Real Hypersurfaces in Complex Grassmannians of Rank Two

It is known that there does not exist any Hopf hypersurface in complex Grassmannians of rank two of complex dimension 2m with constant sectional curvature for m≥3. The purpose of this article is to extend the above result, and without the Hopf condition, we prove that there does not exist any locally conformally flat real hypersurface for m≥3.

1-form symmetry, isolated $$ \mathcal{N} $$ = 2 SCFTs, and Calabi-Yau threefolds

We systematically study 4D $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) that can be constructed via type IIB string theory on isolated hypersurface singularities (IHSs) embedded in ℂ4. We show that if a theory in this class has no $$ \mathcal{N} $$ N = 2-preserving exactly marginal deformation (i.e., the theory is isolated as an $$ \mathcal{N} $$ N = 2 SCFT), then it has no 1-form symmetry. This situation is somewhat reminiscent of 1-form symmetry and decomposition in 2D quantum field theory. Moreover, our result suggests that, for theories arising from IHSs, 1-form symmetries originate from gauge groups (with vanishing beta functions). One corollary of our discussion is that there is no 1-form symmetry in IHS theories that have all Coulomb branch chiral ring generators of scaling dimension less than two. In terms of the a and c central charges, this condition implies that IHS theories satisfying $$ a<\frac{1}{24}\left(15r+2f\right) $$ a < 1 24 15 r + 2 f and $$ c<\frac{1}{6}\left(3r+f\right) $$ c < 1 6 3 r + f (where r is the complex dimension of the Coulomb branch, and f is the rank of the continuous 0-form flavor symmetry) have no 1-form symmetry. After reviewing the 1-form symmetries of other classes of theories, we are motivated to conjecture that general interacting 4D $$ \mathcal{N} $$ N = 2 SCFTs with all Coulomb branch chiral ring generators of dimension less than two have no 1-form symmetry.

Life cycle assessment (LCA): informing the development of a sustainable circular bioeconomy?

The role of life cycle assessment (LCA) in informing the development of a sustainable and circular bioeconomy is discussed. We analyse the critical challenges remaining in using LCA and propose improvements needed to resolve future development challenges. Biobased systems are often complex combinations of technologies and practices that are geographically dispersed over long distances and with heterogeneous and uncertain sets of indicators and impacts. Recent studies have provided methodological suggestions on how LCA can be improved for evaluating the sustainability of biobased systems with a new focus on emerging systems, helping to identify environmental and social opportunities prior to large R&D investments. However, accessing economies of scale and improved conversion efficiencies while maintaining compatibility across broad ranges of sustainability indicators and public acceptability remain key challenges for the bioeconomy. LCA can inform, but not by itself resolve this complex dimension of sustainability. Future policy interventions that aim to promote the bioeconomy and support strategic value chains will benefit from the systematic use of LCA. However, the LCA community needs to develop the mechanisms and tools needed to generate agreement and coordinate the standards and incentives that will underpin a successful biobased transition. Systematic stakeholder engagement and the use of multidisciplinary analysis in combination with LCA are essential components of emergent LCA methods. This article is part of the theme issue ‘Bio-derived and bioinspired sustainable advanced materials for emerging technologies (part 1)’.

Polynomially convex embeddings of odd-dimensional closed manifolds

It is shown that any smooth closed orientable manifold of dimension 2 ⁢ k + 1 {2k+1} , k ≥ 2 {k\geq 2} , admits a smooth polynomially convex embedding into ℂ 3 ⁢ k {\mathbb{C}^{3k}} . This improves by 1 the previously known lower bound of 3 ⁢ k + 1 {3k+1} on the possible ambient complex dimension for such embeddings (which is sharp when k = 1 {k=1} ). It is further shown that the embeddings produced have the property that all continuous functions on the image can be uniformly approximated by holomorphic polynomials. Lastly, the same technique is modified to construct embeddings whose images have nontrivial hulls containing no nontrivial analytic disks. The distinguishing feature of this dimensional setting is the appearance of nonisolated CR-singularities, which cannot be tackled using only local analytic methods (as done in earlier results of this kind), and a topological approach is required.

