To see the other types of publications on this topic, follow the link: Weyl functional calculus.
Journal articles on the topic 'Weyl functional calculus'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 journal articles for your research on the topic 'Weyl functional calculus.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.
1
Jefferies, Brian, and Alan McIntosh. "The Weyl calculus and Clifford analysis." Bulletin of the Australian Mathematical Society 57, no. 2 (April 1998): 329–41. http://dx.doi.org/10.1017/s0004972700031695.
Full text
2
Kim, Joonil. "Marcinkiewicz multiplier theorem for the Weyl functional calculus." Mathematische Zeitschrift 258, no. 2 (April 25, 2007): 271–90. http://dx.doi.org/10.1007/s00209-007-0164-x.
Full text
3
Jefferies, Brian, and Bernd Straub. "Lacunas in the Support of the Weyl Calculus for Two Hermitian Matrices." Journal of the Australian Mathematical Society 75, no. 1 (August 2003): 85–124. http://dx.doi.org/10.1017/s1446788700003499.
Full textAbstract:
AbstractThe connection between Clifford analysis and the Weyl functional calculus for a d-tuple of bounded selfadjoint operators is used to prove a geometric condition due to J. Bazer and D. H. Y. Yen for a point to be in the support of the Weyl functional calculus for a pair of hermitian matrices. Examples are exhibited in which the support has gaps.
4
Ricker, Werner J. "The Weyl functional calculus and two-by-two selfadjoint matrices." Bulletin of the Australian Mathematical Society 55, no. 2 (April 1997): 321–25. http://dx.doi.org/10.1017/s0004972700033980.
Full textAbstract:
Let D be a (2 × 2) matrix with distinct eigenvalues λ1 and λ2. There is a basic and well known functional equation which provides a formula for constructing the matrix g (D), for any ℂ-valued function g defined on a subset of ℂ containing {λ1,λ2}, namely .This equation is used to give a direct and transparent proof of the following fact due to Anderson: A pair of (2 × 2) selfadjoint matrices A1 and A2 commute if and only if the Weyl functional calculus of the pair (A1,A2), which is a matrix-valued distribution, has order zero (that is, is a measure).
5
Eydenberg, Michael. "The Weyl Correspondence as a Functional Calculus for Non-Commuting Operators." Rocky Mountain Journal of Mathematics 39, no. 5 (October 2009): 1467–96. http://dx.doi.org/10.1216/rmj-2009-39-5-1467.
Full text
6
Le Merdy, Christian. "Two Results About H∞ Functional Calculus on Analytic umd Banach Spaces." Journal of the Australian Mathematical Society 74, no. 3 (June 2003): 351–78. http://dx.doi.org/10.1017/s1446788700003360.
Full textAbstract:
AbstractLet X be a Banach space with the analytic UMD property, and let A and B be two commuting sectorial operators on X which admit bounded H∞ functional calculi with respect to angles θ1 and θ2 satisfying θ1 + θ2 > π. It was proved by Kalton and Weis that in this case, A + B is closed. The first result of this paper is that under the same conditions, A + B actually admits a bounded H∞ functional calculus. Our second result is that given a Banach space X and a number 1 ≦ p < ∞, the derivation operator on the vector valued Hardy space Hp (R; X) admits a bounded H∞ functional calculus if and only if X has the analytic UMD property. This is an ‘analytic’ version of the well-known characterization of UMD by the boundedness of the H∞ functional calculus of the derivation operator on vector valued Lp-spaces Lp (R; X) for 1 < p < ∞ (Dore-Venni, Hieber-Prüss, Prüss).
7
PAVLOVIĆ, DUšKO. "Categorical logic of names and abstraction in action calculi." Mathematical Structures in Computer Science 7, no. 6 (December 1997): 619–37. http://dx.doi.org/10.1017/s0960129597002296.
Full textAbstract:
Milner's action calculus implements abstraction in monoidal categories, so that familiar λ-calculi can be subsumed together with the π-calculus and the Petri nets. Variables are generalised to names, which allow only a restricted form of substitution.In the present paper, the well-known categorical semantics of the λ-calculus is generalised to the action calculus. A suitable functional completeness theorem for symmetric monoidal categories is proved: we determine the conditions under which the abstraction is definable. Algebraically, the distinction between the variables and the names boils down to the distinction between the transcendental and the algebraic elements. The former lead to polynomial extensions, like, for example, the ring ℤ[x]; the latter lead to algebraic extensions like ℤ[√2] or ℤ[i].Building upon the work of P. Gardner, we introduce action categories, and show that they are related to the static action calculus in exactly the same way as cartesian closed categories are related to the λ-calculus. Natural examples of this structure arise from allegories and cartesian bicategories. On the other hand, the free algebras for any commutative Moggi monad form an action category. The general correspondence of action calculi and Moggi monads will be worked out in a sequel to this work.
8
Doust, Ian, and Qiu Bozhou. "The spectral theorem for well-bounded operators." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 54, no. 3 (June 1993): 334–51. http://dx.doi.org/10.1017/s1446788700031827.
Full textAbstract:
AbstractWell-bounded operators are those which possess a bounded functional calculus for the absolutely continuous functions on some compact interval. Depending on the weak compactness of this functional calculus, one obtains one of two types of spectral theorem for these operators. A method is given which enables one to obtain both spectral theorems by simply changing the topology used. Even for the case of well-bounded operators of type (B), the proof given is more elementary than that previously in the literature.
9
SCHMITT, T. "FUNCTIONALS OF CLASSICAL FIELDS IN QUANTUM FIELD THEORY." Reviews in Mathematical Physics 07, no. 08 (November 1995): 1249–301. http://dx.doi.org/10.1142/s0129055x95000463.
Full textAbstract:
Many methods of modern quantum field theory rely heavily on functionals of classical fields; this notion is however problematic whenever anticommuting fields are present. We propose a calculus for such functionals which avoids the use of auxiliary Grassmann algebras, and which relies on an infinite-dimensional version of Berezin-Leites supermanifold theory. We begin by studying “functional power series expansions” without growth conditions; this already allows to make e.g. the Yang-Mills action functional with fermionic, anticommuting matter fields a well-defined mathematical object. We introduce analytical conditions on power series which enable us to substitute them into each other, and we globalize them to superfunctionals. Also, infinitesimal transformation laws of the fields are discussed.
10
Jacobson, David K., Tanvi P. Honap, Cara Monroe, Justin Lund, Brett A. Houk, Anna C. Novotny, Cynthia Robin, Elisabetta Marini, and Cecil M. Lewis. "Functional diversity of microbial ecologies estimated from ancient human coprolites and dental calculus." Philosophical Transactions of the Royal Society B: Biological Sciences 375, no. 1812 (October 5, 2020): 20190586. http://dx.doi.org/10.1098/rstb.2019.0586.
