on the hyers ulam rassias stability of approximately additive mappings abstract in this paper using an idea from the paper of p gvruta j math anal appl 184 1994 431 436 the results of th m rassias j math anal appl 158 1991 106 113 shall be generalized

entropic particle transport higher order corrections to the fick jacobs diffusion equation transport of point size brownian particles under the influence of a constant and uniform force field through a planar three dimensional channel with smoothly varying axis symmetric periodic side walls is investigated here we employ an asymptotic analysis in the ratio between the difference of the widest and the most narrow constriction divided through the period length of the channel geometry we demonstrate that the leading order term is equivalent to the fick jacobs approximation by use of the higher order corrections to the probability density we show that in the diffusion dominated regime the average transport velocity is obtained as the product of the zeroth order fick jacobs result and the expectation value of the spatially dependent diffusion coefficient d x which substitutes the constant diffusion coefficient in the common fick jacobs equation the analytic findings are corroborated with the precise numerical results of a finite element calculation of the smoluchowski diffusive particle dynamics occurring in a reflection symmetric sinusoidal shaped channel

hasse schmidt derivations and coefficient fields in positive characteristics abstract we show how to express any hasse schmidt derivation of an algebra in terms of a finite number of them under natural hypothesis as an application we obtain coefficient fields of the completion of a regular local ring of positive characteristic in terms of hasse schmidt derivations

optimal space time adaptive wavelet methods for degenerate parabolic pdes we analyze parabolic pdes with certain type of weakly singular or degenerate time dependent coefficients and prove existence and uniqueness of weak solutions in an appropriate sense a localization of the pdes to a bounded spatial domain is justified for the numerical solution a space time wavelet discretization is employed an optimality result for the iterative solution of the arising systems can be obtained finally applications to fractional brownian motion models in option pricing are presented

projecting diffusion along the normal bundle of a plane curve the purpose of this paper is to provide new formulas for the effective diffusion coefficient of a generalized fick jacob s equation obtained by projecting the two dimensional diffusion equation along the normal directions of an arbitrary curve on the plane

mapping of forced diffusion in quasi one dimensional systems diffusion in an external potential in a two dimensional channel of varying cross section is considered we show that a rigorous mapping procedure applied on the corresponding smoluchowski equation yields a one dimensional evolution equation of the fick jacobs type corrected by an effective coefficient d x the procedure enables us to derive this function within a recurrence scheme we test this result on a model of stationary diffusion in a linear cone in a homogeneous potential which is exactly solvable extension of the approximate formulas for d x derived for the diffusion alone is discussed

transport and fluctuation dissipation relations in asymptotic and preasymptotic diffusion across channels with variable section we study the asymptotic and preasymptotic diffusive properties of brownian particles in channels whose section varies periodically in space the effective diffusion coefficient d mathrm eff is numerically determined by the asymptotic behavior of the root mean square displacement in different geometries considering even cases of steep variations of the channel boundaries moreover we compared the numerical results to the predictions from the various corrections proposed in the literature to the well known fick jacobs approximation building an effective one dimensional equation for the longitudinal diffusion we obtain an approximation for the effective diffusion coefficient such a result goes beyond a perturbation approach and it is in good agreement with the actual values obtained by the numerical simulations we discuss also the preasymptotic diffusion which is observed up to a crossover time whose value in the presence of strong spatial variation of the channel cross section can be very large in addition we show how the einstein s relation between the mean drift induced by a small external field and the mean square displacement of the unperturbed system is valid in both asymptotic and preasymptotic regimes

integration of brownian vector fields summary using the wiener chaos decomposition we show that strong solutions of non lipschitzian s d e s are given by random markovian kernels the example of sobolev flows is studied in some detail exhibiting interesting phase transitions

