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This chapter examines how essayistic personae enabled writers and readers to understand personhood as a means of making a unity out of multiplicity. It draws on Thomas Hobbes’s theory of the person to track how essayistic personae both depicted corporate personhood and themselves served as corporate persons, allowing many writers, real or imagined, to write as one. It also uses Locke’s theory of personhood to show how essayistic personae present conscious persons as contingent unities imposed upon multitudinous thoughts and experiences. Essayistic personae not only extended personhood to non-human beings, such as corporations and animals, they also drew attention to the limited nature of personhood for many human beings, including married women and enslaved people.
Building on studies of historical non-Westphalian world orders, this article challenges desires to identify a ‘first’ international. The question ‘when was the first international?’ is fundamental to defining disciplinary boundaries and the ontologies that shape them. Such quests are substantialist rather than relational, limiting our understanding of the relations and diversity of agents involved in world ordering. Existing approaches to the ‘first’ international are caught in a ‘Mesopotamian trap’: a combination of social evolution conceptual models grounded in colonial epistemologies, analytical presentism, and the surviving propaganda of ancient urban rulers. This article proposes ‘dynamic multiplicity’ as a new framework to account for the diversity, complexity, dynamism, and relationality of world orders in past and present. Dynamic multiplicity emphasizes: a quantitative and qualitative multiplicity of actors; never-ending and always unfolding relations; the instability and permeability of social actors; the diachronic nature of social action; hierarchical and heterarchical power relations; the multi-scalar spatiality of the social; and sustained and critical interdisciplinarity. It applies dynamic multiplicity to the case of Sumer and ancient West Asia, a so-called ‘first’ international, to reveal a diversity of durable relational actors and contradict assumptions that international relations necessarily lead to world orders of homogenous unit-types.
This chapter meditates on how Black erotic bodies manifest in a white supremacist world. It contends that said bodies congeal through an amalgamation of fungible gender and material/discursive dispossession. These inheritances afford Black people the opportunity to conjure fugitive freedom practices, such as multiplicity, which enable Black people to harness erotic power in the pursuit of self-determined notions of pleasure and intimacy with themselves and within Black communities. To buttress my argument, I draw on the work of Akwaeke Emezi – namely, their debut novel Freshwater and an essay about their gender transition surgeries – and Audre Lorde’s classic essay, “The Uses of the Erotic: The Erotic as Power,” to illustrate how multiplicity is a freedom practiced undergirded by erotic power such that practitioners need not minimize or eliminate contradictory or complex aspects of themselves in order to access pleasure and intimacy along personal and interpersonal registers.
This book explores the coevolution of firms, sectors, regions, and national economies in the Global South and explains their economic performance as a dynamic outcome of interactions between the multiple levels of innovation systems. This book counters prevailing views on economic development and offers a unique contribution to the literature on economic catch-up. Whereas the traditional linear view of development has taken a “more is better” approach, this book advocates that latecomers should pursue detours or leapfrogging, which conforms with a “less is better” approach. Instead of the conventional prioritization of manufacturing, this book proposes prioritizing domestic ownership and knowledge in specific sectors and regions and asserts that no country has successfully developed a high-income economy without generating a certain number of globally recognized big businesses. Instead of placing priority on free markets as the Washington Consensus does, this book argues that economic catch-up is only possible with active and planned government interventions, which are needed to overcome latecomers’ disadvantages regarding barriers to entry at the middle-income stage.
This article examines and further develops the relationship between the theory of uneven and combined development (UCD), recently taken up by International Relations (IR) scholars to furnish a social theory of ‘the international’, and the Gramscian concept of ‘passive revolution’, which refers to a molecular process of top-down revolution and state formation that preserves ruling-class power by transforming its social base. To this end, the paper: (1) advances a productive distinction between ‘societal’ and ‘(geo)political’ multiplicity, increasing the transdisciplinary potential of UCD and challenging dominant state-centric approaches to IR; (2) demonstrates that UCD is central to creating the conditions for passive revolution; and, (3) argues that UCD illuminates the distinct spatial dimensions of passive revolution, for which the succession of ‘classes’ in time requires the expansion of capitalist social relations in space. To illustrate these claims, the article demonstrates how the American Civil War is best understood as an inter-societal conflict, exacerbated by the coexistence of two social formations within a single state, leading to war. It then shows how, upon victory, the North’s abolition of enslaved labour and the subsequent attempt to re-subsume the South within a single sovereign polity constituted a radical instance of passive revolution.
where $a, \epsilon, \eta \gt 0$, q is L2-subcritical, p is L2-supercritical, $\lambda\in \mathbb{R}$ is an unknown parameter that appears as a Lagrange multiplier and h is a positive and continuous function. It is proved that the numbers of normalized solutions are at least the numbers of global maximum points of h when ϵ is small enough. The solutions obtained are local minimizers and probably not ground state solutions for the lack of symmetry of the potential h. Secondly, the stability of several different sets consisting of the local minimizers is analysed. Compared with the results of the corresponding autonomous equation, the appearance of the potential h increases the number of the local minimizers and the number of the stable sets. In particular, our results cover the Sobolev critical case $p=2N/(N-2)$.
