bluuebunny/crossref_metadata_2025 huggingface dataset:
Clinical Pharmacy: Reflections and Forecasts
Authors: Smith William E
Published: February 2007

2006 marked the 40th year of publication for The Annals. Throughout its history. The Annals has provided important contributions to the development of clinical pharmacy. In 2007, we are continuing to publish articles reflecting on the history of clinical pharmacy through the eyes of practitioners, including those pioneering clinical pharmacy, as well as those who have more recently entered the profession and a well-established specialty. In addition, we are presenting articles and editorials from the early history of The Annals that have given direction and shape to the practice of clinical pharmacy (see page 329).
Kinetics of citrate-induced selenite desorption from montmorillonite as affected by complexation with hydroxyaluminum and hydroxyaluminosilicate ions
Authors: Saha Uttam Kumar , Kozak L. M. , Huang P. M.
Published: February 2007

The citrate-induced desorption kinetics of pre-adsorbed Se from montmorillonite (Mt) and its complexes with hydroxyaluminum (HyA-Mt) and hydroxyaluminosilicate (HAS-Mt) were studied. The mole fraction of pre-adsorbed Se released in 24 h from different clays followed the trends of Mt>> HAS-Mt> HyA-Mt with a significant increase with elevated citrate concentration in the desorbing solution. In contrast, the amount of Se adsorbed per unit mass of different clays followed a clear-cut opposite trend of HyA-Mt>HAS-Mt>>Mt. The Se desorption kinetics in different systems indicated multiple rate characteristics; where an initial fast reaction (0.25–2 h) was followed by a slow reaction (2–16 h). Of the six different kinetic models tested (zero-, first-, and second-order; power function, Elovich, and parabolic diffusion), the second-order rate equation showed the overall best fit to the fast and slow desorption kinetic data from the clays. Based on second-order rate constants, the rates of the mole fraction of Se desorption by citrate from different clay systems at 298 K followed the order Mt > HAS-Mt >> HyA-Mt. For both fast and slow reaction, the rates of desorption increased proportionally with the level of citrate. Replicate experiments conducted across a range of temperature (288–318 K) yielded Arrhenius parameters that followed the order HyA-Mt > HAS-Mt >> Mt. Considering that a lower mole fraction of Se desorption after a particular reaction period, slower desorption kinetics, and a greater activation energy of desorption are the indices of increased adsorption bond strength, the results clearly indicate that HyA- and HAS-interlayering and coatings on Mt not only augmented its Se adsorption affinity and capacity, but also increased the adsorption bond strength. Silication in HyA not only reduced the Se adsorption capacity, but also weakened the adsorption bond strength. This establishes a significant role of HyA/HAS-interlayering and coating on Mt in influencing the rate of citrate-induced release of Se. Reduction in surface-positive potential following citrate adsorption on the clay surface, a direct ligand exchange between Se and citrate, and structural dissolution are possible mechanisms responsible for citrate-induced Se desorption in the present study.
Nontronite particle aggregation induced by microbial Fe(III) reduction and exopolysaccharide production
Authors: Jaisi Deb P. , Dong Hailiang , Kim Jinwook , He Ziqi , Morton John P.
Published: February 2007

Clay particle aggregation affects a number of environmental processes, such as contaminant sorption/desorption, particle movement/deposition, and sediment structure and stability, yet factors that control clay aggregation are not well understood. This study was designed to investigate how microbial reduction of Fe(III) in clay structure, a common process in soils and sediments, affects clay-particle aggregation. Microbial Fe(III) reduction experiments were conducted with Shewanella putrefaciens CN32 in bicarbonate buffer with structural Fe (III) in nontronite as the sole electron acceptor, lactate as the sole electron donor, and AQDS as an electron shuttle. Four size fractions of nontronite (D5–D95 of 0.12–0.22 µm, 0.41–0.69 µm, 0.73–0.96 µm and 1.42–1.78 µm) were used to evaluate size-dependent aggregation kinetics. The extent of Fe(III) bioreduction and the amount of exopolysaccharide (EPS), a major biopolymer secreted by CN32 cells during Fe(III) bioreduction, were measured with chemical methods. Nontronite particle aggregation was determined by photon correlation spectroscopy and scanning electron microscopy. The maximum extent of Fe(III) bioreduction reached 36% and 24% for the smallest and the largest size fractions, respectively. Within the same time duration, the effective diameter, measured at 95% percentile (D95), increased by a factor of 43.7 and 7.7 for these two fractions, respectively. Because there was production of EPS by CN32 cells during Fe(III) reduction, it was difficult to assess the relative role of Fe(III) bioreduction and EPS bridging in particle aggregation. Thus, additional experiments were performed. Reduction of Fe(III) by dithionite was designed to examine the effect of Fe(III) reduction, and pure EPS isolated from CN32 cells was used to examine the effect of EPS. The data showed that both Fe(III) reduction and EPS were important in promoting clay mineral aggregation. In natural environments, the relative importance of these two factors may be dependent on local conditions. These results have important implications for understanding factors in controlling clay particle aggregation in natural environments.
Phosphate and glyphosate adsorption by hematite and ferrihydrite and comparison with other variable-charge minerals
Authors: Gimsing Anne Louise , Borggaard Ole Kragholm
Published: February 2007

