counting spanning trees in self similar networks by evaluating determinants spanning trees are relevant to various aspects of networks generally the number of spanning trees in a network can be obtained by computing a related determinant of the laplacian matrix of the network however for a large generic network evaluating the relevant determinant is computationally intractable in this paper we develop a fairly generic technique for computing determinants corresponding to self similar networks thereby providing a method to determine the numbers of spanning trees in networks exhibiting self similarity we describe the computation process with a family of networks called x y flowers which display rich behavior as observed in a large variety of real systems the enumeration of spanning trees is based on the relationship between the determinants of submatrices of the laplacian matrix corresponding to the x y flowers at different generations and is devoid of the direct laborious computation of determinants using the proposed method we derive analytically the exact number of spanning trees in the x y flowers on the basis of which we also obtain the entropies of the spanning trees in these networks moreover to illustrate the universality of our technique we apply it to some other self similar networks with distinct degree distributions and obtain explicit solutions to the numbers of spanning trees and their entropies finally we compare our results for networks with the same average degree but different structural properties such as degree distribution and fractal dimension and uncover the effect of these topological features on the number of spanning trees

quasi variational inequalities and ergodic impulse control in this paper we solve the general ergodic control problem for reflected diffusion processes and the associated quasi variational inequalities our method relies on some a priori estimates for the solutions of quasi variational inequalities where the discount factor i e the zero order term is set to 0

hamiltonian principle based stress singularity analysis near crack corners of multi material junctions this paper presents a new method for the stress singularity analysis near the crack corners of a multi material junctions the stress singularities near the crack corners of multi dissimilar isotropic elastic material junctions are studied analytically in terms of the methods developed in hamiltonian system the governing equations of plane elasticity in a sectorial domain are derived in hamiltonian form via variable substitution and variational principle respectively both of the methods of global state variable separation and symplectic eigenfunction expansion are used to find the analytical solution of the problem the relationships among the state vectors in different material spaces are obtained by means of coordinate transformation and consistent conditions between the two adjacent domains the expression of the original problem is thus changed into a new form where the solutions of symplectic generalized eigenvalues and eigenvectors are needed the closed form of expressions is established for the stress singularity analysis near the corner with arbitrary vertex angles numerical results are presented with several chosen angles and multi material constants to show the potential of the new method proposed a semi analytical finite element is furthermore developed for the numerical analysis of crack problems

a general solution on stress singularities in an anisotropic wedge abstract this paper presents a general solution for determining the stress singularity order in an anisotropic wedge the order depends on the wedge angle boundary conditions and material properties the characteristic equation which governs the eigenvalues is established from the lekhnitskii s complex function method a domain of one quarter circle is proposed in which the contours of singularity order are plotted for all fiber orientations and a certain wedge angle the numerical results agree well with the open literature for special cases to reduce to strength of stress singularity at the wedge corner the fiber direction corresponding to minimum singularity order can be determined

resistance between two nodes of a ring network abstract the resistance between two nodes in some resistor networks has been studied extensively by mathematicians and physicists given m positive integers m 1 m 2 m n let g m i 1 n be the resistor network with node set v v 1 v 2 v n and with a unit resistor between arbitrary two nodes u v i v v i 1 for i 1 2 n where v i v j 0 if i j and v i m i v n 1 v 1 gervacio 2016 introduces a modified method to compute the resistance between two nodes based on this method in this paper we use the elimination and substitution principles in electrical circuit to obtain the resistance between arbitrary two nodes of g m i 1 n

asymptotic approach to analyze singular stress state in anisotropic multi material application to the rivets the problem of stress singularities due to multi material junctions is described in this paper a semi analytical approach is proposed based on an asymptotic model in the case of anisotropic linear elasticity in three dimensions the advantage of the present method is the quasi explicit knowledge of the stress and displacement fields around the junctions thus after a brief explanation of the approach leading to the mechanical fields around the singular line at the junction between different materials numerical results are presented concerning various configurations of an assembly with rivets included in a bi layer composite that illustrate this method

