Regular Sequence Research Articles

Crystallization Behavior and Properties of Propylene/4-Methyl-1-pentene Copolymers from a Metallocene Catalyst

Copolymers of isotactic polypropylene (iPP) with 4-methyl-1-pentene (iPP4MP) were prepared with a highly isoselective homogeneous organometallic catalyst in a range of 4-methyl-1-pentene (4MP) concentrations between about 1.7 and 14 mol %. Crystallization from the melt at different crystallizations temperatures have been performed to study the effect of 4MP comonomeric units excluded from the crystals on the crystallization of α and γ forms. All samples crystallize in mixtures of α and γ forms, and for each sample, the fraction of γ form increases with increasing crystallization temperature to achieve a maximum value fγ(max), which depends on the 4MP concentration. Compared to the homopolymer, the maximum fractional amount of γ form fγ(max) rapidly increases with increasing 4MP content achieving the highest value of 92% at low 4MP concentration of 2.2 mol %, and decreases with a further increase of 4MP concentration. These data are compared with analogous data of the maximum amount of γ form that develops in copolymers of iPP with ethylene and butene. This allows comparing the different effects of rejection of defects from the crystals, which produces interruption of the regular propene sequences and shortening of the length of the crystallizable sequences, the inclusion of defects into crystals of α and γ forms, and the effect of the crystallization kinetics. Since 4MP comonomeric units are excluded from the crystals, the behavior of iPP4MP copolymers provides the sole interruption effect, which is highly efficient and produces the highest amount of γ form of 92% at low 4MP concentration of nearly 2 mol %. The observed decrease of fγ(max) at higher 4MP concentrations is due to the too slow crystallization rate of the γ form at these 4MP contents that induces the crystallization of the kinetically favored α form. In fact, crystals of γ forms that develop in these copolymers are highly defective and show melting temperatures lower than those of the α form and, therefore, experience low undercooling at high crystallization temperatures. These results demonstrate that in metallocene iPP copolymers containing a significant amount of constitutional defects, the crystallization of the γ form is favored because of the short regular propene sequences, whereas the crystallization of the α form is always kinetically favored.

Merging and disconnecting resonance tongues in a pulsing excitable microlaser with delayed optical feedback.

Excitability, encountered in numerous fields from biology to neurosciences and optics, is a general phenomenon characterized by an all-or-none response of a system to an external perturbation of a given strength. When subject to delayed feedback, excitable systems can sustain multistable pulsing regimes, which are either regular or irregular time sequences of pulses reappearing every delay time. Here, we investigate an excitable microlaser subject to delayed optical feedback and study the emergence of complex pulsing dynamics, including periodic, quasiperiodic, and irregular pulsing regimes. This work is motivated by experimental observations showing these different types of pulsing dynamics. A suitable mathematical model, written as a system of delay differential equations, is investigated through an in-depth bifurcation analysis. We demonstrate that resonance tongues play a key role in the emergence of complex dynamics, including non-equidistant periodic pulsing solutions and chaotic pulsing. The structure of resonance tongues is shown to depend very sensitively on the pump parameter. Successive saddle transitions of bounding saddle-node bifurcations constitute a merging process that results in unexpectedly large regions of locked dynamics, which subsequently disconnect from the relevant torus bifurcation curve; the existence of such unconnected regions of periodic pulsing is in excellent agreement with experimental observations. As we show, the transition to unconnected resonance regions is due to a general mechanism: the interaction of resonance tongues locally at an extremum of the rotation number on a torus bifurcation curve. We present and illustrate the two generic cases of disconnecting and disappearing resonance tongues. Moreover, we show how a pair of a maximum and a minimum of the rotation number appears naturally when two curves of torus bifurcation undergo a saddle transition (where they connect differently).

Study of nonlinear characteristics in hollow cathode discharge in unmagnetized plasmas

AbstractParametric study and nonlinear dynamical analysis of the discharge parameter variations are presented here for a hollow cathode source in the glow discharge regime and later in the radio frequency (RF) discharge regime. A plasma source consisting of a semi‐transparent hollow cathode leads to the generation of nonthermal energetic charged particles and the formation of multiple potential regimes in the plasma column during both the glow discharge as well as the RF discharge regimes. The hollow cathode discharge obtained using this single plasma source exhibits significant mixed‐mode oscillations (MMOs) during the glow discharge regime. Various regular and irregular sequences of MMOs evolved during the progressive change of discharge voltage in the glow discharge regime. During the RF power application across the hollow cathode source, the charged particles oscillate and appear in bursts in the time series. The present study investigates energy distribution among the coherent modes of discharge through the application of the Empirical Mode Decomposition technique. Multiple coherent modes are identified during both discharge regimes that carry most of the discharge energy.

