Norm Of Space Research Articles

2-Rotund norms for unconditional and symmetric sequence spaces

A reflexive Banach space with an unconditional basis admits an equivalent 1-unconditional 2R norm and embeds into a reflexive space with a 1-symmetric 2R norm. Partial results on 1-symmetric 2R renormings of spaces with a symmetric basis are obtained.

Intimate Language in Traditional Markets: Challenging Public Space Norms through Kristeva’s Intertextuality

The use of intimate language in public spaces is a phenomenon that emerges in the interactions of economic actors in traditional markets. Therefore, language intimacy deconstructs social norms that should not be displayed in public spaces. However, language intimacy has emerged in traditional markets for a long time in the interactions of economic actors, including sellers, buyers, porters, parking attendants, and the social gathering community. This research explores how intimate language is articulated in an economic space closely related to the ethnic identity of economic actors in traditional markets in the Jember region. The ethnic diversity in question includes Javanese, Madurese, Chinese/Chinese, and Arab. This phenomenon was researched qualitatively using a post-structuralist approach and applying Julia Kristeva's theory of intertextuality. Data analysis uses two Kristeva concepts, namely intertextuality and suprasegmental. The data is processed by looking at the text production process originating inside and outside the text. The research results show that the intimacy of language, usually used in the private sphere, has succeeded in breaking down the rigidity of language in the public sphere, besides dissolving social relations between economic actors with various ethnicities and social classes. Thus, the use of greetings in intimate language closely related to ethnic identity is experiencing development and merging with the space of familiarity and closeness built by economic actors in traditional markets.

On the fractional heat semigroup and product estimates in Besov spaces and applications in theoretical analysis of the fractional Keller–Segel system

This paper is concerned with the fractional Keller–Segel system in temporal and spatial variables. We consider fractional dissipation for the physical variables including a fractional dissipation mechanism for the chemotactic diffusion, as well as a time fractional variation assumed in the Caputo sense. We analyze the fractional heat semigroup obtaining time decay and integral estimates of the Mittag–Leffler operators in critical Besov spaces, and prove a bilinear estimate derived from the nonlinearity of the Keller–Segel system, without using auxiliary norms. We use these results in order to prove the existence of global solutions in critical homogeneous Besov spaces employing only the norm of the natural persistence space, including the existence of self-similar solutions, which constitutes a persistence result in this framework. In addition, we prove a uniqueness result without assuming any smallness condition on the initial data.

Computational evolution of social norms in well-mixed and group-structured populations

Models of indirect reciprocity study how social norms promote cooperation. In these models, cooperative individuals build up a positive reputation, which in turn helps them in their future interactions. The exact reputational benefits of cooperation depend on the norm in place, which may change over time. Previous research focused on the stability of social norms. Much less is known about how social norms initially evolve when competing with many others. A comprehensive evolutionary analysis, however, has been difficult. Even among the comparably simple space of so-called third-order norms, there are thousands of possibilities, each one inducing its own reputation dynamics. To address this challenge, we use large-scale computer simulations. We study the reputation dynamics of each third-order norm and all evolutionary transitions between them. In contrast to established work with only a handful of norms, we find that cooperation is hard to maintain in well-mixed populations. However, within group-structured populations, cooperation can emerge. The most successful norm in our simulations is particularly simple. It regards cooperation as universally positive, and defection as usually negative-unless defection takes the form of justified punishment. This research sheds light on the complex interplay of social norms, their induced reputation dynamics, and population structure.

Bridging the Self’s worlds: Young girls’ creative TikTok expressions of multimodal literacy during Covid-19

This study investigates three young Chinese girls’ active play on TikTok as a way to engage in global communication during the Covid-19 lockdown in China. In particular, this paper aims to navigate how the girls position themselves in TikTok multimodal literacy play, as well as to inquire into how they practice literacy to deny, negotiate, and/or accept the beauty norms in TikTok virtual space. Situating and exploring these young girls’ stories, the author shares findings from multiple rounds of virtual interviews during the pandemic that highlight the girls’ creativity through multimodal literacy engagement on TikTok; their playful thinking that adopted the pandemic as a way of life and empowered the girls despite uncertainties, doubts, and tensions; and their complex beauty values negotiations embedded in the experiences of the girls’ vibrant interactions on TikTok. Inspired by the girls' literacy practices and gender negotiations, TikTok’s influences on norms of beauty and feminine appearance are discussed. Interrogating the limits of this platform, this work recognizes the possibilities of young girls’ multimodal literacy experiences while encouraging further negotiations, reimaginations, and growth in their celebrations of social media like TikTok.

