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Journal articles on the topic 'Sturm sequence'

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Published: 4 June 2021

Last updated: 25 April 2022

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1

Jo, Ji-Seong, Man-Gi Ko, Sang-Won Cho, and In-Won Lee. "Modified Sturm Sequence Property for Damped Systems." Journal of Engineering Mechanics 132, no. 7 (July 2006): 785–89. http://dx.doi.org/10.1061/(asce)0733-9399(2006)132:7(785).

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2

Evans, D. J. "Sturm sequence analysis of a diagonally bordered matrix." International Journal of Computer Mathematics 51, no. 1-2 (January 1994): 69–79. http://dx.doi.org/10.1080/00207169408804267.

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3

Fu, Hongguang, Lu Yang, and Zhenbing Zeng. "A recursive algorithm for constructing generalized Sturm sequence." Science in China Series E: Technological Sciences 43, no. 1 (December 2000): 32–41. http://dx.doi.org/10.1007/bf02917135.

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4

Cheng, Y. H., and C. K. Law. "On the quasi-nodal map for the Sturm–Liouville problem." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 136, no. 1 (February 2006): 71–86. http://dx.doi.org/10.1017/s0308210500004443.

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We show that the space of Sturm–Liouville operators characterized by H = (q, α, β) ∈ L1 (0, 1) × [0, π)2 such that is homeomorphic to the partition set of the space of all admissible sequences which form sequences that converge to q, α, and β individually. This space, Γ, of quasi-nodal sequences is a superset of, and is more natural than, the space of asymptotically nodal sequences defined in Law and Tsay (On the well-posedness of the inverse nodal problem. Inv. Probl.17 (2001), 1493–1512). The definition of Γ relies on the L1 convergence of the reconstruction formula for q by the exactly nodal sequence.

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5

Açil, M., and N. Bildik. "A SOLUTION TO INVERSE STURM-LIOUVILLE PROBLEMS." Advances in Mathematics: Scientific Journal 10, no. 9 (September 8, 2021): 3165–74. http://dx.doi.org/10.37418/amsj.10.9.6.

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In this study, we recover potential function and separable boundary conditions for the inverse Sturm-Liouville problem in normal form by using two partial subsets of the data which consist of its one spectrum and sequence of endpoints of eigenfunctions.

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6

Bunse-Gerstner, Angelika, and Chunyang He. "On a Sturm Sequence of Polynomials for Unitary Hessenberg Matrices." SIAM Journal on Matrix Analysis and Applications 16, no. 4 (October 1995): 1043–55. http://dx.doi.org/10.1137/s089547989223050x.

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7

Kashiwagi, Mitsuhiro, Itio Hirai, Takurou Katayama, and Walter D. Pilkey. "Sturm sequence recurrence formula for eigensolution of locally modified systems." Finite Elements in Analysis and Design 13, no. 1 (April 1993): 31–36. http://dx.doi.org/10.1016/0168-874x(93)90004-a.

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8

Shorter, Philip J. "On the use of the Sturm sequence to evaluate modal density." Journal of the Acoustical Society of America 108, no. 5 (November 2000): 2557. http://dx.doi.org/10.1121/1.4743493.

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9

Migda, Janusz, Magdalena Nockowska-Rosiak, and Małgorzata Migda. "Properties of Solutions of Generalized Sturm–Liouville Discrete Equations." Bulletin of the Malaysian Mathematical Sciences Society 44, no. 5 (March 19, 2021): 3111–27. http://dx.doi.org/10.1007/s40840-021-01105-y.

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AbstractWe consider discrete Sturm–Liouville-type equations of the form $$\begin{aligned} \varDelta (r_n\varDelta x_n)=a_nf(x_{\sigma (n)})+b_n. \end{aligned}$$ Δ ( r n Δ x n ) = a n f ( x σ ( n ) ) + b n . We present a theory of asymptotic properties of solutions which allows us to control the degree of approximation. Namely, we establish conditions under which for a given sequence y which solves the equation $$\varDelta (r_n\varDelta y_n)=b_n$$ Δ ( r n Δ y n ) = b n , the above equation possesses a solution x with the property $$x_n=y_n+\mathrm {o}(u_n)$$ x n = y n + o ( u n ) , where u is a given positive, nonincreasing sequence. The obtained results are applied to the study of asymptotically periodic solutions. Moreover, these results also allow us to obtain some nonoscillation criteria for the classical Sturm–Liouville equation.