on skew brownian motion we consider the stochastic equation x t w t beta l x 0 t where w is a standard wiener process and l x 0 cdot is the local time at zero of the unknown process x there is a unique solution x and it is adapted to the fields of w if beta leq 1 but no solutions exist if beta 1 in the former case setting alpha beta 1 2 the unique solution x is distributed as a skew brownian motion with parameter alpha this is a diffusion obtained from standard wiener process by independently altering the signs of the excursions away from zero each excursion being positive with probability alpha and negative with probability 1 alpha finally we show that skew brownian motion is the weak limit as n rightarrow infty of n 1 2 s lbrack nt rbrack where s n is a random walk with exceptional behavior at the origin

mapping of diffusion in a channel with soft walls we study diffusion of pointlike particles biased toward the x axis by a quadratic potential u x y ensuremath kappa x y 2 this system mimics a channel with soft walls of some varying effective cross section a x depending on the stiffness ensuremath kappa x we show that diffusion in this geometry can also be mapped rigorously onto the longitudinal coordinate x by a procedure known for channels with hard walls p kalinay and j k percus phys rev e 74 041203 2006 i e we arrive at a one dimensional evolution equation of the fick jacobs type on the other hand the calculation presented serves as a prototype for mapping of the smoluchowski equation with a wide class of potentials u x y varying in both the longitudinal as well as the transverse directions which is necessary for understanding e g stochastic resonance

principal ideals and semi direct products in commutative banach algebras abstract we prove necessary conditions for a commutative banach algebra to be the semi direct product of some subalgebra together with a specified principal ideal

on approximately higher ring derivations abstract in this paper we examine the hyers ulam the isac and rassias type stability and the bourgin type superstability of a functional inequality corresponding to the following functional equation respectively f n x y i 0 n f i x f n i y in particular an additive operator satisfying the above equation is said to be a ring homomorphism respectively a ring derivation if n 0 respectively n 1 and f 0 is an identity operator

driven brownian transport through arrays of symmetric obstacles we numerically investigate the transport of a suspended overdamped brownian particle which is driven through a two dimensional rectangular array of circular obstacles with finite radius two limiting cases are considered in detail namely when the constant drive is parallel to the principal or the diagonal array axes this corresponds to studying the brownian transport in periodic channels with reflecting walls of different topologies the mobility and diffusivity of the transported particles in such channels are determined as functions of the drive and the array geometric parameters prominent transport features like negative differential mobilities excess diffusion peaks and unconventional asymptotic behaviors are explained in terms of two distinct lengths the size of single obstacles trapping length and the lattice constant of the array local correlation length local correlation effects are further analyzed by continuously rotating the drive between the two limiting orientations

lie derivations on banach algebras abstract let d be a lie derivation on a unital complex banach algebra a then for every primitive ideal p of a except for a finite set of them which have finite codimension greater than one there exist a derivation d from a p to itself and a linear functional on a such that q p d a d a p a for all a a where q p denotes the quotient map from a onto a p moreover the preceding decomposition holds for all primitive ideals in the case where d is continuous

on the generalized hyers ulam rassias stability in banach modules over a c algebra abstract in this paper we will investigate the generalized hyers ulam rassias stability of an n dimensional quadratic functional equation in banach modules over a c algebra and unitary elements

the generalized hyers ulam rassias stability of a cubic functional equation abstract in this paper we obtain the general solution and the generalized hyers ulam stability for a cubic functional equation f 2x y f 2x y 2f x y 2f x y 12f x

perturbation of generalized derivations in fuzzy menger normed algebras in this paper we introduce a notion for fuzzy menger normed algebra then we will investigate continuity of algebraic operations in this space we will show that the class of all fuzzy menger normed algebras strictly contains the class of normed algebras finally we will prove hyers ulam rassias superstability of generalized derivation functional equationf ax by vw af x bf y vf w g v w x y v email protected x 0 a email protected c in complete fuzzy menger normed algebras a few applications of our results will be exhibited

on the hyers ulam stability of the functional equations that have the quadratic property abstract the hyers ulam stability of the quadratic functional equation 1 on a restricted domain shall be investigated and the result shall be applied to the study of an asymptotic behavior of that equation furthermore the hyers ulam stability problems of another quadratic equation 4 on a restricted domain shall also be treated under the approximately even or odd condition and some asymptotic behaviors of the quadratic mappings and the additive mappings shall be investigated