Criminal Law Regulation and Conviction Standards of Cyber Violence: Taking the Crime of Cyber Insult and Defamation as an Example

With the advent of the Internet era, interpersonal communication in real space has gradually spread to cyberspace. Whether the legal regulation of real space should follow and restrict the behavior norms of virtual space has become an important issue discussed by the academic community. Although civil law and other laws have certain regulations on the cyberspace, it is not enough to rely solely on general laws such as civil law to limit the escalating problem of online violence in cyberspace. Therefore, discussing the intervention of criminal law has become of utmost importance. Due to the ease of making comments in virtual spaces, as well as the large number of people and a mix of good and bad, the phenomenon of insult, defamation, and wanton abuse is the most widespread. Therefore, online insult and defamation has become a typical manifestation of online violence. The provisions of China's criminal law on the crime of online insult and defamation are still relatively broad and lack specificity, which brings certain difficulties to judicial practice when facing serious consequences of online insult and defamation. By exploring the criminal law regulations and conviction standards for online violence, using case analysis and comparative research methods, the criminal law rules for online insult and defamation can be further refined, effectively punishing and timely preventing online insult and defamation, purifying the online environment, safeguarding the rights and interests of netizens, and promoting the further development of criminal law in virtual space.

Navigating ‘safe’ and ‘non-safe’ queer spaces

Abstract It is well documented that gay people adopt behavioural strategies to navigate the heteronormative expectations and norms of social space. These practices are likely to be particularly pronounced in socially conservative countries which have seen less progress for LGBTQ+ rights. This study examines how two gay men (Rui and Kenni) stylistically negotiate their sexual identities in a socially conservative country – Singapore – by analyzing the variation in two phonetic variables that have been linked to gender and sexuality: Pitch and /s/. We show that both speakers style-shift across queer-friendly and heteronormative environments though the rate and degree of shifting is influenced both by the situated social meanings of the features and the interactional context. Concluding, we argue that research should consider how minoritised individuals are required to style-shift in order to adhere to the hegemonic norms and expectations of society.

A multiparametric family of solutions to the Volterra linear integral equation of the first kind

We study the Volterra integral equation of the first kind with an integral operator of order n, a singularity and a sufficiently smooth kernel in a certain Banach space with weight. It reduces to an integro-differential equation with two terms on the left-hand side. The first term corresponds to an equation for which an explicitly multiparameter family of solutions is constructed. For the second term, we obtain an equation with an operator whose norm in an arbitrary Banach space is arbitrarily small near zero. Such splitting of the integral operator allows one to construct a particular and general solutions to the integro-differential equation in the corresponding Banach space in the form of convergent series. Thus, under certain restrictions on the operator pencil corresponding to a given integral operator, a multi-parameter family of solutions is being constructed for the original integral equation.

Narrative strategies of transrealism: the interplay of satire, fantasy, and science in American dystopian fiction

ABSTRACT The rise of transrealism in the second half of the twentieth century embellished the literary landscape in America with a new mode of expression that offered new understanding of time, space, identity, and social values and norms. This study situates the American novelist Kurt Vonnegut’s Player Piano within this literary context to map out the qualities that distinguish it as a transrealistic fiction. We argue that through innovative coalescence of fantasy and realism, this postmodern novel provides a satirical commentary against the incongruities of the contemporary American society. To analyse the novel, we employ Rudy Rucker’s theorisations of the movement that delineates the transrealist manifesto as a union of realism, fantasy, and science-fiction. The findings reveal that through a satirical representation of the current advancements in technology and their inevitably negative impact on human life and society, the novel provides a dystopian picture of modern life in America. This apocalyptic sentiment is reinforced through a creative convergence of the surreal features of science-fiction, the tropes of naturalistic realism, and the elements of satire that together help to accentuate the deficiencies and ironies of the modern American society as well as the rampant misuse of technology by both individuals and authorities.