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10

Chigansky, Pavel, and Marina Kleptsyna. "Sharp asymptotics in a fractional Sturm-Liouville problem." Fractional Calculus and Applied Analysis 24, no. 3 (June 1, 2021): 715–38. http://dx.doi.org/10.1515/fca-2021-0031.

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Abstract The current research of fractional Sturm-Liouville boundary value problems focuses on the qualitative theory and numerical methods, and much progress has been recently achieved in both directions. The objective of this paper is to explore a different route, namely, construction of explicit asymptotic approximations for the solutions. As a study case, we consider a problem with left and right Riemann-Liouville derivatives, for which our analysis yields asymptotically sharp estimates for the sequence of eigenvalues and eigenfunctions.

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11

Kashiwagi, Mitsuhiro, Itio Hirai, Shin-ichi Ohwaki, and Walter D. Pilkey. "Stable eigensolution of locally modified systems based on the Sturm sequence property." Finite Elements in Analysis and Design 9, no. 2 (June 1991): 133–39. http://dx.doi.org/10.1016/0168-874x(91)90056-5.

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12

WANG, HUI. "A SINGULAR STURM–LIOUVILLE EQUATION INVOLVING MEASURE DATA." Communications in Contemporary Mathematics 15, no. 04 (June 17, 2013): 1250047. http://dx.doi.org/10.1142/s0219199712500472.

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Let α > 0 and let μ be a bounded Radon measure on the interval (-1, 1). We are interested in the equation -(|x|2αu′)′ + u = μ on (-1, 1) with boundary condition u(-1) = u(1) = 0. We identify an appropriate concept of solution for this equation, and we establish some existence and uniqueness results. The cases 0 < α < 1 and α ≥ 1 must be considered separately. We also study the limiting behavior of two different approximation schemes: one is the elliptic regularization and the other is to approximate a measure μ by a sequence of L∞-functions.

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13

Tian, Yu, and Juan J. Nieto. "The Applications of Critical-Point Theory to Discontinuous Fractional-Order Differential Equations." Proceedings of the Edinburgh Mathematical Society 60, no. 4 (March 16, 2017): 1021–51. http://dx.doi.org/10.1017/s001309151600050x.

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AbstractWe consider a fractional equation involving the left and right Riemann–Liouville fractional integrals and with Sturm–Liouville boundary-value conditions. We establish the variational structure of the problem and, by using critical-point theory, the existence of an unbounded sequence of solutions is obtained.

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14

Drignei, Mihaela-Cristina, and Erin Leigh Fagan. "Numerical Reconstruction of Potentials Based on a Sequence of Inverse Sturm–Liouville Problems." International Journal of Computational Methods 14, no. 04 (April 18, 2017): 1750043. http://dx.doi.org/10.1142/s0219876217500438.

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Numerical solutions to inverse Sturm–Liouville problems by three spectra, on a finite interval [Formula: see text] are considered. Dirichlet boundary conditions are assumed to hold at the end-points of the interval [Formula: see text], and either a Dirichlet or a Robin-type interior point condition is imposed at an arbitrary interior point [Formula: see text] of [Formula: see text]. We demonstrate that the numerical solution of the inverse three spectra problem corresponding to an interior point [Formula: see text] depends continuously on [Formula: see text]. This statement is particularly useful when measurements of the input data cannot be obtained at the interior point [Formula: see text], but they can be obtained at a nearby interior point. Consequently, we could solve approximately the original inverse problem by departing slightly from [Formula: see text]. We validate this statement through numerical experiments for sequences of interior points [Formula: see text] converging to [Formula: see text].

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15

Pikula, Milenko, Vladimir Vladicic, and Olivera Markovic. "A solution to the inverse problem for the Sturm-Liouville-type equation with a delay." Filomat 27, no. 7 (2013): 1237–45. http://dx.doi.org/10.2298/fil1307237p.

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The paper is devoted to study of the inverse problem of the boundary spectral assignment of the Sturm-Liouville with a delay. -y'(x) + q(x)y(? ? x) = ?y(x), q ? AS[0, ?], ? ? (0,1] (1) with separated boundary conditions: y(0) = y(?) = 0 (2) y(0) = y'(?) = 0 (3) It is argued that if the sequence of eigenvalues is given ?n(1) and ?n(2) tasks (1-2) and (1-3) respectively, then the delay factor ? ? (0,1) and the potential q ? AS[0, ?] are unambiguous. The potential q is composed by means of trigonometric Fourier coefficients. The method can be easily transferred to the case of ? = 1 i.e. to the classical Sturm-Liouville problem.

