Journal articles: 'Higher-order term'

1

Pientka, Brigitte. "Higher-order term indexing using substitution trees." ACM Transactions on Computational Logic 11, no. 1 (October 2009): 1–40. http://dx.doi.org/10.1145/1614431.1614437.

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Burshtein, D. "Long-term attraction in higher order neural networks." IEEE Transactions on Neural Networks 9, no. 1 (1998): 42–50. http://dx.doi.org/10.1109/72.655028.

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Ito, Akihiro. "Derivation of Skyrme Lagrangian and higher-order term." Physical Review D 41, no. 9 (May 1, 1990): 2930–32. http://dx.doi.org/10.1103/physrevd.41.2930.

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D’Abbicco, Marcello, and Enrico Jannelli. "A damping term for higher-order hyperbolic equations." Annali di Matematica Pura ed Applicata (1923 -) 195, no. 2 (January 29, 2015): 557–70. http://dx.doi.org/10.1007/s10231-015-0477-z.

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Astesiano, Egidio, and Maura Cerioli. "Partial Higher-Order Specifications1." Fundamenta Informaticae 16, no. 2 (March 1, 1992): 101–26. http://dx.doi.org/10.3233/fi-1992-16203.

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In this paper the classes of extensional models of higher-order partial conditional specifications are studied, with the emphasis on the closure properties of these classes. Further it is shown that any equationally complete inference system for partial conditional specifications may be extended to an inference system for partial higher-order conditional specifications, which is equationally complete w.r.t. the class of all extensional models. Then, applying some previous results, a deduction system is proposed, equationally complete for the class of extensional models of a partial conditional specification. Finally, turning the attention to the special important case of termextensional models, it is first shown a sound and equationally complete inference system and then necessary and sufficient conditions are given for the existence of free models, which are also free in the class of term-generated extensional models.

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BALDAN, PAOLO, CLARA BERTOLISSI, HORATIU CIRSTEA, and CLAUDE KIRCHNER. "A rewriting calculus for cyclic higher-order term graphs." Mathematical Structures in Computer Science 17, no. 3 (June 2007): 363–406. http://dx.doi.org/10.1017/s0960129507006093.

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The Rewriting Calculus (ρ-calculus, for short) was introduced at the end of the 1990s and fully integrates term-rewriting and λ-calculus. The rewrite rules, acting as elaborated abstractions, their application and the structured results obtained are first class objects of the calculus. The evaluation mechanism, which is a generalisation of beta-reduction, relies strongly on term matching in various theories.In this paper we propose an extension of the ρ-calculus, called ρg-calculus, that handles structures with cycles and sharing rather than simple terms. This is obtained by using recursion constraints in addition to the standard ρ-calculus matching constraints, which leads to a term-graph representation in an equational style. Like in the ρ-calculus, the transformations are performed by explicit application of rewrite rules as first-class entities. The possibility of expressing sharing and cycles allows one to represent and compute over regular infinite entities.We show that the ρg-calculus, under suitable linearity conditions, is confluent. The proof of this result is quite elaborate, due to the non-termination of the system and the fact that ρg-calculus-terms are considered modulo an equational theory. We also show that the ρg-calculus is expressive enough to simulate first-order (equational) left-linear term-graph rewriting and α-calculus with explicit recursion (modelled using a letrec-like construct).

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Bertolissi, C., P. Baldan, H. Cirstea, and C. Kirchner. "A Rewriting Calculus for Cyclic Higher-order Term Graphs." Electronic Notes in Theoretical Computer Science 127, no. 5 (May 2005): 21–41. http://dx.doi.org/10.1016/j.entcs.2005.01.034.

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Bartušek, Miroslav, Zuzana Došlá, and Mauro Marini. "Oscillation for higher order differential equations with a middle term." Boundary Value Problems 2014, no. 1 (2014): 48. http://dx.doi.org/10.1186/1687-2770-2014-48.

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Yang, Chunxiao, Feiyu Ji, and Qingyan Yin. "Fujita phenomenon in higher-order parabolic equation with nonlocal term." Applicable Analysis 97, no. 6 (March 6, 2017): 1042–48. http://dx.doi.org/10.1080/00036811.2017.1298744.

