algorithms for a multi level network optimization problem in this paper we work on a multi level network optimization problem that integrates into the same model important aspects of i discrete facility location ii topological network design and iii network dimensioning potential applications for the model are discussed stressing its growing importance the multi level network optimization problem treated is defined and a mathematical programming formulation is presented we make use of a branch and bound algorithm based on lagrangean relaxation lower bounds to introduce some new powerful auxiliary algorithms to exactly solve the problem we conduct a set of computational experiments that indicate the quality of the proposed approach

facets and algorithms for capacitated lot sizing the dynamic economic lot sizing model which lies at the core of numerous production planning applications is one of the most highly studied models in all of operations research and yet capacitated multi item versions of this problem remain computationally elusive we study the polyhedral structure of an integer programming formulation of a single item capacitated version of this problem and use these results to develop solution methods for multi item applications in particular we introduce a set of valid inequalities for the problem and show that they define facets of the underlying integer programming polyhedron computational results on several single and multiple product examples show that these inequalities can be used quite effectively to develop an efficient cutting plane branch and bound procedure moreover our results show that in many instances adding certain of these inequalities a priori to the problem formulation and avoiding the generation of cutting planes can be equally effective

on the migrativity of triangular subnorms the a t migrative triangular subnorms where t stands for the three prototype triangular norms namely the product the lukasiewicz t norm and the minimum are investigated in detail the paper gives necessary and sufficient conditions under which a triangular subnorm with a continuous additive generator is a t migrative with respect to any of the three prototype triangular norms

on the structure of special classes of uninorms in this paper the concept of the reidemeister closure condition is adopted in order to characterize associativity of uninorms with a special attention paid to the class of representable uninorms thus conditions replacing the associativity requirement for such uninorms are given further the attention is focused on the uninorms where the underlying t norm and t conorm are idempotent or induce an involutive negator based on the aforementioned results the structure of these classes of uninorms is fully described

a new lagrangean relaxation approach for the hop constrained minimum spanning tree problem abstract we present a new lagrangean relaxation for the hop constrained minimum spanning tree problem hmst the hmst is np hard and models the design of centralized telecommunication networks with quality of service constraints the linear programming lp relaxation of a hop indexed flow based model recently presented in the literature see gouveia l 1998 using variable redefinition for computing lower bounds for minimum spanning and steiner trees with hop constraints informs journal on computing 10 180 188 produces very tight bounds but has the disadvantage of being very time consuming especially for dense graphs in this paper we present a new lagrangean relaxation which is derived from the hop indexed flow based formulation our computational results indicate that the lower bounds given by the new relaxation dominate the lower bounds given by previous lagrangean relaxations our results also show that for dense graphs the new lagrangean relaxation proves to be a reasonable alternative to solving the lp relaxation of the hop indexed model

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

a fractional landweber method for solving backward time fractional diffusion problem abstract in this paper we propose a fractional landweber regularization method for solving a backward time fractional diffusion problem choice rules for both a priori and a posterior regularization parameters are discussed in deriving the corresponding convergence proofs for the backward problem for verification on the theoretical estimates several numerical examples are constructed and compared with some existing works

enhanced formulations and branch and cut for the two level network design problem with transition facilities abstract we consider a new combinatorial optimization problem that combines network design and facility location aspects given a graph with two types of customers and two technologies that can be installed on the edges the objective is to find a minimum cost subtree connecting all customers while the primary customers are served by a primary subtree that is embedded into the secondary subtree in addition besides fixed link installation costs facility opening costs associated to each node where primary and secondary subtree connect have to be paid the problem is called the two level network design problem with transition facilities tlndf we first model the problem on an extended graph where an additional set of arcs corresponds to the installation of node facilities and propose a cut set based model for the tlndf that is defined on this extended graph we present several theoretical results relating families of cut set inequalities on the extended graph with subfamilies of cut set inequalities on the original graph we then show how a standard multi commodity flow model defined on the original graph can be strengthened using disaggregation by technology we prove that the disaggregated compact formulation on the original graph provides the same lower bound as the cut set formulation on the extended graph we develop a branch and cut algorithm for solving the tlndf the performance of this algorithm is improved by separating subfamilies of cut set inequalities on the original graph our computational study confirms the efficiency and applicability of the new approach