singular hypersingular and singular free electromagnetic fields at wedge tips in metamaterials the engineering response of metamaterials has a dramatic impact on the physics optics and engineering communities because they offer electromagnetic properties that are difficult or impossible to achieve with conventional materials in this paper an asymptotic analysis of the electromagnetic fields at multi material wedges composed of metamaterials is proposed this is made possible by removing the assumption of positive electric permittivities and magnetic permeabilities an hypothesis which usually applies to conventional materials exploring the whole range of variability of these electromagnetic properties it is shown that in addition to the classical real eigenvalues 0 1 leading to power law singularities of the type o r 1 as r 0 it is also possible to find imaginary eigenvalues leading to hypersingular solutions as well as nonsingular configurations for a suitable choice of the negative electric permittivities and magnetic permeabilities of the media moreover to fully characterize the asymptotic fields the analysis is not only restricted to the determination of the lowest real and complex eigenvalues but is also extended to the evaluation of the higher order nonsingular ones the obtained analytical results collected in synthetic diagrams are expected to have impact on the design of micro and nano electro mechanical systems

the plane elasticity problem of an isotropic wedge under normal and shear distributed loading application in the case of a multi material problem the problem of a multi material composite wedge under a normal and shear loading at its external faces is considered with a variable separable solution the stress and displacement fields are determined using the equilibrium conditions for forces and moments and the appropriate airy stress function the infinite isotropic wedge under shear and normal distributed loading along its external faces is examined for different values of the order n of the radial coordinate r the proposed solution is applied to the elastostatic problem of a composite isotropic k materials infinite wedge under distributed loading along its external faces applications are made in the case of the two materials composite wedge under linearly distributed loading along its external faces and in the case of a three materials composite wedge under a parabolically distributed loading along its external faces

two point resistances in an apollonian network the computation of resistance between two nodes in a resistor network is a classical problem in electric theory and graph theory based on the apollonian packing andrade et al introduced a deterministic growing type of networks a k phys rev lett 94 018702 2005 prltao0031 900710 1103 physrevlett 94 018702 in this paper first a recursive algorithm for computing resistance between any two nodes in a k is given then as explanations using the algorithm explicit expressions for some resistances in a k are obtained

the order of stress singularities for bonded and disbonded three material junctions abstract in plane solutions are given for the order of the stress singularity at an internal point in an elastic isotropic solid where three wedges of different materials meet the three interfaces are either all perfectly bonded or a disbond is introduced along one interface one feature of this three material junction that is not present for the corresponding two material case is that each interface is geometrically different and therefore the singular behavior is dependent on which interface is disbonded each material and geometrical combination therefore gives rise to four problems one with perfect bonding at all interfaces and three cases of an interface disbond numerical results are presented for selected three material junctions new results for two material junctions and wedges that serve as special cases for the present study are also presented

the spectrum of infinite regular line graphs let g be an infinite d regular graph and l g its line graph we consider discrete laplacians on g and l g and show the exact relation between the spectrum of ag and that of al g our method is also applicable to di d2 semiregular graphs subdivision graphs and para line graphs

stress singularities in anisotropic multi material wedges and junctions abstract the general problem of stress singularities in anisotropic multi material wedges and junctions due to geometric and material discontinuities is investigated the anisotropic wedges and junctions discussed here comprise two or three materials with different geometric configurations and different material properties the interfaces in multi material junctions are either all perfectly bonded or a disbond is introduced along one interface the order of stress singularities is obtained by solving the characteristic equations that are developed from the boundary conditions of the problem numerical examples for the order of stress singularities are given for the general problem including two and three material wedges a crack terminating at an interface between two materials bonded and disbonded two and three material junctions as well an extra root of the characteristic equations in addition to three roots corresponding to higher singular stresses is observed for the cases of disbonded anisotropic two and three material junctions the stress singularities affected by geometric configurations and material properties of anisotropic materials are also investigated

