Ambient Space Research Articles

Generalized Wintgen inequality for BI-SLANT submanifolds in conformal Sasakian space form with quarter-symmetric connection

PurposeIn 1979, P. Wintgen obtained a basic relationship between the extrinsic normal curvature the intrinsic Gauss curvature, and squared mean curvature of any surface in a Euclidean 4-space with the equality holding if and only if the curvature ellipse is a circle. In 1999, P. J. De Smet, F. Dillen, L. Verstraelen and L. Vrancken gave a conjecture of Wintgen inequality, named as the DDVV-conjecture, for general Riemannian submanifolds in real space forms. Later on, this conjecture was proven to be true by Z. Lu and by Ge and Z. Tang independently. Since then, the study of Wintgen’s inequalities and Wintgen ideal submanifolds has attracted many researchers, and a lot of interesting results have been found during the last 15 years. The main purpose of this paper is to extend this conjecture of Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection.Design/methodology/approachThe authors used standard technique for obtaining generalized Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection.FindingsThe authors establish the generalized Wintgen inequality for bi-slant submanifold in conformal Sasakian space form endowed with a quarter symmetric metric connection, and also find conditions under which the equality holds. Some particular cases are also stated.Originality/valueThe research may be a challenge for new developments focused on new relationships in terms of various invariants, for different types of submanifolds in that ambient space with several connections.

Low-CP-Rank Tensor Completion via Practical Regularization

Dimension reduction is analytical methods for reconstructing high-order tensors that the intrinsic rank of these tensor data is relatively much smaller than the dimension of the ambient measurement space. Typically, this is the case for most real world datasets in signals, images and machine learning. The CANDECOMP/PARAFAC (CP, aka Canonical Polyadic) tensor completion is a widely used approach to find a low-rank approximation for a given tensor. In the tensor model (Sanogo and Navasca in 2018 52nd Asilomar conference on signals, systems, and computers, pp 845–849, https://doi.org/10.1109/ACSSC.2018.8645405, 2018), a sparse regularization minimization problem via ell _1 norm was formulated with an appropriate choice of the regularization parameter. The choice of the regularization parameter is important in the approximation accuracy. Due to the emergence of the massive data, one is faced with an onerous computational burden for computing the regularization parameter via classical approaches (Gazzola and Sabaté Landman in GAMM-Mitteilungen 43:e202000017, 2020) such as the weighted generalized cross validation (WGCV) (Chung et al. in Electr Trans Numer Anal 28:2008, 2008), the unbiased predictive risk estimator (Stein in Ann Stat 9:1135–1151, 1981; Vogel in Computational methods for inverse problems, 2002), and the discrepancy principle (Morozov in Doklady Akademii Nauk, Russian Academy of Sciences, pp 510–512, 1966). In order to improve the efficiency of choosing the regularization parameter and leverage the accuracy of the CP tensor, we propose a new algorithm for tensor completion by embedding the flexible hybrid method (Gazzola in Flexible krylov methods for lp regularization) into the framework of the CP tensor. The main benefits of this method include incorporating the regularization automatically and efficiently as well as improving accuracy in the reconstruction and algorithmic robustness. Numerical examples from image reconstruction and model order reduction demonstrate the efficacy of the proposed algorithm.

Foetal Images on Political Posters: Bodily Intimacy, Public Display and the Mutability of Photographic Meaning

Prenatal images on anti-abortion campaign posters in the Irish referendum of 2018 were an overwhelming presence in the ambient spaces of Irish towns and cities, and generated a strong public reaction. This article examines this aspect of the visual and material ephemera of the referendum campaign in order to critique the continued use of in utero images within conservative reproductive politics. The article places existing accounts of the uses and abuses of foetal imagery into an Irish context. Referencing feminist critiques of prenatal images, ethnographic studies of ultrasound, Peter Paul Verbeek’s discussion of these photographic practices as complex imbrications of the human and technological and paying attention to a striking, oppositional use of a sonogram by the Spanish photographer Laia Abril, this article will interrogate the assumed stability of meaning which motivates the adoption of prenatal images by anti-abortion campaigns.

