K-Theory of non-linear projective toric varieties

We define a category of quasi-coherent sheaves of topological spaces on projective toric varieties and prove a splitting result for its algebraic K-theory, generalising earlier results for projective spaces. The splitting is expressed in terms of the number of interior lattice points of dilations of a polytope associated to the variety. The proof uses combinatorial and geometrical results on polytopal complexes. The same methods also give an elementary explicit calculation of the cohomology groups of a projective toric variety over any commutative ring.

The algebraic density property for affine toric varieties

In this paper we generalize the algebraic density property to not necessarily smooth affine varieties relative to some closed subvariety containing the singular locus. This property implies the remarkable approximation results for holomorphic automorphisms of the Andersén–Lempert theory. We show that an affine toric variety X satisfies this algebraic density property relative to a closed T-invariant subvariety Y if and only if X∖Y≠TX∖Y≠T. For toric surfaces we are able to classify those which possess a strong version of the algebraic density property (relative to the singular locus). The main ingredient in this classification is our proof of an equivariant version of Brunella's famous classification of complete algebraic vector fields in the affine plane.

Monodromy calculations for some differential equations

In vielen Teilgebieten der Mathematik ist es w"{u}nschenswert, die Monodromiegruppe einer homogenen linearen Differenzialgleichung zu verstehen. Es sind nur wenige analytische Methoden zur Berechnung dieser Gruppe bekannt, daher entwickeln wir im ersten Teil dieser Arbeit eine numerische Methode zur Approximation ihrer Erzeuger.rnIm zweiten Abschnitt fassen wir die Grundlagen der Theorie der Uniformisierung Riemannscher Fl"achen und die der arithmetischen Fuchsschen Gruppen zusammen. Auss erdem erkl"aren wir, wie unsere numerische Methode bei der Bestimmung von uniformisierenden Differenzialgleichungen dienlich sein kann. F"ur arithmetische Fuchssche Gruppen mit zwei Erzeugern erhalten wir lokale Daten und freie Parameter von Lam'{e} Gleichungen, welche die zugeh"origen Riemannschen Fl"achen uniformisieren. rnIm dritten Teil geben wir einen kurzen Abriss zur homologischen Spiegelsymmetrie und f"uhren die $widehat{Gamma}$-Klasse ein. Wir erkl"aren wie diese genutzt werden kann, um eine Hodge-theoretische Version der Spiegelsymmetrie f"ur torische Varit"aten zu beweisen. Daraus gewinnen wir Vermutungen "uber die Monodromiegruppe $M$ von Picard-Fuchs Gleichungen von gewissen Familien $f:mathcal{X}rightarrow bbp^1$ von $n$-dimensionalen Calabi-Yau Variet"aten. Diese besagen erstens, dass bez"uglich einer nat"urlichen Basis die Monodromiematrizen in $M$ Eintr"age aus dem K"orper $bbq(zeta(2j+1)/(2 pi i)^{2j+1},j=1,ldots,lfloor (n-1)/2 rfloor)$ haben. Und zweitens, dass sich topologische Invarianten des Spiegelpartners einer generischen Faser von $f:mathcal{X}rightarrow bbp^1$ aus einem speziellen Element von $M$ rekonstruieren lassen. Schliess lich benutzen wir die im ersten Teil entwickelten Methoden zur Verifizierung dieser Vermutungen, vornehmlich in Hinblick auf Dimension drei. Dar"uber hinaus erstellen wir eine Liste von Kandidaten topologischer Invarianten von vermutlich existierenden dreidimensionalen Calabi-Yau Variet"aten mit $h^{1,1}=1$.

A Smooth Four-Dimensional G-Hilbert Scheme

2000 Mathematics Subject Classification: 14C05, 14L30, 14E15, 14J35.

On the Mumford-Tate conjecture for Abelian varieties with reduction conditions

In this thesis we study Galois representations corresponding to abelian varieties with certain reduction conditions. We show that these conditions force the image of the representations to be "big," so that the Mumford-Tate conjecture (:= MT) holds. We also prove that the set of abelian varieties satisfying these conditions is dense in a corresponding moduli space.

