Let ? be a K -invariant compactly supported distribution on noncompact Riemannian symmetric space X = G / . If the spherical Fourier transform ˜ ( ? ) is slowly decreasing, it known that right convolution operator c : f ? ? maps E onto In this paper, we prove converse of result. We also has fundamental solution if and only decreasing.

We show that the additive Borcherds lifts of vector-valued non-holomorphic Eisenstein series are orthogonal for [Formula: see text]. Using this we give another proof they have a meromorphic continuation, calculate their Fourier expansion and functional equation analogous to classical case. Moreover, will investigate image lift sufficient condition surjectivity.

Contents Introduction 2 1. Homology theory and cycle map 6 2. Kato homology 11 3. Vanishing theorem 15 4. Bertini theorem over a discrete valuation ring 19 5. Surjectivity of cycle map 22 6. Blowup formula 24 7. A moving lemma 26 8. Proof of main theorem 28 9. Applications of main theorem 31 Appendix A. Resolution of singularities for embedded curves 34 References 39

Linear cellular automata have a canonical representation in terms of labeled de Bruijn graphs. We will show that these graphs, construed as semiautomata, provide a natural setting for the study of cellular automata. For example, we give a simple algorithm to determine reversibility and surjectivity of the global maps. We also comment on Wolfram’s question about the growth rates of the minimal f...

Linear cellular automata have a canonical representation in terms of labeled de Bruijn graphs. We will show that these graphs, construed as semiau-tomata, provide a natural setting for the study of cellular automata. For example, we give a simple algorithm to determine reversibility and surjectivity of the global maps. We also comment on Wolfram's question about the growth rates of the minimal ...

The evolution of one-way infinite cellular automata can be described by the firstorder theory of phase-space, which uses one-step evolution as its main predicate. Formulas in this logic can be used to express properties of the global map such as surjectivity. A complete implementation of the decision algorithm is provided, as well as methods for manipulating the Büchi automata on which the deci...