The present investigation is motivated by finding and developing an easily understandable solution in the context of unified quantum and gravitational theories. Model-based methods are applied, with emphasis on struct...The present investigation is motivated by finding and developing an easily understandable solution in the context of unified quantum and gravitational theories. Model-based methods are applied, with emphasis on structural descriptions by introducing some strong hypotheses. A subset of the introduced hypotheses led to a surprising understanding of the internal structure and construction of quarks, neutrons, protons and more complex atomic nuclei. The research work therefore focused mainly on the model-based interpretation of subatomic processes. The results obtained so far and presented in this paper are new. They consist of a generic description model for the structure of atomic nuclei. This model contains two important structural links that originate from the initial phase of the cosmological big bang. They hold atomic parts together and are involved in many known nuclear fusion and fission processes. Modifications of them, including the electron-positron annihilation process, are necessary and will be described. A new interpretation of the strong forces from the Standard Model is possible and will be given. In addition, the formation processes for electron and positron particles are considered. Based on the structural relationships, a deeper understanding of matter transformations (transmutations), early cosmological processes and dark matter has been achieved. All challenges of this work are the logical conclusions from the used hypotheses on two structural links. They need to be further investigated and verified by theoretical and experimental works. The postulated particle in this paper, as accompanying product in the electron-positron annihilation, will play a major role for the future investigations.展开更多
This paper deals with the FEEDBACK VERTEX SET problem on undirected graphs, which asks for the existence of a vertex set of bounded size that intersects all cycles. Due it is theoretical and practical importance,the p...This paper deals with the FEEDBACK VERTEX SET problem on undirected graphs, which asks for the existence of a vertex set of bounded size that intersects all cycles. Due it is theoretical and practical importance,the problem has been the subject of intensive study. Motivated by the parameter ecology program we attempt to classify the parameterized and kernelization complexity of FEEDBACK VERTEX SET for a wide range of parameters.We survey known results and present several new complexity classifications. For example, we prove that FEEDBACK VERTEX SET is fixed-parameter tractable parameterized by the vertex-deletion distance to a chordal graph. We also prove that the problem admits a polynomial kernel when parameterized by the vertex-deletion distance to a pseudo forest, a graph in which every connected component has at most one cycle. In contrast, we prove that a slightly smaller parameterization does not allow for a polynomial kernel unless NP coNP=poly and the polynomial-time hierarchy collapses.展开更多
文摘The present investigation is motivated by finding and developing an easily understandable solution in the context of unified quantum and gravitational theories. Model-based methods are applied, with emphasis on structural descriptions by introducing some strong hypotheses. A subset of the introduced hypotheses led to a surprising understanding of the internal structure and construction of quarks, neutrons, protons and more complex atomic nuclei. The research work therefore focused mainly on the model-based interpretation of subatomic processes. The results obtained so far and presented in this paper are new. They consist of a generic description model for the structure of atomic nuclei. This model contains two important structural links that originate from the initial phase of the cosmological big bang. They hold atomic parts together and are involved in many known nuclear fusion and fission processes. Modifications of them, including the electron-positron annihilation process, are necessary and will be described. A new interpretation of the strong forces from the Standard Model is possible and will be given. In addition, the formation processes for electron and positron particles are considered. Based on the structural relationships, a deeper understanding of matter transformations (transmutations), early cosmological processes and dark matter has been achieved. All challenges of this work are the logical conclusions from the used hypotheses on two structural links. They need to be further investigated and verified by theoretical and experimental works. The postulated particle in this paper, as accompanying product in the electron-positron annihilation, will play a major role for the future investigations.
基金supported by the European Research Council through Starting Grant 306992 "Parameterized Approximation"
文摘This paper deals with the FEEDBACK VERTEX SET problem on undirected graphs, which asks for the existence of a vertex set of bounded size that intersects all cycles. Due it is theoretical and practical importance,the problem has been the subject of intensive study. Motivated by the parameter ecology program we attempt to classify the parameterized and kernelization complexity of FEEDBACK VERTEX SET for a wide range of parameters.We survey known results and present several new complexity classifications. For example, we prove that FEEDBACK VERTEX SET is fixed-parameter tractable parameterized by the vertex-deletion distance to a chordal graph. We also prove that the problem admits a polynomial kernel when parameterized by the vertex-deletion distance to a pseudo forest, a graph in which every connected component has at most one cycle. In contrast, we prove that a slightly smaller parameterization does not allow for a polynomial kernel unless NP coNP=poly and the polynomial-time hierarchy collapses.
