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This paper concerns the dynamic stability of the steady three‐dimensional (3‐D) wave structure of a planar normal shock front intersecting perpendicularly to a planar solid wall for unsteady potential flows. The stability problem can be formulated as a free boundary problem of a quasi‐linear hyperbolic equation of second order in a dihedral‐space domain between the shock front and the solid wall. The key difficulty is brought by the edge singularity of the space domain, the intersection curve between the shock front and the solid wall. Different from the two‐dimensional (2‐D) case, for which the singular part of the boundary is only a point, it is a curve for the 3‐D case in this paper. This difference brings new difficulties to the mathematical analysis of the stability problem. A modified partial hodograph transformation is introduced such that the extension technique developed for the 2‐D case can be employed to establish the well‐posed theory for the initial‐boundary value problem of the linearized hyperbolic equation of second order in a dihedral‐space domain. Moreover, the extension technique is improved in this paper such that loss of regularity in the a priori estimates on the shock front does not occur. Thus, the classical nonlinear iteration scheme can be constructed to prove the existence of the solution to the stability problem, which shows the dynamic stability of the steady planar normal shock without applying the Nash–Moser iteration method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the sum-product problem of obtaining lower bounds for the size of the set A + A A + A := { a + b/ c + d : a, b, c, d ϵ A, c + d ≢= 0 } , for an arbitrary finite set A of real numbers. The main result is the bound ǀA + A/ A + Aǀ ⪢ ǀAǀ2+2/25 ǀA : Aǀ1/25 log ǀAǀ , where A : A denotes the ratio set of A. This improves on a result of Balog and the author ('New sum-product estimates for real and complex numbers', Discrete Comput. Geom. 53 (2015) 825- 846), provided that the size of the ratio set is subquadratic in ǀAǀ; that is, we establish that (inline equation) ǀA + A A + Aǀ ⪡ ǀAǀ2 ⇒ ǀA : Aǀ ⪢ ǀAǀ2 log25 ǀAǀ . This extremal result answers a question similar to some conjectures in a recent paper of the author and Zhelezov ('A bound on the multiplicative energy of a sum set and extremal sumproduct problems', Moscow J. Comb. Number Theory 5 (2015) 53-70). [ABSTRACT FROM AUTHOR]

A point » in the complex plane is said to be free if the group generated by the matricesformula hereis free. The paper gives an infinite family of polynomials whose roots are the non-free points. The main idea in the paper is to employ a symmetry relation. [ABSTRACT FROM AUTHOR]

Let G be a finite group, and let κ(G) be the probability that elements g, h∈G are conjugate, when g and h are chosen independently and uniformly at random. The paper classifies those groups G such that κ(G)≥¼, and shows that G is abelian whenever . It is also shown that κ(G)|G| depends only on the isoclinism class of G.Specializing to the symmetric group Sn, the paper shows that κ(Sn)≤C/n2 for an explicitly determined constant C. This bound leads to an elementary proof of a result of Flajolet et al., that κ(Sn) ∼ A/n2 as n→∞ for some constant A. The same techniques provide analogous results for ρ(Sn), the probability that two elements of the symmetric group have conjugates that commute. [ABSTRACT FROM PUBLISHER]

The cyclotomic Birman–Murakami–Wenzl (or BMW) algebras were introduced by Häring-Oldenburg as a generalization of the BMW algebras associated with the cyclotomic Hecke algebras of type G(k, 1, n) (also known as Ariki–Koike algebras) and type B knot theory. In the PhD thesis of the second author and previous work of the authors, these algebras are shown to be free of rank kn (2n−1)!! over ground rings with parameters satisfying the so-called ‘admissibility conditions’, the most general conditions under which these results can hold. These conditions are build from the representation theory of and are necessary and sufficient in order for these results to hold. (A review of these admissibility conditions and their differences with others used in the literature is provided in this paper.) Furthermore, may be topologically realized, in terms of affine/cylindrical tangles, as a cyclotomic version of the Kauffman tangle algebra, and bases that can be explicitly described both algebraically and diagrammatically were obtained. In this paper, it is shown that these bases combined with a carefully constructed lifting of an arbitrary cellular basis of the Ariki–Koike algebras yield a cellular basis of the cyclotomic BMW algebras, in the sense of Graham and Lehrer, thereby establishing cellularity of the algebra under the most general conditions available in the literature. [ABSTRACT FROM PUBLISHER]

