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Journal articles on the topic 'Non-singular terms'

Author: Grafiati

Published: 24 August 2024

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1

Ibrahim, Sobhy El-sayed. "Singular non-selfadjoint differential operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 124, no. 4 (1994): 825–41. http://dx.doi.org/10.1017/s0308210500028687.

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A characterisation is obtained of all the regularly solvable operators and their adjoints generated by general ordinary quasidifferential expressions inThe domains of these operators are described in terms of boundary conditions involving thesolutions ofM[u] =λwuand the adjoint equationat both singular end-pointsaandb.These results are an extension of those proved in [3], by Evans and Ibrahim, to the case of two singular end-points of the interval (a, b), and a generalisation of those in [10] and [13] concerning selfadjoint andJ-selfadjoint differential operators, whereJdenotes complex conjugation.

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2

Ma, H., L. G. Zhao, and Y. H. Chen. "Non-singular terms for multiple cracks in anisotropic elastic solids." Theoretical and Applied Fracture Mechanics 27, no. 2 (June 1997): 129–34. http://dx.doi.org/10.1016/s0167-8442(97)00014-1.

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3

Guarnotta, Umberto, Salvatore A. Marano, and Dumitru Motreanu. "On a Singular Robin Problem with Convection Terms." Advanced Nonlinear Studies 20, no. 4 (November 1, 2020): 895–909. http://dx.doi.org/10.1515/ans-2020-2093.

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AbstractIn this paper, the existence of smooth positive solutions to a Robin boundary-value problem with non-homogeneous differential operator and reaction given by a nonlinear convection term plus a singular one is established. Proofs chiefly exploit sub-super-solution and truncation techniques, set-valued analysis, recursive methods, nonlinear regularity theory, as well as fixed point arguments. A uniqueness result is also presented.

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4

Mohammed, Ahmed, and Giovanni Porru. "Large solutions for non-divergence structure equations with singular lower order terms." Nonlinear Analysis: Real World Applications 35 (June 2017): 470–82. http://dx.doi.org/10.1016/j.nonrwa.2016.12.002.

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5

Poliakovsky, Arkady. "Γ-limits of singular perturbation problems involving energies with non-local terms." Journal of Mathematical Analysis and Applications 464, no. 2 (August 2018): 1010–50. http://dx.doi.org/10.1016/j.jmaa.2018.01.078.

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6

Wringe, Bill. "Making the Lightness of Being Bearable: Arithmetical Platonism, Fictional Realism and Cognitive Command." Canadian Journal of Philosophy 38, no. 3 (September 2008): 453–87. http://dx.doi.org/10.1353/cjp.0.0026.

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In this paper I wish to defend a minimalist version of arithmetical Platonism — which I shall refer to as ‘minimal Platonism’ — from an objection which alleges that an advocate of this view is committed to an unduly capacious ontology. The objection, which I shall call the ‘Lightness of Being’ objection, runs as follows. The minimal Platonist is committed to the claim that arithmetical objects, such as numbers, exist provided that two conditions are met. The first is that terms for numerals are singular terms — where something's being a singular term is judged on the basis of purely syntactic criteria. The second is that some sentences in which these singular terms feature are non-trivially true. However, the names of fictional characters are also singular terms (when judged by the metaphysically lightweight criteria used by advocates of minimal Platonism).

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7

Couch, W. E., M. Surovy, and R. J. Torrence. "Some singular motions of non-Abelian Toda lattices." Canadian Journal of Physics 78, no. 2 (March 2, 2000): 99–112. http://dx.doi.org/10.1139/p00-025.

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Motions of finite Toda lattices are known to be associated with linear wave equations whose general solutions can be expressed in terms of progressing waves, and this association is known to generalize to finite non-Abelian Toda lattices of n x n matrices and systems of n coupled linear wave equations. We present a nontrivial family of non-Abelian Toda lattice motions that can be specialized to ones that are not finite, but not infinitely extendible either, as they contain nonvanishing but singular matrices of rank (n s). In these cases we give a natural continuation of the lattice dynamics by means of nonsingular matrices of dimension (n s) x (n s), and describe how to find s progressing wave solutions of the associated system of n coupled linear wave equations.PACS No.: 5.45-a

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8

Wang, Yong. "Affine connections on singular warped products." International Journal of Geometric Methods in Modern Physics 18, no. 05 (February 22, 2021): 2150076. http://dx.doi.org/10.1142/s0219887821500766.

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In this paper, we introduce semi-symmetric metric Koszul forms and semi-symmetric non-metric Koszul forms on singular semi-Riemannian manifolds. Semi-symmetric metric Koszul forms and semi-symmetric non-metric Koszul forms and their curvature of semi-regular warped products are expressed in terms of those of the factor manifolds. We also introduce Koszul forms associated with the almost product structure on singular almost product semi-Riemannian manifolds. Koszul forms associated with the almost product structure and their curvature of semi-regular almost product warped products are expressed in terms of those of the factor manifolds. Furthermore, we generalize the results in [O. Stoica, The geometry of warped product singularities, Int. J. Geom. Methods Mod. Phys. 14(2) (2017) 1750024, arXiv:1105.3404.] to singular multiply warped products.