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16

Behrndt, Jussi, Seppo Hassi, Henk de Snoo, and Rudi Wietsma. "Monotone convergence theorems for semi-bounded operators and forms with applications." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140, no. 5 (October 2010): 927–51. http://dx.doi.org/10.1017/s030821050900078x.

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AbstractLet Hn be a monotone sequence of non-negative self-adjoint operators or relations in a Hilbert space. Then there exists a self-adjoint relation H∞ such that Hn converges to H∞ in the strong resolvent sense. This result and related limit results are explored in detail and new simple proofs are presented. The corresponding statements for monotone sequences of semi-bounded closed forms are established as immediate consequences. Applications and examples, illustrating the general results, include sequences of multiplication operators, Sturm–Liouville operators with increasing potentials, forms associated with Kreĭn–Feller differential operators, singular perturbations of non-negative self-adjoint operators and the characterization of the Friedrichs and Kreĭn–von Neumann extensions of a non-negative operator or relation.

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17

Akhtyamov, A. M., and Kh R. Mamedov. "Uniqueness theorem for Inverse Sturm–Liouville Problem with Nonseparated Boundary Conditions." Proceedings of the Mavlyutov Institute of Mechanics 11, no. 2 (2016): 167–70. http://dx.doi.org/10.21662/uim2016.2.024.

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Consider the string, which vibrates in a medium with the variable elasticity coefficient q(x). Interesting to follow the inverse problem: is it possible to determine the variable elasticity coefficient q(x) by the natural frequencies of string vibrations. In 1946, G. Borg has been shown that a spectrum of frequencies is not sufficient to uniquely identify the medium elasticity coefficient q(x). He offered the use of two frequency spectrum to uniquely identify of the medium elasticity coefficient q(x). The second frequency spectrum is obtained by fastening the string to change at one of its ends to the other fastening. It was shown that these two frequency spectra already sufficient to uniquely identify q(x) and the boundary conditions of both problems. The case where the string fastening at one end depends on the other end fastening, is more difficult to solve. The boundary conditions, appropriate for the occasion, called nonseparated. Two spectra (of two boundary value problems) to restore both q(x), and the nonseparated boundary conditions are not enough. In modern studies the spectra of the two eigenvalues boundary problems and an infinite sequence of signs is generally used for an uniqueness recovery. While this approach is useful in theoretical mathematics, it is inconvenient for the mechanics, because not clear the physical meaning of the corresponding sequence of signs. In this article, instead of the two spectra and the sequence of signs as the spectral data are offered to use 7 of the eigenvalues of the initial boundary value problem, the spectrum, and the so-called norming constants of other boundary value problem. The physical sense of these data is quite clear. The first 7 eigenvalues of an initial boundary problem mean the first 7 natural frequencies of string vibrations. Norming constants represent norms from eigenfunctions. The spectrum and norming constants express a so-called spectral function. The spectral function gives a frequency spectrum with columns of vibrations amplitudes characteristics for string vibrations with other types of fastening.

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18

Muratbekov, M. B., and M. M. Muratbekov. "Smoothness and approximative properties of solutions of the singular nonlinear Sturm-Liouville equation." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 100, no. 4 (December 30, 2020): 113–24. http://dx.doi.org/10.31489/2020m4/113-124.

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It is known that the eigenvalues λn(n = 1, 2, ...) numbered in decreasing order and taking the multiplicity of the self-adjoint Sturm-Liouville operator with a completely continuous inverse operator L^{−1} have the following property (*) λn → 0, when n → ∞, moreover, than the faster convergence to zero so the operator L^{−1} is best approximated by finite rank operators. The following question: - Is it possible for a given nonlinear operator to indicate a decreasing numerical sequence characterized by the property (*)? naturally arises for nonlinear operators. In this paper, we study the above question for the nonlinear Sturm-Liouville operator. To solve the above problem the theorem on the maximum regularity of the solutions of the nonlinear Sturm-Liouville equation with greatly growing and rapidly oscillating potential in the space L2(R) (R = (−∞, ∞)) is proved. Twosided estimates of the Kolmogorov widths of the sets associated with solutions of the nonlinear SturmLiouville equation are also obtained. As is known, the obtained estimates of Kolmogorov widths give the opportunity to choose approximation apparatus that guarantees the minimum possible error.

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19

Ramadan, T. A. "Sturm-Sequence Properties of Recurrence Dispersion Functions of Periodic Waveguide Arrays: Theory and Applications." Journal of Lightwave Technology 27, no. 20 (October 2009): 4548–62. http://dx.doi.org/10.1109/jlt.2009.2024962.