In a previous paper, the author and Swinarski constructed the moduli spaces of stable maps, ℳ̄g, n(Pr, d) via geometric invariant theory (GIT). That paper required the base field to be the complex numbers, a restriction that this paper removes: here the coarse moduli spaces of stable maps are constructed via GIT over a more general base. [ABSTRACT FROM PUBLISHER]

In this paper we continue the study (initiated in a previous paper) of linear Koszul duality, a geometric version of the standard duality between modules over symmetric and exterior algebras. We construct this duality in a very general setting and prove its compatibility with morphisms of vector bundles and base change. [ABSTRACT FROM AUTHOR]

Let Kn ={x-n∶xie0 for 1didn} and suppose that f∶Kn’Kn is nonexpansive with respect to the -1-norm and f(0)=0. It is known that for every x-Kn there exists a periodic point ¾=¾x-Kn (so fp(¾)=¾ for some minimal positive integer p=p¾) and fk(x) approaches {fj(¾)∶0dj [ABSTRACT FROM AUTHOR]

The paper proves several weighted imbedding theorems for domains with fractal boundaries. The weights considered are distances to the boundary to certain powers, and the domains are so-called s-John domains. The paper also proves, in the general setting, that the existence of an imbedding implies compactness of the imbedding for lower exponents. Moreover, following Maz'ya, the paper reformulates the imbedding theorems in the language of local isoperimetric and capacity estimates. [ABSTRACT FROM AUTHOR]

In an attempt to prove all the identities given in Ramanujan's first two letters to G. H. Hardy, G. N. Watson devoted a paper to the evaluation of G1353. At the end of his paper, Watson remarked that his proof was not rigorous as he had assumed certain identities (see (1.1) and (1.2)) which he found empirically. In this paper, we use class field theory, Galois theory and Kronecker's limit formula to justify Watson's assumptions. We shall then use our results to compute some new values of Gn. [ABSTRACT FROM AUTHOR]

Throughout this paper, r will denote a prime. Our object in this paper and another is to describe the finite irreducible subgroups of L(r):=SL(r, ), where denotes the field of complex numbers. The cases for small degrees are known (see [14] for r=2 and r=3; [1] and [23-25] for r=5 and r=7; [13, 18]). The imprimitive irreducible subgroups of L(r) are necessarily monomial because r is a prime, and we describe these in another paper [4]. In this paper, we show how the classification of finite simple groups can be used to classify the finite primitive groups of prime degree. Much of the necessary work has already been done by V. Landazuri and G. M. Seitz (see Lemma 1.3 below). [ABSTRACT FROM AUTHOR]

1. Some groups with the small index propertyIn this paper we shall use the methods of the paper [6] by Hodges, Hodkinson, Lascar and Shelah to show that the free group of countably infinite rank and certain relatively free groups of countably infinite rank have the small index property. [ABSTRACT FROM AUTHOR]

This paper studies the structure of inner functions under the operation of composition, and in particular the notions or primeness and semiprimeness. Results proved include the density of prime finite Blaschke products in the set of finite Blaschke products, the semiprimeness of finite products of thin Blaschke products and their approximability by prime Blaschke products. An example of a nonsemiprime Blaschke product that is a Frostman Blaschke product is also provided. [ABSTRACT FROM AUTHOR]

Abstract: This paper explores further the connection between Langlands duality and T‐duality for compact simple Lie groups, which appeared in work of Daenzer–van Erp and Bunke–Nikolaus. We show that Langlands duality gives rise to isomorphisms of twisted K‐groups, but that these K‐groups are trivial except in the simplest case of SU ( 2 ) and SO ( 3 ). Along the way we compute explicitly the map on H 3 induced by a covering of compact simple Lie groups, which is either 1 or 2 depending in a complicated way on the type of the groups involved. We also give a new method for computing twisted K‐theory using the Segal spectral sequence, which is better adapted to many problems involving compact groups. Finally we study a duality for orientifolds based on complex Lie groups with an involution. [ABSTRACT FROM AUTHOR]

