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Journal articles on the topic 'Lambda-matrix'

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1

Leung, A. Y. T. "Lambda matrix flexibility." Journal of Sound and Vibration 148, no. 3 (1991): 521–31. http://dx.doi.org/10.1016/0022-460x(91)90482-y.

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2

Dzhaliuk, N. S., and V. M. Petrychkovych. "The structure of solutions of the matrix linear unilateral polynomial equation with two variables." Carpathian Mathematical Publications 9, no. 1 (2017): 48–56. http://dx.doi.org/10.15330/cmp.9.1.48-56.

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We investigate the structure of solutions of the matrix linear polynomial equation $A(\lambda)X(\lambda)+B(\lambda)Y(\lambda)=C(\lambda),$ in particular, possible degrees of the solutions. The solving of this equation is reduced to the solving of the equivalent matrix polynomial equation with matrix coefficients in triangular forms with invariant factors on the main diagonals, to which the matrices $A (\lambda), B(\lambda)$ \ and \ $C(\lambda)$ are reduced by means of semiscalar equivalent transformations. On the basis of it, we have pointed out the bounds of the degrees of the matrix polynomi
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3

Srivastava, J. K., and B. K. Srivastava. "Matrix transformations involving certain Banach space valued sequence spaces." Tamkang Journal of Mathematics 31, no. 2 (2000): 85–100. http://dx.doi.org/10.5556/j.tkjm.31.2000.400.

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In this paper for Banach spaces $X$ and $Y$ we characterize matrix classes $ (\Gamma (X,\lambda)$, $ l_\infty(Y,\mu))$, $ (\Gamma(X,\lambda),C(Y,\mu))$, $ (\Gamma(X,\lambda)$, $ c_0(Y,\mu))$, $ (\Gamma(X,\lambda)$, $ \Gamma^*(Y,\mu))$, $ (l_1(X,\lambda)$, $ \Gamma(Y,\mu))$ and $ (c_0(X,\lambda)$, $ c_0(Y,\mu))$ of bounded linear operators involving $ X$- and $ Y$-valued sequence spaces. Further as an application of the matrix class $ (c_0(X,\lambda)$, $ c_0(Y,\mu))$ we investigate the Banach space $ B(c_0(X,\lambda)$, $ c_0(Y,\mu))$ of all bounded linear mappings of $ c_0(x,\lambda)$ to $ c_0(
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4

Lopez-Rodriguez, Pedro. "The Nevanlinna parametrization for a matrix moment problem." MATHEMATICA SCANDINAVICA 89, no. 2 (2001): 245. http://dx.doi.org/10.7146/math.scand.a-14340.

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We obtain the Nevanlinna parametrization for an indeterminate matrix moment problem, giving a homeomorphism between the set $V$ of solutions to the matrix moment problem and the set $\mathcal V$ of analytic matrix functions in the upper half plane such that $V(\lambda )^*V(\lambda )\le I$. We characterize the N-extremal matrices of measures (those for which the space of matrix polynomials is dense in their $L^2$-space) as those whose corresponding matrix function $V(\lambda )$ is a constant unitary matrix.
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5

Ahmad, Sk, and Rafikul Alam. "On Wilkinson's problem for matrix pencils." Electronic Journal of Linear Algebra 30 (February 8, 2015): 632–48. http://dx.doi.org/10.13001/1081-3810.3145.

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Suppose that an n-by-n regular matrix pencil A -\lambda B has n distinct eigenvalues. Then determining a defective pencil E−\lambda F which is nearest to A−\lambda B is widely known as Wilkinson’s problem. It is shown that the pencil E −\lambda F can be constructed from eigenvalues and eigenvectors of A −\lambda B when A − \lambda B is unitarily equivalent to a diagonal pencil. Further, in such a case, it is proved that the distance from A −\lambda B to E − \lambdaF is the minimum “gap” between the eigenvalues of A − \lambdaB. As a consequence, lower and upper bounds for
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6

Chu, Moody T., T. Y. Li, and Tim Sauer. "Homotopy Method for General $\lambda $-Matrix Problems." SIAM Journal on Matrix Analysis and Applications 9, no. 4 (1988): 528–36. http://dx.doi.org/10.1137/0609043.

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7

Rokne, J. "Including iterations for the lambda-matrix eigenproblem." Computing 35, no. 2 (1985): 207–18. http://dx.doi.org/10.1007/bf02260506.

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8

Julio, Ana, and Ricardo Soto. "The role of certain Brauer and Rado results in the nonnegative inverse spectral problems." Electronic Journal of Linear Algebra 36, no. 36 (2020): 484–502. http://dx.doi.org/10.13001/ela.2020.4935.