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20

Liu, Xiaoyun. "On Inverse Nodal Problem and Multiplicities of Eigenvalues of a Vectorial Sturm-Liouville Problem." Journal of Function Spaces 2020 (July 2, 2020): 1–6. http://dx.doi.org/10.1155/2020/6953602.

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An m-dimensional vectorial inverse nodal Sturm-Liouville problem with eigenparameter-dependent boundary conditions is studied. We show that if there exists an infinite sequence ynj,rx,λnj,r2j=1∞ of eigenfunctions which are all vectorial functions of type (CZ), then the potential matrix Qx and A are simultaneously diagonalizable by the same unitary matrix U. Subsequently, some multiplicity results of eigenvalues are obtained.

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21

Ferreira, Milton, M. Manuela Rodrigues, and Nelson Vieira. "A fractional analysis in higher dimensions for the Sturm-Liouville problem." Fractional Calculus and Applied Analysis 24, no. 2 (April 1, 2021): 585–620. http://dx.doi.org/10.1515/fca-2021-0026.

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Abstract In this work, we consider the n-dimensional fractional Sturm-Liouville eigenvalue problem, by using fractional versions of the gradient operator involving left and right Riemann-Liouville fractional derivatives. We study the main properties of the eigenfunctions and the eigenvalues of the associated fractional boundary problem. More precisely, we show that the eigenfunctions are orthogonal and the eigenvalues are real and simple. Moreover, using techniques from fractional variational calculus, we prove in the main result that the eigenvalues are separated and form an infinite sequence, where the eigenvalues can be ordered according to increasing magnitude. Finally, a connection with Clifford analysis is established.

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22

Malyutin, V. B. "Approximate evaluation of functional integrals with centrifugal potential." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 55, no. 2 (June 28, 2019): 152–57. http://dx.doi.org/10.29235/1561-2430-2019-55-2-152-157.

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Approximate evaluation of functional integrals containing a centrifugal potential is considered. By a centrifugal potential is understood a potential arising from a centrifugal force. A combination of the method based on expanding into a series of the eigenfunctions of a Hamiltonian generating a functional integral and the Sturm sequence method for the eigenvalue problem is used for approximate evaluation of functional integrals. This combination allows one to significantly reduce a computation time and a used computer memory volume in comparison to other known methods.

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23

CEDERBAUM, I. "SPECTRAL PROPERTIES OF ADMITTANCE MATRICES OF RESISTIVE TREE NETWORKS." Journal of Circuits, Systems and Computers 04, no. 01 (March 1994): 53–70. http://dx.doi.org/10.1142/s0218126694000041.

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In this paper spectral properties of the admittance matrix of a resistive network whose underlying graph forms a general tree are studied. The algebraic presentation of the network is provided by its real node admittance matrix with respect to one of its terminal vertices, considered to be the root of the tree. The spectral properties of this matrix are studied by application of the theory of two-element-kind (R, C) networks. A mechanical analogue of a particular case of a similar problem, corresponding to a linear tree has been studied in the classical work of Gantmacher and Krein.7 Generalization of the study to networks based on trees of arbitrary structure calls for a modification of the mathematical approach. Instead of polynomial Sturm sequences applied in Ref. 7 the paper applies sequences of rational functions obeying the two basic Sturm conditions. In the special case of a linear tree these rational functions turn out to be polynomials, and the results are equivalent to those in Ref. 7. For a general tree the paper takes into consideration any root—leaf path of the tree. It is shown that the conditions on such a path are similar to those taking place on a linear tree. Some difference occurs in the number of sign reversals in the sequence of coordinates of characteristic vectors. In the case of a linear tree this number depends only on the position of the corresponding characteristic frequency in the spectrum of the matrix. In the case of a root-leaf path of a general tree, this number has to be normally decreased. The correction (which might be zero) is equal to the number of poles of the determinant of the reduced admittance matrix corresponding to the path considered, which does not exceed the characteristic frequency.

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24

Ayryan, E. A., M. Hnatic, and V. B. Malyutin. "Approximate evaluation of functional integrals generated by the relativistic Hamiltonian." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 56, no. 1 (April 6, 2020): 72–83. http://dx.doi.org/10.29235/1561-2430-2020-56-1-72-83.

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An approximate evaluation of matrix-valued functional integrals generated by the relativistic Hamiltonian is considered. The method of evaluation of functional integrals is based on the expansion in the eigenfunctions of Hamiltonian generating the functional integral. To find the eigenfunctions and the eigenvalues the initial Hamiltonian is considered as a sum of the unperturbed operator and a small correction to it, and the perturbation theory is used. The eigenvalues and the eigenfunctions of the unperturbed operator are found using the Sturm sequence method and the reverse iteration method. This approach allows one to significantly reduce the computation time and the used computer memory compared to the other known methods.

