stability of homomorphisms for a 3d cauchy jensen type functional equation on c ternary algebras abstract in this paper we investigate homomorphisms between c ternary algebras and derivations on c ternary algebras associated with the following cauchy jensen type additive functional equation f x y 2 z f x z 2 y f y z 2 x 2 f x f y f z

optimal system invariant solutions and evolution of weak discontinuity for isentropic drift flux model abstract inequivalent classes of similarity solutions for isentropic drift flux two phase flow model are obtained by using one dimensional optimal classifications the optimality of this classification is shown in a constructive manner i e by constructing various invariant functions including conditional and numerical invariants further with the help of invariant solution we discuss the evolution of weak discontinuity which displays the nature of the general solution

combined effect of pores concavity and aspect ratio on the elastic properties of a porous material the present paper focuses on materials containing superellipsoidal pores described by equation x 1 2 p x 2 2 p x 3 2 p 1 this shape is concave when 0 p p 0 5 they are oblate when 1 combined effect of two shape factors parameter p describing the concavity and aspect ratio describing extend of oblateness prolateness on compliance contribution tensor is analyzed numerically and approximated analytically for most important case of p 1 it is shown that in this case the combined effect is equal to the product of two effects considered separately the obtained approximate expressions are used to calculate the effective elastic properties of a heterogeneous material containing pores of superellipsoidal shape

on some differential invariants for a family of diffusion equations the equivalence transformation algebra le and some of its differential invariants for the class of equations ut h u ux x f x u ux h 0 are obtained using these invariants we characterize subclasses which can be mapped by means of an equivalence transformation into the well studied family of equations vt vkvx x

on a countable dimensional subalgebra of the equivalence algebra for equations vtt f x vx vxx g x vx the analysis of the equations vtt f x vx vxx g x vx initiated by ibragimov et al j math phys 32 2988 1991 is continued the preliminary group classification of these equations with respect to a countable dimensional subalgebra of their equivalence algebra is presented this subalgebra is an extension of the 10 dimensional subalgebra considered by ibragimov et al the result of the work is a table of nonequivalent equations possessing an additional symmetry

a group classification of the general second order coupled diffusion system we classify second order systems of coupled heat diffusion equations the underlying system contains several unknown functions the forms of which are specified via the method of group classification in particular the canonical forms of the low dimensional lie algebras and the lie algebras of higher dimension provide a means to specify the functional forms of these arbitrary functions

group classification of unsteady boundary layer equations of a class of non newtonian fluids two dimensional unsteady boundary layer equations of a general model of non newtonian fluids were investigated in this study in this model the shear stress is taken as an arbitrary function of the velocity gradient group classification of the equations with respect to shear stress is done using two different approaches 1 classical theory 2 equivalence transformations both approaches yield identical results it is found that the principle lie algebra extends only for cases of newtonian and power law flows

classifying evolution equations a lie point symmetry classification of evolution equations in 1 1 time space dimensions was presented a combination of the standard lie algorithm for point symmetry and the equivalence group of th

homomorphisms in c ternary algebras and jb triples abstract in this paper we investigate homomorphisms between c ternary algebras and derivations on c ternary algebras and homomorphisms between j b triples and derivations on j b triples associated with the following apollonius type additive functional equation f z x f z y 1 2 f x y 2 f z x y 4

group classification of three dimensional boundary layer equations of a class of non newtonian fluids group classification of three dimensional boundary layer equations of a class of non newtonian fluids in which thee stress is an arbitrary function of rates of strain is made group classification of the equations with respect to shear stress is done by using equivalence transformations special cases such as arbitrary stress newtonian fluids and power law fluids are treated

second order differential invariants of a family of diffusion equations an equivalence transformation algebra for a class of nonlinear diffusion equations is found after having obtained the second order differential invariants with respect to we get some results which allow us to linearize a subclass of the equations considered

cavities vis a vis rigid inclusions elastic moduli of materials with polygonal inclusions in this paper we explore the correspondence between rigid inclusions and cavities dundurs 1989 j appl mech 56 786 790 as applied to the effective elastic moduli of materials with polygonal rigid inclusions and cavities in the analysis we use a complex variable method of elasticity and a conformal transformation to solve for the stress field due to a single rigid inclusion then we use a far field approach to obtain the effective elastic constants of composites with a dilute concentration of rigid polygonal inclusions by employing the dundurs correspondence we can automatically obtain the result for the effective elastic moduli of materials with cavities finally we use effective medium theories to predict the elastic moduli of materials containing a finite concentration of inclusions