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9

BÜRGER, R., A. GARCIA, K. H. KARLSEN, and J. D. TOWERS. "On an extended clarifier-thickener model with singular source and sink terms." European Journal of Applied Mathematics 17, no. 3 (June 2006): 257–92. http://dx.doi.org/10.1017/s0956792506006619.

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A one-dimensional model of clarifier-thickener units in engineering applications can be expressed as a conservation law with a flux that is discontinuous with respect to the spatial variable. This model also includes a singular feed source. In this paper, the clarifier-thickener model studied in a previous paper (Numer. Math.97 (2004) 25–65) is extended by a singular sink through which material is extracted from the unit. A difficulty is that in contrast to the singular source, the sink term cannot be incorporated into the flux function; rather, the sink is represented by a new non-conservative transport term. To focus on the new analytical difficulties arising due to this non-conservative term, a reduced problem is formulated, which contains the new sink term of the extended clarifier-thickener model, but not the source term and flux discontinuities. The paper is concerned with numerical methods for both models (extended and reduced) and with the well-posedness analysis for the reduced problem. For the reduced problem, a definition of entropy solutions, based on Kružkov-type entropy functions and fluxes, is provided. Jump conditions are derived and uniqueness of the entropy solution is shown. Existence of an entropy solution is shown by proving convergence of a monotone difference scheme. Two variants of the numerical scheme are introduced. Numerical examples illustrate that all three variants converge to the entropy solution, but introduce different amounts of numerical diffusion.

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10

Galybin, A. N. "Non singular terms in stresses near the tip of an arbitrarily loaded edge crack." International Journal of Fracture 80, no. 2-3 (April 1996): R31—R36. http://dx.doi.org/10.1007/bf00012674.

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11

Gupta, A. J., B. M. Pandeya, and A. K. Chaturvedi. "SP-INJECTIVITY OF MODULES AND RINGS." Asian-European Journal of Mathematics 05, no. 04 (December 2012): 1250053. http://dx.doi.org/10.1142/s1793557112500532.

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Let >M and N be two R-modules. NR is called singular M-p-injective if for every singular M-cyclic submodule X of MR, every homomorphism from X to N can be extended to a homomorphism from M to N. MR is quasi-singular prinicipally injective if M is a singular M-p-injective module. It is shown that a ring R is right non-singular if and only if every right R-module is singular R-p-injective if and only if factors of singular R-p-injective modules are singular R-p-injective. A singular R-module M is injective if and only if M is N-sp-injective for every R-module N. Finally, we characterize quasi-sp-injective modules in terms of their endomorphism rings.

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12

Fontaine, Matthieu. "Singular Terms, Identity, and the Creation of Fictional Characters." Disputatio 11, no. 54 (December 1, 2019): 207–29. http://dx.doi.org/10.2478/disp-2019-0017.

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Abstract How to interpret singular terms in fiction? In this paper, we address this semantic question from the perspective of the Artifactual Theory of Fiction (ATF). According to the ATF, fictional characters exist as abstract artifacts created by their author, and preserved through the existence of copies of an original work and a competent readership. We pretend that a well-suited semantics for the ATF can be defined with respect to a modal framework by means of Hintikka’s world lines semantics. The question of the interpretation of proper names is asked in relation to two inference rules, problematic when applied in intensional contexts: the Substitution of Identicals and Existential Generalization. The former fails because identity is contingent. The latter because proper names are not necessarily linked to well-identified individuals. This motivates a non-rigid interpretation of proper names in fiction, although cross-fictional reference (e.g. to real entities) is made possible by the interpretative efforts of the reader.

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13

Sun, Huaqing, and Bing Xie. "Spectra of a class of non-symmetric operators in Hilbert spaces with applications to singular differential operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 4 (February 15, 2019): 1769–90. http://dx.doi.org/10.1017/prm.2018.110.

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AbstractThis paper is concerned with a class of non-symmetric operators, that is, 𝒥-symmetric operators, in Hilbert spaces. A sufficient condition for λ ∈ C being an element of the essential spectrum of a 𝒥-symmetric operator is given in terms of the number of linearly independent solutions of a certain homogeneous equation, and a characterization for points of the essential spectrum plus the set of all eigenvalues of a 𝒥-symmetric operator is obtained in terms of the numbers of linearly independent solutions of certain inhomogeneous equations. As direct applications, the corresponding results are obtained for singular 𝒥-symmetric Hamiltonian systems and their special forms of singular Sturm-Liouville equations with complex-valued coefficients, which enable us to study the spectra of singular 𝒥-symmetric differential expressions using numerous tools available in the fundamental theory of differential equations.

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14

Yang, Yongyu, Wei Pan, Shanlong Yao, Changzheng Cheng, and Qiaoguo Wu. "Analysis of the non-singular stress terms for the sharp notches under anti-plane loading." Engineering Fracture Mechanics 245 (March 2021): 107583. http://dx.doi.org/10.1016/j.engfracmech.2021.107583.

