Bibliografie tematiche / Complete equational theories

Letteratura scientifica selezionata sul tema "Complete equational theories"

Autore: Grafiati

Pubblicato: 8 giugno 2024

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Articoli di riviste sul tema "Complete equational theories":

Hölldobler, Steffen. "Conditional equational theories and complete sets of transformations". Theoretical Computer Science 75, n. 1-2 (1990): 85–110. http://dx.doi.org/10.1016/0304-3975(90)90063-n.

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Cerna, David M., e Temur Kutsia. "Higher-order pattern generalization modulo equational theories". Mathematical Structures in Computer Science 30, n. 6 (20 maggio 2020): 627–63. http://dx.doi.org/10.1017/s0960129520000110.

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Abstract (sommario):

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 time.

Fages, François, e 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, n. 03 (giugno 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 theory of the variety is decidable.

Ésik, Z. "Equational properties of fixed-point operations in cartesian categories: An overview". Mathematical Structures in Computer Science 29, n. 06 (24 maggio 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 structure and exhibit interesting cases where the interaction between the iteration category structure and the additive structure can be captured by a finite number of identities. This includes the iteration category of monotonic or continuous functions over complete lattices equipped with the least fixed-point operation and the binary supremum operation as addition, the categories of simulation, bisimulation, or language equivalence classes of processes, context-free languages, and others. Finally, we exhibit a finite equational system involving residuals, which is sound and complete for monotonic or continuous functions over complete lattices in the sense that it proves all of their identities involving the operations and constants of cartesian categories, the least fixed-point operation and binary supremum, but not involving residuals.

Amy, Matthew. "Complete Equational Theories for the Sum-Over-Paths with Unbalanced Amplitudes". Electronic Proceedings in Theoretical Computer Science 384 (23 agosto 2023): 127–41. http://dx.doi.org/10.4204/eptcs.384.8.

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Mordido, Andreia, e Carlos Caleiro. "Probabilistic logic over equations and domain restrictions". Mathematical Structures in Computer Science 29, n. 06 (8 marzo 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 system, and, additionally, that the axiomatization of domain restrictions enjoys a suitable subterm property. For this purpose, we provide a polynomial reduction to Satisfiability Modulo Theories. As a consequence, we get that validity in the logic is also decidable. Furthermore, under the assumption that the rewriting system that defines the equational basis underlying the logic is also subterm convergent, we show that the resulting satisfiability problem is NP-complete, and thus the validity problem is coNP-complete.We test the logic with meaningful examples in information security, namely by verifying and estimating the probability of the existence of offline guessing attacks to cryptographic protocols.

ÉSIK, ZOLTÁN. "Equational axioms associated with finite automata for fixed point operations in cartesian categories". Mathematical Structures in Computer Science 27, n. 1 (8 aprile 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. We also prove a stronger result that concerns identities associated with finite automata with a distinguished initial state.

Aguirre, Alejandro, e Lars Birkedal. "Step-Indexed Logical Relations for Countable Nondeterminism and Probabilistic Choice". Proceedings of the ACM on Programming Languages 7, POPL (9 gennaio 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 respect to the induced contextual preorders. For may-equivalence we use step-indexing over the natural numbers whereas for must-equivalence we index over the countable ordinals. We then show than the probabilities of may- and must-termination coincide with the maximal and minimal probabilities of termination under all schedulers. Finally we derive the equational theory induced by contextual equivalence and show that it validates the distributive combination of the algebraic theories for probabilistic and nondeterministic choice.

Carette, Titouan, Emmanuel Jeandel, Simon Perdrix e Renaud Vilmart. "Completeness of Graphical Languages for Mixed State Quantum Mechanics". ACM Transactions on Quantum Computing 2, n. 4 (31 dicembre 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 languages beyond pure quantum mechanics to reason about mixed states and general quantum operations, i.e., completely positive maps. Intuitively, such an extension relies on the axiomatisation of a discard map that allows one to get rid of a quantum system, an operation that is not allowed in pure quantum mechanics. We introduce a new construction, the discard construction , which transforms any †-symmetric monoidal category into a symmetric monoidal category equipped with a discard map. Roughly speaking this construction consists in making any isometry causal. Using this construction, we provide an extension for several graphical languages that we prove to be complete for general quantum operations. However, this construction fails for some fringe cases like Clifford+T quantum mechanics, as the category does not have enough isometries.