Abstract: The goal of this paper is to study when uniform Roe algebras have certain C ∗‐algebraic properties in terms of the underlying space: in particular, we study properties like having stable rank one or real rank zero that are thought of as low dimensional, and connect these to low dimensionality of the underlying space in the sense of the asymptotic dimension of Gromov. Some of these results (for example, on stable rank one, cancellation, strong quasidiagonality, and finite decomposition rank) give definitive characterizations, while others (on real rank zero) are only partial and leave a lot open. We also establish results about K‐theory, showing that all K 0‐classes come from the inclusion of the canonical Cartan in low‐dimensional cases, but not in general; in particular, our K‐theoretic results answer a question of Elliott and Sierakowski about vanishing of K 0 groups for uniform Roe algebras of non‐amenable groups. Along the way, we extend some results about paradoxicality, proper infiniteness of projections in uniform Roe algebras, and supramenability from groups to general metric spaces. These are ingredients needed for our K‐theoretic computations, but we also use them to give new characterizations of supramenability for metric spaces. [ABSTRACT FROM AUTHOR]

Let g be an eigenform of weight k+2 on Γ0(p)∩Γ1(N) with p ∤ N. If g is non-critical (that is, of slope less than k+1), using the methods of Amice–Vélu and Višik, one can attach [‘Distributions p-adiques associées aux séries de Hecke’, Journées Arithmétiques de Bordeaux (Conf., Univ. Bordeaux, Bordeaux, 1974), Astérisque 24–25 (Soc. Math. France, Paris, 1975) 119–131 (French)] and Višik [Mat. Sb. (N.S.) 99 (1976) 248–260], then one can attach a p-adic L-function to g which is uniquely determined by its interpolation property together with a bound on its growth. However, in the critical slope case, the corresponding growth bound is too large to uniquely determine the p-adic L-function with its standard interpolation property.In this paper, using the theory of overconvergent modular symbols, we give a natural definition of p-adic L-functions in this critical slope case. If, moreover, the modular form is not in the image of theta, then the p-adic L-function satisfies the standard interpolation property. [ABSTRACT FROM PUBLISHER]

Let f=(f1, …, fl):U→Kl, with K=ℝ or ℂ, be a K-analytic mapping defined on an open set U⊂Kn, and let Φ be a smooth function on U with compact support. In this paper, we give a description of the possible poles of the local zeta function attached to (f, Φ) in terms of a log-principalization of the ideal ℐf=(f1, …, fl). When f is a non-degenerate mapping, we give an explicit list for the possible poles of ZΦ(s, f) in terms of the normal vectors to the supporting hyperplanes of a Newton polyhedron attached to f, and some additional vectors (or rays) that appear in the construction of a simplicial conical subdivision of the first orthant. These results extend the corresponding results of Varchenko to the case l≥1, and K=ℝ or ℂ. In the case l=1 and K=ℝ, Denef and Sargos proved that the candidate poles induced by the extra rays required in the construction of a simplicial conical subdivision can be discarded from the list of candidate poles. We extend the Denef–Sargos result to arbitrary l≥1. This yields, in general, a much shorter list of candidate poles, which can, moreover, be read off immediately from Γ(f). [ABSTRACT FROM PUBLISHER]

This paper extends results of M. van den Berg on two-term asymptotics for the trace of Schrödinger operators when the Laplacian is replaced by non-local (integral) operators corresponding to rotationally symmetric stable processes and other closely related Lévy processes. [ABSTRACT FROM PUBLISHER]

In this article, we show that all admissible rational maps with fixed or period 2 cluster cycles can be constructed by the mating of polynomials. We also investigate the polynomials that make up the matings that construct these rational maps. In the one-cluster case, one of the polynomials must be an n-rabbit and in the two-cluster case, one of the maps must be either f, a ‘double rabbit’, or g, a secondary map that lies in the wake of the double rabbit f. There is also a very simple combinatorial way of classifying the maps which must partner the aforementioned polynomials to create rational maps with cluster cycles. Finally, we also investigate the multiplicities of the shared matings arising from the matings in the paper. [ABSTRACT FROM PUBLISHER]

