Universal Extension Research Articles

Continuity of the stabilizer map and irreducible extensions

Let G be a locally compact group. For every G -flow X , one can consider the stabilizer map x \mapsto G_{x} , from X to the space \mathrm{Sub}(G) of closed subgroups of G . This map is not continuous in general. We prove that if one passes from X to the universal irreducible extension of X , the stabilizer map becomes continuous. This result provides, in particular, a common generalization of a theorem of Frolík (that the set of fixed points of a homeomorphism of an extremally disconnected compact space is open) and a theorem of Veech (that the action of a locally compact group on its greatest ambit is free). It also allows to naturally associate to every G -flow X a stabilizer G -flow \mathrm{S}_{G}(X) in the space \mathrm{Sub}(G) , which generalizes the notion of stabilizer uniformly recurrent subgroup associated to a minimal G -flow introduced by Glasner and Weiss.

Extensions of curves with high degree with respect to the genus

We classify linearly normal surfaces $S \subset \mathbf{P}^{r+1}$ of degree $d$ such that $4g-4 \leq d \leq 4g+4$, where $g>1$ is the sectional genus (it is a classical result that for larger $d$ there are only cones). We apply this to the study of the extension theory of pluricanonical curves and genus $3$ curves, whenever they verify Property $N_2$, using and slightly expanding the theory of integration of ribbons of the authors and E.~Sernesi. We compute the corank of the relevant Gaussian maps, and we show that all ribbons over such curves are integrable, and thus there exists a universal extension. We carry out a similar program for linearly normal hyperelliptic curves of degree $d\geq 2g+3$. We classify surfaces having such a curve $C$ as a hyperplane section, compute the corank of the relevant Gaussian maps, and prove that all ribbons over $C$ are integrable if and only if $d=2g+3$. In the latter case we obtain the existence of a universal extension.

The universal vector extension of an abeloid variety

Let $A$ be an abelian variety over a complete non-Archimedean field $K$. The universal cover of the Berkovich space attached to $A$ reflects the reduction behaviour of $A$. In this paper the universal cover of the universal vector extension $E(A)$ of $A$ is described. In a forthcoming paper ( arXiv:2007.04659), this will be one of the crucial tools to show that rigid analytic functions on $E(A)$ are all constant.

A note on the Gauss–Manin connection for abelian schemes

We study differential forms on the universal vector extension A^{\natural} of an abelian scheme A in characteristic zero, and derive a new construction of the D -group scheme structure on A^{\natural} . This gives, in particular, a rather simple description of the Gauss–Manin connection on the de Rham cohomology of A in terms of global algebraic differential forms on A^{\natural} . The key ingredient is the computation of the coherent cohomology of A^{\natural} , due to Coleman and Laumon.

Determination of Comfort Zones in Landscape Planning in Niğde

Our cities, most of which do not show planned development, are turning into ecosystems that threaten the living life of the natural and cultural environment as a result of many environmental problems such as increasing human and building density and incorrect land use. This negative situation has the opportunity to be resolved with urban planning in which the physical structure of the city is balanced and with landscape plans that will create open and green areas in the city that contribute positively to human and environmental health. The urban heat island effect, which has emerged as a result of intense urbanization in recent years, creates problems for city residents. Unfortunately, most cities in the world face this negative climate phenomenon. It becomes difficult to combat the heat island effect, especially in cities where construction density increases unconsciously. Ecological planning appears as a factor that will prevent these problems from turning into important environmental problems in the future. The most important component to be considered in ecological planning is climate. In this study, thermal comfort areas were tried to be determined along Dr Sami Yağız Street, which is one of the most frequently used areas of Niğde. Temperature and humidity measurements were taken at 25 points at equal intervals on both sides of the street. Measurements were made on different days of the week and at 4 different times during the day. The obtained values were transferred to ArcGIS 10.3 software and maps were produced. A universal linear extension system was used in the evaluation of climate data, and climate factors and bioclimatically suitable areas on the street were determined and evaluated in terms of comfort level. It has been determined that the humidity rate in the study area varies according to measurement hours, and there is no significant change in temperature.

New estimates of Rychkov's universal extension operator for Lipschitz domains and some applications

AbstractGiven a bounded Lipschitz domain , Rychkov showed that there is a linear extension operator for , which is bounded in Besov and Triebel‐Lizorkin spaces. In this paper, we introduce some new estimates for the extension operator and give some applications. We prove the equivalent norms for general Besov and Triebel‐Lizorkin spaces. We also derive some quantitative smoothing estimates of the extended function and all its derivatives on up to the boundary.

