Order Terms Research Articles

ON RESIDUES AND CONJUGACIES FOR GERMS OF 1-D PARABOLIC DIFFEOMORPHISMS IN FINITE REGULARITY

AbstractWe study conjugacy classes of germs of nonflat diffeomorphisms of the real line fixing the origin. Based on the work of Takens and Yoccoz, we establish results that are sharp in terms of differentiability classes and order of tangency to the identity. The core of all of this lies in the invariance of residues under low-regular conjugacies. This may be seen as an extension of the fact (also proved in this article) that the value of the Schwarzian derivative at the origin for germs of $C^3$ parabolic diffeomorphisms is invariant under $C^2$ parabolic conjugacy, though it may vary arbitrarily under parabolic $C^1$ conjugacy.

Symmetry and monotonicity of singular solutions to p-Laplacian systems involving a first order term

Abstract We consider positive singular solutions (i.e. with a non-removable singularity) of a system of PDEs driven by p-Laplacian operators and with the additional presence of a nonlinear first order term. By a careful use of a rather new version of the moving plane method, we prove the symmetry of the solutions. The result is already new in the scalar case.

Geometric Particle-In-Cell discretizations of a plasma hybrid model with kinetic ions and mass-less fluid electrons

We explore the possibilities of applying structure-preserving numerical methods to a plasma hybrid model with kinetic ions and mass-less fluid electrons satisfying the quasi-neutrality relation. The numerical schemes are derived by finite element methods in the framework of finite element exterior calculus (FEEC) for field variables, Particle-In-Cell (PIC) methods for the Vlasov equation, and splitting methods in time based on an anti-symmetric bracket proposed. Conservation properties of energy, quasi-neutrality relation, positivity of density, and divergence-free property of the magnetic field are given irrespective of the used resolution and metric. Local quasi-interpolation is used for dealing with the current terms in order to make the proposed methods more efficient. The implementation has been done in the framework of the Python package STRUPHY [1], and has been verified by extensive numerical experiments.

Austropallene halanychi sp. nov., a new species of sea spider (Pycnogonida, Callipallenidae) from the Ross Sea, Antarctica

Here we present Austropallene halanychisp. nov., a new species of pycnogonid within the family Callipallenidae (Pycnogonida), collected from the Ross Sea, Antarctica. While retaining key morphological features known for the genus Austropallene Hodgson, 1915a, the new species is distinguished from congeners by its much larger size, along with the combined absence of a denticle on the inner surface of the fixed finger of the chelifore claw along with the presence of small conical outgrowths where the fixed finger of the chelifore claw meets the movable finger on both the dorsal and ventral sides, and also the ability to fully close the chelifore claw. Additionally, the complete mitochondrial genome of A. halanychi is consistent with other members of the genus Austropallene in terms of gene order and directionality. A phylogenetic tree consisting of mitochondrial protein-coding gene data places A. halanychi as sister to Austropallene cornigera (Möbius, 1902). Additionally, a phylogenetic tree constructed using partial COI data from other callipallenids placed the new species in a clade containing the genus Austropallene. The combination of molecular data in addition to key morphological differences from similar species in the genus leaves no doubt that the new taxon is a new Antarctic species of Austropallene.

The Geometric–Arithmetic index of trees with a given total domination number

Let G=(V,E) be a simple connected graph with vertex set V and edge set E. In Vukičević and Furtula (2009), Vukičević defined a new topological index, named geometric–arithmetic index of a graph G and denoted by GA(G), as GAG=∑uv∈E2dudvdu+dv,where du and dv denote the degrees of vertices u and v, respectively. We obtain an upper bound for the geometric–arithmetic index of trees in terms of order and the total domination number, and we characterize the extremal trees for this bound. Additionally, by a known relation between the geometric–arithmetic and arithmetic–geometric indices, we get a new lower bound for the arithmetic–geometric index.

Gauge-Invariant Lagrangian Formulations for Mixed-Symmetry Higher-Spin Bosonic Fields in AdS Spaces

