6j, 9j symbols and 3jm factors for the group chainD 5 ⊃C 5

A complete set of nontrivial inequivalent 6j and 9j symbols for the double groupD ₅ and the complete set of 3jm factors (equivalently isoscalar factors) associated with the group chainD ₅ ⊃C ₅ are calculated using the most general phase choices specified by Butler.     

Integration-mediated prediction enrichment of quantitative model for Hsp90 inhibitors as anti-cancer agents: 3D-QSAR study

The present study describes a systematic 3D-QSAR study consisting of pharmacophore modeling, docking, and integration of ligand-based and structure-based drug design approaches, applied on a dataset of 72 Hsp90 inhibitors as anti-cancer agents. The best pharmacophore model, with one H-bond donor (HBD), one H-bond acceptor (HBA), one hydrophobic_aromatic (Hy_Ar), and two hydrophobic_aliphatic (Hy_Al) features, was developed using the Catalyst/HypoGen algorithm on a training set of 35 compounds. The model was further validated using test set, external set, Fisher’s randomization method, and ability of the pharmacophoric features to complement the active site amino acids. Docking analysis was performed using Hsp90 chaperone (PDB-Id: 1uyf) along with water molecules reported to be crucial for binding and catalysis (Sgobba et al. ChemMedChem 4:1399–1409, 2009). Furthermore, an integration of the ligand-based as well as structure-based drug design approaches was done leading to the integrated model, which was found to be superior over the best pharmacophore model in terms of its predictive ability on internal [integrated model 2: R _(train) = 0.954, R _(test) = 0.888; Hypo-01: R _(train) = 0.912 and R _(test) = 0.819] as well as on external data set [integrated model 2: R _(ext.set) = 0.801; Hypo-01: R _(ext.set) = 0.604].     

A rigorous lower bound for the stability regions of the quadratic map

We establish a lower bound on the measure of the set of stable parameters a for the quadratic map Q_a(x)=ax(1−x). For these parameters, we prove that Q_a either has a single stable periodic orbit or a period-doubling bifurcation. From this result, we also obtain a non-trivial upper bound on the set of stochastic parameters for Q_a.     

Solitons on Noncommutative Orbifold T 2/Z N

Following the construction of the projection operators on T ² presented by Gopakumar, Headrick and Spradlin, we construct a set of projection operators on the integral noncommutative orbifold T ²/G(G=Z _N , N=2, 3, 4, 6) which correspond to a set of solitons on T ²/Z _N in noncommutative field theory. In this way, we derive an explicit form of projector on T ²/Z ₆ as an example. We also construct a complete set of projectors on T ²/Z _N by series expansions for integral case.     

Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated (r 12-)MR-CI IV. The helium dimer (He 2)

The helium dimer interaction potential is computed using the recently proposed (explicitly correlated) r ₁₂-MR-ACPF (averaged coupled-pair functional) method and a [11s8p6d5f4g] basis set. With an MR-ACPF ansatz that contains 121 references we obtain interaction energies that are close to full CI. In a smaller reference space containing 9 functions, however, even by successively adding [3h] and [2i] functions to the basis set mentioned above, the basis set limit could not be reached. While convergence to the basis set limit is slow, it nevertheless is monotonic and therefore allows for extrapolation to the limit. We obtain basis set corrections at R = 4 a ₀ and 5.6 a ₀ which we further extend to all distances and which we apply to the potential energy curve mentioned above. From our calculations, we conclude that a very recent potential which has been calculated using the SAPT (symmetry adapted perturbation theory) method, and which previously was assumed to be the most accurate available, is insufficiently repulsive at short distances. We correct our extrapolated potential for retardation and finally calculate the expectation value of the interatomic distance (?R?) and dissociation energy (D ₀) by solving the Schrödinger equation of the vibrating ⁴He₂. Our results (?R? = 41 ± 13 Å and D ₀ = 2.2 ± 1.0 mK) are in acceptable agreement with very recent calculations in the literature, but they disagree with a recent experiment.     

A set of hyperspherical harmonics especially suited for three-body collisions in a plane

We obtain a set of four-dimensional hyperspherical harmonics in closed form. These harmonics are not only quantized with respect to the rotation group (O ₂), but are an irreducible basis for the permutation groupS ₃. An additional symmetry is found which allows us to write hyperspherical harmonics classified with respect to a 12 element groupS ₃×i×O ₂. We give a set of three mutually commuting operators whose eigenvalues uniquely characterize each spherical harmonic with respect to degree, symmetry, and angular momentum in the plane.     

