pinecone/core-2020-05-10-deduplication huggingface dataset:
The Central Hull and Central Kernel in JBW*-Triples

AbstractThe complete lattice I(A) of weak*-closed inner ideals in a JBW*-triple A has as its centre the complete Boolean algebra ZI(A) of weak*-closed ideals in A. The annihilator L⊥ of the subset L of A consists of elements b of A for which {LbA} is equal to zero, and the kernel Ker(L) of L consists of those elements b in A for which {LbL} is equal to zero. For each element J of I(A), J⊥ also lies in I(A), and A enjoys the generalized Peirce decompositionA=J⊕MJ⊥⊕J1,where J1 is the intersection of the kernels of J and J⊥. To investigate the properties of the weak*-closed subspace J1 of A, which is not, in general, a subtriple, the notions of the central hull c(L) and central kernel k(L) of a subspace L are introduced. These are, respectively, the smallest element of ZI(A) containing L and the largest element of ZI(A) contained in L. For any element J of I(A), the relationships that exist between the central hull and central kernel of J and J⊥ are examined and it is shown that (J1)⊥∩J is the weak*-closed ideal k(J), that (J1)⊥∩J⊥ is the weak*-closed ideal k(J⊥), and, when J is a Peirce inner ideal, that (J1)⊥ is the weak*-closed ideal (k(J)⊕Mk(J⊥))
Basically Full Ideals in Local Rings

AbstractLet A be a finitely generated module over a (Noetherian) local ring (R,M). We say that a nonzero submodule B of A is basically full in A if no minimal basis for B can be extended to a minimal basis of any submodule of A properly containing B. We prove that a basically full submodule of A is M-primary, and that the following properties of a nonzero M-primary submodule B of A are equivalent: (a) B is basically full in A; (b) B=(MB):AM; (c) MB is the irredundant intersection of μ(B) irreducible ideals; (d) μ(C)≤μ(B) for each cover C of B. Moreover, if B is an M-primary submodule of A, then B*:=(MB):AM is the smallest basically full submodule of A containing B and B↦B* is a semiprime operation on the set of nonzero M-primary submodules B of A. We prove that all nonzero M-primary ideals are closed with respect to this operation if and only if M is principal. In relation to the closure operation B↦B*, we define and study the bf-reductions of an M-primary submodule D of A; that is, the M-primary submodules C of D such that C⊆D⊆C*. If G(M) denotes the form ring of R with respect to M and G+(M) its maximal homogeneous ideal, we prove that Mn=(Mn)* for all (resp. for all large) positive integers n if and only if grade(G+(M))>0 (resp. grade(M)>0). For a regular local ring (R,M), we consider the M-primary monomial ideals with respect to a fixed regular system of parameters and determine necessary and sufficient conditions for such an ideal to be basically full
Construction of Modules with Finite Homological Dimensions

AbstractA new homological dimension, called G*-dimension, is defined for every finitely generated module M over a local noetherian ring R. It is modeled on the CI-dimension of Avramov, Gasharov, and Peeva and has parallel properties. In particular, a ring R is Gorenstein if and only if every finitely generated R-module has finite G*-dimension. The G*-dimension lies between the CI-dimension and the G-dimension of Auslander and Bridger. This relation belongs to a longer sequence of inequalities, where a strict inequality in any place implies equalities to its right and left. Over general local rings, we construct classes of modules that show that a strict inequality can occur at almost every place in the sequence
Finite Affine Groups: Cycle Indices, Hall–Littlewood Polynomials, and Probabilistic Algorithms

AbstractThe study of asymptotic properties of the conjugacy class of a random element of the finite affine group leads one to define a probability measure on the set of all partitions of all positive integers. Four different probabilistic understandings of this measure are given—three using symmetric function theory and one using Markov chains. This leads to non-trivial enumerative results. Cycle index generating functions are derived and are used to compute the large dimension limiting probabilities that an element of the affine group is separable, cyclic, or semisimple and to study the convergence to these limits. The semisimple limit involves both Rogers–Ramanujan identities. This yields the first examples of such computations for a maximal parabolic subgroup of a finite classical group
The Generalized Terwilliger Algebra and its Finite-dimensional Modules when d=2

