Terms Of Invariants Research Articles

Automated model discovery for textile structures: The unique mechanical signature of warp knitted fabrics

Textile fabrics have unique mechanical properties, which make them ideal candidates for many engineering and medical applications: They are initially flexible, nonlinearly stiffening, and ultra-anisotropic. Various studies have characterized the response of textile structures to mechanical loading; yet, our understanding of their exceptional properties and functions remains incomplete. Here we integrate biaxial testing and constitutive neural networks to automatically discover the best model and parameters to characterize warp knitted polypropylene fabrics. We use experiments from different mounting orientations, and discover interpretable anisotropic models that perform well during both training and testing. Our study shows that constitutive models for warp knitted fabrics are highly sensitive to an accurate representation of the textile microstructure, and that models with three microstructural directions outperform classical orthotropic models with only two in-plane directions. Strikingly, out of 214=16,384 possible combinations of terms, we consistently discover models with two exponential linear fourth invariant terms that inherently capture the initial flexibility of the virgin mesh and the pronounced nonlinear stiffening as the loops of the mesh tighten. We anticipate that the tools we have developed and prototyped here will generalize naturally to other textile fabrics–woven or knitted, weft knit or warp knit, polymeric or metallic–and, ultimately, will enable the robust discovery of anisotropic constitutive models for a wide variety of textile structures. Beyond discovering constitutive models, we envision to exploit automated model discovery for the generative material design of wearable devices, stretchable electronics, and smart fabrics, as programmable textile metamaterials with tunable properties and functions. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN. Statement of significanceTextile structures are rapidly gaining popularity in many biomedical applications including tissue engineering, wound healing, and surgical repair. A precise understanding of their unique mechanical properties is critical to tailor them to their specific functions. Here we integrate mechanical testing and machine learning to automatically discover the best models for knitted polypropylene fabrics. We show that warp knitted fabrics possess a complex symmetry with three distinct microstructural directions. Along these, the behavior is dominated by an exponential linear term that characterize the initial flexibility of the virgin mesh and the nonlinear stiffening as the loops of the fabric tighten. We expect that our technology will generalize naturally to other fabrics and enable the robust discovery of complex anisotropic models for a wide variety of textile structures.

The cosmological constant emerging from a symmetry invariant

The cosmological constant is normally introduced as an additional term entering the Einstein–Hilbert (EH) action. In this letter, we demonstrate that, instead, it appears naturally from the standard EH action as an invariant term emerging from spacetime symmetries. We then demonstrate that the same constraint emerging from this invariant suppresses the short wavelength modes and it favors the long wavelength ones. In this way, inside the proposed formulation, the observed value for the vacuum energy density is obtained naturally from the zero-point quantum fluctuations.

Noether symmetry in new extended modified f(R,G,T) theory of gravity

This study is dedicated to investigate the Noether symmetry approach in a newly introduced gravitational theory known as [Formula: see text] gravity, where [Formula: see text] is the function of Ricci scalar [Formula: see text], trace of energy–momentum tensor [Formula: see text], and the Gauss–Bonnet invariant term [Formula: see text]. The Noether symmetry approach plays a supportive role in generating models and then determining the exact solutions by using the conserved quantities. For this purpose, the flat Friedmann–Robertson–Walker space–time is selected to observe cosmic evolution. The set of partial differential equations is calculated in the background [Formula: see text] modified theory gravity. We further examine the four different [Formula: see text] gravity models and calculate the conserved quantities to investigate the exact solutions. The three models show the increasing behavior of the cosmic scale factor that supports the expansion of universe. In fourth model, we are able to get the corresponding conserved quantity only and it is anticipated that this model will also support the expansion of universe.