The Moduli of Flat PGL(2,ℝ) Connections on¶Riemann Surfaces

Suppose X is a compact Riemann surface with genus g>1. Each class [σ] ∈ Hom(π₁(X),PGL(2,ℝ))/PGL(2,ℝ) is associated with the first and second Stiefel–Whitney classes w ₁([σ]) and w ₂([σ]). The set of representation classes with a fixed w ₁≠ 0 has two connected components. These two connected components are characterized by w ₂ being 0 or 1. For each fixed w ₁≠ 0, we prove that the component, characterized by w ₂= 0, contains an open dense set diffeomorphic to the total space of a vector bundle of rank 2g−2 over a once punctured algebraic torus of dimension g−1. The other component, characterized by w ₂= 1, contains an open dense set diffeomorphic to the total space of a vector bundle of rank 2g−2 over an algebraic torus of dimension g−1. Received: 2 January 1997 / Accepted: 28 November 1998     

Basis set limit binding energies of hydrogen bonded clusters

The utility of the recently developed extrapolation method to estimate the binding energies of weakly bound clusters at the basis set limit exploiting the similar basis set convergence behaviour of correlation energies of the monomer and cluster in correlated calculations (J. chem. Phys., 116, 5389 (2002)) was tested for small to medium (HF)_n and (H₂O)_n (n = 2–5) clusters using various correlation consistent cc-pVXZ (X= D,T,Q,5) basis sets containing different numbers of diffuse functions and 6–31G type basis sets at the MP2 and CCSD(T) level for which accurate basis set limits are available for comparison. It is shown that the basis set limit binding energies estimated by this extrapolation method with modest size of basis sets (cc-pVDZ/cc-pVTZ or 6–3 1 G(d,p)/6-3 IG(2df,2pd)) are much closer to the exact basis set limits than the estimates by commonly used X ^?3 extrapolation or counterpoise corrected binding energies, signifying the importance of this extrapolation method for the study of large weakly bound clusters. It is also shown that the inclusion of appropriate diffuse functions in the basis sets can significantly improve the accuracy of the estimated basis set limits by this extrapolation method. For (HF)_n clusters the MP2 and CCSD(T) basis set limits estimated by this extrapolation method with aug-cc-pVDZ and aug-cc-pVTZ basis sets are 18.4 (18.5) and 18.9 (18.9) for the dimer, 61.8 (62) and 63.2 (63) for the trimer, 113.5 and 114.7 (116) for the tetramer, and 155.2 and 156.3 (158) for the pentamer, respectively, with the values in parentheses representing the apparent basis set limits, with the numbers in units of kJ mol^?1. The corresponding results for (H₂O)_n clusters are 20.5 (20.5) and 20.6 (20.7) for (H₂O)₂, and 60.5 (61) and 60.1 (60) for (H₂O)₃, respectively.     

Class two analogue of T. Y. Thomas's theorem and different types of embeddings of static spherically symmetric space-times

A Riemannian space of embedding class two is characterised by two symmetric tensors a _ij , b _ij and a vector s_i, satisfying the equations of Gauss, Codazzi and Ricci. It is proved that the Gauss equations together with one set of Codazzi equations imply the other set of Codazzi equations and the Ricci equations, provided that the matrix of the tensor b _ij (or a _ij ) is nonsingular. (The class m generalisation of the result has also been suggested). The result so proved has further been utilized in finding explicitly the a _ij 's and b _ij 's in the case of the static spherically symmetric line element. It is further indicated that the a _ij 's and b _ij 's so obtained are responsible for the different types of embeddings of the spacetime considered.     

The Newhouse set has a positive Hausdorff dimension

The Newhouse phenomenon of infinitely many coexisting periodic attractors is studied in its simplest form. One shows that the corresponding parameter set (the Newhouse set)J _N has a strictly positive Hausdorff dimension. This result is stronger than that of Tedeschini-Lalli and Yorke [Commun. Math. Phys.106, 635 (1986)] concerning the Lebesgue measure of the Newhouse set; and is complementary to our knowledge on the topological properties ofJ _N, namely it is a residual set, hence uncountable and everywhere dense in a parameter interval.     

