The \u3csup\u3e13\u3c/sup\u3eC-NMR Solid State Spectroscopy of Various Classes of Coals

The 13C-NMR spectra of various classes of coal obtained in the solid state show two resonances, one of which is assigned to aromatic carbon and the other to aliphatic carbon. The resonances are very broad with the high field resonance centered at about 7 ppm below tetramethylsilane and a low field resonance centered at about 140 ppm below tetramethysilane. Based on our previous solid state 13C-NMR studies of graphite and diamond, the high field resonance is typical of a sp3 carbon whereas the low fields resonance is assigned to a sp2 carbon whereas the low fields resonance is assigned to a sp2 carbon. It is found that the antracitic coals have more aromatic (sp2) carbons than the bituminous, subbituminous and lignite coals. The analytical implications of this technique are briefly discussed

The Solid State \u3csup\u3e13\u3c/sup\u3eC-NMR Spectra of Some Carbides

The utility of NMR spectroscopy to the study of liquids or solids dissolved in liquids is well known. This technique has been used infrequently to studies in the solid state[I,2]. Work has been done on diamond, graphite and coa113-6]. The 13C-NMR of ebony and ivory have been studied by the magic angle technique[7]. The solid state 13C-NMR spectra of graphite and diamond can be interpreted in terms of tetrahedral (sp3) and trigonal planar (sp2) carbon atoms[8]. We now report our investigations using solid state 13C-NMR spectroscopy to study various types of carbides

A Solid State \u3csup\u3e13\u3c/sup\u3eC-NMR Study of Diamonds and Graphites

The 13C-NMR spectra of gem quality and industrial diamonds show two resonances with the more intense resonance at high field. Two resonances are also shown in 13C-NMR spectra of various graphites; however, the low field resonance is of greater intensity than the high field resonance in the graphites. The resonances are very broad and they are assigned to graphite type (sp2) carbon and diamond type (sp3) carbon

Exact norm-conserving stochastic time-dependent Hartree-Fock

We derive an exact single-body decomposition of the time-dependent Schroedinger equation for N pairwise-interacting fermions. Each fermion obeys a stochastic time-dependent norm-preserving wave equation. As a first test of the method we calculate the low energy spectrum of Helium. An extension of the method to bosons is outlined.Comment: 21 pages, 3 figures, LaTeX fil

On Recurrent Reachability for Continuous Linear Dynamical Systems

The continuous evolution of a wide variety of systems, including continuous-time Markov chains and linear hybrid automata, can be described in terms of linear differential equations. In this paper we study the decision problem of whether the solution $\boldsymbol{x}(t)$ of a system of linear differential equations $d\boldsymbol{x}/dt=A\boldsymbol{x}$ reaches a target halfspace infinitely often. This recurrent reachability problem can equivalently be formulated as the following Infinite Zeros Problem: does a real-valued function $f:\mathbb{R}_{\geq 0}\rightarrow\mathbb{R}$ satisfying a given linear differential equation have infinitely many zeros? Our main decidability result is that if the differential equation has order at most $7$, then the Infinite Zeros Problem is decidable. On the other hand, we show that a decision procedure for the Infinite Zeros Problem at order $9$ (and above) would entail a major breakthrough in Diophantine Approximation, specifically an algorithm for computing the Lagrange constants of arbitrary real algebraic numbers to arbitrary precision.Comment: Full version of paper at LICS'1

Affordable spectral measurements of translucent materials

We present a spectral measurement approach for the bulk optical properties of translucent materials using only low-cost components. We focus on the translucent inks used in full-color 3D printing, and develop a technique with a high spectral resolution, which is important for accurate color reproduction. We enable this by developing a new acquisition technique for the three unknown material parameters, namely, the absorption and scattering coefficients, and its phase function anisotropy factor, that only requires three point measurements with a spectrometer. In essence, our technique is based on us finding a three-dimensional appearance map, computed using Monte Carlo rendering, that allows the conversion between the three observables and the material parameters. Our measurement setup works without laboratory equipment or expensive optical components. We validate our results on a 3D printed color checker with various ink combinations. Our work paves a path for more accurate appearance modeling and fabrication even for low-budget environments or affordable embedding into other devices

The Solid State \u3csup\u3e13\u3c/sup\u3eC-NMR and \u3csup\u3e19\u3c/sup\u3eF-NMR Spectra of Some Graphite Fluorides

The solid state 13C nuclear magnetic resonance spectra of fluorinated graphites show two resonances, one of which is assigned to aromatic carbon and the other to aliphatic carbon. The resonances are very broad with the high-field resonance centered at about 35 ppm below tetramethylsilane (TMS) and a low-field resonance centered at about 160 ppm below tetramethylsilane. The high-field resonance is typical of an sp3-like carbon and the low-field resonance is assigned to sp2-like carbons. It is found that the aromatic resonance in graphite decreases with an increase in fluorination of the graphite fluorides examined in this study. The 19F nuclear magnetic resonance spectra of C4F and CF1 each show one resonance. The fluorine resonance in C4F is 180 ppm above CFCI3 whereas the fluorine resonance in CF1 is 55 ppm above CFCI3. These peaks are in the range for fluorine bonded to aromatic and aliphatic carbons, respectively

Jet Spaces in Modern Hamiltonian Biomechanics

In this paper we propose the time-dependent Hamiltonian form of human biomechanics, as a sequel to our previous work in time-dependent Lagrangian biomechanics [1]. Starting with the Covariant Force Law, we first develop autonomous Hamiltonian biomechanics. Then we extend it using a powerful geometrical machinery consisting of fibre bundles and jet manifolds associated to the biomechanical configuration manifold. We derive time-dependent, dissipative, Hamiltonian equations and the fitness evolution equation for the general time-dependent human biomechanical system. Keywords: Human biomechanics, covariant force law, configuration manifold, jet manifolds, time-dependent Hamiltonian dynamicsComment: 16 pages, 3 figure