Let f be an orientation-preserving circle homeomorphism and Φ (f) the Douady–Earle extension of f, and let ||f||cr be the cross-ratio distortion norm of f and K(Φ (f)) be the maximal dilatation of Φ (f). As a consequence of results in [A. Douady and C. J. Earle, ‘Conformally natural extension of homeomorphisms of circle’, Acta Math. 157 (1986) 23–48 and M. Lehtinen, ‘The dilatation of Beurling–Ahlfors extensions of quasisymmetric functions’, Ann. Acad. Sci. Fenn. Ser. A I Math. 8 (1983) 187–191], ln K(Φ (f)) has an upper bound depending on ||f||cr exponentially. In this paper, we first show that ln K(Φ (f)) has an upper bound depending on ||f||cr linearly. Then we extensively study the Douady–Earle extension of a very simple map fλ which depends on a real non-negative parameter λ. For this example, we show that, as λ→∞, (1) our new upper bound on ln K(Φ (fλ)) is substantially smaller than the one given by Douady and Earle in terms of the maximal dilatation of the extremal extension of fλ, and (2) the Douady–Earle extension Φ (fλ) stays exponentially far away from being extremal. Finally, we show that , in general, our upper bound on ln K(Φ (f)) implies the one of Douady and Earle when ||f||cr is large enough. [ABSTRACT FROM AUTHOR]

This paper is a continuation of [N. Ghoussoub and A. Moradifam, ‘On the best possible remaining term in the improved Hardy inequality’, Proc. Natl. Acad. Sci. USA 105 (2008) 13746–13751] and [N. Ghoussoub and A. Moradifam, ‘Bessel pairs and optimal Hardy and Hardy–Rellich inequalities’, Math. Ann. 349 (2011) 1–57], where the authors introduced a general approach for improved Hardy and Hardy–Rellich-type inequalities. In this paper, we present equivalent conditions on a pair of positive radial functions V and W on a ball B in Rn, n≥1, and b∈ℝ so that the following inequalities hold and Then we present various classes of optimal weighted Hardy–Rellich inequalities on H2 ∩ H01. The proofs are based on decomposition into spherical harmonics. This type of inequalities is important in the study of the systems of second-order elliptic equations as well as fourth-order elliptic equations with Navier boundary condition. [ABSTRACT FROM PUBLISHER]

We give a corrected and strengthened statement and proof of the ‘p-adic analytic arc lemma’ in a paper of the author (J. London Math. Soc. (2) 73 (2006) 367–379). We show that the analytic arc is guaranteed to exist for p ≥ 5 and give a counterexample showing that this sometimes cannot be done when p = 2. [ABSTRACT FROM PUBLISHER]

In a paper of 2003, Külshammer, Olsson and Robinson defined ℓ-blocks for the symmetric groups, where ℓ>1 is an arbitrary integer. In this paper, we give a definition for the defect group of the principal ℓ-block. We then check that, in the Abelian case, we have an analogue of one of Broué's conjectures. [ABSTRACT FROM PUBLISHER]

For a hyperbolic knot, the excellent component of the character curve is the one containing the complete hyperbolic structure on the complement of the knot. The paper explains a method of computing the excellent component of the character variety of tunnel number 1 knots. [ABSTRACT FROM AUTHOR]

The paper gives a formula for the probability that a randomly chosen elliptic curve over a finite field has a prime number of points. Two heuristic arguments in support of the formula are given as well as experimental evidence. The paper also gives a formula for the probability that a randomly chosen elliptic curve over a finite field has kq points where k is a small number and q is a prime. [ABSTRACT FROM AUTHOR]

The paper considers a mixing Smale space, the relations of stable and unstable equivalence on such a space and the C*-algebras which are constructed from them. In general, these associations are not functorial. However, it is shown that, if one restricts to the class of s-resolving, finite-to-one factor maps, then the construction of the stable C*-algebra is contravariant, while that of the unstable C*-algebra is covariant. The paper also discusses the constructions of these C*-algebras for Smale spaces which are not mixing. [ABSTRACT FROM AUTHOR]

In this paper we study the second‐order parabolic equation ∂tu(t,x)=∇ċa(t,x)ċ∇u(t,x)‐b(t,x)ċ∇u(t,x)+∇b∩(t,x)u(t,x)u(t,x)+V(t,x)(1) in a domain [0,T]×Rd ⊂ Rd+1, where a = (aij)dij=1 is matrix of bounded measurable coefficients, b=(bj)dj=1 , and bˆ = (bˆl)dj=1 are measurable (in general, singular) vector fields, V is a measurable potential, T is a fixed positive number, and ∂tu = ∂u/∂t, and we employ the notation ∇ċaċ∇u= d∑i,j=1∂xiaij∂xju,bċ∇u = d∑j=1bj∂xju, ∇∩bu = d∑j=1 ∂xj (∩bju). We introduce a new class of coefficients in the lower‐order terms for which we prove the existence and the uniqueness of the weak fundamental solution, and for this we derive Gaussian upper and lower bounds. [ABSTRACT FROM AUTHOR]