Universal lifting properties of abelian semigroup actions

In this paper, we prove that every action of a commutative cancellative semigroup can be extended to an invertible action in some kinds of categories, and this extension has universal lifting property. And the universal extension functor preserves all limits in the categorical point of view, especially, it preserves inverse limits and products. Moreover, we give some applications in dynamical systems.

Could “Synodality” Defeat “Co-Responsibility”?

Could “Synodality” Defeat “Co-Responsibility”? John C. Cavadini ALTHOUGH THE Preparatory Document for the sixteenth Ordinary General Assembly of the Synod of Bishops,1 and, even more, the Working Document for the Continental Stage of the “synodal journey” both feature the idea of “co-responsibility” in the Church, could it be the case that the notion of “synodality” as “the form, the style and the structure of the Church” (PD 2) tends in actuality to the erasure of “co-responsibility” as having any meaning independent of “synodality”? And, since the possibilities of genuine lay leadership in the Church derive from the idea of “co-responsibility,” could it be that “synodality,” though intending the contrary, actually tends towards the erasure of authentic lay leadership in the Church? That is the question that motivates this essay, which presents itself as an exercise in theology, that is, in “faith seeking understanding,” where the mystery of faith of which we are seeking deeper understanding is the mystery of the Church. I. The history of Co-Responsibility The idea of “Coresponsibility in the Church” emerged on the postconciliar scene in 1968 with the publication of the monograph of the same name written by Léon-Joseph Cardinal [End Page 289] Suenens.2 (We will return to a consideration of this book momentarily.) The term re-emerged in the twenty-first century with remarks of Pope Benedict XVI, which largely went unnoticed until they were brought back into prominence by a few scattered voices, perhaps most prominent among them the Most Rev. Charles J. Chaput as archbishop of Denver and, later, of Philadelphia.3 Benedict’s remarks are found, primarily, in two of his allocutions. The first and most substantial was his May 26, 2009 “Address to the Pastoral Convention of the Diocese of Rome,” speaking as the local bishop in his cathedral, the Lateran Basilica of St. John, with the title “Co-responsible for the Church’s Being and Action,” and the subtitle “Church Membership and Pastoral Co-responsibility.”4 The context of the speech is the Diocese of Rome’s renewed commitment to the priority of pastoral work in the local parishes. The second, much briefer, allocution was the 2012 “Message on the Occasion of the Sixth Ordinary Assembly of the International Forum of Catholic Action.”5 As I attempted to describe in an earlier essay,6 Benedict’s idea of co-responsibility flows from the mystery of the Church as expressed by the “twin images” featured as descriptions of the mystery of communion in the Church by Vatican II. This communion ultimately originates in the Trinity and is effected by the Eucharist: [End Page 290] The Church, which originates in the Trinitarian God, is a mystery of communion. . . . This communion is captured under the twin images of the “People of God” and the “Body of Christ,” where “People of God” expresses the continuity of the Church’s history, [and] “Body of Christ” expresses the universality inaugurated in the Cross and in the Lord’s Resurrection. By the “continuity of the Church’s history,” Benedict has in mind continuity with Israel, chosen with an orientation to a salvation with universal extension, an orientation to the Cross, for “in the Cross, St. Paul says, Christ broke down the wall of separation.” It is in Christ, as his body, that “we really become the People of God”: In giving us his Body, he reunites us in this Body of his to make us one. In the communion of the “Body of Christ” we all become one people, the People of God, in which to cite St Paul again all are one and there are no longer distinctions or differences between Greek and Jew, the circumcised and the uncircumcised, the barbarian, the Scythian, the slave, the Jew, but Christ is all in all. He has broken down the wall of distinction. This is why it is “in Christ” that we really become the people of God: “For us Christians, therefore, ‘Body of Christ’ is not only an image, but a true concept, because Christ makes us the gift of his real Body, not only an image of it. Risen, Christ unites us all...

Limiting embeddings of Besov-type and Triebel-Lizorkin-type spaces on domains and an extension operator

In this paper, we study limiting embeddings of Besov-type and Triebel-Lizorkin-type spaces, text {id}_tau : {B}_{p_1,q_1}^{s_1,tau _1}(Omega ) hookrightarrow {B}_{p_2,q_2}^{s_2,tau _2}(Omega ) and text {id}_tau : {F}_{p_1,q_1}^{s_1,tau _1}(Omega ) hookrightarrow {F}_{p_2,q_2}^{s_2,tau _2}(Omega ), where Omega subset {{{mathbb {R}}}^d} is a bounded domain, obtaining necessary and sufficient conditions for the continuity of text {id}_tau . This can also be seen as the continuation of our previous studies of compactness of the embeddings in the non-limiting case. Moreover, we also construct Rychkov’s linear, bounded universal extension operator for these spaces.