preliminary group classification of equations vtt f x vx vxx g x vx a classification is given of equations vtt f v vx vxx g x vx admitting an extension by one of the principal lie algebra of the equation under consideration the paper is one of few applications of a new algebraic approach to the problem of group classification the method of preliminary group classification the result of the work is a wide class of equations summarized in table ii

generalized additive mapping in banach modules and isomorphisms between c algebras abstract let x y be vector spaces it is shown that if an odd mapping f x y satisfies the functional equation 1 r f j 1 d x j r j 0 1 j 1 d j l r f j 1 d 1 j x j r c l d 1 c l 1 d 1 1 j 1 d f x j then the odd mapping f x y is additive and we prove the hyers ulam stability of the functional equation 1 in banach modules over a unital c algebra as an application we show that every almost linear bijection h a b of a unital c algebra a onto a unital c algebra b is a c algebra isomorphism when h 2 n r n u y h 2 n r n u h y for all unitaries u a all y a and n 0 1 2

on the stability of the linear mapping in banach modules abstract we prove the generalized hyers ulam rassias stability of the linear mapping in banach modules over a unital banach algebra

group analysis and exact solutions of a class of variable coefficient nonlinear telegraph equations a complete group classification of a class of variable coefficient 1 1 dimensional telegraph equations f x utt h u ux x k u ux is given by using a compatibility method and additional equivalence transformations a number of new interesting nonlinear invariant models which have nontrivial invariance algebras are obtained furthermore the possible additional equivalence transformations between equations from the class under consideration are investigated exact solutions of special forms of these equations are also constructed via classical lie method and generalized conditional transformations local conservation laws with characteristics of order 0 of the class under consideration are classified with respect to the group of equivalence transformations a complete group classification of a class of variable coefficient 1 1 dimensional telegraph equations f x utt h u ux x k u ux is given by using a compatibility method and additional equivalence transformations a number of new interesting nonlinear invariant models which have nontrivial invariance algebras are obtained furthermore the possible additional equivalence transformations between equations from the class under consideration are investigated exact solutions of special forms of these equations are also constructed via classical lie method and generalized conditional transformations local conservation laws with characteristics of order 0 of the class under consideration are classified with respect to the group of equivalence transformations

a group analysis approach for a nonlinear differential system arising in diffusion phenomena we consider a class of second order partial differential equations which arises in diffusion phenomena and following a new approach we look for a lie invariance classification via equivalence transformations a class of exact invariant solutions containing an arbitrary function is obtained

lie group classification of the nonlinear generalized kompaneets equations with two functional parameters we study the nonlinear generalized kompaneets equations gkes with two functional parameters by using the lie ovsiannikov algorithm we carried out the group classification of the equations it is shown that the kernel algebra of the full groups of the gkes is the one dimensional lie algebra we obtained nine non equivalent up to transformations from the equivalence group nonlinear gkes that allow wider invariance algebras than the kernel one we found a number of exact solutions of those gkes which have the maximal symmetry properties

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

complete group classification of a class of nonlinear wave equations preliminary group classification became a prominent tool in the symmetry analysis of differential equations due to the paper by ibragimov torrisi and valenti j math phys 32 2988 2995 1991 10 1063 1 529042 in this paper the partial preliminary group classification of a class of nonlinear wave equations was carried out via the classification of one dimensional lie symmetry extensions related to a fixed finite dimensional subalgebra of the infinite dimensional equivalence algebra of the class under consideration in the present paper we implement the complete group classification of the same class up to both usual and general point equivalence using the algebraic method of group classification this includes the complete preliminary group classification of the class and finding those lie symmetry extensions which are not associated with subalgebras of the equivalence algebra the complete preliminary group classification is based on listing all inequivalent subalgebras of the whole infinite dimensi