network design problem with relays a genetic algorithm with a path based crossover and a set covering formulation abstract the network design problem with relays arises in telecommunications and distribution systems where the payload must be reprocessed at intermediate stations called relays on the route from its origin to its destination in fiber optic networks for example optical signals may be regenerated several times to overcome signal degradation because of attenuation and other factors given a network and a set of commodities the network design problem with relays involves selecting network edges determining a route for each commodity and locating relays to minimize the network design cost this paper presents a new formulation to the problem based on set covering constraints the new formulation is used to design a genetic algorithm with a specialized crossover mutation operator which generates a feasible path for each commodity and the locations of relays on these paths are determined by solving the corresponding set covering problem computational experiments show that the proposed approach can outperform other approaches particularly on large size problems

multicommodity flow models for spanning trees with hop constraints abstract in this paper we compare the linear programming relaxations of undirected and directed multicommodity flow formulations for the terminal layout problem with hop constraints hop constraints limit the number of hops links between the computer center and any terminal in the network these constraints model delay constraints since a smaller number of hops decreases the maximum delay transmission time in the network they also model reliability constraints because with a smaller number of hops there is a lower route loss probability hop constraints are easily modelled with the variables involved in multicommodity flow formulations we give some empirical evidence showing that the linear programming relaxation of such formulations give sharp lower bounds for this hop constrained network design problem on the other hand these formulations lead to very large linear programming models therefore for bounding purposes we also derive several lagrangean based procedures from a directed multicommodity flow formulation and present some computational results taken from a set of instances with up to 40 nodes

on the bounded hop mst problem on random euclidean instances the d dimh hops mst problem is defined as follows given a set s of points in the d dimensional euclidean space and ses find a minimum cost spanning tree for s rooted at s with height at most h we investigate the problem for any constant h and d 0 we prove the first nontrivial lower bound on the solution cost for almost all euclidean instances i e the lower bound holds with high probability then we introduce an easy to implement fast divide et impera heuristic and we prove that its solution cost matches the lower bound

initial value boundary value problems for fractional diffusion wave equations and applications to some inverse problems abstract we consider initial value boundary value problems for fractional diffusion wave equation t u x t l u x t where 0 2 where l is a symmetric uniformly elliptic operator with t independent smooth coefficients first we establish the unique existence of the weak solution and the asymptotic behavior as the time t goes to and the proofs are based on the eigenfunction expansions second for 0 1 we apply the eigenfunction expansions and prove i stability in the backward problem in time ii the uniqueness in determining an initial value and iii the uniqueness of solution by the decay rate as t iv stability in an inverse source problem of determining t dependent factor in the source by observation at one point over 0 t

a dynamic programming algorithm for the local access telecommunication network expansion problem abstract in this paper we consider the local access telecommunication network expansion problem in which growing demand can be satisfied by expanding cable capacities and or installing concentrators in the network the problem is known to be np hard we prove that the problem is weakly np hard and present a pseudo polynomial dynamic programming algorithm for the problem with time complexity o nb 2 and storage requirements o nb where n refers to the size of the network and b to an upper bound on concentrator capacity the cost structure in the network is assumed to be decomposable but may be non convex non concave and node and edge dependent otherwise this allows for incorporation of many aspects occurring in practical planning problems computational results indicate that the algorithm is very efficient and can solve medium to large scale problems to optimality within fractions of seconds to minutes

reducing the hierarchical network design problem abstract the hierarchical network design problem hndp can be seen as a minimum spanning tree problem involving two weight functions it is shown that the hndp is a special case of the directed steiner tree problem theorems are given to obtain optimal arcs that are used in a lagrangean relaxation of the linear programming model reduction tests reducing the size of the problem graph and or eliminating variables from this program are specialized and developed for the hndp the presented techniques are illustrated on example problems from the literature and computational results for the reduction tests are given