Adsorption by synthetic 2-line ferrihydrite and hematite of glyphosate and phosphate, separately and together, was compared with adsorption results for goethite, gibbsite and two kaolinites in order to determine adsorption differences and similarities, in particular competition and phosphate preference, of these variable-charge minerals. Hematite rapidly adsorbed both compounds, while adsorption by ferrihydrite was slow, in particular of glyphosate, probably because of very slow diffusion of the bulky glyphosate molecules into interior sites in ferrihydrite particles. Accordingly, the Langmuir adsorption capacity of glyphosate (GAC) was considerably smaller (1.85 µmol m−2)than GAC for hematite (2.61 µmol m−2). The phosphate adsorption capacities (PAC) for ferrihydrite and hematite were more alike, 2.91 µmol m−2 and 2.85 µmol m−2, respectively. Differences between surface coordination (mono- or bidentate) may also contribute to the observed differences but conflicting information about the nature of the surface complexes makes this a difficult contributary factor to assess. The minerals were found to exhibit great variation in extent of competition and phosphate preference. Little competition and phosphate preference characterized hematite adsorption, while phosphate almost completely outcompeted glyphosate on goethite; ferrihydrite adsorption fell between these extremes. These differences may be attributed to different numbers of common (competitive) and specific (selective) adsorption sites on the three Fe oxides with a decreasing number of common sites in the order: goethite>>ferrihydrite>hematite, i.e. almost all goethite sites are common but with strong phosphate preference, while most hematite sites are specific for either glyphosate or phosphate. Alternatively, the result may be explained by adsorption in more planes, e.g. glyphosate adsorption onto the inner-Helmholtz-plane-adsorbed phosphate. For all six minerals compared, desorption of glyphosate following phosphate addition was found to be significantly correlated with the difference between the amounts of phosphate and glyphosate adsorbed indicating that this difference may be used as a competition index for predicting the influence of phosphate on glyphosate adsorption.
Deafness in Sub-Saharan Africa
Authors: Kiyaga Nassozi B , Moores Donald F
Published: February 2007

Deaf education in sub-Saharan Africa originated in the 19th century,
primarily through efforts by hearing European missionaries who
typically followed their homelands' oral-only practices. But education
became available to only a fraction of the deaf population. In the 20th
century, Andrew Foster, a deaf African American missionary and Gallaudet
University's first African American graduate, had unparalleled impact
on deaf education in the region, establishing 31 schools for the Deaf,
training a generation of deaf leaders, and introducing his concept
of Total Communication, which embraced both American and indigenous
signs. Nigeria, Kenya, Uganda, and South Africa have provided leadership
in deaf education, but throughout the region there is growing acceptance
of sign language use in school, and secondary and postsecondary education
for the Deaf is increasingly available. Some national constitutions
safeguard the rights of citizens with disabilities and even recognize
indigenous sign languages. International disability organizations,
particularly the World Federation of the Deaf, have helped change
attitudes and train leaders. Despite some grim present realities,
prospects for continued progress are good.
Measuring Students' Metacognition in Real-Life Situations
Authors: Al-Hilawani Yasser A
Published: February 2007

Metacognitive performance of four groups of students (hearing
high-achieving, hearing average-achieving, hearing underachieving, and
deaf and hard of hearing) in first through third grade in the United
Arab Emirates was examined and compared. Metacognition was measured using
analyses of pictures depicting real-life problematic events, situations,
and behaviors. Participants drew on their ability to apply problem
solving and logical reasoning through visual analysis and discrimination
of test materials rather than through verbal analysis. Results revealed
that metacognition is influenced by students' age. Older students
scored significantly higher on the metacognitive measure than younger
students. Further analysis indicated that hearing high-achieving students
scored significantly higher on the test than the other three groups when
the age variable was controlled for. Deaf and hard of hearing students
performed similarly to age-matched hearing students in applying reasoning
skills to real-life situations.
An Intersubjective Developmental Perspective on Interactions Between Deaf and Hearing Mothers and Their Deaf Infants
Authors: Loots Gerrit , Devise Isabel
Published: February 2007

Most research into interactions between mothers and their infants
with hearing impairments focuses on mothers' and infants' behaviors
separately, speculating about the interplay among these behaviors
and their effects on child development. In the present article, an
intersubjective developmental theory focusing on the development of the
"interworld" between deaf and hearing mothers and their deaf infants is
used to integrate and interpret the seemingly incoherent research on
early mother-deaf child interaction. Inspired by Stern's work (e.g.,
Stern, 1985), the intersubjective developmental theory distinguishes
four stages in the development of intersubjectivity: emerging (birth-2
months), physical (2-8 months), existential (8-13 months), and symbolic
(13 months and older), each characterized by a different type of
mother-infant interaction. The integration of research findings on
early mother-deaf child interaction into these four developmental stages
offers new perspectives that can advance research and resolve certain
early-intervention issues.
The possible dimensions of the higher secant varieties
Authors: Catalano-Johnson Michael L.
Published: February 2007