Spatial Cognition of the Visually Impaired: A Case Study in a Familiar Environment.

This paper aims to explore the factors influencing the spatial cognition of the visually impaired in familiar environments. Massage hospitals are some of the few places that can provide work for the visually impaired in China. Studying the spatial cognition of the visually impaired in a massage hospital could be instructive for the design of working environments for the visually impaired and other workplaces in the future. First, the subjective spatial cognition of the visually impaired was evaluated by object layout tasks for describing the spatial relationships among object parts. Second, physiological monitoring signal data, including the electrodermal activity, heart rate variability, and electroencephalography, were collected while the visually impaired doctors walked along prescribed routes based on the feature analysis of the physical environment in the hospital, and then their physiological monitoring signal data for each route were compared. The visual factors, physical environmental factors, and human-environment interactive factors that significantly impact the spatial cognition of visually impaired people were discussed. (1) visual acuity affects the spatial cognition of the visually impaired in familiar environments; (2) the spatial cognition of the visually impaired can be promoted by a longer staying time and the more regular sequence of a physical environment; (3) the spatial comfort of the visually impaired can be improved by increasing the amount of greenery; and (4) the visual comfort of the visually impaired can be reduced by rich interior colors and contrasting lattice floor tiles.

Calculation of the stressed-strained state of rotating anisotropic cylindrical shells with a hole based on variational RVR-method

This paper proposes a new variational RVR-method for calculating the three-dimensional stressed-strained state of statically loaded shell elements of structures with holes of arbitrary shapes and sizes. The scientifically substantiated RVR method is based on the use of the Reissner variational principle, the Vekua method, the theory of R-functions by Rvachev, and the general equations of the spatial theory of elasticity. The use of mixed Reissner variational principle leads to an increase in the accuracy of solving boundary value problems due to the independent variation of the displacement vector and the stress tensor. The Vekua method makes it possible to replace the solution to a three-dimensional problem with a regular sequence of solutions to two-dimensional problems. The theory of R-functions at the analytical level takes into account the geometric information of boundary value problems, which is necessary for the construction of solution structures that accurately satisfy all boundary conditions. At the same time, the developed algorithm for bilateral integral accuracy assessment makes it possible to automate the search for such a number of approximations in which the process of convergence of solutions becomes stable. The possibilities of the RVR method are shown in numerous examples of solving boundary problems of calculating cylindrical shells with an elliptical hole when setting centrifugal loads according to a deformed scheme. Calculations according to the specified load scheme of the anisotropic cylinder lead (at certain values of the angular velocity of rotation) to a significant increase in stresses. Therefore, to obtain reliable results, it is necessary to set a centrifugal load that takes into account the change in the size of the body in the process of its deformation. The characteristic features of the proposed RVR-method, which can be used effectively in the manufacture of shell elements of structures in various branches of technology, are discussed.

Elasticity of Semiflexible ZigZag Nanosprings with a Point Magnetic Moment.

Kinks can appear along the contour of semiflexible polymers (biopolymers or synthetic ones), and they affect their elasticity and function. A regular sequence of alternating kink defects can form a semiflexible nanospring. In this article, we theoretically analyze the elastic behavior of such a nanospring with a point magnetic dipole attached to one end while the other end is assumed to be grafted to a rigid substrate. The rod-like segments of the nanospring are treated as weakly bending wormlike chains, and the propagator (Green's function) method is used in order to calculate the conformational and elastic properties of this system. We analytically calculate the distribution of orientational and positional fluctuations of the free end, the force-extension relation, as well as the compressional force that such a spring can exert on a planar wall. Our results show how the magnetic interaction affects the elasticity of the semiflexible nanospring. This sensitivity, which is based on the interplay of positional and orientational degrees of freedom, may prove useful in magnetometry or other applications.

A note on $${\varvec{d}}$$-sequences and regular sequences of quadrics

A note on $${\varvec{d}}$$-sequences and regular sequences of quadrics

Model of Crystallization Behavior of Isotactic Polypropylene: The Role of Defects

AbstractThe crystallization behavior of propene–ethylene (iPPC2), propene–butene (iPPC4), propene–pentene (iPPC5), and propene–hexene (iPPC6) isotactic copolymers, prepared with single center metallocene catalysis, is described. Thanks to the perfectly random distribution of comonomers along the macromolecules, these copolymers can be considered as model for the crystallization behavior of isotactic polypropylene (iPP) that is mainly defined by the average length of the regular propene sequences. A model of the crystallization behavior of iPP is described based on the definition of a double effect of defects (stereodefects and comonomers), the interruption effect of defects excluded from the crystals that shortens the length of the crystallizable propene sequences inducing crystallization of the γ form, and the effect of inclusion of defects in the crystals of α form, γ form or δ form that induces the crystallization of the form whose lattice is less disturbed by the defect.