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15

Zhang, Zhijun. "Boundary blow-up elliptic problems with nonlinear gradient terms and singular weights." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 138, no. 6 (November 12, 2008): 1403–24. http://dx.doi.org/10.1017/s0308210506000643.

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By Karamata regular variation theory, a perturbation method and construction of comparison functions, we show the exact asymptotic behaviour of solutions near the boundary to nonlinear elliptic problems Δu ± |Δu|q = b(x)g(u), u > 0 in Ω, u|∂Ω = ∞, where Ω is a bounded domain with smooth boundary in ℝN, q > 0, g ∈ C1[0, ∞) is increasing on [0, ∞), g(0) = 0, g′ is regularly varying at infinity with positive index ρ and b is non-negative in Ω and is singular on the boundary.

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16

Vîjîitu, Viorel. "Holomorphic convexity of pseudoconvex spaces in terms of the rank of structural sheaf." Forum Mathematicum 34, no. 2 (March 1, 2022): 455–68. http://dx.doi.org/10.1515/forum-2021-0262.

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Abstract We prove that a pseudoconvex complex space X of pure dimension n + 1 {n+1} is holomorphically convex provided that its singular set has only compact connected components (e.g., X has isolated singularities) and rank x ⁡ 𝒪 X = n {\operatorname{rank}_{x}\mathscr{O}_{X}=n} for all smooth points x outside a compact set of X. This extends a known result due to Ohsawa asserting that a weakly 1-complete, smooth complex surface is holomorphically convex if it admits a globally defined non-constant holomorphic function. We also revise an example of Markoe concerning non-invariance of holomorphic convexity under normalization.

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17

Hristov, Jordan. "Response functions in linear viscoelastic constitutive equations and related fractional operators." Mathematical Modelling of Natural Phenomena 14, no. 3 (2019): 305. http://dx.doi.org/10.1051/mmnp/2018067.

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This study addresses the stress–strain relaxation functions of solid polymers in the framework of the linear viscoelasticity with aim to establish the adequate fractional operators emerging from the hereditary integrals. The analysis encompasses power-law and non-power-law materials, thus allowing to see the origins of application of the tools of the classical fractional calculus with singular memory kernels and the ideas leading towards fractional operators with non-singular (regular) kernels. A step ahead in modelling with hereditary integrals is the decomposition of non-power-law relaxation curves by Prony series, thus obtaining discrete relaxation kernels with a finite number of terms. This approach allows for seeing the physical background of the newly defined Caputo–Fabrizio time fractional derivative and demonstrates how other constitutive equations could be modified with non-singular fading memories. The non-power-law relaxation curves also allow for approximations by the Mittag–Leffler function of one parameter that leads reasonably into stress–strain hereditary integrals in terms of Atangana–Baleanu fractional derivative of Caputo sense. The main outcomes of the analysis done are the demonstrated distinguishes between the relaxation curve behaviours of different materials and are therefore the adequate modelling with suitable fractional operators.

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18

Woodward, James. "Supervenience and Singular Causal Statements." Royal Institute of Philosophy Supplement 27 (March 1990): 211–46. http://dx.doi.org/10.1017/s1358246100005129.

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In his recent book, Causation: A Realistic Approach, Michael Tooley discusses the following thesis, which he calls the ‘thesis of the Humean Supervenience of Causal Relations’:(T) The truth values of all singular causal statements are logically determined by the truth values of statements of causal laws, together with the truth values of non-causal statements about particulars (p. 182).(T) represents one version of the ‘Humean’ idea that there is no more factual content to the claim that two particular events are causally connected than that they occur, instantiate some law or regularity, and perhaps bear some appropriate non-causal (e.g. spatio-temporal) to each other. This is an idea that is tacitly or explicitly assumed in most familiar accounts of singular causal statements. For example (T) is assumed by many probabilistic theories of singular causal statements, by theories which attempt to analyse singular causal statements in terms of necessary and sufficient conditions, and, as I shall argue below, by David Lewis' counterfactual theory.

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19

Gao, Penglin, and Linzhi Wu. "Non-singular acoustic cloak derived by the ray tracing method with rotationally symmetric transformations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2186 (February 2016): 20150348. http://dx.doi.org/10.1098/rspa.2015.0348.

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Recently, the ray tracing method has been used to derive the non-singular cylindrical invisibility cloaks for out-of-plane shear waves, which is impossible via the transformation method directly owing to the singular push-forward mapping. In this paper, the method is adopted to design a kind of non-singular acoustic cloak. Based on Hamilton's equations of motion, eikonal equation and pre-designed ray equations, we derive several constraint equations for bulk modulus and density tensor. On the premise that the perfect matching conditions are satisfied, a series of non-singular physical profiles can be obtained by arranging the singular terms reasonably. The physical profiles derived by the ray tracing method will degenerate to the transformation-based solutions when taking the transport equation into consideration. This illuminates the essence of the newly designed cloaks that they are actually the so-called eikonal cloaks that can accurately control the paths of energy flux but with small disturbance in energy distribution along the paths. The near-perfect invisible performance has been demonstrated by the numerical ray tracing results and the pressure distribution snapshots. Finally, a kind of reduced cloak is conceived, and the good invisible performance has been measured quantitatively by the normalized scattering width.