Manifolds with Many Rarita–Schwinger Fields

The Rarita–Schwinger operator is the twisted Dirac operator restricted to $$\nicefrac 32$$ 3 2 -spinors. Rarita–Schwinger fields are solutions of this operator which are in addition divergence-free. This is an overdetermined problem and solutions are rare; it is even more unexpected for there to be large dimensional spaces of solutions. In this paper we prove the existence of a sequence of compact manifolds in any given dimension greater than or equal to 4 for which the dimension of the space of Rarita–Schwinger fields tends to infinity. These manifolds are either simply connected Kähler–Einstein spin with negative Einstein constant, or products of such spaces with flat tori. Moreover, we construct Calabi–Yau manifolds of even complex dimension with more linearly independent Rarita–Schwinger fields than flat tori of the same dimension.

Finiteness and infiniteness results for Torelli groups of (hyper-)Kähler manifolds

The Torelli group $$\mathcal T(X)$$ T ( X ) of a closed smooth manifold X is the subgroup of the mapping class group $$\pi _0(\mathrm {Diff}^+(X))$$ π 0 ( Diff + ( X ) ) consisting of elements which act trivially on the integral cohomology of X. In this note we give counterexamples to Theorem 3.4 by Verbitsky (Duke Math J 162(15):2929–2986, 2013) which states that the Torelli group of simply connected Kähler manifolds of complex dimension $$\ge 3$$ ≥ 3 is finite. This is done by constructing under some mild conditions homomorphisms $$J: \mathcal T(X) \rightarrow H^3(X;\mathbb Q)$$ J : T ( X ) → H 3 ( X ; Q ) and showing that for certain Kähler manifolds this map is non-trivial. We also give a counterexample to Theorem 3.5 (iv) in (Verbitsky in Duke Math J 162(15):2929–2986, 2013) where Verbitsky claims that the Torelli group of hyperkähler manifolds are finite. These examples are detected by the action of diffeomorphsims on $$\pi _4(X)$$ π 4 ( X ) . Finally we confirm the finiteness result for the special case of the hyperkähler manifold $$K^{[2]}$$ K [ 2 ] .

Chern-Yamabe problem and Chern-Yamabe soliton

Let [Formula: see text] be a compact complex manifold of complex dimension [Formula: see text] endowed with a Hermitian metric [Formula: see text]. The Chern-Yamabe problem is to find a conformal metric of [Formula: see text] such that its Chern scalar curvature is constant. In this paper, we prove that the solution to the Chern-Yamabe problem is unique under some conditions. On the other hand, we obtain some results related to the Chern-Yamabe soliton.

COVID 19 and Increased Security Challenges in Northern Nigeria: Interrogating Armed Banditry in Northwestern Nigeria

The COVID 19 pandemic has become a global health issue that now intersects with security issues, especially in African countries. The outbreak of the virus in Africa has halted political, economic and social activities, including countering armed violence. Nigeria is one of the African countries that is faced with security challenges, ranging from Boko Haram insurgency, rural banditry, farmers-herders clash, kidnapping, robbery to piracy among others. However, much attention has concentrated on mitigating the spread of COVID 19 pandemic and the provisions of palliatives to cushion the effects of the abrupt stoppage of formal and informal economic activities. This study examines the intersections between the pandemic and armed banditry in Northwestern. It appears that armed bandits have intensified attacks on communities, against the background of government’s anti-COVID policy. Government has equally re-strategized in responding to the bandits’ attacks. The study gathered data from documented sources and media reports and were analyzed, using content analysis. The study observed that the armed bandits used the COVID 19 lock down policy to increase attacks on some communities, thereby providing a complex dimension to rural banditry in Northwestern Nigeria. This led to increased air and land offensive by the Nigerian military against the bandits. This study recommends among others that government should increase surveillance and adopt strict measures on movements to curtail the activities of the bandits.

Monitoring and Analysis of Auto Body Precision Based on Big Data

In this paper, a Hadoop-based big data system for auto body precision is established. The system unifies the elements that affect auto body precision into a big data platform, which is more efficient than traditional management methods. Using big data analysis, we devised algorithms to improve the efficiency and accuracy of body precision monitoring. Furthermore, we developed techniques to analyze complex dimension deviation problems using a correlation analysis method, principal component analysis (PCA), and improved PCA method. We further established failure modes and devised monitoring and diagnosis models based on time series analysis.

A characterization of ruled hypersurfaces in complex space forms in terms of the Lie derivative of shape operator

<abstract><p>In this paper, it is proved that if a non-Hopf real hypersurface in a nonflat complex space form of complex dimension two satisfies Ki and Suh's condition (J. Korean Math. Soc., 32 (1995), 161–170), then it is locally congruent to a ruled hypersurface or a strongly $ 2 $-Hopf hypersurface. This extends Ki and Suh's theorem to real hypersurfaces of dimension greater than or equal to three.</p></abstract>