Relevant bibliographies by topics / Complete equational theories

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Complete equational theories'

Author: Grafiati
Published: 8 June 2024

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Journal articles on the topic "Complete equational theories"

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Hölldobler, Steffen. "Conditional equational theories and complete sets of transformations." Theoretical Computer Science 75, no. 1-2 (1990): 85–110. http://dx.doi.org/10.1016/0304-3975(90)90063-n.

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Cerna, David M., and Temur Kutsia. "Higher-order pattern generalization modulo equational theories." Mathematical Structures in Computer Science 30, no. 6 (2020): 627–63. http://dx.doi.org/10.1017/s0960129520000110.

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AbstractWe consider anti-unification for simply typed lambda terms in theories defined by associativity, commutativity, identity (unit element) axioms and their combinations and develop a sound and complete algorithm which takes two lambda terms and computes their equational generalizations in the form of higher-order patterns. The problem is finitary: the minimal complete set of such generalizations contains finitely many elements. We define the notion of optimal solution and investigate special restrictions of the problem for which the optimal solution can be computed in linear or polynomial
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Fages, François, and Gérard Huet. "Complete sets of unifiers and matchers in equational theories." Theoretical Computer Science 43 (1986): 189–200. http://dx.doi.org/10.1016/0304-3975(86)90175-1.

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ÉSIK, Z. "THE POWER OF THE GROUP-IDENTITIES FOR ITERATION." International Journal of Algebra and Computation 10, no. 03 (2000): 349–73. http://dx.doi.org/10.1142/s0218196700000145.

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It has been shown that the axioms of iteration theories capture the equational properties of iteration in several different models related to computer science. Iteration theories are axiomatizable by the Conway identities and the group-identities corresponding to the finite (simple) groups. In this paper we provide a complete analysis of these identities by giving a concrete description of the free theories in the variety axiomatized by the Conway identities and any given subcollection of the group-identities. It follows that when the group-identities are effectively given, the equational theo
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Ésik, Z. "Equational properties of fixed-point operations in cartesian categories: An overview." Mathematical Structures in Computer Science 29, no. 06 (2019): 909–25. http://dx.doi.org/10.1017/s0960129518000361.

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AbstractSeveral fixed-point models share the equational properties of iteration theories, or iteration categories, which are cartesian categories equipped with a fixed point or dagger operation subject to certain axioms. After discussing some of the basic models, we provide equational bases for iteration categories and offer an analysis of the axioms. Although iteration categories have no finite base for their identities, there exist finitely based implicational theories that capture their equational theory. We exhibit several such systems. Then we enrich iteration categories with an additive
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Amy, Matthew. "Complete Equational Theories for the Sum-Over-Paths with Unbalanced Amplitudes." Electronic Proceedings in Theoretical Computer Science 384 (August 23, 2023): 127–41. http://dx.doi.org/10.4204/eptcs.384.8.

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Mordido, Andreia, and Carlos Caleiro. "Probabilistic logic over equations and domain restrictions." Mathematical Structures in Computer Science 29, no. 06 (2019): 872–95. http://dx.doi.org/10.1017/s096012951800035x.

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AbstractWe propose and study a probabilistic logic over an algebraic basis, including equations and domain restrictions. The logic combines aspects from classical logic and equational logic with an exogenous approach to quantitative probabilistic reasoning. We present a sound and weakly complete axiomatization for the logic, parameterized by an equational specification of the algebraic basis coupled with the intended domain restrictions.We show that the satisfiability problem for the logic is decidable, under the assumption that its algebraic basis is given by means of a convergent rewriting s
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ÉSIK, ZOLTÁN. "Equational axioms associated with finite automata for fixed point operations in cartesian categories." Mathematical Structures in Computer Science 27, no. 1 (2015): 54–69. http://dx.doi.org/10.1017/s0960129515000031.

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The axioms of iteration theories, or iteration categories, capture the equational properties of fixed point operations in several computationally significant categories. Iteration categories may be axiomatized by the Conway identities and identities associated with finite automata. We show that the Conway identities and the identities associated with the members of a subclass $\mathcal{Q}$ of finite automata is complete for iteration categories iff for every finite simple group G there is an automaton Q ∈ $\mathcal{Q}$ such that G is a quotient of a group in the monoid M(Q) of the automaton Q.
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Aguirre, Alejandro, and Lars Birkedal. "Step-Indexed Logical Relations for Countable Nondeterminism and Probabilistic Choice." Proceedings of the ACM on Programming Languages 7, POPL (2023): 33–60. http://dx.doi.org/10.1145/3571195.

