maps between non commutative spaces let j be a graded ideal in a not necessarily commutative graded k algebra a a 0 a 1 in which dim k a i for all i we show that the map a a j induces a closed immersion i proj nc a j proj nc a between the non commutative projective spaces with homogeneous coordinate rings a and a j we also examine two other kinds of maps between non commutative spaces first a homomorphism a b between not necessarily commutative n graded rings induces an affine map proj nc b u proj nc a from a non empty open subspace u c proj nc b second if a is a right noetherian connected graded algebra not necessarily generated in degree one and a n is a veronese subalgebra of a there is a map proj nc a proj nc a n we identify open subspaces on which this map is an isomorphism applying these general results when a is a quotient of a weighted polynomial ring produces a non commutative resolution of a closed subscheme of a weighted projective space

graded maximal cohen macaulay modules over noncommutative graded gorenstein isolated singularities abstract in this paper we define a notion of noncommutative graded isolated singularity and study as gorenstein isolated singularities and the categories of graded maximal cohen macaulay modules over them in particular for an as gorenstein algebra a of dimension d 2 we show that a is a graded isolated singularity if and only if the stable category of graded maximal cohen macaulay modules over a has the serre functor using this result we also show the existence of cluster tilting objects in the categories of graded maximal cohen macaulay modules over veronese subalgebras of certain as regular algebras

gorenstein subrings of invariants under hopf algebra actions abstract this paper concerns conditions on the action of a finite dimensional semisimple hopf algebra on an artin schelter regular algebra that force the subring of invariants to satisfy the artin schelter gorenstein condition classical results such as watanabe s theorem and stanley s theorem are extended from the case of a group action to the context of a hopf algebra action a hopf algebra version of the homological determinant is introduced and it becomes an important tool in the generalization from group actions to hopf algebra actions

the structure of as gorenstein algebras abstract in this paper we define a notion of as gorenstein algebra for n graded algebras and show that symmetric as regular algebras of gorenstein parameter 1 are exactly preprojective algebras of quasi fano algebras this result can be compared with the fact that symmetric graded frobenius algebras of gorenstein parameter 1 are exactly trivial extensions of finite dimensional algebras the results of this paper suggest that there is a strong interaction between classification problems in noncommutative algebraic geometry and those in representation theory of finite dimensional algebras

stickelberger elements and modular parametrizations of elliptic curves in the present paper we shall give evidence to support the claim conjecture i below and 1 3 that every elliptic curve a o which can be parametrized by modular functions admits a canonical modular parametrization whose properties can be related to intrinsic properties of a in particular we will see how such a parametrizat ion can be used to prove some rather pleasant integrality properties of stickelberger elements ad p adic l functions attached to a in addition if conjecture i is true then we can give an intrinsic characterization of the isomorphism class of a special elliptic curve in the q isogeny class of a distinguished by modular considerations for most of the paper we have opted for the concrete approach and defined modular parametrizations in terms of x i n definition 1 1 however to justify our view of these parametrizations as being canonical we begin here with a more intrinsic definition recall that shimura 19 chap 6 see w 1 of this paper has defined a compatible system of canonical models of modular curves xs ses where 5 p is a certain collection of open subgroups of the group gl 2 az over the finite adeles a i of q we define the adelic upper half plane to be the pro variety ll m xs and give the q structure induced by the s field of modular functions whose q expansions at the 0 cusp have coefficients in q a modular parametrization of a is a q morphism a which sends

noncommutative projective schemes an analogue of the concept of projective scheme is defined for noncommutative n graded algebras using the quotient category c of graded right a modules modulo its full subcategory of torsion modules we define proj a c a s where a is the object corresponding to the module aa and s is the autoequivalence defined by the shift of degrees the triples equivalent to proj a for a right noetherian graded algebra a are characterized in terms of a condition on extensions