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20

Akbardoost, J., and M. R. Ayatollahi. "Experimental analysis of mixed mode crack propagation in brittle rocks: The effect of non-singular terms." Engineering Fracture Mechanics 129 (October 2014): 77–89. http://dx.doi.org/10.1016/j.engfracmech.2014.05.016.

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21

Lee, Ouk Sub, Min Ku Han, and Sung Kyung Hong. "Effects of non-singular stress terms and birefringent coefficient on caustics under various fracture mode loadings." KSME Journal 3, no. 2 (September 1989): 159–63. http://dx.doi.org/10.1007/bf02953602.

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22

GYONGYOSI, LASZLO, and SANDOR IMRE. "QUANTUM SINGULAR VALUE DECOMPOSITION BASED APPROXIMATION ALGORITHM." Journal of Circuits, Systems and Computers 19, no. 06 (October 2010): 1141–62. http://dx.doi.org/10.1142/s0218126610006797.

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Singular Value Decomposition (SVD) is one of the most useful techniques for analyzing data in linear algebra. SVD decomposes a rectangular real or complex matrix into two orthogonal matrices and one diagonal matrix. The proposed Quantum-SVD algorithm interpolates the non-uniform angles in the Fourier domain. The error of the Quantum-SVD approach is some orders lower than the error given by ordinary Quantum Fourier Transformation. Our Quantum-SVD algorithm is a fundamentally novel approach for the computation of the Quantum Fourier Transformation (QFT) of non-uniform states. The presented Quantum-SVD algorithm is based on the singular value decomposition mechanism, and the computation of Quantum Fourier Transformation of non-uniform angles of a quantum system. The Quantum-SVD approach provides advantages in terms of computational structure, being based on QFT and multiplications.

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23

Shafiullah, K. Shah, M. Sarwar, and Th Abdeljawad. "Theoretical and computational results for implicit non-singular hybrid fractional differential equation subject to multi-terms non-local initial conditions." Journal of Mathematics and Computer Science 36, no. 02 (July 15, 2024): 207–17. http://dx.doi.org/10.22436/jmcs.036.02.05.

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24

Petitta, Francesco. "A non-existence result for nonlinear parabolic equations with singular measures as data." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 139, no. 2 (March 25, 2009): 381–92. http://dx.doi.org/10.1017/s0308210507001163.

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In this paper we prove a non-existence result for nonlinear parabolic problems with zero lower-order terms whose model iswhere Δp=div(|∇u|p−2∇u) is the usual p-laplace operator, λ is measure concentrated on a set of zero parabolic r-capacity (1<p<r) and q is large enough.

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25

Berman, Robert J., and Gerard Freixas i Montplet. "An arithmetic Hilbert–Samuel theorem for singular hermitian line bundles and cusp forms." Compositio Mathematica 150, no. 10 (August 19, 2014): 1703–28. http://dx.doi.org/10.1112/s0010437x14007325.

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AbstractWe prove arithmetic Hilbert–Samuel type theorems for semi-positive singular hermitian line bundles of finite height. This includes the log-singular metrics of Burgos–Kramer–Kühn. The results apply in particular to line bundles of modular forms on some non-compact Shimura varieties. As an example, we treat the case of Hilbert modular surfaces, establishing an arithmetic analogue of the classical result expressing the dimensions of spaces of cusp forms in terms of special values of Dedekind zeta functions.

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26

Deutsch, Harry. "Semantics for Natural Kind Terms1." Canadian Journal of Philosophy 23, no. 3 (September 1993): 389–411. http://dx.doi.org/10.1080/00455091.1993.10717328.

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According to the well-known Kripke-Putnam view developed inNaming and Necessityand ‘The Meaning of Meaning’, proper names and ‘natural kind terms’ - words for natural substances, species, and phenomena (‘water’, ‘rose’, ‘light’) - are non-descriptional and rigid. A singular term isrigidif it has the same referent in every possible world (and with respect to other extension-determining parameters, such as the passage of time), and isnon-descriptionalif, roughly speaking, its referent (at a possible world or other parameter) is not secured by purely descriptive conditions analytically tied to the term. Thus, ‘the inventor of bifocals’ is nonrigid and descriptional, while ‘the unique even and prime integer’ is rigid and descriptional, and ‘Noam Chomsky’ is rigid and non-descriptional.

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27

Biagi, Stefano, Alessandro Calamai, Cristina Marcelli, and Francesca Papalini. "Boundary value problems associated with singular strongly nonlinear equations with functional terms." Advances in Nonlinear Analysis 10, no. 1 (November 12, 2020): 684–706. http://dx.doi.org/10.1515/anona-2020-0131.

