2 resultados para Points and lines

em Digital Commons - Michigan Tech


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With the introduction of the mid-level ethanol blend gasoline fuel for commercial sale, the compatibility of different off-road engines is needed. This report details the test study of using one mid-level ethanol fuel in a two stroke hand held gasoline engine used to power line trimmers. The study sponsored by E3 is to test the effectiveness of an aftermarket spark plug from E3 Spark Plug when using a mid-level ethanol blend gasoline. A 15% ethanol by volume (E15) is the test mid-level ethanol used and the 10% ethanol by volume (E10) was used as the baseline fuel. The testing comprises running the engine at different load points and throttle positions to evaluate the cylinder head temperature, exhaust temperature and engine speed. Raw gas emissions were also measured to determine the impact of the performance spark plug. The low calorific value of the E15 fuel decreased the speed of the engine along with reduction in the fuel consumption and exhaust gas temperature. The HC emissions for E15 fuel and E3 spark plug increased when compared to the base line in most of the cases and NO formation was dependent on the cylinder head temperature. The E3 spark plug had a tendency to increase the temperature of the cylinder head irrespective of fuel type while reducing engine speed.

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This dissertation concerns the intersection of three areas of discrete mathematics: finite geometries, design theory, and coding theory. The central theme is the power of finite geometry designs, which are constructed from the points and t-dimensional subspaces of a projective or affine geometry. We use these designs to construct and analyze combinatorial objects which inherit their best properties from these geometric structures. A central question in the study of finite geometry designs is Hamada’s conjecture, which proposes that finite geometry designs are the unique designs with minimum p-rank among all designs with the same parameters. In this dissertation, we will examine several questions related to Hamada’s conjecture, including the existence of counterexamples. We will also study the applicability of certain decoding methods to known counterexamples. We begin by constructing an infinite family of counterexamples to Hamada’s conjecture. These designs are the first infinite class of counterexamples for the affine case of Hamada’s conjecture. We further demonstrate how these designs, along with the projective polarity designs of Jungnickel and Tonchev, admit majority-logic decoding schemes. The codes obtained from these polarity designs attain error-correcting performance which is, in certain cases, equal to that of the finite geometry designs from which they are derived. This further demonstrates the highly geometric structure maintained by these designs. Finite geometries also help us construct several types of quantum error-correcting codes. We use relatives of finite geometry designs to construct infinite families of q-ary quantum stabilizer codes. We also construct entanglement-assisted quantum error-correcting codes (EAQECCs) which admit a particularly efficient and effective error-correcting scheme, while also providing the first general method for constructing these quantum codes with known parameters and desirable properties. Finite geometry designs are used to give exceptional examples of these codes.