Let X ⊂ P be an irreducible closed subvariety of projective space. The k th higher secant variety of X , denoted X k , is the closure of the union of all linear spaces spanned by k points of X . Let a k ( X ) = dim ( X k ) -dim ( X k -1 ). It is known that the sequence a k ( X ) is nonincreasing, and that there may be at most one 1 in such a sequence. We prove that these two conditions are also sufficient conditions for an arbitrary sequence λ k of nonnegative integers to be the a k ( X )'s for an irreducible variety X . To this end we exhibit the ideals of the higher secant varities of rational normal scrolls as determinantal ideals. This allows us to compute their dimensions, showing that there is in fact always a rational normal scroll X such that a k ( X ) = λ k for any sequence λ k satisfying the two conditions above.
Lie algebras graded by 3-graded root systems and Jordan pairs covered by grids
Authors: Neher Erhard
Published: February 2007

Let R be an irreducible root system. A Lie Algebra L is called graded by R if L is graded with grading group the root lattice of R such that the only nonzero homogeneous subspaces of L have degree 0 or a root in R , the grading is induced by the adjoint action of a split Cartan subalgebra of a finite-dimensional simple Lie subalgebra of L with root system R , and L is generated by the homogeneous subspaces of nonzero degree. This class of Lie algebras was introduced and studied by S. Berman and R. Moody in Invent. Math. 108 (1992), where, in particular, a classification up to central equivalence is given in the simply-laced case. The doubly-laced cases have recently been classified by G. Benkart and E. Zelmanov. Let R be a 3-graded root system, i.e., R is not of type E_8, F_4 or G_2. In this paper, Lie algebras graded by R are described in a unified way, without case-by-case considerations. Namely, it is shown that a Lie algebra L is 3-graded if and only if L is a central extension of the Tits-Kantor-Koecher algebra of a Jordan pair covered by a grid whose associated 3-graded root system is isomorphic to R . This result is then used to classify Lie algebras graded by R : we give the classification of Jordan pairs covered by a grid and describe their Tits-Kantor-Koecher algebras. One of the advantages of this approach is that it works over rings containing 1/2 and 1/3, and also for infinite root systems. Another application is the description of Slodowy's intersection matrix algebras arising from multiply-affinized Cartan matrices.
Mixed buchsbaum-rim multiplicities
Authors: Kleiman Steven , Thorup Anders
Published: February 2007

We prove the results about mixed Buchsbaum-Rim multiplicities announced in [6, (9.10)(ii), p. 224], including a general mixed-multiplicity formula. In addition, we identify these multiplicities as the coefficients of the "leading form" of the appropriate Buchsbaum-Rim polynomial in three variables, and we prove a positivity theorem. In fact, we define the multiplicities as the degrees of certain zero-dimensional "mixed twisted" Segre classes, and we develop an encompassing general theory of these new rational equivalence classes in all dimensions. In parallel, we develop a theory of pure "twisted" Segre classes, and we recover the main results in [6] about the pure Buchsbaum-Rim multiplicities, the polar multiplicities, and so forth. Moreover, we identify the additivity theorem [6, (6.7b)(i), p. 205] as giving a sort of residual-intersection formula, and we show its (somewhat unexpected) connection to the mixed-multiplicity formula. Also, we work in a more general setup than in [6], and we develop a new approach, based on the completed normal cone.
Higher Picard varieties and the height pairing
Authors: Künnemann Klaus
Published: February 2007

Let X be a smooth projective variety which is defined over a number field. Beilinson and Bloch have defined under suitable asssumptions height pairings between Chow groups of homologically trivial cycles on X. Beilinson has also formulated a hard Lefschetz and a Hodge index conjecture for these Chow groups. We show that the restriction of the height pairing to cycles algebraically equivalent to zero can be computed via Abel-Jacobi maps in terms of the Néron-Tate height pairing on the higher Picard varieties of X . This description is used in the case where X is an abelian variety to prove a consequence of Beilinson conjectures. Namely, we prove a hard Lefschetz and a Hodge index theorem for the groups of cycles algebraically equivalent to zero modulo incidence equivalence.
The valuative condition and R-Hopf algebra orders in KC p 3
Authors: Underwood Robert
Published: February 2007

Let K be a finite extension of Q p endowed with the p-adic valuation and let R be its ring of integers. In this paper we give a complete classification of R-Hopf algebra orders in the group ring KC p 3 . For an arbitrary Hopf order H , we show that either the group scheme SpH or the group scheme SpH *, with H * the linear dual, can be viewed as the middle term of the Baer product of a distinguished extension with a generically trivial extension. Using this characterization we then compute algebra generators for either H or H *.
A simple proof of Kostant's theorem that U (g) is free over its center
Authors: Bernstein Joseph , Lunts Valery
Published: February 2007

In this paper we present a simple proof of the fundamental result by B. Kostant which claims that the universal enveloping algebra of a reductive Lie algebra g is free over its center. We also indicate how this result allows to simplify the proof of another important result of B. Kostant—the description of the algebra of functions on the nilpotent cone. We use this technique to prove some generalizations of Kostant's theorem. We also deduce from it a way to check which subalgebras of g are "centrally free."
On the Bézout problem and area of interpolating varieties in C n
Authors: Li Bao Qin , Taylor B. A.
Published: February 2007