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Bartušek, M., M. Cecchi, Z. Došlá, and M. Marini. "Asymptotics for higher order differential equations with a middle term." Journal of Mathematical Analysis and Applications 388, no. 2 (April 2012): 1130–40. http://dx.doi.org/10.1016/j.jmaa.2011.10.059.

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Gasiński, Leszek. "Evolution hemivariational inequality with hysteresis operator in higher order term." Acta Mathematica Sinica, English Series 24, no. 1 (January 2008): 107–20. http://dx.doi.org/10.1007/s10114-007-0997-6.

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Dix, Julio G., Dillip Kumar Ghose, and Radhanath Rath. "Oscillation of a higher order neutral differential equation with a sub-linear delay term and positive and negative coefficients." Mathematica Bohemica 134, no. 4 (2009): 411–25. http://dx.doi.org/10.21136/mb.2009.140673.

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KORCHEMSKY, G. P. "MATRIX MODEL PERTURBED BY HIGHER ORDER CURVATURE TERMS." Modern Physics Letters A 07, no. 33 (October 30, 1992): 3081–100. http://dx.doi.org/10.1142/s0217732392002470.

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The critical behavior of the D=0 matrix model with the potential perturbed by a nonlocal term generating touchings between random surfaces is studied. It is found that the phase diagram of the model has many features of the phase diagram of discretized Polyakov’s bosonic string with higher order curvature terms included. It contains the phase of smooth (Liouville) surfaces, the intermediate phase and the phase of branched polymers. The perturbation becomes irrelevant at the first phase and dominates at the third one.

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Almutairi, Alanoud, Omar Bazighifan, and Youssef N. Raffoul. "Oscillation Results for Nonlinear Higher-Order Differential Equations with Delay Term." Symmetry 13, no. 3 (March 10, 2021): 446. http://dx.doi.org/10.3390/sym13030446.

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The aim of this work is to investigate the oscillation of solutions of higher-order nonlinear differential equations with a middle term. By using the integral averaging technique, Riccati transformation technique and comparison technique, several oscillatory properties are presented that unify the results obtained in the literature. Some examples are presented to demonstrate the main results.

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15

Grace, Said R., Jehad Alzabut, and Kamaleldin Abodayeh. "Oscillation theorems for higher order dynamic equations with superlinear neutral term." AIMS Mathematics 6, no. 6 (2021): 5493–501. http://dx.doi.org/10.3934/math.2021325.

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16

Kronenberger, William G., and David B. Pisoni. "Assessing Higher Order Language Processing in Long-Term Cochlear Implant Users." American Journal of Speech-Language Pathology 28, no. 4 (November 19, 2019): 1537–53. http://dx.doi.org/10.1044/2019_ajslp-18-0138.

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Purpose The purpose of this study was to describe and explain individual differences in complex/higher order language processing in long-term cochlear implant (CI) users relative to normal-hearing (NH) peers. Method Measures of complex/higher order language processing indexed by the Clinical Evaluation of Language Fundamentals–Fourth Edition (CELF-4) Core Language subtests were obtained from 53 long-term (≥ 7 years) CI users aged 9–29 years and 60 NH controls who did not differ in age, gender, or nonverbal IQ. Vocabulary knowledge and fast, automatic language processing (rapid phonological coding, verbal rehearsal speed, and speech intelligibility) were also assessed. Results CI users showed weaker performance than NH controls on all CELF-4 Core Language subtests. These differences remained for Formulated Sentences and Recalling Sentences even when vocabulary knowledge was statistically controlled. About 50% of the CI sample scored within the range of the NH sample on Formulated Sentences and Recalling Sentences, while the remaining 50% scored well below the NH sample on these subtests. Vocabulary knowledge, rapid phonological coding, verbal rehearsal speed, and speech intelligibility were more strongly correlated with CELF-4 subtest scores in the CI sample than in the NH sample. Conclusions Weaknesses in complex, higher order language processing shown by a subgroup of CI users compared to NH peers may result from delays in fast, automatic processing of language. These at-risk domains of language functioning could serve as targets for novel interventions for deaf children who experience suboptimal spoken language outcomes following cochlear implantation.