Injectivity theorems with multiplier ideal sheaves for higher direct images under Kähler morphisms

The purpose of this paper is to establish injectivity theorems for higher direct image sheaves of canonical bundles twisted by pseudo-effective line bundles and multiplier ideal sheaves. As applications, we generalize Koll'ar's torsion freeness and Grauert-Riemenschneider's vanishing theorem. Moreover, we obtain a relative vanishing theorem of Kawamata-Viehweg-Nadel type and an extension theorem for holomorphic sections from fibers of morphisms to the ambient space. Our approach is based on transcendental methods and works for Kahler morphisms and singular hermitian metrics with non-algebraic singularities.

Kähler–Ricci solitons induced by infinite-dimensional complex space forms

We exhibit families of non trivial (i.e. not Kaehler-Einstein) radial Kaehler-Ricci solitons (KRS), both complete and not complete, which can be Kaehler immersed into infinite dimensional complex space forms. This result shows that the triviality of a KRS induced by a finite dimensional complex space form proved in [12] does not hold when the ambient space is allowed to be infinite dimensional. Moreover, we show that the radial potential of a radial KRS induced by a non-elliptic complex space form is necessarily defined at the origin.

A transform approach to polycyclic and serial codes over rings

In this paper, a transform approach is used for polycyclic and serial codes over finite local rings in the case that the defining polynomials have no multiple roots. This allows us to study them in terms of linear algebra and invariant subspaces as well as understand the duality in terms of the transform domain. We also make a characterization of when two polycyclic ambient spaces are Hamming-isometric.

Time-smoothing for parabolic variational problems in metric measure spaces

In 2013, Masson and Siljander determined a method to prove that the minimal p-weak upper gradient $$g_{f_\varepsilon }$$ for the time mollification $$f_\varepsilon $$ , $$\varepsilon >0$$ , of a parabolic Newton–Sobolev function $$f\in L^p_\mathrm {loc}(0,\tau ;N^{1,p}_\mathrm {loc}(\Omega ))$$ , with $$\tau >0$$ and $$\Omega $$ open domain in a doubling metric measure space $$(\mathbb {X},d,\mu )$$ supporting a weak (1, p)-Poincaré inequality, $$p\in (1,\infty )$$ , is such that $$g_{f-f_\varepsilon }\rightarrow 0$$ as $$\varepsilon \rightarrow 0$$ in $$L^p_\mathrm {loc}(\Omega _\tau )$$ , $$\Omega _\tau $$ being the parabolic cylinder $$\Omega _\tau :=\Omega \times (0,\tau )$$ . Their approach involved the use of Cheeger’s differential structure, and therefore exhibited some limitations; here, we shall see that the definition and the formal properties of the parabolic Sobolev spaces themselves allow to find a more direct method to show such convergence, which relies on p-weak upper gradients only and which is valid regardless of structural assumptions on the ambient space, also in the limiting case when $$p=1$$ .

Word of Honor and brand homonationalism with “Chinese characteristics”: the dangai industry, queer masculinity and the “opacity” of the state

ABSTRACT Examining the dangai phenomenon and the web series Word of Honor (WoH), this paper investigates the entanglement of neoliberal management of queer desires, authoritarian regulation of consumer-citizenship, and traffic in various forms of nationalism. Creating an ambient space for queer agency, danmei practices is often regarded as utilizing queer “opacity” as liberatory strategy to outfox the state and societal constraints on non-normative gender and sexuality. Yet the dangai industry in the People’s Republic of China (PRC) shows that the economization of queerness finds “opaque” ways to profit through managing risk and anxiety of “missing out” even when a state explicitly censors queer commodities. Situating WoH in the “she economy,” the paper demonstrates the ways in which queer potential dangai is cahooted with neoliberal and authoritarian state imperatives for fostering proper gendered consumer-subjects and heteronormative social harmony for national building through embracing the “beautiful, powerful” but “caring and loving” nuan nan (“warm men”). Drawing connections between the newly constructed soft masculinity and other cultural exports such as the “wolf warrior,” the paper argues that dangai allows the militant masculinity to be “homonationalized” in service of rebranding Chinese nationalism in a time when Chinese global expansion is fiercely criticized on the global stage.

Subdivision of Maps of Digital Images

A digital image is a finite set of integer lattice points in an ambient Euclidean space together with a suitable adjacency relation between points. Subdivision, which is a process of enlarging a digital image in the photographic sense, provides a basic tool for operating with digital images. But given a map of digital images, there is as yet no general way to define a map of their subdivisions that might reasonably be called a subdivision of the map. In this paper, we construct such maps of subdivisions when the map of digital images has a 1- or 2-dimensional domain. From our constructions we deduce path covering and homotopy covering results that play a role in our development of the digital fundamental group.

