analytic solutions of a nonlinear convective equation in population dynamics analytic solutions are presented for a simple nonlinear convective equation of use in population dynamics in spite of its simplicity the equation predicts rich behavior including a velocity inversion transition stability considerations are also presented

analytic solutions for nonlinear waves in coupled reacting systems abstract we analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit an analytic solution is found for traveling waves the procedure is used to find oscillatory as well as solitary waves a comparison is made between exact solutions and solutions of the piecewise linearized system showing how the linearization affects the amplitude and frequency of the solutions

statistical mechanical considerations in the theory of the spread of the hantavirus abstract calculations in the theory of the spread of epidemics are described with particular focus on the estimation of motion parameters describing rodents that are the carriers of the hantavirus epidemic the data considered are of the mark recapture kind i e those collected by capturing tagging and recapturing the animals in a prescribed finite region of space the theoretical tool used is the fokker planck equation its characteristic quantities being the diffusion constant which describes the motion of the rodents and the attractive potential which addresses their tendency to live near their burrows the measurements are addressed through simple analytical calculations of the mean squared displacement of the animals relevant to the specific probing window in space corresponding to the trapping region a fourier prescription is provided to extract the home range of the animals from the observations applications of the theory to rodent movement in panama and new mexico are mentioned and several on going generalizations of current models of hantavirus epidemic spread are introduced

hurst exponents for interacting random walkers obeying nonlinear fokker planck equations abstract anomalous diffusion of random walks has been extensively studied for the case of non interacting particles here we study the evolution of nonlinear partial differential equations by interpreting them as fokker planck equations arising from interactions among random walkers we extend the formalism of generalized hurst exponents to the study of nonlinear evolution equations and apply it to several illustrative examples they include an analytically solvable case of a nonlinear diffusion constant and three nonlinear equations which are not analytically solvable the usual fisher equation which contains a quadratic nonlinearity a generalization of the fisher equation with density dependent diffusion constant and the nagumo equation which incorporates a cubic rather than a quadratic nonlinearity we estimate the generalized hurst exponents

results from variants of the fisher equation in the study of epidemics and bacteria the fisher equation which combines di usive motion of individuals with nonlinearities arising from their growth and competition processes is analyzed generalized and applied to the dynamics of bacteria pattern formation and the spread of epidemics analytic solutions are also presented for some exactly soluble and physically relevant variants of the equation c

weighted tent spaces with whitney averages factorization interpolation and duality in this paper we introduce a new scale of tent spaces which covers the weighted tent spaces of coifman meyer stein and of hofmann mayboroda mcintosh and some other tent spaces considered by dahlberg kenig pipher and auscher axelsson in studying boundary value problems for elliptic systems the strong factorizations within our tent spaces with applications to quasi banach complex interpolation and to multiplier duality theory are then established this way we unify and extend the corresponding results obtained by coifman meyer stein cohn verbitsky and hytonen rosen

memory controlled diffusion memory effects require for their incorporation into random walk models an extension of the conventional equations the linear fokker planck equation for the probability density p stackrel p vec r t is generalized by including nonlinear and nonlocal spatial temporal memory effects the realization of the memory kernel is restricted due the conservation of the basic quantity p a general criteria is given for the existence of stationary solutions in case the memory kernel depends on p polynomially transport may be prevented owing to the delay effects a finite amount of particles remains localized and the further transport is terminated for diffusion with nonlinear memory effects we find an exact solution in the long time limit although the mean square displacement exhibits diffusive behavior higher order cumulants offer differences to diffusion and they depend on the memory strength

revisited fisher s equation in a new outlook a fractional derivative approach abstract the well known fisher equation with fractional derivative is considered to provide some characteristics of memory embedded into the system the modified model is analyzed both analytically and numerically a comparatively new technique residual power series method is used for finding approximate solutions of the modified fisher model a new technique combining sinc collocation and finite difference method is used for numerical study the abundance of the bird species phalacrocorax carbois considered as a test bed to validate the model outcome using estimated parameters we conjecture non diffusive and diffusive fractional fisher equation represents the same dynamics in the interval memory index 0 8384 0 9986 we also observe that when the value of memory index is close to zero the solutions bifurcate and produce a wave like pattern we conclude that the survivability of the species increases for long range memory index these findings are similar to fisher observation and act in a similar fashion that advantageous genes do

