Статті в журналах: "Non-compact problems"

1

Ellis, John, K. Enqvist, and D. V. Nanopoulos. "Non-compact supergravity solves problems." Physics Letters B 151, no. 5-6 (February 1985): 357–62. http://dx.doi.org/10.1016/0370-2693(85)91654-5.

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2

Cavalier, L. "Inverse problems with non-compact operators." Journal of Statistical Planning and Inference 136, no. 2 (February 2006): 390–400. http://dx.doi.org/10.1016/j.jspi.2004.06.063.

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3

Hofmann, Bernd, and G. Fleischer. "Stability Rates for Linear Ill-Posed Problems with Compact and Non-Compact Operators." Zeitschrift für Analysis und ihre Anwendungen 18, no. 2 (1999): 267–86. http://dx.doi.org/10.4171/zaa/881.

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4

Gajic, Ljiljana. "On some optimization problems in not necessarily locally convex space." Yugoslav Journal of Operations Research 18, no. 2 (2008): 167–72. http://dx.doi.org/10.2298/yjor0802167g.

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In this note, by using O. Hadzic's generalization of a fixed point theorem of Himmelberg, we prove a non - cooperative equilibrium existence theorem in non - compact settings and a generalization of an existence theorem for non - compact infinite optimization problems, all in not necessarily locally convex spaces.

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5

Aussel, Didier, and Asrifa Sultana. "Quasi-variational inequality problems with non-compact valued constraint maps." Journal of Mathematical Analysis and Applications 456, no. 2 (December 2017): 1482–94. http://dx.doi.org/10.1016/j.jmaa.2017.06.034.

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6

O'Regan, Donal. "Boundary value problems on noncompact intervals." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 4 (1995): 777–99. http://dx.doi.org/10.1017/s0308210500030341.

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7

Molica Bisci, Giovanni, and Simone Secchi. "Elliptic problems on complete non-compact Riemannian manifolds with asymptotically non-negative Ricci curvature." Nonlinear Analysis 177 (December 2018): 637–72. http://dx.doi.org/10.1016/j.na.2018.04.019.

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8

Singh, Vishal, Hossain Chizari, and Farzad Ismail. "Non-unified Compact Residual-Distribution Methods for Scalar Advection–Diffusion Problems." Journal of Scientific Computing 76, no. 3 (March 5, 2018): 1521–46. http://dx.doi.org/10.1007/s10915-018-0674-1.

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9

Rahaman, Mijanur, and Rais Ahmad. "Weak and strong mixed vector equilibrium problems on non-compact domain." Journal of the Egyptian Mathematical Society 23, no. 2 (July 2015): 352–55. http://dx.doi.org/10.1016/j.joems.2014.06.007.

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10

Fieseler, K. H., and K. Tintarev. "Semilinear elliptic problems and concentration compactness on non-compact Riemannian manifolds." Journal of Geometric Analysis 13, no. 1 (March 2003): 67–75. http://dx.doi.org/10.1007/bf02930997.

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11

Wang, Xiangsheng. "Elliptic boundary value problem on non-compact G-manifolds." International Journal of Mathematics 28, no. 04 (April 2017): 1750025. http://dx.doi.org/10.1142/s0129167x17500252.

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In this paper, an equality between the Hochs–Mathai type index and the Atiyah–Patodi–Singer type index is established when the manifold and the group action are both non-compact, which generalizes a result of Ma and Zhang for compact group actions. As a technical preparation, a problem concerning the Fredholm property of the global elliptic boundary value problems of the Atiyah–Patodi–Singer type on a non-compact manifold is studied.

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12

DUC, DUONG MINH. "VARIATIONAL PROBLEMS OF CERTAIN FUNCTIONALS." International Journal of Mathematics 06, no. 04 (August 1995): 503–35. http://dx.doi.org/10.1142/s0129167x95000195.

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We get the existence and regularity of minimizers of certain functionals, which may be degenerate and have non-polynomial growth. Applying these results we can find exponentially harmonic maps in every homotopy class of maps from a connected Riemannian C4-manifold into [Formula: see text], where [Formula: see text] is a compact Riemannian C4-manifold.

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13

de Andrade, Bruno, and Claudio Cuevas. "Compact almost automorphic solutions to semilinear Cauchy problems with non-dense domain." Applied Mathematics and Computation 215, no. 8 (December 2009): 2843–49. http://dx.doi.org/10.1016/j.amc.2009.09.025.

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14

Wegert, E., and M. A. Efendiev. "Nonlinear Riemann—Hilbert problems with Lipschitz continuous boundary condition." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 4 (August 2000): 793–800. http://dx.doi.org/10.1017/s0308210500000421.

