contravariantly finite subcategories closed under predecessors abstract let a be an artin algebra and moda be the category of finitely generated right a modules we prove that an additive full subcategory c of moda closed under predecessors is contravariantly finite if and only if its right ext orthogonal is covariantly finite or if and only if the ext injectives in c define a cotilting module over the support algebra of c or equivalently if and only if c is the support of the representable functors given by the ext injectives

on the periodicity of non homogeneous markov chains and systems abstract we firstly recall the concept of an nhms and introduce concepts and known results necessary for the study of asymptotic periodicity of the vector of expectations variances and covariances of the state sizes this sequence of vectors is called the variability of population structures we then proceed to prove some useful propositions and lemmas for the establishment of the basic results that follow note that some of these lemmas have a power and usefulness of their own finally we provide two theorems where we study the asymptotic periodicity of the variability of population structures when the inherent non homogeneous markov chain is uniquely determined by a sequence of arbitrary stochastic matrices all with the same incidence matrix following that an illustrative example from the area of manpower systems is provided in this example the results in the basic theorems of the previous section are illustrated numerically we conclude with an appendix where we firstly introduce the necessary concepts and known results needed in order to study the periodicity and asymptotic periodicity of an infinite product of finite arbitrary stochastic matrices we then proceed to study the periodicity and asymptotic periodicity of non homogeneous markov chains in their full possible generality it is very important to note that similar results hold also for an infinite product of non negative matrices

the left and right parts of the module category of crossed product group algebras let g be a finite group k be a field with characteristic not dividing the order of g a nd b e at wistedkg module algebra such that g or g for short exists as a crossed product algebra in this paper we study the relationship between the class l g or r g which consists of all finitely generated indecomposable g modules whose predecessors or successors have projective dimension or injective dimension at most one and the class l or r then we study those properties which rely on the left or right part of that are preserved under the extension of crossed product group algebra g

on the representation dimension of tilted and laura algebras abstract we prove that the representation dimension of a tilted or of a strict laura algebra is at most three

asymptotic behavior of nonhomogeneous semi markov systems abstract we study the asymptotic behavior of a nonhomogeneous semi markov system population in discrete time after a series of definitions lemmas and theorems we firstly establish the conditions under which the ergodic behavior of a nonhomogeneous semi markov chain exists and then find the limit of the basic matrix of the chain q n s in closed form finally the existence of the asymptotic population structure of the nonhomogeneous semi markov system is studied and the limit is provided in closed analytic form

stochastic equilibria in nonhomogeneous markov population replacement processes this paper is an exposition on the dynamic stochastic equilibria in multi type time dependent markov population processes for different types of environmental behaviour the joint multivariate cumulant generating function of the various population sizes at any time is derived together with the covariance structure both with and without time lags an asymptotic analysis shows that there are either one or several equilibria of dynamic character depending critically on the behaviour of the system parameters as well as on the total population size the possible stochastic equilibria are characterized as stable or unstable according to whether or not they are independent of initial conditions

nonstationary cyclic behavior in markov systems abstract we introduce the concept of the nonstationary cyclic markov system as a natural extension of the cyclic systems found in recent literature we find the sets of d cyclic asymptotically attainable structures and establish the relationships that exist between these structures for a nonhomogeneous markov system in a deterministic or stochastic environment the inherent connection between nonstationary cyclicity and stochastic environment is examined also we investigate the conditions under which there exists a geometric convergence to the equilibrium

two sided gluings of tilted algebras we study the class of algebras a satisfying the property all but at most finitely many non isomorphic indecomposable a modules are such that all their predecessors have projective dimension at most one or all their successors have injective dimension at most one such a class includes the tilted algebras d happel c ringel trans amer math soc 274 1982 399 443 the quasi tilted algebras d happel i reiten s smalo mem am math soc 120 1996 575 the shod algebras f u coelho m lanzilotta manuscripta mathematica 100 1999 1 11 the weakly shod f u coelho m lanzilotta preprint 2001 and the left and right glued algebras i assem f u coelho j pure appl algebra 96 3 1994 225 243

semi markov migration process in a stochastic market in credit risk abstract in the present the idea of stochastic market environment comes into play to express the changes in general economy which affects any industry in small or great amounts of turbulence we model the evolution of the market among its possible states as an f inhomogeneous semi markov process this idea leads us to modeling the migration process of defaultable bonds as different f inhomogeneous semi markov process the survival probabilities of a defaultable bond in every credit grade are found the asymptotic behaviour of the survival probabilities is established under certain conditions also it is proved under what conditions the convergence is geometrically fast the stochastic foundation of the general stochastic discrete time market is provided by proving that the market is viable if and only if there exists an equivalent martingale measure from which we construct the forward probability measure and under which the discounted default free bond price process for all possible states of the market is a martingale the term structure of credit spread and the change of real world probability measure to forward probability measure are studied in the form of a theorem it is proved that under certain conditions changing the real probability measure to a forward probability measure does not affect the inhomogeneous semi markov process modeling the migration of defaultable bonds that is it is proved that it only changes the basic parameters and we provide a relation among the transition probabilities under the two measures finally parameter estimation and calibration of the inhomogeneous semi markov chain in stochastic environment is being provided