factorization of tent spaces and hankel operators it is shown that the factorization tpq tp t q for tent spaces proved by r r coifman et al 1985 j funct anal 62 304 335 for p q q 2 holds true for all 0 p q from this certain strong factorization theorems are derived for spaces hps of fractional derivatives of hp functions and more general triebel spaces in particular it is proved that hps hp bmoas applications considered include characterizations of symbols of bounded hankel operators h hp hqs complex interpolation of tent spaces and carleson measure theorems for derivatives of hp functions

non hermitian localization and population biology the time evolution of spatial fluctuations in inhomogeneous d dimensional biological systems is analyzed a single species continuous growth model in which the population disperses via diffusion and convection is considered time independent environmental heterogeneities such as a random distribution of nutrients or sunlight are modeled by quenched disorder in the growth rate linearization of this model of population dynamics shows that the fastest growing localized state dominates in a time proportional to a power of the logarithm of the system size using an analogy with a schr odinger equation subject to a constant imaginary vector potential we propose a delocalization transition for the steady state of the nonlinear problem at a critical convection threshold separating localized and extended states in the limit of high convection velocity the linearized growth problem in d dimensions exhibits singular scaling behavior described by a d ensuremath 1 dimensional generalization of the noisy burgers equation with universal singularities in the density of states associated with disorder averaged eigenvalues near the band edge in the complex plane the burgers mapping leads to unusual transverse spreading of convecting delocalized populations

a biparametric family of eighth order methods with their third step weighting function decomposed into a one variable linear fraction and a two variable generic function this paper proposes a biparametric family of three step eighth order multipoint iterative methods with optimal efficiency index in the sense of kung traub for simple roots of nonlinear equations we employ their third step weighting function decomposed into king s linear fractional function and a two variable function to construct such a family of optimal methods development and convergence analysis on the proposed methods is fully described in addition to numerical experiments including comparison with existing methods

stability results on interpolation scales of quasi banach spaces and applications we investigate the stability of fredholm properties on interpolation scales of quasi banach spaces this analysis is motivated by problems arising in pde s and several applications are presented

the neumann problem for elliptic equations with non smooth coefficients in this paper we study the neumann and regularity problems for divergence form symmetric elliptic operators l div av where a aifix is a matrix of bounded measurable functions and ellipticity is the existence of a 0 such that 2 114 2 ais ir 21412 for all i r we assume that l is defined in the unit ball b but the methods of proof are sufficiently general to allow b to be a bounded starlike lipschitz domain the neumann problem lu 0 in b avun q f

a new family of eighth order iterative methods for solving nonlinear equations a family of eighth order iterative methods with four evaluations for the solution of nonlinear equations is presented kung and traub conjectured that an iteration method without memory based on n evaluations could achieve optimal convergence order 2 n 1 the new family of eighth order methods agrees with the conjecture of kung traub for the case n 4 therefore this family of methods has efficiency index equal to 1 682 numerical comparisons are made with several other existing methods to show the performance of the presented methods

population persistence in weakly coupled sinks abstract we consider a single species population obeying a saturated growth model with spatial diffusion taken into account explicitly strong spatial heterogeneity is considered represented by a position dependent reproduction rate the geometry of the problem is that of two patches where the reproductive rate is positive surrounded by unfavorable patches where it is negative we focus on the particular case where the population would not persist in the single patches sinks we find by means of an analytical derivation supplemented by a numerical calculation the conditions for the persistence of the population in the compound system of weakly connected patches we show that persistence is possible even if each individual patch is a sink where the population would go extinct the results are of particular relevance for ecological management at the landscape level showing that small patches may harbor populations as long as the connectivity with adjacent patches is maintained microcosmos experiences with bacteria could be performed for experimental verification of the predictions

pattern formation in terms of semiclassically limited distribution on lower dimensional manifolds for the nonlocal fisher kolmogorov petrovskii piskunov equation we have investigated the pattern formation in systems described by the nonlocal fisher kolmogorov petrovskii piskunov equation for the cases where the dimension of the pattern concentration domain is lower than that of the domain of independent variables we have obtained a system of integro differential equations which describe the dynamics of the concentration domain and the semiclassically limited density distribution for a pattern in the class of trajectory concentrated functions also asymptotic large time solutions have been obtained that describe the semiclassically limited distribution for a quasi steady state pattern on the concentration manifold the approach is illustrated by an example for which the analytical solution is in good agreement with the results of numerical calculations