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Developing denotational models for higher-order languages that combine probabilistic and nondeterministic choice is known to be very challenging. In this paper, we propose an alternative approach based on operational techniques. We study a higher-order language combining parametric polymorphism, recursive types, discrete probabilistic choice and countable nondeterminism. We define probabilistic generalizations of may- and must-termination as the optimal and pessimal probabilities of termination. Then we define step-indexed logical relations and show that they are sound and complete with respec
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Carette, Titouan, Emmanuel Jeandel, Simon Perdrix, and Renaud Vilmart. "Completeness of Graphical Languages for Mixed State Quantum Mechanics." ACM Transactions on Quantum Computing 2, no. 4 (2021): 1–28. http://dx.doi.org/10.1145/3464693.

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There exist several graphical languages for quantum information processing, like quantum circuits, ZX-calculus, ZW-calculus, and so on. Each of these languages forms a †-symmetric monoidal category (†-SMC) and comes with an interpretation functor to the †-SMC of finite-dimensional Hilbert spaces. In recent years, one of the main achievements of the categorical approach to quantum mechanics has been to provide several equational theories for most of these graphical languages, making them complete for various fragments of pure quantum mechanics. We address the question of how to extend these lan
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Dissertations / Theses on the topic "Complete equational theories"

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Clément, Alexandre. "Langages graphiques pour le contrôle quantique et l'optique linéaire." Electronic Thesis or Diss., Université de Lorraine, 2023. http://www.theses.fr/2023LORR0093.

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Dans le modèle usuel de calcul quantique, des opérations sur des données quantiques sont contrôlées de manière essentiellement classique. Un contrôle lui aussi quantique est cependant possible, mais a été peu étudié en comparaison. En particulier, il manque au contrôle quantique un formalisme permettant de l'exprimer de manière simple afin de raisonner efficacement sur des processus l'impliquant. La première contribution de cette thèse est de poser les fondations d'un cadre formel dédié au contrôle quantique, sous la forme d'un langage graphique. Notre principal résultat concernant ce langage
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DE, LEO ROBERTO. "On some geometrical and analytical problems arising from the theory of Isometric Immersion." Doctoral thesis, Università degli Studi di Cagliari, 2011. http://hdl.handle.net/11584/266285.

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Bensedik, Ahmed. "Sur quelques problèmes elliptiques de type Kirchhoff et dynamique des fluides." Phd thesis, Université Jean Monnet - Saint-Etienne, 2012. http://tel.archives-ouvertes.fr/tel-00971279.

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Cette thèse est composée de deux parties indépendantes. La première est consacrée à l'étude de quelques problèmes elliptiques de type de Kirchhoff de la forme suivante : -M(ʃΩNul² dx) Δu = f(x, u) xЄΩ ; u(x) = o xЄƋΩ où Ω cRN, N ≥ 2, f une fonction de Carathéodory et M une fonction strictement positive et continue sur R+. Dans le cas où la fonction f est asymptotiquement linéaire à l'infini par rapport à l'inconnue u, on montre, en combinant une technique de troncature et la méthode variationnelle, que le problème admet au moins une solution positive quand la fonction M est non décroissante. E
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Bardestani, Mohammad. "On some Density Theorems in Number Theory and Group Theory." Thèse, 2012. http://hdl.handle.net/1866/8936.

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Gowers, dans son article sur les matrices quasi-aléatoires, étudie la question, posée par Babai et Sos, de l'existence d'une constante $c>0$ telle que tout groupe fini possède un sous-ensemble sans produit de taille supérieure ou égale a $c|G|$. En prouvant que, pour tout nombre premier $p$ assez grand, le groupe $PSL_2(\mathbb{F}_p)$ (d'ordre noté $n$) ne posséde aucun sous-ensemble sans produit de taille $c n^{8/9}$, il y répond par la négative. Nous allons considérer le probléme dans le cas des groupes compacts finis, et plus particuliérement des groupes profinis $SL_k(\mathbb{Z}_p)$ et $
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Books on the topic "Complete equational theories"

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Schapira, Pierre. Index theorem for elliptic pairs. Société mathématique de France, 1994.

