Distribution Of Poles Research Articles

On the Distribution of Zeros and Poles of Rational Approximants on Intervals

The distribution of zeros and poles of best rational approximants is well understood for the functions f(x) = |x|α, α > 0. If f ∈ C[−1, 1] is not holomorphic on [−1, 1], the distribution of the zeros of best rational approximants is governed by the equilibrium measure of [−1, 1] under the additional assumption that the rational approximants are restricted to a bounded degree of the denominator. This phenomenon was discovered first for polynomial approximation. In this paper, we investigate the asymptotic distribution of zeros, respectively, a‐values, and poles of best real rational approximants of degree at most n to a function f ∈ C[−1, 1] that is real‐valued, but not holomorphic on [−1, 1]. Generalizations to the lower half of the Walsh table are indicated.

Electrospinning PVDF/EC fibre from a binary solvent system

The influence of the composition of a binary component solvent on the surface morphology and diameter distribution of poly(vinylidene fluoride)/ethyl cellulose (PVDF/EC) fibres produced by electrospinning technology was investigated. Acetone (56°C) and N-methyl pyrrolidone (NMP) (203°C) binary solvent system was introduced and electrospinning was performed by changing the solution concentration, the applied voltage and the volume ratio of NMP/acetone. The results show that the morphology of PVDF/EC electrospun fibres is greatly influenced by the solution concentration and the volume ratio of NMP/acetone. PVDF/EC fibres prepared from NMP/acetone binary solvent system is much better than that prepared with a single component solvent system, and is very diverse with the volume ratios of the binary solvent system. The morphology of the fibres changed from beads (starting mass ratio of 12 wt% or pure NMP solvent) to full developed fibres as mass ratio increased to 16 wt% with the volume ratio of NMP/acetone (6/4, 5/5, 4/6, 3/7). Beadless fibres were normally obtained within the voltage applied and their average diameter decreased with increasing the applied voltage.

Cambrian paleomagnetism in the Bateni Ridge: evolution of the Kuznetsk Alatau island arc ( southern Siberia)

We present paleomagnetic data on the Cambrian volcanosedimentary complexes of the Bateni Ridge, which correspond to the evolution of the Kuznetsk Alatau island arc. The paleomagnetic poles which served as the basis for the apparent polar-wander path (APWP) were determined. The paleomagnetic data were compared with those on the Cambrian poles for other fragments of the Kuznetsk Alatau island arc. For example, the APWP of the Bateni fragment corresponds to that of the Kiya (Martaiga) fragment of the eastern slope of the Kuznetsk Alatau. The distribution of the paleomagnetic poles suggests that the relative drift of the Kuznetsk Alatau arc fragments and the entire island arc system resulted from large-amplitude strike-slips. In the Cambrian, this paleoarc moved from ∼10° N to ∼10° S and rotated more than 50° clockwise. In the paleomagnetic record, its accretion is reflected in the coincidence of the Late Cambrian–Early Ordovician poles on the eastern slope of the Kuznetsk Alatau with one another and the coeval poles for the Siberian craton. This coincidence also suggests that the general structure of the present Kuznetsk Alatàu formed as early as the Early Caledonian. Nevertheless, the differences in the position of the poles on the western and eastern slopes of the Kuznetsk Alatau suggest that strike-slip activity along the Kuznetsk–Altai deep fault (the major one in the region) continued in the Late Paleozoic and, probably, in the Mesozoic.

Total internal reflection in gain medium slab

The problem of light propagation through a slab of gain medium is studied in terms of the transfer matrix pole distribution. Identifying the lasing by the existence of the poles in the upper half-space of the complex frequencies, we demonstrate that under the condition of total internal reflection lasing may be observed at a finite thickness of the slab; further increase in the thickness results in the quenching of lasing. However, in the latter case the amplification of reflected wave is possible.

Binary asteroid population. 2. Anisotropic distribution of orbit poles of small, inner main-belt binaries

Our photometric observations of 18 main-belt binary systems in more than one apparition revealed a strikingly high number of 15 having positively re-observed mutual events in the return apparitions. Our simulations of the survey showed that it cannot be due to an observational selection effect and that the data strongly suggest that poles of mutual orbits between components of binary asteroids in the primary size range 3–8km are not distributed randomly: The null hypothesis of an isotropic distribution of the orbit poles is rejected at a confidence level greater than 99.99%. Binary orbit poles concentrate at high ecliptic latitudes, within 30° of the poles of the ecliptic. We propose that the binary orbit poles oriented preferentially up/down-right are due to either of the two processes: (i) the YORP tilt of spin axes of their parent bodies toward the asymptotic states near obliquities 0° and 180° (pre-formation mechanism) or (ii) the YORP tilt of spin axes of the primary components of already formed binary systems toward the asymptotic states near obliquities 0° and 180° (post-formation mechanism). The alternative process of elimination of binaries with poles closer to the ecliptic by dynamical instability, such as the Kozai effect due to gravitational perturbations from the Sun, does not explain the observed orbit pole concentration. This is because for close binary asteroid systems, the gravitational effects of primary’s irregular shape dominate the solar-tide effect.

