On spaces of modular forms spanned by eta-quotients

An eta-quotient of level N   is a modular form of the shape f(z)=_∏δ|Nη(δz)^_rδ$f(z)={\prod }_{\delta |N}\eta {(\delta z)}^{r_{\delta }}$. We study the problem of determining levels N   for which the graded ring of holomorphic modular forms for _Γ0(N)${\Gamma }_0(N)$ is generated by (holomorphic, respectively weakly holomorphic) eta-quotients of level N  . In addition, we prove that if f(z)$f(z)$ is a holomorphic modular form that is non-vanishing on the upper half plane and has integer Fourier coefficients at infinity, then f(z)$f(z)$ is an integer multiple of an eta-quotient. Finally, we use our results to determine the structure of the cuspidal subgroup of _J0(2^k)(Q)$J_0(2^k)(\mathbb{Q})$.     

Conduction band splitting and transport properties of Bi2Se3

Detailed transport studies of single crystals of Bi₂Se₃ were made in the temperature range of 2–300 K, and the data were analyzed in terms of a model consisting of two groups of electrons—a centrosymmetrical lower conduction band and an upper conduction band located away from the Γ-point. Very good agreement with the experimental data is obtained assuming the electrons are scattered on acoustic phonons and ionized impurities. A rather strong influence of the latter mechanism is attributed to a large number of charged selenium vacancies in Bi₂Se₃. The fitted transport parameters were used to calculate the electronic portion of the thermal conductivity that, in turn, allowed for the determination of the lattice thermal conductivity. The Debye model provides a good approximation to the temperature dependence of the lattice thermal conductivity.     

Enhanced catalytic performance of Ce-MCM-41-supported Rh for CO oxidation

Research on Chemical Intermediates - 1wt%Rh/Ce-MCM-41 catalysts were prepared by the incipient wet impregnation method using mesoporous Ce-MCM-41 materials as supports where the Si/Ce molar ratios...     

Explicit bounds for second-order difference equations and a solution to a question of Stevi?

This note gives explicit, applicable bounds for solutions of a wide class of second-order difference equations with nonconstant coefficients. Among the applications is an affirmative answer to a recent question of Stevi?.     

An Old Argument Against Co-location

I defend an old argument against co-location—the view that human animals are distinct from, but co-located with human persons. The argument is drawn from St. Thomas Aquinas. In order to respond to the argument, co-locationists have to endorse at least one of a trio of claims, none of which is obviously correct. Further, two of the options do not seem to be the sort of positions that should be flowing out of the acceptance of a general metaphysical position. I conclude that co-locationism is more costly than generally thought.     

Hemoglobin as a nitrite anhydrase: modeling methemoglobin-mediated N2O3 formation