effective elastic properties of solids with defects of irregular shapes pores and defects in real materials often have very irregular shapes thus micromechanical modeling based on the analytical solutions of elasticity becomes inapplicable the objective of this paper is to present a computational procedure to calculate the contribution of the irregularly shaped defects into the effective moduli of two dimensional elastic solids in this procedure the cavity compliance tensor is constructed numerically for an individual defect and then used in the elastic potential based approach to predict the effective moduli of porous solids two computational methods are used in this paper to calculate the components of a cavity compliance tensor finite element analysis and numerical conformal mapping application of this procedure to the regular hole shapes produces results that are in good correspondence with analytical predictions

lie group theory and analytical solutions for the axially accelerating string problem abstract transverse vibrations of a string moving with time dependent velocity v t have been investigated analytical solutions of the problem are found using the systematic approach of lie group theory group classification with respect to the arbitrary velocity function has been performed using a newly developed technique of equivalence transformations from the symmetries of the partial differential equation the method for deriving exact solutions for the arbitrary velocity case is shown special cases of interest such as constant velocity constant acceleration harmonically varying velocity and exponentially decaying velocity are investigated in detail finally for a simply supported strip approximate solutions are presented for the exponentially decaying and harmonically varying cases

group classification of nonlinear wave equations we perform complete group classification of the general class of quasilinear wave equations in two variables this class may be seen as a generalization of the nonlinear d alembert liouville sin sinh gordon and tzitzeica equations we derive a number of new genuinely nonlinear invariant models with high symmetry properties in particular we obtain four classes of nonlinear wave equations that admit five dimensional invariance groups

elastic fields generated by inhomogeneities far field asymptotics its shape dependence and relation to the effective elastic properties we discuss connections between the effective elastic properties of a solid with inhomogeneities and the far field asymptotics of the elastic fields generated by them we focus on the dependence of the far field asymptotics on the inhomogeneity shape this shape dependence in the inhomogeneity problem is in contrast with shape independence of the far field in the eigenstrain problem for the latter the far field applies to inclusions of any shape we show that the external fields in the eigenstrain and the inhomogeneity problems are interrelated by the same tensor that characterizes the compliance contribution of an inhomogeneity

accuracy of the replacement relations for materials with non ellipsoidal inhomogeneities abstract in this paper we focus on replacement relation that links the property contribution tensors of inhomogeneities having the same shape but different elastic properties we check the possibility to apply the relations originally derived for ellipsoidal inhomogeneities sevostianov kachanov 2007 to ones of non ellipsoidal shape we discuss inhomogeneities of superspherical shape described by equation x 2 p y 2 p z 2 p 1 and show that the replacement relations can be used in the rank of convex shapes p 0 5 while for concave shapes the error is significant in practical applications it means that for materials with convex inhomogeneities results obtained for effective elastic constants of a porous material can be used to approximately evaluate effective properties of a composite of the same morphology

hodograph type transformations abstract we consider second order evolution equations of the form u t f 1 u u x u xx f 2 u u x and third order of the form u t f 1 u u x u xxx f 2 u u x u xx for each of these equations we construct point transformations which relate them with an equation of the same form these mappings have the property that one of the old independent variable depends on the new dependent variable this property leads us to hodograph type transformations in most of the results presented both the hodograph type transformation and the relating equations contain arbitrary functions and or arbitrary parameters certain choices of these functions and parameters make one of the two relating equations linear or integrable or a well known equation for the second order evolution equations we construct hodograph type transformations which connect them with a class of linear equations which are not of the same form

effective elastic properties of solids with two dimensional inclusions of irregular shapes abstract a computational procedure to calculate the contribution of irregularly shaped inclusions into the effective moduli of two dimensional elastic solids is proposed this procedure is based on the analysis of a representative volume element subjected to a prescribed macrostress for each type of inclusion the compliance contribution tensor is constructed using a combination of kolosov muskhelishvili complex variable technique and numerical conformal mapping application of this procedure to regularly shaped inhomogeneities produces results that are in good correspondence with analytical predictions the effective properties are first derived in the approximation of non interacting inclusions then several first order micromechanical models for interacting inclusions are considered

lie symmetries and reductions of multi dimensional boundary value problems of the stefan type a new definition of lie invariance for nonlinear multi dimensional boundary value problems bvps is proposed by the generalization of known definitions to much wider classes of bvps the class of 1 3 dimensional nonlinear bvps of the stefan type modeling the process of melting and evaporation of metals is studied in detail using the definition proposed the group classification problem for this class of bvps is solved and some reductions with physical meaning to bvps of lower dimensionality are made examples of how to construct exact solutions of the 1 3 dimensional nonlinear bvp with the correctly specified coefficients are presented