Note on the Role of Symmetry in Scattering from Isospectral Graphs and Drums

We discuss scattering from pairs of isospectral quantum graphs constructed using the method described in the papers of Parzanchevski, Band and Ben-Shach. It was shown in the paper of Band et al. that scattering matrices of such graphs have the same spectrum and polar structure, provided that infinite leads are attached in a way which preserves the symmetry of isospectral construction. In the current paper we compare this result with the conjecture put forward by Okada et al. that the pole distribution of scattering matrices in the exterior of isospectral domains in R2 is different.

Step-Growth Polymerization of Poly(phenylcarbosilane) and Its Structural and Physical Properties

The polymerization and molecular weight distribution of poly(phenylcarbosilane) (PPCS) depend on the temperature and pressure conditions under which it is synthesized using the Kumada rearrangement reaction. Its degree of polymerization is related not only to its physical properties such as solubility and boiling point but also to its chemical structure. In this study, soluble PPCS having a weight-average molecular weight (Mw) in the range of 2,500–3,000 was selectively isolated through distillation or fractional precipitation, and its chemical structure and physical properties were studied via FT-IR, NMR, GPC, and thermal analysis. The analytical data indicate that the Si–CH2–Si backbone and Si–Si bond are formed through step-growth polymerization and are clearly detected after purification. The differences in the thermal behavior of PPCS in air and in nitrogen were also investigated.

Nuclear relocalisation of cytoplasmic poly(A)-binding proteins PABP1 and PABP4 in response to UV irradiation reveals mRNA-dependent export of metazoan PABPs

Poly(A)-binding protein 1 (PABP1) has a fundamental role in the regulation of mRNA translation and stability, both of which are crucial for a wide variety of cellular processes. Although generally a diffuse cytoplasmic protein, it can be found in discrete foci such as stress and neuronal granules. Mammals encode several additional cytoplasmic PABPs that remain poorly characterised, and with the exception of PABP4, appear to be restricted in their expression to a small number of cell types. We have found that PABP4, similarly to PABP1, is a diffusely cytoplasmic protein that can be localised to stress granules. However, UV exposure unexpectedly relocalised both proteins to the nucleus. Nuclear relocalisation of PABPs was accompanied by a reduction in protein synthesis but was not linked to apoptosis. In examining the mechanism of PABP relocalisation, we found that it was related to a change in the distribution of poly(A) RNA within cells. Further investigation revealed that this change in RNA distribution was not affected by PABP knockdown but that perturbations that block mRNA export recapitulate PABP relocalisation. Our results support a model in which nuclear export of PABPs is dependent on ongoing mRNA export, and that a block in this process following UV exposure leads to accumulation of cytoplasmic PABPs in the nucleus. These data also provide mechanistic insight into reports that transcriptional inhibitors and expression of certain viral proteins cause relocation of PABP to the nucleus.

Widespread inclination shallowing in Permian and Triassic paleomagnetic data from Laurentia: Support from new paleomagnetic data from Middle Permian shallow intrusions in southern Illinois (USA) and virtual geomagnetic pole distributions

Recent paleomagnetic work has highlighted a common and shallow inclination bias in continental redbeds. The Permian and Triassic paleomagnetic records from Laurentia are almost entirely derived from such sedimentary rocks, so a pervasive inclination error will expectedly bias the apparent polar wander path of Laurentia in a significant way. The long-standing discrepancy between the apparent polar wander paths of Laurentia and Gondwana in Permian and Triassic time may be a consequence of such a widespread data-pathology. Here we present new Middle Permian paleomagnetic data from igneous rocks and a contact metamorphosed limestone from cratonic Laurentia. The exclusively reversed Middle Permian magnetization is hosted by low-Ti titanomagnetite and pyrrhotite and yields a paleomagnetic pole at 56.3°S, 302.9°E (A 95 = 3.8, N = 6). This pole, which is unaffected by inclination shallowing, suggests that a shallow inclination bias may indeed be present in the Laurentian records. To further consider this hypothesis, we conduct a virtual geomagnetic pole distribution analysis, comparing theoretical expectations of a statistical field model (TK03.GAD) against published data-sets. This exercise provides independent evidence that the Laurentian paleomagnetic data is widely biased, likely because of sedimentary inclination shallowing. We estimate the magnitude of this error from our model results and present and discuss several alternative corrections.