fast heuristics for the steiner tree problem with revenues budget and hop constraints this article describes and compares three heuristics for a variant of the steiner tree problem with revenues which includes budget and hop constraints first a greedy method which obtains good approximations in short computational times is proposed this initial solution is then improved by means of a destroy and repair method or a tabu search algorithm computational results compare the three methods in terms of accuracy and speed

convex combinations of uninorms and triangular subnorms abstract the problem whether a non trivial convex combination of two continuous triangular norms can be a t norm was extensively studied in the last decades bringing the negative answer in all examined special cases on the other hand in the field of non continuous t norms including left continuous t norms several examples were found including mainly a convex combination of an migrative t norm and the drastic product t norm or a convex combination of ordinal sums of product related t subnorms recently convex combinations of uninorms were discussed in 18 since any uninorm with the neutral element e 0 1 restricted to 0 e 2 is isomorphic to a t norm this investigation extends the original problem of a convex combination of t norms given by alsina frank and schweizer in this work we will study convex combinations of uninorms further covering uninorms with continuous underlying functions uninorms with different neutral elements and representable uninorms we will also show that convex combinations of triangular subnorms play a major role in this investigation

a dual ascent procedure for large scale uncapacitated network design the fixed charge network design problem arises in a variety of problem contexts including transportation communication and production scheduling we develop a family of dual ascent algorithms for this problem this approach generalizes known ascent procedures for solving shortest path plant location steiner network and directed spanning tree problems our computational results for several classes of test problems with up to 500 integer and 1 98 million continuous variables and constraints show that the dual ascent procedure and an associated drop add heuristic generate solutions that in almost all cases are guaranteed to be within 1 to 4 of optimality moreover the procedure requires no more than 150 seconds on an ibm 3083 computer the test problems correspond to dense and sparse networks including some models that arise in freight transport

some results on the convex combination of uninorms abstract it is well known that under some conditions a convex combination of the drastic product t d and the strict triangular norm is still a triangular norm uninorms as a special kind of generalization of both triangular norms and triangular conorms have been widely used in fuzzy set theory in this paper the convex combination of uninorms is studied some properties of the class of uninorms with the underlying triangular norm t d are presented firstly then the convex combination of this class of uninorms is discussed and it is shown that only in some trivial cases the convex combination is still a uninorm

generalizing the migrativity of continuous t norms this paper generalizes the migrativity of triangular norms t norms for short precisely we find those continuous t norms t which satisfy t l 1x l 2y email protected 3t x y where l email protected 0 1 i 1 2 3 are given it is worth pointing out that this paper provides a new characterization of the product t norm

lot size models with back logging strong reformulations and cutting planes we examine mixed integer programming reformulations of the uncapacitated lot sizing problem with backlogging first we consider the effect of using a standard reformulation technique for fixed charge network flow problems which involves the introduction of new variables leading to a known plant location reformulation and a shortest path reformulation each of these reformulations is strong in the sense that its linear programming relaxation solves the lot sizing problem secondly we attempt to treat the problem in the space of the original variables we give an implicit description of the convex hull of solutions and show how the problem of finding a violated cutting plane can be solved as a linear program we also describe a family of strong valid inequalities which can be generated rapidly by a heuristic and which have proved effective in a cut generation algorithm the efficiency of both the shortest path formulation and the cutting plane algorithm have been tested on a series of multi item capacitated lot sizing problems with backlogging near optimal solutions have been found to problems with 8 periods and up to 100 times

some observations about the convex combination of continuous triangular norms abstract the convex combination of continuous triangular norms is discussed let c 1 be the class of all nilpotent t norms c 2 be the class of all strict t norms and c 3 be the class of all continuous non archimedean t norms it is shown that for any t norms t 1 t 2 which are taken from two different classes of c i i 1 2 3 the convex combination t 1 t 1 t 2 is not associative for any 0 1 the case of two continuous non archimedean t norms is also investigated by our results the problem of whether or not two continuous t norms can be combined with each other is reduced to that of whether two strict or two nilpotent t norms can be combined with each other or not