Nitrite has recently been recognized as a storage form of NO in blood and as playing a key role in hypoxic vasodilation. The nitrite ion is readily reduced to NO by hemoglobin in red blood cells, which, as it happens, also presents a conundrum. Given NO’s enormous affinity for ferrous heme, a key question concerns how it escapes capture by hemoglobin as it diffuses out of the red cells and to the endothelium, where vasodilation takes place. Dinitrogen trioxide (N₂O₃) has been proposed as a vehicle that transports NO to the endothelium, where it dissociates to NO and NO₂. Although N₂O₃ formation might be readily explained by the reaction Hb‐Fe³⁺+NO₂^?+NO?Hb‐Fe²⁺+N₂O₃, the exact manner in which methemoglobin (Hb‐Fe³⁺), nitrite and NO interact with one another is unclear. Both an “Hb‐Fe³⁺‐NO₂^?+NO” pathway and an “Hb‐Fe³⁺‐NO+NO₂^?” pathway have been proposed. Neither pathway has been established experimentally. Nor has there been any attempt until now to theoretically model N₂O₃ formation, the so‐called nitrite anhydrase reaction. Both pathways have been examined here in a detailed density functional theory (DFT, B3LYP/TZP) study and both have been found to be feasible based on energetics criteria. Modeling the “Hb‐Fe³⁺‐NO₂^?+NO” pathway proved complex. Not only are multiple linkage‐isomeric (N‐ and O‐coordinated) structures conceivable for methemoglobin–nitrite, multiple isomeric forms are also possible for N₂O₃ (the lowest‐energy state has an N? N‐bonded nitronitrosyl structure, O₂N? NO). We considered multiple spin states of methemoglobin–nitrite as well as ferromagnetic and antiferromagnetic coupling of the Fe³⁺ and NO spins. Together, the isomerism and spin variables result in a diabolically complex combinatorial space of reaction pathways. Fortunately, transition states could be successfully calculated for the vast majority of these reaction channels, both M_S=0 and M_S=1. For a six‐coordinate Fe³⁺‐O‐nitrito starting geometry, which is plausible for methemoglobin–nitrite, we found that N₂O₃ formation entails barriers of about 17–20 kcal mol^?1, which is reasonable for a physiologically relevant reaction. For the “Hb‐Fe³⁺‐NO+NO₂^?” pathway, which was also found to be energetically reasonable, our calculations indicate a two‐step mechanism. The first step involves transfer of an electron from NO₂^? to the Fe³⁺–heme–NO center ({FeNO}⁶) , resulting in formation of nitrogen dioxide and an Fe²⁺–heme–NO center ({FeNO}⁷). Subsequent formation of N₂O₃ entails a barrier of only 8.1 kcal mol^?1. From an energetics point of view, the nitrite anhydrase reaction thus is a reasonable proposition. Although it is tempting to interpret our results as favoring the “{FeNO}⁶+NO₂^?” pathway over the “Fe³⁺‐nitrite+NO” pathway, both pathways should be considered energetically reasonable for a biological reaction and it seems inadvisable to favor a unique reaction channel based solely on quantum chemical modeling.     

Properties of the nonsymmetric Robinson–Schensted–Knuth algorithm

We introduce a generalization of the Robinson–Schensted–Knuth insertion algorithm for semi-standard augmented fillings whose basement is an arbitrary permutation σ∈S _n . If σ is the identity, then our insertion algorithm reduces to the insertion algorithm introduced by the second author (Sémin. Lothar. Comb. 57:B57e, 2006) for semi-standard augmented fillings and if σ is the reverse of the identity, then our insertion algorithm reduces to the original Robinson–Schensted–Knuth row insertion algorithm. We use our generalized insertion algorithm to obtain new decompositions of the Schur functions into nonsymmetric elements called generalized Demazure atoms (which become Demazure atoms when σ is the identity). Other applications include Pieri rules for multiplying a generalized Demazure atom by a complete homogeneous symmetric function or an elementary symmetric function, a generalization of Knuth’s correspondence between matrices of non-negative integers and pairs of tableaux, and a version of evacuation for composition tableaux whose basement is an arbitrary permutation σ.     

Thermal imaging of microwave fields inside the surfatron and the microwave plasma torch

A new method is introduced for imaging microwave fields, such as those found in microwave-plasma support structures. The method relies upon the darkening that such fields cause in heat-sensitive paper, such as that used in some telefax printers. With this new method, the microwave-frequency electric fields inside two microwave-plasma support structures, the surfatron and the microwave plasma torch, have been measured and subsequently imaged in three dimensions. The images reveal that the surfatron and microwave plasma torch have different operational behavior. As expected, the electric field strength inside the surfatron exponentially falls off down the length of the quartz plasma tube. The field inside the microwave plasma torch initially diminishes, but then increases in strength towards the end of the tube. An aerosol was introduced into the surfatron to observe the effect of water vapor on the electric field strength and distribution. The exponential axial decay of the electric field in the ‘dry’ surfatron plasma, characteristic of a surface wave propagating down a quartz plasma tube, is extended further down the quartz tube in the ‘wet’ plasma. A drop in plasma conductivity is likely the origin of the elongated propagation of the surface wave.