Blockchain Papers

Ramiro Fontes

We study the Banach dual of the one-parameter stochastic integral δ_L(u) = ∫₀^T u_t dL_t for a symmetric γ-stable Lévy process with γ ∈ (1,2). The natural integrand exponent is p ∈ (1,γ): the small-jump integrability ∫|z|^p ν_γ(dz) < ∞ holds iff p < γ, so this is not an arbitrary L^p but the unique scale dictated by the singularity of the Lévy measure at the origin. On this scale, the operator-covariant derivative D_L := δ_L^* : L^q(Ω) → H_L^* is the Banach dual of the one-parameter integral. Since p < 2, the Riesz identification H_L^* ≅ H_L is unavailable, and the Banach setting is forced. The principal result is structural: D_L is strictly more restricted than the standard Malliavin add-a-point operator D_{t,z}F = F(ω + δ_(t,z)) − F(ω) on Poisson space, which is the dual of the full two-parameter compensated Poisson integral ∫∫ h(s,z) Ñ(ds,dz). By Lévy-Itô, the one-parameter integrand of δ_L has the special form h(s,z) = u(s) · z — linear in z — whereas full martingale representation on Lévy space uses general h(s,z). The representability obstruction quantifies the resulting gap precisely: centered functionals depending nonlinearly on jump sizes — canonically, the centered large-jump count #{|ΔL_s| > 1} − E[#{|ΔL_s| > 1}] — lie in ker(D_L) yet are detected by the standard add-a-point operator. The obstruction is a property of the one-parameter integral, not a feature of jump processes themselves. The factorization (Theorem A) holds on the closed proper subspace im(δ_L) ⊊ L^p_0(Ω) and characterizes precisely which functionals admit one-parameter representation. Theorem B (product rule with Leibniz defect) is a standalone duality identity: its proof uses only the definition of D_L, the Lévy-Itô formula, and Hölder's inequality, and it does not invoke (H3) or the factorization machinery. Theorem C — the strongest technical result — identifies ker(D_L) and the annihilator of im(δ_L) via L^q-L^p truncation in the jump variable, showing the annihilator is infinite-dimensional even within the first chaos. The framework has been formally verified in the Lean 4 proof assistant (2,439 lines, zero sorry, zero axioms) using Mathlib. To our knowledge, this is the first formalization of the operator-covariant derivative framework with its representability obstruction in any proof assistant. The formalization includes proved Poisson mean and variance identities, a constructed compound Poisson path, a compensated-integral interface with derived Banach-side consequences, a concrete first-chaos orthogonality model, and the full abstract theorem pipeline — all machine-checked from clearly isolated stochastic-analysis assumptions.

Odetunde OS Taiwo OA

In 1990s the government adopted D-by-D policy with a very good intention of reforming its local governments and let them enjoy the decision making powers promised by the D-by-D policy. One of the crucial of elements of decentralization was fiscal decentralization which gives the local jurisdictions to exercise adequate authority over important decisions with regard to setting development priorities, financing local services, revenue mobilization and expenditure authority continue. This article explored the perception of council on exercise of their fiscal authority in selected local authorities in Tanzania. The findings show that council exercise reasonable authority over revenues mobilization, the setting of the local tax rates and full expenditure authority over the locally generated revenue and also the discretionary grants.

