Vibrational spectroscopy of phthalocyanine and naphthalocyanine in sandwich-type (na)phthalocyaninato and porphyrinato rare earth complexes : (Part 10) The infrared and Raman characteristics of phthalocyanine in heteroleptic bis(phthalocyaninato) rare earth complexes with decreased molecular symmetry

The infrared (IR) spectroscopic data for a series of eleven heteroleptic bis(phthalocyaninato) rare earth complexes MIII(Pc)[Pc(α-OC5H11)4] (M = Sm–Lu, Y) [H2Pc = unsubstituted phthalocyanine, H2Pc(α-OC5H11)4 = 1,8,15,22-tetrakis(3-pentyloxy)phthalocyanine] have been collected with 2 cm−1 resolution. Raman spectroscopic properties in the range of 500–1800 cm−1 for these double-decker molecules have also been comparatively studied using laser excitation sources emitting at 632.8 and 785 nm. Both the IR and Raman spectra for M(Pc)[Pc(α-OC5H11)4] are more complicated than those of homoleptic bis(phthalocyaninato) rare earth analogues due to the decreased molecular symmetry of these double-decker compounds, namely C4. For this series, the IR Pc√− marker band appears as an intense absorption at 1309–1317 cm−1, attributed to the pyrrole stretching. With laser excitation at 632.8 nm, Raman vibrations derived from isoindole ring and aza stretchings in the range of 1300–1600 cm−1 are selectively intensified. In contrast, when excited with laser radiation of 785 nm, the ring radial vibrations of isoindole moieties and dihedral plane deformations between 500 and 1000 cm−1 for M(Pc)[Pc(α-OC5H11)4] intensify to become the strongest scatterings. Both techniques reveal that the frequencies of pyrrole stretching, isoindole breathing, isoindole stretchings, aza stretchings and coupling of pyrrole and aza stretchings depend on the rare earth ionic size, shifting to higher energy along with the lanthanide contraction due to the increased ring-ring interaction across the series. The assignments of the vibrational bands for these compounds have been made and discussed in relation to other unsubstituted and substituted bis(phthalocyaninato) rare earth analogues, such as M(Pc)2 and M(OOPc)2 [H2OOPc = 2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyanine].

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.

A Stochastic View of Optimal Regret through Minimax Duality

We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over joint distributions of the adversary's action sequence, of the difference between a sum of minimal expected losses and the minimal empirical loss. We show that the optimal regret has a natural geometric interpretation, since it can be viewed as the gap in Jensen's inequality for a concave functional--the minimizer over the player's actions of expected loss--defined on a set of probability distributions. We use this expression to obtain upper and lower bounds on the regret of an optimal strategy for a variety of online learning problems. Our method provides upper bounds without the need to construct a learning algorithm; the lower bounds provide explicit optimal strategies for the adversary. Peter L. Bartlett, Alexander Rakhlin

Interocular symmetry in myopic anisometropia

Purpose: To investigate the interocular symmetry of optical, biometric and biomechanical characteristics between the fellow eyes of myopic anisometropes. Methods: Thirty-four young, healthy myopic anisometropic adults (≥ 1 D spherical equivalent difference between eyes) without amblyopia or strabismus were recruited. A range of biometric and optical parameters were measured in both eyes of each subject including; axial length, ocular aberrations, intraocular pressure (IOP), corneal topography and biomechanics. Ocular sighting dominance was also measured. Results: Mean absolute spherical equivalent anisometropia was 1.70 ± 0.74 D and there was a strong correlation between the degree of anisometropia and the interocular difference in axial length (r = 0.81, p < 0.001). The more and less myopic eyes displayed a high degree of interocular symmetry for the majority of biometric, biomechanical and optical parameters measured. When the level of anisometropia exceeded 1.75 D, the more myopic eye was more likely to be the dominant sighting eye than for lower levels of anisometropia (p=0.002). Subjects with greater levels of anisometropia (> 1.75 D) also showed high levels of correlation between the dominant and non-dominant eyes in their biometric, biomechanical and optical characteristics. Conclusions: Although significantly different in axial length, anisometropic eyes display a high degree of interocular symmetry for a range of anterior eye biometrics and optical parameters. For higher levels of anisometropia, the more myopic eye tends to be the dominant sighting eye.