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Tesi sul tema "Complete equational theories":

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 est l'introduction d'une théorie équationnelle complète, c'est à dire d'un ensemble d'équations permettant de transformer un diagramme, par réécriture locale successive, en n'importe quel autre diagramme représentant le même programme ou processus physique. Une deuxième contribution est l'application de ce formalisme d'une part au problème de l'optimisation des ressources dans les processus impliquant un contrôle quantique, et d'autre part à la caractérisation de l'équivalence observationnelle des canaux de communication quantiques. La troisième contribution de cette thèse est l'introduction d'un langage pour les circuits optiques linéaires. Nous l'équipons d'une théorie équationnelle complète, ainsi que d'une forme normale simple, accessible par un système de réécriture fortement normalisant et confluent. La dernière contribution de cette thèse, peut-être la plus importante, est l'introduction d'une théorie équationnelle complète pour le langage des circuits quantiques. Nous nous appuyons pour cela sur une correspondance entre les circuits quantiques et les circuits optiques, qui nous permet de transférer la théorie équationnelle déjà obtenue pour les circuits optiques
In the models of quantum computing usually considered, some quantum data is manipulated by means of operations which are controlled in an essentially classical way. Controlling these operations in a quantum way is actually possible, but has been much less studied. In particular, quantum control misses a formalism in which one could represent it in a simple way in order to efficiently reason on processes involving it. The first contribution of this thesis is to lay the foundations of a formal framework dedicated to quantum control, in the form of a graphical language. Our main result about this language is the introduction of a complete equational theory, that is, a set of equations that makes it possible, by successive local rewriting, to transform a given diagram into any other diagram representing the same program or physical process. A second contribution is to apply this formalism, on the one hand, to the problem of resource optimisation of processes involving quantum control, and on the other hand, to the characterisation of the observational equivalence of quantum communication channels. A third contribution of this thesis is to introduce a language for linear optical circuits. We equip this language with a complete equational theory, together with a simple normal form, reachable via a strongly normalising and confluent rewriting system. The last contribution of this thesis, maybe the most significant one, is to introduce a complete equational theory for the language of quantum circuits. We obtain this result by exploiting a correspondence between quantum circuits and optical circuits, which allows us to transfer the equational theory already obtained for optical circuits

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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Abstract (sommario):

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. Et si f(x, u) = |u|p-1 u + λg(x), où p >0, λ un paramètre réel et g une fonction de classe C1 et changeant de signe sur Ω, alors sous certaines hypothèses sur M, il existe deux réels positifs λ. et λ. tels que le problème admet des solutions positives si 0 < λ <λ. et n'admet pas de solutions positives si λ > λ.. Dans la deuxième partie, on étudie deux problèmes soulevés en dynamique des fluides. Le premier est une généralisation d'un modèle décrivant la propagation unidirectionnelle dispersive des ondes longues dans un milieu à deux fluides. En écrivant le problème sous la forme d'une équation de point fixe, on montre l'existence d'au moins une solution positive. On montre ensuite sa symétrie et son unicité. Le deuxième problème consiste à prouver l'existence de la vitesse, la pression et la température d'un fluide non newtonien, incompressible et non isotherme, occupant un domaine borné, en prenant en compte un terme de convection. L'originalité dans ce travail est que la viscosité du fluide ne dépend pas seulement de la vitesse mais aussi de la température et du module du tenseur des taux de déformations. En se basant sur la notion des opérateurs pseudo-monotones, le théorème de De Rham et celui de point fixe de Schauder, l'existence du triplet, (vitesse, pression, température) est démontré