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Li, Yaohan, You Dong, and Jing Qian. "Higher-order analysis of probabilistic long-term loss under nonstationary hazards." Reliability Engineering & System Safety 203 (November 2020): 107092. http://dx.doi.org/10.1016/j.ress.2020.107092.

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Williams, Leena E., and Anthony Holtmaat. "Higher-Order Thalamocortical Inputs Gate Synaptic Long-Term Potentiation via Disinhibition." Neuron 101, no. 1 (January 2019): 91–102. http://dx.doi.org/10.1016/j.neuron.2018.10.049.

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19

Aptekarev, A. I., V. A. Kalyagin, and E. B. Saff. "Higher-Order Three-Term Recurrences and Asymptotics of Multiple Orthogonal Polynomials." Constructive Approximation 30, no. 2 (October 25, 2008): 175–223. http://dx.doi.org/10.1007/s00365-008-9032-0.

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20

Frasca, Marco, and Asatur Zh Khurshudyan. "Green’s functions for higher order nonlinear equations." International Journal of Modern Physics C 29, no. 10 (October 2018): 1850104. http://dx.doi.org/10.1142/s0129183118501048.

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The well-known Green’s function method has been recently generalized to nonlinear second-order differential equations. In this paper, we study possibilities of exact Green’s function solutions of nonlinear differential equations of higher order. We show that, if the nonlinear term satisfies a generalized homogeneity property, then the nonlinear Green’s function can be represented in terms of the homogeneous solution. Specific examples and a numerical analysis support the advantage of the method. We show how, for the Bousinesq and Kortweg–de Vries equations, we are forced to introduce higher order Green’s functions to obtain the solution to the inhomogeneous equation. The method proves to work also in this case supporting our generalization that yields a closed form solution to a large class of nonlinear differential equations, providing also a formula easily amenable to numerical evaluation.

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Vaughan, Robert C., and Trevor D. Wooley. "The asymptotic formula in Waring’s problem: Higher order expansions." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 742 (September 1, 2018): 17–46. http://dx.doi.org/10.1515/crelle-2015-0098.

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Abstract When {k>1} and s is sufficiently large in terms of k, we derive an explicit multi-term asymptotic expansion for the number of representations of a large natural number as the sum of s positive integral k-th powers.

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Li, Yu. "Tensor mode perturbation of cosmology with higher order holonomy corrections." Canadian Journal of Physics 94, no. 9 (September 2016): 945–52. http://dx.doi.org/10.1139/cjp-2016-0178.

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In this paper, we discuss the tensor mode perturbation in the frame of loop quantum cosmology with higher order holonomy corrections. We get the dynamics of the background near the bounce and far from the bounce. Based on the solutions of the effective Friedmann equation, we deduce the effective gravitational wave equation and get the quantum corrections in both the mass term and source term. We solve the gravitational wave equation near the bounce and discuss the situation far from the bounce. We also find the new terms arose only when one considers the higher order corrections.

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23

Bojarski, Bogdan, Lizaveta Ihnatsyeva, and JUHA KINNUNEN JUHA KINNUNEN. "How to Recognize Polynomials in Higher Order Sobolev Spaces." MATHEMATICA SCANDINAVICA 112, no. 2 (June 1, 2013): 161. http://dx.doi.org/10.7146/math.scand.a-15239.

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This paper extends characterizations of Sobolev spaces by Bourgain, Brézis, and Mironescu to the higher order case. As a byproduct, we obtain an integral condition for the Taylor remainder term, which implies that the function is a polynomial. Similar questions are also considered in the context of Whitney jets.

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Fried, Daniel, Peter Jansen, Gustave Hahn-Powell, Mihai Surdeanu, and Peter Clark. "Higher-order Lexical Semantic Models for Non-factoid Answer Reranking." Transactions of the Association for Computational Linguistics 3 (December 2015): 197–210. http://dx.doi.org/10.1162/tacl_a_00133.