Gradient Flow of the Sinai–Ruelle–Bowen Entropy

Motivated by an extension to Gallavotti–Cohen Chaotic Hypothesis, we study local and global existence of a gradient flow of the Sinai–Ruelle–Bowen entropy functional in the space of transitive Anosov maps. For the space of expanding maps on the unit circle, we equip it with a Hilbert manifold structure using a Sobolev norm in the tangent space of the manifold. Under the additional measure-preserving assumption and a slightly modified metric, we show that the gradient flow exists globally and every trajectory of the flow converges to a unique limiting map where the SRB entropy attains the maximal value. In a simple case, we obtain an explicit formula for the flow’s ordinary differential equation representation. This gradient flow has close connection to a nonlinear partial differential equation, a gradient-dependent diffusion equation.

Becoming response-able with a protest placard: white under(-)standing in encounters with the Black German Other

Abstract This paper emerged from an encounter with the Black Lives Matter placard I understand that I will never understand but I stand with you in Leipzig, Germany, and it centers white understanding as a constitutive practice of whiteness. This is mainly a theoretical contribution (learning towards the philosophical), although it includes some interview data and observations from protest participation. I contribute to raciolinguistics by reading the concept of the white listening subject through Barad’s new materialist notion of apparatuses, asking what exactly constitutes white understanding. This allows me to bring out the potentials and pitfalls (i.e. the counter/productivity) of white understanding as a reflective practice, which I put into conversation with my embodied practice of under-standing (i.e. standing under) the placard at a BLM protest in Berlin. I show how the white body is measured by a Black norm in the protest space, producing a productive discomfort filled with opportunities for becoming response-able towards the Black Other, but also towards whiteness. Considering the ethico-esthetic framing of this collection, I pursue an aesthethics of wor(l)ding that inter-rupts, dis/entangles, and walks around with and in words. It gestures towards what we usually leave out when pursuing one analytical avenue over another.

Embeddings of a Multi-Weighted Anisotropic Sobolev Type Space

Parameters such as various integral and differential characteristics of functions, smoothness properties of regions and their boundaries, as well as many classes of weight functions cause complex relationships and embedding conditions for multi-weighted anisotropic Sobolev type spaces. The desire not to restrict these parameters leads to the development of new approaches based on the introduction of alternative definitions of spaces and norms in them or on special localization methods. This article examines the embeddings of multi-weighted anisotropic Sobolev type spaces with anisotropy in all the defining characteristics of the norm of space, including differential indices, summability indices, as well as weight coefficients. The applied localization method made it possible to obtain an embedding for the case of an arbitrary domain and weights of a general type, which is important in applications in differential operators’ theory, numerical analysis.

Excursus on modulation spaces via metaplectic operators and related time-frequency representations

We provide a comprehensive overview of the theoretical framework surrounding modulation spaces and their characterizations, particularly focusing on the role of metaplectic operators and time-frequency representations. We highlight the metaplectic action which is hidden in their construction and guarantees equivalent (quasi-)norms for such spaces. In particular, this work provides new characterizations via the submanifold of shift-invertible symplectic matrices. Similar results hold for the Wiener amalgam spaces.

Explicit P1 Finite Element Solution of the Maxwell-Wave Equation Coupling Problem with Absorbing b. c.

In this paper, we address the approximation of the coupling problem for the wave equation and Maxwell’s equations of electromagnetism in the time domain in terms of electric field by means of a nodal linear finite element discretization in space, combined with a classical explicit finite difference scheme for time discretization. Our study applies to a particular case where the dielectric permittivity has a constant value outside a subdomain, whose closure does not intersect the boundary of the domain where the problem is defined. Inside this subdomain, Maxwell’s equations hold. Outside this subdomain, the wave equation holds, which may correspond to Maxwell’s equations with a constant permittivity under certain conditions. We consider as a model the case of first-order absorbing boundary conditions. First-order error estimates are proven in the sense of two norms involving first-order time and space derivatives under reasonable assumptions, among which lies a CFL condition for hyperbolic equations. The theoretical estimates are validated by numerical computations, which also show that the scheme is globally of the second order in the maximum norm in time and in the least-squares norm in space.