finite element analysis of anisotropic materials with singular inplane stress fields abstract a finite element formulation is developed for the analysis of singular stress states at material and geometric discontinuities in anisotropic materials loaded inplane the displacement field of the sectorial element is quadratic in the angular coordinate direction and exponential in the radial direction measured from the singular point the formulation of yamada and okumura 1983a b is extended to take into account the anisotropy of the material the stress and displacement fields are obtained when the order of the stress singularity is real as well as complex when the order of the stress singularity is complex it is shown that the angular variation of the stress and displacement fields can be expressed in an infinite number of ways results for the displacement and stress fields obtained when the order of the stress singularity is complex can be made to match already published results once a similarity transformation is applied the simplicity and accuracy of the formulation are demonstrated by comparison to several analytical solutions for both isotropic and anisotropic multi material wedges and junctions with and without disbonds the nature and rate of convergence associated with the element suggests that it could be used in developing enriched elements for use with standard elements to yield accurate and computationally efficient solutions to problems having complex global geometries

two point resistances in a family of self similar x y flower networks abstract the computation of resistance between two nodes in networks is a fundamental problem in both electric theory and graph theory in this paper first a recursive algorithm for computing resistance between any two nodes in a family of self similar x y flower networks is given the x y flower networks display rich behavior as observed in a large variety of real systems then as explanations using the algorithm explicit expressions for some resistances in 1 3 flower networks and 2 2 flower networks are obtained

recursion transform method for computing resistance of the complex resistor network with three arbitrary boundaries we develop a general recursion transform r t method for a two dimensional resistor network with a zero resistor boundary as applications of the r t method we consider a significant example to illuminate the usefulness for calculating resistance of a rectangular m ifmmode times else texttimes fi n resistor network with a null resistor and three arbitrary boundaries a problem never solved before since green s function techniques and laplacian matrix approaches are invalid in this case looking for the exact calculation of the resistance of a binary resistor network is important but difficult in the case of an arbitrary boundary since the boundary is like a wall or trap which affects the behavior of finite network in this paper we obtain several general formulas of resistance between any two nodes in a nonregular m ifmmode times else texttimes fi n resistor network in both finite and infinite cases in particular 12 special cases are given by reducing one of the general formulas to understand its applications and meanings and an integral identity is found when we compare the equivalent resistance of two different structures of the same problem in a resistor network

enrichment of finite elements with numerical solutions for singular stress fields enriched 2 d and 3 d finite elements are formulated for analysis of solids having multi material junction and wedge configurations that create singular stress fields due to the material and or geometric discontinuities the order and angular variation of the displacements associated with the singular fields are determined from a separate special finite element eigenanalysis and used in the enrichment process the use of these numerically determined singular fields allows enriched elements to be developed for complex configurations for which analytical fields are not available in addition to this added flexibility of application the current formulation applies to elements that may or may not be in direct contact with the singular point this allows multiple layers of enriched elements to be used around the singular point and traditional mesh refinement studies to be carried out in the enriched element region previous enriched formulations have not provided this important capability for cases where analytical fields are available such as cracked solids the performance of elements developed with the current approach is shown to be equivalent to that obtained using analytically enriched elements mesh refinement techniques using enriched elements are described that allow accurate stress distributions and generalized stress intensity factors to be directly determined the importance of high order numerical integration use of multiple layers of enriched elements and proper choice of the size of the enriched region are demonstrated by comparison to existing solutions for solids with cracks application of enriched element modelling to a 2 d bi material wedge and a 3 d stepped thickness anisotropic composite laminate is demonstrated 1997 john wiley sons ltd