data regularization for a backward time fractional diffusion problem we investigate a backward problem for a time fractional diffusion process in inhomogeneous media which aims to determine the initial status of some physical field such as temperature for slow diffusion from its present measurement data this problem is well known to be ill posed due to the rapid decay of the forward process by using the eigenfunction expansion we construct a new regularizing scheme with an explicit solution for the noisy input data with the number of truncation terms as a regularizing parameter the convergence rate depending on the choice of strategy of the regularizing parameter is given based on the asymptotic behavior of the mittag leffler function numerical implementations are presented to show the validity of the proposed scheme for several models

heuristics lps and trees on trees network design analyses we study a class of models known as overlay optimization problems composed of base and overlay subproblems linked by the requirement that the overlay solution be contained in the base solution in some telecommunication settings a feasible base solution is a spanning tree and the overlay solution is an embedded steiner tree or path for the general overlay optimization problem we describe a composite heuristic solution procedure that selects the better of two feasible solutions obtained by independently solving the base and the overlay subproblems and establish worst case performance guarantees as a function of the worst case bounds for the subproblems for the composite heuristic as well as an lp relaxation of the model for certain special cases both the heuristic and the lp relaxation have a worst case bound of 4 3 we extend this analysis to multiple overlays on the same base solution producing the first known worst case bounds approximately proportional to the square root of the number of commodities for the uncapacitated multicommodity network design problem in a companion paper we develop heuristic performance guarantees for various new multi tier survivable network design models that incorporate both multiple facility types and differential node connectivity levels

a dual based algorithm for multi level network design given an undirected network with l possible facility types for each edge and a partition of the nodes into l levels or grades the multi level network design mlnd problem seeks a fixed cost minimizing design that spans all the nodes and connects the nodes at each level by facilities of the corresponding or higher grade this problem generalizes the well known steiner network problem and the hierarchical network design problem and has applications in telecommunication transportation and electric power distribution network design in a companion paper we studied alternative model formulations for a two level version of this problem and analyzed the worst case performance of several heuristics based on steiner network and spanning tree solutions this paper develops a dual based algorithm for the mlnd problem the method first performs problem preprocessing to fix certain design variables and then applies a dual ascent procedure to generate upper and lower bounds on the optimal value we report extensive computational results on large random two level test problems containing up to 500 nodes and 5 000 edges with varying cost structures the integer programming formulation of the largest of these problems has 20 000 integer variables and over 5 million constraints our tests indicate that the dual based algorithm is very effective producing solutions that are within 0 9 of optimality

convex combinations of continuous t norms with the same diagonal function abstract the problem of whether a non trivial convex combination of two continuous t norms with the same diagonal function can be a t norm is studied it is shown that in both cases of two nilpotent and of two strict t norms a non trivial convex combination of t norms with common diagonal function is associative only if the two t norms involved coincide for general continuous t norms a similar result follows an example of a convex class of non continuous t norms is also included

fundamental kernel based method for backward space time fractional diffusion problem based on kernel based approximation technique we devise in this paper an efficient and accurate numerical scheme for solving a backward space time fractional diffusion problem bstfdp the kernels used in the approximation are the fundamental solutions of the space time fractional diffusion equation expressed in terms of inverse fourier transform of mittag leffler functions the use of inverse fast fourier transform ifft technique enables an accurate and efficient evaluation of the fundamental solutions and gives a robust numerical algorithm for the solution of the bstfdp since the bstfdp is intrinsic ill posed we apply the standard tikhonov regularization technique to obtain a stable solution to the highly ill conditioned resultant system of linear equations for choosing optimal regularization parameter we combine the regularization technique with the generalized cross validation gcv method for an optimal placement of the source points in the use of fundamental solutions meanwhile the proposed algorithm also speeds up the previous method given in dou and hon 2014 several numerical examples are constructed to verify the accuracy and efficiency of the proposed method