Superpotentials of D-branes in Calabi-Yau manifolds with several moduli by mirror symmetry and blown-up

We study B-brane superpotentials depending on several closed- and open-moduli on Calabi-Yau hypersurfaces and complete intersections. By blowing up the ambient space along a curve wrapped by B-branes in a Calabi-Yau manifold, we obtain a blow-up new manifold and the period integral satisfying the GKZ-system. Via mirror symmetry to A-model, we calculate the superpotentials and extract Ooguri-Vafa invariants for concrete examples of several open-closed moduli in Calabi-Yau manifolds.

Twisted virtual bikeigebras and twisted virtual handlebody-knots

In this paper, we generalize unoriented handlebody-links to the twisted virtual case, obtaining Reidemeister moves for handlebody-links in ambient spaces of the form [Formula: see text] for [Formula: see text] a compact closed 2-manifold up to stable equivalence. We introduce a related algebraic structure known as twisted virtual bikeigebras whose axioms are motivated by the twisted virtual handlebody-link Reidemeister moves. We use twisted virtual bikeigebras to define [Formula: see text]-colorability for twisted virtual handlebody-links and define an integer-valued invariant [Formula: see text] of twisted virtual handlebody-links. We provide example computations of the new invariants and use them to distinguish some twisted virtual handlebody-links.

Pythagorean Isoparametric Hypersurfaces in Riemannian and Lorentzian Space Forms

We introduce the notion of a Pythagorean hypersurface immersed into an n+1-dimensional pseudo-Riemannian space form of constant sectional curvature c∈−1,0,1. By using this definition, we prove in Riemannian setting that if an isoparametric hypersurface is Pythagorean, then it is totally umbilical with sectional curvature φ+c, where φ is the Golden Ratio. We also extend this result to Lorentzian ambient space, observing the existence of a non totally umbilical model.

On an $$L^2$$ extension theorem from log-canonical centres with log-canonical measures

With a view to prove an Ohsawa-Takegoshi type $L^2$ extension theorem with $L^2$ estimates given with respect to the log-canonical (lc) measures, a sequence of measures each supported on lc centres of specific codimension defined via multiplier ideal sheaves, this article is aiming at providing evidence and possible means to prove the $L^2$ estimates on compact K\"ahler manifolds $X$. A holomorphic family of $L^2$ norms on the ambient space $X$ is introduced which is shown to "deform holomorphically" to an $L^2$ norm with respect to an lc-measure. Moreover, the latter norm is shown to be invariant under a certain normalisation which leads to a "non-universal" $L^2$ estimate on compact $X$. Explicit examples on $\mathbb{P}^3$ with detailed computation are presented to verify the expected $L^2$ estimates for extensions from lc centres of various codimensions and to provide hint for the proof of the estimates in general.

On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties

We prove several results concerning the intersection cohomology and the perverse filtration associated with a Lagrangian fibration of an irreducible symplectic variety. We first show that the perverse numbers only depend on the deformation equivalence class of the ambient variety. Then we compute the border of the perverse diamond, which further yields a complete description of the intersection cohomology of the Lagrangian base and the invariant cohomology classes of the fibers. Lastly, we identify the perverse and Hodge numbers of intersection cohomology when the irreducible symplectic variety admits a symplectic resolution. These results generalize some earlier work by the second and third authors in the nonsingular case.

A Heuristic Method to Approximate the Closest Vector Problem

The closest vector problem, or CVP for short, is a fundamental lattice problem. The purpose of this challenge is to identify a lattice point in its ambient space that is closest to a given point. This is a provably hard problem to solve, as it is an NP-hard problem. It is considered to be more difficult than the shortest vector problem (SVP), in which the shortest nonzero lattice point is required. There are three types of algorithms that can be used to solve CVP: Enumeration algorithms, Voronoi cell computation and seiving algorithms. Many algorithms for solving the relaxed variant, APPROX-CVP, have been proposed: The Babai nearest algorithm or the embedding technique. In this work we will give a heuristic method to approximate the closest vector problem to a given vector using the embeding technique and the reduced centered law.