Symmetry of in-shoe force signatures in athletes under field conditions : an application for injury prevention

The aetiology behind overuse injuries such as stress fractures is complex and multi-factorial. In sporting events where the loading is likely to be uneven (e.g. hurdling and jumps), research has suggested that the frequency of stress fractures seems to favour the athlete’s dominant limb. The tendency for an individual to have a preferred limb for voluntary motor acts makes limb selection a possible factor behind the development of unilateral overuse injuries, particularly when repeatedly used during high loading activities. The event of sprint hurdling is well suited for the study of loading asymmetry as the hurdling technique is repetitive and the limb movement asymmetrical. Of relevance to this study is the high incidence of Navicular Stress Fractures (NSF) in hurdlers, with suggestions there is a tendency for the fracture to develop in the trail leg foot, although this is not fully accepted. The Ground Reaction Force (GRF) with each foot contact is influenced by the hurdle action, with research finding step-to-step loading variations. However, it is unknown if this loading asymmetry extends to individual forefoot joints, thereby influencing stress fracture development. The first part of the study involved a series of investigations using a commercially available matrix style in-shoe sensor system (FscanTM, Tekscan Inc.). The suitability of insole sensor systems and custom made discrete sensors for use in hurdling-related training activities was assessed. The methodology used to analyse foot loading with each technology was investigated. The insole and discrete sensors systems tested proved to be unsuitable for use during full pace hurdling. Instead, a running barrier task designed to replicate the four repetitive foot contacts present during hurdling was assessed. This involved the clearance of a series of 6 barriers (low training hurdles), place in a straight line, using 4 strides between each. The second part of the study involved the analysis of "inter-limb" and "within foot loading asymmetries" using stance duration as well as vertical GRF under the Hallux (T1), the first metatarsal head (M1) and the central forefoot peak pressure site (M2), during walking, running, and running with barrier clearances. The contribution to loading asymmetry that each of the four repetitive foot contacts made during a series of barrier clearances was also assessed. Inter-limb asymmetry, in forefoot loading, occurred at discrete forefoot sites in a non-uniform manner across the three gait conditions. When the individual barrier foot contacts were compared, the stance duration was asymmetrical and the proportion of total forefoot load at M2 was asymmetrical. There were no significant differences between the proportion of forefoot load at M1, compared to M2; for any of the steps involved in the barrier clearance. A case study testing experimental (discrete) sensors during full pace sprinting and hurdling found that during both gait conditions, the trail limb experienced the greater vertical GRF at M1 and M2. During full pace hurdling, increased stance duration and vertical loading was a characteristic of the trail limb hurdle foot contacts. Commercially available in-shoe systems are not suitable for on field assessment of full pace hurdling. For the use of discrete sensor technology to become commonplace in the field, more robust sensors need to be developed.

Interocular corneal symmetry in refractive error groups

Purpose: To examine between eye differences in corneal higher order aberrations and topographical characteristics in a range of refractive error groups. Methods: One hundred and seventy subjects were recruited including; 50 emmetropic isometropes, 48 myopic isometropes (spherical equivalent anisometropia ≤ 0.75 D), 50 myopic anisometropes (spherical equivalent anisometropia ≥ 1.00 D) and 22 keratoconics. The corneal topography of each eye was captured using the E300 videokeratoscope (Medmont, Victoria, Australia) and analyzed using custom written software. All left eye data were rotated about the vertical midline to account for enantiomorphism. Corneal height data were used to calculate the corneal wavefront error using a ray tracing procedure and fit with Zernike polynomials (up to and including the eighth radial order). The wavefront was centred on the line of sight by using the pupil offset value from the pupil detection function in the videokeratoscope. Refractive power maps were analysed to assess corneal sphero-cylindrical power vectors. Differences between the more myopic (or more advanced eye for keratoconics) and the less myopic (advanced) eye were examined. Results: Over a 6 mm diameter, the cornea of the more myopic eye was significantly steeper (refractive power vector M) compared to the fellow eye in both anisometropes (0.10 ± 0.27 D steeper, p = 0.01) and keratoconics (2.54 ± 2.32 D steeper, p < 0.001) while no significant interocular difference was observed for isometropic emmetropes (-0.03 ± 0.32 D) or isometropic myopes (0.02 ± 0.30 D) (both p > 0.05). In keratoconic eyes, the between eye difference in corneal refractive power was greatest inferiorly (associated with cone location). Similarly, in myopic anisometropes, the more myopic eye displayed a central region of significant inferior corneal steepening (0.15 ± 0.42 D steeper) relative to the fellow eye (p = 0.01). Significant interocular differences in higher order aberrations were only observed in the keratoconic group for; vertical trefoil C(3,-3), horizontal coma C(3,1) secondary astigmatism along 45 C(4, -2) (p < 0.05) and vertical coma C(3,-1) (p < 0.001). The interocular difference in vertical pupil decentration (relative to the corneal vertex normal) increased with between eye asymmetry in refraction (isometropia 0.00 ± 0.09, anisometropia 0.03 ± 0.15 and keratoconus 0.08 ± 0.16 mm) as did the interocular difference in corneal vertical coma C (3,-1) (isometropia -0.006 ± 0.142, anisometropia -0.037 ± 0.195 and keratoconus -1.243 ± 0.936 μm) but only reached statistical significance for pair-wise comparisons between the isometropic and keratoconic groups. Conclusions: There is a high degree of corneal symmetry between the fellow eyes of myopic and emmetropic isometropes. Interocular differences in corneal topography and higher order aberrations are more apparent in myopic anisometropes and keratoconics due to regional (primarily inferior) differences in topography and between eye differences in vertical pupil decentration relative to the corneal vertex normal. Interocular asymmetries in corneal optics appear to be associated with anisometropic refractive development.

