Multiple quantum magic-angle spinning NMR with cross-polarization: spectral editing of high-resolution spectra of half-integer quadrupolar nuclei

An experiment is presented that combines the techniques of multiple-quantum magic-angle spinning (MQMAS) and cross-polarization (CP) between spin-1/2 and half-integer quadrupolar spin nuclei. This technique, referred to as CP MQMAS, allows the coordination of the spin-1/2 nuclei within a quadrupole system to be determined, which demonstrates its usefulness for spectral editing. The radio-frequency (rf) pulse sequences and necessary phase-cycling are developed and examined. A novel approach of incorporating a \u27z-filter\u27 between the two techniques allowed us to optimize our new procedure, CP MQMAS, as two unique experiments prior to their coupling. Experimental details concerning the manipulations necessary to produce and detect multiple-quantum (MQ) NMR spectra of half-integer quadrupole nuclei are presented. Additionally, the spin dynamics of CP from a spin-1/2 nucleus to the central transition of a quadrupolar nucleus during magic-angle spinning (MAS) are examined. For quadrupolar systems the CP process operates most efficiently using very low rf field strengths, which is markedly different than that used in conventional CP between spin-1/2 nuclei. When low rf field strengths are used, no longer can the Hamiltonians from the second-order quadrupolar interaction, MAS speed and carrier frequency(s) offset be treated as negligible. Finally, as the MQMAS technique requires very high rf field strengths, and CP very low rf field strengths, it can be seen that the CP MQMAS technique demands high-quality linear power amplifiers;As a preliminary test of the CP MQMAS experiment, we chose 19F→27Al cross-polarization in a fluorinated triclinic, chabazite-like AlPO4 aluminophosphate sample. This material contains three equally populated crystallographic sites for aluminum: one site octahedrally coordinated to four oxygen and two fluorine atoms, and two sites that are tetrahedrally coordinated as AlO4. The results displayed that while all three aluminum environments were resolved in the MQMAS experiment, only that Al coordinated to the fluorine atoms was resolved in the CP MQMAS experiment;Our second CP MQMAS experiment was accomplished using 1H→27Al cross-polarization to the study of a calcined and fully rehydrated AlPO4-11 aluminophosphate sample. This is a much more complicated system as it involves five unique aluminum environments that can only be resolved if MQMAS NMR is employed. The application of the CP MQMAS technique allows one to determine the positions of the water molecules within the AlPO4-11 framework

Updates of PDFs for the 2nd LHC run

I present results on continuing updates in PDFs within the framework now called MMHT14 due to both theory improvements and the inclusion of new data sets, including most of the up-to-date LHC data. A new set of PDFs is essentially finalised, with no changes expected to the PDFs presented here.Comment: 6 pages, 5 figures. Proceedings of the 37th International Conference of High-Energy Physics (ICHEP2014), 2-9 July 2014, Valencia, Spai

Spectral representation of the resolvent of a discrete operator

AbstractLet T be a discrete linear operator in a Hilbert space H with spectrum σ(T) = λii = 1∞, let Rλ(T) denote the resolvent of T, and let Pi denote the projection of H onto the generalized eigenspace N((γi,I − T)mj) along R((γi, I − T)mj), where mi is the ascent of the operator λiI − T. In this paper it is shown that Rγ = ∑∞i=1∑mjj=1(−Ni)j−1Pi(γ − γ)j+∑∞j=0(γo − γ)jRγ0(T∞)j+1(I− P∞) in B(H) for all λ ϵ ϱ(T), where Ni is the restriction of λiI − T to is the restriction of T to N((γi,I − T)mj), T∞ D(T)⋃⋃∞i=1R((γiI−T)mj), P∞=∑∞i=1Pi (strong convergence), and λ0 is a fixed but arbitrary point in C. This spectral representation is valid provided there exists M > 0 such that ∥∑i = 1N Pi ∥ ⩽ M, N = 1, 2, …, and generalizes results that apply to self-adjoint, normal, and spectral operators. The results of this paper are applied to represent the resolvent of a differential operator L in L2[0, 1] having infinitely many eigenvalues with ascent mi = 2 and are also applied to represent the resolvent of an operator T with P∞≠I

Spectral theory for a differential operator: Characteristic determinant and Green's function

AbstractFor a two-point differential operator L in L2[a, b], it is shown that the Green's function has the representation G(t, s; λ) = H(t, s; λ)D(λ) for λ belonging to the resolvent set θ(L), where D(λ) is the characteristic determinant and H(t, s; λ) is an entire function in the λ variable admitting a power series expansion about any point λ0∈C. This representation is given several applications: first, to calculate the coefficient operators in the Laurent series for the resolvent Rλ(L) about each point λ0 in the spectrum σ(L), and second, to relate the algebraic multiplicity v(λ0) of an eigenvalue λ0 to the ascent m0 of the operator λ0I − L

Three Concurrent Phases of Massive-Star Evolution in a Pulsar-Wind Nebula

The nebular material associated the the SNR G54.1+0.3 (hereafter G54) contains the the first reported instance of triggered star formation in the immediate vicinity of a Pulsar and its Wind Nebula (PWN). With 2MASS and Spitzer colors and followup near-IR spectroscopy, we have discovered the presence of a hot, massive and most likely evolved Be-type star among the cluster of stars hosted by the pulsar. This star has probably triggered cloud collapse and formation of at least 11 YSOs, which ring the nebula. In this unique cluster are now identified three concurrent stages of stellar evolution, from massive star birth, post-Main-Sequence transition, and stellar death

A least squares approach to reduce stable discrete linear systems preserving their stability

AbstractA new stability preserving model reduction algorithm for discrete linear SISO-systems based on a least squares approach is proposed. Similar to the Padé approximation, an equation system for the Markov parameters involving a high dimensional Hankel matrix is considered. It is proved that approximate solutions, computed via the Moore–Penrose pseudo-inverse, give rise to a stability preserving reduction scheme. Furthermore, the proposed algorithm is compared to the balanced truncation method, showing comparable performance of the reduced systems

How does municipal policy affect state and local actions? Evidence from land conservation spending

Understanding responses to government action is critical for developing efficient policy. In the context of land conservation, this paper examines whether municipal policy has a crowding-in or crowding-out effect on neighboring municipalities’ actions and state government actions. Importantly, we focus on municipal conservation referendums, which allow us to use a regression discontinuity framework for causal inference. Using data from Massachusetts and New Jersey, our findings suggest municipal conservation decisions have no effect on neighboring local governments’ or the state’s conservation activity

Searching for the determinants of climate change interest

A meaningful CO2 mitigation policy is unlikely at the national level in the United States. What is currently happening and what is much more likely to occur in the future is city and regional level efforts of mitigation and adaptation. This paper aims to understand the geographic and socioeconomic characteristics of metropolitan areas and regions that lead to engagement with the issue of climate change. We use geographically explicit, internet search data from Google to measure information seeking behavior, which we take to translate into engagement, attention and interest. Our spatial hotspot analysis creates a map that potentially could be harnessed by policymakers to gauge mitigation support or adaptation potential. The results of our multivariate analysis suggest that socioeconomic factors are the strongest determinants of search behavior and that climate and geography have little to no impact. With regard to political ideology, we find evidence of a non-linear, inverse-U relationship with maximum search activity occurring in metropolitan areas with a near even political split, suggesting parity may be good for engagement