The time evolution of bias

ABSTRACT We investigate the time evolution of bias of cosmic density fields. We perform numerical simulations of the evolution of the cosmic web for the conventional Λ cold dark matter (ΛCDM) model. The simulations cover a wide range of box sizes $L=256\rm{-}1024\,h^{-1}\, {\rm Mpc}$, and epochs from very early moments z = 30 to the present moment z = 0. We calculate spatial correlation functions of galaxies, ξ(r), using dark matter particles of the biased Lambda cold dark mattter (ΛCDM) simulation. We analyse how these functions describe biasing properties of the evolving cosmic web. We find that for all cosmic epochs the bias parameter, defined through the ratio of correlation functions of selected samples and matter, depends on two factors: the fraction of matter in voids and in the clustered population, and the luminosity (mass) of galaxy samples. Gravity cannot evacuate voids completely, thus there is always some unclustered matter in voids, and the bias parameter of galaxies is always greater than unity, over the whole range of evolution epochs. We find that for all cosmic epochs bias parameter values form regular sequences, depending on galaxy luminosity (particle density limit), and decreasing with time.

Visual over auditory superiority in sensorimotor timing under optimized condition.

Auditory over visual advantage in temporal processing is generally appreciated, such as the well-established auditory superiority in sensorimotor timing. To test for a possible visual superiority in temporal processing, here, we present a data set composed of a large 60 subjects sample and a data set including eight smaller samples of approximately 15 subjects, showing that synchronization to a temporally regular sequence was more stable for a visual bouncing ball (VB) than for auditory tones (ATs). The results demonstrate that vision can be superior over audition in sensorimotor timing under optimized conditions, challenging the generally believed auditory superiority in temporal processing. In contrast to the auditory-specific biological substrates of timing in sensorimotor interaction, the present finding points to tight visual-motor cortical coupling in sensorimotor timing.

Compression of the Synchrotron Mössbauer X-ray Photon Waveform in an Oscillating Resonant Absorber

A technique to transform the waveform of a 14.4 keV photon (time dependence of the photon detection probability or, equivalently, the intensity of the single-photon wave packet) into a regular sequence of short, nearly bandwidth-limited pulses with a controlled number of pulses is proposed. It is based on coherent forward scattering of single X-ray photons from a synchrotron Mössbauer source (SMS) in an optically thick, vibrating, recoilless 57Fe resonant absorber. The possibility of compressing the waveform of an SMS photon into a single short bell-shaped pulse is predicted. The experiment is proposed for compressing a 100 ns duration 14.4 keV single-photon wave packet produced by SMS at the European Synchrotron Radiation Facility (ESRF) into a single bell-shaped pulse of less than 20 ns duration and more than twice the peak intensity. Such single-photon coherent pulses are promising for applications in the fast-developing field of X-ray quantum optics, including possible implementation of quantum memory.

Regular sequences on squares of monomial ideals

We use initially regular sequences that consist of linear sums to explore the depth of $$R/I^2$$ , when I is a monomial ideal in a polynomial ring R. We give conditions under which these linear sums form regular or initially regular sequences on $$R/I^2$$ . We then obtain a criterion for when $${{\,\mathrm{depth}\,}}R/I^2>1$$ and a lower bound on $${{\,\mathrm{depth}\,}}R/I^2$$ .

Аналитическая постановка проблемы свободы в контексте социально-правовой аргументации

The author addresses the problem of free will as a prerequisite for the moral, and, consequently, legal responsibility of a person as a legal entity and concentrates on its formulation in analytic philosophy. The latter proceeds from the contradiction between a person’s free will and the determinism of objective processes. The peculiarity of this formulation of the problem of free will stems from the characteristic features of analytic philosophy: its anti-historicism, anti-metaphysics, scientism, logicism, naturalism of common sense, and value neutrality. Considering the grounds on which a person can be deemed free, we come to the conclusion that these grounds are extremely problematic in the light of both competing analytic theories, i.e. compatibilism and incompatibilism. While the former, in the spirit of D. Hume, is forced to look for means to describe a person’s free actions as necessary elements in the chain of a regular sequence of events, the latter faces the problem of substantiating indeterminism, clarifying its types and the level of implementation of unconditioned processes that make the action free. The development of an analytical understanding of free will leads to the paradoxical conclusion that the latter is a condition for including an individual into the crime–punishment chain of legal determination. In other words, a person must be free to get in the zone of action of a certain type of causal dependence. The logicism of the analytical type of philosophizing makes such conclusions unacceptable, which further problematizes free will. The author comes to the conclusion that the analytical approach to the problem of free will immanently contains its denial or formalization and is, therefore, alien to the traditional socio-legal discourse based on the assumption of unshakable, a priori grounds for a legal person’s free will. In the final part of the article, the author explains why the analytical formulation is inapplicable to the problem of freedom for social philosophy of the value type, but relevant for reflective social philosophy.