AbstractTerwilliger [J. Algebraic Combin.1 (1992), 363–388] considered the C-algebra generated by a given Bose Mesner algebra M and the associated dual Bose Mesner algebra M*. This algebra is now known as the Terwilliger algebra and is usually denoted by T. Terwilliger showed that each vanishing intersection number and Krein parameter of M gives rise to a relation on certain generators of T. These relations are often called the triple product relations. They determine much of the structure of T, though not all of it in general. To illuminate the role these relations play, the current author introduced [J. Algebra233 (2000), 213–252] a generalization T of T. To go from T to T, we replace M and M* with a pair of dual character algebras C and C*. The dimensions of C and C* are equal; let d+1 denote this common dimension. Intuitively, T is the associative C-algebra with identity generated by C and C* subject to the analogues of Terwilliger's triple product relations. T is infinite-dimensional and noncommutative in general. In this paper we study T and its finite-dimensional modules when d=2 and T has no “extra” vanishing intersection numbers or dual intersection numbers. In this case we show T is C-algebra isomorphic to M3(C)⊕A, where M3(C) denotes the C-algebra consisting of all 3-by-3 matrices with entries in C and A denotes the associative C-algebra with identity generated by the symbols e and f subject to the relations e2=e and f2=f. We find a basis for A and we determine the center of A. We classify the finite-dimensional indecomposable A-modules up to isomorphism. There are four such A-modules in every odd dimension, and in every even dimension these modules are parameterized by a single complex number. We also classify the finite-dimensional irreducible A-modules up to isomorphism. Using our results concerning A, we find a basis for T, we describe the center of T, and we classify both the finite-dimensional indecomposable and the finite-dimensional irreducible T-modules up to isomorphism
Generalized Green Classes

AbstractGeneralized Green classes are introduced; some basic properties of members in a generalized Green class are studied. Finally, we apply the results to H(Λ), the Ringel–Hall algebra of a finite-dimensional hereditary algebra Λ over a finite field. In particular, it is proved that H(Λ) belongs to a suitable generalized Green class, and that there is direct decomposition of spaces H(Λ)=C(Λ)⊕J, where C(Λ) is the composition algebra of Λ and J is a twisted Hopf ideal of H(Λ), which is exactly the orthogonal complement of C(Λ)
Bounds in the Theory of Finite Covers

AbstractWe give an upper bound for the number of conjugacy classes of closed subgroups of the full wreath product FWrWSym(Ω) which project onto Sym(Ω). Here, Ω is infinite, W is the set of n-tuples of distinct elements from Ω (for some finite n), F is a finite nilpotent group, and the topology on the wreath product is that of pointwise convergence in its imprimitive permutation action. The result addresses a problem which arises in a natural model-theoretic context about classifying certain types of finite covers
Algebras Generated by Reciprocals of Linear Forms

AbstractLet Δ be a finite set of nonzero linear forms in several variables with coefficients in a field K of characteristic zero. Consider the K-algebra C(Δ) of rational functions generated by {1/α∣α∈Δ}. Then the ring ∂(V) of differential operators with constant coefficients naturally acts on C(Δ). We study the graded ∂(V)-module structure of C(Δ). We especially find standard systems of minimal generators and a combinatorial formula for the Poincaré series of C(Δ). Our proofs are based on a theorem by Brion–Vergne [4] and results by Orlik–Terao [9]
Free Akivis Algebras, Primitive Elements, and Hyperalgebras

AbstractFree Akivis algebras and primitive elements in their universal enveloping algebras are investigated. It is proved that subalgebras of free Akivis algebras are free and that finitely generated subalgebras are finitely residual. Decidability of the word problem for the variety of Akivis algebras is also proved.The conjecture of K. H. Hofmann and K. Strambach (Problem 6.15 in [Topological and analytic loops, in “Quasigroups and Loops Theory and Applications,” Series in Pure Mathematics (O. Chein, H. O. Pflugfelder, and J. D. H. Smith, Eds.), Vol. 8, pp. 205–262, Heldermann Verlag, Berlin, 1990]) on the structure of primitive elements is proved to be not valid, and a full system of primitive elements in free nonassociative algebra is constructed.Finally, it is proved that every algebra B can be considered as a hyperalgebra, that is, a system with a series of multilinear operations that plays a role of a tangent algebra for a local analytic loop, where the hyperalgebra operations on B are interpreted by certain primitive elements
Affine varieties with equivalent cylinders