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Using a norm inequality for singular integral operators in pairs of weighted Lebesgue spaces we are able to prove existence and uniqueness results for solutions of nonlinear RiemannHilbert problems with non-compact Lipschitz continuous restriction curves.

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15

Gérard, Patrick, and Sandrine Grellier. "Inverse spectral problems for compact Hankel operators." Journal of the Institute of Mathematics of Jussieu 13, no. 2 (April 18, 2013): 273–301. http://dx.doi.org/10.1017/s1474748013000121.

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AbstractGiven two arbitrary sequences $({\lambda }_{j} )_{j\geq 1} $ and $({\mu }_{j} )_{j\geq 1} $ of real numbers satisfying $$\begin{eqnarray*}\displaystyle \vert {\lambda }_{1} \vert \gt \vert {\mu }_{1} \vert \gt \vert {\lambda }_{2} \vert \gt \vert {\mu }_{2} \vert \gt \cdots \gt \vert {\lambda }_{j} \vert \gt \vert {\mu }_{j} \vert \rightarrow 0, &&\displaystyle\end{eqnarray*}$$ we prove that there exists a unique sequence $c= ({c}_{n} )_{n\in { \mathbb{Z} }_{+ } } $, real valued, such that the Hankel operators ${\Gamma }_{c} $ and ${\Gamma }_{\tilde {c} } $ of symbols $c= ({c}_{n} )_{n\geq 0} $ and $\tilde {c} = ({c}_{n+ 1} )_{n\geq 0} $, respectively, are selfadjoint compact operators on ${\ell }^{2} ({ \mathbb{Z} }_{+ } )$ and have the sequences $({\lambda }_{j} )_{j\geq 1} $ and $({\mu }_{j} )_{j\geq 1} $, respectively, as non-zero eigenvalues. Moreover, we give an explicit formula for $c$ and we describe the kernel of ${\Gamma }_{c} $ and of ${\Gamma }_{\tilde {c} } $ in terms of the sequences $({\lambda }_{j} )_{j\geq 1} $ and $({\mu }_{j} )_{j\geq 1} $. More generally, given two arbitrary sequences $({\rho }_{j} )_{j\geq 1} $ and $({\sigma }_{j} )_{j\geq 1} $ of positive numbers satisfying $$\begin{eqnarray*}\displaystyle {\rho }_{1} \gt {\sigma }_{1} \gt {\rho }_{2} \gt {\sigma }_{2} \gt \cdots \gt {\rho }_{j} \gt {\sigma }_{j} \rightarrow 0, &&\displaystyle\end{eqnarray*}$$ we describe the set of sequences $c= ({c}_{n} )_{n\in { \mathbb{Z} }_{+ } } $ of complex numbers such that the Hankel operators ${\Gamma }_{c} $ and ${\Gamma }_{\tilde {c} } $ are compact on ${\ell }^{2} ({ \mathbb{Z} }_{+ } )$ and have sequences $({\rho }_{j} )_{j\geq 1} $ and $({\sigma }_{j} )_{j\geq 1} $, respectively, as non-zero singular values.

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16

Mazepa, E. A., and D. K. Ryaboshlykova. "Boundary-value problems for the inhomogeneous Schr"odinger equation with variations of its potential on non-compact Riemannian manifolds." Issues of Analysis 28, no. 3 (November 2021): 113–28. http://dx.doi.org/10.15393/j3.art.2021.10911.

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17

Infante, Gennaro. "EIGENVALUES OF SOME NON-LOCAL BOUNDARY-VALUE PROBLEMS." Proceedings of the Edinburgh Mathematical Society 46, no. 1 (January 27, 2003): 75–86. http://dx.doi.org/10.1017/s0013091501001079.

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AbstractWorking on a suitable cone of continuous functions, we give new results for integral equations of the form $\lambda u(t)=\int_{G}k(t,s)f(s,u(s))\,\mathrm{d} s:=Tu(t)$, where $G$ is a compact set in $\mathbb{R}^{n}$ and $k$ is a possibly discontinuous function that is allowed to change sign. We apply our results to prove existence of eigenvalues of some non-local boundary-value problems.AMS 2000 Mathematics subject classification: Primary 34B10. Secondary 34B18; 47H10; 47H30

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18

Fang, Yi. "Minimal annuli in R3 bounded by non-compact complete convex curves in parallel planes." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 60, no. 3 (June 1996): 369–88. http://dx.doi.org/10.1017/s1446788700037885.

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AbstractIn this paper we consider the Plateau problem for surfaces of annular type bounded by a pair of convex, non-compact curves in parallel planes. We prove that for certain symmetric boundaries there are solutions to the non-compact Plateau problems (Theorem B). Except for boundaries consisting of a pair of parallel straight lines, these are the first known examples.