In this paper we obtain the precise bounds on the size of discrete interpolating varieties for weighted spaces of entire functions in several complex variables, and Bezout estimates for entire holomorphic maps with "big" Jacobians.
Descent on fibrations over the projective line
Authors: Skorobogatov Alexei N.
Published: February 2007

We formulate a general set-up for the descent method of J.-L. Colliot-Thélène and J.-J. Sansuc applied to varieties fibred over the projective line over a number field. This makes it possible to prove that the Manin obstruction to the Hasse principle and weak approximation is the only one provided there are only few "degenerate" fibres (usually two, three in some cases), and that "sufficiently many" smooth k -fibres satisfy the Hasse principle and weak approximation. We introduce a new concept of what should be called a "degenerate" fibre, the so called "split" fibres, the property which depends only on the generic fibre and not on the choice of a particular model. This yields a simpler and more general approach to the previous results of that kind.
Automorphic forms with degenerate Fourier coefficients
Authors: Li Jian-Shu
Published: February 2007

The main theme of this paper is that singular automorphic forms on classical groups are given by theta series liftings. We establish several inequalities relating the automorphic multiplicities of a given representation and that of its abstract theta lift. Our methods allow one to lift noncuspidal, square integrable automorphic forms when the dual pair involved is in the stable range. In this way we construct new families of singular automorphic forms, many of which are clearly unipotent. In fact, starting from one-dimensional representations and repeating the procedure (of lifting in the stable range), one may obtain all automorphic forms which are quadratic unipotent in the sense of Moeglin.
Evolution of singularities, generalized Liapunov function and generalized integral for an ideal incompressible fluid
Authors: Shnirelman A.
Published: February 2007

The Liapunov Function is a continuous function, defined in the phase space of a dynamical system, which grows along every trajectory. Its existence means certain irreversibility of the system. Generalized Liapunov Function is a continuous function with values in some topological vector space with a cone, and it grows along every trajectory in the sense of the partial order, defined by the cone. In this work we construct a Generalized Liapunov Function in the phase space of 2-dimensional ideal incompressible fluid. This function is defined in the terms of weak singularities of the flow. Likewise, we find the Generalized Integral; this is a continuous function, defined in the phase space of the fluid, assuming its values in some topological vector space, which is constant along every trajectory. This implies the existence of (a lot of) scalar valued Liapunov Functions and new integrals for the fluid. We also obtain precise result concerning propagation of singularities for the Euler equations, using the Generalized Liapunov Function.
Algebraic Chern-Simons theory
Authors: Bloch Spencer , Esnault Hélène
Published: February 2007

A theory of secondary characteristic classes analogous to the classical Chern-Simons theory is developed for algebraic vector bundles. Applications are made to questions involving finer charcterisitic classes for bundles with connection and to the Griffiths group of algebraic cycles.
Singular integral operators with rough kernels supported by subvarieties
Authors: Fan Dashan , Pan Yibiao
Published: February 2007

In this paper we study the mapping properties of singular Radon transforms defined by translates of a subvariety. The singular kernels considered here are of Calderón-Zygmund type, but are allowed to be very rough both on the unit sphere and in the radial direction. We prove, among other things, that such singular integral operators are bounded on the Lebesgue spaces.
Representing homology classes by locally flat surfaces of minimum genus
Authors: Lee Ronnie , Wilczyński Dariusz M.
Published: February 2007

A necessary and sufficient condition is given for a nontrivial homology class of a simply connected 4-manifold to be represented by a simple, topologically locally flat embedding of a compact Riemann surface. This result extends the embedding theorem of the 2-sphere, proved by the authors in K-Theory 7 (1993), to the case of a surface of any genus. As a consequence, the computation of the least genus of a locally flat surface is obtained for any homology class of even divisibility. The computation of the least genus is also settled for certain (and perhaps all) classes of odd divisibility. In the case of a minimum genus surface it is shown that the constructed embedding is often nonsmoothable. For example, all but nine homology classes in the complex projective plane contain such a nonsmoothable surface. A similar result holds for any class of nonnegative self intersection in a K3 surface.
Defects for ample divisors of abelian varieties, Schwarz lemma, and hyperbolic hypersurfaces of low degrees
Authors: Siu Yum-Tong , Yeung Sai-Kee
Published: February 2007

We prove that the defect vanishes for a holomorphic map f from the affine complex line to an abelian variety A and for an ample divisor D in A . The proof uses the translational invariance of the Zariski closure of the k -jet space of the image of f and the theorem of Riemann Roch to construct a nonidentically zero meromorphic k -jet differential whose pole divisor is dominated by a divisor equivalent to pD and which vanishes along the k -jet space of D to order q with p / q smaller than a prescribed small positive number. Then estimates involving the theta function with divisor D and the logarithmic derivative lemma are used. We also prove a pointwise Schwarz lemma which gives the vanishing of the pullback, by a holomorphic map from the affine complex line to a compact complex manifold, of a holomorphic jet differential vanishing on an ample divisor. This pointwise Schwarz lemma is a slight modification of a statement whose proof Green and Griffiths sketched in their alternative treatment of Bloch's theorem on entire curves in abelian varieties. The log-pole case of the pointwise Schwarz lemma is also given. We construct examples of hyperbolic hypersurface whose degree is only 16 times the square of its dimension.
A Kakeya-type problem for circles
Authors: Wolff Thomas
Published: February 2007