Neonatal Early Onset Sepsis (EOS) Calculator plus Universal Serial Physical Examination (SPE): A Prospective Two-Step Implementation of a Neonatal EOS Prevention Protocol for Reduction of Sepsis Workup and Antibiotic Treatment.

Current neonatal early-onset sepsis (EOS) guidelines lack consensus. Recent studies suggest three different options for EOS risk assessment among infants born ≥35 wks gestational age (GA), leading to different behaviors in the sepsis workup and antibiotic administration. A broad disparity in clinical practice is found in Neonatal Units, with a large number of non-infected newborns evaluated and treated for EOS. Broad spectrum antibiotics in early life may induce different short- and long-term adverse effects, longer hospitalization, and early mother-child separation. In this single-center prospective study, a total of 3002 neonates born in three periods between 2016 and 2020 were studied, and three different workup algorithms were compared: the first one was based on the categorical risk assessment; the second one was based on a Serial Physical Examination (SPE) strategy for infants with EOS risk factors; the third one associated an informatic tool (Neonatal EOS calculator) with a universal extension of the SPE strategy. The main objective of this study was to reduce the number of neonatal sepsis workups and the rate of antibiotic administration and favor rooming-in and mother–infant bonding without increasing the risk of sepsis and mortality. The combined strategy of universal SPE with the EOS Calculator showed a significant reduction of laboratory tests (from 33% to 6.6%; p < 0.01) and antibiotic treatments (from 8.5% to 1.4%; p < 0.01) in term and near-term newborns. EOS and mortality did not change significantly during the study period.

Invertible analytic functions on Drinfeld symmetric spaces and universal extensions of Steinberg representations

Recently, Gekeler proved that the group of invertible analytic functions modulo constant functions on Drinfeld’s upper half space is isomorphic to the dual of an integral generalized Steinberg representation. In this note, we show that the group of invertible functions is the dual of a universal extension of that Steinberg representation. As an application, we show that lifting obstructions of rigid analytic theta cocycles of Hilbert modular forms in the sense of Darmon–Vonk can be computed in terms of mathcal {L}-invariants of the associated Galois representation. The same argument applies to theta cocycles for definite unitary groups.

A New Approach to Fractional Kinetic Evolutions

Kinetic equations describe the limiting deterministic evolution of properly scaled systems of interacting particles. A rather universal extension of the classical evolutions, that aims to take into account the effects of memory, suggests the generalization of these evolutions obtained by changing the standard time derivative with a fractional one. In the present paper, extending some previous notes of the authors related to models with a finite state space, we develop systematically the idea of CTRW (continuous time random walk) modelling of the Markovian evolution of interacting particle systems, which leads to a more nontrivial class of fractional kinetic measure-valued evolutions, with the mixed fractional order derivatives varying with the change of the state of the particle system, and with variational derivatives with respect to the measure variable. We rigorously justify the limiting procedure, prove the well-posedness of the new equations, and present a probabilistic formula for their solutions. As the most basic examples we present the fractional versions of the Smoluchovski coagulation and Boltzmann collision models.

Categorification of the elliptic Hall algebra

We show that the central charge k reduction of the universal central extension of the elliptic Hall algebra is isomorphic to the trace, or zeroth Hochschild homology, of the quantum Heisenberg category of central charge k . As an application, we construct large families of representations of the universal extension of the elliptic Hall algebra.

Classification of classical Friedrichs differential operators: One-dimensional scalar case

&lt;p style='text-indent:20px;'&gt;The theory of abstract Friedrichs operators, introduced by Ern, Guermond and Caplain (2007), proved to be a successful setting for studying positive symmetric systems of first order partial differential equations (Fried-richs, 1958), nowadays better known as Friedrichs systems. Recently, Antonić, Michelangeli and Erceg (2017) presented a purely operator-theoretic description of abstract Friedrichs operators, allowing for application of the universal operator extension theory (Grubb, 1968). In this paper we make a further theoretical step by developing a decomposition of the graph space (maximal domain) as a direct sum of the minimal domain and the kernels of corresponding adjoints. We then study one-dimensional scalar (classical) Friedrichs operators with variable coefficients and present a complete classification of admissible boundary conditions.&lt;/p&gt;

On the Universal Extensions in Tannakian Categories

Abstract We use the notion of universal extension in a linear abelian category to study extensions of variations of mixed Hodge structure and convergent and overconvergent isocrystals. The results we obtain apply, for example, to prove the exactness of some homotopy sequences for these categories and to study $F$-able isocrystals.