diffusion in a two dimensional channel with curved midline and varying width reduction to an effective one dimensional description diffusion in a narrow two dimensional channel with a midline that need not be straight and a width that may vary is reduced to an effective one dimensional equation of motion this equation takes the form of the fick jacobs equation with a spatially varying effective diffusivity the effective diffusivity includes a contribution that comes from the slope of the midline as well as the usual term stemming from variations in the channel width along the length of the channel our derivation of our equation of motion is completely rigorous and is based on an asymptotic expansion in a small dimensionless parameter that characterizes the channel width for a channel that has a straight midline or wall our equation of motion reduces to zwanzig s equation r zwanzig j phys chem 96 3926 1992 our derivation therefore provides a rigorous proof of the validity of the latter equation finally the equation of motion is solved analytically for channels with curved midline and constant width

a fixed point method for perturbation of bimultipliers and jordan bimultipliers in c ternary algebras let a be a c ternary algebra a c bilinear t a a a is called a c ternary algebra bi multiplier if it satisfies t abc d t a b cd t a bcd abt c d for all a b c d a also the mapping t a a a is a called c ternary algebra jordan bimultiplier if it satisfies t aaa a t a a aa t a aaa aat a a for all a a using the fixed point method we investigate the generalized hyers ulam rassias stability of bimultipliers and jordan bimultipliers in c ternary algebras the concept of hyers ulam rassias stability originated from the th m rassias stability theorem that appeared in his paper th m rassias proc am math soc 72 297 1978

lenses in skew brownian flow we consider a stochastic flow in which individual particles follow skew brownian motions with each one of these processes driven by the same brownian motion one does not have uniqueness for the solutions of the corresponding stochastic differential equation simultaneously for all real initial conditions due to this lack of the simultaneous strong uniqueness for the whole system of stochastic differential equations the flow contains lenses that is pairs of skew brownian motions which start at the same point bifurcate and then coalesce in a finite time the paper contains qualitative and quantitative distributional results on the geometry of the flow and lenses

on a generalized nonlinear functional equation abstract the paper deals with the functional equation f x f f u x f v x under some special assumptions concerning the given functions u v and f our main result extends some results in the literature

on the stability of functional equations in banach spaces the paper is devoted to some results on the problem of s m ulam for the stability of functional equations in banach spaces the problem was posed by ulam 60 years ago

generalized hyers ulam rassias stability of n sesquilinear quadratic mappings on banach modules over c algebras assume that x is a left banach module over a unital c algebra a it is shown that almost every n sesquilinear quadratic mapping h xxxxx n a is an n sesquilinear quadratic mapping when h rx y z 1 z n h x ry z 1 z n h x y rz 1 z 2 z n h x y z 1 z 2 rz n rh x y z 1 z 2 z n r 0 r 1 holds for all x y z 1 z email protected x moreover we prove the generalized hyers ulam rassias stability of an n sesquilinear quadratic mapping on a left banach module over a unital c algebra

stability of exponential equations in schwartz distributions abstract we reformulate the superstability of exponential equation and cosine functional equation j a baker the stability of cosine equation proc amer math soc 80 1980 411 416 in some spaces of generalized functions such as the schwartz distributions sato hyperfunctions and gelfand generalized functions which completes the previous results of partial generalizations of the stability problems j chung a distributional version of functional equations and their stabilities nonlinear anal 62 2005 1037 1051 j chung s y chung d kim the stability of cauchy equations in the space of schwartz distributions j math anal appl 295 2004 107 114

control of logic gates by dichotomous noise in energetic and entropic systems we consider the stochastic response of a nonlinear dynamical system towards a combination of input signals the response can assume binary values if the state of the system is considered to be the output and the system can make transitions between two states separated by an energetic or entropic barrier we show how the input output correspondence can be controlled by an external exponentially correlated dichotomous noise optimizing the logical response which exhibits a maximum at an intermediate value of correlation time this resonance manifests itself as a logical resonance correlation effect and sets the condition for performance of the stochastic system as a logic gate the role of asymmetry of the dichotomous noise is examined and the results on numerical simulations are correlated with a two state model using a master equation approach