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Lexical semantic models provide robust performance for question answering, but, in general, can only capitalize on direct evidence seen during training. For example, monolingual alignment models acquire term alignment probabilities from semi-structured data such as question-answer pairs; neural network language models learn term embeddings from unstructured text. All this knowledge is then used to estimate the semantic similarity between question and answer candidates. We introduce a higher-order formalism that allows all these lexical semantic models to chain direct evidence to construct indirect associations between question and answer texts, by casting the task as the traversal of graphs that encode direct term associations. Using a corpus of 10,000 questions from Yahoo! Answers, we experimentally demonstrate that higher-order methods are broadly applicable to alignment and language models, across both word and syntactic representations. We show that an important criterion for success is controlling for the semantic drift that accumulates during graph traversal. All in all, the proposed higher-order approach improves five out of the six lexical semantic models investigated, with relative gains of up to +13% over their first-order variants.

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Goncharov, Sergey, Stefan Milius, Lutz Schröder, Stelios Tsampas, and Henning Urbat. "Towards a Higher-Order Mathematical Operational Semantics." Proceedings of the ACM on Programming Languages 7, POPL (January 9, 2023): 632–58. http://dx.doi.org/10.1145/3571215.

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Compositionality proofs in higher-order languages are notoriously involved, and general semantic frameworks guaranteeing compositionality are hard to come by. In particular, Turi and Plotkin’s bialgebraic abstract GSOS framework, which has been successfully applied to obtain off-the-shelf compositionality results for first-order languages, so far does not apply to higher-order languages. In the present work, we develop a theory of abstract GSOS specifications for higher-order languages, in effect transferring the core principles of Turi and Plotkin’s framework to a higher-order setting. In our theory, the operational semantics of higher-order languages is represented by certain dinatural transformations that we term pointed higher-order GSOS laws . We give a general compositionality result that applies to all systems specified in this way and discuss how compositionality of the SKI calculus and the λ-calculus w.r.t. a strong variant of Abramsky’s applicative bisimilarity are obtained as instances.

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Lin, Ren Bing. "Exponential Decay of Global Solutions for some Quasilinear Higher-Order Wave Equation." Applied Mechanics and Materials 336-338 (July 2013): 2233–37. http://dx.doi.org/10.4028/www.scientific.net/amm.336-338.2233.

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KREUZER, ALEXANDER P. "NON-PRINCIPAL ULTRAFILTERS, PROGRAM EXTRACTION AND HIGHER-ORDER REVERSE MATHEMATICS." Journal of Mathematical Logic 12, no. 01 (June 2012): 1250002. http://dx.doi.org/10.1142/s021906131250002x.

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We investigate the strength of the existence of a non-principal ultrafilter over fragments of higher-order arithmetic. Let [Formula: see text] be the statement that a non-principal ultrafilter on ℕ exists and let [Formula: see text] be the higher-order extension of ACA0. We show that [Formula: see text] is [Formula: see text]-conservative over [Formula: see text] and thus that [Formula: see text] is conservative over PA. Moreover, we provide a program extraction method and show that from a proof of a strictly [Formula: see text] statement ∀ f ∃ g A qf(f, g) in [Formula: see text] a realizing term in Gödel's system T can be extracted. This means that one can extract a term t ∈ T, such that ∀ f A qf(f, t(f)).

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Ohno, Nobutada, and Dai Okumura. "Higher-Order Stress due to Self Energy of Geometrically Necessary Dislocations." Key Engineering Materials 340-341 (June 2007): 173–78. http://dx.doi.org/10.4028/www.scientific.net/kem.340-341.173.

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The self energy of geometrically necessary dislocations (GNDs) in single crystals is considered to inevitably introduce a higher-order stress as the work conjugate to slip gradient. It is pointed out that this higher-order stress changes stepwise in response to in-plane slip gradient and thus explicitly influences the initial yielding of polycrystals. The self energy of GNDs is then incorporated into the strain gradient plasticity theory of Gurtin (2002). The resulting theory is applied to 2D and 3D model crystal grains of diameter D, leading to a D-1-dependent term with a coefficient determined by grain shape. This size effect term is verified using published experimental data of several polycrystalline metals. It is thus found that the D-1-dependent term is successful for predicting not only the grain size dependence of initial yield stress but also the dislocation cell size dependence of flow stress in the submicron to several micron range of D.

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Liu, Weiwei, and Lishan Liu. "Existence of Positive Solutions for a Higher-Order Fractional Differential Equation with Multi-Term Lower-Order Derivatives." Mathematics 9, no. 23 (November 26, 2021): 3031. http://dx.doi.org/10.3390/math9233031.