decoupled formulation of piezoelectric elasticity under generalized plane deformation and its application to wedge problems abstract this paper presents the formulation of piezoelectric elasticity under generalized plane deformation derived from the three dimensional theory there are four decoupled classes in the generalized plane deformation formulation i e when l 3 l 2 0 l 3 l 3 0 l 3 l 2 0 or l 3 l 3 l 2 0 only the inplane fields of the first class and the antiplane field of the second class include the piezoelectric effect several examples of wedge problem often encountered in smart structures such as sensors or actuators are studied to examine the stress singularity near the apex of the structure the bonded materials to the pzt 4 wedge are pzt 5 graphite epoxy or aluminum conductor the influencing factors on the singular behavior of the electro elastic fields include the wedge angle material type poling direction and the boundary and interface conditions the numerical results of the first case are compared with xu s graphs and some comments are made in detail in addition some new results regarding the antiplane stress singularity of the second class are obtained via the case study the coupled singularity solutions under generalized plane deformation are also investigated to seek the conditions of the weakest or vanishing singular stress fields

valuation of investments in real assets with implications for the stock prices a general model for the valuation of natural resource investments is formulated and analyzed within a stochastic control theoretic framework using dynamic programming the value of such an investment with a general payoff function is determined under the assumption that the commodity price process is given by a stochastic differential equation the analysis results in closed form analytic solutions which can easily be computed and exhibits qualitatively different optimal behaviors depending on parameter values implications for stocks and options are also considered

a sequential entry problem with forced exits we consider a continuous time optimal stopping problem with multiple entries and forced exits the value for such an optimization problem with a general payoff function is solved in closed form under the assumption that the state process is a geometric brownian motion and the forced exits come in according to a poisson process the effect due to the forced exits is analyzed it is shown that the presence of the forced exits is a true risk meaning that it will reduce the value and enlarge the continuation region if and only if the entry cost is large enough compared to the running cost

recursive calculation of effective resistances in distance regular networks based on bose mesner algebra and christoffel darboux identity recently jafarizadeh et al j phys a math theor 40 4949 2007 have given a method for calculation of effective resistance two point resistance on distance regular networks where the calculation was based on stratification introduced by jafarizadeh and salimi j phys a 39 1 2006 and stieltjes transform of the spectral distribution stieltjes function associated with the network also jafarizadeh et al j phys a math theor 40 4949 2007 have shown that effective resistances between a node and all nodes belonging to the same stratum with respect to r i belonging to the ith stratum with respect to are the same in this work an algorithm for recursive calculation of the effective resistances in an arbitrary distance regular resistor network is provided where the derivation of the algorithm is based on the bose mesner algebra stratification of the network spectral techniques and christoffel darboux identity it is shown that the effective resistance on a dista

resistance distances in composite graphs the resistance distance between any two vertices of a connected graph is defined as the effective resistance between them in the electrical network constructed from the graph by replacing each edge with a unit resistor let g h g h g h g h g h gh and g h be the join product composition direct product strong product corona and rooted product of two graphs g and h respectively in this paper formulae for resistance distances of these composite graphs are given in terms of parameters of the parent graphs and some properties are established explicit formulae are obtained for resistance distances of some classes of graphs including rook graphs diagonal mesh graphs and generalized double graphs

a new variable order singular boundary element for two dimensional stress analysis a new variable order singular boundary element for two dimensional stress analysis is developed this element is an extension of the basic three node quadratic boundary element with the shape functions enriched with variable order singular displacement and traction fields which are obtained from an asymptotic singularity analysis both the variable order of the singularity and the polar profile of the singular fields are incorporated into the singular element to enhance its accuracy the enriched shape functions are also formulated such that the stress intensity factors appear as nodal unknowns at the singular node thereby enabling direct calculation instead of through indirect extrapolation or contour integral methods numerical examples involving crack notch and corner problems in homogeneous materials and bimaterial systems show the singular element s great versatility and accuracy in solving a wide range of problems with various orders of singularities the stress intensity factors which are obtained agree very well with those reported in the literature copyright 2002 john wiley sons ltd

a model for investments in the natural resource industry with switching costs we consider a model for investment decisions in the natural resource industry with switching costs this model gives rise to a problem combining features of both absolutely continuous and impulse stochastic control that we explicitly solve the solution takes qualitatively different forms depending on parameter values