Full textAbstract:
Human microbiome studies are increasingly incorporating macroecological approaches, such as community assembly, network analysis and functional redundancy to more fully characterize the microbiome. Such analyses have not been applied to ancient human microbiomes, preventing insights into human microbiome evolution. We address this issue by analysing published ancient microbiome datasets: coprolites from Rio Zape ( n = 7; 700 CE Mexico) and historic dental calculus ( n = 44; 1770–1855 CE, UK), as well as two novel dental calculus datasets: Maya ( n = 7; 170 BCE-885 CE, Belize) and Nuragic Sardinians ( n = 11; 1400–850 BCE, Italy). Periodontitis-associated bacteria ( Treponema denticola , Fusobacterium nucleatum and Eubacterium saphenum ) were identified as keystone taxa in the dental calculus datasets. Coprolite keystone taxa included known short-chain fatty acid producers ( Eubacterium biforme, Phascolarctobacterium succinatutens ) and potentially disease-associated bacteria ( Escherichia , Brachyspira) . Overlap in ecological profiles between ancient and modern microbiomes was indicated by similarity in functional response diversity profiles between contemporary hunter–gatherers and ancient coprolites, as well as parallels between ancient Maya, historic UK, and modern Spanish dental calculus; however, the ancient Nuragic dental calculus shows a distinct ecological structure. We detected key ecological signatures from ancient microbiome data, paving the way to expand understanding of human microbiome evolution. This article is part of the theme issue ‘Insights into health and disease from ancient biomolecules’.
11
Sharyn, S. V. "Application of the functional calculus to solving of infinite dimensional heat equation." Carpathian Mathematical Publications 8, no. 2 (December 30, 2016): 313–22. http://dx.doi.org/10.15330/cmp.8.2.313-322.
Full textAbstract:
In this paper we study infinite dimensional heat equation associated with the Gross Laplacian. Using the functional calculus method, we obtain the solution of appropriate Cauchy problem in the space of polynomial ultradifferentiable functions. The semigroup approach is considered as well.
12
Baltag, Alexandru, and Johan van Benthem. "A Simple Logic of Functional Dependence." Journal of Philosophical Logic 50, no. 5 (March 24, 2021): 939–1005. http://dx.doi.org/10.1007/s10992-020-09588-z.
Full textAbstract:
AbstractThis paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized assignment semantics for first order logic. The expressive strength, complete proof calculus and meta-properties of LFD are explored. Various language extensions are presented as well, up to undecidable modal-style logics for independence and dynamic logics of changing dependence models. Finally, more concrete settings for dependence are discussed: continuous dependence in topological models, linear dependence in vector spaces, and temporal dependence in dynamical systems and games.
13
Gabbay, Michael. "A proof-theoretic treatment of λ-reduction with cut-elimination: λ-calculus as a logic programming language." Journal of Symbolic Logic 76, no. 2 (June 2011): 673–99. http://dx.doi.org/10.2178/jsl/1305810770.
Full textAbstract:
AbstractWe build on an existing a term-sequent logic for the λ-calculus. We formulate a general sequent system that fully integrates αβη-reductions between untyped λ-terms into first order logic.We prove a cut-elimination result and then offer an application of cut-elimination by giving a notion of uniform proof for λ-terms. We suggest how this allows us to view the calculus of untyped αβ-reductions as a logic programming language (as well as a functional programming language, as it is traditionally seen).
14
Francfort, G., and J. Sivaloganathan. "On conservation laws and necessary conditions in the calculus of variations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 132, no. 6 (December 2002): 1361–71. http://dx.doi.org/10.1017/s0308210500002146.
Full textAbstract:
It is well known from the work of Noether that every variational symmetry of an integral functional gives rise to a corresponding conservation law. In this paper, we prove that each such conservation law arises directly as the Euler-Lagrange equation for the functional on taking suitable variations around a minimizer.
15
Brealey, Jaelle C., Henrique G. Leitão, Tom van der Valk, Wenbo Xu, Katia Bougiouri, Love Dalén, and Katerina Guschanski. "Dental Calculus as a Tool to Study the Evolution of the Mammalian Oral Microbiome." Molecular Biology and Evolution 37, no. 10 (May 28, 2020): 3003–22. http://dx.doi.org/10.1093/molbev/msaa135.
Full textAbstract:
Abstract Dental calculus, the calcified form of the mammalian oral microbial plaque biofilm, is a rich source of oral microbiome, host, and dietary biomolecules and is well preserved in museum and archaeological specimens. Despite its wide presence in mammals, to date, dental calculus has primarily been used to study primate microbiome evolution. We establish dental calculus as a valuable tool for the study of nonhuman host microbiome evolution, by using shotgun metagenomics to characterize the taxonomic and functional composition of the oral microbiome in species as diverse as gorillas, bears, and reindeer. We detect oral pathogens in individuals with evidence of oral disease, assemble near-complete bacterial genomes from historical specimens, characterize antibiotic resistance genes, reconstruct components of the host diet, and recover host genetic profiles. Our work demonstrates that metagenomic analyses of dental calculus can be performed on a diverse range of mammalian species, which will allow the study of oral microbiome and pathogen evolution from a comparative perspective. As dental calculus is readily preserved through time, it can also facilitate the quantification of the impact of anthropogenic changes on wildlife and the environment.
16
Massa, Enrico, Danilo Bruno, Gianvittorio Luria, and Enrico Pagani. "Geometric constrained variational calculus I: Piecewise smooth extremals." International Journal of Geometric Methods in Modern Physics 12, no. 05 (May 2015): 1550061. http://dx.doi.org/10.1142/s0219887815500619.
Full textAbstract:
A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic constraints. Special attention is paid to the tensorial aspects of the theory. As far as the kinematical foundations are concerned, a fully covariant scheme is developed through the introduction of the concept of infinitesimal control. The standard classification of the extremals into normal and abnormal ones is discussed, pointing out the existence of an algebraic algorithm assigning to each admissible curve a corresponding abnormality index, related to the co-rank of a suitable linear map. Attention is then shifted to the study of the first variation of the action functional. The analysis includes a revisitation of Pontryagin's equations and of the Lagrange multipliers method, as well as a reformulation of Pontryagin's algorithm in Hamiltonian terms. The analysis is completed by a general result, concerning the existence of finite deformations with fixed endpoints.
17
OSHIMA, YOICHI. "TIME-DEPENDENT DIRICHLET FORMS AND RELATED STOCHASTIC CALCULUS." Infinite Dimensional Analysis, Quantum Probability and Related Topics 07, no. 02 (June 2004): 281–316. http://dx.doi.org/10.1142/s021902570400158x.
Full textAbstract:
Analytic and probabilistic properties of symmetric or non-symmetric Dirichlet forms are well studied. But the processes with parabolic generators are out of the framework of symmetric Dirichlet forms. To cover these cases, we have introduced the time-dependent Dirichlet forms and studied their properties so far. In this expository article, we intend to explain in detail the analytic and probabilistic properties for time-dependent Dirichlet forms parallel to the symmetric Dirichlet forms. New results on a characterization of the minimal α-excessive function dominating a quasi-continuous function as well as the correspondence between additive functionals and smooth mesures are given. In particular, we emphasized the existence of the nontrivial semipolar sets under our settings.
18
FLORINDO, JOÃO BATISTA, MÁRIO DE CASTRO, and ODEMIR MARTINEZ BRUNO. "ENHANCING VOLUMETRIC BOULIGAND–MINKOWSKI FRACTAL DESCRIPTORS BY USING FUNCTIONAL DATA ANALYSIS." International Journal of Modern Physics C 22, no. 09 (September 2011): 929–52. http://dx.doi.org/10.1142/s0129183111016701.
