Castelnuovo-Mumford regularity by approximation

The Castelnuovo-Mumford regularity of a module gives a rough measure of its complexity. We bound the regularity of a module given a system of approximating modules whose regularities are known. Such approximations can arise naturally for modules constructed by inductive combinatorial means. We apply these methods to bound the regularity of ideals constructed as combinations of linear ideals and the module of derivations of a hyperplane arrangement as well as to give degree bounds for invariants of finite groups.     

Degree bounds for syzygies of invariants

Suppose that G is a linearly reductive group. Good degree bounds for generators of invariant rings were given in (Proc. Amer. Math. Soc. 129 (4) (2001) 955). Here we study minimal free resolutions of invariant rings. For finite linearly reductive groups G it was recently shown in (Adv. Math. 156 (1) (2000) 23, Electron Res. Announc. Amer. Math. Soc. 7 (2001) 5, Adv. Math. 172 (2002) 151) that rings of invariants are generated in degree at most the group order |G|. In characteristic 0 this degree bound is a classical result by Emmy Noether (see Math. Ann. 77 (1916) 89). Given an invariant ring of a finite linearly reductive group G, we prove that the ideal of relations of a minimal set of generators is generated in degree at most ?2|G|.     

Electronic structure and Fermi surface of Bi2Sr2CaCu2O8

Applying angle-resolved photoemission spectroscopy of high angular and energy resolution we have measured the electronic structure of single crystals of Bi₂Sr₂CaCu₂O₈ near the Fermi energy. Along the high symmetry direction X a band is observed to disperse upwards and to cross the Fermi level, whose unoccupied part constitutes the hole-like carriers responsible for the superconductivity. From spectra along the M direction we find evidence for an electron pocket around the M point. The measured band widths appear to be drastically reduced compared with band structure calculations indicating strong electronic correlation effects. From the observation of Fermi-Dirac-like cut-offs in the spectra due to band crossings through the Fermi level we can confirm the existence and, in particular, the shape of the Fermi surface as calculated by band structure calculations.     

Improved method for the determination of sulfur components in natural gas

Determination of trace concentrations of sulfur components in natural gas is a true analytical challenge. Only analytical procedures based on gas chromatography can meet the sensitivity and accuracy requirements dictated by environmental regulation institutions and modern chemical industry. In the present contribution the sample pretreatment and chromatographic separation steps have been evaluated and optimized based on the use of a flamebased sulfur chemiluminescence detector (SCD) for target compound detection. The proposed instrument consists of a programmed temperature vaporizing (PTV) injector employing a liner packed with Chromosorb 104, a 4 μm thick film apolar column and a flame-based SCD. Using a 13 mL sample loop the detection limit achievable with the new method is 3 μg S/m³. The precision of replicate measure. ments is generally in the range of 5–15% relative standard deviation. Lower detection limits can be achieved by preconcentrating larger sample volumes, e.g. 100 mL.     

EFFECTS OF DOSE FRACTIONATION ON ULTRAVIOLET SURVIVAL OF ESCHERICHIA COLI

Abstract— Exposure of E. coli B/r and B at low average dose rates of u.v. radiation (2537 Å), produced either by fractionated doses or by continuous irradiation at a very low dose rate (80 ergs/mm²/hr), results in much increased survival compared to single exposure at high dose rate. This increase is attributed to repair taking place during the irradiation period. The effect is small in the repair-deficient strains E. coli B_8-1_, and C syn- , and is absent in phage T1 and T4, which cannot undergo repair in the extracellular state. However, the prolonged time available for repair in these experiments accounts for only a very minor part of the increase in survival. The principal factor apparently is that the number of lesions present at any time remains relatively low. Presumably complete repair, not only the excision step, can occur in buffer during the irradiation period. This interpretation is supported by experiments in which cells were exposed to combinations of highly fractionated irradiation and single-dose irradiation. We therefore propose that mutual interference in repair, possibly by overlapping of repair regions in complementary DNA strands, reduces considerably the repair efficiency if many lesions are present. This hypothesis explains the 'shouldered' survival curves of B/r and possibly other E. coli strains as due to decreasing repair efficiency with increasing u.v. dose     