We deduce a non-linear commutator higher-spin (HS) symmetry algebra which encodes unitary irreducible representations of the AdS group—subject to a Young tableaux Y(s1,…,sk) with k≥2 rows—in a d-dimensional anti-de Sitter space. Auxiliary representations for a deformed non-linear HS symmetry algebra in terms of a generalized Verma module, as applied to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints, are found explicitly in the case of a k=2 Young tableaux. An oscillator realization over the Heisenberg algebra for the Verma module is constructed. The results generalize the method of constructing auxiliary representations for the symplectic sp(2k) algebra used for mixed-symmetry HS fields in flat spaces [Buchbinder, I.L.; et al. Nucl. Phys. B 2012, 862, 270–326]. Polynomial deformations of the su(1,1) algebra related to the Bethe ansatz are studied as a byproduct. A nilpotent BRST operator for a non-linear HS symmetry algebra of the converted constraints for Y(s1,s2) is found, with non-vanishing terms (resolving the Jacobi identities) of the third order in powers of ghost coordinates. A gauge-invariant unconstrained reducible Lagrangian formulation for a free bosonic HS field of generalized spin (s1,s2) is deduced. Following the results of [Buchbinder, I.L.; et al. Phys. Lett. B 2021, 820, 136470.; Buchbinder, I.L.; et al. arXiv 2022, arXiv:2212.07097], we develop a BRST approach to constructing general off-shell local cubic interaction vertices for irreducible massive higher-spin fields (being candidates for massive particles in the Dark Matter problem). A new reducible gauge-invariant Lagrangian formulation for an antisymmetric massive tensor field of spin (1,1) is obtained.

ВПЛИВ УКРАЇНСЬКО-АНГЛІЙСЬКИХ МОВНИХ КОНТАКТІВ ХХІ СТ. НА ЛЕКСИЧНИЙ СКЛАД УКРАЇНСЬКОЇ МОВИ

The influence of the twenty first century Ukrainian English language contacts is analysed in the paper. The largest thematic spheres of concentration of anglicisms are determined. Graphic and morphological adaptation of anglicisms is analysed. The problem of pseudoanglicisms and pseudofriends is also discussed. Prediction concerning future development of Ukrainian-English mixture / surzhyk is made. The theory of language contacts is the basis of the investigation. The term language contact has a broad and narrower interpretation. According to a broad interpretation, two or more languages are in contact if one and the same person uses them in turn. In this case we have the situation of obligatory bilingualism. According to a narrower interpretation, bilingualism is not obligatory. In such a case borrowing takes place under different social-political, cultural and historic, trade and economic and other relations. Just the second case of language contacts is considered in our paper. Vocabulary is the most susceptible to changing sphere of language says one of the main postulates of language contacts theory. Just that very case one can observe in the Ukrainian language of late. The last decade of the XX-th century and 23 years of the XXI-st century are marked by rapid growth of direct contacts of Ukrainian language with numerous European languages. The English language plays a special part among them. The new socio-political and cultural relations caused circumstances of active penetration of anglicisms into the Ukrainian language. Means of mass information play essential role in spreading anglicisms among speakers of Ukrainian beginning from using the foreign term in order to inform about something to borrowing this term. Hence the sources of our investigation were selected, namely Ukrainian newspapers and weekly magazine.

Inferiority and Superiority Complex: Examination in Terms of Gender, Birth Order and Psychological Symptoms

Inferiority and superiority complex are personality structures that point to unhealthy development in Adlerian theory. In this study, the aim was to examine inferiority and superiority complex in terms of socio-demographic characteristics of adult individuals, and to determine the predictive relationships between psychological symptoms and inferiority and superiority complex. A total of 361 (205 females, 156 males) adults between the ages of 18 and 62, reached through the convenient sampling method, participated in the study. Data were collected through the Turkish Version of the Adlerian Inferiority and Superiority Complex Shortened Scales, the Symptom Check List, and the Personal Information Form. In the study, it was found that the main effects of gender and birth order were significant in inferiority complex, while the main effect of birth order was significant in superiority complex. Gender main effect for superiority complex and gender-birth order interaction effect for both complexes were not significant. In addition, it was determined that psychological symptoms were a significant predictor of inferiority complex, but not a significant predictor of superiority complex.

What policy functions are reflected in the distribution of financial support for parents by child age and birth order? An analysis of 28 European countries

AbstractMotivated by the growing prominence of fertility incentivisation and long‐term child development in European family policymaking, this paper examines the distribution of financial support for parents over the course of childhood and between birth orders in Europe. We use the term ‘older‐oriented age bias’ to refer to support that is more generous for older children and the term ‘younger‐oriented age bias’ for more generous support for younger children. Similarly, we refer to distribution patterns tilted towards later birth orders as ‘later‐oriented parity bias’ and to those that favour earlier birth orders as ‘earlier‐oriented parity bias’. Based on a list of four classical policy functions of financial support for parents (child cost compensation, fertility incentivisation, child poverty reduction, and child development), we formulate six (sets of) hypotheses for the age and parity distribution of financial support for parents. To assess these distribution patterns, we examine monthly financial support (allowance‐ and tax‐based) for the first four birth orders at child ages 2, 9, and 17 in low‐income and middle‐income households across 28 European countries as of January 2021. We find that European welfare states typically provide more generous support for younger children, while the support distribution in terms of birth orders depends on pre‐support household income. We also find considerable cross‐country heterogeneity, with fertility incentivisation and (especially) child development being reflected by more countries than child cost compensation and poverty reduction. Our analysis sheds light on previously underexplored trends and implications in the design of financial support for parents in Europe.