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It is said that a list $\Lambda =\{\lambda _{1},\ldots ,\lambda _{n}\}$ of complex numbers is realizable, if it is the spectrum of a nonnegative matrix $A$. It is said that $\Lambda $ is universally realizable if it is realizable for each possible Jordan canonical form allowed by $\Lambda$. This work does not contain new results. As its title says, its goal is to show and emphasize the relevance and importance of certain results, by Brauer and Rado, in the study of nonnegative inverse spectral problems. It is shown that virtually all known results, which give sufficient conditions for $\Lambda
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9

Gupta, M., and L. R. Acharya. "Approximation numbers of matrix transformations and inclusion maps." Tamkang Journal of Mathematics 42, no. 2 (2011): 193–203. http://dx.doi.org/10.5556/j.tkjm.42.2011.924.

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In this paper we establish relationships of the approximation numbers of matrix transformations acting between the vector-valued sequence spaces spaces of the type $\lambda(X)$ defined corresponding to a scalar-valued sequence space $\lambda$ and a Banach space $(X,\|.\|)$ as $$\lambda(X)=\{\overline x=\{x_i\}: x_i\in X, \forall~i\in \mathbb{N},~\{\|x_i\|_X\}\in \lambda\};$$ with those of their component operators. This study leads to a characterization of a diagonal operator to be approximable. Further, we compute the approximation numbers of inclusion maps acting between $\ell^p(X)$ spaces f
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10

Kokabifar, E., G. B. Loghmani, and Panayiotis Psarrakos. "On the distance from a weakly normal matrix polynomial to matrix polynomials with a prescribed multiple eigenvalue." Electronic Journal of Linear Algebra 31 (February 5, 2016): 71–86. http://dx.doi.org/10.13001/1081-3810.2921.

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Consider an$n\times n matrix polynomial P(\lambda). An upper bound for a spectral norm distance from P(\lambda) to the set of n \times n matrix polynomials that have a given scalar μ in C as a multiple eigenvalue was obtained by Papathanasiou and Psarrakos (2008). This paper concerns a refinement of this result for the case of weakly normal matrix polynomials. A modified method is developed and its efficiency is verified by two illustrative examples. The proposed methodology can also be applied to general matrix polynomials.
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11

Taylor, Dane, Juan G. Restrepo, and François G. Meyer. "Ensemble-based estimates of eigenvector error for empirical covariance matrices." Information and Inference: A Journal of the IMA 8, no. 2 (2018): 289–312. http://dx.doi.org/10.1093/imaiai/iay010.

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Abstract Covariance matrices are fundamental to the analysis and forecast of economic, physical and biological systems. Although the eigenvalues $\{\lambda _i\}$ and eigenvectors $\{\boldsymbol{u}_i\}$ of a covariance matrix are central to such endeavours, in practice one must inevitably approximate the covariance matrix based on data with finite sample size $n$ to obtain empirical eigenvalues $\{\tilde{\lambda }_i\}$ and eigenvectors $\{\tilde{\boldsymbol{u}}_i\}$, and therefore understanding the error so introduced is of central importance. We analyse eigenvector error $\|\boldsymbol{u}_i -
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12

Batzke, Leonhard. "Sign Characteristics of Regular Hermitian Matrix Pencils under Generic Rank-1 and Rank-2 Perturbations." Electronic Journal of Linear Algebra 30 (February 8, 2015): 760–94. http://dx.doi.org/10.13001/1081-3810.2014.

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The spectral behavior of regular Hermitian matrix pencils is examined under certain structure-preserving rank-1 and rank-2 perturbations. Since Hermitian pencils have signs attached to real (and infinite) blocks in canonical form, it is not only the Jordan structure but also this so-called sign characteristic that needs to be examined under perturbation. The observed effects are as follows: Under a rank-1 or rank-2 perturbation, generically the largest one or two, respectively, Jordan blocks at each eigenvalue lambda are destroyed, and if lambda is an eigenvalue of the perturbation, also one n
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13

Guo-yong, Jiang, and Jin Xing-nan. "On the Calculation of the Matrix Elements in the Hyperspherical Harmonic Method for ${}_{\Lambda\Lambda}^6{\rm He}$ and $_\Lambda^9$." Communications in Theoretical Physics 9, no. 1 (1988): 33–39. http://dx.doi.org/10.1088/0253-6102/9/1/33.

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14

Colombo, V., and P. Ravetto. "Determination of neutron transport equation eigenvalues as lambda-matrix latent roots / Bestimmung der Eigenwerte der Neutronentransportgleichung als latente Wurzeln einer Lambda-Matrix." Kerntechnik 54, no. 1 (1989): 38–43. http://dx.doi.org/10.1515/kern-1989-540114.

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15

Soto, Ricardo, Elvis Valero, Mario Salas, and Hans Nina. "Nonnegative generalized doubly stochastic matrices with prescribed elementary divisors." Electronic Journal of Linear Algebra 30 (February 8, 2015): 704–20. http://dx.doi.org/10.13001/1081-3810.3168.