We prove full Hausdorff dimension in a variant of the Kakeya problem involving circles in the plane, and also sharp estimates for the relevant maximal function. These results can also be formulated in terms of the wave equation in two space variables. A novelty in our approach is the use of ideas from computational geometry.
A Roth theorem for amenable groups
Authors: Bergelson Vitaly , McCutcheon Randall , Zhang Qing
Published: February 2007

We prove the following mean ergodic theorem: for any two commuting measure preserving actions { T g } and { S g } of a countable amenable group G on a probability space ( X, A , μ), lim n →∞ 1/|Φ n | Σ g ∈Φ n φ( T g x )ψ( S g T g x ) exist in L 1 ( X, A , μ) for any φ, ψ, ∈ L 2 ( X, A , μ), where {Φ n } is any left Følner sequence for G . This generalizes Furstenberg's ergodic Roth theorem, which corresponds to the case G = Z , T g = S g , as well as a more general result of Conze and Lesigne (which corresponds to the case G = Z with no restrictions on T g and S g ). The limit is identified, and two combinatorial corollaries are obtained. The first of these states that in any subset E ⊂ G × G which is of positive upper density (with regard to any left Følner sequence in G × G ), we may find triangular configurations of the form {( a, b ), ( ga, b ), ( ga, gb )}. This result has as corollaries Roth's theorem on arithmetic progressions of length three and a theorem of Brown and Buhler guaranteeing solutions to the equation x + y = 2 z in any sufficiently big subset of an abelian group of odd order. The second corollary states that if G × G × G is partitioned into finitely many cells, one of these cells contains configurations of the form {( a, b, c ), ( ga, b, c ,), ( ga, gb, c ), ( ga, gb, gc )}.
Large scale behavior of kernels of Schrödinger operators
Authors: Colding Tobias H. , Minicozzi William P.
Published: February 2007

In this paper, we study the asymptotic behavior of solutions to Schrödinger equations on manifolds with nonnegative Ricci curvature and Euclidean volume growth. As a first application, we get a sharp asymptotic estimate on the Green's function for the Laplacian which sharpens results of Li and Yau. Next we establish a definite gap in the possible rates of decay of exterior harmonic functions on these manifolds. When the manifold also has quadratic curvature decay, we get supremum estimates on the C 2 norm of the Green's function; this has function theoretic implications for these manifolds. We then give a generalization to manifolds with nonnegative Ricci curvature outside a compact set. Finally, we study Schrödinger operators where the potential decays quadratically at infinity. In this setting, we obtain a geometric version at infinity of a classical theorem of Bers.
Weighted Strichartz estimates and global existence for semilinear wave equations
Authors: Georgiev Vladimir , Lindblad Hans , Sogge Christopher D.
Published: February 2007

In this paper we prove a sharp global existence theorem in all dimensions for nonlinear wave equations with power-type nonlinearities. The proof is based on a weighted Strichartz estimate involving powers of the Lorentz distance.
On supports of induced representations for symplectic and odd-orthogonal groups
Authors: Jantzen Chris
Published: February 2007

Let G be Sp (2 n, F ) (resp. SO (2 n + 1, F )), where F is a p -adic field of characteristic zero. In this paper, we give a correspondence which associates to an irreducible representation π of G an m -tuple of irreducible representations of lower rank symplectic (resp. orthogonal) groups based on the supercuspidal support of π. We show that this correspondence respects the induction and Jacquet module functors (in a sense to be made precise), as well as verifying a number of other useful properties. In essence, this correspondence allows one to isolate the effects of the different families of supercuspidal representations of general linear groups which appear in the support of π.
Cells of Harish-Chandra modules for real classical groups
Authors: McGovern William M.
Published: February 2007

We compute the W -module structure of a large number of cells of Harish-Chandra modules for a classical group G , where W is the complex Weyl group.
Isotropy of semisimple group actions on manifolds with geometric structure
Authors: Szaro John P.
Published: February 2007

We prove results concerning isotropy of noncompact semisimple Lie group actions that preserve pseudo-Riemannian or affine structures on compact or finite volume manifolds. For example, if a Lie group G acts locally faithfully on a connected compact complete affine manifold M and preserves the affine structure, then the connected component of the identity of each isotropy subgroup is a compact extension of a solvable group. This is a consequence of the result that nontrivial affine actions of connected groups locally isomorphic to SL 2 [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] on such manifolds cannot have fixed points. We also prove that if G is connected semisimple without compact factors and acts isometrically and topologically transitively on a connected finite volume pseudo-Riemannian M , then the action must be (everywhere) locally free. This answers affirmatively a special case of a conjecture by G. D'Ambra and M. Gromov. With only the assumption that no factor of G acts trivially, local freeness is also assured when M is compact and complete.
Gradient estimates for variable coefficient parabolic equations and singular perturbation problems
Authors: Caffarelli Luis A. , Kenig Carlos E.
Published: February 2007

In this article we prove, via monotonicity formulas, interior and boundary gradient estimates for solutions to second order parabolic equations, in divergence form, with Dini top order coefficients. We then prove uniform Lipschitz estimates for solutions of singular perturbation problems, using the previous results, and two phase monotonicity formulas.
Functional independence of the singularities of a class of Dirichlet series
Authors: Kaczorowski J. , Perelli A.
Published: February 2007