A well-known cancellation problem asks when, for two algebraic varieties V1, V2 ⊆ Cn, the isomorphism of the cylinders V1 × C and V2 × C implies the isomorphism of V1 and V2. In this paper, we address a related problem: when the equivalence (under an automorphism of Cn+1) of two cylinders V1 × C and V2 × C implies the equivalence of their bases V1 and V2 under an automorphism of Cn. We concentrate here on hypersurfaces and show that this problem establishes a strong connection between the cancellation conjecture of Zariski and the embedding conjecture of Abhyankar and Sathaye. We settle the problem in the affirmative for a large class of polynomials. On the other hand, we give examples of equivalent cylinders with inequivalent bases. (Those cylinders, however, are not hypersurfaces.) Another result of interest is that, for an arbitrary field K, the equivalence of two polynomials in m variables under an automorphism of K[x1,⋯,xn], n ≥ m, implies their equivalence under a tame automorphism of K[x1,⋯,x2n]. © 2002 Elsevier Science (USA).postprin
Pseudocharacters and the Problem of Expressibility for Some Groups

AbstractFor a class of extensions of free products of groups, a description is given of the space of the real-valued functions ϕ defined on the group G and satisfying the conditions (1) the set {ϕ(xy)−ϕ(x)−ϕ(y)∣x,y∈G} is bounded; and (2) ϕ(xn)=nϕ(x) for any x∈G and any n∈Z (the set of integers).Let G be an arbitrary group and let S be its subset such that S−1=S. Suppose gr(S) is the subgroup of G generated by S. Denote by lS(g) the length of an element g∈gr(S) relative to the set S. Let V be a finite subset of a free group F of countable rank, and let the verbal subgroup V(F) be a proper subgroup of F. For arbitrary group G, denote by (G) the set of values in the group G of all the words from the set V. This paper establishes the infinity of the set {lS(g):g∈V(G)}, where G belongs to a class of extension of free products of groups, S=(G)∪(G)−1
On Embeddings of Countable Generalized Soluble Groups into Two-Generated Groups

AbstractStrengthening a theorem of L. G. Kovács and B. H. Neumann on embeddings of countable SN*- and SI*-groups into two-generated SN*- and SI*-groups, we establish embeddability of fully ordered countable SN-, SN*-, SI-, and SI*- groups into appropriate fully ordered two-generated groups of the same type. Moreover, for an arbitrary non-trivial word set V⊆F∞ the mentioned two-generated group can be chosen such that the verbal V-subgroup of the latter contains the order isomorphic copy of an initial countable group. These embeddings are subnormal but not, in general, normal
Finite-Dimensional Representations of a Quantum Double

AbstractLet k be a field and let An(ω) be the Taft's n2-dimensional Hopf algebra. When n is odd, the Drinfeld quantum double D(An(ω)) of An(ω) is a ribbon Hopf algebra. In a previous paper we constructed an n4-dimensional Hopf algebra Hn(p,q) which is isomorphic to D(An(ω)) if p≠0 and q=ω−1, and studied the irreducible representations of Hn(1,q). We continue our study of Hn(p,q), and we examine the finite-dimensional representations of H3(1,q), equivalently, of D(A3(ω)). We investigate the indecomposable left H3(1,q)-module, and describe the structures and properties of all indecomposable modules and classify them when k is algebraically closed. We also give all almost split sequences in modH3(1,q), and the Auslander–Reiten quiver of H3(1,q)
Predisposing factors and consequences of occupational status for long-term unemployed youth: a longitudinal examination

In a longitudinal study, long-term unemployed youth were assessed at T1 on measures of psychological health (self-esteem and psychological distress), general ability, and literacy levels. At T2, three occupational groups were established (those employed at T2, those continuously unemployed between T1-T2, and those unemployed at T2 who had been in the paid work force between T1-T2). These three groups were examined, firstly, in relation to predisposing factors for occupational status, and, secondly, in relation to psychological health consequences of occupational status. Psychological health was not identified as a predictor of occupational status. Reductions in psychological distress occurred at T2 for the employed group only. No changes occurred in self-esteem for any group. General ability, literacy levels, and length of unemployment were identified as predisposing factors for occupational status. Those with higher general ability, better literacy and shorter periods of unemployment at T1 were more likely to be employed at T2.Griffith Health, School of Applied PsychologyFull Tex
An improved method for the large-scale processing of woad (Isatis tinctoria) for possible commercial production of woad indigo