Full textAbstract:
This work proposes and studies the concept of Functional Data Analysis transform, applying it to the performance improving of volumetric Bouligand–Minkowski fractal descriptors. The proposed transform consists essentially in changing the descriptors originally defined in the space of the calculus of fractal dimension into the space of coefficients used in the functional data representation of these descriptors. The transformed descriptors are used here in texture classification problems. The enhancement provided by the FDA transform is measured by comparing the transformed to the original descriptors in terms of the correctness rate in the classification of well known datasets.
19
Dhersin, Jean-Stéphane, and Laurent Serlet. "A Stochastic Calculus Approach for the Brownian Snake." Canadian Journal of Mathematics 52, no. 1 (February 1, 2000): 92–118. http://dx.doi.org/10.4153/cjm-2000-004-3.
Full textAbstract:
AbstractWe study the “Brownian snake” introduced by Le Gall, and also studied by Dynkin, Kuznetsov, Watanabe. We prove that Itô’s formula holds for a wide class of functionals. As a consequence, we give a new proof of the connections between the Brownian snake and super-Brownian motion. We also give a new definition of the Brownian snake as the solution of a well-posed martingale problem. Finally, we construct a modified Brownian snake whose lifetime is driven by a path-dependent stochastic equation. This process gives a representation of some super-processes.
20
SCHMÜDGEN, KONRAD. "THE QUANTUM QUARTER PLANE AND THE REAL QUANTUM PLANE." International Journal of Mathematics 13, no. 03 (May 2002): 279–321. http://dx.doi.org/10.1142/s0129167x02001307.
Full textAbstract:
Suppose q≠±1 is a complex number of modulus one. Let [Formula: see text] be the *-algebra with two hermitean generators x and y satisfying the relation xy=qyx. Using Hilbert space representations of [Formula: see text] and the Weyl calculus of pseudodifferential operators we construct *-algebras of "functions" on the quantum quarter plane [Formula: see text] and on the real quantum plane [Formula: see text] which are left module *-algebras for the Hopf *-algebra [Formula: see text]. We define covariant positive linear functionals hk, k∈ℤ2, and study the actions of the *-algebras [Formula: see text] and [Formula: see text] on the associated Hilbert spaces. Quantum analogs of the partial Fourier transforms and the Fourier transform are found. A differential calculus on the "function" *-algebras is also developed and investigated.
21
STREICHER, Th, and B. REUS. "Classical logic, continuation semantics and abstract machines." Journal of Functional Programming 8, no. 6 (November 1998): 543–72. http://dx.doi.org/10.1017/s0956796898003141.
Full textAbstract:
One of the goals of this paper is to demonstrate that denotational semantics is useful for operational issues like implementation of functional languages by abstract machines. This is exemplified in a tutorial way by studying the case of extensional untyped call-by-name λ-calculus with Felleisen's control operator [Cscr ]. We derive the transition rules for an abstract machine from a continuation semantics which appears as a generalization of the ¬¬-translation known from logic. The resulting abstract machine appears as an extension of Krivine's machine implementing head reduction. Though the result, namely Krivine's machine, is well known our method of deriving it from continuation semantics is new and applicable to other languages (as e.g. call-by-value variants). Further new results are that Scott's D∞-models are all instances of continuation models. Moreover, we extend our continuation semantics to Parigot's λμ-calculus from which we derive an extension of Krivine's machine for λμ-calculus. The relation between continuation semantics and the abstract machines is made precise by proving computational adequacy results employing an elegant method introduced by Pitts.
22
Leipholz, H. H. E. "On Some Developments in Direct Methods of the Calculus of Variations." Applied Mechanics Reviews 40, no. 10 (October 1, 1987): 1379–92. http://dx.doi.org/10.1115/1.3149540.
Full textAbstract:
One of the significant events in mathematical physics, in this century, is the introduction and further development of the so-called direct methods which were first applied by Rayleigh and Ritz to possibly extremum but at least stationary variational problems; they have been extended by Galerkin to problems which are not even stationary but involve only variations in the sense of the principle of virtual work. It is shown in this paper how, in the course of a further development of direct methods, the question of a proper choice of coordinate functions and of a proof of convergence of the method in the case of nonextremum and nonstationary variational functionals have been solved. Since an application of direct methods depends largely on the availability of basic functionals preferably with at least the property of stationarity, it is shown how such functionals can be obtained by switching from the conventional energy space to more abstract spaces involving adjoint problems or variations of operators rather than functions. Also, the question of an application of direct methods to initial value problems has been considered, as well as a modification of Galerkin’s equations which allows one to avoid cumbersome boundary conditions. To sum up, one can say: the paper shows how recent research has made direct methods much more general and more broadly applicable than was the case at the time of their introduction to mathematical physics at the beginning of this century.
23
Chevreau, Bernard, and Aurelian Crăciunescu. "Factorizations in preduals associated to ρ-contractions." Annals of West University of Timisoara - Mathematics and Computer Science 53, no. 1 (July 1, 2015): 3–17. http://dx.doi.org/10.1515/awutm-2015-0001.
Full textAbstract:
Abstract We establish directly factorization results for classes of ρ-contractions, corresponding to those obtained for certain classes of contractions. As an example of result which is not an immediate consequence of the fact that any ρ-contraction is similar to an ordinary contraction we give an "optimal" characterization of absolutely continuous ρ-contractions whose associated functional calculus has Property (Aא₀). Along the way we show that a ρ-contraction is absolutely continuous if and only if it admits an absolutely continuous unitary ρ-dilation generalizing a well- known result for usual contractions.
24
Backhoff, Julio, Giovanni Conforti, Ivan Gentil, and Christian Léonard. "The mean field Schrödinger problem: ergodic behavior, entropy estimates and functional inequalities." Probability Theory and Related Fields 178, no. 1-2 (June 23, 2020): 475–530. http://dx.doi.org/10.1007/s00440-020-00977-8.
Full textAbstract:
Abstract We study the mean field Schrödinger problem (MFSP), that is the problem of finding the most likely evolution of a cloud of interacting Brownian particles conditionally on the observation of their initial and final configuration. Its rigorous formulation is in terms of an optimization problem with marginal constraints whose objective function is the large deviation rate function associated with a system of weakly dependent Brownian particles. We undertake a fine study of the dynamics of its solutions, including quantitative energy dissipation estimates yielding the exponential convergence to equilibrium as the time between observations grows larger and larger, as well as a novel class of functional inequalities involving the mean field entropic cost (i.e. the optimal value in (MFSP)). Our strategy unveils an interesting connection between forward backward stochastic differential equations and the Riemannian calculus on the space of probability measures introduced by Otto, which is of independent interest.
25
Lazarevic, Mihailo. "Biologically inspired control and modeling of (bio)robotic systems and some applications of fractional calculus in mechanics." Theoretical and Applied Mechanics 40, no. 1 (2013): 163–87. http://dx.doi.org/10.2298/tam1301163l.
Full textAbstract:
In this paper, the applications of biologically inspired modeling and control of (bio)mechanical (non)redundant mechanisms are presented, as well as newly obtained results of author in mechanics which are based on using fractional calculus. First, it is proposed to use biological analog-synergy due to existence of invariant features in the execution of functional motion. Second, the model of (bio)mechanical system may be obtained using another biological concept called distributed positioning (DP), which is based on the inertial properties and actuation of joints of considered mechanical system. In addition, it is proposed to use other biological principles such as: principle of minimum interaction, which takes a main role in hierarchical structure of control and self-adjusting principle (introduce local positive/negative feedback on control with great amplifying), which allows efficiently realization of control based on iterative natural learning. Also, new, recently obtained results of the author in the fields of stability, electroviscoelasticity, and control theory are presented which are based on using fractional calculus (FC).
