Unbounded Sets Research Articles

A fractional Michael–Simon Sobolev inequality on convex hypersurfaces

The classical Michael-Simon and Allard inequality is a Sobolev inequality for functions defined on a submanifold of Euclidean space. It is governed by a universal constant independent of the manifold, but displays on the right-hand side an additional $L^p$ term weighted by the mean curvature of the underlying manifold. We prove here a fractional version of this inequality on hypersurfaces of Euclidean space that are boundaries of convex sets. It involves the Gagliardo semi-norm of the function, as well as its $L^p$ norm weighted by the fractional mean curvature of the hypersurface. As an application, we establish a new upper bound for the maximal time of existence in the smooth fractional mean curvature flow of a convex set. The bound depends on the perimeter of the initial set instead of on its diameter.

Cellular Distribution Pattern of tjp1 (ZO-1) in Xenopus laevis Oocytes Heterologously Expressing Claudins

Epithelial barriers constitute a fundamental requirement in every organism, as they allow the separation of different environments and set boundaries against noxious and other adverse effectors. In many inflammatory and degenerative diseases, epithelial barrier function is impaired because of a disturbance of the paracellular seal. Recently, the Xenopus laevis oocyte has been established as a heterologous expression model for the analysis of transmembrane tight junction protein interactions and is currently considered to be a suitable screening model for barrier effectors. A prerequisite for this application is a physiological anchoring of claudins to the cytoskeleton via the major scaffolding protein tjp1 (tight junction protein 1, ZO-1). We have analyzed the oocyte model with regard to the interaction of heterologously expressed claudins and tjp1. Our experiments have revealed endogenous tjp1 expression in protein and mRNA analyses of unfertilized Xenopus laevis oocytes expressing human claudin 1 (CLDN1) to claudin 5 (CLDN5). The amphibian cell model can therefore be used for the analysis of claudin interactions.Graphical

The augmented Lagrangian method can approximately solve convex optimization with least constraint violation

There are many important practical optimization problems whose feasible regions are not known to be nonempty or not, and optimizers of the objective function with the least constraint violation prefer to be found. A natural way for dealing with these problems is to extend the nonlinear optimization problem as the one optimizing the objective function over the set of points with the least constraint violation. This leads to the study of the shifted problem. This paper focuses on the constrained convex optimization problem. The sufficient condition for the closedness of the set of feasible shifts is presented and the continuity properties of the optimal value function and the solution mapping for the shifted problem are studied. Properties of the conjugate dual of the shifted problem are discussed through the relations between the dual function and the optimal value function. The solvability of the dual of the optimization problem with the least constraint violation is investigated. It is shown that, if the least violated shift is in the domain of the subdifferential of the optimal value function, then this dual problem has an unbounded solution set. Under this condition, the optimality conditions for the problem with the least constraint violation are established in term of the augmented Lagrangian. It is shown that the augmented Lagrangian method has the properties that the sequence of shifts converges to the least violated shift and the sequence of multipliers is unbounded. Moreover, it is proved that the augmented Lagrangian method is able to find an approximate solution to the problem with the least constraint violation and it has linear rate of convergence under an error bound condition. The augmented Lagrangian method is applied to an illustrative convex second-order cone constrained optimization problem with least constraint violation and numerical results verify our theoretical results.

When hands stop moving, interaction keeps going

Abstract This study explores moments in signed and spoken conversation when manual production is on hold and its resulting interactive ramifications. Typically, the temporal structure of gesture and sign can be decomposed into a stream of distinct manual phases. There are moments, however, when this activity is stopped. This may happen for various reasons, e.g., when seeking attention, holding the floor or during overlaps. Holds have mostly been examined in sign languages regarding prosody, syntax, and corresponding to vowel lengthening in spoken languages. In gesture studies, they have been overlooked for not deemed relevant in the gesture-speech interface. By combining contrastive and multimodal analyses, this paper examines the relevance of holds as potential meaning-making practices deployed by LSFB signers and its comparison to Belgian French speakers. In 3 hours of video-recorded material drawn from 3 multimodal corpora, the following question is addressed: what are the roles of holds in the management of interaction within and across languages/modalities? While most of linguistic work considers manual movements to express referential content, the observations here push to reconsider the common boundary set between what constitutes gestural/linguistic phenomena in one language and what does not.

An exploration of setting healthy personal boundaries as a veterinary professional – part 1: at work and beyond

A personal boundary is a behavioural or emotional metaphorical wall that we erect to ensure our physical and psychological safety. These are important for keeping us in healthy and sustainable relationships. We draw personal boundaries to protect what is uniquely ours: our body, resources, intellect, emotions and behaviour. Therefore, where we draw them is specific to us based on our ethics, values, priorities, experiences, feelings and needs. Veterinary professionals may struggle to set boundaries because they may be driven by compassion or empathy, or have perfectionistic or people-pleasing tendencies. This is the first of a series of two articles addressing what personal boundaries are and why we need them. Why veterinary professionals struggle to set healthy boundaries is also discussed.