Vein development during folding in the upper brittle crust: The case of tourmaline-rich veins of eastern Elba Island, northern Tyrrhenian Sea, Italy

Detailed structural analysis of tourmaline-rich veins hosted in the contact aureole of the ∼6 Ma Porto Azzurro granite in southeastern Elba Island, northern Tyrrhenian Sea is presented. Using geometric features of the veins, the physical conditions at the time of vein formation are estimated, namely the stress ratio (Φ = ( σ 2 − σ 3)/( σ 1 − σ 3)), driving stress ratio ( R′ = ( P f − σ 3)/( σ 1 − σ 3)) and fluid overpressure (Δ P o = P f − σ 3). Two vein sets (A veins and B veins) have been recognized based on orientation and thickness distributions and infilling material. Analysis of vein pole distributions indicates Φ = 0.57 and R′ = 0.24 for the A veins and Φ = 0.58 and R′ = 0.47 for the B veins, and fluid pressures less than the intermediate stress magnitude. Analysis of geometric features of the veins gives estimated fluid overpressures of between ∼16 MPa (A veins) and ∼32 MPa (B veins). We propose a model for the tectonic environment of vein development, in which formation of secondary permeability in the deforming thermal aureole of the Porto Azzurro pluton was controlled by ongoing development of fracture systems in the hinge zone of a regional NNW–SSE trending fold that favored transport and localization of hydrothermal fluids.

Kinetics and Molecular Weight Characterization of Poly (2-Ethylhexyl Acrylate) and Liquid Crystal (5CB) Composites

The effect of initiator and liquid crystal 4-cyano-4′-n-pentylbiphenyl (5CB) concentrations on the monomer conversion and molecular weight distributions of the polymer in the free-radical polymerization of 2-ethylhexylacrylate (2-EHA) has been studied and characterized using Fourier transform infrared spectroscopy, differential scanning calorimetry, and gel permeation chromatography. A slight effect of the concentration of the photoinitiator has been observed both on the monomer conversion and the molecular weight distribution of poly (2-EHA). Increasing the amount of 5CB in the initial mixture leads to a decrease of conversion, glass transition temperature of the polymer, molar mass of polymer and of the polydispersity.

Fast Padé transform in the theory of resonances: exact solution of the harmonic inversion problem

We present the fast Padé transform (FPT) as a polynomial quotient for the Green or response function from signal processing, spectroscopy and resonant scattering theory. Specific illustrations are given for nuclear magnetic resonance spectroscopy within the problem of harmonic inversion, quantification or spectral analysis. Here, the input time signal points or auto-correlation functions are given via measurements or computations, and the task is to reconstruct the unknown components as the harmonic variables in terms of the fundamental complex frequencies and amplitudes. The FPT solves the harmonic inverse problem exactly by retrieving the true number of resonances with all their proper spectral parameters. This output list is finalized by means of Froissart doublets or pole-zero confluences for unequivocal disentangling of the physical/genuine from unphysical/spurious contents of the analysed time signal. Stability of investigated systems under external perturbations is especially challenged by the presence of noise. The FPT can assess the system's stability through determining the locations and distributions of spectral poles and zeros in the complex frequency plane. This permits identification of the regions that are void of noise, and gives the possibility for improved system performance under more stable conditions with full signal-noise separation. The FPT can provide a number of important biophysical and chemical quantities, including the density of states and abundance or concentrations of all the physical constituents from the investigated substance.