26
Charlesworth, Ian, Ken Dykema, Fedor Sukochev, and Dmitriy Zanin. "Simultaneous Upper Triangular Forms for Commuting Operators in a Finite von Neumann Algebra." Canadian Journal of Mathematics 72, no. 5 (May 15, 2019): 1188–245. http://dx.doi.org/10.4153/s0008414x19000282.
Full textAbstract:
AbstractThe joint Brown measure and joint Haagerup–Schultz projections for tuples of commuting operators in a von Neumann algebra equipped with a faithful tracial state are investigated, and several natural properties are proved for these. It is shown that the support of the joint Brown measure is contained in the Taylor joint spectrum of the tuple, and also in the ostensibly smaller left Harte spectrum. A simultaneous upper triangularization result for finite commuting tuples is proved, and the joint Brown measure and joint Haagerup–Schultz projections are shown to behave well under the Arens multivariate holomorphic functional calculus of such a commuting tuple.
27
ASHTEKAR, ABHAY. "POLYMER GEOMETRY AT PLANCK SCALE AND QUANTUM EINSTEIN EQUATIONS." International Journal of Modern Physics D 05, no. 06 (December 1996): 629–48. http://dx.doi.org/10.1142/s0218271896000400.
Full textAbstract:
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge equivalent connections. This calculus does not use any background fields (such as a metric) and thus well-suited to a fully non-perturbative treatment of quantum gravity. Using this framework, quantum geometry is examined. Fundamental excitations turn out to be one-dimensional, rather like polymers. Geometrical observables such as areas of surfaces and volumes of regions are purely discrete spectra. Continuum picture arises only upon coarse graining of suitable semi-classical states. Next, regulated quantum diffeomorphism constraints can be imposed in an anomaly-free fashion and the space of solutions can be given a natural Hilbert space structure. Progress has also been made on the quantum Hamiltonian constraint in a number of directions. In particular, there is a recent approach based on a generalized .Wick transformation which maps solutions to the Euclidean quantum constraints to those of the Lorentzian theory. These developments are summarized. Emphasis is on conveying the underlying ideas and overall pictures rather than technical details.
28
Mishra, Lakshmi Narayan, Shikha Pandey, and Vishnu Narayan Mishra. "King type generalization of Baskakov operators based on (𝑝, 𝑞) calculus with better approximation properties." Analysis 40, no. 4 (November 1, 2020): 163–73. http://dx.doi.org/10.1515/anly-2019-0054.
Full textAbstract:
AbstractApproximation using linear positive operators is a well-studied research area. Many operators and their generalizations are investigated for their better approximation properties. In the present paper, we construct and investigate a variant of modified (p,q)-Baskakov operators, which reproduce the test function x^{2}. We have determined the order of approximation of the operators via K-functional and second order, the usual modulus of continuity, weighted and statistical approximation properties. In the end, some graphical results which depict the comparison with (p,q)-Baskakov operators are explained and a Voronovskaja type result is obtained.
29
SAPORITO, YURI F. "FIRST-ORDER ASYMPTOTICS OF PATH-DEPENDENT DERIVATIVES IN MULTISCALE STOCHASTIC VOLATILITY ENVIRONMENT." International Journal of Theoretical and Applied Finance 21, no. 03 (May 2018): 1850024. http://dx.doi.org/10.1142/s0219024918500243.
Full textAbstract:
In this paper, we extend the first-order asymptotics analysis of Fouque et al. to general path-dependent financial derivatives using Dupire’s functional Itô calculus. The main conclusion is that the market group parameters calibrated to vanilla options can be used to price to the same order exotic, path-dependent derivatives as well. Under general conditions, the first-order condition is represented by a conditional expectation that could be numerically evaluated. Moreover, if the path-dependence is not too severe, we are able to find path-dependent closed-form solutions equivalent to the first-order approximation of path-independent options derived in Fouque et al. Additionally, we exemplify the results with Asian options and options on quadratic variation.
30
Sun, Lin, Xinchao Meng, Jiucheng Xu, and Shiguang Zhang. "An Image Segmentation Method Based on Improved Regularized Level Set Model." Applied Sciences 8, no. 12 (November 26, 2018): 2393. http://dx.doi.org/10.3390/app8122393.
Full textAbstract:
When the level set algorithm is used to segment an image, the level set function must be initialized periodically to ensure that it remains a signed distance function (SDF). To avoid this defect, an improved regularized level set method-based image segmentation approach is presented. First, a new potential function is defined and introduced to reconstruct a new distance regularization term to solve this issue of periodically initializing the level set function. Second, by combining the distance regularization term with the internal and external energy terms, a new energy functional is developed. Then, the process of the new energy functional evolution is derived by using the calculus of variations and the steepest descent approach, and a partial differential equation is designed. Finally, an improved regularized level set-based image segmentation (IRLS-IS) method is proposed. Numerical experimental results demonstrate that the IRLS-IS method is not only effective and robust to segment noise and intensity-inhomogeneous images but can also analyze complex medical images well.
31
Taheri, Ali. "Sufficiency theorems for local minimizers of the multiple integrals of the calculus of variations." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 131, no. 1 (February 2001): 155–84. http://dx.doi.org/10.1017/s0308210500000822.
Full textAbstract:
Let Ω ⊂ Rn be a bounded domain and let f : Ω × RN × RN×n → R. Consider the functional over the class of Sobolev functions W1,q(Ω;RN) (1 ≤ q ≤ ∞) for which the integral on the right is well defined. In this paper we establish sufficient conditions on a given function u0 and f to ensure that u0 provides an Lr local minimizer for I where 1 ≤ r ≤ ∞. The case r = ∞ is somewhat known and there is a considerable literature on the subject treating the case min(n, N) = 1, mostly based on the field theory of the calculus of variations. The main contribution here is to present a set of sufficient conditions for the case 1 ≤ r < ∞. Our proof is based on an indirect approach and is largely motivated by an argument of Hestenes relying on the concept of ‘directional convergence’.
32
CHAVAN, SAMEER. "ON A FRIEDRICHS EXTENSION RELATED TO UNBOUNDED SUBNORMALS-II." Glasgow Mathematical Journal 50, no. 1 (January 2008): 97–109. http://dx.doi.org/10.1017/s0017089507003941.
Full textAbstract:
AbstractWe study the Friedrichs extensions of unbounded cyclic subnormals. The main result of the present paper is the identification of the Friedrichs extensions of certain cyclic subnormals with their closures. This generalizes as well as complements the main result obtained in [5]. Such characterizations lead to abstract Galerkin approximations, generalized wave equations, and bounded${\mathcal H}^{\infty}$-functional calculi.
33
Di Cosmo, Roberto. "Deciding type isomorphisms in a type-assignment framework." Journal of Functional Programming 3, no. 4 (October 1993): 485–525. http://dx.doi.org/10.1017/s0956796800000861.