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Abstract We study boundary value problems associated with singular, strongly nonlinear differential equations with functional terms of type $$\big({\it \Phi}(k(t)\,x'(t))\big)' + f(t,{{\mathcal{G}}}_x(t))\,\rho(t, x'(t)) = 0,$$ on a compact interval [a, b]. These equations are quite general due to the presence of a strictly increasing homeomorphism Φ, the so-called Φ-Laplace operator, of a non-negative function k, which may vanish on a set of null measure, and moreover of a functional term Gx. We look for solutions, in a suitable weak sense, which belong to the Sobolev space W1,1([a, b]). Under the assumptions of the existence of a well-ordered pair of upper and lower solutions and of a suitable Nagumo-type growth condition, we prove an existence result by means of fixed point arguments.

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28

Zhang, Haiqiang, Hairong Fang, and Qi Zou. "Non-singular terminal sliding mode control for redundantly actuated parallel mechanism." International Journal of Advanced Robotic Systems 17, no. 2 (March 1, 2020): 172988142091954. http://dx.doi.org/10.1177/1729881420919548.

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In this article, the trajectory tracking control is developed by implementing a non-singular terminal sliding mode control for the redundantly actuated parallel mechanism system. The proposed control scheme could guarantee that the tracking errors converge to zero asymptotically. The problem of singularity with regard to conventional terminal sliding mode control scheme can be eliminated with the presented novel non-singular terminal sliding mode surface as well. The corresponding stability of the proposed control scheme has also been proved theoretically in terms of Lyapunov method. In addition, simulations and experiments are conducted for trajectory tracking to validate the effectiveness of the proposed scheme. The illustrative results demonstrate that the proposed scheme is available to solve the uncertainties and external disturbances with self-tuning in real time. Furthermore, the prominent characteristics of the presented control scheme are quick convergence, high accuracy, and high robustness, which can achieve excellent tracking performance as compared with computed torque control scheme and conventional sliding mode control scheme.

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29

Mesloub, Said, and Reem K. Alhefthi. "On a Singular Non local Fractional System Describing a Generalized Timoshenko System with Two Frictional Damping Terms." Fractal and Fractional 7, no. 7 (June 28, 2023): 514. http://dx.doi.org/10.3390/fractalfract7070514.

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This paper concerns a nonhomogeneous singular fractional order system, with two frictional damping terms. This system can be considered as a generalization of the so-called Timoshenko system. Results on the existence, uniqueness, and continuous dependence on the solution were obtained via an energy approach, which mainly relies on a priori bounds and density arguments. The approach relies on functional analysis tools and operator theory. Very few results concerning the well-posedness of fractional order Timoshenko systems can be found in the literature. Our results generalize and improve the previous ones and significantly boost the development of the used method.

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CHO, KOJI, and ATSUSHI NAKAYASHIKI. "DIFFERENTIAL STRUCTURE OF ABELIAN FUNCTIONS." International Journal of Mathematics 19, no. 02 (February 2008): 145–71. http://dx.doi.org/10.1142/s0129167x08004595.

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The space of Abelian functions of a principally polarized abelian variety (J,Θ) is studied as a module over the ring [Formula: see text] of global holomorphic differential operators on J. We construct a [Formula: see text] free resolution in case Θ is non-singular. As an application, in the case of dimensions 2 and 3, we construct a new linear basis of the space of abelian functions which are singular only on Θ in terms of logarithmic derivatives of the higher-dimensional σ-function.

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Chen, Yujuan, and Mingxin Wang. "Boundary blow-up solutions for elliptic equations with gradient terms and singular weights: existence, asymptotic behaviour and uniqueness." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 141, no. 4 (July 15, 2011): 717–37. http://dx.doi.org/10.1017/s0308210510000363.

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This paper deals with the non-negative boundary blow-up solutions of the equation ∆u = b(x)up + c(x)uσ|∇u|q in Ω ⊂ ℝ,N, where b(x), c(x) ∈ Cγ (Ω,ℝ+) for some 0 < γ < 1 and can be vanishing or singular on the boundary, and p, σ and q are non-negative constants. The existence and asymptotic behaviour of such a solution near the boundary are investigated, and we show how the nonlinear gradient term affects the results. As a consequence of the asymptotic behaviour, we also show the uniqueness result.

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32

Yin, Honghui, and Zuodong Yang. "Existence and non-existence of entire positive solutions for quasilinear systems with singular and super-linear terms." Differential Equations & Applications, no. 2 (2010): 241–49. http://dx.doi.org/10.7153/dea-02-16.

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JIRIMUTU, HAI-JUN WANG, WEI-NING ZHANG, and CHEUK-YIN WONG. "QUARK MODEL WITH A REGULARIZED BREIT POTENTIAL." International Journal of Modern Physics E 18, no. 03 (March 2009): 729–45. http://dx.doi.org/10.1142/s021830130901277x.

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The Breit interaction contains terms that are singular in nature and cannot be used non-perturbatively for quark–antiquark bound state studies. We regularize the Breit interaction by subtraction such that the interaction is not singular at the origin but the intermediate and long-range parts of the interaction remain unchanged. With the regularized quark–antiquark potential and the confining potential, the solution of [Formula: see text] bound states are therefore stable possessing wave functions that can be used for future applications in other study of scattering and reaction problems.