Holographic RG from an exact RG: Locality and general coordinate invariance in the bulk

In earlier papers it was shown that the correct kinetic term for scalar, vector gauge field and the spin two field in AdSD+1 space is obtained starting from the exact renormalization group (ERG) equation for a CFTD perturbed by scalar composite, conserved vector current, and conserved traceless energy momentum tensor respectively. In this paper interactions are studied, and it is shown that a flipped version of the Polchinski ERG equation that evolves toward the UV can be written down and is useful for making contact with the usual AdS/CFT prescriptions for correlation function calculations. The scalar-scalar-spin-2 interaction in the bulk is derived from the ERG equation in the large N semiclassical approximation. It is also shown that after mapping to AdS the interaction is local on a scale of the bare cutoff rather than the moving cutoff (which would have corresponded to the anti–de Sitter scale). The map to AdSD+1 plays a crucial role in this locality. The local nature of the coupling ensures that this interaction term in the bulk action is obtained by gauge fixing a general coordinate invariant scalar kinetic term in the bulk action. A wave function renormalization of the scalar field is found to be required for a mutually consistent map of the two fields to AdSD+1. Published by the American Physical Society 2024

Boundary blow-up solutions for the Monge-Ampère equation with an invariant gradient type term

We prove existence and non-existence of the boundary blow-up solutions for the Monge–Ampère equation of the form detD2u+g(u)ϕ(∇u,D2u)=b(x)f(u) in a smooth, bounded, strictly convex domain Ω⊂Rn(n≥2), where b∈C∞(Ω) is positive in Ω, the pair of functions f and g satisfies conditions of Keller–Osserman type on [0,∞), and ϕ:Rn×Rn2→R is a quadratic term which is invariant for both the gradient ∇u and the Hessian D2u in the sense discussed by Kazdan and Kramer (1978).

Measurement invairance and construct validity of the Turkish version of the learner autonomy scale in a sample of high and secondary school students

The goal of this research is to adapt the 24-item "Learner Autonomy Scale" developed by Sereti and Giossos (2018) in higher education samples into Turkish by examining the psychometric properties of high school and secondary school samples, and to determine whether these groups are equivalent in terms of measurement invariance. The scale was applied in high school (n = 475) and secondary school (n = 395) samples consisting of 870 students. Different from the original four-factor scale form, EFA applied to both groups revealed a two-factor (factor load range: .308-.775) and 21-item. Correlation values (r = .209-.392, p˂.001) indicate that the factors are not strongly related. The factors produced adequate internal consistency coefficients (α = .706-.866; ω = .708-.871) and were validated by meeting the fit indices accepted in the literature for CFA. Measurement invariance tests revealed strong invariance for the structural and metric tests and partial invariance for the scalar test in high school and secondary school samples. More research is needed to determine why the intersections of items 19, 20, and 21 are not invariant. The main contribution to "learner autonomy" in this study is the adaptation and justification of a valid and reliable measurement tool for determining autonomy in the adolescent age group. The use of the adapted scale in different educational environments and in the examination of "autonomy" by adapting it specific to the field (science, mathematics, etc.) will provide important implications for further theoretical studies.

Hybrid star within [formula omitted] gravity

The purpose of this work is to investigate some interesting features of a static anisotropic relativistic stellar object composed of two different types of fluid distributions typically termed as quark matter (QM) and ordinary baryonic matter (OBM) together with Krori–Barua type (KB) ansatz in the regime of modified f(G) gravity, where G being the Gauss–Bonnet invariant term. In order to explain the correlation between pressure and matter density for the quark matter distribution within the compact object, we have taken into consideration the well-known MIT bag equation of state (EoS) whereas there is a simple linear correlation between pressure and matter density for ordinary baryonic matter. Furthermore, using graphical representations for varying parameters, the physical credibility of our obtained solutions has been intensively examined by regularity checking of the metric coefficients and matter variables, energy conditions, mass function, and causality conditions. For these analyses, we consider a particular compact stellar candidate 4U 1538-52. Finally, we found that the resulting outcome depicts the viability of the considered hybrid stellar model.

Role of time variant and invariant terms on soil moisture spatio‐temporal variability in a subhumid coastal wetland