Full textAbstract:
AbstractThis paper provides a formal treatment of isomorphic types for languages equipped with an ML style polymorphic type inference mechanism. The results obtained make less justified the commonplace feeling that (the core of) ML is a subset of second order λ-calculus: we can provide an isomorphism of types that holds in the core ML language, but not in second order λ-calculus. This new isomorphism allows to provide a complete (and decidable) axiomatization of all the types isomorphic in ML style languages, a relevant issue for thetype as specificationsparadigm in library searches. This work is a very extended version of Di Cosmo (1992): we provide both a thorough theoretical treatment of the topic and describe a practical implementation of a library search system so that the paper can be used as a reference both by those interested in the formal theory of ML style languages, and by those simply concerned with implementation issues. The new isomorphism can also be used to extend the usual ML type-inference algorithm, as suggested by Di Cosmo (1992). Building on that proposal, we introduce a better type-inference algorithm that behaves well in the presence of non-functional primitives like references and exceptions. The algorithm described here has been implemented easily as a variation to the Caml-Light 0.4 system.
34
Petrişor, Silviu Mihai, and Ghiţă Bârsan. "Calculus and Implementation of a TRTR Industrial Robot Servicing a Flexible Manufacturing Cell Destined for the AAV Building Industry." Applied Mechanics and Materials 332 (July 2013): 171–80. http://dx.doi.org/10.4028/www.scientific.net/amm.332.171.
Full textAbstract:
The authors of this paper aims to highlight the basic design of a flexible manufacturing cell with parallel organization destined for the assembly of tires on AAV carcasses shafts, operation performed by a TRTR serial-modular industrial robot. The paper describes, in detail: the direct and inverse geometric modeling of the mechanical structure, the direct kinematic modeling of the industrial robot under study, by calculating and illustrating, by means of time development graphs, the column vectors of the generalized coordinates as well as the prehension device characteristic point trajectory that define, at a given moment, its position, orientation and movement within the flexible manufacturing cell proposed for implementation. The final part of the paper presents, based on several functional parameters mandatory for the building of the FMC, the calculus of economic indicators necessary for the optimum functioning of the cell as well as for determining the value of the robot included in its activity and of the overall flexible manufacturing system.
35
Nolte, Bodo, Sigmar Kempfle, and Ingo Schäfer. "Does a Real Material Behave Fractionally? Applications of Fractional Differential Operators to the Damped Structure Borne Sound in Viscoelastic Solids." Journal of Computational Acoustics 11, no. 03 (September 2003): 451–89. http://dx.doi.org/10.1142/s0218396x03002024.
Full textAbstract:
Time dependent analysis of the dynamic damped behavior of continua are mathematically modelled by partial differential equations. One obtains uniqueness, existence and stability (well posed problems) by the implementation of the correct initial boundary conditions. However, by taking memory effects into consideration, any change in the past of the system changes the future dynamic behavior. Classical damping descriptions fail when describing the behavior of many materials, like teflon. This is because in classical theory the operators are local ones. The implementation of fractional time derivatives into the partial differential equations is an alternative technique to overcome these problems. Thereby the time derivative operator is a global one, memory effects in structure borne sound can be calculated. In this paper the theory of fractional time derivative operators and their application in continuum mechanics is presented. The main result when using this method for damping behavior is that a global operator is needed which takes the whole history into account. We call this theory the functional calculus method instead of the well-known fractional calculus with the use of initial conditions. In order to show the efficiency of this method the calculated impulse response of a viscoelastic rod is compared with measurements. It is shown that the damping behavior is described much better than by other models with comparably few parameters. Moreover, it is the only one that works in a wide frequency range and can describe the dispersion of the resonance frequencies. The implementation of this damping description in a Boundary Element Code is an application of dynamics of 3D continua in the frequency domain.
36
Shieh, Tien-Tsan, and Daniel E. Spector. "On a new class of fractional partial differential equations II." Advances in Calculus of Variations 11, no. 3 (July 1, 2018): 289–307. http://dx.doi.org/10.1515/acv-2016-0056.
Full textAbstract:
AbstractIn this paper we continue to advance the theory regarding the Riesz fractional gradient in the calculus of variations and fractional partial differential equations begun in an earlier work of the same name. In particular, we here establish an {L^{1}} Hardy inequality, obtain further regularity results for solutions of certain fractional PDE, demonstrate the existence of minimizers for integral functionals of the fractional gradient with non-linear dependence in the field, and also establish the existence of solutions to corresponding Euler–Lagrange equations obtained as conditions of minimality. In addition, we pose a number of open problems, the answers to which would fill in some gaps in the theory as well as to establish connections with more classical areas of study, including interpolation and the theory of Dirichlet forms.
37
Musilová, Jana, and Stanislav Hronek. "The calculus of variations on jet bundles as a universal approach for a variational formulation of fundamental physical theories." Communications in Mathematics 24, no. 2 (December 1, 2016): 173–93. http://dx.doi.org/10.1515/cm-2016-0012.
Full textAbstract:
Abstract As widely accepted, justified by the historical developments of physics, the background for standard formulation of postulates of physical theories leading to equations of motion, or even the form of equations of motion themselves, come from empirical experience. Equations of motion are then a starting point for obtaining specific conservation laws, as, for example, the well-known conservation laws of momenta and mechanical energy in mechanics. On the other hand, there are numerous examples of physical laws or equations of motion which can be obtained from a certain variational principle as Euler-Lagrange equations and their solutions, meaning that the \true trajectories" of the physical systems represent stationary points of the corresponding functionals.It turns out that equations of motion in most of the fundamental theories of physics (as e.g. classical mechanics, mechanics of continuous media or fluids, electrodynamics, quantum mechanics, string theory, etc.), are Euler-Lagrange equations of an appropriately formulated variational principle. There are several well established geometrical theories providing a general description of variational problems of different kinds. One of the most universal and comprehensive is the calculus of variations on fibred manifolds and their jet prolongations. Among others, it includes a complete general solution of the so-called strong inverse variational problem allowing one not only to decide whether a concrete equation of motion can be obtained from a variational principle, but also to construct a corresponding variational functional. Moreover, conservation laws can be derived from symmetries of the Lagrangian defining this functional, or directly from symmetries of the equations.In this paper we apply the variational theory on jet bundles to tackle some fundamental problems of physics, namely the questions on existence of a Lagrangian and the problem of conservation laws. The aim is to demonstrate that the methods are universal, and easily applicable to distinct physical disciplines: from classical mechanics, through special relativity, waves, classical electrodynamics, to quantum mechanics.
38
Veselovska, Natalia, Alexander Malakov, and Sergiy Burlaka. "MATHEMATICAL MODELING OF THE MECHANISM POST-TRAILED KPP-4.2." ENGINEERING, ENERGY, TRANSPORT AIC, no. 4(107) (December 20, 2019): 5–10. http://dx.doi.org/10.37128/2520-6168-2019-4-1.
Full textAbstract:
Maintaining the required cut height minimizes losses and ensures continuous shoe contact with the surface. Thus the excessive pressure of the shoe destroys the stubble and leads to its accelerated wear, and insufficient pressure is accompanied by increased losses and provokes the galloping of the header. An analytical solution to the problem of modeling the mechanism of the KPP-4.2 hanging is an iterative execution of the analysis procedures based on the formed hypothesis, as well as the procedures of comparison and selection of options in the procedure of parametric synthesis. It is a choice of a combination of internal parameters of the flattening device, which, while satisfying the functional limitations, simultaneously stabilize the whole mechanism. A study and analysis of the hanging mechanism of a mower-conditioner trailed KPP-4.2 using methods of theoretical mechanics, differential and integral calculus, probability theory, mathematical modeling and computer software. A geometric model has been created for calculating and optimizing the operation of the hanging mechanism. The MVA KPP-4.2 output parameters were calculated for three different cut heights.