estimating the parameters of weibull distribution using simulated annealing algorithm weibull distribution plays an important role in failure distribution modeling in reliability studies it is a hard work to estimate the parameters of weibull distribution this distribution has three parameters but for simplicity a parameter is omitted and as a result the estimation of the others will be easily done when the three parameter distribution is of interest the estimation procedure will be quite boring maximum likelihood estimation is a good method which is usually used to elaborate on the parameter estimation the likelihood function formed for the parameter estimation of a three parameter weibull distribution is very hard to maximize many researchers have studied this maximization problem in this paper we have briefly discussed this problem and proposed a new approach based on the simulated algorithm to solve that

on quantum groups associated to non noetherian regular algebras of dimension 2 we investigate homological and ring theoretic properties of universal quantum linear groups that coact on artin schelter regular algebras a n of global dimension 2 especially with central homological codeterminant or central quantum determinant as classified by zhang the algebras a n are connected mathbb n graded algebras that are finitely generated by n indeterminants of degree 1 subject to one quadratic relation in the case when the homological codeterminant of the coaction is trivial we show that the quantum group of interest defined independently by manin and by dubois violette and launer is artin schelter regular of global dimension 3 and also skew calabi yau homologically smooth of dimension 3 for central homological codeterminant we verify that the quantum groups are noetherian and have finite gelfand kirillov dimension precisely when the corresponding comodule algebra a n satisfies these properties that is if and only if n 2 we have similar results for arbitrary homological codeterminant if we require that the quantum groups are involutory we also establish conditions when hopf quotients of these quantum groups that also coact on a n are cocommutative

searching for kummer congruences in an infinite slope family we consider powers of a grossencharacter the corresponding l functions twisted with quadratic dirichlet characters and their central critical values we state several conjectures concerning kummer type congruences between these numbers for a ramified prime and describe specific numerical data in support of these conjectures

mckay correspondence for semisimple hopf actions on regular graded algebras i abstract in establishing a more general version of the mckay correspondence we prove auslander s theorem for actions of semisimple hopf algebras h on noncommutative artin schelter regular algebras a of global dimension two where a is a graded h module algebra and the hopf action on a is inner faithful with trivial homological determinant we also show that each fixed ring a h under such an action arises as an analogue of a coordinate ring of a kleinian singularity

on l functions of elliptic curves and cyclotomic towers in this paper we shall strengthen a recent theorem of ralph greenberg 1 concerning l functions of elliptic curves and anticyclotomic towers let k be an imaginary quadratic field and m an abelian extension of k possibly of infinite degree we say that the extension m k is anticyclotomic if m is galois over q and if the nontrivial element of gal k q acts on gal m k by inversion now fix a finite set p of rational primes and consider the compositum in an algebraic closure of k of all anticyclotomic extensions of k which are unramified outside p we denote this compositum by l and refer to it as the maximal anticyclotomic extension of k unramified outside p the field l may also be described as the union of all ring class fields of k with conductor divisible only by primes in p class field theory shows that gal l k is isomorphic to the product of a finite group and the group

noncommutative complete intersections abstract several generalizations of a commutative ring that is a graded complete intersection are proposed for a noncommutative graded k algebra these notions are justified by examples from noncommutative invariant theory

coates wiles towers in dimension two let k be an imaginary quadratic field and e an elliptic curve defined over k with complex multiplication by the ring of integers of k in 1977 coates and wiles proved that if e k has positive rank then the hasse weil zeta function l e k s of e has a zero at s 1 2 such curves exist precisely when the class number of k is one subsequent work 1 extended the result to a wider class of cm curves another proof emerged from rubin s important work on the tate shafarevich group 13 14 see also 10 12 coates and wiles used formal groups and iwasawa theoretic techniques to relate the special value of l e f s to elliptic units employing more classical techniques stark and gupta combined to give a different proof of the theorem 21 4 although the two proofs have different flavors they include the same ingredients let p be one of infinitely many suitably chosen primes of k and k the field obtained by adjoining the p torsion of e to k there is a unique prime p of k lying over p let q be a point of infinite order in e k q c pe k and 5 l q k q let v 2 be the gr6ssencharakter of e and f2 a fundamental