local time flow related to skew brownian motion burdzy s research partially supported by nsf grant dms 9700721 chen s research partially supported by nsa grant mda904 99 1 0104

on the hyers ulam stability of linear mappings abstract let e1 be a real normed vector space and e2 a real banach space s m ulam posed the problem when does a linear mapping near an approximately linear mapping e1 e2 exist we give a new generalized solution to this problem an example illustrates when the answer to this question is negative the behaviour of bounded approximately additive mappings which do not satisfy hyers uiam stability is also investigated

on the cauchy rassias stability of a generalized additive functional equation let x and y be banach spaces and f x y an odd mapping we solve the following generalized additive functional equation rf j 1dxjr j 0 1 j 1d j lrf j 1d 1 j xjr cld 1 cl 1d 1 1 j 1df xj for all x1 xd x moreover we deal with the above functional equation in banach modules over a c algebra and obtain generalizations of the cauchy rassias stability the concept of cauchy rassias stability for the linear mapping was originated from th m rassias s stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

stability of c inner products abstract in this paper we investigate the stability of the inner products in hilbert c modules over unital c algebras

approximately vanishing of topological cohomology groups in this paper we establish the pexiderized stability of coboundaries and cocycles and use them to investigate the hyers ulam stability of some functional equations we prove that for each banach algebra a banach a bimodule x and positive integer n hn a x 0 if and only if the nth cohomology group approximately vanishes

prime like elements and semi direct products in commutative banach algebras we develop results which show that elements in the radical of a commutative banach algebra are often precluded from having prime like properties if we avoid certain exceptional situations involving torsion elements this makes the proof of the singer wermer conjecture conceptually much clearer it also motivates the definition of an element havingregular powersand allows us to strengthen our previous results concerning necessary conditions for a commutative banach algebra a to be the semidirect product of some subalgebra together with a specified principal idealsa or equivalently concerning necessary conditions for there to be an algebraicsplittingof the short exact sequence0 sa a a sa 0for some given elementsin a in particular we show that if a is aradicalbanach algebra andshas regular powers then no such splitting is possible

a generalization of the hyers ulam rassias stability of approximately additive mappings abstract in this paper we prove a generalization of the stability of approximately additive mappings in the spirit of hyers ulam and rassias

isomorphisms between c ternary algebras in this paper we prove the hyers ulam rassias stability of homomorphisms in c ternary algebras and of derivations on c ternary algebras for the following generalized cauchy jensen additive mapping 2f j 1pxj2 j 1dyj j 1pf xj 2 j 1df yj this is applied to investigate isomorphisms between c ternary algebras the concept of hyers ulam rassias stability originated from the rassias stability theorem that appeared in his paper on the stability of the linear mapping in banach spaces see proc amr math soc 72 297 300 1978

local power series quotients of commutative banach and frechet algebras we consider the relationship between derivations and local power series quotients for a locally multiplicatively convex frechet algebra in 2 we derive necessary conditions for a commutative frechet algebra to have a local power series quotient our main result here is proposition 2 6 which shows that if the generating element has finite closed descent the algebra cannot be simply a radical algebra with identity adjoined it must have nontrivial representation theory if the generating element does not have finite closed descent then the algebra cannot be a banach algebra and the generating element must be locally nilpotent but non nilpotent in an associated quotient algebra in 3 we consider a fundamental situation which leads to local power series quotients let d be a derivation on a commutative radical frechet algebra r with identity adjoined we show in theorem 3 10 that if the discontinuity of d is not concentrated in the jacobson radical then r has a local power series quotient the question of whether such a derivation can have a separating ideal so large it actually contains the identity element has been recently settled in the affirmative by c j read

some results on stability of extended derivations abstract in this paper we prove the generalized hyers ulam rassias stability of extended derivations on unital banach algebras associated to a generalized jensen equation