THE Σ1-DEFINABLE UNIVERSAL FINITE SEQUENCE

AbstractWe introduce the $\Sigma _1$ -definable universal finite sequence and prove that it exhibits the universal extension property amongst the countable models of set theory under end-extension. That is, (i) the sequence is $\Sigma _1$ -definable and provably finite; (ii) the sequence is empty in transitive models; and (iii) if M is a countable model of set theory in which the sequence is s and t is any finite extension of s in this model, then there is an end-extension of M to a model in which the sequence is t. Our proof method grows out of a new infinitary-logic-free proof of the Barwise extension theorem, by which any countable model of set theory is end-extended to a model of $V=L$ or indeed any theory true in a suitable submodel of the original model. The main theorem settles the modal logic of end-extensional potentialism, showing that the potentialist validities of the models of set theory under end-extensions are exactly the assertions of S4. Finally, we introduce the end-extensional maximality principle, which asserts that every possibly necessary sentence is already true, and show that every countable model extends to a model satisfying it.

A geometric model of an arbitrary differentially closed field of characteristic zero

We give an elementary construction of an arbitrary differentially closed field and of a universal extension of a differential field in terms of Nash function fields. We also give a characterization of any Archimedean ordered differentially closed field in terms of Nash functions.

Optimization of Distributed Integrated Multi-energy System Considering Industrial Process Based on Energy Hub

As a typical scenario of distributed integrated multi-energy system (DIMS), industrial park contains complex production constraints and strong associations between industrial productions and energy demands. The industrial production process (IPP) consists of controllable subtasks and strict timing constraints. Taking IPP as a control variable of optimal scheduling, it is an available approach that models the IPP as material flow into an extension energy hub (EH) to achieve the optimization of industrial park. In this paper, considering the coupling between the production process and energy demands, a model of IPP is proposed by dividing the process into different adjustable steps, including continuous subtask, discrete subtask, and storage subtask. Then, a transport model of material flow is used to describe the IPP in an industrial park DIMS. Based on the concept of EH, a universal extension EH model is proposed considering the coupling among electricity, heat, cooling, and material. Furthermore, an optimal scheduling method for industrial park DIMS is proposed to improve the energy efficiency and operation economy. Finally, a case study of a typical battery factory is shown to illustrate the proposed method. The simulation results demonstrate that such a method reduces the operation cost and accurately reflects the operation state of the industrial factory.

A Manin–Mumford Theorem for the Maximal Compact Subgroup of a Universal Vectorial Extension of a Product of Elliptic Curves

Abstract We study the intersection of an algebraic variety with the maximal compact subgroup of a universal vectorial extension of a product of elliptic curves. For this intersection we show a Manin–Mumford-type statement. This answers some questions posed by Corvaja–Masser–Zannier, which arose in connection with their investigation of the intersection of an algebraic curve with the maximal compact subgroup of various algebraic groups. In particular they proved that these intersections are finite for universal vectorial extensions of elliptic curves. Using Khovanskii’s zero-estimates combined with a stratification result of Gabrielov–Vorobjov and recent work of the authors, we obtain effective bounds for this intersection that only depend on the degree of the algebraic variety and the dimension of the group. As a corollary, we obtain new uniform results of Manin–Mumford type for additive extensions of certain abelian varieties.

Teaching Bauhaus principles: on the importance of questioning why some things work too well

ABSTRACTJean Baudrillard warns that the Bauhaus was ‘the genesis of the universal extension of design’ responsible for developing the simulacrum of the Real (Holt, 55), and the past three decades have seen a steadily growing scholarly resistance to the ubiquitous– taught everywhere–Bauhaus design approach. For a design teacher, however, it can be hard to argue with mainstream success. Bauhaus art techniques contained in art books from Gyorgy Kepes’ (1945) Language of Vision to Molly Bang's Picture This (2000) are quick and easy for student designers to grasp and have a remarkable impact in accelerating their abilities in composition and visual analysis. Recent ‘brain science’ appears to confirm some Bauhaus principles with reference to perception.This article examines the disconnect between narrow mainstream understandings of Bauhaus design principles, the broad scope of its impact in design and arts education practice, and the expanding body of work critiquing the Bauhaus. I examine the ideological positioning of the Bauhaus, its dominant traits, its tradition of Total Theatre, and its colonial spread. To address Baudrillard's concern, I seek ways to encourage student awareness of the forces that shape their environment while acknowledging that marketplace design has expectations and demands. Tracing the connection between the Bauhaus and semiotics theorists, I argue that design processes should feed on the social hierarchies, patterns and rituals embedded in the cultural practice of making relational spaces. If contextual awareness frames the work, Bauhaus principles can serve anti-colonial projects.