ОСОБИНЕ ПОРОДИЧНИХ ПРАКСИ ДЕЦЕ У НУКЛЕАРНИМ ПОРОДИЦАМА

The topic of this paper is concerned with the characteristics of nuclear family practices from the children perspective. The idea from which this paper starts is that family practices enable the stability of family life, but also leave space for it to change. As such, they enable us to distance ourselves from the idea of a family as a static phenomenon and offer a deeper insight into the intrafamilial dynamics. Through the experience of what is everyday and common in family life, but also of fluidity and activity in lifes of family members, we gain insight into the way of life of a family, the relationships among its members, and the ways in which family defines itself in relation to others. The aim of the research was to examine whether the relationship between parents and children is gender based, what is the division of roles in the family, as well as how the family sets boundaries between its members, and how to individuals who are not considered family members.

P‐46: New Type of Unbounded Screen Full Attachment TV Set

This article uses the film and LCD screen full bonding method to generate a new type of fully bonded LCD screen form, which can not only solve the difficulties of borderless screen design, process production, and assembly difficulties, but also improve the light efficiency of the TV set and reduce the cost. The research makes the TV set thinner and more aesthetic.

A new adaptive output-feedback controller against unknown control directions and intrinsic growth

ABSTRACT This paper addresses global output-feedback stabilisation in the context of unknown control directions and intrinsic unmeasurable-states-dependent growth, and focuses on rectifying the substantial deficiencies in the related works and developing a new adaptive output-feedback controller essentially reducing conservativeness. First, a varying parameter which takes value 1 or , instead of in an unbounded countable set, is specialised to capture the unknown control direction and accordingly a supervisory mechanism is delicately constructed to decide when to switch the parameter from 1 to or from to 1. A dynamic high gain, rather than a switching one, is appointed to compensate the serious system uncertainties. Then, the wanted controller is constructed, for which the design functions and design parameters are recursively generated by backstepping method (instead of analytically defined owing to the unknown control coefficients). Based on the designations and supervisory mechanism, it turns out that no Zeno phenomenon occurs, and global boundedness and convergence (to zero) hold, both for the resulting closed-loop system. An example is given to show the effectiveness and the advantage of the proposed scheme.

Statistical machine-learning-based predictive control using barrier functions for process operational safety

In this work, we present statistical model predictive control with Control Lyapunov-Barrier Functions (CLBF) built using machine learning approaches, and analyze closed-loop stability and safety properties in probability using statistical machine learning theory. A feedforward neural network (FNN) is used to construct the Control Barrier Function, and a generalization error bound can be obtained for this FNN via the Rademacher complexity method. The FNN Control Barrier Function is incorporated in a CLBF-based model predictive controller (MPC), which is used to control a nonlinear process subject to input constraints. The stability and safety properties of the closed-loop system under the sample-and-hold implementation of FNN-CLBF-MPC are evaluated in a statistical sense. We use a chemical process example to demonstrate the relation between various factors of building an FNN model and the generalization error, as well as the probabilities of closed-loop safety and stability for both bounded and unbounded unsafe sets.

Minimal Pairs of Convex Sets Which Share a Recession Cone

Robinson introduced a quotient space of pairs of unbounded convex sets which share their recession cone. In this paper minimal pairs of unbounded convex sets, i.e., minimal representations of elements of Robinson's quotient spaces, are investigated. The fact that a minimal pair having a property of translation is reduced is proved. In the case of pairs of two-dimensional sets a formula for finding an equivalent minimal pair is given, a criterion of minimality of a pair of sets is presented, reducibility of all minimal pairs is proved, and nontrivial examples are shown. Shephard--Weil--Schneider's criterion for polytopal summand of a compact convex set is generalized to unbounded convex sets. Finally, minimal pairs of unbounded convex sets are applied to finding Hartman's minimal representation of differences of convex functions.

Absentees: On Variously Missing Persons. Daniel Heller-Roazen. New York: Zone Books, 2021. Pp. 317.

<i>Absentees: On Variously Missing Persons</i>. Daniel Heller-Roazen. New York: Zone Books, 2021. Pp. 317.

МЕТОД ПОСТАНОВКИ ГРАНИЧНЫХ УСЛОВИЙ ПРИ ЧИСЛЕННОМ РЕШЕНИИ ЗАДАЧ ГАЗОДИНАМИКИ В ОБЛАСТЯХ СЛОЖНОЙ ФОРМЫ

The question of setting boundary conditions for a two-dimensional supersonic gas flow in accessible forms is considered. An alternative method of setting boundary conditions on the body surface is proposed. The results of the calculation of double Mach reflection of a shock wave from a flat wall and the gas flow inside of liquid-propellant rocket engine using alternative method are presented and analyzed. The conclusion about the possibility of applying the new method in further calculations is made.