Metastability and Low Lying Spectra¶in Reversible Markov Chains

We study a large class of reversible Markov chains with discrete state space and transition matrix P _N . We define the notion of a set of metastable points as a subset of the state space Γ _N such that (i) this set is reached from any point x∈Γ _N without return to x with probability at least b _N , while (ii) for any two points x, y in the metastable set, the probability T ^{− 1} _{x , y} to reach y from x without return to x is smaller than a _{N − 1}< b _N . Under some additional non-degeneracy assumption, we show that in such a situation: (i) To each metastable point corresponds a metastable state, whose mean exit time can be computed precisely. (ii) To each metastable point corresponds one simple eigenvalue of 1 −P _N which is essentially equal to the inverse mean exit time from this state. Moreover, these results imply very sharp uniform control of the deviation of the probability distribution of metastable exit times from the exponential distribution. Received: 1 August 2000 / Accepted: 19 November 2001     

Julia Sets in Parameter Spaces

Given a complex number λ of modulus 1, we show that the bifurcation locus of the one parameter family {f _b (z)=λz+b z ²+z ³} _{b ∈ ℂ} contains quasi-conformal copies of the quadratic Julia set J(λz+z ²). As a corollary, we show that when the Julia set J(λz+z ²) is not locally connected (for example when z↦λz+z ² has a Cremer point at 0), the bifurcation locus is not locally connected. To our knowledge, this is the first example of complex analytic parameter space of dimension 1, with connected but non-locally connected bifurcation locus. We also show that the set of complex numbers λ of modulus 1, for which at least one of the parameter rays has a non-trivial accumulation set, contains a dense G _δ subset of S ¹. Received: 22 September 2000 / Accepted: 16 January 2001     

Vicinal Fluorine–Proton Coupling Constants: II. Individual Substituent Effects

The angular dependence and the effect of individual substituents upon the NMR vicinal fluorine–proton couplings3JFHhave been studied using data sets of experimental and calculated couplings. Coupling constants for a series of fluoroethane derivatives, CHXF–CH3and CH2F–CH2X(X= CH3, NH2, OH, and F), were calculated by means of the SCFab initioand semiempirical INDO/FPT methods. The calculated couplings reproduce correctly the main experimental trends in spite of the limitation in the calculation because of lack of electronic correlation and the use of medium size basis set. The individual substituent effects ΔKXiniare described by quadratic expressions on the relative electronegativities of substituents ΔχXi(ΔKXini=k0ni+kniΔχXi+ kniiΔχ2Xi). A selected data set of 58 experimental couplings, ranging from 1.9 to 44.4 Hz, has been collected from the literature. An extended Karplus equation with 16 coefficients that includes the electronegativity substituent effects has been derived from the experimental data set with a root-mean-square deviation of 1.2 Hz.     

Intrinsic resistive switching and memory effects in silicon oxide

Resistive switching behaviors are described in silicon oxide (SiO _x ) systems employing vertical E/SiO _x /E (E denotes the electrode) structures. The switching is largely independent of the electrode material and attributed to the intrinsic properties of SiO _x . Based on the recent experimental observation (Yao et al. in Nano Lett. 10:4105, 2010) of a silicon filament embedded in the SiO _x matrix, we further discuss the switching mechanism in light of the measured electrical phenomena. The set voltages are largely SiO _x -thickness independent, consistent with the mechanistic picture of point switching in the silicon filament. The multi-state switching and shifts in the set voltages with respect to the reset voltages are consistent with an electrochemical redox process (Si ↔ SiO _y ) at the switching site.     

Bifurcation frequency for unimodal maps

We consider some natural one-parameter unfoldingsf , of a unimodal mapf ₀ whose periodic points are hyperbolic and whose critical point is nondegenerate and eventually periodic. Among other facts, it follows from our theorems that, if the Julia set off ₀ does not contain intervals, the relative measure of the bifurcation set is zero at zero.     

High resolution study of the v 7 + v 8 band of ethylene (C2H4) at 1889 cm-1

The v ₇ + v ₈ A-type band of C₂H₄ has been recorded between 1932 and 1847 cm^-1 with a resolution of 0·06 cm^-1. The transitions with K _-1 ? 8> and J ? 2>5 have been assigned. Although slight Coriolis resonances perturb the band, the analysis has been made easy through the use of an elaborate set of asymmetric top computer programmes. The band centre and a set of upper state constants have been obtained. With these constants, 288 observed upper state energy levels have been fitted with a standard deviation of 0·021 cm^-1.

Using very simple expressions, we have predicted all the resonance effects perturbing the levels of ethylene near 2000 cm^-1. This led us to the identification of the v ₄ + v ₈ and v ₈ + v ₁₀ combination bands in low resolution spectra.     