ZAREMBA, SALEM AND THE FRACTAL NATURE OF GHOST DISTRIBUTIONS

AbstractMotivated by near-identical graphs of two increasing continuous functions—one related to Zaremba’s conjecture and the other due to Salem—we provide an explicit connection between fractals and regular sequences by showing that the graphs of ghost distributions, the distribution functions of measures associated to regular sequences, are sections of self-affine sets. Additionally, we provide a sufficient condition for such measures to be purely singular continuous. As a corollary, and analogous to Salem’s strictly increasing singular continuous function, we show that the ghost distributions of the Zaremba sequences are singular continuous.

Crystallization Behavior of Isotactic Propene-Octene Random Copolymers

The crystallization behavior of random propene-octene isotactic copolymers (iPPC8) prepared with a homogeneous metallocene catalyst has been studied. Samples of iPPC8 with low octene content up to about 7 mol% were isothermally crystallized from the melt at various crystallization temperatures. The samples crystallize in mixtures of the α and γ forms of isotactic polypropylene (iPP). The relative amount of γ form increases with increasing crystallization temperature, and a maximum amount of γ form (fγ(max)) is achieved for each sample. The crystallization behavior of iPPC8 copolymers is compared with the crystallization from the melt of propene–ethylene, propene–butene, propene–pentene, and propene–hexene copolymers. The results show that the behavior of iPPC8 copolymers is completely different from those described in the literature for the other copolymers of iPP. In fact, the maximum amount of γ form achieved in samples of different copolymers of iPP generally increases with increasing comonomer content, while in iPPC8 copolymers the maximum amount of γ form decreases with increasing octene content. The different behaviors are discussed based on the inclusion of co-monomeric units in the crystals of α and γ forms of iPP or their exclusion from the crystals. In iPPC8 copolymers, octene units are excluded from the crystals giving only the interruption effect that shortens the length of regular propene sequences, inducing crystallization of the γ form at low octene concentrations, lower than 2 mol%. At higher octene concentration, the crystallization of the kinetically favored α form prevails.

Graph-based representation for identifying individual travel activities with spatiotemporal trajectories and POI data

Individual daily travel activities (e.g., work, eating) are identified with various machine learning models (e.g., Bayesian Network, Random Forest) for understanding people’s frequent travel purposes. However, labor-intensive engineering work is often required to extract effective features. Additionally, features and models are mostly calibrated for individual trajectories with regular daily travel routines and patterns, and therefore suffer from poor generalizability when applied to new trajectories with more irregular patterns. Meanwhile, most existing models cannot extract features to explicitly represent regular travel activity sequences. Therefore, this paper proposes a graph-based representation of spatiotemporal trajectories and point-of-interest (POI) data for travel activity type identification, defined as Gstp2Vec. Specifically, a weighted directed graph is constructed by connecting regular activity areas (i.e., zones) detected via clustering individual daily travel trajectories as graph nodes, with edges denoting trips between pairs of zones. Statistics of trajectories (e.g., visit frequency, activity duration) and POI distributions (e.g., percentage of restaurants) at each activity zone are encoded as node features. Next, trip frequency, average trip duration, and average trip distance are encoded as edge weights. Then a series of feedforward neural networks are trained to generate low-dimensional embeddings for activity nodes through sampling and aggregating spatiotemporal and POI features from their multihop neighborhoods. Activity type labels collected via travel surveys are used as ground truth for backpropagation. The experiment results with real-world GPS trajectories show that Gstp2Vec significantly reduces feature engineering efforts by automatically learning feature embeddings from raw trajectories with minimal prepossessing efforts. It not only enhances model generalizability to receive higher identification accuracy on test individual trajectories with diverse travel patterns, but also obtains better efficiency and robustness. In particular, our identification of the most common daily travel activities (e.g., Dwelling and Work) for people with diverse travel patterns outperforms state-of-the-art classification models.