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19

an Huef, Astrid, S. Kaliszewski, and Iain Raeburn. "Extension problems and non-Abelian duality for C*-algebras." Bulletin of the Australian Mathematical Society 75, no. 2 (April 2007): 229–38. http://dx.doi.org/10.1017/s0004972700039162.

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Suppose that H is a closed subgroup of a locally compact group G. We show that a unitary representation U of H is the restriction of a unitary representation of G if and only if a dual representation Û of a crossed product C*(G) ⋊ (G/H) is regular in an appropriate sense. We then discuss the problem of deciding whether a given representation is regular; we believe that this problem will prove to be an interesting test question in non-Abelian duality for crossed products of C*-algebras.

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20

S GARCIA, ELINO. "An Exploration of Synthetic Division for Non-Linear Polynomial Divisors." International Multidisciplinary Research Journal 4, no. 1 (March 6, 2022): 11–21. http://dx.doi.org/10.54476/iimrj02.

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As a goal of developing alternative algorithm on division of polynomials whose dividend is 𝑎1𝑥 𝑛 + 𝑎2𝑥 𝑛−1 + 𝑎3𝑥 𝑛−2 + ⋯ + 𝑎𝑛𝑥 + 𝑎𝑛+1 and the divisor is 𝑏1𝑥 𝑚 + 𝑏2𝑥 𝑚−1 + 𝑏3𝑥 𝑚−2 … + 𝑏𝑚𝑥 + 𝑏𝑚+1, where 𝑛 > 𝑚, 𝑎1 ≠ 0, 𝑏1 ≠ 0, and 𝑎𝑖 ′𝑠and 𝑏𝑖 ′𝑠including 𝑎𝑛+1 and 𝑏𝑚+1 are constant, the researcher explored the synthetic division in compact form.The researcher believes that the algorithm in this study is a good alternative in dividing polynomials of higher degrees. In the said compact form, division of only some distinct pairs of non-linear polynomials were presented and served as reference problems for the researcher during the initial exploration. The Division Algorithm for Polynomials theorem was applied in exploring the problems with quadratic, cubic and quartic divisors. This resulted to the development of formulas for the coefficients 𝑡1of the quotient 𝑄(𝑥) and coefficients 𝑟1 of the remainder 𝑅(𝑥) which were considered important parts of the algorithm. Aside from the condition for the inapplicability for non-linear divisors, additional conditions were provided to the problems where the usual synthetic division is inappropriate. At the end, the algorithm on division of polynomials of higher degrees by non-linear divisors was developed using basic research. Illustrative examples of dividing polynomials using the developed algorithms with monic (𝑏1 = 1) and non-monic (𝑏1 ≠ 1) divisors were provided. Results were verified through other existing methods: long division and synthetic division in compact form.

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21

Boffi, Daniele. "Finite element approximation of eigenvalue problems." Acta Numerica 19 (May 2010): 1–120. http://dx.doi.org/10.1017/s0962492910000012.

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We discuss the finite element approximation of eigenvalue problems associated with compact operators. While the main emphasis is on symmetric problems, some comments are present for non-self-adjoint operators as well. The topics covered include standard Galerkin approximations, non-conforming approximations, and approximation of eigenvalue problems in mixed form. Some applications of the theory are presented and, in particular, the approximation of the Maxwell eigenvalue problem is discussed in detail. The final part tries to introduce the reader to the fascinating setting of differential forms and homological techniques with the description of the Hodge–Laplace eigenvalue problem and its mixed equivalent formulations. Several examples and numerical computations complete the paper, ranging from very basic exercises to more significant applications of the developed theory.

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22

Geffner, Tomas, and Hector Geffner. "Compact Policies for Fully Observable Non-Deterministic Planning as SAT." Proceedings of the International Conference on Automated Planning and Scheduling 28 (June 15, 2018): 88–96. http://dx.doi.org/10.1609/icaps.v28i1.13880.

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Fully observable non-deterministic (FOND) planning is becoming increasingly important as an approach for computing proper policies in probabilistic planning, extended temporal plans in LTL planning, and general plans in generalized planning. In this work, we introduce a SAT encoding for FOND planning that is compact and can produce compact strong cyclic policies. Simple variations of the encodings are also introduced for strong planning and for what we call, dual FOND planning, where some non-deterministic actions are assumed to be fair (e.g., probabilistic) and others unfair (e.g., adversarial). The resulting FOND planners are compared empirically with existing planners over existing and new benchmarks. The notion of ``probabilistic interesting problems'' is also revisited to yield a more comprehensive picture of the strengths and limitations of current FOND planners and the proposed SAT approach.

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23

Sengupta, T. K., V. Lakshmanan, and V. V. S. N. Vijay. "A new combined stable and dispersion relation preserving compact scheme for non-periodic problems." Journal of Computational Physics 228, no. 8 (May 2009): 3048–71. http://dx.doi.org/10.1016/j.jcp.2009.01.003.