fuzzy semi markov migration process in credit risk we explore the rating system used by credit agencies with a focus on problems that justify the use of fuzzy set theory we prove that a fuzzy market is viable if and only if an equivalent martingale measure exists from which we construct the forward probability measure and under which the discounted price of a default free bond is a martingale we model the evolution of credit migration of a defaultable bond as an inhomogeneous semi markov process with fuzzy states we study the effects of changing the real probability measure to a forward probability measure in addition we investigate the asymptotic behaviour of the survival probability in each fuzzy state given in the absence of default finally we discuss parameter estimation and calibration of the inhomogeneous markov chain with fuzzy states

periodicity of asymptotically attainable structures in nonhomogeneous markov systems we find the sets of d periodic asymptotically attainable structures and we establish the periodicities that exist between these structures for a nonhomogeneous markov system in the case where the imbedded nonhomogeneous markov chain is periodic with period d also it is proved that under certain conditions each converging subsequence of the sequence of relative structures has a geometric rate of convergence

asymptotic variability of nonhomogeneous markov systems under cyclic behaviour abstract in this paper the asymptotic variability of nonhomogeneous markov systems under cyclic behaviour is studied it is found that the sequence of vectors of means variances and covariances splits into d subsequences which converge where d is the period of the cyclic finally an illustration of the present results with data from a manpower system is given

proofs of conjectures on the karpelevich arcs in the region of eigenvalues of stochastic matrices abstract the subset of the complex plane that consists of all eigenvalues of all stochastic matrices of a fixed order was completely determined by karpelevich 1951 the boundary of this region consists of so called karpelevich arcs johnson and paparella 2017 6 made several conjectures on properties of these arcs in this paper we prove two of their conjectures specifically we prove that the karpelevich arcs are regular differentiable curves and establish that some powers of certain karpelevich arcs correspond to some other karpelevich arcs

on the composite of two irreducible morphisms in radical cube abstract we study here when there are irreducible morphisms h x y and h y z between indecomposable modules such that the composite h h is a non zero morphism in r 3 x z in particular we characterize the representation finite string algebras and the tilted algebras having such irreducible morphisms

coverings of laura algebras the standard case abstract in this paper we study the covering theory of laura algebras we prove that if a connected laura algebra is standard that is has a standard connecting component then it has galois coverings associated to the coverings of the connecting component as a consequence the first hochschild cohomology group of a standard laura algebra vanishes if and only if it has no proper galois coverings

characterizations of algebras with small homological dimensions abstract we introduce the class of double tilted algebras containing the class of tilted algebras and prove various characterizations in particular we show that the class of double tilted algebras is the class of all artin algebras whose ar quiver admits a faithful double section with a natural property moreover we prove that the class of double tilted algebras coincides with the class of all artin algebras of global dimension three for which every indecomposable finitely generated module has projective or injective dimension at most one we also describe the structure of the category of finitely generated modules as well as the ar quiver of double tilted algebras

on the limiting behaiour of a nonhomogeneour markov chain model in manpower systems summary we study the limiting structure of an expanding manpower system where the nonhomogeneous markov chain model proposed by young vassiliou 1974 is applicable the limiting structure and the relative limiting structure exist under certain conditions which are easily met in practical situations finally the problem of weak ergodicity in the above manpower systems is studied necessary and sufficient conditions are provided for weak ergodicity

a characterization of cycle finite generalized double tilted algebras abstract we provide a new characterization of cycle finite generalized double tilted algebras by the existence of a faithful module which is the middle of at most finitely many short chains

on generalized standard auslander reiten components having only finitely many non directing modules abstract let be a connected component of the auslander reiten quiver mod a of an artin algebra we show that is quasi directed if and only if the paths in ind a having end points in satisfy certain conditions moreover we describe the shapes of such components and identify the classes of algebras to which they are related

weakly shod algebras abstract we study the class of algebras having a path of nonisomorphisms from an indecomposable injective module to an indecomposable projective module and any such path is bounded by a fixed number we show that such an algebra is an iteration of one point extensions starting at a product of tilted algebras this allows us to describe for instance its auslander reiten quiver

the left and the right parts of a module category abstract in this paper we study for an artin algebra the class l a and r a which is a full subcategory of the category moda of finitely generated a modules and which consists of all indecomposable a modules whose predecessors and successors have projective dimension and injective dimension respectively at most one we consider quotient algebras of a which contain the information on these classes then define and characterize those algebras for which the class is l a is contravariantly finite and r a is covariantly finite respectively