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This paper deals with the study of the existence of positive solutions for a class of nonlinear higher-order fractional differential equations in which the nonlinear term contains multi-term lower-order derivatives. By reducing the order of the highest derivative, the higher-order fractional differential equation is transformed into a lower-order fractional differential equation. Then, combining with the properties of left-sided Riemann–Liouville integral operators, we obtain the existence of the positive solutions of fractional differential equations utilizing some weaker conditions. Furthermore, some examples are given to demonstrate the validity of our main results.

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Kuo, Yih-Shiuan, May-Yung Yen, and Pei-Yu Lin. "Short-term effect of atropine on higher-order aberrations in myopic children." Journal of the Chinese Medical Association 84, no. 4 (March 31, 2021): 441–45. http://dx.doi.org/10.1097/jcma.0000000000000495.

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Taşdemir, Erkan. "Global dynamics of a higher order difference equation with a quadratic term." Journal of Applied Mathematics and Computing 67, no. 1-2 (January 11, 2021): 423–37. http://dx.doi.org/10.1007/s12190-021-01497-x.

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HIROUCHI, Tomoyuki, Tomohito TSURU, and Yoji SHIBUTANI. "Grain Growth Predictions by Multi-Phase-Field Modeling with Higher-Order Term." TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series A 77, no. 782 (2011): 1723–34. http://dx.doi.org/10.1299/kikaia.77.1723.

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Meinke, K. "Proof theory of higher-order equations: conservativity, normal forms and term rewriting." Journal of Computer and System Sciences 67, no. 1 (August 2003): 127–73. http://dx.doi.org/10.1016/s0022-0000(03)00048-5.

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Li, Wan-Tong, Xian-Ling Fan, and Cheng-Kui Zhong. "Unbounded positive solutions of higher-order difference equations with singular nonlinear term." Computers & Mathematics with Applications 39, no. 3-4 (February 2000): 177–84. http://dx.doi.org/10.1016/s0898-1221(99)00343-0.

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Thandapani, E., M. Maria Susai Manuel, John R. Graef, and Paul W. Spikes. "Oscillation of a higher order neutral difference equation with a forcing term." International Journal of Mathematics and Mathematical Sciences 22, no. 1 (1999): 147–54. http://dx.doi.org/10.1155/s0161171299221473.

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Sham, T. L. "The determination of the elastic T-term using higher order weight functions." International Journal of Fracture 48, no. 2 (March 1991): 81–102. http://dx.doi.org/10.1007/bf00018392.

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37

Jo, Seong Ho, and Je Hyun Seo. "Short-term change in higher-order aberrations after mitomycin-C-augmented trabeculectomy." International Ophthalmology 39, no. 1 (December 22, 2017): 175–88. http://dx.doi.org/10.1007/s10792-017-0802-1.

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38

Lohakare, Santosh V., Francisco Tello-Ortiz, S. K. Tripathy, and B. Mishra. "Bouncing Cosmology in Modified Gravity with Higher-Order Gauss–Bonnet Curvature Term." Universe 8, no. 12 (November 29, 2022): 636. http://dx.doi.org/10.3390/universe8120636.

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In this paper, we studied the bouncing behavior of the cosmological models formulated in the background of the Hubble function in the F(R,G) theory of gravity, where R and G, respectively, denote the Ricci scalar and Gauss–Bonnet invariant. The actions of the bouncing cosmology are studied with a consideration of the different viable models that can resolve the difficulty of singularity in standard Big Bang cosmology. Both models show bouncing behavior and satisfy the bouncing cosmological properties. Models based on dynamical, deceleration, and energy conditions indicate the accelerating behavior at the late evolution time. The phantom at the bounce epoch is analogous to quintessence behavior. Finally, we formulate the perturbed evolution equations and investigate the stability of the two bouncing solutions.

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Kan, Nahomi, and Kiyoshi Shiraishi. "Critical Combinations of Higher-Order Terms in Einstein-Maxwell Theory and Compactification." Advances in High Energy Physics 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/404508.