Potential vision tester using adaptive optics, Maxwellian view, and small pupil.

We demonstrate a free-space, trolley-mounted potential vision tester (PVT), designed to study and improve the accuracy of visual acuity (VA) measurements in the aging eye. Key features include a high-resolution visual display presented in Maxwellian view, a 3 mm pupil to limit wavefront (WF) aberrations, and a moderate cost deformable mirror to induce or correct higher order optical aberrations. The visual display supported accurate measurement of visual acuities down to 20/5. The moderate cost, piezo deformable mirror induced seven nominal aberrations, calibrated as 0, -0.32, -0.23, + 0.27, and +0.39 microns spherical aberration; + 0.49 microns Y coma; and -0.51 microns X coma. A custom Hartmann Shack (HS) calibration (HSc) system demonstrated that induced aberrations were repeatable and stable. A Badal optometer provided the coarse focus. WF aberrations were measured for five normal subjects with a commercially available HS device (HSP) (OCULUS Pentacam AXL Wave), providing estimates of WF errors for 3 mm and other pupil sizes. VA was measured using four alternative forced-choice for a single black on white E stimulus in each trial. Using the method of constant stimuli yielded robust standard deviation measurements. The 50% fit for VA plotted against induced aberration resulted in linear functions for each subject for the range of our positive and negative spherical aberration data. Subjects differed, but higher order terms were unnecessary to describe data across spherical aberrations.

Zombie cats on the quantum-classical frontier: Wigner-Moyal and semiclassical limit dynamics of quantum coherence in molecules.

In this paper, we investigate the time evolution of quantum coherence-the off-diagonal elements of the density matrix of a multistate quantum system-from the perspective of the Wigner-Moyal formalism. This approach provides an exact phase space representation of quantum mechanics. We consider the coherent evolution of nuclear wavepackets in a molecule with two electronic states. For harmonic potentials, the problem is analytically soluble for both a fully quantum mechanical description and a semiclassical description. We highlight the serious deficiencies of the semiclassical treatment of coherence for general systems and illustrate how even qualitative accuracy requires higher order terms in the Moyal expansion to be included. The model provides an experimentally relevant example of a molecular Schrödinger's cat state. The alive and dead cats of the exact two-state quantum evolution collapse into a "zombie" cat in the semiclassical limit-an averaged behavior, neither alive nor dead, leading to significant errors. The inclusion of the Moyal correction restores a faithful simultaneously alive and dead representation of the cat that is experimentally observable.

OGBN P02 Longer term symptom control following revision anti-reflux surgery: a cohort of 379 patients

Abstract Background Symptom recurrence after primary hiatus hernia surgery is an established problem and revision anti-reflux surgery may be indicated in select cases of recurrence after primary surgery. Previous studies on this subject are of small number and often lack objective measures. Our aim is to review the long term post operative outcomes and assess the impact of revisional anti reflux surgery on symptom improvement and quality of life measures. Methods A prospectively maintained single-surgeon database of revisional hiatus hernia surgery from 1992 to 2022 was retrospectively evaluated. The results of the pre operative assessments were collated to identify the symptomatic, anatomical and physiological indications. Validated scoring systems including GIQLI, Visick, Dakkak and Reflux Symptom Index scores were compared pre-operatively and post-operatively. Post-operative GIQLI scores were measured in the first 12 months (short term), 12 to 36 months (medium term) and after 36 months (long term) in order to obtain a trend in patient reported outcomes. Questions assessing heartburn, dysphagia, and regurgitation were analysed to determine progress of these specific symptoms. Results The dataset consisted of 379 patients, of whom 59% were female. The average age at the time of first revisional surgery was 59 years (range 19-91). Laparoscopic surgery was performed in 90% of primary operations compared to 68% of revision operations. There was overall improvement in outcomes as demonstrated in this table. Additionally, evaluation of symptoms specific questions of the GIQLI showed a statistically significant improvement in dysphagia scores in the long term category (p = 0.0210). Conclusions There is a global improvement in long term control of reflux and dysphagia symptoms following revision hiatus hernia surgery showed. However, volume regurgitation symptoms were not shown to be consistently improved post operatively. This may be due to an underlying motility disorder in these patients or the potential of dysmotility caused by revision surgery from injury to the vagus nerve. Caution should be exercised when considering revision anti reflux surgery in this patient cohort.