Changes in hip joint contact stress during a gait cycle based on the individualized modeling method of “gait-musculoskeletal system-finite element”

ObjectiveTo construct a comprehensive simulation method of “gait-musculoskeletal system (MS)-finite element (FE)” for analysis of hip joint dynamics characteristics and the changes in the contact stress in the hip throughout a gait cycle.MethodsTwo healthy volunteers (male and female) were recruited. The 3D gait trajectories during normal walking and the CT images including the hip and femur of the volunteers were obtained. CT imaging data in the DICOM format were extracted for subjected 3D hip joint reconstruction. The reconstructed 3D model files were used to realize the subject-specific registration of the pelvis and thigh segment of general musculoskeletal model. The captured marker trajectory data were used to drive subject-specific musculoskeletal model to complete inverse dynamic analysis. Results of inverse dynamic analysis were exported and applied as boundary and load settings of the hip joint finite element in ABAQUS. Finally, the finite element analysis (FEA) was performed to analyze contact stress of hip joint during a gait cycle of left foot.ResultsIn the inverse dynamic analysis, the dynamic changes of the main hip-femoral muscle force with respect to each phase of a single gait cycle were plotted. The hip joint reaction force reached a maximum value of 2.9%BW (body weight) and appeared at the end of the terminal stance phase. Twin peaks appeared at the initial contact phase and the end of the terminal stance phase, respectively. FEA showed the temporal changes in contact stress in the acetabulum. In the visual stress cloud chart, the acetabular contact stress was mainly distributed in the dome of the acetabulum and in the anterolateral area at the top of the femoral head during a single gait cycle. The acetabular contact area was between 293.8 and 998.4 mm2, and the maximum contact area appear at the mid-stance phase or the loading response phase of gait. The maximum contact stress of the acetabulum reached 6.91 MPa for the model 1 and 6.92 MPa for the model 2 at the terminal stance phase.ConclusionsThe “Gait-MS-FE” technology is integrated to construct a comprehensive simulation framework. Based on human gait trajectories and their CT images, individualized simulation modeling can be achieved. Subject-specific gait in combination with an inverse dynamic analysis of the MS provides pre-processing parameters for FE simulation for more accurate biomechanical analysis of hip joint.Graphical abstract

A classical [formula omitted] spin system with discrete out-of-plane anisotropy: Variational analysis at surface and vortex scalings

We consider a classical Heisenberg system of S2 spins on a square lattice of spacing ɛ. We introduce a magnetic anisotropy by constraining the out-of-plane component of each spin to take only finitely many values. Computing the Γ-limit of a suitable scaling of the energy functional as ɛ→0 we prove that, in the continuum description, the system concentrates energy at the boundary of sets in which the out-of-plane component of the spin is constant. In a second step we analyze a different scaling of the energy and we prove that, in each of such phases, the energy can further concentrate on finitely many points corresponding to vortex-like singularities of the in-plane components of the spins.

A new insight into the effects of agglomerate parameters on internal dynamics of proton exchange membrane fuel cell by an advanced impedance dimension model

The oxygen reduction reaction with a relatively slow reaction rate is critical for proton exchange membrane (PEM) fuel cell performance. At present, a substantial part of the previous numerical study respecting the optimization design of the cathode catalyst layer (CCL) mainly focuses on the polarization curve output and oxygen local transport. In this paper, for the first time, a two-dimensional multiphase PEM fuel cell impedance model coupled with an improved electrochemical kinetics model considering the cathode agglomerate construction is proposed, which can reproduce the measured electrochemical impedance spectroscopy (EIS) under different current densities, reactant stoichiometries and inlet humidity only with a single boundary set. Based on this, the effects of five CCL design parameters (Pt loading, carbon loading, catalyst layer thickness, ionomer volume fraction, and agglomerate radius) on the EIS and critical internal dynamics are comprehensively investigated. Meanwhile, each dynamics loss of simulated EIS is identified by the distribution of relaxation time and equivalent circuit model to support quantitative analysis. These works offer a deeper understanding and new insight into the effects of CCL parameters on PEM fuel cell internal dynamics, which can help material optimization and system controller design.