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This paper provides sufficient conditions for the existence of nonnegative generalized doubly stochastic matrices with prescribed elementary divisors. These results improve previous results and the constructive nature of their proofs allows for the computation of a solution matrix. In particular, this paper shows how to transform a generalized stochastic matrix into a nonnegative generalized doubly stochastic matrix, at the expense of increasing the Perron eigenvalue, but keeping other elementary divisors unchanged. Under certain restrictions, nonnegative generalized doubly stochastic matrices
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16

BRUNO DE MALAFOSSE, BRUNO DE MALAFOSSE, and EBERHARD MALKOWSKY. "On the Banach algebra (w_{\infty}(\Lambda),w_{\infty}(\Lambda)) and applications to the solvability of matrix equations in w_{\infty}(\Lambda)." Publicationes Mathematicae Debrecen 85, no. 1-2 (2014): 197. http://dx.doi.org/10.5486/pmd.2014.5915.

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17

Karaman, Özkan. "Spectral Properties of Nonhomogenous Differential Equations with Spectral Parameter in the Boundary Condition." Analele Universitatii "Ovidius" Constanta - Seria Matematica 22, no. 2 (2014): 109–20. http://dx.doi.org/10.2478/auom-2014-0036.

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AbstractIn this paper, using the boundary properties of the analytic functions we investigate the structure of the discrete spectrum of the boundary value problem (0.1)$$\matrix{\hfill {iy_1^\prime + q_1 \left(x \right)y_2 - \lambda y_1 = \varphi _1 \left(x \right)\;\;} & \hfill {} \cr \hfill {- iy_2^\prime + q_2 \left(x \right)y_1 - \lambda y_2 = \varphi _2 \left(x \right),} & \hfill {x \in R_ + } \cr }$$ and the condition (0.2)$$\left({a_1 \lambda + b_1 } \right)y_2 \left({0,\lambda } \right) - \left({a_2 \lambda + b_2 } \right)y_1 \left({0,\lambda } \right) = 0$$ where q1,q2, φ1, φ2
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18

Soto, Ricardo, Ana Julio, and Macarena Collao. "Brauer's theorem and nonnegative matrices with prescribed diagonal entries." Electronic Journal of Linear Algebra 35 (February 1, 2019): 53–64. http://dx.doi.org/10.13001/1081-3810.3886.

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The problem of the existence and construction of nonnegative matrices with prescribed eigenvalues and diagonal entries is an important inverse problem, interesting by itself, but also necessary to apply a perturbation result, which has played an important role in the study of certain nonnegative inverse spectral problems. A number of partial results about the problem have been published by several authors, mainly by H. \v{S}migoc. In this paper, the relevance of a Brauer's result, and its implication for the nonnegative inverse eigenvalue problem with prescribed diagonal entries is emphasized.
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19

HONG, SHAOFANG, and K. S. ENOCH LEE. "ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF RECIPROCAL POWER LCM MATRICES." Glasgow Mathematical Journal 50, no. 1 (2008): 163–74. http://dx.doi.org/10.1017/s0017089507003953.

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AbstractLet$\{x_i\}_{i=1}^{\infty}$be an arbitrary strictly increasing infinite sequence of positive integers. For an integern≥1, let$S_n=\{x_1, {\ldots}\, x_n\}$. Letr>0 be a real number andq≥ 1 a given integer. Let$\lambda _n^{(1)}\, {\le}\, {\ldots}\, {\le}\, \lambda _n^{(n)}$be the eigenvalues of the reciprocal power LCM matrix$(\frac{1}{[x_i, x_j]^r})$having the reciprocal power${1\over {[x_i, x_j]^r}}$of the least common multiple ofxiandxjas itsi,j-entry. We show that the sequence$\{\lambda _n^{(q)}\}_{n=q}^{\infty}$converges and${\rm lim}_{n\, {\rightarrow}\, \infty}\lambda _n^{(q)}=
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20

Bueno, M. I., Madeline Martin, Javier Perez, Alexander Song, and Irina Viviano. "Explicit Block-Structures for Block-Symmetric Fiedler-like pencils." Electronic Journal of Linear Algebra 34 (February 21, 2018): 472–99. http://dx.doi.org/10.13001/1081-3810.3667.

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In the last decade, there has been a continued effort to produce families of strong linearizations of a matrix polynomial $P(\lambda)$, regular and singular, with good properties, such as, being companion forms, allowing the recovery of eigenvectors of a regular $P(\lambda)$ in an easy way, allowing the computation of the minimal indices of a singular $P(\lambda)$ in an easy way, etc. As a consequence of this research, families such as the family of Fiedler pencils, the family of generalized Fiedler pencils (GFP), the family of Fiedler pencils with repetition, and the family of generalized Fie
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21

El Khalil, Abdelouahed. "A bifurcation result involving Sobolev trace embedding and the duality mapping of W1,p." Moroccan Journal of Pure and Applied Analysis 3, no. 2 (2017): 186–98. http://dx.doi.org/10.1515/mjpaa-2017-0015.