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24

S. Garcia, Elino. "An Exploration of Synthetic Division for Non-Linear Polynomial Divisors." International Multidisciplinary Research Journal 4, no. 1 (March 23, 2022): 10–21. http://dx.doi.org/10.54476/1286801.

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As a goal of developing alternative algorithm on division of polynomials whose dividend is 𝑎1𝑥 𝑛 + 𝑎2𝑥 𝑛−1 + 𝑎3𝑥 𝑛−2 + ⋯ + 𝑎𝑛𝑥 + 𝑎𝑛+1 and the divisor is 𝑏1𝑥 𝑚 + 𝑏2𝑥 𝑚−1 + 𝑏3𝑥 𝑚−2 … + 𝑏𝑚𝑥 + 𝑏𝑚+1, where 𝑛 > 𝑚, 𝑎1 ≠ 0, 𝑏1 ≠ 0, and 𝑎𝑖 ′𝑠and 𝑏𝑖 ′𝑠including 𝑎𝑛+1 and 𝑏𝑚+1 are constant, the researcher explored the synthetic division in compact form.The researcher believes that the algorithm in this study is a good alternative in dividing polynomials of higher degrees. In the said compact form, division of only some distinct pairs of non-linear polynomials were presented and served as reference problems for the researcher during the initial exploration. The Division Algorithm for Polynomials theorem was applied in exploring the problems with quadratic, cubic and quartic divisors. This resulted to the development of formulas for the coefficients 𝑡1of the quotient 𝑄(𝑥) and coefficients 𝑟1 of the remainder 𝑅(𝑥) which were considered important parts of the algorithm. Aside from the condition for the inapplicability for non-linear divisors, additional conditions were provided to the problems where the usual synthetic division is inappropriate. At the end, the algorithm on division of polynomials of higher degrees by non-linear divisors was developed using basic research. Illustrative examples of dividing polynomials using the developed algorithms with monic (𝑏1 = 1) and non-monic (𝑏1 ≠ 1) divisors were provided. Results were verified through other existing methods: long division and synthetic division in compact form. Keywords: synthetic division, high school algebra, short division

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25

Gordin, V. A. "COMPACT FINITE-DIFFERENCE SCHEMES FOR WEAKLY NON-LINEAR PROBLEMS AND BOUNDARY CONDITIONS IMITATING CAUCHY PROBLEM." XXII workshop of the Council of nonlinear dynamics of the Russian Academy of Sciences 47, no. 1 (April 30, 2019): 32–37. http://dx.doi.org/10.29006/1564-2291.jor-2019.47(1).9.

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Compact finite-difference schemes are well known and provide high accuracy order for differential equation with constant coefficients. Algorithms for constructing compact schemes of the 4-th order for boundary value problems with variable (smooth or jump) coefficient are developed. For the diffusion equations with a smooth variable coefficient and the Levin – Leontovich equation, compact finite-difference schemes are also constructed and their 4-th order is experimentally confirmed. The method of constructing compact schemes of the 4-th order can be generalized to partial differential equations and systems with weak nonlinearity, for example, for the Fisher – Kolmogorov – Petrovsky – Piskunov equation, for the nonlinear Schrödinger equation or for the Fitzhugh – Nagumo system. For such nonlinear problems, a combination of simple explicit schemes and relaxation is used. Richardson’s extrapolation increases the order of the circuits to the 6-th. To approximate multidimensional problems with discontinuous coefficients, for example, the two-dimensional stationary diffusion equation in inhomogeneous media, it is necessary to estimate the possible asymptotics of solutions in the vicinity of the boundary line’s breaks. To do this, we use generalized eigen-functions in the angle, which can be used as a set of test functions and build compact difference schemes approximating the problem on triangular grids with high order of accuracy. The asymptotics along the radius of these generalized eigen-functions (in polar coordinates in the vicinity of the vertex of the angle) have irrational indices which can be found from a special dispersion equation and which determine the indices of the corresponding Bessel functions along the radius. For a number of difference schemes approximating the most important evolutionary equations of mathematical physics, it is possible to construct special boundary conditions imitating the Cauchy problem (ICP) on the whole space. These conditions depend not only on the original equation, but also on the type of the difference scheme, and even on the coefficients of the corresponding differential equation. The ICP conditions are determined with accuracy to a gauge. But the choice of this gauge turns out to be essential with numerical implementation. The role of rational approximations of the Pade – Hermite type of the symbol of the corresponding pseudo-differential operator is important. Examples of movie solutions of problems with ICP conditions for various finite-difference schemes approximating the basic mathematical physics equations, see https://cs.hse.ru/mmsg/transbounds. The study was realized within the framework of the Academic Fund Program at the National Research University – Higher School of Economics (HSE) in 2016–2017 (grant No. 16-05-0069) and by the Russian Academic Excellence Project «5–100».

