monomial subrings in arbitrary dimension abstract we study the seminormalization and weak normalization of subrings of z t1 tn generated by monomials this generalizes our earlier results with n 1

the concentrated solutions on the nonhomogeneous scalar curvature problem abstract we consider the following scalar curvature equation u 1 e k x u 2 1 in r n if k x is nonhomogeneous at the critical points we give the precise description on the concentrated solutions which contains the necessary and existence on the two peak solutions here we generalize the results of cao noussair yan in 6 to the nonhomogeneous case

graded integral domains and nagata rings abstract let r r be an integral domain graded by an arbitrary torsionless grading monoid for any f r let c f be the ideal of r generated by the homogeneous components of f and let n h g r c g v r in this paper we study relationships between the ideal theoretic properties of r n h and the homogeneous ideal theoretic properties of r for example we show that r is a graded krull domain if and only if r n h is a dedekind domain if and only if r n h is a pid and that if r contains a unit of nonzero degree then r is a p v md if and only if r n h is a prufer domain if and only if each ideal of r n h is extended from a homogeneous ideal of r

reinforced random walk leta i i 1 be a sequence of nonnegative numbers difine a nearest neighbor random motion overrightarrow x x 0 x 1 on the integers as follows initially the weight of each interval i i 1 i an integer equals 1 if at timen an interval i i 1 has been crossed exactlyk times by the motion its weight is 1 sum limits j 1 k a j given x 0 x 1 x n i0 i1 in the probability thatx n 1 isi n 1 ori n 1 is proportional to the weights at timen of the intervals i n 1 i n and i n iin 1 we prove that overrightarrow x either visits all integers infinitely often a s or visits a finite number of integers eventually oscillating between two adjacent integers a s and that mathop lim limits n to infty x n n 0 a s for much more general reinforcement schemes we provep overrightarrow x visits all integers infinitely often p overrightarrow x has finite range 1

random walk with memory a reinforced random walk on the d dimensional lattice is considered it is shown that this walk is equivalent to an iterated function system ifs criteria for the existence of limit cycles are given numerical results and conjectures about the quantitative behavior of the walk are stated

divisorial ideals and invertible ideals in a graded integral domain let r oapr r be an integral domain graded by an arbitrary torsionless grading monoid z in this paper we study v ideals and invertible ideals of r in section 3 we determine necessary and sufficient conditions for an integral v ideal of r to be homogeneous whenever it contains a nonzero homogeneous element this condition is equivalent to each integral v ideal z of r of finite type being equal to xj for some x e r the homogeneous quotient field of r and some homogeneous integral v ideal j of r either condition holds if r is integrally closed but not conversely in the special case that r is a z graded integral domain each integral u ideal z of r is equal to x z for some x e r and some homogeneous integral v ideal z of r if and only if r is integrally closed with respect to homogeneous x e r of positive degree these results are then applied to the semigroup ring r x r our results generalize work of querre 181 in the polynomial ring case in section 4 we show that many of the results in section 3 on u ideals carry over to invertible ideals in section 5 we study the relationship between invertible ideals or v ideals of r to invertible ideals or v ideals of r if r c r is an inert extension we show that the natural homomorphism pic r hpic r is an isomorphism where hpic r is the homogeneous picard group of homogeneous invertible ideals of r we investigate the natural homomorphism 4 pic r pit r and give sufficient conditions for

the divisibility orders of zn abstract we establish an algorithm that up to isomorphism determines all the divisibility orders of z n and describes them in terms of the archimedean total orders of z i 1 i n

the elementary action on unimodular rows over a monoid ring in this paper we prove that for a commutative noetherian ring r with krull dim r d max d 2 3 hitherto the special case m 72 was obtained in su bassvasershtein s classical results imply the transitivity only for n b d 2 r the key step is the consideration of finitely generated normal monoids the proof we give here uses some density properties of integer lattices

diagonal subalgebras of bigraded algebras and embeddings of blow ups of projective spaces let v be closed subscheme of inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i defined by a homogeneous ideal i a k x 1 x n and let x be the n 1 fold obtained by blowing up inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i along v if one embeds x in some projective space one is led to consider the subalgebra k i e c of a for some positive integers c and e the aim of this paper is to study ring theoretic properties of k i e c this is achieved by developing a theory which enables us to describe the local cohomology of certain modules over generalized segre products of bigraded algebras these results are applied to the study of the cohen macaulay property of the homogeneous coordinate ring of the blow up of the projective space along a complete intersection we also study the koszul property of diagonal subalgebras of bigraded standard k algebras

homogeneous splitting sets of a graded integral domain abstract let r r be a graded integral domain and let h be the set of nonzero homogeneous elements of r in this paper we study when h is a t splitting set of r and the saturated multiplicative subsets s of r such that h s t where t t h s t v r for all s s

prufer v multiplication domains and related domains of the form d ds γ abstract let d be an integral domain s be a saturated multiplicative subset of d with d d s and be a nonzero torsion free grading monoid with 0 let d s be the semigroup ring of over d s 0 and d s d d s i e d s f d s f 0 d we show that d s is a pvmd resp gcd domain ggcd domain if and only if d is a pvmd resp gcd domain ggcd domain is a valuation semigroup and s is a t splitting resp splitting d splitting set of d

phase transition in reinforced random walk and rwre on trees a random walk on an infinite tree is given a particular kind of positive feedback so edges already traversed are more likely to be traversed in the future using exchangeability theory the process is shown to be equivalent to a random walk in a random environment rwre that is to say a mixture of markov chains criteria are given to determine whether a rwre is transient or recurrent these criteria apply to show that the reinforced random walk can vary from transient to recurrent depending on the value of an adjustable parameter measuring the strength of the feedback the value of the parameter at the phase transition is calculated

generalized krull domains and the composite semigroup ring d e γ abstract let d e be an extension of integral domains be a nonzero torsion free additive grading monoid with quotient group g such that 0 set 0 and r d e in this paper we show that if g satisfies the ascending chain condition on cyclic subgroups then r is a generalized krull domain resp generalized unique factorization domain if and only if d e d is a generalized krull domain resp generalized unique factorization domain and is a generalized krull semigroup resp weakly factorial gcd semigroup

self attracting diffusions case of the constant interaction in this paper we study a self attracting diffusion in the case of a constant self attraction and for dimension larger than two we prove that this process converges almost surely