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Pipkin, A. C. A course on integral equations. Springer-Verlag, 1991.

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Pipkin, A. C. A course on integral equations. Springer-Verlag, 1991.

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Biase, Fausto. Fatou Type Theorems: Maximal Functions and Approach Regions. Birkhäuser Boston, 1997.

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Alekseev, V. B. Abel's theorem in problems and solutions based on the lectures of professor V.I. Arnold. Kluwer Academic, 2003.

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Alekseev, V. B. Abel's theorem in problems and solutions based on the lectures of professor V.I. Arnold. Kluwer Academic Publishers, 2004.

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Real solutions to equations from geometry. American Mathematical Society, 2011.

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Conference Board of the Mathematical Sciences and National Science Foundation (U.S.), eds. Ergodic theory and fractal geometry. Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 2014.

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Southeast Geometry Seminar (15th 2009 University of Alabama at Birmingham). Geometric analysis, mathematical relativity, and nonlinear partial differential equations: Southeast Geometry Seminars Emory University, Georgia Institute of Technology, University of Alabama, Birmingham, and the University of Tennessee, 2009-2011. Edited by Ghomi Mohammad 1969-. American Mathematical Society, 2013.

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Harmonic maps and differential geometry: A harmonic map fest in honour of John C. Wood's 60th birthday, September 7-10, 2009, Cagliari, Italy. American Mathematical Society, 2011.

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Book chapters on the topic "Complete equational theories"

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Kim, Dohan, and Christopher Lynch. "Equational Theorem Proving Modulo." In Automated Deduction – CADE 28. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79876-5_10.

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AbstractUnlike other methods for theorem proving modulo with constrained clauses [12, 13], equational theorem proving modulo with constrained clauses along with its simplification techniques has not been well studied. We introduce a basic paramodulation calculus modulo equational theories E satisfying certain properties of E and present a new framework for equational theorem proving modulo E with constrained clauses. We propose an inference rule called Generalized E-Parallel for constrained clauses, which makes our inference system completely basic, meaning that we do not need to allow any paramodulation in the constraint part of a constrained clause for refutational completeness. We present a saturation procedure for constrained clauses based on relative reducibility and show that our inference system including our contraction rules is refutationally complete.
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Fiore, Marcelo, and Philip Saville. "Relative Full Completeness for Bicategorical Cartesian Closed Structure." In Lecture Notes in Computer Science. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-45231-5_15.

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AbstractThe glueing construction, defined as a certain comma category, is an important tool for reasoning about type theories, logics, and programming languages. Here we extend the construction to accommodate ‘2-dimensional theories’ of types, terms between types, and rewrites between terms. Taking bicategories as the semantic framework for such systems, we define the glueing bicategory and establish a bicategorical version of the well-known construction of cartesian closed structure on a glueing category. As an application, we show that free finite-product bicategories are fully complete relative to free cartesian closed bicategories, thereby establishing that the higher-order equational theory of rewriting in the simply-typed lambda calculus is a conservative extension of the algebraic equational theory of rewriting in the fragment with finite products only.
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Bulmer, Michael. "Inductive theories from equational systems." In Learning and Reasoning with Complex Representations. Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/3-540-64413-x_29.

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Xu, Liu-Jun, and Ji-Ping Huang. "Theory for Thermal Wave Control: Transformation Complex Thermotics." In Transformation Thermotics and Extended Theories. Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-5908-0_3.

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AbstractIn this chapter, we develop a transformation theory for controlling wavelike temperature fields (called thermal waves herein) in conduction and advection. We first unify these two basic heat transfer modes by coining a complex thermal conductivity whose real and imaginary parts are related to conduction and advection. Consequently, the conduction-advection process supporting thermal waves is described by a complex conduction equation, thus called complex thermotics. We then propose the principle for transforming complex thermal conductivities. We further design three metamaterials to control thermal waves with cloaking, concentrating, and rotating functions. Experimental suggestions are also provided based on porous media.
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Narasimhan, Raghavan, and Yves Nievergelt. "The Inhomogeneous Cauchy-Riemann Equation and Runge’s Theorem." In Complex Analysis in One Variable. Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0175-5_18.