This article examines how images on a sarcophagus involved Roman viewers in processes of thinking by analogy and so invited them to engage in meditation on death. This more thanatological slant is sidelined in current approaches that emphasise how exemplary figures on sarcophagi consoled the bereaved and praised the dead. Building on these approaches, together with work on the mediating role played by artefacts in thought, this article proposes that analogies on sarcophagi also invited the living to think about their own death and the possibilities and limitations of analogy for thanatological reflection. It argues, further, that sarcophagi should be read more expansively, allowing for figures and scenes to have more than one identity rather than collapsing them into one: this multiplicity reinforces meditation on death. The article focuses on Roman sarcophagi that feature Adonis, with emphasis on the Rinuccini sarcophagus; this unusual sarcophagus explicitly juxtaposes real-life and mythological scenes.
Democracy, sovereignty, citizenship, and the rule of law are foundational yet contested concepts. Their foundational role has been extensively discussed with reference to modern nation-states and global order, and their contested quality has come to the fore through norm contestation. This chapter suggests that contestation’s move into the limelight represents an opportunity to address the future of democracies. It argues that first, norm contestedness is expected due to its value- and practice-based roots. Second, contestedness has implications for everyday norm-use and academic norm-conceptualization. This chapter conceives norms and their multiple contestations as the constitutive ‘glue’ of global ordering rather than as a ‘means’ towards implementing governance rules. This chapter identifies a conceptual gap between state-negotiated norms of global governance and societal contestation of norms. It recalls Tully’s ‘Unfreedom of the Moderns’ claim and the central role of agonism in including the multitude of affected stakeholders in establishing norms of governance. Using the cycle-grid model, this chapter frames democracy from below.
In this paper, we prove the Fukui–Kurdyka–Paunescu conjecture, which says that sub-analytic arc-analytic bi-Lipschitz homeomorphisms preserve the multiplicities of real analytic sets. We also prove several other results on the invariance of the multiplicity (respectively, degree) of real and complex analytic (respectively, algebraic) sets. For instance, still in the real case, we prove a global version of the Fukui–Kurdyka–Paunescu conjecture. In the complex case, one of the results that we prove is the following: if $(X,0)\subset (\mathbb {C}^{n},0)$, $(Y,0)\subset (\mathbb {C}^{m},0)$ are germs of analytic sets and $h\colon (X,0)\to (Y,0)$ is a semi-bi-Lipschitz homeomorphism whose graph is a complex analytic set, then the germs $(X,0)$ and $(Y,0)$ have the same multiplicity. One of the results that we prove in the global case is the following: if $X\subset \mathbb {C}^{n}$, $Y\subset \mathbb {C}^{m}$ are algebraic sets and $\phi \colon X\to Y$ is a semi-algebraic semi-bi-Lipschitz homeomorphism such that the closure of its graph in $\mathbb {P}^{n+m}(\mathbb {C})$ is an orientable homological cycle, then ${\rm deg}(X)={\rm deg}(Y)$.
The occurrence of multi-hit events and the separation distance between multi-hit ion pairs field evaporated from III-nitride semiconductors can potentially provide insights on neighboring chemistry, crystal structure, and field conditions. In this work, we quantify the range of variation in major III-N and III-III ion-pair separation to establish correlations with bulk composition, growth method, and ion-pair chemistry. The analysis of ion-pair separation along the AlGaN/GaN heterostructure system allows for comparison of Ga-N and Ga-Ga ion-pair separation between events evaporated from pure GaN and Al0.3Ga0.7N. From this, we aim to define a relative measure for the bond length of ion pairs within an AlGaN/GaN heterostructure. The distributions of pair separation revealed a distinct bimodal behavior that is unique to Al-N2+ ion pairs, suggesting the occurrence of both co-evaporation and molecular dissociation. Finally, we demonstrated that the two modes of ion-pair events align with the known variation in the surface electric field of the AlGaN(0001) structure. These findings demonstrate the utility of atom probe tomography in studying the crystallographic nature of nitride semiconductors.
This chapter considers how the Routine Dynamics debate around technology, artifacts and materiality has evolved over the course of the past two decades. In reviewing the progress achieved so far, I show how the field is gearing up to address the important challenges posed, among other things, by new forms of artifacts and technology, and new ways of organizing. In so doing, I discuss how the latest advances in routines and materiality (artifacts at the centre, performativity and multiplicity/fluid ontology) can help us address the theoretical, methodological and empirical challenges raised by contemporary material phenomena. I conclude by laying out an agenda for future studies of routines, technology, artifacts and materiality.
