on generalized variational inequalities involving relaxed lipschitz and relaxed monotone operators abstract we consider the solvability based on iterative algorithms of the generalized variational inequality gvi problems involving the relaxed lipschitz and relaxed monotone operators

fractional calculus and continuous time finance ii the waiting time distribution we complement the theory of tick by tick dynamics of financial markets based on a continuous time random walk ctrw model recently proposed by scalas et al 4 and we point out its consistency with the behaviour observed in the waiting time distribution for bund future prices traded at liffe london

generalized strongly nonlinear quasivariational inequalities abstract in this paper we prove an existence theorem of solutions and develop the algorithms of approximating solutions for a generalized strongly nonlinear variational inequality and a generalized strongly nonlinear complementarity problem an algorithm for finding the approximate solution of generalized strongly nonlinear quasivariational inequalities and generalized strongly nonlinear quasicomplementarity problems is also given as special cases these results include the corresponding results of fang and peterson noor siddiqi and ansari and ding

auxiliary principle and iterative algorithms for generalized set valued strongly nonlinear mixed variational like inequalities in this paper we extend the auxiliary principle technique to study a class of generalized set valued strongly nonlinear mixed variational like inequalities we prove the existence of a solution of the auxiliary problem for the generalized set valued strongly nonlinear mixed variational like inequalities construct the iterative algorithm for the generalized set valued strongly nonlinear mixed variational like inequalities and show the existence of a solution of the generalized set valued strongly nonlinear mixed variational like inequality by using the auxiliary principle technique we also prove the convergence of iterative sequences generated by the algorithm

beyond the poisson renewal process a tutorial survey after sketching the basic principles of renewal theory and recalling the classical poisson process we discuss two renewal processes characterized by waiting time laws with the same power asymptotics defined by special functions of mittag leffler and of wright type we compare these three processes with each other

perturbed proximal point algorithms for generalized quasivariational inclusions abstract in this paper we study a class of generalized quasivariational inclusions by using the properties of the resolvent operator associated with a maximal monotone mapping in hilbert space we have established an existence theorem of solutions for generalized quasivariational inclusions suggesting a new iterative algorithm and a perturbed proximal point algorithm for finding approximate solutions which strongly converge to the exact solution of the generalized quasivariational inclusions as special cases some known results in this field are also discussed

towards a statistical theory of texture evolution in polycrystals most technologically useful materials possess polycrystalline microstructures composed of a large number of small monocrystalline grains separated by grain boundaries the energetics and connectivity of the grain boundary network play a crucial role in determining the properties of a material across a wide range of scales a central problem in materials science is to develop technologies capable of producing an arrangement of grains a texture that provides for a desired set of material properties one of the most challenging aspects of this problem is to understand the role of topological reconfigurations during coarsening here we propose an upscaling procedure suitable for large complex systems the procedure is based on numerical experimentation combined with stochastic tools and consists of large scale numerical simulations of a system at a microscopic level statistical analysis of the microscopic data and formulation of the model based on stochastic characteristics predicted by the statistical analysis this approach promises to be valuable in establishing the effective model of microstructural evolution in realistic two and three dimensional systems to test ideas we use our upscaling procedure to study the mesoscopic behavior of a reduced one dimensional network of grain boundaries despite the simplicity of its formulation this model exhibits highly nontrivial behavior characterized by growth and disappearance of grain boundaries and develops probability distributions similar to those observed in higher dimensional simulations here we focus on the grain deletion events which are common to all coarsening systems

fractional calculus and continuous time finance in this paper we present a rather general phenomenological theory of tick by tick dynamics in financial markets many well known aspects such as the levy scaling form follow as particular cases of the theory the theory fully takes into account the non markovian and non local character of financial time series predictions on the long time behaviour of the waiting time probability density are presented finally a general scaling form is given based on the solution of the fractional diffusion equation

algorithm of solutions for mixed implicit quasi variational inequalities with fuzzy mappings abstract in this paper by applying the auxiliary variational principle technique some existence theorems of solutions for a class of mixed implicit quasi variational inequalities with fuzzy mappings are proved in hilbert spaces a novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed the convergence criteria is also given as special cases of these results the open problem put forward by noor is answered positively our results are new and generalize a number of known results to mixed implicity quasi variational inequalities with fuzzy mappings

algorithms of solutions for completely generalized mixed implicit quasi variational inclusions in this paper by applying resolvent operator technique an existence theorem of solutions for a class of completely generalized mixed implicit quasi variational inclusions involving relaxed lipschitz generalized pseudo contractive and relaxed monotone set valued mappings is proved in hilbert spaces a novel and innovative iterative algorithm to compute approximate solutions is suggested and analyzed the convergence criteria is also given these results of existence algorithm and convergence are new and unify and generalize some corresponding results in recent literatures

