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1,251 result(s) for "Pendant"
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Ascending Bi-Pendant Domination Decomposition of Path and Cycle
Let G = ( V , E ) be a simple connected graph. A pendant dominating set S of a graph G is a bi-pendant dominating set if V - S also contains pendant vertex. The least cardinality of the bi-pendant dominating set in G is called the bi-pendant domination number of G denoted by γ b p e ( G ). If G 1 , G 2 , G 3 , …, G n are connected edge disjoint sub graphs of G with E ( G ) = E ( G 1 ) ∪ E ( G 2 ) ∪ E ( G 3 ) …∪ E ( G n ), then G 1 , G 2 , G 3 , …, G n is said to be decomposition of G. In this paper, we define Ascending Bi-Pendant Domination Decomposition (ABPDD) and discuss the values of m in P m and C m which admits APBDD into n -parts.
Pendant Graphs: Unveiling Regularity, Irregularity, and Support Vertices
This paper investigates Pendant Graphs, which are graphs that contain pendant vertices. It introduces a new perspective on the regularity and irregularity of pendant graphs, and discusses their relationship with Highly Irregular Graphs. Additionally, this work introduces a novel graph based on the concept derived from (m, k) Regular Graphs. The (m, k) regular graphs are closely related to Pendant Graph. The paper also delves into the nature and characteristics of pendant vertices. By exploring the characteristics of pendant vertices and defining the Cyclic Dendrimer Graph, the paper significantly contributes to both Graph Theory and Chemical Graph Theory.
The Sense of Semblance
Holocaust artworks intuitively must fulfill at least two criteria: artistic (lest they be merely historical documents) and historical (lest they distort the Holocaust or become merely artworks). The Sense of Semblance locates this problematic within philosophical aesthetics, as a version of the conflict between aesthetic autonomy and heteronomy, and argues that Adorno's dialectic of aesthetic semblance describes the normative demand that artworks maintain a dynamic tension between the two. The Sense of Semblance aims to move beyond familiar debates surrounding postmodernism by demonstrating the usefulness of contemporary theories of meaning and understanding, including those from the analytic tradition. Pickford shows how the causal theory of names, the philosophy of tacit knowledge, the analytic philosophy of quotation, Sartre's theory of the imaginary, the epistemology of testimony, and Walter Benjamin's dialectical image can help explicate how individual artworks fulfill artistic and historical desiderata. In close readings of Celan's poetry, Holocaust memorials in Berlin, the quotational artist Heimrad Backer, Claude Lanzmann's film Shoah, and Art Spiegelman's graphic novel Maus, Pickford offers interpretations that, in their precision, specificity, and clarity, inaugurate a dialogue between contemporary analytic philosophy and contemporary art. The Sense of Semblance is the first book to incorporate contemporary analytic philosophy in interpretations of art and architecture, literature, and film about the Holocaust.
Estonian sheet pendants from the 11th to the 13th century: chronological aspects: Department of Archaeology, Institute of History and Archaeology, University of Tartu, Ulikooli 18, 50090 Tartu, Estonia
Sheet pendants are Christian-symbolic metal plate pendants that were widespread in Estonia from the 11th to the 17th century, with at least 1115 items found. This article focuses on Estonian sheet pendants from the 11th to the 13th century, aiming to refine their dating. Among the 222 known Estonian sheet pendants from this period, 30 can be confidently dated to the 11th century, two to the 11th century or the very beginning of the 12th century, one to the 11th-12th centuries, 159 to the 13th century, and 30 to the 12th-13th centuries. No sheet pendants have been found in Estonia that can be exclusively dated to the 12th century. It remains unclear whether sheet pendants were not worn as jewellery in Estonia during the 12th century or whether this chronological distribution of the sheet pendants under study reflects the current state of research, methodological issues in archaeology, or historical events. The article proposes several hypotheses to explain this chronological distribution. Future research will be required to determine whether any of these hypotheses are correct. KEYWORDS archaeology, Viking Ages, Middle Ages, jewellery, sheet pendants.
Mechanically Robust, Recyclable, and Self‐Healing Polyimine Networks
To achieve energy saving and emission reduction goals, recyclable and healable thermoset materials are highly attractive. Polymer copolymerization has been proven to be a critical strategy for preparing high‐performance polymeric materials. However, it remains a huge challenge to develop high‐performance recyclable and healable thermoset materials. Here, polyimine dynamic networks based on two monomers with bulky pendant groups, which not only displayed mechanical properties higher than the strong and tough polymers, e.g., polycarbonate, but also excellent self‐repairing capability and recyclability as thermosets are developed. Owing to the stability of conjugation effect by aromatic benzene rings, the final polyimine networks are far more stable than the reported counterparts, exhibiting excellent hydrolysis resistance under both alkaline condition and most organic solvents. These polyimine materials with conjugation structure can be completely depolymerized into monomers recovery in an acidic aqueous solution at ambient temperature. Resulting from the bulky pendant units, this method allows the exchange reactions of conjugation polyimine vitrimer easily within minutes for self‐healing function. Moreover, the introduction of trifluoromethyl diphenoxybenzene backbones significantly increases tensile properties of polyimine materials. This work provides an effective strategy for fabricating high‐performance polymer materials with multiple functions. CO‐polyimine materials (PIMs) films are successfully synthesized by copolymerization and evaluated. Owing to the presence of π–π conjugation effects and steric effects as well as the high cross‐linking density of dynamic imine bonds, CO‐PIMs films as thermosets not only exhibit excellent mechanical strength and self‐healable behavior, water, and solvent resistance but also closed‐loop recycling.
Maximal hitting times for random walks on bicyclic graphs with a given number of pendant vertices
Let HG (x, y) be the expected hitting time from vertex x to vertex y for the first time on a simple connected graph G and φ(G) = maxx,y∈V(G) HG (x, y). Let G n t be the set of simple connected graphs with n vertices and t pendant vertices. In this paper, we proved the upper bound of the φ(G) for G ∈ G n t and determined the extremal graph in all n-vertex bicyclic graphs with given t pendant vertices.
Interplay of electro thermo solutal advection and internal electrohydrodynamics governed enhanced evaporation of droplets
The article experimentally examines and theoretically establishes the influence of electric field on the evaporation kinetics of pendant droplets. It is observed that the evaporation of saline-pendant droplets can be augmented by the application of an external alternating electric field. The evaporation behaviour is modulated by an increase in the field strength and frequency. The classical diffusion driven evaporation model is found insufficient in predicting the improved evaporation rates. The change in surface tension due to field constraint is also unable to explain the observed physics. Consequently, the internal hydrodynamics of the droplet is investigated through particle image velocimetry. The electric field is found to induce enhanced internal advection, which improves the evaporation rates. A scaled analytical model is proposed to quantify the role of internal electrohydrodynamics, electro-thermal and electro-solutal effects. Stability maps reveal that the advection is caused nearly equally by the electro-solutal and electro-thermal effects within the droplet. The model is able to illustrate the influence played by the governing thermal and solutal Marangoni number, the electro-Prandtl and electro-Schmidt number, and the associated electrohydrodynamic number. The magnitude of the internal circulation can be predicted by the proposed model, which validates the proposed mechanism.
Laplacian eigenvalue distribution based on some graph parameters
Let G be a connected graph on n vertices. For an interval I, denote by mGI the number of Laplacian eigenvalues of G which lie in I. In this paper, we obtain several bounds on mGI in terms of various structural parameters of the graph G, including chromatic number, pendant vertices, and the number of vertices with degree n − 1.