A splitting result for the algebraic K-theory of projective toric schemes

Suppose X is a projective toric scheme defined over a ring R and equipped with an ample line bundle L . We prove that its K-theory has a direct summand of the form K(R)(k+1) where k = 0 is minimal such that L?(-k-1) is not acyclic. Using a combinatorial description of quasi-coherent sheaves we interpret and prove this result for a ring R which is either commutative, or else left noetherian.

Analytical calculation of far infrared spectra of ice in terms of a molecular model

Wideband far infrared (FIR) spectra of complex permittivity e(p) of ice are calculated in terms of a simple analytical theory based on the method of dipolar autocorrelation functions. The molecular model represents a revision of the model recently presented for liquid water in Adv. Chem. Phys. 127 (2003) 65. A composite two-fractional model is proposed. The model is characterised by three phenomenological potential wells corresponding to the three FIR bands observed in ice. The first fraction comprises dipoles reorienting in a rather narrow and deep hat-like well; these dipoles generate the librational band centred at the frequency approximate to 880 cm(-1). The second fraction comprises elastically interacting particles; they generate two nearby bands placed around frequency 200 cm(-1). For description of one of these bands the harmonic oscillator (HO) model is used, in which translational oscillations of two charged molecules along the H-bond are considered. The other band is produced by the H-bond stretch, which governs hindered rotation of a rigid dipole. Such a motion and its dielectric response are described in terms of a new cut parabolic (CP) model applicable for any vibration amplitude. The composite hat-HO-CP model results in a smooth epsilon(nu) ice spectrum, which does not resemble the noise-like spectra of ice met in the known literature. The proposed theory satisfactorily agrees with the experimental ice spectrum measured at - 7 degrees C. The calculated longitudinal optic-transverse optic (LO-TO) splitting occurring at approximate to 250 cm(-1) qualitatively agrees with the measured data. (c) 2004 Elsevier B.V. All rights reserved.

The Teaching Space Allocation Problem with splitting

A standard problem within universities is that of teaching space allocation which can be thought of as the assignment of rooms and times to various teaching activities. The focus is usually on courses that are expected to fit into one room. However, it can also happen that the course will need to be broken up, or ‘split’, into multiple sections. A lecture might be too large to fit into any one room. Another common example is that of seminars or tutorials. Although hundreds of students may be enrolled on a course, it is often subdivided into particular types and sizes of events dependent on the pedagogic requirements of that particular course. Typically, decisions as to how to split courses need to be made within the context of limited space requirements. Institutions do not have an unlimited number of teaching rooms, and need to effectively use those that they do have. The efficiency of space usage is usually measured by the overall ‘utilisation’ which is basically the fraction of the available seat-hours that are actually used. A multi-objective optimisation problem naturally arises; with a trade-off between satisfying preferences on splitting, a desire to increase utilisation, and also to satisfy other constraints such as those based on event location and timetabling conflicts. In this paper, we explore such trade-offs. The explorations themselves are based on a local search method that attempts to optimise the space utilisation by means of a ‘dynamic splitting’ strategy. The local moves are designed to improve utilisation and satisfy the other constraints, but are also allowed to split, and un-split, courses so as to simultaneously meet the splitting objectives.

Nitrogen-15 and Oxygen-18 Natural Abundance of Potassium Chloride Extractable Soil Nitrate Using the Denitrifier Method

In agroecosystems, most isotopic investigations of NO3- involve the use of tracers that are artificially enriched in 15N. Although the dual isotope composition of NO3-— d15N and d18O is especially beneficial for understanding the origin and fate of NO3-, its use for KCl-extractable soil NO3- has been hampered by the lack of a suitable analytical technique. Our objective was to test whether the denitrifier method, whereby NO3- is reduced to N2O before mass spectrometric analysis, can be used to determine the N and O isotopic composition of NO3- from 2 M KCl soil extracts. Several internationally accepted NO3- standards were dissolved in 2 M KCl, the conventional extractant for soil inorganic N, and inoculated with the bacterial strain Pseudomonas aureofaciens (ATCC no. 13985). The standard deviation of the NO3- standards analyzed did not exceed 0.2‰ for d15N and 0.3‰ for d18O values. After appropriate corrections, differences between our measured and consensus d15N and d18O values of standard NO3- generally were within the standard deviations given for the consensus values. Both d15N and d18O values were reproducible among separate analytical runs. The method was also tested on genuine 2 M KCl extracts from unfertilized and fertilized soils. Depending on N fertilization, the soils had distinct d15N and d18O values, which were attributed to amendment with NH4NO3 fertilizer. Hence, our data indicate that the denitrifier method provides a fast, reliable, precise, and accurate way of simultaneously analyzing the natural abundances of 15N and 18O in KCl-extractable soil NO3-.

Laser annealing of sputtered silicon for wafer-bonding applications

Sputtered silicon is investigated as a bonding layer for transfer of pre-processed silicon layers to various insulating substrates. Although the material appears suitable for low temperature processing, previous work has shown that gas trapped in the pores of the sputtered material is released at temperatures above 350 degrees C and further increases of temperature lead to destruction of any bonded interface. Pre-annealing at 1000 degrees C before bonding drives out gas and/or seals the surface, but for device applications where processing temperatures must be kept below about 300 degrees C, this technique cannot be used. In the current work, we have investigated the effect of excimer laser-annealing to heat the sputtered silicon surface to high temperature whilst minimising heating of the underlying substrate. Temperature profile simulations are presented and the results of RBS, TEM and AFM used to characterise the annealed layers. The results verify that gases are present in the sub-surface layers and suggest that while sealing of the surface is important for suppression of the out-diffusion of gases, immediate surface gas removal may also play a role. The laser-annealing technique appears to be an effective method of treating sputtered silicon, yielding a low roughness surface suitable for wafer bonding, thermal splitting and layer transfer.

