Description:
This paper is concerned with the linkedness of Cartesian products of complete graphs. A graph with at least 2k vertices is k-linked if, for every set of 2k distinct vertices organised in arbitrary k pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We show that the Cartesian product Kd1+1 × Kd2+1 of complete graphs Kd1+1 and Kd2+1 is
Description:
This paper is concerned with the linkedness of Cartesian products of complete graphs. A graph with at least 2k vertices is k-linked if, for every set of 2k distinct vertices organised in arbitrary k pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We show that the Cartesian product Kd1+1 × Kd2+1 of complete graphs Kd1+1 and Kd2+1 is
Description:
A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least 2k vertices is k-linked if, for every set of k disjoint pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We say that a polytope is k-linked if its graph is k-linked. In a previous paper [3] we proved that every cubical d-polytope is ⌊d/2⌋-linked. Here we strengthen this result by establishing the ⌊(d+1)/2⌋-linkedness of cubical d-polytopes, for every d≠3. A graph G is strongly k-linked if it has at least 2k+1 vertices and, for every vertex v of G, the subgraph G−v is k-linked. We say that a polytope is (strongly) k-linked if its graph is (strongly) k-linked. In this paper, we also prove that every cubical d-polytope is strongly ⌊d/2⌋-linked, for every d≠3. These results are best possible for this class of polytopes.
Description:
A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least 2k vertices is k-linked if, for every set of k disjoint pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We say that a polytope is k-linked if its graph is k-linked. In a previous paper [3] we proved that every cubical d-polytope is
Description:
A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least 2k vertices is k-linked if, for every set of k disjoint pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We say that a polytope is k-linked if its graph is k-linked. In a previous paper [3] we proved that every cubical d-polytope is ⌊d/2⌋-linked. Here we strengthen this result by establishing the ⌊(d+1)/2⌋-linkedness of cubical d-polytopes, for every d≠3. A graph G is strongly k-linked if it has at least 2k+1 vertices and, for every vertex v of G, the subgraph G−v is k-linked. We say that a polytope is (strongly) k-linked if its graph is (strongly) k-linked. In this paper, we also prove that every cubical d-polytope is strongly ⌊d/2⌋-linked, for every d≠3. These results are best possible for this class of polytopes.
Description:
A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least 2k vertices is k-linked if, for every set of k disjoint pairs of vertices, there are k vertex-disjoint paths joining the vertices in the pairs. We say that a polytope is k-linked if its graph is k-linked. In a previous paper [3] we proved that every cubical d-polytope is
Description:
Delamination is a typical failure mode of composite materials caused by weak bonding. It arises when a crack initiates and propagates under a destructive loading. Given the physical law characterizing the properties of the interlayer adhesive between the bonded bodies, we consider the problem of computing the propagation of the crack front and the stress field along the contact boundary. This leads to a hemivariational inequality, which after discretization by finite elements we solve by a nonconvex bundle method, where upper- C 1 criteria have to be minimized. As this is in contrast with other classes of mechanical problems with non-monotone friction laws and in other applied fields, where criteria are typically lower- C 1 , we propose a bundle method suited for both types of nonsmoothness. We prove its global convergence in the sense of subsequences and test it on a typical delamination problem of material sciences.
Description:
We associate with each convex optimization problem posed on some locally convex space with an infinite index set T, and a given non-empty family H formed by finite subsets of T, a suitable Lagrangian-Haar dual problem. We provide reverse H-strong duality theorems, H-Farkas type lemmas and optimality theorems. Special attention is addressed to infinite and semi-infinite linear optimization problems.
Description:
Background: There has been a rapid shift toward the adoption of virtual health care services in Australia. It is unknown how widely virtual care has been implemented or evaluated for the care of older adults in Australia. Objective: We aimed to review the literature evaluating virtual care initiatives for older adults across a wide range of health conditions and modalities and identify key challenges and opportunities for wider adoption at both patient and system levels in Australia. Methods: A scoping review of the literature was conducted. We searched MEDLINE, Embase, PsycINFO, CINAHL, AgeLine, and gray literature (January 1, 2011, to March 8, 2021) to identify virtual care initiatives for older Australians (aged
Description:
Background: There has been a rapid shift toward the adoption of virtual health care services in Australia. It is unknown how widely virtual care has been implemented or evaluated for the care of older adults in Australia. Objective: We aimed to review the literature evaluating virtual care initiatives for older adults across a wide range of health conditions and modalities and identify key challenges and opportunities for wider adoption at both patient and system levels in Australia. Methods: A scoping review of the literature was conducted. We searched MEDLINE, Embase, PsycINFO, CINAHL, AgeLine, and gray literature (January 1, 2011, to March 8, 2021) to identify virtual care initiatives for older Australians (aged
Description:
The paper presents a comparative study of the finite element method (FEM) and the scaled boundary finite element method (SBFEM) for the numerical evaluation of the volume‐averaged stress of composites. Two‐dimensional meso‐scale models of concrete represented by digital images and discretized using an automatic mesh generation algorithm are considered. The different computational approaches are discussed and compared with respect to accuracy and efficiency for both scenarios.
Description:
Mobile devices are widely used for uploading/downloading media files such as audio, video and images to/from the remote servers. These devices have limited resources and are required to offload resource-consuming media processing tasks to the clouds for further processing. Migration of these tasks means that the media services provided by the clouds need to be authentic and trusted by the mobile users. The existing schemes for secure exchange of media files between the mobile devices and the clouds have limitations in terms of memory support, processing load, battery power, and data size. These schemes lack the support for large-sized video files and are not suitable for resource-constrained mobile devices. This paper proposes a secure, lightweight, robust, and efficient scheme for data exchange between the mobile users and the media clouds. The proposed scheme considers High Efficiency Video Coding (HEVC) Intra-encoded video streams in unsliced mode as a source for data hiding. Our proposed scheme aims to support real-time processing with power-saving constraint in mind. Advanced Encryption Standard (AES) is used as a base encryption technique by our proposed scheme. The simulation results clearly show that the proposed scheme outperforms AES-256 by decreasing the processing time up to 4.76% and increasing the data size up to 0.72% approximately. The proposed scheme can readily be applied to real-time cloud media streaming.