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We discuss the role of a particular combination of higher derivative terms in higher dimensional theories, particularly in the background of spontaneous compactification. Two classes of theories are proposed in this paper. The first model as a generalization of the critical gravity with the Maxwell field could have a de Sitter solution. We consider the Lanczos-Lovelock term and Horndeski term as well as the higher-order Maxwell term for the second model, which contains a possible longer expansion time for the inflationary phase. It is interesting that both models can be regarded as the generalization of the Randjbar-Daemi, Salam and Strathdee (RSS) model and give the well behavior for inflation stage under the specific assumptions.

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Peters, Norbert, Jonas Boschung, Michael Gauding, Jens Henrik Goebbert, Reginald J. Hill, and Heinz Pitsch. "Higher-order dissipation in the theory of homogeneous isotropic turbulence." Journal of Fluid Mechanics 803 (August 19, 2016): 250–74. http://dx.doi.org/10.1017/jfm.2016.489.

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The two-point theory of homogeneous isotropic turbulence is extended to source terms appearing in the equations for higher-order structure functions. For this, transport equations for these source terms are derived. We focus on the trace of the resulting equations, which is of particular interest because it is invariant and therefore independent of the coordinate system. In the trace of the even-order source term equation, we discover the higher-order moments of the dissipation distribution, and the individual even-order source term equations contain the higher-order moments of the longitudinal, transverse and mixed dissipation distribution functions. This shows for the first time that dissipation fluctuations, on which most of the phenomenological intermittency models are based, are contained in the Navier–Stokes equations. Noticeably, we also find the volume-averaged dissipation $\unicode[STIX]{x1D700}_{r}$ used by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82–85) in the resulting system of equations, because it is related to dissipation correlations.

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Lai, Xian-Jing, and Jie-Fang Zhang. "Higher-Order Approximations for Symmetrical Regular Long Wave Equation." Zeitschrift für Naturforschung A 61, no. 12 (December 1, 2006): 607–14. http://dx.doi.org/10.1515/zna-2006-1201.

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In this work, we extend the application of “the modified reductive perturbation method” to the symmetrical regular long wave equation and try to obtain the contribution of higher-order terms in the perturbation expansion. It is shown that the lowest-order term in the expansion is governed by the nonlinear Schrödinger equation while the second- and third-order terms are governed by the linear Schrödinger equation. By employing the hyperbolic tangent method, progressive wave type solutions are obtained for the first-, second- and third-order terms in the perturbation expansion. - PACS numbers: 02.30.Jr, 42.25.Bs, 42.81.Dp, 43.35.Kp

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Stevic, Stevo, Mohammed Alghamdi, Abdullah Alotaibi, and Elsayed Elsayed. "On a class of solvable higher-order difference equations." Filomat 31, no. 2 (2017): 461–77. http://dx.doi.org/10.2298/fil1702461s.

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Closed form formulas for well-defined solutions of the next difference equation xn = xn-2xn-k-2/xn-k(an + bnxn-2xn-k-2), n ? N0, where k ? N, (an)n?N0, (bn)n?N0, and initial values x-i, i = 1,k+2 are real numbers, are given. Long-term behavior of well-defined solutions of the equation when (an)n?N0 and (bn)n?N0 are constant sequences is described in detail by using the formulas. We also describe the domain of undefinable solutions of the equation. Our results explain and considerably improve some recent results in the literature.

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Mabel Lizzy, R., K. Balachandran, and Yong-Ki Ma. "Controllability of nonlinear stochastic fractional higher order dynamical systems." Fractional Calculus and Applied Analysis 22, no. 4 (August 27, 2019): 1063–85. http://dx.doi.org/10.1515/fca-2019-0056.

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Abstract This paper deals with the study of controllability of stochastic fractional dynamical systems with 1 < α ≤ 2. Necessary and sufficient condition for controllability of linear stochastic fractional system is obtained. Sufficient conditions for controllability of stochastic fractional semilinear systems, integrodifferential systems, systems with neutral term, systems with delays in control and systems with Lévy noise is formulated and established. The solution is obtained in terms of Mittag-Leffler operator functions by considering bounded operators. The Banach fixed point theorem is used to obtain the desired results from an equivalent nonlinear integral equation of the given system.