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Narasimhan, Raghavan, and Yves Nievergelt. "The Inhomogeneous Cauchy-Riemann Equation and Runge’s Theorem." In Complex Analysis in One Variable. Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0175-5_5.

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Narasimhan, Raghavan. "The Inhomogeneous Cauchy-Riemann Equation and Runge’s Theorem." In Complex Analysis in one Variable. Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4757-1106-6_5.

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Liao, Liangwen, and Chung-Chun Yang. "Malmquist-Yosida Type Theorems for Algebraic Differential Equations." In Finite or Infinite Dimensional Complex Analysis and Applications. Springer US, 2004. http://dx.doi.org/10.1007/978-1-4613-0221-6_12.

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Wen, Chih-Yung, Yazhong Jiang, and Lisong Shi. "Introduction." In Engineering Applications of Computational Methods. Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0876-9_1.

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AbstractWith the rapid development of electronic computers, numerical computation has become an important paradigm of scientific discovery as well as a powerful tool for engineering research. Solving complex problems in a computational fashion is more than applying theories, equations, and formulas. Computational methods, also called algorithms or schemes, have strong influences on the outcomes of computations.
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Błocki, Zbigniew. "The Calabi–Yau Theorem." In Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23669-3_5.

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Conference papers on the topic "Complete equational theories"

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Ruth, D. Alan, and J. Michael McCarthy. "SphinxPC: An Implementation of Four Position Synthesis for Planar and Spherical 4R Linkages." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/dac-3860.

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Abstract This paper presents the basic theory and algorithmic structure of a design system that implements four position synthesis for both planar and spherical four bar linkages. The formalism uses complex numbers to define the equation of a planar triangle and quaternions to define the equation of a spherical triangle. These equations form the basis of a parallel implementation of these design theories. The theory and major functional components of SphinxPC are described and examples are presented.
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Leishear, Robert A. "Derivations for Hoop Stresses Due to Shock Waves in a Tube." In ASME 2007 Pressure Vessels and Piping Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/pvp2007-26722.

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Equations describing the hoop stresses in a pipe due to water hammer have been presented in the literature in a series of papers, and this paper discusses the complete derivation of the pertinent equations. The derivation considers the pipe wall response to a water hammer induced shock wave moving along the inner wall of the pipe. Factors such as fluid properties, pipe wall materials, pipe dimensions, and damping are considered. These factors are combined to present a single, albeit rather complicated, equation to describe the pipe wall vibrations and hoop stresses as a function of time. This
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Pomytkin, S. P., and K. А. Gukasjan. "MODELING OF THE COOL CREEPIN THE FRAMEWORK OF THE HARDENING THEORIES ON THE STEPWISE LOADING." In MODELING AND SITUATIONAL MANAGEMENT THE QUALITY OF COMPLEX SYSTEMS. Saint Petersburg State University of Aerospace Instrumentation, 2021. http://dx.doi.org/10.31799/978-5-8088-1558-2-2021-2-8-15.

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In the framework of the hardening hypothesis, the creep behavior of a titanium alloy at room temperature is modeled at stepwise stress change both increasing and decreasing load. Methods for the identification of material constants and functions included in constitutive equations of the hardening theories are considered in detail. The prospects for the computational-experimental method proposed by Rybakina for determination of material constants in some versions of the hardening theory are noted. The results of the creep modeling of titanium alloy confirm the existing theoretical possibilities
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Watteaux, R., N. Mureithi, and D. Pelletier. "Determination of Coupling Force Derivatives in Tube Bundles Using the Shape Sensitivity Equation Method." In ASME 2007 Pressure Vessels and Piping Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/pvp2007-26061.

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Flow induced vibration of tube bundles remains an important problem in the nuclear industry. A number of theories modeling fluidelastic instability have been developed. In those theories, understanding the influence of a tube on its neighbors is of primary importance. Since it is very difficult and time consuming to measure the complete set of cross-coupling effects, numerical simulations could provide a valuable alternative. The main purpose of this paper is to propose the Sensitivity Equation Method (SEM) as a new approach to finding the inter-cylinder coupling effects, which are usually qua
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Miyazaki, T., and N. Hirayama. "A Theoretical Solution of Three-Dimensional Flows in Subsonic, Transonic and Supersonic Turbomachines: An Exact Solution and its Numerical Method." In ASME 1986 International Gas Turbine Conference and Exhibit. American Society of Mechanical Engineers, 1986. http://dx.doi.org/10.1115/86-gt-111.