stress singularity analysis in three dimensional bonded structure abstract stress analysis for joints between two isotropic materials is performed using three dimensional boundary element method with rongved s fundamental solution rongved l 1955 force interior to one of two joined semi infinite solids in second midwestern conf on solid mechanics pp 1 13 which satisfies boundary conditions at the interface the stress distribution around the vertex of the joint is precisely examined and the order of stress singularity obtained in three dimensional analysis is compared with that in two dimensional analysis it is shown that the order of the stress singularity along the stress singularity line which is the intersection of the interface with the free surface varies from the value in plane strain to that in plane stress as the opposite side free surface is approached the order of stress singularity in the spherical coordinates centered at the vertex is next investigated when singularity lines with a singularity order meet with each other at the vertex the order of stress singularity is larger than that for plane strain and plane stress when the vertex angle between two side free surfaces is varied the order of stress singularity is also altered in particular a bound at which singularity disappears at the plane for dundurs composite parameters is examined for a cubic dissimilar material it is demonstrated that the bound varies little in comparison with the one obtained from the two dimensional theory

optimal switching in an economic activity under uncertainty this paper considers the problem of finding the optimal sequence of opening starting and closing stopping times of a multi activity production process given the costs of opening running and closing the activities and assuming that the state of the economic system is a stochastic process the problem is formulated as an extended impulse control problem and solved using stochastic calculus as an application the optimal starting and stopping strategy are explicitly found for a resource extraction when the price of the resource is following a geometric brownian motion

on the singularities of the thermo electro elastic fields near the apex of a piezoelectric bonded wedge based on the generalized lekhnitskii formulation and mellin transform the thermo electro elastic fields of a piezoelectric bonded wedge are investigated in this paper from the potential theory in a wedge shaped region a general form of the temperature change is proposed as a particular solution in the generalized lekhnitskii formulation the emphasis is on the singular behavior near the apex of the piezoelectric bonded wedge including singularity orders and angular functions which can be computed numerically the interface between two materials can be either perfectly bonded namely type a so that the continuity of electric displacements holds or a thin electrode namely type b so that the electric potential is grounded case studies of pzt 5h pzt 4 and graphite epoxy pzt 4 bonded wedges reveal that in most cases the type b continuity condition has more severe singularities than type a due to the mixed boundary point of the electrostatics at the apex of the wedge the results of this study show that the reduction or disappearance of singularity orders is possible through the appropriate selection of poling fiber orientations and wedge angles

theory of resistor networks the two point resistance the resistance between two arbitrary nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the laplacian matrix associated with the network explicit formulae for two point resistances are deduced for regular lattices in one two and three dimensions under various boundary conditions including that of a mobius strip and a klein bottle the emphasis is on lattices of finite sizes we also deduce summation and product identities which can be used to analyse large size expansions in two and higher dimensions

edge singularities in anisotropic composites abstract the stress singularity at the vertex of an anistropic wedge has the form r f r as r 0 where 0 f is a real function of the polar coordinates r in many cases f is independent of r the explicit form of f r depends on the eigenvalues of the elasticity constants called p here and on the order of singularity k when k is real k if k is complex is the real part of k the p s are all complex and consist of 3 pairs of complex conjugates which reduce to i when the material is isotropic the function f depends not only on p and k it also depends on whether p and k are distinct roots of the corresponding determinants in this paper we present the function f r in terms of p and k for the cases when p and k are single roots as well as when they are multiple roots the relationship between the complex variable z introduced in the analysis and the polar coordinates r is interpreted geometrically after presenting the form of f for individual cases a general form of f is given in eqn 74 we also show that the stress singularity at the crack tip of general anisotropic materials has the order of singularity 1 2 which is at least a multiple root of order 3 the implication of this on the form f r is discussed

resistance distance in potting networks abstract on a resistor network the resistance distance is the effective resistance r u v between two nodes u v of the network in this paper we study a family of self similar and symmetric networks named potting networks and obtain a recursion formula to calculate resistance distances