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26

Ignatyev, Mikhail. "Inverse scattering problem for Sturm-Liouville operator on non-compact A-graph. Uniqueness result." Tamkang Journal of Mathematics 46, no. 4 (December 22, 2015): 401–22. http://dx.doi.org/10.5556/j.tkjm.46.2015.1806.

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We consider a connected metric graph with the following property: each two cycles can have at most one common point. Such graphs are called A-graphs. On noncompact A-graph we consider a scattering problem for Sturm--Liouville differential operator with standard matching conditions in the internal vertices. Transport, spectral and scattering problems for differential operators on graphs appear frequently in mathematics, natural sciences and engineering. In particular, direct and inverse problems for such operators are used to construct and study models in mechanics, nano-electronics, quantum computing and waveguides. The most complete results on (both direct and inverse) spectral problems were achieved in the case of Sturm--Liouville operators on compact graphs, in the noncompact case there are no similar general results. In this paper, we establish some properties of the spectral characteristics and investigate the inverse problem of recovering the operator from the scattering data. A uniqueness theorem for such inverse problem is proved.

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27

Ghimenti, Marco G., and Anna Maria Micheletti. "Compactness and blow up results for doubly perturbed Yamabe problems on manifolds with non umbilic boundary." Mathematical Biosciences and Engineering 30, no. 4 (2022): 1209–35. http://dx.doi.org/10.3934/era.2022064.

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<abstract><p>We study the stability of compactness of solutions for the Yamabe boundary problem on a compact Riemannian manifold with non umbilic boundary. We prove that the set of solutions of Yamabe boundary problem is a compact set when perturbing the mean curvature of the boundary from below and the scalar curvature with a function whose maximum is not too positive. In addition, we prove the counterpart of the stability result: there exists a blowing up sequence of solutions when we perturb the mean curvature from above or the mean curvature from below and the scalar curvature with a function with a large positive maximum.</p></abstract>

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28

Hofmann, B., D. Düvelmeyer, and K. Krumbiegel. "APPROXIMATE SOURCE CONDITIONS IN TIKHONOV REGULARIZATION‐NEW ANALYTICAL RESULTS AND SOME NUMERICAL STUDIES." Mathematical Modelling and Analysis 11, no. 1 (March 31, 2006): 41–56. http://dx.doi.org/10.3846/13926292.2006.9637301.

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We present some new ideas and results for finding convergence rates in Tikhonov regularization for ill‐posed linear inverse problems with compact and non‐compact forward operators based on the consideration of approximate source conditions and corresponding distance functions. The new results and studies complement and extend in numerous points the recent papers [5, 7, 8, 10] that also exploit the distance functions originally introduced in [2] which measure the violation of a moderate source condition that works as a benchmark. In this context, we distinguish as in [8] logarithmic, power and exponential decay rates for the distance functions and their consequences. Under specific range inclusions the decay rate of distance functions is verified explicitly, whereas in [10] this result is also used but formulated only in an implicit manner. Applications to non‐compact multiplication operators are briefly reviewed from [8]. An important new result is that we can show for compact operators a one‐to‐one correspondence between the maximal power type decay rates for the distance functions and maximal exponents of Holder rates in Tikhonov regularization linked by the specific singular value expansion of the solution element. Some numerical studies on simple integration illustrate the compact operator case and the specific situation of discretized problems. Finally, some ideas of generalization are mentioned concerning the fact that the benchmark of the distance function can be shifted.

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29

Mazepa, Elena. "On Solvability of Boundary Value Problems of the Poisson Equation on Non-Compact Riemannian Manifolds." Vestnik Volgogradskogo gosudarstvennogo universiteta. Serija 1. Mathematical Physics and Computer Modeling 20, no. 3 (September 2017): 136–47. http://dx.doi.org/10.15688/mpcm.jvolsu.2017.3.10.

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30

Long, Guangqing, Xiaoyuan Huang, Aimei Tan, and Gnaneshwar Nelakanti. "Discrete product integration methods for eigen-problems of a class of non-compact integral operators." Applied Mathematics and Computation 219, no. 15 (April 2013): 7964–72. http://dx.doi.org/10.1016/j.amc.2013.02.034.

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31

Majidian, H., and E. Babolian. "An interpolation degenerate kernel method for eigenvalue problems of a class of non-compact operators." Applied Mathematics Letters 23, no. 8 (August 2010): 825–30. http://dx.doi.org/10.1016/j.aml.2010.01.019.

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32

Talgorn, Bastien, and Michael Kokkolaras. "Compact implementation of non-hierarchical analytical target cascading for coordinating distributed multidisciplinary design optimization problems." Structural and Multidisciplinary Optimization 56, no. 6 (July 3, 2017): 1597–602. http://dx.doi.org/10.1007/s00158-017-1726-0.