hopf dense galois extensions with applications abstract let h be a finite dimensional hopf algebra and let a be a left h module algebra motivated by the study of the isolated singularities of a h and the endomorphism ring end a h a we introduce the concept of hopf dense galois extensions in this paper hopf dense galois extensions yield certain equivalences between the quotient categories over a and a h a special class of hopf dense galois extensions consists of the so called densely group graded algebras which are weaker versions of strongly graded algebras a weaker version of dade s theorem holds for densely group graded algebras as applications we recover the classical equivalence of the noncommutative projective scheme over a noetherian n graded algebra a and its d th veronese subalgebra a d respectively hopf dense galois extensions are also applied to the study of noncommutative graded isolated singularities

on the conjecture of birch and swinnerton dyer in this paper we complete rubin s partial verification of the conjecture for a large class of elliptic curves with complex multiplication by q c

elliptic curves with complex multiplication and the conjecture of birch and swinnerton dyer 1 quick review of elliptic curves 2 2 elliptic curves over c 4 3 elliptic curves over local fields 6 4 elliptic curves over number fields 12 5 elliptic curves with complex multiplication 15 6 descent 22 7 elliptic units 27 8 euler systems 37 9 bounding ideal class groups 43 10 the theorem of coates and wiles 47 11 iwasawa theory and the main conjecture 50 12 computing the selmer group 61

estimating the four parameters of the burr iii distribution using a hybrid method of variable neighborhood search and iterated local search algorithms abstract the burr iii distribution properly approximates many familiar distributions such as normal lognormal gamma weibull and exponential distributions it plays an important role in reliability engineering statistical quality control and risk analysis models the burr iii distribution has four parameters known as location scale and two shape parameters the estimation process of these parameters is controversial although the maximum likelihood estimation mle is understood as a straightforward method in parameters estimation using mle to estimate the burr iii parameters leads to maximize a complicated function with four unknown variables where using a conventional optimization such as the gradient method is difficult in this paper to circumvent the difficulty of maximizing the burr iii likelihood function a meta heuristics hybrid approach is proposed which composes of a variable neighborhood search vns along with an iterated local search ils algorithm in the proposed algorithm different heuristic local search methods are investigated to promote the ils algorithm performance furthermore the taguchi technique is employed to tune the parameters the results of some numerical examples and a simulation study indicate satisfactory performance of the proposed algorithm

semisimple hopf actions on commutative domains abstract let h be a semisimple so finite dimensional hopf algebra over an algebraically closed field k of characteristic zero and let a be a commutative domain over k we show that if a arises as an h module algebra via an inner faithful h action then h must be a group algebra this answers a question of e kirkman and j kuzmanovich and partially answers a question of m cohen the main results of this article extend to working over k of positive characteristic on the other hand we obtain results on hopf actions on weyl algebras as a consequence of the main theorem

a stochastic model related to the richards type growth curve estimation by means of simulated annealing and variable neighborhood search for a richards type curve a diffusion process is constructed the distribution and main characteristics of the process are analyzed the estimation of the parameters is addressed by maximum likelihood a procedure for bounding the parametric space is established vnd and sa algorithms are used for estimating the parameters a stochastic diffusion model related to a reformulation of the richards growth curve is proposed the main characteristics of the process are studied and the problem of maximum likelihood estimation for the parameters of the process is considered since a complex system of equations appears whose solution cannot be guaranteed via the classic numerical procedures we suggest the use of metaheuristic optimization algorithms such as simulated annealing and variable neighborhood search given that the space of solutions is continuous and unbounded some strategies are suggested for bounding it and a description is provided for the application of the selected algorithms in the case of the variable neighborhood search algorithm a hybrid method is proposed in which it is combined with simulated annealing some examples based on simulated sample paths are developed in order to test the validity of the bounding method for the space of solutions and a comparison is made between the application of both methods