Let T be a self-affine tile in n defined by an integral expanding matrix A and a digit set D. The paper gives a necessary and sufficient condition for the connectedness of T. The condition can be checked algebraically via the characteristic polynomial of A. Through the use of this, it is shown that in 2, for any integral expanding matrix A, there exists a digit set D such that the corresponding tile T is connected. This answers a question of Bandt and Gelbrich. Some partial results for the higher-dimensional cases are also given. [ABSTRACT FROM AUTHOR]

My paper [2], which appeared in the special issue dedicated to the late Professor Brian Hartley, contained an error in Lemma 2.2 as a result of overlooking the case that the exponents ki on p. 359 may be divisible by arbitrary powers of p, which was pointed out by Professor H. Smith. In order to overcome this situation all of Section 2, except Lemma 2.1, has been rewritten. However this does not cause any change in the rest of the paper. In particular the original assertions remain correct. [ABSTRACT FROM AUTHOR]

A diffeomorphism f of the disk has a periodic orbit 5, and the paper considers the minimal topological entropy l(f, 5) in the isotopy class of f with respect to this orbit. The structure of the periodic orbits with l(f, 5) = 0 has been studied lately and is now well understood. For l(f, 5) non-zero, the paper obtains a lower bound of l(f, 5) that depends only on the period of 5 and which improves previously known estimates. This result is a consequence of a stronger bound in the case where the isotopy class is pseudo-Anosov. It is obtained by studying the induced dynamics on a graph. [ABSTRACT FROM AUTHOR]

The paper proves that a set which contains spheres centered at all points of a set of Hausdorff dimension greater than 1 must have positive Lebesgue measure. It also proves the corresponding result for circles, provided that the set of centers has Hausdorff dimension greater than 3/2. [ABSTRACT FROM AUTHOR]

Let 2 d m d n. The paper gives necessary and sufficient conditions on the parameters s1, s2, &, sm, p1, p2, &, pm such that the Jacobian determinant extends to a bounded operator from s1p1 × s2p2 × & × smpm into 52. Here all spaces are defined on n or on domains ©‚n. In almost all cases the regularity of the Jacobian determinant is calculated exactly. [ABSTRACT FROM AUTHOR]

In this paper we shall prove the main part ((3) implies (1)) of the following theorem. The proof of the theorem will be completed in a forthcoming paper [6]. [ABSTRACT FROM AUTHOR]

Let ” be a finite quiver, that is, a finite directed graph, k be a commutative ring, and k” be the semigroup ring of paths in ”. In this paper we compute the Hochschild homology of the following classes of algebras:(1) k”/5n, where 5 is the arrow ideal;(2) k”/I where I is an ideal generated by quadratic monomials.In Section 2 we establish the notation, and recall a projective resolution of k”0, the degree 0 part in k”, over a monomial algebra which is due to Anick and Green. This resolution is then used in Section 3 as the building block in the construction of a resolution of a truncated or quadratic monomial algebra A, over its enveloping algebra (in the Hochschild sense), Ae. The fact that a monomial algebra possesses a fine grading then enables us to compute the homology.The results obtained extend results by Liu and Zhang [3] and Geller, Reid and Weibel [2]. [ABSTRACT FROM AUTHOR]

In this paper, we investigate two problems concerning a class of higher order uniformly elliptic operators with measurable coefficients. In our first result, we prove a stability estimate for the resolvent of such an operator under perturbation of its principal coefficients in Lp spaces. Our second result is a regularity theorem concerning the smoothing properties of the resolvent, and it provides a sufficient condition under which the first result can be applied. [ABSTRACT FROM AUTHOR]

This paper defines the n-fold central Haagerup tensor product —ni=1-h- of a von Neumann algebra -, and shows that the map ¸z∶—ni =1-h-’CB(-n-1, -) given byformula hereis an isometry. [ABSTRACT FROM AUTHOR]