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 $Sp_{2k}(\mathbb{Z}_p)$. La premiére partie de cette thése est dédiée à l'obtention de bornes inférieures et supérieures exponentielles pour la mesure suprémale des ensembles sans produit. La preuve nécessite d'établir préalablement une borne inférieure sur la dimension des représentations non-triviales des groupes finis $SL_k(\mathbb{Z}/(p^n\mathbb{Z}))$ et $Sp_{2k}(\mathbb{Z}/(p^n\mathbb{Z}))$. Notre théoréme prolonge le travail de Landazuri et Seitz, qui considérent le degré minimal des représentations pour les groupes de Chevalley sur les corps finis, tout en offrant une preuve plus simple que la leur. La seconde partie de la thése à trait à la théorie algébrique des nombres. Un polynome monogéne $f$ est un polynome unitaire irréductible à coefficients entiers qui endengre un corps de nombres monogéne. Pour un nombre premier $q$ donné, nous allons montrer, en utilisant le théoréme de densité de Tchebotariov, que la densité des nombres premiers $p$ tels que $t^q -p$ soit monogéne est supérieure ou égale à $(q-1)/q$. Nous allons également démontrer que, quand $q=3$, la densité des nombres premiers $p$ tels que $\mathbb{Q}(\sqrt[3]{p})$ soit non monogéne est supérieure ou égale à $1/9$.
Gowers in his paper on quasirandom groups studies a question of Babai and Sos asking whether there exists a constant $c > 0$ such that every finite group $G$ has a product-free subset of size at least $c|G|$. Answering the question negatively, he proves that for sufficiently large prime $p$, the group $\mathrm{PSL}_2(\mathbb{F}_p)$ has no product-free subset of size $\geq cn^{8/9}$, where $n$ is the order of $\mathrm{PSL}_2(\mathbb{F}_p)$. We will consider the problem for compact groups and in particular for the profinite groups $\SL_k(\mathh{Z}_p)$ and $\Sp_{2k}(\mathbb{Z}_p)$. In Part I of this thesis, we obtain lower and upper exponential bounds for the supremal measure of the product-free sets. The proof involves establishing a lower bound for the dimension of non-trivial representations of the finite groups $\SL_k(\mathbb{Z}/(p^n\mathbb{Z}))$ and $\Sp_{2k}(\mathbb{Z}/(p^n\mathbb{Z}))$. Indeed, our theorem extends and simplifies previous work of Landazuri and Seitz, where they consider the minimal degree of representations for Chevalley groups over a finite field. In Part II of this thesis, we move to algebraic number theory. A monogenic polynomial $f$ is a monic irreducible polynomial with integer coefficients which produces a monogenic number field. For a given prime $q$, using the Chebotarev density theorem, we will show the density of primes $p$, such that $t^q-p$ is monogenic, is greater than or equal to $(q-1)/q$. We will also prove that, when $q=3$, the density of primes $p$, which $\mathbb{Q}(\sqrt[3]{p})$ is non-monogenic, is at least $1/9$.

Libri sul tema "Complete equational theories":

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

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

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

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Biase, Fausto. Fatou Type Theorems: Maximal Functions and Approach Regions. Boston, MA: 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. Dordrecht: 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. Boston: Kluwer Academic Publishers, 2004.

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Sottile, Frank. Real solutions to equations from geometry. Providence, R.I: American Mathematical Society, 2011.

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Furstenberg, Harry. Ergodic theory and fractal geometry. Providence, Rhode Island: 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. A cura di Ghomi Mohammad 1969-. Providence, Rhode Island: American Mathematical Society, 2013.

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

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Capitoli di libri sul tema "Complete equational theories":

Kim, Dohan, e Christopher Lynch. "Equational Theorem Proving Modulo". In Automated Deduction – CADE 28, 166–82. Cham: 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.

Fiore, Marcelo, e Philip Saville. "Relative Full Completeness for Bicategorical Cartesian Closed Structure". In Lecture Notes in Computer Science, 277–98. Cham: 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.

Bulmer, Michael. "Inductive theories from equational systems". In Learning and Reasoning with Complex Representations, 78–91. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/3-540-64413-x_29.

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Xu, Liu-Jun, e Ji-Ping Huang. "Theory for Thermal Wave Control: Transformation Complex Thermotics". In Transformation Thermotics and Extended Theories, 19–33. Singapore: 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.

Narasimhan, Raghavan, e Yves Nievergelt. "The Inhomogeneous Cauchy-Riemann Equation and Runge’s Theorem". In Complex Analysis in One Variable, 315–30. Boston, MA: Birkhäuser Boston, 2001. http://dx.doi.org/10.1007/978-1-4612-0175-5_18.