39
Ebenbeck, Matthias, and Patrik Knopf. "Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 71. http://dx.doi.org/10.1051/cocv/2019059.
Full textAbstract:
We investigate a distributed optimal control problem for a diffuse interface model for tumor growth. The model consists of a Cahn–Hilliard type equation for the phase field variable, a reaction diffusion equation for the nutrient concentration and a Brinkman type equation for the velocity field. These PDEs are endowed with homogeneous Neumann boundary conditions for the phase field variable, the chemical potential and the nutrient as well as a “no-friction” boundary condition for the velocity. The control represents a medication by cytotoxic drugs and enters the phase field equation. The aim is to minimize a cost functional of standard tracking type that is designed to track the phase field variable during the time evolution and at some fixed final time. We show that our model satisfies the basics for calculus of variations and we present first-order and second-order conditions for local optimality. Moreover, we present a globality condition for critical controls and we show that the optimal control is unique on small time intervals.
40
Marco, F. J., J. A. Lopez, and M. J. Martinez. "A time-dependent extension to Brouwer's method for orbital elements correction." Symposium - International Astronomical Union 172 (1996): 199–202. http://dx.doi.org/10.1017/s0074180900127354.
Full textAbstract:
One of the most popular methods for orbital elements correction, by means of O-C calculus, is based on Brouwer's method [2], which is very well adapted for integrating short periods of time. We propose a general method to integrate over long intervals of time, when we have good observations, based upon a time-dependent functional relation between the derivatives of all elements with respect to all variations in the initial elements. First, we verify the truth of the unrestricted hypothesis by means of the proposed analytical method and a numerical derivation. In [6], we have incorporated a correction frame model jointly with this general method and, then, we have constructed the residual function which is minimized by the least squares method. But, as we are going to see later, there are correlations between the parameters frame correction model and the initial elements involved in the adjustment. They are obtained here, as well as an expression for the equinox correction from these frame parameters. Finally, by means of a simply weighted method, with the observations from MPC's magnetic tape, in FK4 system, we obtain an estimation for these frame parameters and an equinox correction which is in great accord with the adopted value (see [3]).
41
Phillips, John. "Self-Adjoint Fredholm Operators And Spectral Flow." Canadian Mathematical Bulletin 39, no. 4 (December 1, 1996): 460–67. http://dx.doi.org/10.4153/cmb-1996-054-4.
Full textAbstract:
AbstractWe study the topology of the nontrivial component, , of self-adjoint Fredholm operators on a separable Hilbert space. In particular, if {Bt} is a path of such operators, we can associate to {Bt} an integer, sf({Bt}), called the spectral flow of the path. This notion, due to M. Atiyah and G. Lusztig, assigns to the path {Bt} the net number of eigenvalues (counted with multiplicities) which pass through 0 in the positive direction. There are difficulties in making this precise — the usual argument involves looking at the graph of the spectrum of the family (after a suitable perturbation) and then counting intersection numbers with y = 0.We present a completely different approach using the functional calculus to obtain continuous paths of eigenprojections (at least locally) of the form . The spectral flow is then defined as the dimension of the nonnegative eigenspace at the end of this path minus the dimension of the nonnegative eigenspace at the beginning. This leads to an easy proof that spectral flow is a well-defined homomorphism from the homotopy groupoid of onto Z. For the sake of completeness we also outline the seldom-mentioned proof that the restriction of spectral flow to is an isomorphism onto Z.
42
Karolak, Stanislaw. "Réflexions Sur la Théorie de L'article de Gustave Guillaume." Lingvisticæ Investigationes. International Journal of Linguistics and Language Resources 10, no. 1 (January 1, 1986): 131–51. http://dx.doi.org/10.1075/li.10.1.05kar.
Full textAbstract:
This paper is concerned with the analysis of the theory of the French article presented in the classical work by Guillaume "Le problème de l'article et sa solution dans la langue française". The paper emphasizes Guillaume's search for the semantic nature of the relationships determining the distribution of articles. The paper supports Guillaume, who seems to claim, contrary to what is commonly believed, that the function of the articles is non inherent in them, but that it is determined by the semantic properties of the nouns which select them. Treating this claim as the starting point, the paper focuses on the analysis of various senses of noun phrases, carried out in terms of the functional calculus. The applied method invalidates the extensional theory of the noun accepted by Guillaume, as well as a number of generalisations made by him. The paper shows logical and semantic conditions of some rules governing the use of the article. They differ from those proposed by Guillaume in that they seem to reach a deeper level of linguistic mechanisms. On the other hand, the emphasis is laid on Guillaume's subtle analysis and detailed observations, which stand in a sharp contrast to his rather vague generalizations.
43
Pejovic, Branko, Vladan Micic, Mitar Perusic, Goran Tadic, Ljubica Vasiljevic, and Slavko Smiljanic. "Proposal for determining changes in entropy of semi ideal gas using mean values of temperature functions." Chemical Industry 68, no. 5 (2014): 615–28. http://dx.doi.org/10.2298/hemind130825090p.
Full textAbstract:
In a semi-ideal gas, entropy changes cannot be determined through the medium specific heat capacity in a manner as determined by the change of internal energy and enthalpy, i.e. the amount of heat exchanged. Taking this into account, the authors conducted two models through which it is possible to determine the change in the specific entropy of a semi-ideal gas for arbitrary temperature interval using the spread sheet method, using the mean values of the appropriate functions. The idea is to replace integration, which occurs here in evitably, with mean values of the previous functions. The models are derived based on the functional dependence of the actual specific heat capacity on the temperature. The theorem used is that of the mean value of a function as well as the mathematical properties of the definite integral. The mean value of a fractional function is determined via its integrand while the logarithmic functions were performed by applying a suitable transformation of the differential calculus. The relations derived relation, using the computer program, have enabled the design of appropriate thermodynamic tables through which it is possible to determine the change in entropy of arbitrary state changes in an efficient and rational manner, without the use of calculus or finished forms. In this way, the change in the entropy of a semi-ideal gas is determined for an arbitrary temperature interval using the method which is analogous to that applied in determining the change of internal energy and enthalpy or the amount of heat exchanged, which was the goal of the work. Verification of the proposed method for both the above functions was performed for a a few characteristic semi-ideal gases where change c(T) is significant, for the three adopted temperature intervals, for the characteristic change of state. This was compared to the results of the classical integral and the proposed method through the prepared tables. In certain or special cases, it is possible to apply the presented method also in determining the change in entropy of the real gas. Apart from that, the paper shows that the change in entropy for the observed characteristic case can be represented or graphically determined using the planimetric method of diagrams with suitably selected coordinates.
44
Gabbay, D. M., and V. B. Shehtman. "Undecidability of modal and intermediate first-order logics with two individual variables." Journal of Symbolic Logic 58, no. 3 (September 1993): 800–823. http://dx.doi.org/10.2307/2275098.