wright functions as scale invariant solutions of the diffusion wave equation the time fractional diffusion wave equation is obtained from the classical diffusion or wave equation by replacing the first or second order time derivative by a fractional derivative of order 0 2 using the similarity method and the method of the laplace transform it is shown that the scale invariant solutions of the mixed problem of signalling type for the time fractional diffusion wave equation are given in terms of the wright function in the case 0 1 and in terms of the generalized wright function in the case 1 2 the reduced equation for the scale invariant solutions is given in terms of the caputo type modification of the

compact matrix pseudogroups the compact matrix pseudogroup is a non commutative compact space endowed with a group structure the precise definition is given and a number of examples is presented among them we have compact group of matrices duals of discrete groups and twisted deformed su n groups the representation theory is developed it turns out that the tensor product of representations depends essentially on their order the existence and the uniqueness of the haar measure is proved and the orthonormality relations for matrix elements of irreducible representations are derived the form of these relations differs from that in the group case this is due to the fact that the haar measure on pseudogroups is not central in general the corresponding modular properties are discussed the haar measures on the twistedsu 2 group and on the finite matrix pseudogroup are found

set valued resolvent equations and mixed variational inequalities in this paper we introduce and study a new class of variational inequalities which is called the generalized set valued mixed variational inequality the resolvent operator technique is used to establish the equivalence among generalized set valued variational inequalities fixed point problems and the generalized set valued resolvent equations this equivalence is used to study the existence of a solution of set valued variational inequalities and to suggest a number of iterative algorithms for solving variational inequalities and related optimization problems the results proved in this paper represent a significant refinement and improvement of the previously known results in this area

on mittag leffler type functions in fractional evolution processes abstract we review a variety of fractional evolution processes so defined being governed by equations of fractional order whose solutions turn out to be related to mittag leffler type functions the chosen equations are the simplest of the fractional calculus and include the abel integral equations of the second kind which are relevant in typical inverse problems and the fractional differential equations which govern generalized relaxation and oscillation phenomena

error estimation and step size control for delay differential equation solvers based on continuously embedded runge kutta sarafyan methods abstract this paper considers the use of continuously embedded runge kutta sarafyan methods for the solution of delay differential equations it discusses simple ways to improve the error estimation and step size selection strategies for delay solvers based on sarafyan methods numerical results are given which demonstrate the manner in which these estimates improve the accuracy of the solvers in a natural way

generalized implicit quasivariational inclusions with fuzzy set valued mappings abstract in this paper we introduce and study a new class of generalized implicit quasivariational inclusions with fuzzy set valued mappings a existence theorem of solutions is proved without compactness assumptions a new iterative algorithm is suggested and analyzed the convergence of iterative sequence generated by the new algorithm is also given as special cases some known results are also discussed

time changed geometric fractional brownian motion and option pricing with transaction costs abstract this paper deals with the problem of discrete time option pricing by a fractional subdiffusive black scholes model the price of the underlying stock follows a time changed geometric fractional brownian motion by a mean self financing delta hedging argument the pricing formula for the european call option in discrete time setting is obtained

asymptotic solutions of decoupled continuous time random walks with superheavy tailed waiting time and heavy tailed jump length distributions we study the long time behavior of decoupled continuous time random walks characterized by superheavy tailed distributions of waiting times and symmetric heavy tailed distributions of jump lengths our main quantity of interest is the limiting probability density of the position of the walker multiplied by a scaling function of time we show that the probability density of the scaled walker position converges in the long time limit to a nondegenerate one only if the scaling function behaves in a certain way this function as well as the limiting probability density are determined in explicit form also we express the limiting probability density which has heavy tails in terms of the fox h function and find its behavior for small and large distances

general strongly nonlinear variational inequalities abstract in this paper we develop iterative algorithms for finding approximate solutions for new classes of variational and quasivariational inequalities which include as a special case some known results in this field it is shown that the solutions of the iterative schemes converge to the exact solutions

diffusion entropy technique applied to the study of the market activity abstract the present work briefly summarizes the results obtained in palatella et al eur phys j b 38 2004 671 using the diffusion entropy technique and adds some new results regarding the dow jones index time series we show that time distances between peaks of volatility or activity are distributed following an asymptotic power law which ultimately recovers an exponential behavior we discuss these results in comparison with the tarch model the ornstein uhlenbeck stochastic volatility model and a multi agent model we conclude that both arch and stochastic volatility models better describe the observed experimental evidences

generalized multivalued quasi variational inequalities in this paper we introduce and study a new class of variational inequalities known as generalized multivalued quasi variational inequalities this class is the most general and unifying one using essentially the projection technique we establish the equivalence between this class and the implicit wiener hopf equations this equivalence is used to suggest a number of iterative algorithms for solving the generalized multivalued quasi variational inequalities the convergence analysis of these algorithms is also studied the results proved in this paper represent a significant improvement and refinement of the previously known results in this area

resolvent operator technique for generalized implicit variational like inclusion in banach space a new class of g accretive mappings is introduced and studied in banach space by using the properties of g accretive mappings the concept of resolvent operators associated with the classical m accretive operators is extended and an iterative algorithm for a new class of generalized implicit variational like inclusion involving g accretive mappings and its convergence results are established in banach space