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33

Meskhi, Alexander. "On a measure of non-compactness for singular integrals." Journal of Function Spaces and Applications 1, no. 1 (2003): 35–43. http://dx.doi.org/10.1155/2003/927590.

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It is proved that there exists no weight pair(v, w)for which a singular integral operator is compact from the weighted Lebesgue spaceLwp(Rn)toLvp(Rn). Moreover, a measure of non-compatness for this operator is estimated from below. Analogous problems for Cauchy singular integrals defined on Jordan smooth curves are studied.

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34

Infante, Gennaro, and J. R. L. Webb. "NONLINEAR NON-LOCAL BOUNDARY-VALUE PROBLEMS AND PERTURBED HAMMERSTEIN INTEGRAL EQUATIONS." Proceedings of the Edinburgh Mathematical Society 49, no. 3 (October 2006): 637–56. http://dx.doi.org/10.1017/s0013091505000532.

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AbstractMotivated by some non-local boundary-value problems (BVPs) that arise in heat-flow problems, we establish new results for the existence of non-zero solutions of integral equations of the form$$ u(t)=\gamma(t)\alpha[u]+\int_{G}k(t,s)f(s,u(s))\,\mathrm{d}s, $$where $G$ is a compact set in $\mathbb{R}^{n}$. Here $\alpha[u]$ is a positive functional and $f$ is positive, while $k$ and $\gamma$ may change sign, so positive solutions need not exist. We prove the existence of multiple non-zero solutions of the BVPs under suitable conditions. We show that solutions of the BVPs lose positivity as a parameter decreases. For a certain parameter range not all solutions can be positive, but for one of the boundary conditions we consider we show that there are positive solutions for certain types of nonlinearity. We also prove a uniqueness result.

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35

GOLODETS, VALENTIN YA, and SERGEY D. SINEL'SHCHIKOV. "On the conjugacy and isomorphism problems for stabilizers of Lie group actions." Ergodic Theory and Dynamical Systems 19, no. 2 (April 1999): 391–411. http://dx.doi.org/10.1017/s014338579913013x.

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The spaces of subgroups and Lie subalgebras with the group actions by conjugations are considered for real Lie groups. Our approach allows one to apply the properties of algebraically regular transformation groups to finding the conditions when those actions turn out to be type I. It follows, in particular, that in this case the stability groups for all the ergodic actions of such groups are conjugate (for example when the stability groups are compact). The isomorphism of the stability groups for ergodic actions is also established under some assumptions. A number of examples of non-conjugate and non-isomorphic stability groups are presented.

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36

Marraffa, Valeria, and Bianca Satco. "Stieltjes Differential Inclusions with Periodic Boundary Conditions without Upper Semicontinuity." Mathematics 10, no. 1 (December 24, 2021): 55. http://dx.doi.org/10.3390/math10010055.

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We are studying first order differential inclusions with periodic boundary conditions where the Stieltjes derivative with respect to a left-continuous non-decreasing function replaces the classical derivative. The involved set-valued mapping is not assumed to have compact and convex values, nor to be upper semicontinuous concerning the second argument everywhere, as in other related works. A condition involving the contingent derivative relative to the non-decreasing function (recently introduced and applied to initial value problems by R.L. Pouso, I.M. Marquez Albes, and J. Rodriguez-Lopez) is imposed on the set where the upper semicontinuity and the assumption to have compact convex values fail. Based on previously obtained results for periodic problems in the single-valued cases, the existence of solutions is proven. It is also pointed out that the solution set is compact in the uniform convergence topology. In particular, the existence results are obtained for periodic impulsive differential inclusions (with multivalued impulsive maps and finite or possibly countable impulsive moments) without upper semicontinuity assumptions on the right-hand side, and also the existence of solutions is derived for dynamic inclusions on time scales with periodic boundary conditions.

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37

Dello Russo, Anahí, and Ana E. Alonso. "Mixed Finite Element Analysis of Eigenvalue Problems on Curved Domains." Computational Methods in Applied Mathematics 14, no. 1 (January 1, 2014): 1–33. http://dx.doi.org/10.1515/cmam-2013-0014.

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Abstract. In this paper we present a theoretical framework for the analysis of the numerical approximations of a particular class of eigenvalue problems by mixed/hybrid methods. More precisely, we are interested in eigenproblems which are defined over curved domains or have internal curved boundaries and which may be associated with non-compact inverse operators. To do this, we consider external domain approximations $\Omega _{h}$ of the original domain $\Omega $, i.e., $\Omega _{h} \lnot \subset \Omega $. Sufficient conditions to ensure good convergence properties and optimal error bounds for the external approximations of the eigenfunction/eigenvalue pairs are established. Then, these results are applied to the study of the Stokes eigenvalue problem with slip boundary condition defined on a curved non-convex two-dimensional domain.