The paper shows that, if the operator T∶A(³)’B(³) is compact for almost every ³“, then T∶F()’F([Bmacron]) is compact when F([Xmacron])=(X)SK or F([Xmacron])=(X)SJ is the interpolation functor constructed for infinite families of Banach spaces and S satisfies certain conditions. [ABSTRACT FROM AUTHOR]

The paper studies projective stationary sets. The Projective Stationary Reflection Principle is the statement that every projective stationary set contains an increasing continuous --chain of length É1. It is shown that, if Martin's Maximum holds, then the Projective Stationary Reflection Principle holds. Also, this principle is equivalent to the Strong Reflection Principle. The paper shows that the saturation of the nonstationary ideal on É1 is equivalent to a certain kind of reflection. [ABSTRACT FROM AUTHOR]

The theory of heights for rational points on arithmetic elliptic curves is becoming well known. An important fact in the basic theory is the relationship between the naïve and the canonical height of a rational point; in fact, they differ by a uniformly bounded amount. The paper provides a generalisation of this fact from the point of view of heights of polynomials, rather than heights of points. This concept is extended to polynomials in several variables. [ABSTRACT FROM AUTHOR]

The paper shows that the times spent in [0, + ∞) by certain processes Y which are defined by perturbations of Brownian motion involving reflection at maxima and minima are beta distributed. This result relies heavily on Ray-Knight theorems for such perturbed Brownian motions. [ABSTRACT FROM AUTHOR]

The paper gives simple necessary and sufficient conditions for a closed 4-manifold to be homotopy equivalent to the mapping torus of a self homotopy equivalence of a PD3-complex. This is a homotopy analogue of the Stallings and Farrell fibration theorems available in other dimensions. The paper also considers 4-manifolds which admit a geometry of Euclidean factor type and complex surfaces which fibre over S1. [ABSTRACT FROM AUTHOR]

The first person to consider the discrepancy of sequences of the type (±nÃ)ne1 (where 0<Ã<1) was H. Behnke. The subject was taken up again by one of the authors of this paper, who gave a detailed description of the discrepancy's behaviour if either 0<Ã<½ or Ã=½ and ±2 - or Ã=½ and ±-2--. In this paper, we study the case of sequences (±-n)ne1 where ±>0 and ±2--. Bothformula hereare expressed as maxima of finitely many numbers which involve class numbers of imaginary quadratic fields in many cases. [ABSTRACT FROM AUTHOR]

Let G be a locally compact group not necessarily unimodular. Let ¼ be a regular and bounded measure on G. We study, in this paper, the following integral equation,formula hereThis equation generalizes the functional equation for spherical functions on a Gel'fand pair. We seek solutions Æ in the space of continuous and bounded functions on G. If À is a continuous unitary representation of G such that À(¼) is of rank one, then tr(À(¼)À(x)) is a solution of 0(¼). (Here, tr means trace). We give some conditions under which all solutions are of that form. We show that 0(¼) has (bounded and) integrable solutions if and only if G admits integrable, irreducible and continuous unitary representations. We solve completely the problem when G is compact. This paper contains also a list of results dealing with general aspects of 0(¼) and properties of its solutions. We treat examples and give some applications. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to give characterizations of weights for which reverse inequalities of Hölder type for quasi-monotone functions are satisfied. Our inequalities with general weights and with sharp constants complement the results of [2, 8, 9] and [16, 17] for the values of parameters p and q with 1dpdq<∞. [ABSTRACT FROM AUTHOR]

In this paper, we prove the following theorems. (i) Let G be a graph of minimum degree ´e5. If G is embeddable in a surface à and satisfies (´-5)#V(G)#+6Ç(Ã)e0, then G is edge reconstructible. (ii) Any graph of minimum degree 4 that triangulates a surface is edge reconstructible. (iii) Any graph which triangulates a surface of characteristic Çe0 is edge reconstructible. [ABSTRACT FROM AUTHOR]