Embracing Kindness and Setting Boundaries in Online Teaching

The National Teaching & Learning ForumVolume 31, Issue 4 p. 3-4 E-Learning Explained Embracing Kindness and Setting Boundaries in Online Teaching Carly M. Lesoski, Carly M. LesoskiSearch for more papers by this author Carly M. Lesoski, Carly M. LesoskiSearch for more papers by this author First published: 09 May 2022 https://doi.org/10.1002/ntlf.30327Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. Volume31, Issue4May 2022Pages 3-4 RelatedInformation

Introduction

When future scholars come to assess the humanities in our time, they will probably call it the age of buzzwords. Whereas previous generations of academics pledged allegiance to their intellectual heroes—Marx! Foucault!—that fervor seems to have shifted to catchy conceptual slogans. Anthropocene! Spatial Turn! New Materialism! Buzzwords dot conference papers and grant proposals, they ooze cognitive certainty, and those who chronicle our academic trajectory a few decades from now will surely wonder whether we really had a clear idea of what we were talking about. (Message to posterity: we were wondering about that, too.)Against this background, the guiding question of this roundtable is anything but tongue-in-cheek. The New Materialism is no longer a nascent intellectual current that has yet to reach conceptual maturity. We have a multitude of publications from a diverse and multidisciplinary group of scholars, and that provides us with fodder for a first assessment from the viewpoint of an empirically minded discipline. What are the approaches that matter for the historian's craft, and specifically for those who engage with the history of agriculture in one way or another? How does the New Materialism frame our understanding of topics, narratives, and intellectual goals? And what do we need to change in established readings, if anything? After all, agricultural history has never been nonmaterial because it's hard to imagine a nonmaterial agriculture—though a former Monsanto CEO once tried his best to suggest otherwise.The following interventions explore these questions with different case studies in mind and with different types of intellectual ambitions. Some scale the philosophical heights of the literature while others feel more comfortable with their feet on the ground (or, on a personal note, with their intellectual existence at sea). They engage with straw, ontology, and Robert Frost, among other things, and there is no obvious hierarchy. There is something unsettled and unrefined at the heart of the New Materialism debate, something that defies categorization and intellectual order. It is a bit like dealing with a monster that we thought was dormant for a long time—though monsters provide a poor metaphor owing to their inherent anthropomorphism. It would seem that, in engaging with the inherent power of the material, we are truly at the mercy of the elements.Going through these contributions and the literature that they survey, it seems that there is no obvious template for writing new materialist histories. There are a few paths that have been explored, there are recurring themes and challenges, but those who seek a checklist for their graduate seminars will come away disappointed. But maybe that is the entire point of engaging with the New Materialism? If matter really matters, we are reckoning with forces beyond our control, that lack a sense of human decency, and were around before the word. It is no small challenge to come to terms with forces of this kind. But if the following comments prove anything, it is that we need to try.This roundtable grew out of a session at the Agricultural History Society meeting in June 2021. Albert Way encouraged us to publish our views in the pages of Agricultural History and assured quick publication, though speed is a mixed blessing in academic endeavors and material flows alike. As you will see below, I had second thoughts about the circle of invitees when I penned my own comment. But even within the set boundaries, the following conversation may be inspiring and inconclusive in equal measure, and I trust that readers will find that an important insight in its own right. When it comes to the material, we are wrestling with a subversive force that will keep us on edge for the foreseeable future.

Microbial | electrochemical CO2 reduction: To integrate or not to integrate?

Microbial | electrochemical CO2 reduction: To integrate or not to integrate?

Analytical Solutions to Minimum-Norm Problems

For G∈Rm×n and g∈Rm, the minimization min∥Gψ−g∥2, with ψ∈Rn, is known as the Tykhonov regularization. We transport the Tykhonov regularization to an infinite-dimensional setting, that is min∥T(h)−k∥, where T:H→K is a continuous linear operator between Hilbert spaces H,K and h∈H,k∈K. In order to avoid an unbounded set of solutions for the Tykhonov regularization, we transform the infinite-dimensional Tykhonov regularization into a multiobjective optimization problem: min∥T(h)−k∥andmin∥h∥. We call it bounded Tykhonov regularization. A Pareto-optimal solution of the bounded Tykhonov regularization is found. Finally, the bounded Tykhonov regularization is modified to introduce the precise Tykhonov regularization: min∥T(h)−k∥with∥h∥=α. The precise Tykhonov regularization is also optimally solved. All of these mathematical solutions are optimal for the design of Magnetic Resonance Imaging (MRI) coils.

Boundary singular solutions of a class of equations with mixed absorption-reaction

We study properties of positive functions satisfying (E) $$\;-\Delta u+u^p-M|\nabla u|^q=0$$ is a domain $$\text{\O}mega $$ or in $${\mathbb {R}}^{_N}_+$$ when $$p>1$$ and $$1<q<\min \{p,2\}$$ . We concentrate our research on the solutions of (E) vanishing on the boundary except at one point. This analysis depends on the existence of separable solutions in $${\mathbb {R}}^{_N}_+$$ . We construct various types of positive solutions with an isolated singularity on the boundary. We also study conditions for the removability of compact boundary sets and the Dirichlet problem associated to (E) with a measure as boundary data.