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AbstractWe consider the perturbed nonlinear boundary condition problem$$\left\{ {\matrix{ { - \Delta _p u} \hfill & = \hfill & {\left| u \right|^{p - 2} u + f\left( {\lambda ,x,u} \right)\,{\rm{in}}\,\Omega } \hfill \cr {\left| {\nabla u} \right|^{p - 2} \nabla u.\nu } \hfill & = \hfill & {\lambda \rho \left( x \right)\left| u \right|^{p - 2} u\,{\rm{on}}\,\Gamma .} \hfill \cr } } \right.$$Using the Sobolev trace embedding and the duality mapping defined on W1,p(Ω), we prove that this problem bifurcates from the principal eigenvalue λ1 of the eigenvalue problem$$\left\{ {\matri
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22

Bueno Cachadina, Maria Isabel, Javier Perez, Anthony Akshar, Daria Mileeva, and Remy Kassem. "Linearizations for Interpolatory Bases - a Comparison: New Families of Linearizations." Electronic Journal of Linear Algebra 36, no. 36 (2020): 799–833. http://dx.doi.org/10.13001/ela.2020.5183.

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One strategy to solve a nonlinear eigenvalue problem $T(\lambda)x=0$ is to solve a polynomial eigenvalue problem (PEP) $P(\lambda)x=0$ that approximates the original problem through interpolation. Then, this PEP is usually solved by linearization. Because of the polynomial approximation techniques, in this context, $P(\lambda)$ is expressed in a non-monomial basis. The bases used with most frequency are the Chebyshev basis, the Newton basis and the Lagrange basis. Although, there exist already a number of linearizations available in the literature for matrix polynomials expressed in these base
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23

Lancaster, Peter, and Ion Zaballa. "Spectral theory for self-adjoint quadratic eigenvalue problems - a review." Electronic Journal of Linear Algebra 37 (March 19, 2021): 211–46. http://dx.doi.org/10.13001/ela.2021.5361.

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Many physical problems require the spectral analysis of quadratic matrix polynomials $M\lambda^2+D\lambda +K$, $\lambda \in \mathbb{C}$, with $n \times n$ Hermitian matrix coefficients, $M,\;D,\;K$. In this largely expository paper, we present and discuss canonical forms for these polynomials under the action of both congruence and similarity transformations of a linearization and also $\lambda$-dependent unitary similarity transformations of the polynomial itself. Canonical structures for these processes are clarified, with no restrictions on eigenvalue multiplicities. Thus, we bring together
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24

Afkhami, Mojgan, Mehdi Hassankhani, and Kazem Khashyarmanesh. "Distance between the spectra of graphs with respect to normalized Laplacian spectra." Georgian Mathematical Journal 26, no. 2 (2019): 227–34. http://dx.doi.org/10.1515/gmj-2017-0051.

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Abstract Let {G_{n}} and {G_{n}^{\prime}} be two nonisomorphic graphs on n vertices with spectra (with respect to the adjacency matrix) \lambda_{1}\geq\lambda_{2}\geq\cdots\geq\lambda_{n}\quad\text{and}\quad\lambda% ^{\prime}_{1}\geq\lambda^{\prime}_{2}\geq\cdots\geq\lambda^{\prime}_{n}, respectively. Define the distance between the spectra of {G_{n}} and {G_{n}^{\prime}} as \lambda(G_{n},G^{\prime}_{n})=\sum_{i=1}^{n}(\lambda_{i}-\lambda^{\prime}_{i})% ^{2}\quad\biggl{(}\text{or use }\sum_{i=1}^{n}\lvert\lambda_{i}-\lambda^{% \prime}_{i}\rvert\biggr{)}. Define the cospectrality of {G_{n}} by
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25

Zhang, Qiu Zhao, Shu Bi Zhang, and Wan Li Liu. "A New Approach for GNSS Ambiguity Decorrelation." Advanced Materials Research 403-408 (November 2011): 1968–71. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.1968.

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Integer carrier phase ambiguity resolution is the key to fast and high-precision Global navigation satellite system(GNSS) positioning and application. LAMBDA method is one of the best methods for fixing integer ambiguity. The principle of LAMBDA is discussed. For incompleteness of Cholesky decomposition and complexity of Integer Gauss transformation, a new approach for GNSS ambiguity decorrelation is proposed based on symmetric pivoting strategy and united inverse integer strategy. The new algorithm applies symmetric pivoting strategy to ambiguity covariance matrix while doing Cholesky decompo
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26

Toyonaga, Kenji, and Charles Johnson. "Application of an identity for subtrees with a given eigenvalue." Electronic Journal of Linear Algebra 30 (February 8, 2015): 964–73. http://dx.doi.org/10.13001/1081-3810.3215.