Geomagnetic secular variation and the statistics of palaeomagnetic directions

In this study, we examine the role of palaeosecular variation (PSV) in the use of statistics for palaeomagnetic studies, and we provide new reliability criteria for palaeomagnetic poles or directions.We first conclude that Fisher statistics should not be applied to average palaeomagnetic directions but to virtual geomagnetic pole (VGP) distributions instead. Secondly, we strongly advocate that typical properties of geomagnetic field behaviour are taken into account in the assessment of palaeomagnetic data sets. The latitude-dependent properties (E, S, k) provide useful guidelines for the reliability of a palaeomagnetic data set. A reliable assessment of these properties depends on the (sufficient) number of palaeomagnetic samples being taken. Therefore, as an additional instrument of assessing data sets, we provide a N-dependent A95 envelope, bounded by an upper limit A95max, and a lower limit A95min that helps to ascertain whether or not a distribution has sufficiently well-sampled PSV and therefore geomagnetic field behaviour. Applying these criteria is indispensable for studies of geomagnetic behaviour, or for studies aiming at using TK03.GAD for inclination error correction through the elongation/inclination (E/I) method. For palaeomagnetic studies aimed at geological reconstructions, they form helpful guidelines and increase the confidence in the rocks having faithfully recorded the field. An analysis of published Eastern Mediterranean data shows that the vast majority of studies do not conform to the Van der Voo criteria, in particular with respect to N and A95. We have provided criteria that are on the one hand more lenient (lower N may still provide relevant information), and on the other hand more strict (for high N the criterion of A95 < 16° should be adapted to a requirement of lower A95, e.g. A95 80).

Pole placement in non connected regions for descriptor models

Abstract This paper proposes a method to compute a static state feedback control law which achieves a non strict pole assignment on a continuous or a discrete descriptor system. The specification on the closed-loop poles is given in terms of D -stability, i.e. in terms of a pole-clustering region D . In this work, the clustering region is possibly non path-connected since it can result from the union of disjoint and non symmetric subregions. Such a choice, which is original when the design of linear descriptor systems is concerned, is made possible by a technique that enables a partial pole placement via aggregation. The distribution of the finite poles in various subregions can be chosen. Some key steps of the procedure are addressed through strict LMI (Linear Matrix Inequalities). This is an extension of a previous work from conventional to descriptor models. Therefore, not only stability is to be ensured but also, because of infinite poles, regularity and causality or impulse freeness (the whole of those properties being termed admissibility).

The influence of preparation parameters on size and charge distributions of poly (butylcyanoacrylate) nanoparticles evaluated by response surface modelling (RSM)

The influence of preparation parameters on size and charge distributions of poly (butylcyanoacrylate) nanoparticles evaluated by response surface modelling (RSM)

Palaeomagnetism of Precambrian dyke swarms in the North China Shield: The ∼1.8 Ga LIP event and crustal consolidation in late Palaeoproterozoic times

The North China Shield (NCS) is cut by a laterally-extensive dyke swarm emplaced at 1.78–1.76 Ga when an extensional regime succeeded regional metamorphism and completion of cratonisation by ∼1.85 Ga. Palaeomagnetic study of these dykes and adjoining metamorphic country rocks identifies a dominant shallow axis comprising a contiguous population with NE to N declinations and rare opposite polarity. Dykes with NE shallow magnetic declination (A1, D/ I = 36/−1°) recognised from previous study and emplaced in granulite terranes in the north are displaced by more northerly declinations (A2, D/ I = 8/2°) in lower grade metamorphic terranes to the south. Contact tests indicate a primary cooling-related origin to these magnetisations although tests are in part ambiguous because magnetisations in the granulite basement are comparable. Petrologic and rock magnetic considerations imply that magnetisation of the dykes occurred during uplift from depths as deep as 20 km following the peak of metamorphism at ∼1.85 Ga. A temporal migration A2 → A1 is implied by the higher crustal level and earlier acquisition of the former, and the deeper source and later acquisition of the latter. A third population of dyke magnetisations (A3, D/ I = 18/43°) is distributed towards steeper inclinations and close to the Mesozoic-Recent palaeofield. These are either partial or complete overprints of A1–A2 magnetisations with greater degrees of alteration indicated by demagnetisation and thermomagenetic spectra, or are much younger dykes of Mesozoic-Tertiary age. A minority fourth (later Precambrian but presently undated) dual polarity population has a magnetisation (11 dykes, D/ I = 108/7°) with contact tests indicating a primary cooling-related origin. The ∼1.78–1.76 Ga time of emplacement of the dominant dyke swarms in this study is widely represented by contemporaneous igneous rocks in other major shields linked to major Large Igneous Province (LIP)-related events. The new definition of a ∼1.83–1.76 Ga APW swathe from the North China Shield permits a comparison with other shields and yields a constraint to continental configurations during the late Palaeoproterozoic. A quasi-integral reconstruction of Palaeopangaea is tested here and supported by conformity of predominantly of uplift-related palaeopoles from the ∼1.90–1.70 Ga tectono-thermal belts and from SW → NE trending APW implied by the distribution of poles from the ∼1.80 Ga igneous suites including the LIP events. This trend incorporates the A2 → A1 migration and the granulite terrane cooling polar swathe from North China. The reconstruction indicates that continental crust consolidated in Palaeoproterozoic times by accretion of ∼2.3–1.7 Ga orogenic belts around a hemispheric and crescent-shape core already established by Late Archaean times. The North China Shield is interpreted to have bordered the western cratonic margin of the Indian Shield in a proximity supported by correlation of geological features and suggested by a number of previous workers. The Central Orogenic Zone of the North China shield characterised by tectono-thermal activity prior to ∼1.85 Ga was then contiguous with a comparable zone running through the centre of the Indian Shield and continuing into the Capricorn Belt of Western Australia. The ∼1.78–1.76 Ga dykes in North China continue into dyke swarms in the South India Shield and may have been sourced in a plume-related LIP focussed near the continental margin in the Xiong’er Aulacogen.