Singular orthotropic functionals with nonstandard growth conditions

We pursue the study of a model convex functional with orthotropic structure and nonstandard growth conditions, this time focusing on the sub-quadratic case. We prove that bounded local minimizers are locally Lipschitz. No restrictions on the ratio between the highest and the lowest growth rates are needed. The result holds also in presence of a non-autonomous lower order term, under sharp integrability assumptions. Finally, we prove higher differentiability of bounded local minimizers as well.

Anomalous Temperature-Induced Particle Size Reduction in Manganese Oxide Nanoparticles.

The intricate role of temperature in the structure-property relationship of manganese oxide nanoparticles (Mn3O4 NPs) remains an open question. In this study, we successfully synthesized Mn3O4 NPs using the hydrothermal method with two differing temperatures, namely, 90 and 150 °C. Interestingly, a smaller average particle size is found when Mn3O4 NPs are synthesized at 150 °C compared to 90 °C, corresponding to 46.54 and 63.37 nm, respectively. This was confirmed by the time variation of temperature setting of 150 °C where the size evolution was insignificant, indicating a competing effect of nucleation and growth particles. Under varying NaOH concentrations (2-6 M) at 150 °C, a reduction in the particle size is found at the highest NaOH concentration (6 M). The particle grows slightly, indicating that the growth state is dominant compared to the nucleation state at low concentrations of NaOH. This finding implies that the high nucleation rate originates from the excessive monomer supply in the high-temperature reaction. In terms of crystallinity order, the structural arrangement of Mn3O4 NPs (150 °C) is largely decreased; this is likely due to a facile redox shift to the higher oxidation state of manganese. In addition, the higher ratio of adsorbed oxygen and lattice oxygen in Mn3O4 NPs at 150 °C is indirectly due to the higher oxygen vacancy occupancies, which supported the crystallinity decrease. Our findings provide a new perspective on manganese oxide formation in hydrothermal systems.

Regularity results for local solutions to some anisotropic elliptic equations

In this paper we study the higher integrability of local solutions for a class of anisotropic equations with lower order terms whose growth coefficients lay in Marcinkiewicz spaces. A condition for the boundedness of such solutions is also given.

Revisiting Maxwell-Smoluchowski theory: Low surface roughness in straight channels

The Maxwell-Smoluchowski (MS) theory of gas diffusion is revisited here in the context of gas transport in straight channels in the Knudsen regime of large mean free path. This classical theory is based on a phenomenological model of gas-surface interaction that posits that a fraction ϑ of molecular collisions with the channel surface consists of diffuse collisions, i.e., the direction of post-collision velocities is distributed according to the Knudsen Cosine Law, and a fraction 1−ϑ undergoes specular reflection. From this assumption one obtains the value D=2−ϑϑDK for the self-diffusivity constant, where DK is a reference value corresponding to ϑ=1. In this paper we show that ϑ can be expressed in terms of micro- and macro-geometric parameters for a model consisting of hard spheres colliding elastically against a rigid surface with prescribed microgeometry.Our refinement of the MS theory is based on the observation that the classical surface scattering operator associated to the microgeometry has a canonical velocity space diffusion approximation by a generalized Legendre differential operator whose spectral theory is known explicitly. More specifically, starting from an explicit description of the effective channel surface microgeometry—a concept which incorporates both the actual surface microgeometry and the molecular radius—and using this operator approximation, we show that ϑ can be resolved into easily obtained geometric parameters, ϑ=λh/C, having the following interpretation: C is a macroscopic parameter determined by the shape of the channel cross-section; h is a parameter that precisely captures the degree of roughness of the effective microgeometry, and λ is a parameter that characterizes the overall curvature of the surface microgeometry independent of h. Thus ϑ is resolved as the quotient of microscopic (λh) over macroscopic (C) signature parameters of the channel geometry. The identity ϑ=λh/C holds up to higher order terms in the roughness parameter h, so our main result better applies to well polished, or low roughness, surfaces.