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Narasimhan, Raghavan, e Yves Nievergelt. "The Inhomogeneous Cauchy-Riemann Equation and Runge’s Theorem". In Complex Analysis in One Variable, 97–114. Boston, MA: 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, 100–118. Boston, MA: Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4757-1106-6_5.

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Liao, Liangwen, e Chung-Chun Yang. "Malmquist-Yosida Type Theorems for Algebraic Differential Equations". In Finite or Infinite Dimensional Complex Analysis and Applications, 181–91. Boston, MA: Springer US, 2004. http://dx.doi.org/10.1007/978-1-4613-0221-6_12.

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Wen, Chih-Yung, Yazhong Jiang e Lisong Shi. "Introduction". In Engineering Applications of Computational Methods, 1–5. Singapore: 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.

Błocki, Zbigniew. "The Calabi–Yau Theorem". In Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics, 201–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23669-3_5.

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Atti di convegni sul tema "Complete equational theories":

Ruth, D. Alan, e 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.

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 equation is also compared to another theoretical prediction for hoop stresses, which is also derived herein. Specifically, the two theories predict different maximum stresses, and the differences between these predictions are graphically displayed.

Pomytkin, S. P., e 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 and limitations of the hardening hypothesis fully.

Watteaux, R., N. Mureithi e 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 quantified by the derivatives of lift and drag coefficients of all tubes with respect to the coordinates of the reference tube’s location.

Miyazaki, T., e 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 associated with Wu’s model is omitted. The numerical method is easy to accomplish in the whole flow regions, because numerical procedures are done mainly along the boundaries. Numerical examples given are limited to those for subsonic and shock free transonic flows.

Nabelek, Patrik, e 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 ocean waves. Common classical nonlinear wave theories include the (2+1)D KP equation and the (1+1)D Korteweg-de Fries (KdV) equation. As described by Osborne [2010], the invariance nature of these nonlinear wave equations can be characterized in an exact manner by their corresponding nonlinear frequency or wave-number spectrum parallel to the linear case. A nonlocal dbar model was used by Ablowitz, Bar-Yaacov and Fokas [1983], and Zakharov and Manakov [1984] to solve the KP equation by the inverse scattering transform (IST). In this study we discuss the use of the nonlocal dbar problem (NDP) to compute the soliton solutions by the inverse scattering transform, and finite-genus solutions to the KdV equation, and undular bores (dispersive shockwaves). We also discuss the use of NDP to produce soliton solutions and the calculation of periodic finite-genus solutions to the KP equation using Riemann theta functions and complex algebraic geometry.

Harris, C. B., J. K. Brown, M. E. Paige, D. E. Smith e D. J. Russell. "Ultrafast Studies Designed to Test the Fundamental Statistical Assumptions Underlying Chemical Reactivity in Liquids". In International Conference on Ultrafast Phenomena. Washington, D.C.: 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.

Henry, Charles H. "Phase Noise in Semiconductor Lasers and its Reduction by Optical Feedback". In Semiconductor Lasers. Washington, D.C.: 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 equations for a Fabry-Perot laser with arbitrary facet reflectivities are derived. Optical feedback can be represented by a complex, frequency dependent, facet reflectivity r(ω)exp(iϕ(ω)). The effect of optical feedback is to reduce the adiabatic chirp by F and to reduce the Lorentzian linewidth by F2, where and τ is the round trip time in the laser cavity and α is the linewidth parameter[2].

Azzam, R. M. A. "Extrema of the magnitude and phase of a complex function of a real variable". In OSA Annual Meeting. Washington, D.C.: 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 ratio of complex reflection coefficients for the p and s polarizations, p(ϕ) =R p (ϕ)/R s (ϕ), are considered as functions of the angle of incidence ϕ. It is found that the same (cubic) equation1 that determines the pseudo-Brewster angle of minimum |R p | also determines a new angle at which the reflection phase shift δ p = argR p exhibits a minimum of its own. Likewise, the same (quartic) equation2 that determines the second Brewster angle of minimum | ρ | also determines angles of incidence at which the differential reflection phase shift Δ = argρ experiences a minimum and a maximum. Angular positions and magnitudes of all extrema are exactly calculated for a specific case that represents light reflection by the vacuum —Al or glass—aqueous dye solution interface.

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.