The increasing use of alternative crops has meant the introduction of new technologies to process their products. In this work, an alternative method is presented for the extraction of natural indigo from woad (Isatis tinctoria) based on a technique used to extract indigo from Indigofera spp. This method does not rely on the old fermentation procedure used throughout Northern Europe and is cheap, clean and efficient. Evolved from laboratory-based tests, it involves steeping the leaves at low pH in warm water and extracting the indigo at a higher pH, followed by ultra-filtration of the product, which is then left to air-dry. Problems encountered during the development of the technique and how they were overcome are discussed. © 1998 Silsoe Research Institute
Non destructive identification of wolly peache using impact response near infrared spectroscopy

A procedure which combines impact response and near-infrared sensing in a two-step classification method has been developed for identification of woolly peaches. Two hundred and seventy Maycrest peaches from three ripeness stages at harvest, stored during 0, 1, 2, 3 and 4 weeks at 1 and 5°C, were tested by non-destructive techniques (non-destructive impact and near-infrared spectroscopy) in order to assess woolliness (also known as mealiness in apples). Destructive mechanical tests (Magness–Taylor, confined compression and shear rupture) were used as a reference method to identify woolly fruits. Non-destructive impact data were processed by discriminant analysis to segregate into two texture categories (crispy–firm–hard and non-crispy–non-firm–soft). In the same way, discriminant analysis techniques were used to classify into three juicy categories (low juicy, medium juicy and high juicy), according to the near-infrared second derivative curve. Combining non-destructive impact and near-infrared spectroscopy, not crispy, not firm and soft fruit from the low juicy group were classified as woolly. The percentage of correctly classified fruits in both categories was 80%. The conditions about the experimental factors which enhance woolliness obtained from the destructive procedures were confirmed by the non-destructive procedure
On the Asymptotic Worst Case Behavior of Harmonic Fit

In the parametric bin packing problem we must pack a list of items with size smaller than or equal to 1/r in a minimal number of unit-capacity bins. Among the approximation algorithms, the class of Harmonic Fit algorithms (HFM) plays an important role. Lee and Lee (J. Assoc. Comput. Mach. 32 (1985), 562-572) and Galambos (Ann. Univ. Sci. Budapest Sect. Comput. 9 (1988), 121-126) provide upper bounds for the asymptotic worst case ratio of HFM and show tightness for certain values of the parameter M. In this paper we provide worst case examples that meet the known upper bound for additional values of M, and we show that for remaining values of M the known upper bound is not tight. For the classical bin packing problem (r = 1), we prove an asymptotic worst case ratio of 12/7 for the case M = 4 and 1.7 for the case M = 5. We give improved lower bounds for some interesting cases that are left open
A Network-Flow Technique for Finding Low-Weight Bounded-Degree Spanning
  Trees

The problem considered is the following. Given a graph with edge weights
satisfying the triangle inequality, and a degree bound for each vertex, compute
a low-weight spanning tree such that the degree of each vertex is at most its
specified bound. The problem is NP-hard (it generalizes Traveling Salesman
(TSP)). This paper describes a network-flow heuristic for modifying a given
tree T to meet the constraints. Choosing T to be a minimum spanning tree (MST)
yields approximation algorithms with performance guarantee less than 2 for the
problem on geometric graphs with L_p-norms. The paper also describes a
Euclidean graph whose minimum TSP costs twice the MST, disproving a conjecture
made in ``Low-Degree Spanning Trees of Small Weight'' (1996)
Data-Collection for the Sloan Digital Sky Survey: a Network-Flow
  Heuristic

The goal of the Sloan Digital Sky Survey is ``to map in detail one-quarter of
the entire sky, determining the positions and absolute brightnesses of more
than 100 million celestial objects''. The survey will be performed by taking
``snapshots'' through a large telescope. Each snapshot can capture up to 600
objects from a small circle of the sky. This paper describes the design and
implementation of the algorithm that is being used to determine the snapshots
so as to minimize their number. The problem is NP-hard in general; the
algorithm described is a heuristic, based on Lagriangian-relaxation and
min-cost network flow. It gets within 5-15% of a naive lower bound, whereas
using a ``uniform'' cover only gets within 25-35%.Comment: proceedings version appeared in ACM-SIAM Symposium on Discrete
  Algorithms (1998
Shortest-Path Routing in Arbitrary Networks