Connection Between Weighted Tail, Orlicz, Grand Lorentz And Grand Lebesgue Norms

We prove that the norm of functions in a suitable Grand Lorentz space built on a measure space, equipped with sigma finite diffuse measure, coincides with the norm in a suitable exponential Grand Lebesgue Space space as well as coincides with the so-called exponential tail norm, which may be quite described as norm in a suitable Banach rearrangement invariant space. We also exhibit comparisons with exponential Orlicz norms.

Operator Space Complexification Transfigured

Abstract Given a finite group $G$, a central subgroup $H$ of $G$, and an operator space $X$ equipped with an action of $H$ by complete isometries, we construct an operator space $X_{G}$ equipped with an action of $G$ that is unique under a “reasonable” condition. This generalizes the operator space complexification $X_{c}$ of $X$. As a linear space $X_{G}$ is the space obtained from inducing the representation of $H$ to $G$ (in the sense of Frobenius). Indeed a main achievement of our paper is the induced representation construction in the category of operator spaces. This has been hitherto elusive even for Banach spaces since it is not clear how to norm the induced space. We show that for a large class of group actions the induced space has a unique operator space norm.

A discontinuous Galerkin finite element method for the Oldroyd model of order one

In this work, we analyze a discontinuous Galerkin finite element method for the equations of motion that arise in the 2D Oldroyd model of order one. We investigate the existence and uniqueness of semidiscrete discontinuous solutions, as well as the consistency of the scheme. We derive new a priori and regularity results for the discrete solution and establish optimal error estimates in ‐norm in time and energy norm in space for the velocity and ‐norm in both time and space for the pressure. Uniform estimates are derived for sufficiently small data. We next apply the backward Euler method to the semidiscrete formulation and establish optimal fully discrete error estimates. At the end, we conduct numerical experiments to support our theoretical results and analyze the findings.

Parameter Conditions for Boundedness of Two Integral Operators in Weighted Lebsgue Space and Calculation of Operator Norms

Firstly, Hilbert-type integral inequalities with best constant factors are established for two non-homogeneous kernels. Then, by utilizing the relationship between the Hilbert-type inequality and the integral operator of same kernel, the parameter conditions for two integral operators with non-homogeneous kernels in weighted Lebesgue space to be bounded and the formula for calculating the operator norm are obtained.

Philly Elmo Rises: Black Eccentricity and the Street Fantastic During the George Floyd Uprisings/Riots, May 2020

ABSTRACT: During the May 2020 uprisings/riots in Philadelphia, a Black person dressed in a white T-shirt, black athletic pants, and the headpiece of an Elmo mascot costume posed in front of a burning trash can next to a police barricade. “Philly Elmo,” as they were called, became an icon of irreverent radicalism with a touch of Philadelphia idiosyncrasy to social media users who circulated the image of this unique figure. From this ephemeral digital archive, I recognize that Philly Elmo’s unruly, frivolous performance is a manifestation of the Black street fantastic , those unrefined acts cultivated from the urban landscape and limited funds that denote a Black eccentric’s emotionality when disrupting the norms of space and ritual. In this work, I question how the study of Black life and experience can preserve the memory of atypical Black reactions to injustice that may seem disrespectful to the legacy of solemn and joyful Black protest.

Buildings, valuated matroids, and tropical linear spaces

AbstractAffine Bruhat–Tits buildings are geometric spaces extracting the combinatorics of algebraic groups. The building of parameterizes flags of subspaces/lattices in or, equivalently, norms on a fixed finite‐dimensional vector space, up to homothety. It has first been studied by Goldman and Iwahori as a piecewise‐linear analogue of symmetric spaces. The space of seminorms compactifies the space of norms and admits a natural surjective restriction map from the Berkovich analytification of projective space that factors the natural tropicalization map. Inspired by Payne's result that the analytification is the limit of all tropicalizations, we show that the space of seminorms is the limit of all tropicalized linear embeddings and prove a faithful tropicalization result for compactified linear spaces. The space of seminorms is in fact the tropical linear space associated to the universal realizable valuated matroid.