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KUMAR, SARMISHTHA. "LAGRANGIAN AND HAMILTONIAN FORMULATIONS OF HIGHER ORDER CHERN–SIMONS THEORIES." International Journal of Modern Physics A 18, no. 09 (April 10, 2003): 1613–22. http://dx.doi.org/10.1142/s0217751x03013594.

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We consider models involving the higher (third) derivative extension of the Abelian Chern–Simons (CS) topological term in D = 2 + 1 dimensions. The polarization vectors in these models reveal an identical structure with the corresponding expressions for usual models which contain, at most, quadratic structures. We also investigate the Hamiltonian structure of these models and show how Wigner's little group acts as a gauge generator.

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Schmitt, Michael. "On the Capabilities of Higher-Order Neurons: A Radial Basis Function Approach." Neural Computation 17, no. 3 (March 1, 2005): 715–29. http://dx.doi.org/10.1162/0899766053019953.

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Higher-order neurons with k monomials in n variables are shown to have Vapnik-Chervonenkis (VC) dimension at least nk + 1. This result supersedes the previously known lower bound obtained viak-term monotone disjunctive normal form (DNF) formulas. Moreover, it implies that the VC dimension of higher-order neurons with k monomials is strictly larger than the VC dimension of k-term monotone DNF. The result is achieved by introducing an exponential approach that employs gaussian radial basis function neural networks for obtaining classifications of points in terms of higher-order neurons.

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PARK, SUNGWOO, and HYEONSEUNG IM. "Type-safe higher-order channels with channel locality." Journal of Functional Programming 19, no. 1 (January 2009): 107–42. http://dx.doi.org/10.1017/s0956796808006989.

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AbstractAs a means of transmitting not only data but also code encapsulated within functions, higher-order channels provide an advanced form of task parallelism in parallel computations. In the presence of mutable references, however, they pose a safety problem because references may be transmitted to remote threads where they are no longer valid. This paper presents an ML-like parallel language with type-safe higher-order channels. By type safety, we mean that no value written to a channel contains references, or equivalently, that no reference escapes via a channel from the thread where it is created. The type system uses a typing judgment that is capable of deciding whether the value to which a term evaluates contains references or not. The use of such a typing judgment also makes it easy to achieve another desirable feature of channels, channel locality, that associates every channel with a unique thread for serving all values addressed to it. Our type system permits mutable references in sequential computations and also ensures that mutable references never interfere with parallel computations. Thus, it provides both flexibility in sequential programming and ease of implementing parallel computations.

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Hughes, Rohan P. J., Scott A. Read, Michael J. Collins, and Stephen J. Vincent. "Higher order aberrations and retinal image quality during short-term accommodation in children." Vision Research 188 (November 2021): 74–84. http://dx.doi.org/10.1016/j.visres.2021.07.004.

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Cao, Rui. "Travelling Wave Solutions for Nonlinear Schrödinger Equation with a Higher-Order Dispersive Term." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/979252.

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A nonlinear Schrödinger equation with a higher-order dispersive term describing the propagation of ultrashort femtosecond pulses in optical fibres is considered and is transformed into a second-order nonlinear ordinary differential equation. We investigate the exact travelling wave solutions of the nonlinear Schrödinger equation using three methods, namely, the auxiliary equation method, the first integral method, and the direct integral method. As a result, Jacobi elliptic function solution, hyperbolic function solution, trigonometric function solution, and rational solution with parameters are obtained successfully. When the parameters are taken as special values, the two known solitary wave solution and periodic wave solution are derived from the solutions obtained. The aim of the paper is to compare the efficiency of the three methods.

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Uchida, Yuji, and Fuminori Fujimoto. "Effect of Higher-Order Spherical Aberration Term on Transfer Function in Electron Microscopy." Japanese Journal of Applied Physics 25, Part 1, No. 4 (April 20, 1986): 644–47. http://dx.doi.org/10.1143/jjap.25.644.

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SHAO, Changcheng, and Toshiya IINUMA. "G0100-2-2 Finite Element Method Having Higher-Order Consistency with Source Term." Proceedings of the JSME annual meeting 2010.1 (2010): 13–14. http://dx.doi.org/10.1299/jsmemecjo.2010.1.0_13.

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Journal articles on the topic 'Higher-order term'

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