a note on generalized derivations in banach algebras abstract in this note we characterize a complex banach algebra a admitting a generalized derivation g such that the cardinality of the spectrum g x is exactly one for all x a

flows coalescence and noise we are interested in stationary fluid random evolutions with independent increments under some mild assumptions we show they are solutions of a stochastic differential equation sde there are situations where these evolutions are not described by flows of diffeomorphisms but by coalescing flows or by flows of probability kernels in an intermediate phase for which there exist a coalescing flow and a flow of kernels solution of the sde a classification is given all solutions of the sde can be obtained by filtering a coalescing motion with respect to a subnoise containing the gaussian part of its noise thus the coalescing motion cannot be described by a white noise

asymptotic behavior of generalized derivations on c algebras with applications we consider generalized derivations on c algebra and we will first study the conditions for a linear generalized derivation on c algebra then we prove some theorems involving approximate linear generalized derivations on c algebra so approximate linear generalized derivations on c algebra are characterized

modified trif s functional equations in banach modules over a c algebra and approximate algebra homomorphisms abstract we prove the hyers ulam rassias stability of modified trif s functional equations in banach modules over a unital c algebra it is applied to show the stability of banach algebra homomorphisms between banach algebras associated with modified trif s functional equations in banach algebras

ulam stability problem for quadratic mappings of euler lagrange abstract the purpose of this paper is to solve the stability problem of ulam for an approximate mapping f a b of the following quadratic functional equation of euler lagrange a b aq x a b bq y q ax by abq x y for all x y a with a and b linear spaces

variational problem of some quadratic functionals in complex analysis suppose we are given a pair of marked closed riemann surfacess twith the same genus we minimize the modified dirichlet integral for mappings ofsontot which is endowed with some weight in terms of conformal metric on the target surfacet in this paper it is demonstrated that the minimal harmonic map exists and it proves to be teichmuller

biased diffusion in confined media test of the fick jacobs approximation and validity criteria we study biased diffusive transport of brownian particles through narrow spatially periodic structures in which the motion is constrained in lateral directions the problem is analyzed under the perspective of the fick jacobs equation which accounts for the effect of the lateral confinement by introducing an entropic barrier in a one dimensional diffusion the validity of this approximation based on the assumption of an instantaneous equilibration of the particle distribution in the cross section of the structure is analyzed by comparing the different time scales that characterize the problem a validity criterion is established in terms of the shape of the structure and of the applied force it is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure the criterion can be visualized by means of a diagram representing the regions where the fick jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure

kinetic equations for diffusion in the presence of entropic barriers we use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers the result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers we analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description the corresponding kinetic equation named the fick jacobs equation is obtained and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries the method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature

comment on approximate ternary jordan derivations on banach ternary algebras bavand savadkouhi et al j math phys 50 042303 2009 let a be a banach ternary algebra over c and x a ternary banach a module a c linear mapping d a a x x is called a ternary jordan derivation if d xxx a d x xx x xd x x x xxd x x for all x a bavand savadkouhi et al j math phys 50 042303 2009 investigated ternary jordan derivations on banach ternary algebras associated with the following functional equation f x y z 4 f 3x y 4z 4 f 4x 3z 4 2f x and proved the generalized ulam hyers stability of ternary jordan derivations on banach ternary algebras the mapping f in lemma 2 2 of bavand savadkouhi et al is identically zero and all of the results are trivial in this note we correct the statements of the results and the proofs

isomorphisms between c ternary algebras abstract in this paper we prove the hyers ulam rassias stability of homomorphisms in c ternary algebras and of derivations on c ternary algebras for the following cauchy jensen additive mappings 0 1 f x y 2 z f x y 2 z f x 2 f z 0 2 f x y 2 z f x y 2 z f y 0 3 2 f x y 2 z f x f y 2 f z these are applied to investigate isomorphisms between c ternary algebras the concept of hyers ulam rassias stability originated from the th m rassias stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