minimal spanning trees with a constraint on the number of leaves abstract in this paper we discuss minimal spanning trees with a constraint on the number of leaves tree topologies appear when designing centralized terminal networks the constraint on the number of leaves arises because the software and hardware associated to each terminal differs accordingly with its position in the tree usually the software and hardware associated to a degree 1 terminal is cheaper than the software and hardware used in the remaining terminals because for any intermediate terminal j one needs to check if the arrival message is destined to that node or to any other node located after node j as a consequence that particular terminal needs software and hardware for message routing on the other hand such equipment is not needed in degree 1 terminals assuming that the hardware and software for message routing in the nodes is already available the above discussion motivates a constraint stating that a tree solution has to contain exactly a certain number of degree 1 terminals we present two different formulations for this problem and some lower bounding schemes derived from them we discuss a simple local exchange heuristic and present computational results taken from a set of complete graphs with up to 40 nodes integer linear programming formulations for related problems are also discussed at the end

a branch and cut algorithm for the hierarchical network design problem the hierarchical network design problem consists of locating a minimum cost bi level network on a graph the higher level sub network is a path visiting two or more nodes the lower level sub network is a forest connecting the remaining nodes to the path we optimally solve the problem using an ad hoc branch and cut procedure relaxed versions of a base model are solved using an optimization package and if binary variables have fractional values or if some of the relaxed constraints are violated in the solution cutting planes are added once no more cuts can be added branch and bound is used the method for finding valid cutting planes is presented finally we use different available test instances to compare the procedure with the best known published optimal procedure with good results in none of the instances we needed to apply branch and bound but only the cutting planes

modeling and heuristic worst case performance analysis of the two level network design problem this paper studies a multi facility network synthesis problem called the two level network design tlnd problem that arises in the topological design of hierarchical communication transportation and electric power distribution networks we are given an undirected network containing two types of nodes primary and secondary and fixed costs for installing either a primary or a secondary facility on each edge primary nodes require higher grade interconnections than secondary nodes using the more expensive primary facilities the tlnd problem seeks a minimum cost connected design that spans all the nodes and connects primary nodes via edges containing primary facilities the design can use either primary or secondary edges to connect the secondary nodes the tlnd problem generalizes the well known steiner network problem and the hierarchical network design problem in this paper we study the relationship between alternative model formulations for this problem e g directed and undirected models an

design of survivable networks with vulnerability constraints abstract we consider the network design problem with vulnerability constraints ndpvc which simultaneously addresses resilience against failures network survivability and bounds on the lengths of each communication path hop constraints solutions to the ndpvc are subgraphs containing a path of length at most h st for each commodity s t and a path of length at most h s t between s and t after at most k 1 edge failures we first show that a related and well known problem from the literature the hop constrained survivable network design problem k hsndp that addresses the same two measures produces solutions that are too conservative in the sense that they might be too expensive in practice or may even fail to provide feasible solutions we also explain that the reason for this difference is that mengerian like theorems not hold in general when considering hop constraints three graph theoretical characterizations of feasible solutions to the ndpvc are derived and used to propose integer linear programming formulations in a computational study we compare these alternatives with respect to the lower bounds obtained from the corresponding linear programming relaxations and their capability of solving instances to proven optimality in addition we show that in many cases the solutions produced by solving the ndpvc are cheaper than those obtained by the related khsndp

continuous weakly cancellative triangular subnorms i their web geometric properties abstract the paper studies web geometric properties of continuous weakly cancellative t subnorms particularly it studies the reidemeister closure condition which is known from web geometry as a visual characterization of those loops that are associative as a result the paper delimits a subset of the domain of a continuous weakly cancellative t subnorm in which the reidemeister closure condition is necessarily satisfied

characterization of continuous t norms compatible with zadeh s probability of fuzzy events in this work we study the concept of p z compatibility which holds for those t norms for which zadeh s probability of fuzzy events fulfills kolmogorov s axioms whether a probability satisfies kolmogorov s axioms or not depends almost exclusively on the t norm and dual t conorm used to define intersection and union respectively of fuzzy sets in order to better understand fuzzy probability theory we provide a complete characterization of the p z compatible continuous t norms