Constraining the Surface Gravitational Redshift of Proto Neutron Stars with New Nucleon Coupling Constants

A new set of nucleon coupling constants (CZ11) is obtained for the relativistic mean field (RMF) theory based on the recent experimental information on the symmetry energy derived from the data from NSCL/MSU. The surface gravitational redshift of a proto neutron star (PNS) is examined within the RMF framework for the baryon octet system by using this set of parameters. It is found that the surface gravitational redshift for CZ11 is smaller than that for GL97. For the CZ11 parameter set, the surface gravitational redshift of a PNS at T=15 MeV is smaller than that at T=0 MeV. It is also found that the surface gravitational redshift corresponding to M _max/R for the CZ11 parameter set is smaller by about 10 percent than that for GL97, with M _max being the maximum mass and R being the corresponding radius.     

Nondestructive Quantification of Foliar Chlorophyll in an Apple Orchard by Visible/Near-Infrared Reflectance Spectroscopy and Partial Least Squares

Chlorophylls respond rapidly to the current physiological status of a tree and reflect nutrient availability. Visible/near-infrared spectroscopy was attempted to determine foliar chlorophyll content in an apple orchard. Backward interval partial least squares and genetic algorithms were sequentially applied to select an optimized spectral interval and an optimized combination of spectral regions selected from informative regions in model calibration. Backward interval partial least squares was used to remove the noninformative regions, which significantly reduced the number of variables. The subsequent application of genetic algorithms-partial least squares to this reduced domain could lead to an efficient and refined model. The performance of the final model was back-evaluated according to root mean square error of calibration (RMSEC) and the correlation coefficient (R _c ) in the calibration set, and was then tested by root mean square error of prediction (RMSEP) and the correlation coefficient (R _p ) in the prediction set. The optimal backward interval partial least squares-genetic algorithms model was obtained with 5 partial least squares factors with 3 spectral regions and 71 variables selected. The measurement results of the final model were achieved as follows: RMSEC = 0.26, R _c  = 0.91 in the calibration set; and RMSEP = 0.22, R _p  = 0.91 in the prediction set. This experiment showed that visible/near-infrared spectroscopy and backward interval partial least squares-genetic algorithms are useful tools for nondestructively assessing foliar chlorophyll content and may have potential application for field assessments in decision-making and operational fertilizer management programs for apple orchards.     

The infrared spectrum of isoxazole in the range 600–1400 cm−l,including a high-resolution study of the v 7(A′) band at 1370.9 cm−1 and the v 16(A″) band at 764.9 cm−l,together with ab initio studies of the full spectrum

Abstract

The high resolution infrared gas phase spectrum of isoxazole in the range 600–1400 cm^?1 has been recorded and more precise centres obtained for a number of bands; analyses of the v ₇(A′) band at 1370.9cm^?1 and the v ₁₆(A″) band at 764.9cm^?1 have been performed. Use of the Watson Hamiltonian, A-reduction, III^r-representation and simultaneous analysis of the present IR and previous microwave data, has led to rotation constants and quartic centrifugal distortion constants Δ _J , Δ _JK , ΔK, δ _J and δ _K for the ground state and for the v ₁₆ vibrationally excited states. The equilibrium structures and the derived harmonic frequencies have been calculated by ab initio methods using triple zeta+polarization (TZVP) and cc-pVTZ basis sets, with MP2, MP4 and CCSD(T) methods. At each methodology, for closest numerical agreement between the calculated and observed rotation constants, the optimum basis set seems to be TZVP rather than cc-pVTZ basis sets. However, the order of the highest A″ and lowest A′ symmetry vibrations is only resolved by the cc-pVTZ basis set with the MP4 methodology, which does generate the experimental sequence (v ₁₄>v ₁₃) The CCSD(T) methodology does not lead to significant difference over either MP2 or MP4 with the TZVP basis set.     

Indirect Analytic Representation of Foucault's Pendulum

A complex representation of the equations of motion of the Foucault's pendulum is considered and the inverse problem is solved to derive an indirect analytic representation. Both real L _R ⁽ⁱ⁾ and imaginary L _I ⁽ⁱ⁾ parts of the derived complex valued Lagrangian are found to reproduce the equations of motion via the Euler-Lagrange equations. The expressions for L _R ⁽ⁱ⁾ and L _I ⁽ⁱ⁾ are not connected by a gauge term thereby forming a set of inequivalent Lagrangians. In an appropriate limit L _I ⁽ⁱ⁾ is found to reproduce the Lagrangian obtained by implementing the usual Coriolis theorem while in some other limit L _R ⁽ⁱ⁾ and L _I ⁽ⁱ⁾ give the indirect and the direct analytic representations for a set of two uncoupled harmonic oscillators.