asymmetry in shape causing absolute negative mobility we propose a simple classical concept of nanodevices working in an absolute negative mobility anm regime the minimal spatial asymmetry required for anm to occur is embedded in the geometry of the transported particle rather than in the channel design this allows for a tremendous simplification of device engineering thus paving the way toward practical implementations of anm operating conditions and performance of our model device are investigated both numerically and analytically

on fuzzy approximately cubic type mapping in fuzzy banach spaces abstract the first study of the fuzzy approximately cubic mappings in nonlinear analysis is due to mirmostafaee and moslehian 2008 and a fuzzy version of a generalized hyers ulam rassias type stability for the cubic functional equation in the fuzzy normed linear space setting is presented in this note we give an alternative proof of this result using the fixed point method in probabilistic metric spaces moreover we investigate fuzzy generalized hyers ulam rassias stability of an n dimensional cubic type functional equation in fuzzy banach spaces

the availability of logical operation induced by dichotomous noise for a nonlinear bistable system instead of a continuous system driven by gaussian white noise logical stochastic resonance will be investigated in a nonlinear bistable system with two thresholds driven by dichotomous noise which shows a phenomenon different from gaussian white noise we can realize two parallel logical operations by simply adjusting the values of these two thresholds besides to quantify the reliability of obtaining the correct logic output we numerically calculate the success probability and effects of dichotomous noise on the success probability are observed these observations show that the reliability of realizing logical operation in the bistable system can be improved through optimizing parameters of dichotomous noise

stability of a quadratic jensen type functional equation in the spaces of generalized functions abstract making use of the fundamental solution of the heat equation we find the solution and prove the stability theorem of the quadratic jensen type functional equation 9 f x y z 3 f x f y f z 4 f x y 2 f y z 2 f z x 2 in the spaces of schwartz tempered distributions and fourier hyperfunctions

enhancement of entropic transport by intermediates brownian particles confined in a two dimensional enclosure that give rise to a bistable entropic potential are considered with the introduction of an intermediate lobe the mean first passage time from one lobe to another through the intermediate shows a turnover behavior with the variation of the stability of the entropic intermediate the mean escape time shows a minimum for an optimal value of the barrier height of the intermediate state a three state model is proposed to explain the nonmonotonic behavior of the entropic transport

conditional functional equations on restricted domains of measure zero let r02 r2 0 0 r 2 x y r2 x2 y2 and f r02 r g r 2 r in this paper we consider the ulam hyers stability of the functional equations f ux vy uy vx f x y f u v f ux vy uy vx f x y f u v g ux vy uy vx g x y g u v g ux vy uy vx g x y g u v for all x y u v where r4 is of 4 dimensional lebesgue measure zero the above functional equations are modified versions of the equations in 9 11 14 18 24 which arise from number theory and are in connection with characterizations of determinant and permanent of two by two matrices

on the generalized hyers ulam stability of module left derivations let a be a unital normed algebra and let m be a unitary banach left a module if f a m is an approximate module left derivation then f a m is a module left derivation moreover if m a is a semiprime unital banach algebra and f tx is continuous in t r for each fixed x in a then every approximately linear left derivation f a a is a linear derivation which maps a into the intersection of its center z a and its jacobson radical rad a in particular if a is semisimple then f is identically zero

approximate ternary jordan derivations on banach ternary algebras let a be a banach ternary algebra over a scalar field r or c and x be a ternary banach a module a linear mapping d a a x x is called a ternary jordan derivation if d xxx a d x xx x xd x x x xxd x x for all x a in this paper we investigate ternary jordan derivations on banach ternary algebras associated with the following functional equation f x y z 4 f 3x y 4z 4 f 4x 3z 4 2f x moreover we prove the generalized ulam hyers stability of ternary jordan derivations on banach ternary algebras

stability for the functional equation of cubic type abstract in this article we establish the stability of the orthogonally cubic type functional equation 1 2 for all x 1 x 2 x 3 with x i x j i j 1 2 3 where is the orthogonality in the sense of ratz and investigate the stability of the n dimensional cubic type functional equation 1 3 where n 3 is an integer