arbitrary nonlinearities in convective population dynamics with small diffusion convective counterparts of variants of the nonlinear fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for the evolution of population densities the initial value problem is solved explicitly for some cases and for others it is shown how to find traveling wave solutions analytically the effect of adding diffusion to the convective equations is first studied through exact analysis through a piecewise linear representation of the nonlinearity using an appropriate small parameter suggested by that analysis a perturbative treatment is developed to treat the case in which the convective evolution is augmented by a small amount of diffusion

a new optimal eighth order family of iterative methods for the solution of nonlinear equations in this paper a new optimal family of methods for solving nonlinear equations is presented it is proved by analysis of convergence that each member of the family which requires three evaluations of the function and one evaluation of its first derivative per iteration is of optimal order eight numerical comparisons are made with several other existing eighth order methods by using the basins of attraction and through numerical computations to demonstrate the efficiency and the performance of the presented methods

spatial organization of vegetation arising from non local excitation with local inhibition in tropical rainforests abstract the janzen connell jc effect which hypothesizes that recruitment and growth of seedlings is positively correlated to the distance from the parent tree is shown to generate highly organized vegetation biomass spatial patterns when coupled to a revised fisher kolmogorov fk equation spatial organization arises through a novel mechanism of non local activation and local inhibition over a single generation the revised fk model calculations predict a hen and chicks dynamic pattern with mature trees surrounded by new seedlings growing at characteristic spatial distances in agreement with field data over longer timescales the importance of stochastic dynamics such as those associated with randomly occurring light gaps increase thereby causing a substantial deviation between predictions from the deterministic fk model and its stochastic counterpart derived to account for such random disturbances at still longer timescales however statistical measures of the spatial organization specifically the spatial density of mature trees and their minimum spacing converge between these two model representations

a fast algorithm for convolution integrals with space and time variant kernels mathematical models in many fields of the physical sciences involve nonlocal terms which are formally similar to convolution integrals we show that it is possible to approximate a particular class of such integrals which by themselves are not convolutions as a linear combination of convolution integrals allowing for their efficient numerical computation as an o n log n process

periodic solutions of nonlocal semilinear fourth order differential equations abstract in this paper we study the existence of periodic solutions with prescribed wavelength for two classes of nonlocal fourth order nonautonomous differential equations existence of nontrivial solutions for the first equation is proved using clark s theorem existence of nontrivial solutions for the second equation is proved using the symmetric mountain pass theorem

weighted maximal regularity estimates and solvability of non smooth elliptic systems i we develop new solvability methods for divergence form second order real and complex elliptic systems above lipschitz graphs with l 2 boundary data the coefficients a may depend on all

some new function spaces and their applications to harmonic analysis abstract in this paper a family of spaces is introduced which seems well adapted for the study of a variety of questions related to harmonic analysis and its applications these spaces are the tent spaces they provide the natural setting for the study of such things as maximal functions the relevant space here is t p and also square functions where the space t2p is relevant as such these spaces lead to unifications and simplifications of some basic techniques in harmonic analysis thus they are closely related to lp and hardy spaces important parts of whose theory become corollaries of the description of tent spaces also as proc conf harmonic analysis cortona lect notes in math vol 992 springer verlag berlin new york 1983 already indicated where these spaces first appeared explicitly the tent spaces can be used to simplify some of the results related to the cauchy integral on lipschitz curves and multilinear analysis in retrospect one can recognize that various ideas important for tent spaces had been used if only implicitly for quite some time here one should mention carleson s inequality its simplifications and extensions the theory of hardy spaces and atomic decompositions

three step iterative methods with eighth order convergence for solving nonlinear equations a family of eighth order iterative methods for the solution of nonlinear equations is presented the new family of eighth order methods is based on king s fourth order methods and the family of sixth order iteration methods developed by chun et al per iteration the new methods require three evaluations of the function and one evaluation of its first derivative therefore this family of methods has the efficiency index which equals 1 682 kung and traub conjectured that a multipoint iteration without memory based on n evaluations could achieve optimal convergence order 2 n 1 thus we provide a new example which agrees with the conjecture of kung traub for n 4 numerical comparisons are made to show the performance of the presented methods

applicability of the fisher equation to bacterial population dynamics the applicability of the fisher equation which combines diffusion with logistic nonlinearity to population dynamics of bacterial colonies is studied with the help of explicit analytic solutions for the spatial distribution of a stationary bacterial population under a static mask the mask protects bacteria from ultraviolet light the solution which is in terms of jacobian elliptic functions is used to provide a practical prescription to extract fisher equation parameters from observations and to decide on the validity of the fisher equation