NLRexpress-A bundle of machine learning motif predictors-Reveals motif stability underlying plant Nod-like receptors diversity.

Examination of a collection of over 80,000 Plant Nod-like receptors (NLRs) revealed an overwhelming sequence diversity underlying functional specificity of pathogen detection, signaling and cooperativity. The NLR canonical building blocks—CC/TIR/RPW8, NBS and LRR—contain, however, a number of conserved sequence motifs showing a significant degree of invariance amongst different NLR groups. To identify these motifs we developed NLRexpress—a bundle of 17 machine learning (ML)-based predictors, able to swiftly and precisely detect CC, TIR, NBS, and LRR motifs while minimizing computing time without accuracy losses—aimed as an instrument scalable for screening overall proteomes, transcriptomes or genomes for identifying integral NLRs and discriminating them against incomplete sequences lacking key motifs. These predictors were further used to screen a subset of ∼34,000 regular plant NLR sequences. Motifs were analyzed using unsupervised ML techniques to assess the structural correlations hidden underneath pattern variabilities. Both the NB-ARC switch domain which admittedly is the most conserved region of NLRs and the highly diverse LRR domain with its vastly variable lengths and repeat irregularities—show well-defined relations between motif subclasses, highlighting the importance of structural invariance in shaping NLR sequence diversity. The online NLRexpress webserver can be accessed at https://nlrexpress.biochim.ro.

Effect of changes in the menstrual cycle and age on the signal intensity of amide proton transfer imaging in the normal uterus: a preliminary study.

To analyze the effect of changes in the menstrual cycle and age on the signal intensity of amide proton transfer (APT) imaging in normal uterine structures. Thirty-one healthy females (age: 21-50years old) underwent regular pelvic MRI and APT sequences during their menstrual cycle. The APT values of the endometrium, myometrium, and junctional zone were measured. One-way and multi-way analyses of variance were used to analyze the data. Intraindividual difference and Pearson's correlation analyses were also conducted. The APT values of the uterine structures during the menstrual, proliferative, and secretory phases were 3.413 ± 0.682%, 4.776 ± 0.829%, and 5.218 ± 0.772% for the endometrium; 2.966 ± 0.533%, 3.597 ± 0.380%, and 4.324 ± 0.583% for the myometrium; and 1.703 ± 0.393%, 2.362 ± 0.486%, and 2.779 ± 0.528% for the junctional zone. The individual variation in the APT values of the normal uterus during the three menstrual phases was 1.1-1.7%.There were no significant differences in APT values of uterine structures with age. The APT values of the endometrium were greater than those of other structures (P < 0.05).The Pearson correlation coefficients between APT values of uterine structures and menstrual cycle were 0.686, 0.743, and 0.684, respectively. The menstrual cycle had a significant effect on the APT signal intensities of the uterine structures, whereas premenopausal age had no significant effect. Changes in the uterine structures during the menstrual cycle should be considered when using APT to diagnose suspected uterine lesions.

Exceptional complete intersection maps of local rings

This work concerns surjective maps $\varphi\colon R\to S$ of commutative noetherian local rings with kernel generated by a regular sequence that is part of a minimal generating set for the maximal ideal of $R$. The main result provides criteria for detecting such exceptional complete intersection maps in terms of the lattices of thick subcategories of the derived category of complexes of finite length homology. A key input is a characterization of such maps in terms of the truncated Atiyah class of $\varphi$.

Revisiting bright δ Scuti stars and their period–luminosity relation with TESS and Gaia DR3

ABSTRACT We have used NASA’s TESS mission to study catalogued δ Scuti stars. We examined TESS light curves for 434 stars, including many for which few previous observations exist. We found that 62 are not δ Scuti pulsators, with most instead showing variability from binarity. For the 372 δ Scuti stars, we provide a catalogue of the period and amplitude of the dominant pulsation mode. Using Gaia DR3 parallaxes, we place the stars in the period–luminosity (P–L) diagram and confirm previous findings that most stars lie on a ridge that corresponds to pulsation in the fundamental radial mode, and that many others fall on a second ridge that is a factor two shorter in period. This second ridge is seen more clearly than before, thanks to the revised periods and distances. We demonstrate the value of the P–L diagram in distinguishing δ Scuti stars from short-period RR Lyrae stars, and we find several new examples of high-frequency δ Scuti stars with regular sequences of overtone modes, including XX Pyx and 29 Cyg. Finally, we revisit the sample of δ Scuti stars observed by Kepler and show that they follow a tight period–density relation, with a pulsation constant for the fundamental mode of Q = 0.0315 d.