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Quadratic embedding constants of hairy cycle graphs
The quadratic embedding (QE) class of the connected graph G = (V, E) is determined based on its quadratic embedding constant (QEC) of the distance matrix graph G. The distance matrix is a conditionally definite negative, or equivalently if it admits a quadratic embedding in a Hilbert space, or if QEC of the graph G is non-positive. In this study, the classification for the hairy cycle graphs such as bearded cycle graph BC(k,m) for k is even, bearded cycle graph BC(3,m) and broken sun graph BC(4,m) will be calculated, and we derive the formulae of its QEC. These classes of graphs belongs to the QE class.
Journal Article
The spatiality of emotion in early modern China : from dreamscapes to theatricality
\"Emotion takes place. Rather than an interior state of mind in response to the outside world, emotion per se is spatial, at turns embedding us from without, transporting us somewhere else, or putting us ahead of ourselves. In this book, Ling Hon Lam gives a deeply original account of the history of emotions in Chinese literature and culture centered on the idea of emotion as space, which the Chinese call \"emotion-realm\" (qingjing). Lam traces how the emotion-realm underwent significant transformations from the dreamscape to theatricality in sixteenth- to eighteenth-century China. Whereas medieval dreamscapes delivered the subject into one illusory mood after another, early modern theatricality turned the dreamer into a spectator who is no longer falling through endless oneiric layers but pausing in front of the dream. Through the lens of this genealogy of emotion-realms, Lam remaps the Chinese histories of morals, theater, and knowledge production, which converge at the emergence of sympathy, redefined as the dissonance among the dimensions of the emotion-realm pertaining to theatricality.The book challenges the conventional reading of Chinese literature as premised on interior subjectivity, examines historical changes in the spatial logic of performance through media and theater archaeologies, and ultimately uncovers the different trajectories that brought China and the West to the convergence point of theatricality marked by self-deception and mutual misreading. A major rethinking of key terms in Chinese culture from a comparative perspective, The Spatiality of Emotion in Early Modern China develops a new critical vocabulary to conceptualize history and existence.\"-- Provided by publisher.
Book
On the differential structure of metric measure spaces and applications
The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the
duality relations between differentials and gradients of Sobolev functions. This will be achieved without calling into play any sort of
analysis in charts, our assumptions being: the metric space is complete and separable and the measure is Radon and non-negative. (ii) To
employ these notions of calculus to provide, via integration by parts, a general definition of distributional Laplacian, thus giving a
meaning to an expression like
eBook
Applied nonlinear functional analysis : an introduction
The aim of this book is to provide a concise but complete introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in economics, engineering, and physics. This volume gathers the mathematical background needed in order to conduct research or to deal with theoretical problems and applications using the tools of nonlinear functional analysis.
Contents
Basic Topology
Measure Theory
Basic Functional Analysis
Banach Spaces of Functions and Measures
Convex Functions – Nonsmooth Analysis
Nonlinear Analysis
eBook
A blueprint for demonstrating quantum supremacy with superconducting qubits
Quantum information scientists are getting closer to building a quantum computer that can perform calculations that a classical computer cannot. It has been estimated that such a computer would need around 50 qubits, but scaling up existing architectures to this number is tricky. Neill et al. explore how increasing the number of qubits from five to nine affects the quality of the output of their superconducting qubit device. If, as the number of qubits grows further, the error continues to increase at the same rate, a quantum computer with about 60 qubits and reasonable fidelity might be achievable with current technologies. Science , this issue p. 195 Scaling of errors and output with the number of qubits is explored in a five- to nine-qubit device. A key step toward demonstrating a quantum system that can address difficult problems in physics and chemistry will be performing a computation beyond the capabilities of any classical computer, thus achieving so-called quantum supremacy. In this study, we used nine superconducting qubits to demonstrate a promising path toward quantum supremacy. By individually tuning the qubit parameters, we were able to generate thousands of distinct Hamiltonian evolutions and probe the output probabilities. The measured probabilities obey a universal distribution, consistent with uniformly sampling the full Hilbert space. As the number of qubits increases, the system continues to explore the exponentially growing number of states. Extending these results to a system of 50 qubits has the potential to address scientific questions that are beyond the capabilities of any classical computer.
Journal Article
Atlas of the Irish rural landscape
\"The second edition of Atlas of the Irish Rural Landscape is a magnificently illustrated, beautifully written, and thoroughly updated introduction to the hidden riches of the Irish landscape. Topics include archaeology, field and settlement patterns, houses, demesnes, villages and small towns, monuments, woodland, bogs, roads, canals, and a host of other features. The Atlas combines superbly chosen illustrations and cartography with a text amenable to a general reader. Hundreds of maps, diagrams, photographs, and paintings present accessible information suitable for any school, college, or home. New content in the contemporary section takes into account the Celtic Tiger and explores six fresh case studies - Tory Island (Donegal), the Wicklow Uplands, Inistiogue (County Kilkenny), Aughris (County Sligo), Clonfert (County Galway), and Point Lance in Newfoundland. This second edition of the award-winning Atlas of the Irish Rural Landscape continues to increase the visibility of the landscape within national heritage while establishing a proper basis for conservation and planning\"--Publisher description.
Book
A Strong Convergence Theorem for Solving Pseudo-monotone Variational Inequalities Using Projection Methods
Several iterative methods have been proposed in the literature for solving the variational inequalities in Hilbert or Banach spaces, where the underlying operator A is monotone and Lipschitz continuous. However, there are very few methods known for solving the variational inequalities, when the Lipschitz continuity of A is dispensed with. In this article, we introduce a projection-type algorithm for finding a common solution of the variational inequalities and fixed point problem in a reflexive Banach space, where A is pseudo-monotone and not necessarily Lipschitz continuous. Also, we present an application of our result to approximating solution of pseudo-monotone equilibrium problem in a reflexive Banach space. Finally, we present some numerical examples to illustrate the performance of our method as well as comparing it with related method in the literature.
Journal Article