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38

Friderikos, Orestis, Marc Olive, Emmanuel Baranger, Dimitris Sagris, and Constantine David. "A non-intrusive space-time interpolation from compact Stiefel manifolds of parametrized rigid-viscoplastic FEM problems." Computational Mechanics 68, no. 4 (June 30, 2021): 861–83. http://dx.doi.org/10.1007/s00466-021-02050-0.

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39

Dai, Ruxin, Yin Wang, and Xiwei Wang. "Effects of Different High Order Compact Computations for Solving Boundary Layer Problems on Non-Uniform Grids." Journal of Computational Intelligence and Electronic Systems 3, no. 3 (September 1, 2014): 200–211. http://dx.doi.org/10.1166/jcies.2014.1091.

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40

Rodriguez, Armando A., and Munther A. Dahleh. "On the computation of induced norms for non-compact Hankel operators arising from distributed control problems." Systems & Control Letters 19, no. 6 (December 1992): 429–38. http://dx.doi.org/10.1016/0167-6911(92)90074-3.

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41

Liang, Yan, Xiao Ming Wu, Bi Hua Tang, and Yong Le Wu. "Compact LowPass Filter with Wide StopBand Using Non-Uniform Microstrip Resonant Cells." Applied Mechanics and Materials 263-266 (December 2012): 15–19. http://dx.doi.org/10.4028/www.scientific.net/amm.263-266.15.

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In this paper, a novel compact microstrip lowpass filter is designed. The proposed filter which is etched on the 50 Ω microstrip line consists of four non-uniform 1-D microstrip photonic bandgap (PBG) cells with different cutoff frequency.. The demonstration lowpass filter with 2.2 GHz cutoff frequency is designed, fabricated and measured. The measurement results show that the band rejection effect is better than -20 dB from 2.8 GHz to 10 GHz, the insertion is less than 2 dB, and the length of filter is 5.6 cm long. Compared with the conventional filter, the proposed filter has smaller size. Meanwhile, it overcomes the problems of narrow stop-band and low harmonic suppression. Furthermore, the impedance matching is not need to be considered. This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.

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42

Ashton, Brenden, and Ian Doust. "A COMPARISON OF ALGEBRAS OF FUNCTIONS OF BOUNDED VARIATION." Proceedings of the Edinburgh Mathematical Society 49, no. 3 (October 2006): 575–91. http://dx.doi.org/10.1017/s0013091504001130.

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AbstractMotivated by problems in the spectral theory of linear operators, we previously introduced a new concept of variation for functions defined on a non-empty compact subset of the plane. In this paper, we examine the algebras of functions of bounded variation one obtains from these new definitions for the case where the underlying compact set is either a rectangle or the unit circle, and compare these algebras with those previously used by Berkson and Gillespie in their theories of AC-operators and trigonometrically well-bounded operators.

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Matevossian, Hovik A. "Mixed Boundary Value Problems for the Elasticity System in Exterior Domains." Mathematical and Computational Applications 24, no. 2 (June 2, 2019): 58. http://dx.doi.org/10.3390/mca24020058.

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We study the properties of solutions of the mixed Dirichlet–Robin and Neumann–Robin problems for the linear system of elasticity theory in the exterior of a compact set and the asymptotic behavior of solutions of these problems at infinity under the assumption that the energy integral with weight | x | a is finite for such solutions. We use the variational principle and depending on the value of the parameter a, obtain uniqueness (non-uniqueness) theorems of the mixed problems or present exact formulas for the dimension of the space of solutions.

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CORRÊA, F. J. S. A., J. V. GONCALVES, and ANGELO RONCALLI. "ON A CLASS OF FOURTH ORDER NONLINEAR ELLIPTIC EQUATIONS UNDER NAVIER BOUNDARY CONDITIONS." Analysis and Applications 08, no. 02 (April 2010): 185–97. http://dx.doi.org/10.1142/s0219530510001576.

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We employ arguments involving continua of fixed points of suitable nonlinear compact operators and the Lyapunov–Schmidt method to prove existence and multiplicity of solutions in a class of fourth order non-homogeneous resonant elliptic problems. Our main result extends even similar ones known for the Laplacian.

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45

Matevossian, Hovik. "On the Mixed Dirichlet–Steklov-Type and Steklov-Type Biharmonic Problems in Weighted Spaces." Mathematical and Computational Applications 24, no. 1 (February 18, 2019): 25. http://dx.doi.org/10.3390/mca24010025.