a finite element approach to three dimensional singular stress states in anisotropic multi material wedges and junctions abstract a finite element formulation is developed to determine the order and angular variation of singular stress states due to material and geometric discontinuities in anisotropic materials the formulation applies to any two dimensional geometry that is prismatic in the third direction and has three dimensional displacement fields in some special cases the three dimensional fields become uncoupled antiplane and inplane fields and this formulation yields the uncoupled results the formulation provides for the determination of the asymptotic stress and displacement fields present at interior singular points of three dimensional structures the displacement field of the sectorial finite element is quadratic in the angular coordinate direction and asymptotic in the radial direction measured from the singular point the formulation of yamada and okumura 1983 hybrid and mixed finite element methods pp 325 343 wiley chichester for inplane problems is adapted for this purpose the simplicity and accuracy of the formulation are demonstrated by comparison with several analytical solutions for both isotropic and anisotropic multi material wedges and junctions the nature and speed of convergence associated with the element suggests that it could be employed in developing two dimensional and three dimensional enriched elements for use along with standard elements to yield accurate and computationally efficient solutions to problems having complex global geometries leading to singular stress states

scale free and small world properties of sierpinski networks abstract in this paper we construct the evolving networks from sierpinski carpet using the encoding approach in fractal geometry we consider the small similar copies of unit square as nodes of network where two nodes are neighbors if and only if their corresponding copies have common surface for our networks we check their scale free and small world effect by the self similar structures the exponent of power law on degree distribution is log 3 8 which is the hausdorff dimension of the carpet

a finite element analysis of the singular stress fields in anisotropic materials loaded in antiplane shear a finite element formulation is developed to determine the order and angular variation of singular stress states at material and geometric discontinuities in anisotropic materials subject to antiplane shear loading the displacement field of the sectorial element is quadratic in the angular co ordinate direction and asymptotic in the radial direction measured from the singular point the formulation of yamada and okumura14 for in plane problems is adapted for this purpose the simplicity and accuracy of the formulation are demonstrated by comparison to several analytical antiplane shear solutions for both isotropic and anisotropic multi material wedges and junctions with and without disbonds the nature and speed of convergence of the eigensolution suggests that the solution presented here could be used in developing enriched elements for accurate and computationally efficient evaluation of stress intensity factors in problems having complex global geometries

influence of the intermediate material on the order of stress singularity in three phase bonded structure the plane problem for dissimilar materials composed of three isotropic homogeneous wedges with arbitrary angles under surface tractions is analysed using the theory of elasticity the order of singularity in stress fields near the apex of a three phase bonded structure is investigated it is first demonstrated how the order of stress singularity varies with several combinations of material with different properties in cases where the angles of wedge are of 3 3 3 and 2 2 2 when the materials and wedge angles of the side regions are identical the order of stress singularity is additionally studied in detail with the wedge angle of the intermediate region varying in cases where the total angle of the bonded wedge geometry is fixed and not fixed a method reducing the stress singularity in a two phase bonded structure is finally proposed

a small world and scale free network generated by sierpinski pentagon abstract the sierpinski pentagon is used to construct evolving networks whose nodes are all solid regular pentagons in the construction of the sierpinski pentagon up to the stage t and any two nodes are neighbors if and only if the intersection of corresponding pentagons is non empty and non singleton we show that such networks have the small world and scale free effects but are not fractal scaling

finite horizon optimal multiple switching with signed switching costs this paper is concerned with optimal switching over multiple modes in continuous time and on a finite horizon the performance index includes a running reward terminal reward and switching costs that can belong to a large class of stochastic processes particularly the switching costs are modelled by right continuous with left limits processes that are quasi left continuous and can take positive and negative values we provide sufficient conditions leading to a well known probabilistic representation of the value function for the switching problem in terms of interconnected snell envelopes we also prove the existence of an optimal strategy in a suitable class of admissible controls defined iteratively in terms of the snell envelope processes