The main results of the thesis are the following two theorems.

Theorem A: Let A be an absolutely simple abelian variety, End° (A) = k : imaginary quadratic field, g = dim(A). Assume either dim(A) ≤ 4, or A has bad reduction at some prime ϕ, with the dimension of the toric part of the reduction equal to 2r, and gcd(r,g) = 1, and (r,g) ≠ (15,56) or (m -1, m(m+1)/2). Then MT holds.

Theorem B: Let M be the moduli space of abelian varieties with fixed polarization, level structure and a k-action. It is defined over a number field F. The subset of M(Q) corresponding to absolutely simple abelian varieties with a prescribed stable reduction at a large enough prime ϕ of F is dense in M(C) in the complex topology. In particular, the set of simple abelian varieties having bad reductions with fixed dimension of the toric parts is dense.

Besides this we also established the following results:

(1) MT holds for some other classes of abelian varieties with similar reduction conditions. For example, if A is an abelian variety with End° (A) = Q and the dimension of the toric part of its reduction is prime to dim( A), then MT holds.

(2) MT holds for Ribet-type abelian varieties.

(3) The Hodge and the Tate conjectures are equivalent for abelian 4-folds.

(4) MT holds for abelian 4-folds of type II, III, IV (Theorem 5.0(2)) and some 4-folds of type I.

(5) For some abelian varieties either MT or the Hodge conjecture holds.

Varieties of Asian capitalism : toward an institutional theory of Asian enterprise

In this paper we respond to calls for an institution-based perspective on strategy. With its emphasis upon mimetic, coercive, and normative isomorphism, institutional theory has earned a deterministic reputation and seems an unlikely foundation on which to construct a theory of strategy. However, a second movement in institutional theory is emerging that gives greater emphasis to creativity and agency. We develop this approach by highlighting co-evolutionary processes that are shaping the varieties of capitalism (VoC) in Asia. To do so, we examine the extent to which the VoC model can be fruitfully applied in the Asian context. In the spirit of the second movement of institutional theory, we describe three processes in which firm strategy collectively and intentionally feeds back to shape institutions: (1) filling institutional voids, (2) retarding institutional innovation, and (3) deploying institutional escape. We outline the key contributions contained in the articles of this Special Issue and discuss a research agenda generated by the VoC perspective.

An exploration of varieties of visual attention : ERP findings

A set of five tasks was designed to examine dynamic aspects of visual attention: selective attention to color, selective attention to pattern, dividing and switching attention between color and pattern, and selective attention to pattern with changing target. These varieties of visual attention were examined using the same set of stimuli under different instruction sets; thus differences between tasks cannot be attributed to differences in the perceptual features of the stimuli. ERP data are presented for each of these tasks. A within-task analysis of different stimulus types varying in similarity to the attended target feature revealed that an early frontal selection positivity (FSP) was evident in selective attention tasks, regardless of whether color was the attended feature. The scalp distribution of a later posterior selection negativity (SN) was affected by whether the attended feature was color or pattern. The SN was largely unaffected by dividing attention across color and pattern. A large widespread positivity was evident in most conditions, consisting of at least three subcomponents which were differentially affected by the attention conditions. These findings are discussed in relation to prior research and the time course of visual attention processes in the brain.