We deal with the algebraic independence and, more generally, with the functional independence of the singularities of log F j ( s ), j = 1, . . . , N , and of F ' j / F j ( s ), j = 1, . . . , N , where F j ( s ) are functions in the Selberg class. In particular, we prove the following results: (i) If log F 1 ( s ), . . . , log F N ( s ) are linearly independent over [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /], then P (log F 1 ( s ), . . . , log F N ( s ), s ) has infinitely many singularities in the half plane σ ≥ ½, provided P ∈ [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /][ X 1 , . . . , X N +1 ] with deg P > 0 as a polynomial in the first N variables; and (ii) If P ∈ [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /][ X 1 , . . . , X N ] with deg P > 0, then P ( F ' 1 / F 1 ( s ), . . . , F ' N / F N ( s )) is either constant or has infinitely many singularities in the half plane σ ≥ 0.
Eigenvalues of the Laplacian on inhomogeneous membranes
Authors: Laugesen Richard Snyder
Published: February 2007

This paper compares the eigenvalues arising from the vibration of an inhomogeneous circular membrane with the eigenvalues of a homogeneous circular membrane having the same total mass. Assume that on each concentric subdisk the inhomogeneous membrane has at least as much mass as the homogeneous membrane. Then the first eigenvalue of the whole disk (with Dirichlet boundary conditions) is maximal for the homogeneous membrane. Furthermore, the zeta function of the eigenvalues is minimal for the homogeneous disk. Corollaries follow for simply connected surfaces with nonnegative curvature. Stronger results hold in one dimension, for vibrating strings.
Temps d'existence pour l'équation de Klein-Gordon semi-linéaire à données petites périodiques
Authors: Delort J.-M.
Published: February 2007

We study lower bounds for the maximal time of existence T ∈ of a smooth solution to a semi-linear Klein-Gordon equation □ u + u = F ( u, u '), with periodic Cauchy data of small size ∈. If F vanishes at order r at 0, we prove that T ∈ ≥ c ∈ -2 if r = 2, T ∈ ≥ c ∈ -( r -1) | log ∈ | -( r -3) if r ≥ 3. We construct examples showing the optimality of these results for convenient values of r .
Cohomological degrees and Hilbert functions of graded modules
Authors: Doering Luisa Rodrigues , Gunston Tor , Vasconcelos Wolmer V.
Published: February 2007

Making use of the recent construction of cohomological degrees functions, we give several estimates on the relationship between number of generators and degrees of ideals and modules with applications to Hilbert functions. They extend results heretofore known from generalized Cohen-Macaulay local rings to nearly arbitrary local rings. The rules of computation these functions satisfy enables comparison with Castelnuovo-Mumford's regularity in the graded case. As application, we derive sharp improvements on predicting the outcome of effecting Noether normalizations in tangent cones.
The generation of semilinear singularities by a swallowtail caustic
Authors: Joshi Mark S. , Sá Barreto Antônio
Published: February 2007

We construct examples of bounded solutions to a semilinear system P u = f ( z, u ), z ∈ Ω ⊂ [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /], f smooth, P = P · Id, with P a strictly hyperbolic differential operator of second order with smooth coefficients, such that for a time function t of P , the following properties are satisfied: (1) u is conormal to a smooth characteristic hypersurface Σ in t < 0 such that Σ develops a swallowtail singularity at time t = 0; (2) For t > 0, u is singular, not only at Σ, but also on the forward characteristic cone over the swallowtail tip.
Fourier integral operators with cusp singularities
Authors: Greenleaf Allan , Seeger Andreas
Published: February 2007

We study the boundedness properties, on Lebesgue and Sobolev spaces, of Fourier integral operators associated with canonical relations such that at least one of the projections is a simple (Whitney) cusp. In the process, we obtain decay estimates for oscillatory integral operators whose symplectic relations have the same singular structure. Such singularities occur generically for averages over lines and curves in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]. On L 2 , we show that the operators lose 1/3 derivative. To obtain sharp results off of L 2 , we need to impose an additional transversality condition, satisfied by many geometric averaging operators, which leads to the notion of a strong cusp. These estimates can be further improved if we impose curvature conditions on the cusp surface. One application is the L 2 comp → L 2 1/6, loc and L 12/7 comp → L 2 loc boundedness of restrictions of the X-ray transform on [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /] to four-dimensional families of lines satisfying a natural curvature and torsion condition.
A characterization of rational singularities in terms of injectivity of Frobenius maps
Authors: Hara Nobuo
Published: February 2007

The notions of F -rational and F -regular rings are defined via tight closure, which is a closure operation for ideals in a commutative ring of positive characteristic. The geometric significance of these notions has persisted, and K. E. Smith proved that F -rational rings have rational singularities. We now ask about the converse implication. The answer to this question is yes and no. For a fixed positive characteristic, there is a rational singularity which is not F -rational, so the answer is no. In this paper, however, we aim to show that the answer is yes in the following sense: If a ring of characteristic zero has rational singularity, then its modulo p reduction is F -rational for almost all characteristic p . This result leads us to the correspondence of F -regular rings and log terminal singularities.
Subadjunction of log canonical divisors, II
Authors: Kawamata Yujiro
Published: February 2007

