Suppose we have a well-solved optimization problem, such as minimum spanning tree, maximum cut in planar graphs, minimum weight perfect matching, or maximum weight independent set in a bipartite graph. How hard is it to determine whether there exists a solution with a given weight ? Papadimitriou and Yannakakis showed in [PAPADIMITRIOU 82] that these so-called exact versions of the above optimi...

Toroidal shapes are often found in bio-molecules, viruses, proteins and fats, but only recently it was proved experimentally that toroidal structures can support exotic high-frequency electromagnetic excitations that are neither electric or magnetic multipoles. Such excitations, known as toroidal moments, could be playing an important role in enhancing inter-molecular interaction and energy tra...

We show how the elusive toroidal dipole moment appears as a radiative excitation eigenmode in a metamolecule resonator that is formed by pairs of plasmonic nanorods. We analyze one such nanorod configuration—a toroidal metamolecule. We find that the radiative interactions in the toroidal metamolecule can be qualitatively represented by a theoretical model based on an electric point dipole arran...

The M-degree of an edge xy in a graph is the maximum of the degrees of x and y. The M-degree of a graph G is the minimum over M-degrees of its edges. In order to get upper bounds on the game chromatic number, He et al showed that every planar graph G without leaves and 4cycles has M-degree at most 8 and gave an example of such a graph with M-degree 3. This yields upper bounds on the game chroma...

A close relation between the optimal packing of spheres in Rd and minimal energy E (effective conductivity) composites with ideally conducting spherical inclusions is established. The location optimal-design problem yields inclusions. geometrical-packing physical-conductivity problems are stated a periodic toroidal d-dimensional space an arbitrarily fixed number n nonoverlapping per periodicity...

this paper concerns the design and analysis, of a ball type continuously variable transmission, (b-cvt). this b-cvt has a simple kinematic structure, and same as a toroidal cvt, transmits power by friction on the contact points between input and output discs, that are connected to each other by balls. after, a brief introduction of our b-cvt structure, the performance and traction efficiency of...

This paper concerns the design and analysis, of a ball type continuously variable transmission, (B-CVT). This B-CVT has a simple kinematic structure, and same as a toroidal CVT, transmits power by friction on the contact points between input and output discs, that are connected to each other by balls. After, a brief introduction of our B-CVT structure, the performa...

The spatiotemporal self-organization of viscoresistive magnetohydrodynamics in a toroidal geometry is studied. Curl-free toroidal magnetic and electric fields are imposed. It is observed in our simulations that a flow is generated, which evolves from dominantly poloidal to toroidal when the Lundquist numbers are increased. It is shown that this toroidal organization of the flow is consistent wi...

the first ($pi_1$) and the second $(pi_2$) multiplicative zagreb indices of a connected graph $g$, with vertex set $v(g)$ and edge set $e(g)$, are defined as $pi_1(g) = prod_{u in v(g)} {d_u}^2$ and $pi_2(g) = prod_{uv in e(g)} {d_u}d_{v}$, respectively, where ${d_u}$ denotes the degree of the vertex $u$. in this paper we present a simple approach to order these indices for connected graphs on ...

Three-dimensional torus is a common topology of network interconnects of multicomputers due to its simplicity and high scalability. A parallel job submitted to a three-dimensional toroidal machine typically requires an isolated, contiguous, rectangular partition connected as a mesh or a torus. Such partitioning leads to fragmentation and thus reduces resource utilization of the machines. In par...