Bactrocera dorsalis Preference for and performance on two mango varieties at three stages of ripeness

Most tropical fruit flies only lay into mature fruit, but a small number can also oviposit into unripe fruit. Little is known about the link between adult oviposition preference and offspring performance in such situations. In this study we examine the influence of different ripening stages of two mango Mangifera indica L. (Anacardiaceae) varieties on the preference and performance of the Oriental fruit fly, Bactrocera dorsalis (Hendel) (Diptera: Tephritidae), a fly known to be able to develop in unripe fruit. Work was carried out as a series of laboratory-based choice and no-choice oviposition experiments and larval growth trials. In oviposition choice trials, female B. dorsalis demonstrated a preference for ripe fruit of mango variety Namdorkmai over variety Oakrong, but generally the dependent variable most influencing oviposition results was fruit ripening stage. Ripe and fully-ripe mangoes were most preferred for oviposition by B. dorsalis. In contrast, unripe mango was infrequently used by ovipositing females, particularly in choice trials. Consistent with the results of oviposition preference, ripe and fully-ripe mangoes were also best for offspring survival, with a higher percentage of larval survival to pupation and shorter development times in comparison to unripe mango. Changes in Total Soluble Solids, TSS, and skin toughness correlate with changing host use across the ripening stages. Regardless of the mango variety or ripeness stage, B. dorsalis had difficulty penetrating the pericarp of our experimental fruit. Larval survival was also often poor. We discuss the possibility that there may be differences in the ability of laboratory and wild flies to penetrate fruit for oviposition, or that in the field flies more regularly utilize natural fruit wounds as oviposition sites.

Soft toric contact lens prescribing in different countries

There have been significant improvements in toric soft contact lens design over the past decade. Data from our international contact lens prescribing survey were mined to assess recent trends in toric soft contact lens fitting. This survey was conducted by sending up to 1000 survey forms to contact lens fitters in Australia, Canada, Japan, the Netherlands, Norway, the UK and the USA each year between 2000 and 2009. Practitioners were asked to record data relating to the first 10 contact lens fits or refits performed after receiving the forms and to return them to us for analysis. The data revealed a gradual increase in the extent of toric soft lens fitting this century. Excluding Japan – which had a consistently low rate of soft toric lens fitting over the survey period – soft toric lenses now represent over 35% of all soft lenses prescribed; it can be assumed that, on average (and again excluding Japan), all cases of astigmatism 0.75 D or less remains uncorrected among contact lens wearers. Toric lenses are fitted more to those who are older, full-time wearers and reusable lens wearers, and less to those wearing silicone hydrogel and extended wear lenses.

Synchrony of planting and proportions of susceptible varieties affect rice tungro disease epidemics in the Philippines.

Surveys were conducted in the Philippines from 1995 to 1997 to examine relationships between production environment variables (agroecosystem, synchrony of planting, and varieties planted) and the occurrence of rice tungro disease epidemics using correspondence analyses. The sites covered were Isabela, Nueva Ecija, North Cotabato, and Bohol provinces as well as Bicol region. Tungro disease incidence in farmers’ fields was assessed visually based on typical symptoms. In addition, leaf samples were collected from each field and indexed serologically by enzyme-linked immunosorbent assay for the presence of Rice tungro bacilliform (RTBV) and Rice tungro spherical (RTSV) viruses. Thus, relationships between the production environment variables and four disease variables — visual incidence and double RTBV and RTSV, single RTSV, and single RTBV infections — were examined. A higher association was observed between site and varieties planted as well as site and synchrony of planting than between site and agroecosystem or site and disease variables (visual incidence, double RTBV and RTSV and single RTSV infections). Disease variables depended on both varieties planted and synchrony of planting and correspondence analysis revealed that the low disease incidence in Nueva Ecija was associated with synchronous planting while the high disease incidence in Isabela was associated with the planting of susceptible varieties and asynchronous planting. Such findings suggest that the relationship between the last two factors at a given site is critical to predicting tungro occurrence. Moreover, correspondence analysis of the relationship among disease variables revealed that tungro incidence is associated with not only double RTBV and RTSV infections but also single RTSV infections. Implications of these results on tungro epidemiology and management are discussed.