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We studied the properties of generalized solutions in unbounded domains and the asymptotic behavior of solutions of elliptic boundary value problems at infinity. Moreover, we studied the unique solvability of the mixed Dirichlet–Steklov-type and Steklov-type biharmonic problems in the exterior of a compact set under the assumption that generalized solutions of these problems has a bounded Dirichlet integral with weight | x | a . Depending on the value of the parameter a, we obtained uniqueness (non-uniqueness) theorems of these problems or present exact formulas for the dimension of the space of solutions.

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46

FUJII, KAZUYUKI. "STANDARD AND NON-STANDARD QUANTUM MODELS: A NON-COMMUTATIVE VERSION OF THE CLASSICAL SYSTEM OF SU(2) AND SU(1,1) ARISING FROM QUANTUM OPTICS." International Journal of Geometric Methods in Modern Physics 02, no. 05 (October 2005): 783–821. http://dx.doi.org/10.1142/s0219887805000879.

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This is a challenging paper that includes some reviews and new results. Since the non-commutative version of the classical system based on the compact group SU(2) has been constructed in (quant-ph/0502174) by making use of Jaynes–Commings model and so-called quantum diagonalization method in (quant-ph/0502147), we construct a non-commutative version of the classical system based on the non-compact group SU(1,1) by modifying the compact case. In this model the Hamiltonian is not hermite but pseudo hermite, which causes a big difference between the two models. For example, in the classical representation theory of SU(1,1), unitary representations are infinite dimensional from the starting point. Therefore, to develop a unitary theory of non-commutative system of SU(1,1) we need an infinite number of non-commutative systems, which means a kind of second non-commutativization. This is a very hard and interesting problem. We develop a corresponding theory though it is not always enough, and present some challenging problems concerning how classical properties can be extended to the non-commutative case. This paper is arranged for the convenience of readers as the first subsection is based on the standard model (SU(2) system) and the next one is based on the non-standard model (SU(1,1) system). This contrast may make the similarities and differences between the standard and non-standard models clearer.

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47

Angelova, I. Tr. "HIGH-ORDER DIFFERENCE SCHEMES FOR CONVECTION‐DIFFUSION INTERFACE PROBLEMS." Mathematical Modelling and Analysis 10, no. 4 (December 31, 2005): 319–34. http://dx.doi.org/10.3846/13926292.2005.9637290.

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On non‐uniform mesh new high‐order compact finite difference approximations of the solution and the flux to convection‐diffusion interface problems in one‐dimension are constructed and analyzed. Explicit formulas based on new Marchuk integral identities that give O(h2), O(h4), . . . accuracy are derived. New numerical integration quadrature procedures for computing three‐point schemes of any prescribed order of accuracy are developed. Numerical experiments confirm the theoretical results. Straipsnyje sukonstruotos ir analizuojamos naujos aukštos eiles kompaktines baigtiniu skirtumu schemos, aproksimuojančios konvekcijos‐difuzijos saveikos uždavinius vienmačiu atveju. Gautos išreikštines O(h 2), O(h4), … eiles tikslumo formules, pagristos Marchuko integralinemis tapatybemis. Išvestos naujos skaitmeninio integravimo kvadratūrines nurodyto tikslumo formules tritaškiu schemu skaičiavimui. Pateikti skaitiniai eksperimentai, patvirtinantys teorinius rezultatus.

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48

Britt, Steven, Semyon Tsynkov, and Eli Turkel. "Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media using Compact High Order Schemes." Communications in Computational Physics 9, no. 3 (March 2011): 520–41. http://dx.doi.org/10.4208/cicp.091209.080410s.

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AbstractIn many problems, one wishes to solve the Helmholtz equation with variable coefficients within the Laplacian-like term and use a high order accurate method (e.g., fourth order accurate) to alleviate the points-per-wavelength constraint by reducing the dispersion errors. The variation of coefficients in the equation may be due to an inhomogeneous medium and/or non-Cartesian coordinates. This renders existing fourth order finite difference methods inapplicable. We develop a new compact scheme that is provably fourth order accurate even for these problems. We present numerical results that corroborate the fourth order convergence rate for several model problems.

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49

Aminnuddin, Hazim Fadli, Farzad Ismail, Akmal Nizam Mohamed, and Kamil Abdullah. "The Effect of Grid Skewness on Non-Unified Compact Residual Distribution Methods for Scalar Advection Diffusion Problems." CFD Letters 12, no. 3 (March 25, 2020): 58–65. http://dx.doi.org/10.37934/cfdl.12.3.5865.

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50

Mazеpa, Elеna. "The Approximation Approach to Construction of Solutions of Boundary Value Problems on Non-Compact Rieman-nian Manifolds." Vestnik Volgogradskogo gosudarstvennogo universiteta. Serija 1. Mathematica. Physica, no. 5 (December 2015): 25–35. http://dx.doi.org/10.15688/jvolsu1.2015.5.2.

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