The synthesis,interfacial, and colloidal properties of waterborne cationic methacrylic co-polymers

Two cationic polymers with similar composition were prepared by two different polymerization methods. By monitoring the evolution of the molar mass and chemical composition during the reactions together with charge density measurements and calculations, it was concluded that the cationic polymer synthesized by emulsion polymerization had a less uniform compositional distribution than the cationic polymer prepared by solution polymerization. Contributing to the heterogeneity was the hydrolysis of one monomer (dimethylamino ethylmethacrylate (DMAEMA)) during the synthesis. As a result, the polymer prepared by emulsion polymerization had a more blocky structure and was more surface active as supported by static and dynamic surface tensions data. Fluorescence experiments showed that both polymers formed aggregates at very low concentrations of approximately 0.01 wt%. The aggregates of the polymer prepared by emulsion polymerization were compact, whereas the solution polymerization-based polymer aggregates exhibited a rather expanded geometry.     

Membranous and cartilaginous vocal fold adduction in singing

While vocal fold adduction is an important parameter in speech, relatively little has been known on the adjustment of the vocal fold adduction in singing. This study investigates the possibility of separate adjustments of cartilaginous and membranous vocal fold adduction in singing. Six female and seven male subjects, singers and non-singers, were asked to imitate an instructor in producing four phonation types: "aBducted falsetto" (FaB), "aDducted falsetto" (FaD), "aBducted Chest" (CaB), and "aDducted Chest" (CaD). The phonations were evaluated using videostroboscopy, videokymography (VKG), electroglottography (EGG), and audio recordings. All the subjects showed less posterior (cartilaginous) vocal fold adduction in phonation types FaB and CaB than in FaD and CaD, and less membranous vocal fold adduction (smaller closed quotient) in FaB and FaD than in CaB and CaD. The findings indicate that the exercises enabled the singers to separately manipulate (a) cartilaginous adduction and (b) membranous medialization of the glottis though vocal fold bulging. Membranous adduction (monitored via videokymographic closed quotient) was influenced by both membranous medialization and cartilaginous adduction. Individual control over these types of vocal fold adjustments allows singers to create different vocal timbres.     

Focusing light with a reflection photon sieve

An advanced type of diffractive optical element is presented that combines the concept of the photon sieve with an off-axis, off-normal incidence reflection geometry. Compared to transmission optical elements, the signal-to-background ratio is significantly increased by separating the first from other diffraction orders without drastically reducing the size of the smallest diffractive element. The reflection photon sieve produces sharp foci at maximum contrast and offers the advantages of effective heat dissipation and a large working space above the focal plane. Experimental results for a device working at a photon energy of 100 eV are presented and compared to theory.     

Scalable InP integrated wavelength selector based on binary search

We present an InP monolithically integrated wavelength selector that implements a binary search for selecting one from N modulated wavelengths. The InP chip requires only log(2)N optical filters and log(2)N optical switches. Experimental results show nanosecond reconfiguration and error-free wavelength selection of four modulated wavelengths with 2 dB of power penalty.     

Hilbert series of subspace arrangements

The vanishing ideal I of a subspace arrangement V₁∪V₂∪?∪V_m⊆V is an intersection I₁∩I₂∩?∩I_m of linear ideals. We give a formula for the Hilbert polynomial of I if the subspaces meet transversally. We also give a formula for the Hilbert series of the product ideal J=I₁I₂?I_m without any assumptions about the subspace arrangement. It turns out that the Hilbert series of J is a combinatorial invariant of the subspace arrangement: it only depends on the intersection lattice and the dimension function. The graded Betti numbers of J are determined by the Hilbert series, so they are combinatorial invariants as well. We will also apply our results to generalized principal component analysis (GPCA), a tool that is useful for computer vision and image processing.