the influence of crack shape on the effective elasticity of fractured rocks a circle is the basic fracture shape adopted by conventional effective media theories to describe the overall elasticity of cracked solids fractures in rocks do not resemble circles so it is important to find out to what extent the available theoretical results apply to realistic fracture shapes to address this issue we conduct 3d numerical experiments on the so called digital rocks containing irregular cracks that might be partially closed and might intersect each other despite profound deviations of our fracture geometries from circles we find that basic theoretical results originally developed for penny shaped cracks remain valid for arbitrary fracture shapes based on a series of finite element computations we show that as far as the effective elasticity is concerned flat fractures with random in plane irregularities are represented accurately by circular ones we also show that approximate effective elliptical orthotropy established for multiple sets of dry penny shaped cracks embedded in is

reduction of balance laws to conservation laws by means of equivalence transformations a class of partial differential equations a conservation law and two balance laws with three independent variables and involving six arbitrary continuously differentiable functions is considered in the framework of equivalence transformations these are point transformations of differential equations involving arbitrary elements and live in an augmented space of independent dependent and additional variables representing values taken by the arbitrary elements projecting the admitted symmetries into the space of independent and dependent variables we determine some finite transformations mapping the system of balance laws to an equivalent one with the same differential structure but involving different arbitrary elements in particular we are interested in finding an equivalent autonomous system of conservation laws it is shown how the results apply to some physical problems

preliminary group classification for the nonlinear wave equation utt f x u uxx g x u abstract a classification is given for the nonlinear wave equation u t t f x u u x x g x u admitting an extension by one dimension of the principal lie algebra of the equation under consideration the paper is one of the few applications of an algebraic approach to the problem of group classification the method of preliminary group classification a number of new interesting nonlinear invariant models which have nontrivial invariance algebras are obtained the result of the work is a wide class of equations summarized in table form

a group analysis via weak equivalence transformations for a model of tumour encapsulation a symmetry reduction of a pdes system describing the expansive growth of a benign tumour is obtained via a group analysis approach the presence in the model of three arbitrary functions suggests the use of lie symmetries by using the weak equivalence transformations an invariant classification is given which allows us to reduce the initial pdes system to an odes system numerical simulations show a realistic enough description of the physical process

homomorphisms and derivations in proper jcq triples we investigate homomorphisms in proper jcq triples and derivations on proper jcq triples associated with the 3 variable jensen functional equation begin array rcl 2f left frac x y z 2 right f x f y f z end array which was introduced and investigated by park cho and han we moreover prove the hyers ulam rassias stability of homomorphisms in proper jcq triples and of derivations on proper jcq triples this is applied to investigate isomorphisms between proper jcq triples

on computation of the compliance and stiffness contribution tensors of non ellipsoidal inhomogeneities we discuss computation of compliance stiffness contribution tensors of an inhomogeneity of non ellipsoidal shape and the difficulties that may be encountered in this context these issues are illustrated on the example of one specific shape factor concavity convexity of the inhomogeneity shape it is found in particular that the effect of the concavity factor depends on the specific constraint imposed if the inhomogeneity volume is kept constant then its compliance contribution rapidly increases with increasing concavity on the computational side it leads to difficulties related to unusually high requirements to the accuracy of the computed volume averages quantities if on the other hand the characteristic dimensions for example the distance between the farthest points are kept constant then the dependence of the compliance contribution on the concavity factor is almost linear

group invariant solutions and optimal systems for multidimensional hydrodynamics the group properties of the three dimensional 3 d one temperature hydrodynamic equations including nonlinear conduction and a thermal source are presented a subgroup corresponding to axisymmetric geometry is chosen and the details of the construction of the one and two dimensional optimal systems are shown the two dimensional optimal system is used to generate 23 intrinsically different reductions of the 2 d partial differential equations to ordinary differential equations these ordinary differential equations can be solved to provide analytic solutions to the original partial differential equations two example analytic solutions are presented a 2 d axisymmetric flow with a p2 asymmetry and a 3 d spiraling flow

approximate homomorphisms on jb triples abstract it is shown that for an approximate homomorphism f j b of a jb triple j into a jb triple b there exists a unique homomorphism h j b near the approximate homomorphism