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For an Hermitian matrix whose graph is a tree and for a given eigenvalue having Parter vertices, the possibilities for the multiplicity are considered. If V = {v_1, . . . , v_k} is a fragmenting Parter set in a tree relative to the eigenvalue , and T_{i+1} is the component of T−{v_1, v_2, . . . , v_i} in which v_{i+1} lies, it is shown that \sum_{i}^K N_i=m_A(\lambda)+2k−1, in which N_i is the number of components of T_i−v_i in which lambda is an eigenvalue. This identity is applied to make several observations, including about when a set of strong Parter vertices leaves only 3 component
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27

Seeger, Alberto. "Cone-constrained rational eigenvalue problems." Electronic Journal of Linear Algebra 35 (February 1, 2019): 187–203. http://dx.doi.org/10.13001/1081-3810.3835.

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This work deals with the eigenvalue analysis of a rational matrix-valued function subject to complementarity constraints induced by a polyhedral cone $K$. The eigenvalue problem under consideration has the general structure \[ \left(\sum_{k=0}^d \lambda^k A_k + \sum_{k =1}^m \frac{p_k(\lambda)}{q_k(\lambda)} \,B_k\right) x = y , \quad K\ni x \perp y\in K^\ast, \] where $K^\ast$ denotes the dual cone of $K$. The unconstrained version of this problem has been discussed in [Y.F. Su and Z.J. Bai. Solving rational eigenvalue problems via linearization. \emph{SIAM J. Matrix Anal. Appl.}, 32:201--216
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28

Santra, Shyam Sundar. "Necessary and Sufficient Conditions for Oscillation of Solutions to Second-Order Neutral Differential Equations with Impulses." Tatra Mountains Mathematical Publications 76, no. 1 (2020): 157–70. http://dx.doi.org/10.2478/tmmp-2020-0025.

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AbstractIn this work, necessary and sufficient conditions for oscillation of solutions of second-order neutral impulsive differential system\left\{ {\matrix{{{{\left( {r\left( t \right){{\left( {z'\left( t \right)} \right)}^\gamma }} \right)}^\prime } + q\left( t \right){x^\alpha }\left( {\sigma \left( t \right)} \right) = 0,} \hfill & {t \ge {t_0},\,\,\,t \ne {\lambda _k},} \hfill \cr {\Delta \left( {r\left( {{\lambda _k}} \right){{\left( {z'\left( {{\lambda _k}} \right)} \right)}^\gamma }} \right) + h\left( {{\lambda _k}} \right){x^\alpha }\left( {\sigma \left( {{\lambda _k}} \right)} \r
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29

Oliva, W. M., and E. M. Sallum. "Periodic dynamic systems for infected hosts and mosquitoes." Revista de Saúde Pública 30, no. 3 (1996): 218–23. http://dx.doi.org/10.1590/s0034-89101996000300003.

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A mathematical model for the purpose of analysing the dynamic of the populations of infected hosts anf infected mosquitoes when the populations of mosquitoes are periodic in time is here presented. By the computation of a parameter lambda (the spectral radius of a certain monodromy matrix) one can state that either the infection peters out naturally) (lambda <= 1) or if lambda > 1 the infection becomes endemic. The model generalizes previous models for malaria by considering the case of periodic coefficients; it is also a variation of that for gonorrhea. The main motivation for the consi
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30

Figueiredo, Giovany M., Marcelo F. Furtado, and João Pablo P. da Silva. "Existence and multiplicity of positive solutions for a fourth-order elliptic equation." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 2 (2019): 1053–69. http://dx.doi.org/10.1017/prm.2018.145.

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AbstractWe prove existence and multiplicity of solutions for the problem$$\left\{ {\matrix{ {\Delta ^2u + \lambda \Delta u = \vert u \vert ^{2*-2u},{\rm in }\Omega ,} \hfill \hfill \hfill \hfill \cr {u,-\Delta u > 0,\quad {\rm in}\;\Omega ,\quad u = \Delta u = 0,\quad {\rm on}\;\partial \Omega ,} \cr } } \right.$$where$\Omega \subset {\open R}^N$,$N \ges 5$, is a bounded regular domain,$\lambda >0$and$2^*=2N/(N-4)$is the critical Sobolev exponent for the embedding of$W^{2,2}(\Omega )$into the Lebesgue spaces.
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31

Naulin, Raul, and Manuel Pinto. "Asymptotic solutions of nondiagonal linear difference systems." Tamkang Journal of Mathematics 31, no. 3 (2000): 175–92. http://dx.doi.org/10.5556/j.tkjm.31.2000.392.

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This paper, relying on dichotomic properties of the matrix difference system $ W(n+1)=A(n)W(n)A^{-1}(n)$, gives conditions under which a perturbed system $ y(n+1)=(A(n)+B(n))y(n)$, by means of a nonautonomous change of variables $ y(n)=S(n)x(n)$, can be reduced to the form $ x(n+1)=A(n)x(n)$. From this, a theory of asymptotic integration of the perturbed system follows, where the linear system $ x(n+1)=A(n)x(n)$ is nondiagonal. As a consequence of these results, we prove that the diagonal system $ x(n+1)=\Lambda(n)x(n)$ has a Levinson dichotomy iff system $ W(n+1)=\Lambda(n)W(n)\Lambda^{-1}(n)
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32

Bişgin, Mustafa, and Abdulcabbar Sönmez. "Two new sequence spaces generated by the composition of mth order generalized difference matrix and lambda matrix." Journal of Inequalities and Applications 2014, no. 1 (2014): 274. http://dx.doi.org/10.1186/1029-242x-2014-274.