AbstractThe knowledge of soil moisture spatio‐temporal variability is highly relevant for water resources management. This paper reports an analysis of the spatial–temporal variability of soil moisture data for a small to medium‐scale soil‐sensors network in a coastal wetland of southwestern Spain. Measurements were taken from five sites located in the Doñana National Park over the time‐period of one hydrological year from September 2017 to September 2018. The total area of the soil‐sensors network shows an extension about 25 × 3 km. Soil moisture data was separated into time invariant (the temporal mean of the whole period at each site) and time‐variant terms (the deviations of soil moisture from the mean, or anomalies). The time‐invariant component was generally the main contributor to the total spatial variance of soil moisture and it was mostly controlled by the groundwater levels in the area. Nevertheless, the time variant terms have a huge effect on soil moisture variability in very dry states. Characteristic convex time‐dependent patterns for this field site were found between spatially averaged soil moisture and its variability. This information could be used for the up and downscaling of soil moisture from satellite data. Those patterns of relation between spatial mean and variability of soil moisture were only affected by heavy rainfalls giving rise to hysteretic behaviour. This study shows that even though groundwater level is a time‐variant variable, it significantly affects soil moisture's time‐variant but also time‐invariant terms due to the different average groundwater level depths at the different sites.

Finsler metrizabilities and geodesic invariance

We demonstrate that various metrizability problems for Finsler sprays can be reformulated in terms of the geodesic invariance of two tensors, namely the metric and angular tensors. We show that a spray [Formula: see text] is the geodesic spray of some Finsler metric if and only if its metric tensor is geodesically invariant. Moreover, we establish that gyroscopic sprays constitute the largest class of sprays characterized by a geodesic-invariant angular metric. Scalar functions associated with these geodesically invariant tensors will also be invariant, thereby providing first integrals for the given spray.

Topological Strings on Non-commutative Resolutions

In this paper we propose a definition of torsion refined Gopakumar–Vafa (GV) invariants for Calabi–Yau threefolds with terminal nodal singularities that do not admit Kähler crepant resolutions. Physically, the refinement takes into account the charge of five-dimensional BPS states under a discrete gauge symmetry in M-theory. We propose a mathematical definition of the invariants in terms of the geometry of all non-Kähler crepant resolutions taken together. The invariants are encoded in the A-model topological string partition functions associated to non-commutative (nc) resolutions of the Calabi–Yau. Our main example will be a singular degeneration of the generic Calabi–Yau double cover of P3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {P}}^3$$\\end{document} and leads to an enumerative interpretation of the topological string partition function of a hybrid Landau–Ginzburg model. Our results generalize a recent physical proposal made in the context of torus fibered Calabi–Yau manifolds by one of the authors and clarify the associated enumerative geometry.

Homological dimensions of Burch ideals, submodules and quotients

The notion of Burch ideals and Burch submodules were introduced (and studied) by Dao-Kobayashi-Takahashi in 2020 and Dey-Kobayashi in 2022 respectively. The aim of this article is to characterize various local rings in terms of homological invariants of Burch ideals, Burch submodules, or that of the corresponding quotients. Specific applications of our results include the following: Let (R,m) be a commutative Noetherian local ring. Let M=I be an integrally closed ideal of R such that depth(R/I)=0, or M=mN≠0 for some submodule N of a finitely generated R-module L such that either depth(N)⩾1 or L is free. It is shown that: (1) I has maximal projective (resp., injective) complexity and curvature. (2) R is Gorenstein if and only if ExtRn(M,R)=0 for any three consecutive values of n⩾max⁡{depth(R)−1,0}. (3) R is CM (Cohen-Macaulay) if and only if CM-dimR(M) is finite.

Gravastars in f ( R , G , T ) gravity

The article examines the matter of gravitational vacuum stars, or gravastars, in the context of [Formula: see text] gravity, where [Formula: see text], [Formula: see text], and [Formula: see text] refer to the Ricci Scalar, Gauss–Bonnet invariant term, and trace of energy–momentum tensor, respectively. Here, using certain suitable numerical approaches, solutions to the highly nonlinear differential equations are determined. For a well-known [Formula: see text] gravity cosmological model, the main structure of gravastars has been discussed according to core, shell, and external region. It is illustrated graphically how the relationship between mass and radius has evolved for the gravastar under consideration.

Quandle colorings vs. biquandle colorings

Biquandles are generalizations of quandles. As well as quandles, biquandles give us many invariants for oriented classical/virtual/surface links. Some invariants derived from biquandles are known to be stronger than those from quandles for virtual links. However, we have not found an essentially refined invariant for classical/surface links so far. In this paper, we give an explicit one-to-one correspondence between biquandle colorings and quandle colorings for classical/surface links. We also show that biquandle homotopy invariants and quandle homotopy invariants are equivalent. As a byproduct, we can interpret biquandle cocycle invariants in terms of shadow quandle cocycle invariants.