Full textAbstract:
The interest in fragments of predicate logics is motivated by the well-known fact that full classical predicate calculus is undecidable (cf. Church [1936]). So it is desirable to find decidable fragments which are in some sense “maximal”, i.e., which become undecidable if they are “slightly” extended. Or, alternatively, we can look for “minimal” undecidable fragments and try to identify the vague boundary between decidability and undecidability. A great deal of work in this area concerning mainly classical logic has been done since the thirties. We will not give a complete review of decidability and undecidability results in classical logic, referring the reader to existing monographs (cf. Suranyi [1959], Lewis [1979], and Dreben, Goldfarb [1979]). A short summary can also be found in the well-known book Church [1956]. Let us recall only several facts. Herein we will consider only logics without functional symbols, constants, and equality.(C1) The fragment of the classical logic with only monadic predicate letters is decidable (cf. Behmann [1922]).(C2) The fragment of the classical logic with a single binary predicate letter is undecidable. (This is a consequence of Gödel [1933].)(C3) The fragment of the classical logic with a single individual variable is decidable; in fact it is equivalent to Lewis S5 (cf. Wajsberg [1933]).(C4) The fragment of the classical logic with two individual variables is decidable (Segerberg [1973] contains a proof using modal logic; Scott [1962] and Mortimer [1975] give traditional proofs.)(C5) The fragment of the classical logic with three individual variables and binary predicate letters is undecidable (cf. Surańyi [1943]). In fact this paper considers formulas of the following typeφ,ψ being quantifier-free and the set of binary predicate letters which can appear in φ or ψ being fixed and finite.
45
MCBRIDE, CONOR, and JAMES MCKINNA. "The view from the left." Journal of Functional Programming 14, no. 1 (January 2004): 69–111. http://dx.doi.org/10.1017/s0956796803004829.
Full textAbstract:
Pattern matching has proved an extremely powerful and durable notion in functional programming. This paper contributes a new programming notation for type theory which elaborates the notion in various ways. First, as is by now quite well-known in the type theory community, definition by pattern matching becomes a more discriminating tool in the presence of dependent types, since it refines the explanation of types as well as values. This becomes all the more true in the presence of the rich class of datatypes known as inductive families (Dybjer, 1991). Secondly, as proposed by Peyton Jones (1997) for Haskell, and independently rediscovered by us, subsidiary case analyses on the results of intermediate computations, which commonly take place on the right-hand side of definitions by pattern matching, should rather be handled on the left. In simply-typed languages, this subsumes the trivial case of Boolean guards; in our setting it becomes yet more powerful. Thirdly, elementary pattern matching decompositions have a well-defined interface given by a dependent type; they correspond to the statement of an induction principle for the datatype. More general, user-definable decompositions may be defined which also have types of the same general form. Elementary pattern matching may therefore be recast in abstract form, with a semantics given by translation. Such abstract decompositions of data generalize Wadler's (1987) notion of ‘view’. The programmer wishing to introduce a new view of a type $\mathit{T}$, and exploit it directly in pattern matching, may do so via a standard programming idiom. The type theorist, looking through the Curry–Howard lens, may see this as proving a theorem, one which establishes the validity of a new induction principle for $\mathit{T}$. We develop enough syntax and semantics to account for this high-level style of programming in dependent type theory. We close with the development of a typechecker for the simply-typed lambda calculus, which furnishes a view of raw terms as either being well-typed, or containing an error. The implementation of this view is ipso facto a proof that typechecking is decidable.
46
Moor, Oege De. "Categories, relations and dynamic programming." Mathematical Structures in Computer Science 4, no. 1 (March 1994): 33–69. http://dx.doi.org/10.1017/s0960129500000360.
Full textAbstract:
Dynamic programming is a strategy for solving optimisation problems. In this paper, we show how many problems that may be solved by dynamic programming are instances of the same abstract specification. This specification is phrased using the calculus of relations offered by topos theory. The main theorem underlying dynamic programming can then be proved by straightforward equational reasoning.The generic specification of dynamic programming makes use of higher-order operators on relations, akin to the fold operators found in functional programming languages. In the present context, a data type is modelled as an initial F-algebra, where F is an endofunctor on the topos under consideration. The mediating arrows from this initial F-algebra to other F-algebras are instances of fold – but only for total functions. For a regular category ε, it is possible to construct a category of relations Rel(ε). When a functor between regular categories is a so-called relator, it can be extended (in some canonical way) to a functor between the corresponding categories of relations. Applied to an endofunctor on a topos, this process of extending functors preserves initial algebras, and hence fold can be generalised from functions to relations.It is well-known that the use of dynamic programming is governed by the principle of optimality. Roughly, the principle of optimality says that an optimal solution is composed of optimal solutions to subproblems. In a first attempt, we formalise the principle of optimality as a distributivity condition. This distributivity condition is elegant, but difficult to check in practice. The difficulty arises because we consider minimum elements with respect to a preorder, and therefore minimum elements are not unique. Assuming that we are working in a Boolean topos, it can be proved that monotonicity implies distributivity, and this monotonicity condition is easy to verify in practice.
47
Kortbeek, S., S. Bhandal, H. Machida, S. R. Martin, and G. J. Galante. "A135 HEPATOLITHIASIS AND CHOLANGIOPATHY IN PEDIATRIC CYSTIC FIBROSIS: A CASE REPORT." Journal of the Canadian Association of Gastroenterology 3, Supplement_1 (February 2020): 156–57. http://dx.doi.org/10.1093/jcag/gwz047.134.
Full textAbstract:
Abstract Background Liver disease has emerged as an important cause of cystic fibrosis (CF)-associated morbidity due to recent advancements in management and a resultant increase in life expectancy. Although focal biliary cirrhosis remains the pathognomonic finding in CF, other hepatic manifestations exist but are not as well described, particularly in the pediatric population. Aims Present two rare manifestations of pediatric CF-associated liver disease. Methods In this report, we present a pediatric CF patient with chronic abdominal pain who was found to have hepatolithiasis, cholangitis and secondary sclerosing cholangitis. Results A 12-year-old boy with CF was seen for abdominal pain with functional impairment. He had prior evidence of calculi in the common bile duct (CBD) and right intrahepatic (IH) duct, and had undergone endoscopic retrograde cholangiopancreatography (ERCP) twice with sphincterotomy once. Magnetic resonance cholangiopancreatography (MRCP) at presentation showed dilated CBD and bilateral IH ducts with calculi, evidence of acute cholecystitis and early cholangitis. He subsequently underwent a third ERCP with stone retrieval, stent placement and a laparoscopic cholecystectomy. Ursodiol dose was optimized and antibiotics were initiated. Follow-up MRCP showed improvement in CBD and IH duct dilation; the stent was removed. One month later, a fifth ERCP was performed for worsening symptoms associated with a distal filling defect in the left IH duct. Sludge was removed from the CBD and another stent was placed. A sixth ERCP with stent removal showed no stones. Interval MRCP showed resolution of IH calculi, a CBD filling defect suggestive of sludge, and thickening and enhancement of IH bile ducts with focal areas of alternating narrowing and dilation. He was maintained on antibiotics, and his symptoms persisted over the following months despite resolution of sludge, peri-portal edema and duct-wall enhancement. There was a background of increased IH ductal dilation with “beaded appearance”. Interval imaging has demonstrated persistence of these findings with recurrence of hepatolithiasis in both IH ducts, despite improved symptoms. Conclusions This case describes two rare manifestations of pediatric CF-associated liver disease: hepatolithiasis and secondary sclerosing cholangitis. While CFTR dysfunction alone predisposes to gallstone formation, the patient’s clinical course supports a theory for the development of hepatolithiasis resembling that of recurrent pyogenic cholangitis, whereby bacteriobilia from chronic or recurrent infection may promote lithogenesis in the presence of inflammatory bile duct damage. In this patient, secondary sclerosing cholangitis may have resulted from cycles of cholangitis and hepatolithiasis; alternatively, it may represent under-recognized cholangiopathy in the pediatric CF population. Funding Agencies None
48
Barthe, Gilles, Peter Dybjer, and Peter Thiemann. "Special issue on Dependent Type Theory Meets Programming Practice CALL FOR PAPERS." Journal of Functional Programming 11, no. 4 (July 2001): 437. http://dx.doi.org/10.1017/s0956796801004105.