Ruy de Queiroz, Luiz Carlos Pereira, Edward Hermann Hæusler

This volume contains the Proceedings of the 10th Workshop on Logic, Language, Information and Computation (WoLLIC'2003). The Workshop was held in Ouro Preto, Minas Gerais, Brazil from July 29 to August 1, 2003, in the Escola de Minas of the Universidade Federal de Ouro Preto ( UFOP ). WoLLIC is a series of workshops which started in 1994 with the aim of fostering interdisciplinary research in pure and applied logic . The idea is to provide a forum which is large enough in the number of possible interactions between logic and the sciences related to information and computation, and yet is small enough to allow for concrete and useful interaction among participants. Previous versions were held at: Recife (Pernambuco, Brazil) in 1994 and 1995; Salvador (Bahia, Brazil) in 1996; Fortaleza (Ceará, Brazil) in 1997; São Paulo (Brazil) in 1998; Itatiaia (Rio de Janeiro, Brazil) in 1999; Natal (Rio Grande do Norte) in 2000; Brasília (Distrito Federal, Brazil) in 2001; Rio de Janeiro (Brazil) in 2002. Scientific sponsorship comes from the Interest Group in Pure and Applied Logics ( IGPL ), the European Association for Logic, Language and Information ( FoLLI ), the Association for Symbolic Logic ( ASL ), European Association for Theoretical Computer Science ( EATCS ), the Sociedade Brasileira de Computação ( SBC ), and the Sociedade Brasileira de Lógica ( SBL ). Funding was kindly given by:(i) CNPq ( Conselho Nacional de Desenvolvimento Científico e Tecnológico , the scientific and technological development council of the Brazilian Ministério da Ciência e Tecnologia ) (grant 450709/2003-5);(ii) CAPES ( Fundação Coordenação de Apoio ao Aperfeiçoamento de Pessoal de Nível Superior , a Foundation for the Development of Higher-Education under the Brazilian Ministério da Educação e do Desporto ) (grant PAEP0565/03);(iii) FAPEMIG ( Fundação de Amparo à Pesquisa do Estado de Minas Gerais , the Minas Gerais state foundation for the support of scientific research);(iv) Escola de Minas da UFOP ( Universidade Federal de Ouro Preto ). Contributions were received in the form of short papers in all areas related to logic, language, information and computation, including:pure logical systems, proof theory, model theory, algebraic logic, type theory, category theory, constructive mathematics, lambda and combinatorial calculi, program logic and program semantics, logics and models of concurrency, logic and complexity theory, proof complexity, foundations of cryptography (zero-knowledge proofs), descriptive complexity, nonclassical logics, nonmonotonic logic, logic and language, discourse representation, logic and artificial intelligence, automated deduction, foundations of logic programming, logic and computation, and logic engineering. Apart from the contributed papers (15), and the invited talks (5), the programme includes 5 tutorial lectures: 1. Algorithmic Randomness and Derandomization by Eric Allender (Department of Computer Science, Rutgers, the State University of New Jersey, USA) 2. Generalized Quantifiers by Lauri Hella (Department of Mathematics, Statistics and Philosophy, University of Tampere, Finland) 3. Implicit computational complexity by Jean-Baptiste Joinet (Preuves-Programmes-Systèmes, Université Paris 7, France) 4. Proof search foundations for logic programming by Dale Miller (INRIA/Futurs/Saclay, and Laboratoire d'Informatique, École Polytechnique, France) 5. Iterated theory change by Hans Rott (Institut für Philosophie, Universität Regensburg, Germany) All papers in the volume were reviewed by the program committee consisting of Mauricio Ayala-Rinóon ( Departamento de Matemática, Universidade de Brasília, Brazil ) Argimiro Arratia ( Depto. Matematicas, Universidad Simon Bolivar, Venezuela ) Alessandra Carbone ( Institut des Hautes Études Scientifiques, and Université de Paris XII, France ) Marcelo Coniglio ( Centro de Lógica e Epistemologia, Universidade Estadual de Campinas, Brazil ) Gilles Dowek ( INRIA, France ) Arnaud Fleury ( Facoltà di Scienze, Università di Verona, Italy ) Dexter Kozen ( Cornell University, USA ) Maarten Marx ( ILLC, Faculty of Science, Universiteit Amsterdam, The Netherlands ) Anto˚nio Carlos da Rocha Costa ( Escola de Informática, Universidade Católica de Pelotas, Brazil ) Dieter Spreen ( Fachbereich Mathematik, Theoretische Informatik, Universität Siegen, Germany ) Luiz Carlos Pereira ( Departamento de Filosofia, PUC-Rio and UFRJ, Brazil ) Jouko Väänänen ( Department of Mathematics, University of Helsinki, Finland ) Renata Wassermann ( Departamento de Cie˚ncia da Computação, Instituto de Matemática e Estatística, Universidade de São Paulo, Brazil ) The organising committee consisted of Lucília Figueiredo ( Departamento de Computação, Universidade Federal de Ouro Preto, Brazil ) Fred Ulisses Maranhão ( Centro de Informática, Universidade Federal de Pernambuco, Brazil ) Anjolina Grisi de Oliveira ( Center of Informatics, Universidade Federal de Pernambuco, Brazil ) Elaine Pimentel ( Departamento de Matemática, Universidade Federal de Minas Gerais, Brazil ) (Co-Chair) Ruy de Queiroz ( Center of Informatics, Universidade Federal de Pernambuco, Brazil ) (Co-Chair) Maria Angela Weiss ( Departamento de Matemática, Universidade de São Paulo, Brazil ) The volume will be published as volume 84 in the series Electronic Notes in Theoretical Computer Science ( ENTCS ). This series is published electronically through the facilities of Elsevier B.V. and its auspices. The volumes in the ENTCS series can be accessed at the URL http://www.elsevier.nl/locate/entcs A printed version of the current volume has been distributed to the participants at the workshop in Ouro Preto. We are very grateful to the following persons, whose help has been crucial for the success of WoLLIC'2003: Mike Mislove, one of the Managing Editors of the ENTCS series, for his assistance with the use of the ENTCS style files; Thanks are also due to the Department of Mathematics of Universidade Federal de Minas Gerais and the Department of Computing of the Universidade Federal de Ouro Preto, which has provided the logistic support to the organising committee. August 2, 2003 Ruy de Queiroz, Elaine Pimentel, Lucilia Figueiredo