Об алгебраических и определимых замыканиях для теорий абелевых групп

Classifying abelian groups and their elementary theories, a series of characteristics arises that describe certain features of the objects under consideration. Among these characteristics, an important role is played by Szmielew invariants, which define the possibilities of divisibility of elements, orders of elements, dimension of subgroups, and allow describing given abelian groups up to elementary equivalence. Thus, in terms of Szmielew invariants, the syntactic properties of Abelian groups are represented, i.e. properties that depend only on their elementary theories. The work, based on Szmielew invariants, provides a description of the behavior of algebraic and definable closure operators based on two characteristics: degrees of algebraization and the difference between algebraic and definable closures. Thus, possibilities for algebraic and definable closures, adapted to theories of Abelian groups, are studied and described. A theorem on trichotomy for degrees of algebraization is proved: either this degree is minimal, if in the standard models, except for the only two-element group, there are no positively finitely many cyclic and quasi-cyclic parts, or the degree is positive and natural, if in a standard model there are no positively finitely many cyclic and quasi-cyclic parts, except a unique copy of a two-element group and some finite direct sum of finite cyclic parts, and the degree is infinite if the standard model contains unboundedly many nonisomorphic finite cyclic parts or positively finitely many of copies of quasi-finite parts. In addition, a dichotomy of the values of the difference between algebraic closures and definable closures for abelian groups defined by Szmielew invariants for cyclic parts is established. In particular, it is shown that torsion-free abelian groups are quasi-Urbanik.

Virasoro Constraints for Toric Bundles

Abstract We show that the Virasoro conjecture in Gromov–Witten theory holds for the the total space of a toric bundle $E \to B$ if and only if it holds for the base B. The main steps are: (i) We establish a localization formula that expresses Gromov–Witten invariants of E, equivariant with respect to the fiberwise torus action in terms of genus-zero invariants of the toric fiber and all-genus invariants of B, and (ii) we pass to the nonequivariant limit in this formula, using Brown’s mirror theorem for toric bundles.

Vibration of solid and thin-walled slender structures made of soft materials by high-order beam finite elements

In this work, high-order beam (1D) finite element models for the modal analysis of structures made of compressible and nearly-incompressible hyperelastic soft materials are presented in the well-established framework of Carrera Unified Formulation (CUF). In this investigation, the modal behavior of soft structures subjected to progressively increasing loads can be correctly predicted by higher-order structural theories, and the influence of pre-stress conditions applied on the modal response of structures is investigated. The mathematical formulation of hyperelastic isotropic materials is presented in terms of invariants of the right Cauchy–Green strain tensor, obtaining the most general expression of the Piola–Kirchoff 2 stress tensor and tangent elasticity tensor, both independent of the model adopted for the material strain energy function. Governing equations in matrix forms for the static nonlinear analysis and subsequent vibration problem around non-trivial equilibrium states are derived through the Principle of Virtual Displacements (PVD) under a total Lagrangian formulation, defining the fundamental nuclei of stiffness matrices and internal and external forces vector, all independent of expansion theories and kinematic models adopted in the mathematical modeling of finite elements. Actual numerical results are obtained by an iterative Newton–Raphson linearized scheme coupled with line-search algorithms, and they are compared with results obtained by the commercial code ABAQUS. Our proposed models are tested with large strain problems involving hyperelastic slender and thin-walled structures, for which mode aberration such as crossing or bearing are observed.

Семантика терминов имущества в бурятском языке (на примере эд бараа)