computation of resistance distance and kirchhoff index of the two classes of silicate networks abstract the resistance distance between two vertices of a simple connected graph g is equal to the resistance between two equivalent points on an electrical network constructed so as to correspond to g with each edge being replaced by a unit resistor the kirchhoff index of g is the sum of resistance distances between all pairs of vertices in g in this paper the resistance distance between any two arbitrary vertices of a chain silicate network and a cyclic silicate network was procured by utilizing techniques from the theory of electrical networks i e the series and parallel principles the principle of elimination the star triangle transformation and the delta wye transformation two closed formulae for the kirchhoff index of the chain silicate network and the cyclic silicate network were obtained respectively

clique inserted graphs and spectral dynamics of clique inserting abstract motivated by studying the spectra of truncated polyhedra we consider the clique inserted graphs for a regular graph g of degree r 0 the graph obtained by replacing every vertex of g with a complete graph of order r is called the clique inserted graph of g denoted as c g we obtain a formula for the characteristic polynomial of c g in terms of the characteristic polynomial of g furthermore we analyze the spectral dynamics of iterations of clique inserting on a regular graph g for any r regular graph g with r 2 let s g denote the union of the eigenvalue sets of all iterated clique inserted graphs of g we discover that the set of limit points of s g is a fractal with the maximum r and the minimum 2 and that the fractal is independent of the structure of the concerned regular graph g as long as the degree r of g is fixed it follows that for any integer r 2 there exist infinitely many connected r regular graphs or non regular graphs with r as the maximum degree with arbitrarily many distinct eigenvalues in an arbitrarily small interval around any given point in the fractal we also present a formula on the number of spanning trees of any k th iterated clique inserted graph and other related results

a problem of sequential entry and exit decisions combined with discretionary stopping we consider a stochastic control problem that has emerged in the economics literature as an investment model under uncertainty this problem combines features of both stochastic impulse control and optimal stopping the aim is to discover the form of the optimal strategy it turns out that this has a priori rather unexpected features the results that we establish are of an explicit nature we also construct an example whose value function does not possess c1 regularity

optimal exit strategies for investment projects abstract we study the problem of an optimal exit strategy for an investment project which is unprofitable and for which the liquidation costs evolve stochastically the firm has the option to keep the project going while waiting for a buyer or liquidating the assets at immediate liquidity and termination costs the liquidity and termination costs are governed by a mean reverting stochastic process whereas the rate of arrival of buyers is governed by a regime shifting markov process we formulate this problem as a multidimensional optimal stopping time problem with random maturity we characterize the objective function as the unique viscosity solution of the associated system of variational hamilton jacobi bellman inequalities we derive explicit solutions and numerical examples in the case of power and logarithmic utility functions when the liquidity premium factor follows a mean reverting cir process

resistance between two nodes in general position on an m n fan network the resistance between two nodes in general position on a fan network with n radial lines and m transverse lines is determined also a similar result of izmailian kenna and wu j phys a math theor 47 035003 2014 for an m ifmmode times else texttimes fi n cobweb network is reproduced but the method used here is significantly different it avoids the use of the kirchhoff matrix requires the solution of just one instead of two eigenvalue problems and results directly in only a single summation further the current distribution is given explicitly as a byproduct of the method the method is the same as that used by tan zhou and yang j phys a math theor 46 195202 2013 to find the cobweb resistance between center and perimeter for 1 ensuremath le m ensuremath le 3 and general n proof of their conjecture for general m is discussed

percolation in hierarchical scale free nets we study the percolation phase transition in hierarchical scale free nets depending on the method of construction the nets can be fractal or small world the diameter grows either algebraically or logarithmically with the net size assortative or disassortative a measure of the tendency of like degree nodes to be connected to one another or possess various degrees of clustering the percolation phase transition can be analyzed exactly in all these cases due to the self similar structure of the hierarchical nets we find different types of criticality illustrating the crucial effect of other structural properties aside from the scale free degree distribution of the nets