Numerical Computation of Galois Groups

The Galois/monodromy group of a family of geometric problems or equations is a subtle invariant that encodes the structure of the solutions. We give numerical methods to compute the Galois group and study it when it is not the full symmetric group. One algorithm computes generators, while the other studies its structure as a permutation group. We illustrate these algorithms with examples using a Macaulay2 package we are developing that relies upon Bertini to perform monodromy computations.     

On the Delta set and catenary degree of Krull monoids with infinite cyclic divisor class group

Let M be a Krull monoid with divisor class group Z, and let S⊆Z denote the set of divisor classes of M which contain prime divisors. We find conditions on S equivalent to the finiteness of both Δ(M), the Delta set of M, and c(M), the catenary degree of M. In the finite case, we obtain explicit upper bounds on maxΔ(M) and c(M). Our methods generalize and complement a previous result concerning the elasticity of M.     

In situ studies of the active sites for the water gas shift reaction over Cu-CeO2 catalysts: complex interaction between metallic copper and oxygen vacancies of ceria

New information about the active sites for the water gas shift (WGS) reaction over Cu-CeO2 systems was obtained using in-situ, time-resolved X-ray diffraction (TR-XRD), X-ray absorption spectroscopy (TR-XAS, Cu K and Ce L3 edges), and infrared spectroscopy (DRIFTS). Cu-CeO2 nanoparticles prepared by a novel reversed microemulsion method (doped Ce1-xCuxO2 sample) and an impregnation method (impregnated CuOx/CeO2 sample) were studied. The results from all of the samples indicate that both metallic copper and oxygen vacancies in ceria were involved in the generation of active sites for the WGS reaction. Evidence was found for a synergistic Cu-Ovacancy interaction. This interaction enhances the chemical activity of Cu, and the presence of Cu facilitates the formation of O vacancies in ceria under reaction conditions. Water dissociation occurred on the Ovacancy sites or the Cu-Ovacancy interface. No significant amounts of formate were formed on the catalysts during the WGS reaction. The presence of strongly bound carbonates is an important factor for the deactivation of the catalysts at high temperatures. This work identifies for the first time the active sites for the WGS reaction on Cu-CeO2 catalysts and illustrates the importance of in situ structural studies for heterogeneous catalytic reactions.     

Controlling the passage of light through metal microchannels by nanocoatings of phospholipids

The flow of polarized light through a metal film with an array of microchannels is controlled by the phase of an optically active, phospholipid nanocoating, even though the coating does not cover the open area of the microchannels. The molecular details of the assembly (DPPC phospholipid monolayer/bilayer on a hexadecanethiol monolayer on a copper- or nickel-coated microarray) were determined using the infrared, surface-plasmon-mediated, extraordinary transmission of the metal microarrays. Infrared absorption spectra with greatly enhanced absorptions by comparison to literature were recorded and used as a diagnostic for the phase, composition, and molecular geometry of these nanocoatings. This approach presents new tools for nanoscale construction in constricted microspaces, which may ultimately be useful with individual microchannels.     

Faceting and commensurability in crystal structures of colloidal thin films

This Letter investigates the influence of finite size effects on the particle arrangement of thin film colloidal crystals. A rich variety of crystallographic faceting with large single domain microcrystallites is shown. Optical reflectance experiments together with scanning electron microscopy permit the identification of the crystal symmetry and the facet orientation, as well as the exact number of monolayers. When the cell thickness is not commensurable with a high symmetry layering, particles arrange themselves in a periodic distribution of (111)- and (100)-orientated face centered cubic (fcc) microcrystallites separated by planar defects. These structures can be described as a fcc ordering orientated along a vicinal surface, modified by a periodic distribution of fcc (111) stacking faults.     

High resolution electromechanical imaging of ferroelectric materials in a liquid environment by piezoresponse force microscopy

High-resolution imaging of ferroelectric materials using piezoresponse force microscopy (PFM) is demonstrated in an aqueous environment. The elimination of both long-range electrostatic forces and capillary interactions results in a localization of the ac field to the tip-surface junction and allows the tip-surface contact area to be controlled. This approach results in spatial resolutions approaching the limit of the intrinsic domain-wall width. Imaging at frequencies corresponding to high-order cantilever resonances minimizes the viscous damping and added mass effects on cantilever dynamics and allows sensitivities comparable to ambient conditions. PFM in liquids will provide novel opportunities for high-resolution studies of ferroelectric materials, imaging of soft polymer materials, and imaging of biological systems in physiological environments on, ultimately, the molecular level.     

Spin- {\frac{{3}}{{2}}} beyond the Rarita-Schwinger framework

We employ the two independent Casimir operators of the Poincaré group, the squared four-momentum, p², and the squared Pauli-Lubanski vector, W², in the construction of a covariant mass m, and spin- projector in the four-vector spinor, ψ_μ. This projector provides the basis for the construction of an interacting Lagrangian that describes a causally propagating spin- particle coupled to the electromagnetic field by a gyromagnetic ratio of .     

Extended centroid and central closure of semiprime normed algebras. a first approach

In this paper, we classify all the multiplicity-free permutation characters of sporadic simple groups and their automorphism groups. This project is an application of the group theory system GAP, its character table library, and its library of tables of marks.     

On Perturbed Discrete Boundary Value Problems

In this paper, we study nonlinear discrete boundary value problems of the form x ( t +1)= A ( t ) x ( t )+ h ( t )+ k f ( t , x ( t ), k ) subject to Bx (0)+ Dx ( J )= u + k g ( x (0), x ( J ), k ) where k is a "small" parameter. Our main concern is the case of resonance, that is, the situation where the associated linear homogeneous boundary value problem x ( t +1)= A ( t ) x ( t ), Bx (0)+ Dx ( J )=0 admits nontrivial solutions. We establish conditions for the solvability of the nonlinear boundary value problem when k is "small". We also establish qualitative properties of these solutions.     

Cellular NADH and NADPH Conformation as a Real-Time Fluorescence-Based Metabolic Indicator under Pressurized Conditions

Cellular conformation of reduced pyridine nucleotides NADH and NADPH sensed using autofluorescence spectroscopy is presented as a real-time metabolic indicator under pressurized conditions. The approach provides information on the role of pressure in energy metabolism and antioxidant defense with applications in agriculture and food technologies. Here, we use spectral phasor analysis on UV-excited autofluorescence from Saccharomyces cerevisiae (baker’s yeast) to assess the involvement of one or multiple NADH- or NADPH-linked pathways based on the presence of two-component spectral behavior during a metabolic response. To demonstrate metabolic monitoring under pressure, we first present the autofluorescence response to cyanide (a respiratory inhibitor) at 32 MPa. Although ambient and high-pressure responses remain similar, pressure itself also induces a response that is consistent with a change in cellular redox state and ROS production. Next, as an example of an autofluorescence response altered by pressurization, we investigate the response to ethanol at ambient, 12 MPa, and 30 MPa pressure. Ethanol (another respiratory inhibitor) and cyanide induce similar responses at ambient pressure. The onset of non-two-component spectral behavior upon pressurization suggests a change in the mechanism of ethanol action. Overall, results point to new avenues of investigation in piezophysiology by providing a way of visualizing metabolism and mitochondrial function under pressurized conditions.