Growth and poles of meromorphic solutions of some difference equations

This paper is devoted to studying the growth property and the pole distribution of meromorphic solutions f of some complex difference equations with all coefficients being rational functions or of growth S(r,f). We find the lower bound of the lower order, or the relation between lower order and the convergence exponent of poles of meromorphic solutions of such equations.

Study on microneedle technique in enhancement of transdermal nanoparticle delivery

Objective To investigate the microneedle technique in enhancement of transdermal nanoparticle delivery and the distribution of poly (D,L-lactic-co-glycolic acid) (PLGA) nanoparticles in the skin and the transdermal microconduits.Methods Double fluorescent PLGA nanoparticles were used to show the transdermal transport process.Franz diffusion cell was used for the transdermal study.The nanoparticle suspension was added to the donor chamber.The hairless mouse skin in the microneedle group was treated by microneedle technique and that in the control group was not treated.Penetration of nanoparticles was visualized by confocal laser scanning microscopy (CLSM).Distribution of nanoparticle diameter was quantified by HPLC.Results The CLSM images revealed that the nanoparticles were delivered into the microconduits created by microneedles and entered the epidermis and the dermis.The quantitative results showed that no nanoparticles reached the receptor compartment 48 h after addition of the nanoparticles in both groups.In microneedle group the nanoparticle amount was 125.99 μg/cm2 in the epidermis and 55.31 μg/cm2 in the dermis,with the total amount in the skin being 181.30 μg/cm2;in the the control group,the nanoparticle amount was 42.15 μg/cm2 in the epidermis and 32.76 μg/cm2 in the dermis,with the total amount in the skin being 74.91 μg/cm2.Microneedle technique significantly increased the amount of nanoparticles entering the skin (P0.01),and the amount in the epidermis was significantly more than that in the dermis (P0.01).Conclusion Our results suggest that microneedles can enhance the intradermal PLGA nanoparticle delivery,and the nanoparticles deposit in the skin to achieve sustainable drug release,which is beneficial for topical drug administration.

Gradient composition distribution in poly(2,6-dimethylphenylene oxide)/polystyrene blend nanorods

We report formation of nanorods that exhibit a gradient distribution of poly(2,6-dimethylphenylene oxide) and polystyrene (PPO and PS), i.e., the PPO weight fractions in the nanorods increase from top to bottom along the long axis of the nanorods. PPO/PS nanorods with various diameters were prepared by infiltrating porous anodic aluminium oxide (AAO) templates with polymer blend melts. Their morphology was investigated by Fourier transform infrared spectroscopy (FTIR). The gradient distribution of polymer blends in the nanopores is governed by (1) the viscosity difference between the two polymers and (2) the pore diameter. This remains true although PPO/PS blends are compatible in the segmental level. For various diameter nanorods made of PPO/PS blends, the PPO content decreased as the rod diameter became smaller owing to the increased confinement imposed by the nanopores. This leads to a higher rate of capillary rise in smaller nanopores.

Conditions for a Class of Rational Approximants of Fractional Differentiators/Integrators to Enjoy the Interlacing Property

AbstractFractional-order controllers are based on fractional differentiators and integrators, which extend classical integral or derivative actions to improve performance and robustness of feedback loops. The fractional (irrational) operators are usually realized by continued fractions leading to rational approximations. Stable and minimum-phase transfer functions, with interlaced distribution of real zeros and poles, are also requested as suitable approximations. This paper proves that two classes of continued-fractions-based approximations have negative zeros and poles enjoying the interlacing property, for any fractional order v, with |v| < 1, and for any degree, m, of the approximating transfer function.