We extend a subadjunction formula of log canonical divisors as in [Kawamata, Contemp. Math. 207 (1997), 79-88] to the case when the codimension of the minimal center is arbitrary by using the positivity of the Hodge bundles.
High frequency approximation of solutions to critical nonlinear wave equations
Authors: Bahouri Hajer , Gérard Patrick
Published: February 2007

This work is devoted to the description of bounded energy sequences of solutions to the equation (1) □ u + | u | 4 = 0 in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /], up to remainder terms small in energy norm and in every Strichartz norm. The proof relies on scattering theory for (1) and on a structure theorem for bounded energy sequences of solutions to the linear wave equation. In particular, we infer the existence of an a priori estimate of Strichartz norms of solutions to (1) in terms of their energy.
An operator space characterization of dual operator algebras
Authors: Le Merdy Christian
Published: February 2007

This paper is devoted to dual algebras, that is w *-closed algebras of bounded operators on Hilbert space. We give abstract characterizations of unital dual algebras (resp. dual algebras) up to w *-homeomorphic unital complete isometry (resp. complete isomorphism). The results we obtain are natural w *-versions of analogous characterizations due to Blecher-Ruan-Sinclair and Blecher respectively, in the category of operator algebras.
Regularity of a fourth order nonlinear PDE with critical exponent
Authors: Chang Sun-Yung A. , Gursky Matthew J. , Yang Paul C.
Published: February 2007

In this paper we demonstrate the regularity of minimizers for a variational problem, a special case of which arises in spectral theory and conformal geometry. The associated Euler-Lagrange equation is fourth order semilinear; the leading term is the bilaplacian, and lower order terms appear at critical powers.
Small data blow-up for semilinear Klein-Gordon equations
Authors: Keel Markus , Tao Terence
Published: February 2007

Energy heuristics predict global existence from small data for semi-linear Klein-Gordon systems when the nonlinearity has order p > 1 + 2/n. We complement these heuristics and previous rigorous existence results by demonstrating blow-up from small data for p ≤ 1 + 2/n.
F-regularity does not deform
Authors: Singh Anurag K.
Published: February 2007

We show that the property of F-regularity does not deform, and thereby settle a longstanding open question in the theory of tight closure. Specifically, we construct a three dimensional N-graded domain R which is not F-regular (or even F-pure), but has a quotient R / tR which is F-regular. Examples are constructed over fields of characteristic p > 0, as well as over fields of characteristic zero.
Strong and weak F -regularity are equivalent for graded rings
Authors: Lyubeznik Gennady , Smith Karen E.
Published: February 2007

It is shown that the tight closure of a submodule in a Artinian module is the same as its finitistic tight closure, when the modules are graded over a finitely generated [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]-graded ring over a perfect field. As a corollary, it is deduced that for such a graded ring, strong and weak F -regularity are equivalent. As another application, the following conjecture of Hochster and Huneke is proved: Let ( R, m ) be a finitely generated [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /]-graded ring over a field with unique homogeneous maximal ideal m , then R is (weakly) F -regular if and only if R m is (weakly) F -regular.
Exceptional quotient singularities
Authors: Markushevich D. , Prokhorov Yu. G.
Published: February 2007

A singularity is said to be exceptional (in the sense of V. Shokurov), if for any log canonical boundary, there is at most one exceptional divisor of discrepancy -1. This notion is important for the inductive treatment of log canonical singularities. The exceptional singularities of dimension 2 are known: they belong to types E 6 , E 7 , E 8 after Brieskorn. In our previous paper, it was proved that the quotient singularity defined by Klein's simple group in its 3-dimensional representation is exceptional. In the present paper, the classification of all the three-dimensional exceptional quotient singularities is obtained. The main lemma states that the quotient of the affine 3-space by a finite group is exceptional if an only if the group has no semiinvariants of degree 3 or less. It is also proved that for any positive ε, there are only finitely many ε-log terminal exceptional 3-dimensional quotient singularities.
Nonnuclear subalgebras of AF algebras
Authors: Dadarlat Marius
Published: February 2007

We show that any non-type I separable unital AF algebra B can be modeled from inside by a nonnuclear C*-algebra and from outside by a nonexact C*-algebra. More precisely there exist unital separable quasidiagonal C*-algebras A ⊂ B ⊂ C of real rank zero, stable rank one, such that A is nonnuclear, C is nonexact, and both A and C are asymptotically homotopy equivalent to B . In particular A, B and C have the same ordered K-theory groups, hence isomorphic ideal lattices, and, A and B have (affinely) homeomorphic trace spaces.
On minima of the absolute value of certain random exponential sums
Authors: Schlag W.
Published: February 2007

Let T n ( x ) = Σ n j =1 ± e 2π ij 2 x where ± stands for a random choice of sign with equal probability. It is shown here that with high probability min x ε[0,1) | T n ( x )| < n -σ provided n is large and σ < 1/12. Similar results are proved for other powers than squares. The problem of determining the optimal σ is open. For the case T n ( x )= Σ n j =1 r j e 2π ij d x , where d = 2, 3,... is fixed and with standard normal r j we show that the minima are typically on the order of n - d +½ with high probability and for large n .
Ill-posedness for one-dimensional wave maps at the critical regularity
Authors: Tao Terence
Published: February 2007