Varieties of collaboration: The case of an Australian retail union

Much has been written about varieties of collaboration and the interplay between conflict and collaboration in industrial relations. This paper explores the preconditions, processes and outcomes associated with the collaborative strategies of an Australian retail trade union: the Shop, Distributive and Allied Employees' Association. The data were collected from an extensive series of interviews with officials and organisers within the union across all Australian states. We find that despite taking a servicing approach, and indeed never aggressively organising members, the union has managed to achieve a range of outcomes that exceed retail employment conditions in other countries. We argue that this is partly a result of the Australian legislative framework, which is inherently pluralist and supportive of collective bargaining. This environment, whereby unions are not forced to fight to represent members, can be conducive to collaborative employment relations, particularly in industries where the parties do not adopt an adversarialist stance.

Drying kinetics of two grape varieties of Italy

Two varieties of grapes, white grape and red grape grown in the Campania region of Italy were selected for the study of drying characteristics. Comparisons were made with treated and untreated grapes under constant drying condition of 50o C in a conventional drying system. This temperature was selected to represent farm drying conditions. Grapes were purchased from a local market from the same supplier to maintain the same size of grapes and same properties. An abrasive physical treatment was used as pretreatment. The drying curves were constructed and drying kinetics was calculated using several commonly available models. It was found that treated samples show better drying characteristics than untreated samples. The objective of this study is to obtain drying kinetics which can be used to optimize the drying operations in grape drying.

Pharmacokinetics-based elucidation on disparity in clinical effectiveness between varieties of Zhi Zhu Wan, a traditional Chinese medical formula

AIM: Zhi Zhu Wan (ZZW) is a classical Chinese medical formulation used for the treatment of functional dyspepsia that attributed to Spleen-deficiency Syndrome. ZZW contains Atractylodes Rhizome and Fructus Citrus Immaturus, the later originates from both Citrus aurantium L. (BZZW) and Citrus sinensis Osbeck (RZZW). The present study is designed to elucidate disparities in the clinical efficacy of two ZZW varieties based on the pharmacokinetics of naringenin and hesperetin. MEHTOD: After oral administration of ZZWs, blood sample was collected from healthy volunteers at designed time points. Naringenin and hesperetin were detected in plasma by RP-HPLC, pharmacokinetic parameters were processed using mode-independent methods with WINNONLIN. RESULTS: After oral administration of BZZW, both naringenin and hesperetin were detected in plasma, and demonstrated similar pharmacokinetic parameters. Ka was 0.384+/-0.165 and 0.401+/-0.159, T(1/2(ke))(h) was 5.491+/-3.926 and 5.824+/-3.067, the AUC (mg/Lh) was 34.886+/-22.199 and 39.407+/-19.535 for naringenin and hesperetin, respectively. However, in the case of RZZW, only hesperetin was found in plasma, but the pharmacokinetic properties for hesperetin in RZZW was different from that in BZZW. T(max) for hesperetin in RZZW is about 8.515h, and its C(max) is much larger than that of BZZW. Moreover, it was eliminated slowly as it possessed a much larger AUC value. CONCLUSION: The distinct therapeutic orientations of the Chinese medical formula ZZWs with different Fructus Citrus Immaturus could be elucidated based on the pharmacokinetic parameters of constituents after oral administration.

Drying kinetics, quality changes and shrinkage of two grape varieties of Italy

Two varieties of grapes, white grape and red grape grown in the Campania region of Italy were selected for the study of drying characteristics, moisture diffusion, quality changes (colour) and shrinkage behaviour. Comparisons were made with treated and untreated grapes under constant drying condition of 50o C in a conventional drying system. This temperature was selected to represent farm drying conditions. Grapes were purchased from a local market from the same supplier to maintain the same size of grapes and same properties. An abrasive physical treatment was used as pretreatment. The drying curves were constructed and drying kinetics was calculated using several commonly available models. It was found that treated samples shows better drying characteristics than untreated samples. The objective of this study is to obtain drying kinetics which can be used to optimize the drying operations in grape drying.