Detecting Fixed Patterns in Chordal Graphs in Polynomial Time

The Contractibility problem takes as input two graphs G and H, and the task is to decide whether H can be obtained from G by a sequence of edge contractions. The Induced Minor and Induced Topological Minor problems are similar, but the first allows both edge contractions and vertex deletions, whereas the latter allows only vertex deletions and vertex dissolutions. All three problems are NP-complete, even for certain fixed graphs H. We show that these problems can be solved in polynomial time for every fixed H when the input graph G is chordal. Our results can be considered tight, since these problems are known to be W[1]-hard on chordal graphs when parameterized by the size of H. To solve Contractibility and Induced Minor, we define and use a generalization of the classic Disjoint Paths problem, where we require the vertices of each of the k paths to be chosen from a specified set. We prove that this variant is NP-complete even when k=2, but that it is polynomial-time solvable on chordal graphs for every fixed k. Our algorithm for Induced Topological Minor is based on another generalization of Disjoint Paths called Induced Disjoint Paths, where the vertices from different paths may no longer be adjacent. We show that this problem, which is known to be NP-complete when k=2, can be solved in polynomial time on chordal graphs even when k is part of the input. Our results fit into the general framework of graph containment problems, where the aim is to decide whether a graph can be modified into another graph by a sequence of specified graph operations. Allowing combinations of the four well-known operations edge deletion, edge contraction, vertex deletion, and vertex dissolution results in the following ten containment relations: (induced) minor, (induced) topological minor, (induced) subgraph, (induced) spanning subgraph, dissolution, and contraction. Our results, combined with existing results, settle the complexity of each of the ten corresponding containment problems on chordal graphs.     

Development of monolithic catalysts with low noble metal content for diesel vehicle emission control

Topics in Catalysis - Monolith washcoated catalysts with potential for diesel emission control have been developed. Two types of catalysts have been prepared for further study: (1) MnO x supported...     

Target following with motion prediction for unmanned surface vehicle operating in cluttered environments

The capability of following a moving target in an environment with obstacles is required as a basic and necessary function for realizing an autonomous unmanned surface vehicle (USV). Many target following scenarios involve a follower and target vehicles that may have different maneuvering capabilities. Moreover, the follower vehicle may not have prior information about the intended motion of the target boat. This paper presents a trajectory planning and tracking approach for following a differentially constrained target vehicle operating in an obstacle field. The developed approach includes a novel algorithm for computing a desired pose and surge speed in the vicinity of the target boat, jointly defined as a motion goal, and tightly integrates it with trajectory planning and tracking components of the entire system. The trajectory planner generates a dynamically feasible, collision-free trajectory to allow the USV to safely reach the computed motion goal. Trajectory planning needs to be sufficiently fast and yet produce dynamically feasible and short trajectories due to the moving target. This required speeding up the planning by searching for trajectories through a hybrid, pose-position state space using a multi-resolution control action set. The search in the velocity space is decoupled from the search for a trajectory in the pose space. Therefore, the underlying trajectory tracking controller computes desired surge speed for each segment of the trajectory and ensures that the USV maintains it. We have carried out simulation as well as experimental studies to demonstrate the effectiveness of the developed approach.     

The formation of minerals in a chromite-periclase refractory produced from fused materials and its wear in the roof of an open-hearth furnace

Refractories and Industrial Ceramics - An analysis was carried out of certain aspects of the zone-forming process in the roof brick of open-hearth furnaces. It was established that three fissure...     

Use of torch guniting for the repair of open-hearth furnace linings

Conclusions The method and equipment for torch guniting of converters require changes for use in open hearths.It is necessary to develop guniting nozzle designs providing earlier ignition of the fuel and combustion of it in a straight-flow flame.Translated from Ogneupory, No. 3, pp. 44–46, March, 1987.For the start of the discussion see No. 11, 1986 and the continuation No. 12, 1986 and Nos. 1 and 2, 1987.     

The Importance of Long-Term Observations in Assessing the Strength of Polycaproamide Fibre

According to long-term observations, rewinding and slubbing operations have almost no effect on the unit strength of complex and slubbed polycaproamide fibres but affect the relative elongation at break. The stability of the deformation-strength properties of the fibres in time, assessed with the values of the coefficients of variation, during the manufacturing process, including slubbing, improves significantly. The fibre strength is not a function of fluctuations in the content of low-molecular-weight compounds in the initial polymer and its relative viscosity, spinning temperature, and elementary fibre thickness in the undrawn fibre in contrast to the moisture content of polymer going to spinning and the degree of orientational drawing of the fibre.     

High-temperature catalysts with a synergetic effect of Pd and manganese oxides

A synergetic effect in the catalytic activity has been found after palladium introduction in Mn–Al–O systems. The magnitude of the synergetic effect depends on the types of the oxidic manganese species: oxide Mn₃O₄, spinel (Mn, Mg)[Mn, Al]₂O₄ or hexaaluminate (Mn, Mg)LaAl₁₁O₁₉. The synergetic effect of Pd and manganese-containing compounds is observed only if palladium is introduced to the low-temperature precursor of the manganese alumina spinel or manganese hexaaluminate. The synergetic effect is not observed when high-temperature samples with formed spinel or hexaaluminate phases are modified with Pd.