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Schaerer, Roman Pascal, and Manuel Torrilhon. "On Singular Closures for the 5-Moment System in Kinetic Gas Theory." Communications in Computational Physics 17, no. 2 (January 22, 2015): 371–400. http://dx.doi.org/10.4208/cicp.201213.130814a.

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AbstractMoment equations provide a flexible framework for the approximation of the Boltzmann equation in kinetic gas theory. While moments up to second order are sufficient for the description of equilibrium processes, the inclusion of higher order moments, such as the heat flux vector, extends the validity of the Euler equations to non-equilibrium gas flows in a natural way.Unfortunately, the classical closure theory proposed by Grad leads to moment equations, which suffer not only from a restricted hyperbolicity region but are also affected by non-physical sub-shocks in the continuous shock-structure problem if the shock velocity exceeds a critical value. Amore recently suggested closure theory based on the maximum entropy principle yields symmetric hyperbolic moment equations. However, if moments higher than second order are included, the computational demand of this closure can be overwhelming. Additionally, it was shown for the 5-moment system that the closing flux becomes singular on a subset of moments including the equilibrium state.Motivated by recent promising results of closed-form, singular closures based on the maximum entropy approach, we study regularized singular closures that become singular on a subset of moments when the regularizing terms are removed. In order to study some implications of singular closures, we use a recently proposed explicit closure for the 5-moment equations. We show that this closure theory results in a hyperbolic system that can mitigate the problem of sub-shocks independent of the shock wave velocity and handle strongly non-equilibrium gas flows.

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35

Yang, Dong Mei, and Qing Sun. "Non-Fragile Decentralized Control for the Uncertain Singular Large-Scale Systems with Time-Delay." Advanced Materials Research 317-319 (August 2011): 2204–7. http://dx.doi.org/10.4028/www.scientific.net/amr.317-319.2204.

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This paper is concerned with the non-fragile decentralized controller design problem for uncertain singular large-scale system with time-delay. Sufficient condition for the controller is expressed in terms of linear matrix inequalities(LMIs). When this condition is feasible, the desired controller can be obtained with additive gain perturbations and multiplicative gain perturbations. Finally, a numerical example is also given to illustrate the effectiveness.

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Sulaiman, Masagus, and Masagus Firdaus. "English and Indonesian Singular Forms: A Case of Nouns." Anaphora: Journal of Language, Literary, and Cultural Studies 5, no. 2 (December 27, 2022): 162–70. http://dx.doi.org/10.30996/anaphora.v5i2.6906.

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This study is aimed at finding out the similarities, dissimilarities, and possible learning difficulties faced by students learning English and Indonesian singular forms as well as its contribution to TEFL. The researchers used a qualitative research design. The documentation technique was used to collect the data. To analyze the data, the researchers used descriptive analysis. The results showed that there were four similarities and two dissimilarities between English and Indonesian singular forms. The four similarities were in indefinite article, definite article, quantitative adjective, and units of measurement. While the two dissimilarities were in the definite article and definite article. The possible learning difficulties faced by students learning English and Indonesian singular forms were that they were not very familiar with grammar rules and it made them perplexed and created mistakes when writing and speaking. The contribution was as teaching guidance that assists English teachers to create a better teaching Grammar design on singular forms in terms of countable and non-countable nouns.

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George Maria Selvam, A., and S. Britto Jacob. "STABILITY OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS IN THE FRAME OF ATANGANA-BALEANU OPERATOR." Advances in Mathematics: Scientific Journal 10, no. 5 (May 4, 2021): 2319–33. http://dx.doi.org/10.37418/amsj.10.5.3.

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Theory of fractional calculus with singular and non-singular kernels is pioneering and has garnered significant interest recently. Fair amount of literature on the qualitative properties of fractional differential and integral equations involving different types of operators is available. This manuscript aims to analyze the stability of a class of nonlinear fractional differential equation in terms of Atangana-Baleanu-Caputo operator. Sufficient conditions for the existence and uniqueness of solutions are obtained by employing classical fixed point theorems and Banach contraction principle. Also adequate conditions for Hyers-Ulam stability are established. To substantiate our analytic results, an example is provided with numerical simulation.

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Ayatollahi, Majid R., M. R. M. Aliha, and S. Rahmanian. "Finite Element Analysis of an Improved Center Crack Specimen." Key Engineering Materials 347 (September 2007): 441–46. http://dx.doi.org/10.4028/www.scientific.net/kem.347.441.

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A new crack specimen called the diagonally loaded square plate (DLSP) containing an angled central crack is analyzed using the finite element method. The stress intensity factors and the T-stress are calculated for the new specimen in the full range from pure mode I to pure mode II. Unlike the conventional center cracked specimen under uniaxial loading, the improved specimen is able to provide pure mode II. It is shown that the effect of non-singular stress component T in the DLSP specimen is not ignorable relative to the singular stress terms, particularly for mode II dominated loading conditions.