survivable networks linear programming relaxations and the parsimonious property we consider the survivable network design problem the problem of designing at minimum cost a network with edge connectivity requirements as special cases this problem encompasses the steiner tree problem the traveling salesman problem and thek edge connected network design problem we establish a property referred to as the parsimonious property of the linear programming lp relaxation of a classical formulation for the problem the parsimonious property has numerous consequences for example we derive various structural properties of these lp relaxations we present some algorithmic improvements and we perform tight worst case analyses of two heuristics for the survivable network design problem

associativity of triangular norms characterized by the geometry of their level sets associativity of triangular norms is an algebraic property which unlike for example their commutativity is usually understood as hardly visually interpretable this problem has been studied intensively in the last decade and as a result geometric symmetries of triangular norms with involutive level sets have been revealed the presented paper intends to introduce a different approach which gives more general results the inspiration is taken from web geometry a branch of differential geometry and its concept of reidemeister closure condition which is known to provide a geometric characterization of associativity of loops the paper shows that this concept can be adopted successfully for triangular norms so that it characterizes their associativity in a similar way moreover the offered adaptation preserves the beneficial transparency and simplicity of the reidemeister closure condition this way a visual characterization of the associativity based on the geometry of the level sets is provided for general continuous and continuous archimedean triangular norms

compact mixed integer linear programming models to the minimum weighted tree reconstruction problem the minimum weighted tree reconstruction mwtr problem consists of finding a minimum length weighted tree connecting a set of terminal nodes in such a way that the length of the path between each pair of terminal nodes is greater than or equal to a given distance between the considered pair of terminal nodes this problem has applications in several areas namely the inference of phylogenetic trees the modeling of traffic networks and the analysis of internet infrastructures in this paper we investigate the mwtr problem and we present two compact mixed integer linear programming models to solve the problem computational results using two different sets of instances one from the phylogenetic area and another from the telecommunications area show that the best of the two models is able to solve instances of the problem having up to 15 terminal nodes

a kernel based method for the approximate solution of backward parabolic problems a method for approximating the solution of self adjoint parabolic equations backwards in time is presented the technique uses the green s function of the parabolic equation to formulate the problem as a first kind fredholm integral equation and then does a regularized least squares solution of the resulting discrete system error estimates and examples are presented direct knowledge of the kernel of the differential operator is not required

modeling hop constrained and diameter constrained minimum spanning tree problems as steiner tree problems over layered graphs the hop constrained minimum spanning tree problem hmstp is an np hard problem arising in the design of centralized telecommunication networks with quality of service constraints we show that the hmstp is equivalent to a steiner tree problem stp in an appropriate layered graph we prove that the directed cut model for the stp defined in the layered graph dominates the best previously known models for the hmstp we also show that the steiner directed cuts in the extended layered graph space can be viewed as being a stronger version of some previously known hmstp cuts in the original design space moreover we show that these strengthened cuts can be combined and projected into new families of cuts including facet defining ones in the original design space we also adapt the proposed approach to the diameter constrained minimum spanning tree problem dmstp computational results with a branch and cut algorithm show that the proposed method is significantly better than previously known methods on both problems

convex combinations of nilpotent triangular norms abstract in this paper we deal with the open problem of convex combinations of continuous triangular norms stated by alsina frank and schweizer c alsina m j frank b schweizer problems on associative functions aequationes math 66 2003 128 140 problems 5 and 6 they pose a question whether a non trivial convex combination of triangular norms can ever be a triangular norm the main result of this paper gives a negative answer to the question for any pair of continuous archimedean triangular norms with different supports with the help of this result we show that a non trivial convex combination of nilpotent t norms is never a t norm the main result also gives an alternative proof to the result presented by ouyang and fang y ouyang j fang some observations about the convex combination of continuous triangular norms nonlinear anal 68 11 2008 3382 3387 theorem 3 1 in proof of the main theorem we utilize the reidmeister condition known from the web geometry