Full textAbstract:
Modern programming languages rely on advanced type systems that detect errors at compile-time. While the benefits of type systems have long been recognized, there are some areas where the standard systems in programming languages are not expressive enough. Language designers usually trade expressiveness for decidability of the type system. Some interesting programs will always be rejected (despite their semantical soundness) or be assigned uninformative types.There are several remedies to this situation. Dependent type systems, which allow the formation of types that explicitly depend on other types or values, are one of the most promising approaches. These systems are well-investigated from a theoretical point of view by logicians and type theorists. For example, dependent types are used in proof assistants to implement various logics and there are sophisticated proof editors for developing programs in a dependently typed language.To the present day, the impact of these developments on practical programming has been small, partially because of the level of sophistication of these systems and of their type checkers. Only recently, there have been efforts to integrate dependent systems into intermediate languages in compilers and programming languages. Additional uses have been identified in high-profile applications such as mobile code security, where terms of a dependently typed lambda calculus to encode safety proofs.A special issue of the Journal of Functional Programming will be devoted to the interplay between dependent type theory and programming practice. We welcome technical contributions in the field, as well as position papers that:[bull ] make researchers in programming languages aware of new developments and research directions on the theory side;[bull ] point out to theorists practical uses of advanced type systems and urge them to address theoretical problems arising in emerging applications.Authors who are concerned about the appropriateness of a topic are welcome to contact the guest editors. Manuscripts should be unpublished works and not submitted elsewhere. Revised and enhanced versions of papers published in conference proceedings that have not appeared in archival journals are eligible for submission. All submissions will be reviewed according to the usual standards of scholarship and originality.Submissions should be sent to Gilles Barthe (Gilles.Barthe@inria.fr), with a copy to Nasreen Ahmad (nasreen@dcs.gla.ac.uk). Submitted articles should be sent in postscript format, preferably gzipped and uuencoded. In addition, please send, as plain text, title, abstract and contact information.The submission deadline is December 1st, 2001.
49
Firlej, Marcel, Daniel Pieniak, Agata M. Niewczas, Agata Walczak, Ivo Domagała, Anna Borucka, Krzysztof Przystupa, Joanna Igielska-Kalwat, Wojciech Jarosz, and Barbara Biedziak. "Effect of Artificial Aging on Mechanical and Tribological Properties of CAD/CAM Composite Materials Used in Dentistry." Materials 14, no. 16 (August 20, 2021): 4678. http://dx.doi.org/10.3390/ma14164678.
Full textAbstract:
With easy-to-process 3D printing materials and fast production, the quality of dental services can be improved. In the conventional procedure, the dentist makes temporary crowns directly in the patient’s mouth, e.g., from the most commonly used bis-acrylic composites. Temporary crowns made directly in the office without the use of CAD/CAM are often of inferior quality, which directly results in impaired hygiene, poorer masticatory mechanics, greater deposition of plaque, calculus and sediment, and may adversely affect periodontal and gum health. The mechanical strength, resistance to aging and abrasion of 3D printing materials are higher than those of the soft materials used in conventional methods. This translates into durability. The patient leaves the surgery with a restoration of higher utility quality compared to the conventional method. The objective of the paper was to determine the influence of aging in artificial saliva of AM (additive manufacturing) orthodontic composites on their functional properties. For the purpose of the study, fillings well-known worldwide were selected. These were traditional UV-curable resins (M I, M II, M III, M V) and a hybrid material based on a UV-curable resin (M VI). Samples were stored in artificial saliva at 37 ± 1 °C in a thermal chamber for 6 months. Indentation hardness, frictional tests and sliding wear measurements were conducted. A comparison between various materials was made. Descriptive statistics, degradation coefficients, H2E, Archard wear and specific wear rate were calculated. The Weibull statistical test for indentation hardness was performed and Hertzian contact stresses for the frictional association were calculated for unaged (M I, M II, M III, M V, M VI) and aged (M I AS, M II AS, M III AS, M V AS, M VI AS) samples. M I exhibited the lowest average hardness among the unaged materials, while M III AS had the lowest average hardness among the aged materials. Comparably low hardness was demonstrated by the M I AS material. The coefficient of friction values for the aged samples were found to be higher. The lowest wear value was demonstrated by the M I material. The wear resistance of most of the tested materials deteriorated after aging. The M VI AS material had the highest increase in wear. According to the results provided, not only the chemical composition and structure, but also aging have a great impact on the indentation hardness and wear resistance of the tested orthodontic materials.
50
Sapozhnikov, A. Yu, A. A. Kuznetsov, A. S. Mavrina, and G. G. Kulikov. "An Approach to the Transformation of a Virtual Metastructure of a Digital Design Twin of a Machine-building Enterprise Corporate Information System." Bulletin of the South Ural State University. Ser. Computer Technologies, Automatic Control & Radioelectronics 21, no. 2 (May 2021): 5–15. http://dx.doi.org/10.14529/ctcr210201.
Full textAbstract:
Currently, the methodology of system engineering is being formed, the product of which is, as usual, the creation of real objects information models, supplemented by virtual components, and on the contrary, virtual objects, supplemented by real components. For example, an information model of a technological object is a specification of real equipment, supplemented by a specification of the purchased equipment of a technological process and on the contrary. By analogy with general engineering in the field of technical activity, the metastructures of such information models must meet the V-shaped structure of the validation and verification processes. Therefore, models should be regularly checked during their life cycle to ensure that their structure and parameters correspond to real and virtual objects. At the present, there are conditions for a coordinated decision of technological objects system information modeling, taking into account their internal (physical) structure and of the digital environment the external structure. In general theoretical terms, the construction of system models is based on the problem of formal consistent description (grammatical calculus) of the structure and functional regularities of a set of objects and their connections in the subject area under study. The presented approach of the subject area system modeling under consideration is based on the classical model of a machine-building enterprise (MP) educational and production activities and a university. Aim. To apply the principles of the design approach for the formation of a corporate information system (CIS) engineering company metastructure digital twin, to explore the prospects of its application, to show the key information components in the management of subject-oriented knowledge and data, as well as the ability to scale technology in the formation of a digital environment for architecture and modern MP, improving the efficiency of business processes participants interaction. Materials and methods. The principles of the system engineering methodo¬logy (process approach, life cycle, etc.), an integrated approach and structural analysis of the design process according to the SADT (Structured Analysis and Design Technology) methodology, and the TOGAF (The Open Group Architecture Framework) methodology are used. Results. The proposed approach for system modeling the subject area is the development of works of the authors, demonstrates the possibility of scaling on the example of interaction of participants of the REC using part of the University's digital twin KIS enterprises of the real sector of the economy. The requisite of developing a knowledge management model and the increasing role of information search engines are shown. Conclusion. The proposed approach expands the application of the digital twin metastructure, allows correcting the enterprise architecture to improve the efficiency of business processes.