Symmetry is an organizing principle in neuronal dendrotaxis

Symmetry is a fundamental property found in both the physical and natural worlds. Bilateral symmetry is also present in the organization of the brain, however the degree to which symmetry is also an organizing principal between and within the key constituent elements of the nervous system, neurons, is not known. We compared and contrasted the structural organization of principal neurons (PN) in the three subnuclei of the lateral amygdala (LA) of the rat and for comparison also from the infralimbic cortex (IL)...

Two-dimensional self-assembly of a symmetry-reduced tricarboxylic acid

Investigations of the self-assembly of simple molecules at the solution/solid interface can provide useful insight into the general principles governing supramolecular chemistry in two dimensions. Here, we report on the assembly of 3,4′,5-biphenyl tricarboxylic acid (H3BHTC), a small hydrogen bonding unit related to the much-studied 1,3,5-benzenetricarboxylic acid (trimesic acid, TMA), which we investigate using scanning tunneling microscopy (STM) and density functional theory (DFT) calculations. STM images show that H3BHTC assembles by itself into an offset zigzag chain structure that maximizes the surface molecular density in favor of maximizing the number density of strong cyclic hydrogen bonds between the carboxylic groups. The offset geometry creates “sticky” pores that promote solvent coadsorption. Adding coronene to the molecular solution produces a transformation to a high-symmetry host–guest lattice stabilized by a dimeric/trimeric hydrogen bonding motif similar to the TMA flower structure. Finally, we show that the H3BHTC lattice firmly immobilizes the guest coronene molecules, allowing for high-resolution imaging of the coronene structure.

Electronic and vibrational spectra of gaspeite

Visible, near-infrared, IR and Raman spectra of magnesian gaspeite are presented. Nickel ion is the main source of the electronic bands as it is the principal component in the mineral where as the bands in IR and Raman spectra are due to the vibrational processes in the carbonate ion as an entity. The combination of electronic absorption and vibrational spectra (including near-infrared, FTIR and Raman) of magnesian gaspeite are explained in terms of the cation co-ordination and the behaviour of CO32– anion in the Ni–Mg carbonate. The electronic absorption spectrum consists of three broad and intense bands at 8130, 13160 and 22730 cm–1 due to spin-allowed transitions and two weak bands at 20410 and 30300 cm–1 are assigned to spin-forbidden transitions of Ni2+ in an octahedral symmetry. The crystal field parameters evaluated from the observed bands are Dq = 810; B = 800 and C = 3200 cm–1. The two bands in the near-infrared spectrum at 4330 and 5130 cm–1 are overtone and combination of CO32– vibrational modes. For the carbonate group, infrared bands are observed at 1020 cm–1(1 ), 870 cm–1 (2), 1418 cm–1 (3) and 750 cm–1 (4), of which3, the asymmetric stretching mode is most intense. Three well resolved Raman bands at 1571, 1088 and 331 cm–1 are assigned to 3, 1 and MO stretching vibrations.