new formulations of the hop constrained minimum spanning tree problem via miller tucker zemlin constraints abstract given an undirected network with positive edge costs and a natural number p the hop constrained minimum spanning tree problem hmst is the problem of finding a spanning tree with minimum total cost such that each path starting from a specified root node has no more than p hops edges in this paper we develop new formulations for hmst the formulations are based on miller tucker zemlin mtz subtour elimination constraints mtz based liftings in the literature offered for hmst and a new set of topology enforcing constraints we also compare the proposed models with the mtz based models in the literature with respect to linear programming relaxation bounds and solution times the results indicate that the new models give considerably better bounds and solution times than their counterparts in the literature and that the new set of constraints is competitive with liftings to mtz constraints some of which are based on well known strong liftings of desrochers and laporte 1991

optimizing splitter and fiber location in a multilevel optical ftth network due to the emergence of bandwidth requiring services telecommunication operators are being compelled to renew their fix access network most of them favoring the fiber to the home ftth technology this paper focuses on the optimization of ftth deployment which is of prime importance due to the economic stakes the key design issue here is locating splitters and routing fi bers in an existing network infrastructure to which is associated a graph with given capacities on the edges no assumption is made on the structure of the graph first we propose a mixed integer formulation for this decision problem then valid inequalities and problem size reduction schemes are presented finally efficiency of solving approaches is assessed through extensive numerical tests performed on orange real life data

a non local boundary value problem method for parabolic equations backward in time abstract the ill posed parabolic equation backward in time u t a u 0 0 t t u t f subject to the constraint u 0 e with the positive self adjoint unbounded operator a and e 0 being given is regularized by the well posed non local boundary value problem u t a u 0 0 t t u 0 u t f 0 the error estimates of holder type of the regularized solutions are obtained these estimates improve the related results by mel nikova denche and bessila

optimal error bound and simplified tikhonov regularization method for a backward problem for the time fractional diffusion equation in this paper we consider a backward problem for a time fractional diffusion equation such a problem is ill posed the optimal error bound for the problem under a source condition is analyzed a simplified tikhonov regularization method is utilized to solve the problem and its convergence rates are analyzed under an a priori regularization parameter choice rule and an a posteriori regularization parameter choice rule respectively numerical examples show that the proposed regularization method is effective and stable and both parameter choice rules work well

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems

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

on the convex combination of td and continuous triangular norms the problem of when t l 1 l t d lt l 0 1 is a triangular norm where t d is the drastic product and t is a continuous triangular norm is studied it is shown that t l cannot be a triangular norm when t is nilpotent it is also shown that t l is a triangular norm if t is strict and its additive generator f satisfies f lx f x f l for all x 0 1 the cases that t t m and t is the ordinal sum of continuous archimedean summands are also discussed some left continuous t norms which can be combined with each other are given

a dual ascent approach for steiner tree problems on a directed graph the steiner tree problem on a directed graph stdg is to find a directed subtree that connects a root node to every node in a designated node setv we give a dual ascent procedure for obtaining lower bounds to the optimal solution value the ascent information is also used in a heuristic procedure for obtaining feasible solutions to the stdg computational results indicate that the two procedures are very effective in solving a class of stdg s containing up to 60 nodes and 240 directed 120 undirected arcs

designing reliable tree networks with two cable technologies in this paper we introduce a minimal spanning tree problem with generalized hop constraints and primary connectivity constraints the problem is concerned with reliability requirements in a centralized network design problem where two different cable technologies are available the problem is shown to be np hard and as a consequence we derive lower bounding and upper bounding schemes for the problem we formulate the problem as a directed multicommodity flow model due to the size of the corresponding lp model we use lagrangean relaxation together with subgradient optimization to derive lower bounds a lagrangean heuristic is developed to construct feasible solutions the theoretically best lower bound associated to the lagrangean scheme quite often improves on the value of the corresponding lp bound since the relaxed problem does not satisfy the integrality property in fact using the heuristic these bounds can be proved to be even optimal for many of the cases tested these results are taken from a set of complete graphs with up to 40 nodes we also examine a few variations of the main model in particular we shall discuss several different ways of modeling the primary connectivity constraints one outcome of our discussion is that we shall derive an extended and compact representation of the convex hull of directed rooted subtrees when the underlying graph is series parallel