Hammocks have been considered by Brenner [1], who gave a numerical criterion for a finite translation quiver to be the Auslander-Reiten quiver of some representation-finite algebra. Ringel and Vossieck [11] gave a combinatorial definition of left hammocks which generalised the concept of hammocks in the sense of Brenner, as a translation quiver H and an additive function h on H (called the hammock function) satisfying some conditions. They showed that a thin left hammock with finitely many projective vertices is just the preprojective component of the Auslander-Reiten quiver of the category of 5-spaces, where 5 is a finite partially ordered set (abbreviated as 'poset'). An important role in the representation theory of posets is played by two differentiation algorithms. One of the algorithms was developed by Nazarova and Roiter [8], and it reduces a poset 5 with a maximal element a to a new poset 52=a-5. The second algorithm was developed by Zavadskij [13], and it reduces a poset 5 with a suitable pair (a, b) of elements a, b to a new poset 52=(a,b)5. The main purpose of this paper is to construct new left hammocks from a given one, and to show the relationship between these new left hammocks and the Nazarova-Roiter algorithm. In a later paper [5], we discuss the relationship between hammocks and the Zavadskij algorithm. [ABSTRACT FROM AUTHOR]

In this paper we construct quasinilpotent operators without nontrivial invariant subspaces. As well as being interesting in its own right, we believe that this is a sensible (perhaps necessary) first step for addressing the difficult problem of constructing topologically simple Banach algebras. [ABSTRACT FROM AUTHOR]

In this paper, we consider a basic question in commutative algebra: if I and J are ideals of a commutative ring S, when does IJ=I)J? More precisely, our setting will be in a polynomial ring k[x0, &, xn], and the ideals I and J will define subschemes of the projective space nk over k. In this situation, we are able to relate the equality of product and intersection to the behavior of the cohomology modules of the subschemes defined by I and J. By doing this, we are able to prove several general algebraic results about the defining ideals of certain subschemes of projective space.Our main technique in this paper is a study of the deficiency modules of a subscheme V of n. These modules are important algebraic invariants of V, and reflect many of the properties of V, both geometric and algebraic. For instance, when V is equidimensional and dim Ve1, the deficiency modules of V are invariant (up to a shift in grading) along the even liaison class of V [14, 11, 15, 7], although they do not in general completely determine the even liaison class, except in the case of curves in 3 [14]. On the algebraic side, at least for curves in 3, the deficiency modules have been shown to have connections to the number and degrees of generators of the saturated ideal defining V [12]. One of our main goals in this paper is to extend these results to subschemes of arbitrary codimension in any projective space n.We now describe the contents of this paper more precisely. In the first section, we set up our notation and give the basic definitions which we will use. Then we prove our main technical result: if I and J define subschemes V and Y, respectively, of n, we relate the quotient module (I)J)/IJ to the cohomology of V, at least when V and Y meet properly. We are then able to give a different proof of a general statement due to Serre about when there is an equality of intersection and product.In the second section, we give an extension of Dubreil's Theorem on the number of generators of ideals in a polynomial ring. Specifically, our generalization works for an ideal I defining a locally Cohen-Macaulay, equidimensional subscheme V of any codimension in n, and relates the number of generators of the defining ideal to the length of certain Koszul homologies of the cohomology of V. The results in this section depend crucially on the identification done in Section 1 of the intersection modulo the product.Finally, in Section 3, we give an extension of a surprising result of Amasaki [1] showing a lower bound for the least degree of a minimal generator of the ideal of a Buchsbaum subscheme. Originally, Amasaki gave a bound in the case of Buchsbaum curves in 3 (and later gave a natural extension to Buchsbaum codimension 2 subschemes of n [2]). Easier proofs were subsequently given by Geramita and Migliore in [6], based on a determination of the free resolution of the ideal from a resolution of its deficiency module. For Buchsbaum codimension 2 subschemes of n whose intermediate cohomology vanishes, we are able to extend these considerations. [ABSTRACT FROM AUTHOR]

A group is accessible if there is a G-tree T such that every edge stabilizer is finite and every vertex stabilizer has at most one end. A group is inaccessible if it is not accessible. In [6] I began the study of group actions on protrees. These actions arise naturally when considering inaccessible groups. This study is continued in this paper. [ABSTRACT FROM AUTHOR]

This paper studies the asymptotic behaviour of an analytic order-preserving discrete-time dynamical system in Rn, which is usually generated by a periodic cooperative system. The author proves that for such a dynamical system, if every fixed point is Liapunov stable and every positive semi-orbit has compact closure, then every positive semi-orbit converges. This result does not require the assumption ‘strongly’ and gives an affirmative answer to the conjecture proposed by the author in [17] for the analytic case. [ABSTRACT FROM AUTHOR]