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Mikirtumov, Ivan B. "Meaning of proper names in contexts of attitudes: de re naming and fictions." Slovo.ru: Baltic accent 13, no. 2 (2022): 75–98. http://dx.doi.org/10.5922/2225-5346-2022-2-4.

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The author explores the meaning of proper names and other types of singular terms in the context of propositional attitudes, combining the problems of empty names, rigid designators and non-specific reading. An object in the attitudes can be given to the agent as such (de re), in the description (de dicto), as well as in several intermediate ways. From the analysis of the phenomenon of rigid designation, I move on to the theory of the object, where I consider two alternatives — strict, or Leibnizian, and weak. The first explains the actual non-existence by impossibility, the second — by occasionality. Here there are two ways of defining non-existent (fictional) objects — kinship and the counterpart relation, which are realized in frames that are different in their features. Nonspecific character is inherent in the kinship and counterpart relation in different ways. A special case is formed by hybrid worlds in which the real and the fictitious meet. The result of my analysis is five variants of a weakened de re reading of proper names and other singular terms in the context of attitudes. I describe their features, touching on the cognitive effect of narration, which operates with the appropriate attitudes.

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Arcoya, David, José Carmona, and Pedro J. Martínez-Aparicio. "Comparison principle for elliptic equations in divergence with singular lower order terms having natural growth." Communications in Contemporary Mathematics 19, no. 02 (February 20, 2017): 1650013. http://dx.doi.org/10.1142/s0219199716500139.

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In this paper, we are concerned with the zero Dirichlet boundary value problem associated to the quasilinear elliptic equation [Formula: see text] where [Formula: see text] is an open and bounded set in [Formula: see text] ([Formula: see text]), [Formula: see text] is a continuously differentiable real function in [Formula: see text], [Formula: see text] is an elliptic, bounded and symmetric matrix, [Formula: see text] is non-negative and may be singular at zero and [Formula: see text]. We give sufficient conditions on [Formula: see text], [Formula: see text] and [Formula: see text] in order to have a comparison principle and, as a consequence, uniqueness of positive solutions being continuous up to the boundary.

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Santos, C. A. "Non-existence and existence of entire solutions for a quasi-linear problem with singular and super-linear terms." Nonlinear Analysis: Theory, Methods & Applications 72, no. 9-10 (May 2010): 3813–19. http://dx.doi.org/10.1016/j.na.2010.01.017.

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Krepl, Ondřej, and Jan Klusák. "The influence of non-singular terms on the precision of stress description near a sharp material inclusion tip." Theoretical and Applied Fracture Mechanics 90 (August 2017): 85–99. http://dx.doi.org/10.1016/j.tafmec.2017.03.007.

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Diethelm, Kai, Roberto Garrappa, Andrea Giusti, and Martin Stynes. "Why fractional derivatives with nonsingular kernels should not be used." Fractional Calculus and Applied Analysis 23, no. 3 (June 25, 2020): 610–34. http://dx.doi.org/10.1515/fca-2020-0032.

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AbstractIn recent years, many papers discuss the theory and applications of new fractional-order derivatives that are constructed by replacing the singular kernel of the Caputo or Riemann-Liouville derivative by a non-singular (i.e., bounded) kernel. It will be shown here, through rigorous mathematical reasoning, that these non-singular kernel derivatives suffer from several drawbacks which should forbid their use. They fail to satisfy the fundamental theorem of fractional calculus since they do not admit the existence of a corresponding convolution integral of which the derivative is the left-inverse; and the value of the derivative at the initial time t = 0 is always zero, which imposes an unnatural restriction on the differential equations and models where these derivatives can be used. For the particular cases of the so-called Caputo-Fabrizio and Atangana-Baleanu derivatives, it is shown that when this restriction holds the derivative can be simply expressed in terms of integer derivatives and standard Caputo fractional derivatives, thus demonstrating that these derivatives contain nothing new.

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MIDDLETON, CHAD, and GEORGE SIOPSIS. "THE SCHWARZSCHILD SOLUTION IN THE DGP MODEL." Modern Physics Letters A 19, no. 30 (September 28, 2004): 2259–66. http://dx.doi.org/10.1142/s0217732304015555.

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We discuss the Schwarzschild solution in the Dvali–Gabadadze–Porrati (DGP) model. We obtain a perturbative expansion and find the explicit form of the lowest-order contribution. By keeping off-diagonal terms in the metric, we arrive at a perturbative expansion which is valid both far from and near the Schwarzschild radius. We calculate the lowest-order contribution explicitly and obtain the form of the metric both on the brane and in the bulk. As we approach the Schwarzschild radius, the perturbative expansion yields the standard four-dimensional Schwarzschild solution on the brane which is non-singular in the decoupling limit. This non-singular behavior is similar to the Vainshtein solution in massive gravity demonstrating the absence of the van Dam–Veltman–Zakharov (vDVZ) discontinuity in the DGP model.