Splitting submanifolds in rational homogeneous spaces of Picard number one

Let $M$ be a complex manifold. We prove that a compact submanifold $S\subset M$ with splitting tangent sequence (called a splitting submanifold) is rational homogeneous when $M$ is in a large class of rational homogeneous spaces of Picard number one. Moreover, when $M$ is irreducible Hermitian symmetric, we prove that $S$ must be also Hermitian symmetric. The basic tool we use is the restriction and projection map $\pi$ of the global holomorphic vector fields on the ambient space which is induced from the splitting condition. The usage of global holomorphic vector fields may help us set up a new scheme to classify the splitting submanifolds in explicit examples, as an example we give a differential geometric proof for the classification of compact splitting submanifolds with $\dim\geq 2$ in a hyperquadric, which has been previously proven using algebraic geometry.

Morse quasiflats I

Abstract This is the first in a series of papers concerned with Morse quasiflats, which are a generalization of Morse quasigeodesics to arbitrary dimension. In this paper we introduce a number of alternative definitions, and under appropriate assumptions on the ambient space we show that they are equivalent and quasi-isometry invariant; we also give a variety of examples. The second paper proves that Morse quasiflats are asymptotically conical and have canonically defined Tits boundaries; it also gives some first applications.

Uniqueness of 1D Generalized Bi-Schrödinger Flow

We consider the initial value problem for the generalized bi-Schrödinger flow equation for maps from the one-dimensional flat torus into a compact locally Hermitian symmetric space. The governing equation, which is satisfied by sections of the pull-back bundle induced from the flow, is a fourth-order extension of the 1D Schrödinger map flow equation with loss of derivatives. As the author’s previous work, time-local existence of a smooth solution has been obtained by an intrinsic approach based on the geometric energy method. In the present paper, as a continuation of the work, we establish the uniqueness of the solution. To show the uniqueness, we adopt an extrinsic approach to compare two solutions via an isometric embedding into an ambient Euclidean space. We introduce an energy modifying the classical \(H^2\)-energy for the difference of two solutions, which enables us to eliminate the difficulty of the loss of derivatives. In order to achieve this, we establish some useful tools of computation exploiting the geometric structure of the locally Hermitian symmetric space in the ambient Euclidean space.

Coordinate-free compatibility conditions for deformations of material surfaces

The study of material surfaces uses notions from classical differential geometry, such as the covariant gradient, the mean and Gaussian curvatures, and the Peterson–Mainardi–Codazzi and Gauss equations. These notions are traditionally introduced relative to local surface coordinates and involve Christoffel symbols. We proceed instead without recourse to coordinates using direct notation. After developing the formula for the covariant gradient relative to a surface metric, we derive versions of the Peterson–Mainardi–Codazzi and Gauss equations and Gauss’ Theorema Egregium relevant to a deformed material surface. We then apply our framework to kinematically constrained material surfaces. For material surfaces that can sustain only deformations that preserve either angles or lengths, we obtain explicit representations for the covariant gradient relative to the surface metric in terms of the surface gradient. We show also that a deformation of a material surface that preserves angles and areas must be length preserving and vice versa. Finally, we present an alternative derivation of the Peterson–Mainardi–Codazzi and Gauss equations for a deformed material surface subject to the provision that the surface metric derives from the metric for the ambient Euclidean space within which the surface is embedded. An Appendix involving coordinates is included to ease comparisons between our approach to covariant differentiation and associated derivations of the Peterson–Mainardi–Codazzi and Gauss equations and standard coordinate-based approaches.

Tensor Laplacian Regularized Low-Rank Representation for Non-Uniformly Distributed Data Subspace Clustering

Low-Rank Representation (LRR) highly suffers from discarding the locality information of data points in subspace clustering, as it may not incorporate the data structure nonlinearity and the non-uniform distribution of observations over the ambient space. Thus, the information of the observational density is lost by the state-of-art LRR models, as they take a constant number of adjacent neighbors into account. This, as a result, degrades the subspace clustering accuracy in such situations. To cope with deficiency, in this paper, we propose to consider a hypergraph model to facilitate having a variable number of adjacent nodes and incorporating the locality information of the data. The sparsity of the number of subspaces is also taken into account. To do so, an optimization problem is defined based on a set of regularization terms and is solved by developing a tensor Laplacian-based algorithm. Extensive experiments on artificial and real datasets demonstrate the higher accuracy and precision of the proposed method in subspace clustering compared to the state-of-the-art methods. The outperformance of this method is more revealed in presence of inherent structure of the data such as nonlinearity, geometrical overlapping, and outliers.