Circular Economy and Solid Waste Management: Connections from a Bibliometric Analysis

The aim of this study is to conduct a meta-analysis of the research published between 2012 and 2022 on solid waste management (SWM) and the circular economy (CE) using bibliometrics. To this end, the Scopus and Web of Science (WoS) databases were used as sources of publications. Processing was conducted using the R language version 4.2.2 and the Bibliometrix software package version 4.1.2. A theoretical basis was built on the terms in order to present their interactions in the context of scientific debate. The results show that there is a need to create indicators to facilitate the evaluation of SWM. They can be identified from the data collected during the management process. Examples include the volume of material collected, operating costs, and recycling rates. Indicators are important in the waste management process because they help quantify the effectiveness of the management practices adopted, help to identify areas that need improvement, and make it possible to monitor the progress of work over time and the achievement of previously set targets. Two other important results are the maximization of the use of resources by increasing the useful life of the product and the emergence of new sustainable business models with recycling as a driving force. Finally, and perhaps the most disruptive discovery, is the integration of SWM and CE with blockchain technology to reduce the levels of waste production. This shows how new technologies can be used as partners in solving complex problems, such as solid waste (SW).

Longtime behavior of the weakly coupled Euler-Bernoulli plate system with structural damping

In this paper, we study the longtime behavior of the weakly coupled Euler-Bernoulli plate system with one structural damping. The system consists of two plate equations coupled by zero order terms. First, we show that when the coupling coefficient function is a nonzero constant and the damping coefficient function is a positive constant, the optimal energy decay rate of the system is t−23. Then we consider the case that the coupling and damping coefficient functions have compact supports. By Carleman estimate and the frequency domain method, we show that the energy of the system decays logarithmically when the supports of the coupling and damping coefficient functions satisfy suitable assumptions.

Entanglement Entropy of Ground States of the Three-Dimensional Ideal Fermi Gas in a Magnetic Field

We study the asymptotic growth of the entanglement entropy of ground states of non-interacting (spinless) fermions in R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb {R}}}^3$$\\end{document} subject to a constant magnetic field perpendicular to a plane. As for the case with no magnetic field we find, to leading order L2ln(L)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2\\ln (L)$$\\end{document}, a logarithmically enhanced area law of this entropy for a bounded, piecewise Lipschitz region LΛ⊂R3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L\\Lambda \\subset {{\\mathbb {R}}}^3$$\\end{document} as the scaling parameter L tends to infinity. This is in contrast to the two-dimensional case since particles can now move freely in the direction of the magnetic field, which causes the extra ln(L)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ln (L)$$\\end{document} factor. The explicit expression for the coefficient of the leading order contains a surface integral similar to the Widom–Sobolev formula in the non-magnetic case. It differs, however, in the sense that the dependence on the boundary, ∂Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial \\Lambda $$\\end{document}, is not solely on its area but on the “surface perpendicular to the direction of the magnetic field”. We utilize a two-term asymptotic expansion by Widom (up to an error term of order one) of certain traces of one-dimensional Wiener–Hopf operators with a discontinuous symbol. This leads to an improved error term of the order L2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^2$$\\end{document} of the relevant trace for piecewise C1,α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{C}^{1,\\alpha }$$\\end{document} smooth surfaces ∂Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\partial \\Lambda $$\\end{document}.

A Multi-Objective Optimization-Algorithm-Based ANFIS Approach for Modeling Dynamic Customer Preferences with Explicit Nonlinearity

In previous studies, customer preferences were assumed to be static when modeling their preferences based on online reviews. However, in fact, customer preferences for products are dynamic and changing over time. Few research has been conducted to model dynamic customer preferences as the time series data of customer preference are difficult to be obtained. Based on online reviews, an adaptive neuro fuzzy inference system (ANFIS) was introduced to model customer preferences, which can take into account the fuzzy nature of customers’ emotions and the nonlinearity of the model. However, ANFIS is plagued with black box problems, and the nonlinearity of the model cannot be directly demonstrated. To address the above research issues, a multi-objective chaos optimization algorithm (MOCOA)-based ANFIS approach is proposed to generate customer preferences models by using online reviews, which has explicit nonlinear inputs. Firstly, a sentiment analysis approach is used to derive information from online reviews by periods, which is used as the time series data sets of the proposed model. A MOCOA is combined into ANFIS to identify the nonlinear inputs, which include single items, interactive items, and terms of second order and/or higher-order terms. Consequently, the fuzzy rules in ANFIS are expressed in polynomial form, which allows for the explicit representation of the nonlinearity between customer preferences and product attributes. A case study of sweeping robots is used to compare the validation results of the proposed approach with those of ANFIS, subtractive cluster-based ANFIS, fuzzy c-means-based ANFIS, and K-means-based ANFIS. Moreover, the proposed approach provides better performance than the other four approaches in terms of mean relative error and variance of error.