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Sixteenth-century Venetians decorated the walls of their homes with maps as well as pictures of all kinds. A large corpus of inventories of household goods records the location of these wall decorations and, together with books offering advice on the display of maps, provides evidence that maps were intentionally placed in the most public spaces in the house. The manuals also confirm the impression gained from the inventories that the maps were valued for their ability to construct a public identity for the owner. They were versatile objects that could demonstrate that the owner was a cultured, cosmopolitan man educated about the world, reinforce his professional or trade standing, or enhance a military persona, all to the glorification of the family name.

In this paper, we study biharmonic identity maps between Euclidean spaces and warped product spaces of the form R[sup.r]×[sub.f2]R[sup.n−r]. Our main results characterize both orientations of the identity map in terms of partial differential equations: For the map from Euclidean space to the warped space, biharmonicity is equivalent to the warping function satisfying a stationary Hamilton–Jacobi-type equation. While the only global solution is constant, we construct infinitely many explicit local solutions. Conversely, for the map from the warped space to Euclidean space, biharmonicity corresponds to a logarithmic transformation of the warping function satisfying this same PDE. This equation admits abundant explicit nonconstant global solutions and can be reduced to a Liouville-type equation via a suitable transformation.

An identity map idM:M→M is a bijective map from a manifold M onto itself which carries each point of M return to the same point. To study the differential geometry of an identity map idM:M→M, we usually assume that the domain M and the range M admit metrics g and g′, respectively. The main purpose of this paper is to provide a comprehensive survey on the differential geometry of identity maps from various differential geometric points of view.

Critical research, such as that involving the deconstruction of monoracialism, aims to empower and elevate the voices of marginalized populations. When we engage in critical research, whether it be quantitative or qualitative, scholars must recognize how our own lived experiences might shape each stage of the research process. The purpose of this paper is twofold. First, we present scholars with a structured method using a conceptual mapping of social identities combined with written reflection and regularly scheduled debriefings to begin their own explorations of identity. Second, we present our experiences negotiating with monoracialism as we worked to understand our identities as Asian scholars. Through this process we discovered new perspectives on how we, along with our participants, have grappled with socially imposed notions of who we are as Asians.

The rapid increase in antibiotic resistance by various bacterial pathogens underlies the significance of developing new therapies and exploring different drug targets. A fraction of bacterial pathogens abbreviated as ESKAPE by the European Center for Disease Prevention and Control have been considered a major threat due to the rise in nosocomial infections. Here, we compared putative drug binding pockets of twelve essential and mostly conserved metabolic enzymes in numerous bacterial pathogens including those of the ESKAPE group and . The comparative analysis will provide guidelines for the likelihood of transferability of the inhibitors from one species to another. Nine bacterial species including six ESKAPE pathogens, along with and , two non-pathogenic bacteria, have been selected for drug binding pocket analysis of twelve essential enzymes. The amino acid sequences were obtained from Uniprot, aligned using ICM v3.8-4a and matched against the Pocketome encyclopedia. We used known co-crystal structures of selected target enzyme orthologs to evaluate the location of their active sites and binding pockets and to calculate a matrix of pairwise sequence identities across each target enzyme across the different species. This was used to generate sequence maps. High sequence identity of enzyme binding pockets, derived from experimentally determined co-crystallized structures, was observed among various species. Comparison at both full sequence level and for drug binding pockets of key metabolic enzymes showed that binding pockets are highly conserved (sequence similarity up to 100%) among various ESKAPE pathogens as well as . Enzymes orthologs having conserved binding sites may have potential to interact with inhibitors in similar way and might be helpful for design of similar class of inhibitors for a particular species. The derived pocket alignments and distance-based maps provide guidelines for drug discovery and repurposing. In addition they also provide recommendations for the relevant model bacteria that may be used for initial drug testing. Comparing ligand binding sites through sequence identity calculation could be an effective approach to identify conserved orthologs as drug binding pockets have shown higher level of conservation among various species. By using this approach we could avoid the problems associated with full sequence comparison. We identified essential metabolic enzymes among ESKAPE pathogens that share high sequence identity in their putative drug binding pockets (up to 100%), of which known inhibitors can potentially antagonize these identical pockets in the various species in a similar manner.

We study the existence of Fatou components on parabolic skew product maps. We focus on skew products in which each coordinate has a fixed point that is parabolic. As in the geometrically attracting case, we prove that there exists maps F that have one-dimensional disks that are mapped to a point in the Julia set of the restriction of F to an invariant one-dimensional fiber. We first prove a linearization theorem for a one-dimensional map, then for a parabolic skew product. Finally, we apply this result to construct the skew product map described above.

The Atlas of European Values summarizes the beliefs and values of the Europeans in informative graphs, charts and maps. It includes all European countries and shows how Europeans think about work, family, sexuality, religion, politics, and morality.

Let \\[{\\mathcal {R}}\\] be a unital prime \\[*\\]-ring containing a nontrivial symmetric idempotent. For \\[A,B\\in {\\mathcal {R}}\\], the skew commutator and 2-skew commutator are defined, respectively, by \\[{}_*[A,B]=AB-BA^*\\] and \\[{}_*[A,B]_2= {{}_*[A, {{}_*[A,B]}]}\\]. Let \\[\\Phi :{\\mathcal {R}} \\rightarrow {\\mathcal {R}}\\] be a surjective map. We show that (1) \\[\\Phi \\] satisfies \\[{}_*[\\Phi (A),\\Phi (B)] = {{}_*[A,B] }\\] for all \\[A, B\\in {\\mathcal {R}}\\] if and only if there exists \\[\\lambda \\in \\{-1,1\\}\\] such that \\[\\Phi (A)=\\lambda A\\] for all \\[A\\in {\\mathcal {R}}\\]; (2) \\[\\Phi \\] satisfies \\[{}_*[\\Phi (A),\\Phi (B)]_2= {{}_*[A,B]_2}\\] for all \\[A, B\\in {\\mathcal {R}}\\] if and only if there exists \\[\\lambda \\in {\\mathcal {C}}_S \\] with \\[\\lambda ^{3} = I\\] such that \\[\\Phi (A) = \\lambda A \\] for all \\[A \\in {\\mathcal {R}}\\], where I is the unit of \\[{\\mathcal {R}}\\] and \\[{\\mathcal {C}}_S \\] is the symmetric extend centroid of \\[{\\mathcal {R}}\\]. This is then applied to prime \\[\\hbox {C}^*\\]-algebras, factor von Neumann algebras and indefinite self-adjoint standard operator algebras to get a complete invariant for the identity map and to symmetric standard operator algebras as well as matrix algebras.

We study holomorphic maps of C2 tangent to the identity at fixed point which have degenerate characteristic directions. With the help of some new invariants, we give suficient conditions for the existence of attracting domains in these degenerate characteristic directions.

The title of this article is a paraphrase of Cherry’s seminal 1985 article, “Islands Out of the Stream: Isolation and Interaction in Early East Mediterranean Insular Prehistory,” which described the striking paucity of data in Aegean and Eastern Mediterranean insular environments prior to the Early Bronze Age period and emphatically stated the effects of insularity. Following the Anglo-Saxon bio-geographical approach to islands, Cherry asked the question of their initial colonization and searched for their connections to the adjacent mainland (Cherry 1985:14). The historiographical importance of this article lies at the initiation of the theoretical agenda of insularity and interaction, with