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33

Yeşilkayagil, Medine, and Feyzi Başar. "On the Fine Spectrum of the Operator Defined by the Lambda Matrix over the Spaces of Null and Convergent Sequences." Abstract and Applied Analysis 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/687393.

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The main purpose of this paper is to determine the fine spectrum with respect to Goldberg's classification of the operator defined by the lambda matrix over the sequence spaces andc. As a new development, we give the approximate point spectrum, defect spectrum, and compression spectrum of the matrix operator on the sequence spaces andc. Finally, we present a Mercerian theorem. Since the matrix is reduced to a regular matrix depending on the choice of the sequence having certain properties and its spectrum is firstly investigated, our work is new and the results are comprehensive.
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CHEN, BANG-YEN. "SUBMANIFOLDS OF EUCLIDEAN SPACES SATISFYING $\Delta H =AH$." Tamkang Journal of Mathematics 25, no. 1 (1995): 71–81. http://dx.doi.org/10.5556/j.tkjm.25.1994.4427.

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 In [5] the author initiated the study of submanifolds whose mean curvature vector $H$ satisfying the condition $\Delta H =\lambda H$ for some constant $\lambda$ and proved that such submanifolds are either biharmonic or of 1-type or of null 2-type. Submanifolds of hyperbolic spaces and of de Sitter space-times satisfy this condition have been investigated and classified in [6,7]. In this article, we study submanifolds of $E^m$ whose mean curvature vector $H$ satisfies a more general condition; namely, $\Delta H =AH$ for some $m \times m$ matrix $A$. 
 
 
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35

Khan, Sana, Hassan Sajjad, Mehmet Ozdemir, and Ercument Arvas. "Mutual Coupling Compensation in Receiving Arrays and Its Implementation on Software Defined Radios." Applied Computational Electromagnetics Society 35, no. 11 (2021): 1433–34. http://dx.doi.org/10.47037/2020.aces.j.351185.

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Mutual coupling is compensated in a four element uniform linear receiving array using software defined radios. Direction of arrival (DoA) is estimated in real-time for the array with spacing d=lambda/4. The decoupling matrix was measured using a VNA for only one incident angle. After compensation the error in DoA estimation was reduced to 5%. Comparing the DoA results with d=lambda/2 spaced Uniform Linear Array (ULA), 1.2% error was observed. Although, the experiment was performed indoors with a low SNR, the results show a substantial improvement in the estimated DoA after compensation.
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36

Chen, Yanping, and Yong Ding. "Commutators of the fractional integrals for second-order elliptic operators on Morrey spaces." Forum Mathematicum 30, no. 3 (2018): 617–29. http://dx.doi.org/10.1515/forum-2017-0062.

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AbstractLet {L=-\operatorname{div}(A\nabla)} be a second-order divergence form elliptic operator and let A be an accretive, {n\times n} matrix with bounded measurable complex coefficients in {{\mathbb{R}}^{n}}. Let {L^{-\frac{\alpha}{2}}} be the fractional integral associated to L for {0<\alpha<n}. For {b\in L_{\mathrm{loc}}({\mathbb{R}}^{n})} and {k\in{\mathbb{N}}}, the k-th order commutator of b and {L^{-\frac{\alpha}{2}}} is given by(L^{-\frac{\alpha}{2}})_{b,k}f(x)=L^{-\frac{\alpha}{2}}((b(x)-b)^{k}f)(x).In the paper, we mainly show that if {b\in\mathrm{BMO}({\mathbb{R}}^{n})}, {0&lt
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Xu, X., H. He, and D. Hu. "Efficient Reinforcement Learning Using Recursive Least-Squares Methods." Journal of Artificial Intelligence Research 16 (April 1, 2002): 259–92. http://dx.doi.org/10.1613/jair.946.

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The recursive least-squares (RLS) algorithm is one of the most well-known algorithms used in adaptive filtering, system identification and adaptive control. Its popularity is mainly due to its fast convergence speed, which is considered to be optimal in practice. In this paper, RLS methods are used to solve reinforcement learning problems, where two new reinforcement learning algorithms using linear value function approximators are proposed and analyzed. The two algorithms are called RLS-TD(lambda) and Fast-AHC (Fast Adaptive Heuristic Critic), respectively. RLS-TD(lambda) can be viewed as the
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Alves, C. O., G. Ercole, and G. A. Pereira. "Asymptotic behaviour asp→ ∞ of least energy solutions of a (p, q(p))-Laplacian problem." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 6 (2019): 1493–522. http://dx.doi.org/10.1017/prm.2018.111.