Introduction. The article is devoted to the establishment of differential semantic features of the Buryat term ed baraa, presented in the monuments of Old Mongolian writing of the 18th–19th centuries, reflecting the usual legal practice of the Buryats in relation to the totality of things owned by a person. The relevance of the study is due to the interest in the specifics of understanding property relations and the formation of property terms in the Buryat language of that time. Materials and methods. The research material was written sources from the collection “Customary Law of the Khorin Buryats. Monuments of Old Mongolian Writing”, which presents the legislative acts of the Khorin Buryats. The introduction briefly describes the extent to which the problem has been studied and defines the research methodology. Results. Analysis of the texts in which the term under study functions allowed the authors to establish that ed baraa is an invariant term for movable property. Ed baraa serves to designate the totality of household material objects and things in the possession of a person, excluding livestock, in addition, it participates in the implementation of the property rights of the owner in relation to material goods belonging to him. Based on the internal form of the word, ed baraa is a paired word, formed by adding two independent words with a coordinating connection, and having an abstract meaning. The abstractness and collective meaning of the term becomes possible as a result of summing up the meaning of the words and its components, where ed delegates the sign of a relatively large property quantity and represents a characteristic of the components in abstraction from specific signs. Baraa, as a nominee of the nuclear component, carries the attribute ‘small property, household items, belongings’. The internal form of the word contains a key feature of the plurality of goods, which is considered as property. This term implies the semantics that this property can be the subject of purchase and sale; there is an indication of the acquisition of property, since it was a product of labor produced for sale, in order to exchange for other products of labor or money.

Semiclassical analysis of a nonlocal boundary value problem related to magnitude

AbstractWe study a Dirichlet boundary problem related to the fractional Laplacian in a manifold. Its variational formulation arises in the study of magnitude, an invariant of compact metric spaces given by the reciprocal of the ground state energy. Using recent techniques developed for pseudodifferential boundary problems we discuss the structure of the solution operator and resulting properties of the magnitude. In a semiclassical limit we obtain an asymptotic expansion of the magnitude in terms of curvature invariants of the manifold and the boundary, similar to the invariants arising in short-time expansions for heat kernels.

Psychometric properties of the Chinese Family Assessment Instrument: evidence from mainland China.

Regarding the assessment of family functioning in Chinese people, there are several research gaps. First, although there are some instruments in the field, there are very few validated instruments. Second, while some translated measures have been developed, there are very few assessment tools based on indigenous Chinese concepts. Third, compared to Hong Kong, research on family assessment is relatively inactive in mainland China. Fourth, there are very few family assessment tools to assess perceived family functioning in older children and early adolescents. Fifth, few studies used large samples to validate family assessment tools. Sixth, researchers seldom utilized longitudinal data to examine the psychometric properties of family assessment tools. Finally, few studies have examined factorial validity across samples and time to demonstrate the stability of Chinese family assessment measures. In Hong Kong, based on focus group data (i.e., indigenous concepts of family functioning) and an integration with the family science literature, we have developed the Chinese Family Assessment Instrument (C-FAI) to assess perceived family functioning according to the perception of adolescents. Results showed that the C-FAI possessed good reliability and validity. Specifically, five dimensions of the measure (mutuality, communication, conflict, parental concern and parental control) were supported via exploratory factor analysis and confirmatory factor analysis. Convergent validity and reliability of the C-FAI were illustrated. To understand the psychometric properties of the C-FAI in mainland China, we collected three waves of data from students in the period of preadolescence and early adolescence in mainland China (N = 3,732). Based on the data, we examined the psychometric properties of the measure, particularly factor invariance in different samples and at different times. Confirmatory factor analysis provided support for the five dimensions in C-FAI, including factorial invariance in terms of configuration, factor loading, intercepts, and over time. There was evidence for convergent validity and discriminant validity of the measure. Finally, reliability analyses showed that the total C-FAI scale and its subscales are internally consistent. The present findings suggest that family researchers and practitioners can use the C-FAI to objectively assess perceived family functioning in preadolescence and early adolescence in different Chinese communities.

Dynamical complexity in teleparallel Gauss–Bonnet gravity

The stable critical points and their corresponding cosmology are derived in the teleparallel gravity with an added Gauss–Bonnet topological invariant term. We have analyzed the dynamics of the Universe by presenting two cosmological viable models, showing the potential to describe different phases of the evolution of the Universe. The value of the deceleration parameter (q), total equation of state parameter (ωtot) and dark energy equation of state parameter (ωDE) have been presented against each critical point. The existence and stability conditions are also presented. We study the behavior of the phase space trajectories at each critical point. Finally, the evolutionary behavior of the deceleration parameter and the equation of state parameters have been assessed with the initial condition of the dynamical variables, and compatibility has been observed in connection with the present cosmological scenario.