is a directly finite right 0 continuous regular ring and each directly finite factor ring of r is a factor ring of r i by using this we extend to arbitrary right 0 continuous regular rings some of the results obtained by goodearl for directly finite right 0 mcontinuous regular rings

diagonalization of matrices over regular rings abstract square matrices are shown to be diagonalizable over all known classes of von neumann regular rings this diagonalizability is equivalent to a cancellation property for finitely generated projective modules which conceivably holds over all regular rings these results are proved in greater generality namely for matrices and modules over exchange rings where attention is restricted to regular matrices