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AbstractWe study the asymptotic behaviour, asp→ ∞, of the least energy solutions of the problem$$\left\{ {\matrix{ {-(\Delta _p + \Delta _{q(p)})u = \lambda _p \vert u(x_u) \vert ^{p-2}u(x_u)\delta _{x_u}} & {{\rm in}} & \Omega \cr {u = 0} \hfill \hfill \hfill & {{\rm on}} & {\partial \Omega ,} \cr } } \right.$$wherexuis the (unique) maximum point of |u|,$\delta _{x_{u}}$is the Dirac delta distribution supported atxu,$$\mathop {\lim }\limits_{p\to \infty } \displaystyle{{q(p)} \over p} = Q\in \left\{ {\matrix{ {(0,1)} & {{\rm if}} & {N < q(p) < p} \cr {(1,\infty )
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39

Cellmer, S. "On-the-fly Ambiguity Resolution Using an Estimator of the Modified Ambiguity Covariance Matrix for the GNSS Positioning Model Based on Phase Data." Artificial Satellites 47, no. 3 (2012): 81–90. http://dx.doi.org/10.2478/v10018-012-0015-9.

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On-the-fly Ambiguity Resolution Using an Estimator of the Modified Ambiguity Covariance Matrix for the GNSS Positioning Model Based on Phase Data On-the-fly ambiguity resolution (OTF AR) is based on a small data set, obtained from a very short observation session or even from a single epoch observation. In these cases, a classical approach to ambiguity resolution (e.g. the Lambda method) can meet some numerical problems. The basis of the Lambda method is an integer decorrelation of the positive definite ambiguity covariance matrix (ACM). The necessary condition for the proper performing of thi
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Borot, Gaëtan, and Elba Garcia-Failde. "Simple Maps, Hurwitz Numbers, and Topological Recursion." Communications in Mathematical Physics 380, no. 2 (2020): 581–654. http://dx.doi.org/10.1007/s00220-020-03867-1.

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Abstract We introduce the notion of fully simple maps, which are maps with non self-intersecting disjoint boundaries. In contrast, maps where such a restriction is not imposed are called ordinary. We study in detail the combinatorics of fully simple maps with topology of a disk or a cylinder. We show that the generating series of simple disks is given by the functional inversion of the generating series of ordinary disks. We also obtain an elegant formula for cylinders. These relations reproduce the relation between moments and (higher order) free cumulants established by Collins et al. [22],
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Et-Taoui, Boumediene. "Quaternionic equiangular lines." Advances in Geometry 20, no. 2 (2020): 273–84. http://dx.doi.org/10.1515/advgeom-2019-0021.

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AbstractLet 𝔽 = ℝ, ℂ or ℍ. A p-set of equi-isoclinic n-planes with parameter λ in 𝔽r is a set of pn-planes spanning 𝔽r each pair of which has the same non-zero angle arccos $\begin{array}{} \sqrt{\lambda} \end{array}$. It is known that via a complex matrix representation, a pair of isoclinic n-planes in ℍr with angle arccos $\begin{array}{} \sqrt{\lambda} \end{array}$ yields a pair of isoclinic 2n-planes in ℂ2r with angle arccos $\begin{array}{} \sqrt{\lambda} \end{array}$. In this article we characterize all the p-tuples of equi-isoclinic planes in ℂ2r which come via our complex representatio
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Li, Li, Hongwei Ge, Yixin Zhang, and Jianqiang Gao. "Low-density noise removal based on lambda multi-diagonal matrix filter for binary image." Neural Computing and Applications 29, no. 6 (2016): 173–85. http://dx.doi.org/10.1007/s00521-016-2538-7.

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43

SHARMA, SUSHIL, and S. K. VARMA. "HOLDER CONTINUOUS FUNCTIONS AND THEIR ABEL AND LOGARITHMIC MEANS." Tamkang Journal of Mathematics 30, no. 3 (1999): 167–73. http://dx.doi.org/10.5556/j.tkjm.30.1999.4197.

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 Mahapatra and Chandra [8] have obtained the degree of approximation for $f \in H_\alpha(0\le \beta<\alpha\le 1)$ using infinite matrix $A = (a_{nk})$. Mahapatra and Chandra [7] used Euler, Boral and Taylor means. In the present paper we have obtained the analogous results using Abel ($A_\lambda$) and Logarithmic ($L$)-means. 
 
 
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Treibich, Armando. "Hyperelliptic d-Tangential Covers and d× d-Matrix KdV Elliptic Solitons." International Mathematics Research Notices 2020, no. 23 (2018): 9539–58. http://dx.doi.org/10.1093/imrn/rny264.