Actor-network theory has always been an inspiring theoretical and methodological source for Routine Dynamics research. Seeing routines as networks of actants and as a consequence rather than a cause of collective action enabled scholars to move away from a priori assumptions about the world and shift their attention to situated performances, multiplicity, and connections-in action. In this chapter, I provide a brief historical account of actor-network theory highlighting some of its central authors and their work before unravelling how Routine Dynamics scholars have appropriated it—ironically, often as an undercover actor that remains invisible at first sight—and conclude by reflecting on how actor-network theory can continue to be of use for and shape Routine Dynamics research.
Huang and Mendoza’s introduction to the fourth volume of Asian American Literatures in Transition offers a refresher on Lisa Lowe’s formative critical work, Immigrant Acts (1996), published at the beginning of the time period covered in this volume. The authors reframe Lowe’s terms “heterogeneity,” “hybridity,” and “multiplicity” within several watershed moments affecting Asian Americans and other groups in the USA: including the Defense of Marriage Act (1996), the September 11 attacks, the decriminalization of sodomy (2003), the COVID pandemic, and the Black Lives Matter movement. While many of these events exacerbated the vulnerability and precarity of some Asian American groups, the turbulence of the time fueled the Asian American literary imagination as writers in this period drew on more representational strategies for their literary experimentations than in previous periods. This volume covers precisely these tensions: artistic proliferations in the face of injustice, recognition in the face of social erasures, innovation in the face of neoliberal white supremacy’s monopoly on wealth and violence.
Let $T = (T_1, \ldots , T_n)$ be a commuting tuple of bounded linear operators on a Hilbert space $\mathcal{H}$. The multiplicity of $T$ is the cardinality of a minimal generating set with respect to $T$. In this paper, we establish an additive formula for multiplicities of a class of commuting tuples of operators. A special case of the main result states the following: Let $n \geq 2$, and let $\mathcal{Q}_i$, $i = 1, \ldots , n$, be a proper closed shift co-invariant subspaces of the Dirichlet space or the Hardy space over the unit disc in $\mathbb {C}$. If $\mathcal{Q}_i^{\bot }$, $i = 1, \ldots , n$, is a zero-based shift invariant subspace, then the multiplicity of the joint $M_{\textbf {z}} = (M_{z_1}, \ldots , M_{z_n})$-invariant subspace $(\mathcal{Q}_1 \otimes \cdots \otimes \mathcal{Q}_n)^{\perp }$ of the Dirichlet space or the Hardy space over the unit polydisc in $\mathbb {C}^{n}$ is given by
This chapter concludes by emphasizing the multiple character of the law. Summarizing the multiple beings of the law as they have appeared in this book – the law as a distribution machine, the law as a narrative practice, the law as a matter of shuffling documents, the law as a matter of temporal ordering and folding – this chapter raises the question how we may make sense of this multiplicity. Here, I argue we must refuse to reduce these multiplicities to one preferred abstraction. Instead of such hyper-explanations, I argue we must retain multiplicities in order to justice to law’s multi-scalar, multi-temporal, and non-local character. In order to do so, I suggest we think of the law as a hyper-object. The notion of the hyper-object forces us to situate and account for our collaborations with this strange being, so that we will never be able to claim we have apprehended the law in its totality, yet we need not sacrifice description entirely. Such a conception calls for situated accounts, and remains sensitive to the fact that social and legal life is always ongoing, never not concrete, irreducibly multiple.
In the field of socio-legal studies or law and society scholarship, it is rare to find empirically rich and conceptually sophisticated understandings of actual legal practice. This book, in contrast, connects the conceptual and the empirical, the abstract and the concrete, and in doing so shows the law to be an irreducibly social, material and temporal practice. Drawing on cutting-edge work in the social study of knowledge, it grapples with conceptual and methodological questions central to the field: how and where judgment empirically takes place; how and where facts are made; and how researchers might study these local and concrete ways of judging and knowing. Drawing on an ethnographic study of how narratives and documents, particularly case files, operate within legal practices, this book's unique and innovative approach consists of rearticulating the traditional boundaries separating judgment from knowledge, urging us to rethink the way truths are made within law.
Chapter 5 is devoted to studying the non-existence of concentration solutions for other singularly perturbed elliptic problems. Results in this direction are obtained by using a local Pohozaev identity. As an application of these results, the existence of infinitely many sign-changing solutions for the Brezis-Nirenberg problem is proved.
The Lyapunov-Schmidt reduction method and its variants are usually used to construct solutions for elliptic problems without small parameters. In Chapter 4, these methods are adapted to study the Schrodinger equations with subcritical growth. The results in Chapter 4 show that the non-compactness of some elliptic problems may give rise to the existence of infinitely many positive solutions whose energy can be arbitrarily large. Such results cannot be obtained by using the abstract critical points theories.
This paper explores Platonic and Aristotelian thought on multiplicity, forms, and matter, and considers the relationship between Abrahamic and pagan understandings of the order of divine creation.
Let I be a zero-dimensional ideal in the polynomial ring
$K[x_1,\ldots ,x_n]$
over a field K. We give a bound for the number of roots of I in
$K^n$
counted with combinatorial multiplicity. As a consequence, we give a proof of Alon’s combinatorial Nullstellensatz.