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A theoretical solution of a nonviscous flow through subsonic, transonic and supersonic arbitrary turbomachines is presented. The basic relations given by Wu are finally reduced to complex integral equations and then solved rigorously with pseudo-analytic function theories for boundary value problems and conformal mapping theorems which may simplify given flow fields. As the numerical method of the solution successive iteration is used. In the present paper only a schema of computational procedures of the three-dimensional flow is described. Moreover, detailed consideration on problems associat
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Nabelek, Patrik, and Solomon C. Yim. "Riemann-Hilbert Formulation and Solution of Nonlinear Shallow-Water Wave Equations: Nonlocal Dbar Problem as a Unified Approach to Computing Exact Solutions in the Time Domain." In ASME 2023 42nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/omae2023-108051.

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Abstract Linear wave theories and stochastic linear wave spectra are foundational to ocean and coastal engineering. However, there are some important limitations with linear wave theories, and some of which were originally observed experimentally more than a century ago by John Scott Russell. Nonlinearities will cause the linear wave spectra to evolve in time and space as waves move across a basin, or as waves evolve in the ocean and coastal waters, and in coastal channels. Using a nonlinear wave theory can therefore allow researchers and engineers to better capture the dynamic nature of the o
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Harris, C. B., J. K. Brown, M. E. Paige, D. E. Smith, and D. J. Russell. "Ultrafast Studies Designed to Test the Fundamental Statistical Assumptions Underlying Chemical Reactivity in Liquids." In International Conference on Ultrafast Phenomena. Optica Publishing Group, 1986. http://dx.doi.org/10.1364/up.1986.tha2.

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Stochastic theories based on the Langevin or Fokker-Planck equations for describing chemical reactions break down when fluctuations associated with collisions no longer look completely random. This occurs on the picosecond or femtosecond timescale, and consequently, new general dynamical theories for explaining fundamental processes in chemical reactions are needed for ultrafast timescales. The breakdown of stochastic descriptions will be illustrated experimentally and several alternative theoretical approaches for ultrafast phenomena will be discussed.
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Henry, Charles H. "Phase Noise in Semiconductor Lasers and its Reduction by Optical Feedback." In Semiconductor Lasers. Optica Publishing Group, 1987. http://dx.doi.org/10.1364/sla.1987.tub1.

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A theory of spontaneous emission noise is presented based on classical electromagnetic theory[1]. Unlike conventional theories of laser noise, this presentation is valid for open resonators. A local Langevin force is added to the wave equation to account for spontaneous emission. A general expression is found relating the diffusion coefficient of this force to the imaginary part of the dielectric function. The field of laser is found by solving the wave equation by the Green’s function method. The lasing mode is a resonant state associated with a pole in Green’s function. The Langevin rate equ
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Azzam, R. M. A. "Extrema of the magnitude and phase of a complex function of a real variable." In OSA Annual Meeting. Optica Publishing Group, 1987. http://dx.doi.org/10.1364/oam.1987.thf5.

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Given a complex function F(ω) = |F(ω)| exp [jΔ(ω)] of a real argument ω, the extrema of its magnitude |F(ω)| and phase Δ(ω) as functions of ω are determined simultaneously by finding the roots of one common equation, lm[G(ω)] = 0, where G = (F'/F) 2 and F' = ∂F/∂ω. The extrema of |F| and Δ are associated with ReG ᐸ 0 and ReG ᐳ 0, respectively. This easy-to-prove theorem has a wide range of applications in optics and electrical engineering. We offer at least one example of attenuated internal reflection (AIR). In AIR the complex reflection coefficient for the p polarization R p (ϕ) and the rati
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Urso, André C. "An Accurate Approximation of the Orowan Rolling Force Equation for Homogeneous Compression of Metals in Cold Rolling." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0652.

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Abstract The theory of rolling metals has been adequately developed since the mid 1940’s. Of the popular theories, the complex formulations are accurate over a large range of rolling conditions, and the approximate formulations tend to be accurate only on a narrow range. This paper covers the development of an approximate formulation of the Orowan (1943) rolling theory that is applicable over a relatively large range of reductions, material strengths, and strip tensions.
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