fractional master equations and fractal time random walks fractional master equations containing fractional time derivatives of order 0 ensuremath le 1 are introduced on the basis of a recent classification of time generators in ergodic theory it is shown that fractional master equations are contained as a special case within the traditional theory of continuous time random walks the corresponding waiting time density ensuremath psi t is obtained exactly as ensuremath psi t mathit t mathrm ensuremath omega mathrm ensuremath 1 c mathit e mathrm ensuremath omega mathrm ensuremath omega mathit t mathrm ensuremath omega c where mathit e mathrm ensuremath omega mathrm ensuremath omega x is the generalized mittag leffler function this waiting time distribution is singular both in the long time as well as in the short time limit

a new class of generalized nonlinear implicit quasivariational inclusions with fuzzy mappings in this paper we introduce and study a new class of generalized nonlinear implicit quasivariational inclusions with fuzzy mappings an existence theorem of solutions is proved without compactness assumptions a new iterative algorithm is suggested and analysed the convergence of iterative sequences generated by the new algorithm are also given as special cases some known results are also discussed

some aspects of variational inequalities abstract in this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence uniqueness computational properties various generalizations sensitivity analysis and their applications we also propose some open problems with sufficient information and references so that someone may attempt solution s in his her area of special interest we also include some new results which we have recently obtained

multifractal features of financial markets abstract we study the tick dynamical behavior of three assets in financial markets the kospi the won dollar and yen dollar exchange rates using the rescaled range r s analysis the multifractal hurst exponents with long run memory effect can be obtained from those assets and we discuss whether there exists the crossover or not for the hurst exponents at characteristic time scales particularly we find that the probability distribution of returns approaches to a lorentz distribution different from gaussian properties

iterative algorithms for finding approximate solutions for general strongly nonlinear variational inequalities abstract in this paper we study iterative algorithms for finding approximate solutions for general strongly nonlinear variational inequalities which include as a special case some known results in this field our results are the extension and improvements of the results of noor j math anal appl 158 1991 488 455 and siddiqi and ansari j math anal appl 166 1992 386 392

models of anomalous diffusion the subdiffusive case abstract the paper discusses a model for anomalous diffusion processes their one point probability density functions p d f are exact solutions of fractional diffusion equations the model reflects the asymptotic behavior of a jump anomalous random walk process with random jump sizes and random inter jump time intervals with infinite means and variances which do not satisfy the law of large numbers in the case when these intervals have a fractional exponential p d f the fractional komogorov feller equation for the corresponding anomalous diffusion is provided and methods of finding its solutions are discussed finally some statistical properties of solutions of the related langevin equation are studied the subdiffusive case is explored in detail the emphasis is on a rigorous presentation which however would be accessible to the physical sciences audience

maximum norm error analysis of difference schemes for fractional diffusion equations in this study we present several numerical approximation methods for solving the fractional diffusion equations with the riesz space fractional derivative based on the fractional centered difference approximation to the riesz fractional derivative an explicit and an implicit finite difference schemes for solving the space fractional diffusion equations are obtained the stability and global convergence of these two schemes in the maximum norm are analyzed rigorously the convergence order is o h 2 where is the temporal grid size and h is spatial grid size respectively furthermore a numerical scheme for the one dimensional multi term time space fractional diffusion equations is obtained the unconditionally stability and convergence of the scheme in maximum norm are established the convergence orders are 2 in the temporal direction and two in the spatial direction where is the maximum time fractional derivative orders in the equation in addition the extension to the two dimensional case is also discussed finally several numerical examples are provided to show the effectiveness and accuracy of our methods

iterative methods for generalized nonlinear variational inequalities abstract in this paper we establish the equivalence between the generalized nonlinear variational inequalities and the generalized wiener hopf equations this equivalence is used to suggest and analyze a number of iterative algorithms for solving generalized variational inequalities we also discuss the convergence analysis of the proposed algorithms as a special case we obtain various known results from our results

finite time stability for a class of fractional order fuzzy neural networks with proportional delay abstract in this paper we consider a class of fuzzy neural networks of fractional order and proportional time delay we derive sufficient conditions for the finite time stability of the considered system using finite time stability theory and fractional calculus and employing differential inequality techniques the results are obtained in terms of simple algebraic inequalities which can be easily verified in the end we give a numerical example to validate the analytical findings

on the generalized implicit quasivariational inequalities abstract in the present paper we introduce and study a new class of generalized nonlinear implicit quasivariational inequalities for set valued mappings and construct some new iterative algorithms we prove the existence of solutions for this class of generalized nonlinear implicit quasivariational inequalities for set valued mappings without compactness and the convergence of iterative sequences generated by the algorithms we also study a new perturbed iterative algorithm for solving a class of general strongly nonlinear quasivariational inequalities