AbstractWe introduce an on-line protocol which routes any set ofNpackets along shortest paths with congestionCand dilationDthrough an arbitrary network inO(C+D+logN) steps, with high probability. This time bound is optimal up to the additive logN, and it has previously only been reached for bounded-degree leveled networks.Further, we show that the preceding bound holds also for random routing problems withCdenoting the maximum expected congestion over all links. Based on this result, we give applications for random routing in Cayley networks, general node symmetric networks, edge symmetric networks, and de Bruijn networks.Finally, we examine the problems arising when our approach is applied to routing along non-shortest paths, deterministic routing, or routing with bounded buffers
Optimal Point Placement for Mesh Smoothing

We study the problem of moving a vertex in an unstructured mesh of
triangular, quadrilateral, or tetrahedral elements to optimize the shapes of
adjacent elements. We show that many such problems can be solved in linear time
using generalized linear programming. We also give efficient algorithms for
some mesh smoothing problems that do not fit into the generalized linear
programming paradigm.Comment: 12 pages, 3 figures. A preliminary version of this paper was
  presented at the 8th ACM/SIAM Symp. on Discrete Algorithms (SODA '97). This
  is the final version, and will appear in a special issue of J. Algorithms for
  papers from SODA '9
On-Line Paging against Adversarially Biased Random Inputs

In evaluating an algorithm, worst-case analysis can be overly pessimistic.
Average-case analysis can be overly optimistic. An intermediate approach is to
show that an algorithm does well on a broad class of input distributions.
Koutsoupias and Papadimitriou recently analyzed the least-recently-used (LRU)
paging strategy in this manner, analyzing its performance on an input sequence
generated by a so-called diffuse adversary -- one that must choose each request
probabilitistically so that no page is chosen with probability more than some
fixed epsilon>0. They showed that LRU achieves the optimal competitive ratio
(for deterministic on-line algorithms), but they didn't determine the actual
ratio.
  In this paper we estimate the optimal ratios within roughly a factor of two
for both deterministic strategies (e.g. least-recently-used and
first-in-first-out) and randomized strategies. Around the threshold epsilon ~
1/k (where k is the cache size), the optimal ratios are both Theta(ln k). Below
the threshold the ratios tend rapidly to O(1). Above the threshold the ratio is
unchanged for randomized strategies but tends rapidly to Theta(k) for
deterministic ones.
  We also give an alternate proof of the optimality of LRU.Comment: Conference version appeared in SODA '98 as "Bounding the Diffuse
  Adversary
Incremental and Decremental Maintenance of Planar Width

We present an algorithm for maintaining the width of a planar point set
dynamically, as points are inserted or deleted. Our algorithm takes time
O(kn^epsilon) per update, where k is the amount of change the update causes in
the convex hull, n is the number of points in the set, and epsilon is any
arbitrarily small constant. For incremental or decremental update sequences,
the amortized time per update is O(n^epsilon).Comment: 7 pages; 2 figures. A preliminary version of this paper was presented
  at the 10th ACM/SIAM Symp. Discrete Algorithms (SODA '99); this is the
  journal version, and will appear in J. Algorithm
Invertebrates of ancient heavy metal spoil and smelting tip sites in southern Jordan: Thier distribution and use as bioindicators of metalliferous pollution derived from ancient sources

Pyatt, B. Amos, D. Grattan, J. Pyatt, A. Terrell-Nield, C. Invertebrates of ancient heavy metal spoil and smelting tip sites in southern Jordan: Thier distribution and use as bioindicators of metalliferous pollution derived from ancient sources. Journal of Arid Environments. 2002. 52 pp 53-62The invertebrate populations of stony desert sites contaminated by ancient metalliferous activities in the Nabatean, Roman and Byzantine periods were significantly different from those found in adjacent ancient abandoned field systems. Consequently, it is apparent that such invertebrates potentially have uses as biomonitors of metalliferous pollution derived from ancient anthropogenic activities. This is further explored by an analysis of the heavy metal content of certain of these animals; extensive bioaccumulation of copper and especially lead occurred in organisms inhabiting areas associated with ancient metalliferous enterprises.Peer reviewe