Table of contents

Contents § 0. Introduction § 1. General gamma functions § 2. Series of exponential type § 3. The operators of u-differentiation and u-exponentials § 4. Many-dimensional analogues § 5. Series of hypergeometric type § 6. General u-hypergeometric systems

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Contents Introduction § 1. The concept of hyperidentity. Hyperidentities of binary representations 1.1. The concept of hyperidentity: examples 1.2. Binary Cayley theorems for semigroups, idempotent and commutative semigroups, groups and the multiplicative groups of fields 1.3. Stochastic algebras. The concept of coidentity § 2. The category of algebras of the same arithmetic type 2.1. Homomorphisms and automorphisms of algebras of the same arithmetic type 2.2. Hypervarieties of algebras § 3. The category of systems of the same arithmetic type. Nonclassical semantics in second order language § 4. Non-trivial associative and distributive hyperidentities in algebras that are invertible or close to being invertible

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Contents § 1. Introduction. The mathematical model of a tomograph § 2. Statement of results § 3. Reconstruction errors and series of oscillatory integrals § 4. Analysis of critical points § 5. Estimate of the discretization error 5.1. Preliminary remarks 5.2. Proof of Lemma 5.1 5.3. Proof of assertions 1 and 2 of Theorem 2.1 5.4. Proof of assertion 3 of Theorem 2.1 5.5. The formal convergence exponent and sharpness of the estimates 5.6. Concluding remarks Appendix. Estimates of oscillatory integrals 1. Integration by parts 2. The remainder term in the stationary phase method 3. Uniform estimates of one-dimensional oscillatory integrals 4. The regularization error 5. A special class of two-dimensional oscillatory integrals 6. Estimates of principal values of oscillatory integrals Index of notation

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