We show that the wave map equation in R 1+1 is in general ill posed in the critical space Ḣ 1/2 , and the Besov space Ḃ 1/2,1 2 . The problem is attributed to the bad behavior of the one-dimensional bilinear expression D -1 ( fDg ) in these spaces.
Open manifolds with sectional curvature bounded from below
Authors: Xia Changyu
Published: February 2007

In this paper, we study complete open manifolds with sectional curvature bounded from below. We obtain some pinching conditions to insure that such manifolds are diffeomorphic to a Euclidean space.
On the exceptional fibres of Kleinian singularities
Authors: Crawley-Boevey William
Published: February 2007

We give a new proof, avoiding case-by-case analysis, of a theorem of Y. Ito and I. Nakamura which provides a module-theoretic interpretation of the bijection between the irreducible components of the exceptional fibre for a Kleinian singularity, and the nontrivial simple modules for the corresponding finite subgroup of SL (2, [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]). Our proof uses a classification of certain cyclic modules for preprojective algebras.
Hypersurfaces of constant mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity
Authors: Guan Bo , Spruck Joel
Published: February 2007

In this paper we study the problem of finding smooth complete hypersurfaces of constant mean curvature in hyperbolic space with a prescribed asymptotic boundary at infinity. Our main results are proved by deriving a priori global gradient estimates based on the classical maximum principle for elliptic equations.
Convex bodies with a point of curvature do not have Fourier bases
Authors: Iosevich Alex , Katz Nets Hawk , Tao Terry
Published: February 2007

We prove that no smooth symmetric convex body Ω with at least one point of non-vanishing Gaussian curvature can admit an orthogonal basis of exponentials. (The nonsymmetric case was proven in a preprint by M. Kolountzakis). This is further evidence of Fuglede's conjecture, which states that such a basis is possible if and only if Ω can tile [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] d by translations.
On the spectrum of a finite-volume negatively-curved manifold
Authors: Lott John
Published: February 2007

We show that a noncompact manifold with bounded sectional curvature, whose ends are sufficiently Gromov-Hausdorff close to rays, has a finite dimensional space of square-integrable harmonic forms. In the special case of a finite-volume manifold with pinched negative sectional curvature, we show that the essential spectrum of the p -form Laplacian is the union of the essential spectra of a collection of ordinary differential operators associated to the ends. We give examples of such manifolds with curvature pinched arbitrarily close to -1 and with an infinite number of gaps in the spectrum of the function Laplacian.
Q-curves and their Manin ideals
Authors: González Josep , Lario Joan-C.
Published: February 2007

Let C be an elliptic curve over Q and let ω denote its Néron differential (uniquely determined up to sign). According to a conjecture of Manin-Stevens, there is a modular parametrization π: X 1 ( N ) → C defined over Q such that the so-called Manin constant c (π) is equal to 1. The constant c (π) is defined by the equality π*(ω) = c (π) f ( q ) dq/q , where f is a normalized newform of weight 2 on Γ 1 ( N ). In this paper we propose a generalization of the Manin constant as a certain ideal (we call it the Manin ideal) attached to modular parametrizations of elliptic curves defined over number fields. We conjecture that its value is (1), generalizing Manin-Stevens, and show the Manin ideal to be an "integral" ideal involving only primes dividing twice the conductor. Motivated by the Manin ideal considerations, we first study several aspects of building blocks of modular abelian varieties and modular parametrizations of Q -curves. Some examples are included to provide numerical evidence of the generalized conjecture, and the paper also contains the analogous items on the Manin ideals for modular building blocks of higher dimension.
Computations of complex equivariant bordism rings
Authors: Sinha Dev P.
Published: February 2007

We give explicit computations of the coefficients of homotopical complex equivariant cobordism theory MU G , when G is abelian. We present a set of generators which is complete for any abelian group. We present a set of relations which is complete when G is cyclic and which we conjecture to be complete in general. We proceed by first computing the localization of MU G obtained by inverting Euler classes of representations. We then define a family of operations which essentially divide by Euler classes and use these operations to define our generating sets. We give geometric applications of these computations to the study of equivariant genera, circle actions on four-manifolds, and cobordism relations between Lens spaces.
Explicit units and the equivariant Tamagawa number conjecture
Authors: Bley W. , Burns D.
Published: February 2007

Let L/K be a finite abelian extension of number fields of group G . We study the Tamagawa number T Ω( L/K ) of h 0 (Spec L ), considered as a motive defined over K and with coefficients [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /][ G ]. For a large class of extensions L/K we interpret the conjectural vanishing of T Ω( L/K ) in terms of the existence of S -units in L satisfying a variety of explicit conditions. These explicit conditions are in the same spirit as, but are in general much finer than, the conditions studied by Rubin and Popescu. By using this approach we are able to complete the proof that T Ω( L/K ) vanishes for all of the genus field extensions considered by Fröhlich. In the course of proving this result we find that for certain extensions the vanishing of T Ω( L/K ) is a refinement of the main result of Solomon concerning "wild Euler systems."