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HARRIS, ADAM. "SINGULAR LOCI IN HOLOMORPHIC FAMILIES." International Journal of Mathematics 09, no. 03 (May 1998): 277–93. http://dx.doi.org/10.1142/s0129167x98000129.

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Let [Formula: see text] be a proper flat morphism between manifolds, and [Formula: see text] an analytic subset, such that the fibres Xt, for all [Formula: see text], determine a locally trivial deformation of a compact complex manifold. Non-generic fibres Xt, for t ∈ A, may be taken a priori to be singular spaces, or to have a smooth complex structure which is biholomorphically distinct from their generic neighbours. The main theorem of this article provides a sufficient condition for local triviality of the entire family [Formula: see text], in terms of the dimension of A and of the singular subvarieties of certain "degeneracy loci" in [Formula: see text]. Several specific applications of the main theorem are subsequently examined, some of which correspond sharply with examples of "structure-jumping" in complex deformations and "jumping loci" of vector bundles on complex projective space.

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Kamel, Osman M., and Adel S. Soliman. "A Second Order Secular J–S Planetary Theory Part I : Lemma." Mechanics and Mechanical Engineering 22, no. 4 (September 2, 2020): 871–74. http://dx.doi.org/10.2478/mme-2018-0067.

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AbstractA concise lemma is given for the construction of a semi – analytic Hamiltonian second order secular J–S planetary theory using the Jacobi – Radau system of origins and in terms of the non-singular variables of H. Poincaré. We truncate our expansions at the desired power in the eccentricities and the sines of the inclinations.

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Jan, Rashid, Sultan Alyobi, Mustafa Inc, Ali Saleh Alshomrani, and Muhammad Farooq. "A robust study of the transmission dynamics of malaria through non-local and non-singular kernel." AIMS Mathematics 8, no. 4 (2023): 7618–40. http://dx.doi.org/10.3934/math.2023382.

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<abstract><p>It is valuable to measure the epidemiological significance of malaria, since there has been a growing interest in reducing malaria through improved local and national health care systems. We formulate the dynamics of malaria infection via a fractional framework to understand the intricate transmission route of malaria and to identify the role of memory for the control of malaria. The model is investigated for basic results, moreover, the basic reproduction number is determined symbolized by $ \mathcal{R}_0 $. We have shown the local stability of the disease-free steady-state of the system for for $ \mathcal{R}_0 < 1 $. The existence and uniqueness of the solution of the system are examined. The Adams Bashforth approach in fractional form is applied to analyse the numerical outcomes of the mathematical model. Furthermore, in order to realise more efficiently, the Atangana-Baleanu (ABC) fractional nonlocal operator, which was just invented, is used. The stability of the system is investigated through the fixed-point theorems of Krasnoselskii and Banach. The behaviour of the approximation solution is illustrated in terms of graphs across various fractional values and other factors of the systems. After all, a brief analysis of the simulation's findings is provided to explain how infection transmission dynamics occur in society.</p></abstract>

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Chaumont-Frelet, T., and S. Nicaise. "High-frequency behaviour of corner singularities in Helmholtz problems." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 5 (September 2018): 1803–45. http://dx.doi.org/10.1051/m2an/2018031.

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We analyze the singular behaviour of the Helmholtz equation set in a non-convex polygon. Classically, the solution of the problem is split into a regular part and one singular function for each re-entrant corner. The originality of our work is that the “amplitude” of the singular parts is bounded explicitly in terms of frequency. We show that for high frequency problems, the “dominant” part of the solution is the regular part. As an application, we derive sharp error estimates for finite element discretizations. These error estimates show that the “pollution effect” is not changed by the presence of singularities. Furthermore, a consequence of our theory is that locally refined meshes are not needed for high-frequency problems, unless a very accurate solution is required. These results are illustrated with numerical examples that are in accordance with the developed theory.

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Wang, Yifu, Jingxue Yin, and Yuanyuan Ke. "Coexistence Solutions for a Periodic Competition Model with Singular–Degenerate Diffusion." Proceedings of the Edinburgh Mathematical Society 60, no. 4 (December 15, 2016): 1065–75. http://dx.doi.org/10.1017/s001309151600033x.

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AbstractWe investigate a system of singular–degenerate parabolic equations with non-local terms, which can be regarded as a spatially heterogeneous competition model of Lotka–Volterra type. Applying the Leray–Schauder fixed-point theorem, we establish the existence of coexistence periodic solutions to the problem, which, together with the existing literature, gives a complete picture for such a system for all parameters.

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Ishkhanyan and Cesarano. "Generalized-Hypergeometric Solutions of the General Fuchsian Linear ODE Having Five Regular Singularities." Axioms 8, no. 3 (September 2, 2019): 102. http://dx.doi.org/10.3390/axioms8030102.

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We show that a Fuchsian differential equation having five regular singular points admits solutions in terms of a single generalized hypergeometric function for infinitely many particular choices of equation parameters. Each solution assumes four restrictions imposed on the parameters: two of the singularities should have non-zero integer characteristic exponents and the accessory parameters should obey polynomial equations.

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