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.

Granular fertilizer drying and agglomeration in storage

In the manufacture of granular NPK fertilizer the product is cooled before packaging and storage in moisture-proof bags. It has been shown that the temperature of the fertilizer prior to packing is significant in that at high temperatures, drying of the granules takes place in the bag which causes an increase in the humidity of the air surrounding the granules and thus an increase in moisture content at the granule - granule interface. This surface moisture was shown to increase the likelihood of agglomeration in the fertilizer by a capillary adhesion/unconfined yield stress model. An iterative model was set up to establish conditions that would prevent drying occurring, which takes into account fertilizer drying rate, fertilizer cooling rate cooling rate and the effect of coating oils on the drying mechanism.

Filling Ability and Plastic Settlement of Self-Compacting Concrete

The use of self-compacting concrete (SCC) facilitates the placing of concrete by eliminating the need for compaction by vibration. Given the highly flowable nature of such concrete, care is required to ensure excellent filling ability and adequate stability. This is especially important in deep structural members and wall elements where concrete can block the flow, segregate and exhibit bleeding and settlement which can result in local defects that can reduce mechanical properties, durability and quality of surface finish. This paper shows results of an investigation of fresh properties of self-compacting concrete, such as filling ability measured by slump flow and flow time (measured by Orimet) and plastic fresh settlement measured in a column. The SCC mixes incorporated various combinations of fine inorganic powders and admixtures. The slump flow of all SCCs was greater than 580 mm and the time in which the slumping concrete reached 500 rnm was less than 3 s. The flow time was less than 5 s. The results on SCCs were compared to a control mix. The compressive strength and splitting tensile strength of SCCs were also measured. The effects of water/powder ratio, slump and nature of the sand on the fresh settlement were also evaluated. The volume of coarse aggregate and the dosage of superphsticizer were kept constant. It can be concluded that the settlement of fresh self-compacting concrete increased with the increase in water/powder ratio and slump. The nature of sand influenced the maximum settlement.

Effect of Free-Fall Height in Water on Performance of Flowable Concrete

Concrete placed under water should be proportioned to flow readily into place with minimum materials separation. Unlike concrete cast for deep tremie seals, the use of concrete in repairs often necessitates some free fall of the mixture through water. Such placement conditions lead to greater risk of water erosion and segregation, and should be addressed in proportioning highly flowable underwater concrete. This paper evaluates the effect of free-fall height (FFH) of concrete through water on resulting in-place properties. Concrete was cast in blocks measuring 0.54 x 0.44 x 1 m with the initial FFH in water ranging between 0.25 and 0.60 m. In-place compressive and splitting tensile strengths, unit weight, and depth of washed-out and sedimentation materials were determined. In total, 24 highly flowable mixtures with slump flows greater than 500 mm were investigated. The evaluated mixtures were prepared with various hydraulic binders, including conventional Type 10 cement, a binary mixture with 10% of silica fume (SF), and a ternary binder incorporating 20% of fly ash (FA) and 6% of SF. The mixtures were proportioned with water-binder ratios (w/b) ranging between 0.41 and 0.47. Test results show that the increase of FFH of fresh concrete in water can greatly decrease the residual strength and significantly increase the thickness of washed out and sedimentation materials. The incorporation of 10% of SF, or 20% of FA and 6% of SF, and the reduction of the w/b from 0.47 to 0.41 can, however, lead to a significant increase in washout resistance and residual strength. A relationship between residual strength and the coupled factor of free-fall drop of concrete in water and washout resistance is established.

Convergence acceleration of the doubly periodic Green's function for the analysis of thin wire arrays

A method is proposed to accelerate the evaluation of the Green's function of an infinite double periodic array of thin wire antennas. The method is based on the expansion of the Green's function into series corresponding to the propagating and evanescent waves and the use of Poisson and Kummer transformations enhanced with the analytic summation of the slowly convergent asymptotic terms. Unlike existing techniques the procedure reported here provides uniform convergence regardless of the geometrical parameters of the problem or plane wave excitation wavelength. In addition, it is numerically stable and does not require numerical integration or internal tuning parameters, since all necessary series are directly calculated in terms of analytical functions. This means that for nonlinear problem scenarios that the algorithm can be deployed without run time intervention or recursive adjustment within a harmonic balance engine. Numerical examples are provided to illustrate the efficiency and accuracy of the developed approach as compared with the Ewald method for which these classes of problems requires run time splitting parameter adaptation.

Threshold effects in the Teaching Space Allocation Problem with Splitting

Universities aim for good “Space Management” so as to use the teaching space efficiently. Part of this task is to assign rooms and time-slots to teaching activities with limited numbers and capacities of lecture theaters, seminar rooms, etc. It is also common that some teaching activities require splitting into multiple events. For example, lectures can be too large to fit in one room or good teaching practice requires that seminars/tutorials are taught in small groups. Then, space management involves decisions on splitting as well as the assignments to rooms and time-slots. These decisions must be made whilst satisfying the pedagogic requirements of the institution and constraints on space resources. The efficiency of such management can be measured by the “utilisation”: the percentage of available seat-hours actually used. In many institutions, the observed utilisation is unacceptably low, and this provides our underlying motivation: to study the factors that affect teaching space utilisation, with the goal of improving it. We give a brief introduction to our work in this area, and then introduce a specific model for splitting. We present experimental results that show threshold phenomena and associated easy-hard-easy patterns of computational difficulty. We discuss why such behaviour is of importance for space management.