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Abstract More than $40$ years ago I. Krichever developed the Theory of (vector) Baker–Akhiezer functions and devised a criterion for a $d$-marked compact Riemann surface to provide $d\times d$-matrix solutions to the KdV equation. Later on he also found a criterion for a $d$-marked curve to provide $d\times d$-matrix solutions to the Kadomtsev-Petviashvili (KP) equation, doubly periodic with respect to $x$, the 1st KP flow. In particular, when both criteria apply, one should obtain $d\times d$-matrix KdV elliptic solitons. It seems, however, that the latter issue has been completely neglected
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Damascelli, Lucio, and Filomena Pacella. "Morse index and symmetry for elliptic problems with nonlinear mixed boundary conditions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 149, no. 2 (2018): 305–24. http://dx.doi.org/10.1017/prm.2018.29.

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AbstractWe consider an elliptic problem of the type $$\left\{ {\matrix{ {-\Delta u = f(x,u)\quad } \hfill & {{\rm in}\,\Omega } \hfill \cr {u = 0} \hfill & {{\rm on}\,\Gamma _1} \hfill \cr {\displaystyle{{\partial u} \over {\partial \nu }} = g(x,u)} \hfill & {{\rm on}\,\Gamma _2} \hfill \cr } } \right.$$ where Ω is a bounded Lipschitz domain in ℝN with a cylindrical symmetry, ν stands for the outer normal and $\partial \Omega = \overline {\Gamma _1} \cup \overline {\Gamma _2} $.Under a Morse index condition, we prove cylindrical symmetry results for solutions of the above problem.A
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46

Acharya, A., N. Fonseka, J. Quiroa та R. Shivaji. "Σ-Shaped Bifurcation Curves". Advances in Nonlinear Analysis 10, № 1 (2021): 1255–66. http://dx.doi.org/10.1515/anona-2020-0180.

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Abstract We study positive solutions to the steady state reaction diffusion equation of the form: − Δ u = λ f ( u ) ; Ω ∂ u ∂ η + λ u = 0 ; ∂ Ω $$\begin{array}{} \displaystyle \left\lbrace \begin{matrix} -{\it\Delta} u =\lambda f(u);~ {\it\Omega} \\ \frac{\partial u}{\partial \eta}+ \sqrt{\lambda} u=0;~\partial {\it\Omega}\end{matrix} \right. \end{array}$$ where λ > 0 is a positive parameter, Ω is a bounded domain in ℝ N when N > 1 (with smooth boundary ∂ Ω) or Ω = (0, 1), and ∂ u ∂ η $\begin{array}{} \displaystyle \frac{\partial u}{\partial \eta} \end{array}$ is the outward normal deriv
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47

Parks, Robin J., Jonathan L. Bramson, Yonghong Wan, Christina L. Addison, and Frank L. Graham. "Effects of Stuffer DNA on Transgene Expression from Helper-Dependent Adenovirus Vectors." Journal of Virology 73, no. 10 (1999): 8027–34. http://dx.doi.org/10.1128/jvi.73.10.8027-8034.1999.

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ABSTRACT We have analyzed transgene (lacZ) expression from a first-generation adenovirus (Ad) vector in comparison to helper-dependent (hd) Ads deleted for various portions of the viral coding sequences and generated by using the Cre/loxP helper-dependent system (R. J. Parks et al., Proc. Natl. Acad. Sci. USA 93:13565–13570, 1996). An hd vector deleted for approximately 70% of the Ad genome (AdRP1001) provided levels and durations of transgene expression similar to those of a control first generation Ad vector containing an identical expression cassette. Deletion of all Ad sequences from the h
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48

Hu, Bei-bei, Tie-cheng Xia, Ning Zhang, and Jin-bo Wang. "Initial-Boundary Value Problems for the Coupled Higher-Order Nonlinear Schrödinger Equations on the Half-line." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 1 (2018): 83–92. http://dx.doi.org/10.1515/ijnsns-2017-0080.

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AbstractIn this article, we use the unified transform method to analyze the initial-boundary value problem for the coupled higher-order nonlinear Schrödinger equations on the half-line. Suppose that the solution $\{q_1(x,t),q_2(x,t)\}$ exists, we show that it can be expressed in terms of the unique solution of a matrix Riemann–Hilbert problem formulated in the plane of the complex spectral parameter $\lambda$.
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49

Feyzi, BAŞAR. "Survey on the domain of the matrix lambda in the normed and paranormed sequence spaces." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 62, no. 1 (2013): 45–59. http://dx.doi.org/10.1501/commua1_0000000685.

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50

Chen, Xiaokun. "Programming for solving plane rigid frame based on MATLAB." MATEC Web of Conferences 319 (2020): 09003. http://dx.doi.org/10.1051/matecconf/202031909003.

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Based on the idea of the matrix displacement method, this paper designs a program which can be used to solve the internal force of the continuous beam and rigid frame with MATLAB. It mainly demonstrates how to design a program to realize the matrix displacement method with MATLAB. In addition, some techniques are included in order to realize the correspondence between the manual calculation and the computer calculation, such as “Using lambda to locate”, “Crossing out rows and columns” and visual design. Therefore, based on the structural mechanics, combined with the principle of matrix displac
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