on approximation of approximately linear mappings by linear mappings abstract assume a is a normed linear space b is a banach space and f a b is a mapping approximately linear we solve the following ulam problem give conditions in order for a linear mapping near an approximately linear mapping to exist

the stability of a cubic type functional equation with the fixed point alternative abstract in this note we investigate the generalized hyers ulam rassias stability for the new cubic type functional equation f x y 2 z f x y 2 z f 2 x f 2 y 2 f x y 2 f x z 2 f x z 2 f y z 2 f y z by using the fixed point alternative the first systematic study of fixed point theorems in nonlinear analysis is due to g isac and th m rassias internat j math math sci 19 1996 219 228

hyers ulam rassias stability of homomorphisms in quasi banach algebras associated to the pexiderized cauchy functional equation abstract in this paper we prove the hyers ulam rassias stability of homomorphisms in quasi banach algebras associated to the pexiderized cauchy functional equation this is applied to investigate homomorphisms between quasi banach algebras the concept of hyers ulam rassias stability originated from th m rassias stability theorem that appeared in his paper th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300

a perturbation of ring derivations on banach algebras abstract suppose a is a banach algebra and suppose f a a is an approximate ring derivation in the sense of hyers ulam rassias this stability phenomenon was introduced for the first time in the subject of functional equations by th m rassias th m rassias on the stability of the linear mapping in banach spaces proc amer math soc 72 1978 297 300 if a has an approximate identity or if a is semisimple and commutative then we prove that f is an exact ring derivation

effective one dimensional description of confined diffusion biased by a transverse gravitational force diffusion of pointlike noninteracting particles in a two dimensional channel of varying cross section is considered the particles are biased by a constant force in the transverse direction a recurrence mapping procedure is applied which enables the derivation of an effective one dimensional 1d evolution equation that governs the 1d density of the particles in the channel in the limit of stationary flow an extended fick jacobs equation is reached which is corrected by an effective diffusion coefficient d x that depends on the longitudinal coordinate x the result is an approximate formula for d x that also involves the influence of the transverse force the calculations are verified by the stationary diffusion in a linear cone which is exactly solvable

partial stabilities and partial derivations of n variable functions abstract we introduce the concepts of the partial derivations of a function from a normed algebra a 1 a n into a banach algebra b and prove the hyers ulam rassias stability of the function moreover we obtain some results about the applications of derivations such as the extended derivations and the approximately higher derivations

the image of a derivation is contained in the radical in 1955 i m singer and j wermer proved that a bounded derivation on a commutative banach algebra maps into the jacobson radical they conjectured that this result holds even if the derivation is unbounded we give a proof of this conjecture the central idea in the proof is the introduction of the concept of a recalcitrant system of elements in a commutative radical banach algebra such systems put algebraic constraints upon a derivation which prevent the derivation from mapping outside of the radical

approximations of the generalized fick jacobs equation we analyze the generalized fick jacobs equation obtained by a rigorous mapping of the diffusion equation in a quasi one dimensional quasi 1d narrow 2d or 3d channel with varying cross section a x onto the longitudinal coordinate x we show that for constructing approximations and understanding their applicability in practice it is crucial to study the 2d 3d density inside the channel in the regime of stationary flow we present algorithms enabling us to derive approximate formulas for the effective diffusion coefficient involving derivatives of a x higher than a ensuremath x and give examples for 2d channels effects of the boundary conditions at the ends of a finite channel and the case of nonsmooth a x are also discussed

on the stability of an n dimensional cubic functional equation abstract let n 2 be an integer number in this paper we investigate the generalized hyers ulam rassias stability in banach spaces and also banach modules over a banach algebra and a c algebra and the stability using the alternative fixed point of an n dimensional cubic functional equation in banach spaces f j 1 n 1 x j 2 x n f j 1 n 1 x j 2 x n j 1 n 1 f 2 x j 2 f j 1 n 1 x j 4 j 1 n 1 f x j x n f x j x n