Vibrational spectroscopy of phthalocyanine and naphthalocyanine in sandwich-type (na)phthalocyaninato and porphyrinato rare earth complexes: Part 14. The infrared and Raman characteristics of phthalocyanine in “pinwheel-like” homoleptic bis[1,8,15,22-tetrakis(3-pentyloxy)phthalocyaninato] rare earth(III) double-decker complexes

The infrared (IR) spectroscopic data and Raman spectroscopic properties for a series of 13 “pinwheel-like” homoleptic bis(phthalocyaninato) rare earth complexes M[Pc(α-OC5H11)4]2 [M = Y and Pr–Lu except Pm; H2Pc(α-OC5H11)4 = 1,8,15,22-tetrakis(3-pentyloxy)phthalocyanine] have been collected and comparatively studied. Both the IR and Raman spectra for M[Pc(α-OC5H11)4]2 are more complicated than those of homoleptic bis(phthalocyaninato) rare earth analogues, namely M(Pc)2 and M[Pc(OC8H17)8]2, but resemble (for IR) or are a bit more complicated (for Raman) than those of heteroleptic counterparts M(Pc)[Pc(α-OC5H11)4], revealing the decreased molecular symmetry of these double-decker compounds, namely S8. Except for the obvious splitting of the isoindole breathing band at 1110–1123 cm−1, the IR spectra of M[Pc(α-OC5H11)4]2 are quite similar to those of corresponding M(Pc)[Pc(α-OC5H11)4] and therefore are similarly assigned. With laser excitation at 633 nm, Raman bands derived from isoindole ring and aza stretchings in the range of 1300–1600 cm−1 are selectively intensified. The IR spectra reveal that the frequencies of pyrrole stretching and pyrrole stretching coupled with the symmetrical CH bending of –CH3 groups are sensitive to the rare earth ionic size, while the Raman technique shows that the bands due to the isoindole stretchings and the coupled pyrrole and aza stretchings are similarly affected. Nevertheless, the phthalocyanine monoanion radical Pc′− IR marker band of bis(phthalocyaninato) complexes involving the same rare earth ion is found to shift to lower energy in the order M(Pc)2 > M(Pc)[Pc(α-OC5H11)4] > M[Pc(α-OC5H11)4]2, revealing the weakened π–π interaction between the two phthalocyanine rings in the same order.

Raman spectroscopic study of vivianites of different origins

Raman spectroscopy has been used to study a selection of vivianites from different origins. A band is identified at around 3480 cm-1 whose intensity is sample dependent. The band is attributed to the stretching vibration of Fe3+ OH units which are formed through the autooxidation of the vivianite minerals either by self-oxidation or by photocatalytic oxidation according to the reaction: (Fe2+)3(PO4)2·8H2O + 1/2O2 (Fe2+)3– x(Fe3+)x(PO4)2(OH)x·(8–x)H2O in which some of the water of crystallization is converted to hydroxyl anions. Complexity of the OH stretching region through the overlap of broad bands is reflected in the water HOH deformation modes at 1660 cm–1. Using the infrared bands at 3281, 3105 and 3025 cm–1, hydrogen bond distances of 2.734(5), 2.675(2) and 2.655(2) Å are calculated. Vivianites are characterised by an intense band at 950 cm–1 assigned to the PO4 symmetric stretching vibration. Low Raman intensity bands are observed at ~1077, ~1050, 1015 and ~ 985 cm–1 assigned to the phosphate PO4 antisymmetric stretching vibrations. Multiple antisymmetric stretching vibrations are due to the reduced tetrahedral symmetry. This loss of degeneracy is also reflected in the bending modes. Two bands are observed at ~ 423 and ~ 456 cm–1 assigned to the2bending modes. For the vivianites four bands are observed at ~ 584, ~ 571, ~ 545 and ~ 525 cm–1 assigned to the 4modes of vivianite.

Sound radiation characteristics of a box-type structure

The finite element and boundary element methods are employed in this study to investigate the sound radiation characteristics of a box-type structure. It has been shown [T.R. Lin, J. Pan, Vibration characteristics of a box-type structure, Journal of Vibration and Acoustics, Transactions of ASME 131 (2009) 031004-1–031004-9] that modes of natural vibration of a box-type structure can be classified into six groups according to the symmetry properties of the three panel pairs forming the box. In this paper, we demonstrate that such properties also reveal information about sound radiation effectiveness of each group of modes. The changes of radiation efficiencies and directivity patterns with the wavenumber ratio (the ratio between the acoustic and the plate bending wavenumbers) are examined for typical modes from each group. Similar characteristics of modal radiation efficiencies between a box structure and a corresponding simply supported panel are observed. The change of sound radiation patterns as a function of the wavenumber ratio is also illustrated. It is found that the sound radiation directivity of each box mode can be correlated to that of elementary sound sources (monopole, dipole, etc.) at frequencies well below the critical frequency of the plates of the box. The sound radiation pattern on the box surface also closely related to the vibration amplitude distribution of the box structure at frequencies above the critical frequency. In the medium frequency range, the radiated sound field is dominated by the edge vibration pattern of the box. The radiation efficiency of all box modes reaches a peak at frequencies above the critical frequency, and gradually approaches unity at higher frequencies.