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25

Ayryan, Е. A., М. Hnatic, and V. В. Malyutin. "Approximate evaluation of the functional integrals generated by the Dirac equation with pseudospin symmetry." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 57, no. 1 (April 2, 2021): 14–22. http://dx.doi.org/10.29235/1561-2430-2021-57-1-14-22.

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In this paper, the matrix-valued functional integrals generated by the Dirac equation with relativistic Hamiltonian are considered. The Dirac Hamiltonian contains scalar and vector potentials. The sum of the scalar and vector potentials is equal to zero, i.e., the case of pseudospin symmetry is investigated. In this case, a Schrödinger-type equation for the eigenvalues and eigenfunctions of the relativistic Hamiltonian generating the functional integral is constructed. The eigenvalues and eigenfunctions of the Schrödinger-type operator are found using the Sturm sequence method and the reverse iteration method. A method for the evaluation of matrix-valued functional integrals is proposed. This method is based on the relation between the functional integral and the kernel of the evolution operator with the relativistic Hamiltonian and the expansion of the kernel of the evolution operator in terms of the found eigenfunctions of the relativistic Hamiltonian.

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26

Azé, D. "An example of stability for the minima of a sequence of dc functions: Homogenization for a class of nonlinear Sturm-Liouville problems." Mathematical Programming 41, no. 1-3 (May 1988): 127–40. http://dx.doi.org/10.1007/bf01580760.

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27

Hashemi, S. M., and M. J. Richard. "Natural Frequencies of Rotating Uniform Beams with Coriolis Effects." Journal of Vibration and Acoustics 123, no. 4 (April 1, 2001): 444–55. http://dx.doi.org/10.1115/1.1383969.

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A Dynamic Finite Element (DFE) for vibrational analysis of rotating assemblages composed of beams is presented in which the complexity of the acceleration, due to the presence of gyroscopic, or Coriolis forces, is taken into consideration. The dynamic trigonometric shape functions of uncoupled bending and axial vibrations of an axially loaded uniform beam element are derived in an exact sense. Then, exploiting the Principle of Virtual Work together with the nodal approximations of variables, based on these dynamic shape functions, leads to a single frequency dependent stiffness matrix which is Hermitian and represents both mass and stiffness properties. A Wittrick-Williams algorithm, based on a Sturm sequence root counting technique, is then used as the solution method. The application of the theory is demonstrated by two illustrative examples of vertical and radial beams where the influence of Coriolis forces on natural frequencies of the clamped-free rotating beams is demonstrated by numerical results.

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28

Galli, Gianni. "Storm sedimentation in a Quaternary rocky shore sequence (southern Italy)." Neues Jahrbuch für Geologie und Paläontologie - Monatshefte 1989, no. 10 (October 1, 1989): 590–602. http://dx.doi.org/10.1127/njgpm/1989/1989/590.

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29

Godwin, H. J. "Explicit expressions for Sturm sequences." Mathematical Proceedings of the Cambridge Philosophical Society 100, no. 2 (September 1986): 225–27. http://dx.doi.org/10.1017/s0305004100066044.

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Sturm's theorem was announced in 1829 and various proofs were given soon after (see [2], p. 363 for details). It is given in various textbooks on algebra, e.g. in [1], pp. 448–453, where its application to finding the number and location of the real zeros of a polynomial is explained. It has been applied, in conjunction with Givens's method, to finding the eigenvalues of a matrix (see, e.g. [3], p. 494), and has been used recently in a neat computational form by Takeuchi [4] for investigating algebraic fields.

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30

de HOOG, FRANK R., and ROBERT S. ANDERSSEN. "ASYMPTOTIC FORMULAS FOR DISCRETE EIGENVALUE PROBLEMS IN LIOUVILLE NORMAL FORM." Mathematical Models and Methods in Applied Sciences 11, no. 01 (February 2001): 43–56. http://dx.doi.org/10.1142/s0218202501000738.

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In the analysis of both continuous and discrete eigenvalue problems, asymptotic formulas play a central and crucial role. For example, they have been fundamental in the derivation of results about the inversion of the free oscillation problem of the Earth and related inverse eigenvalue problems, the computation of uniformly valid eigenvalues approximations, the proof of results about the behavior of the eigenvalues of Sturm–Liouville problems with discontinuous coefficients, and the construction of a counterexample to the Backus–Gilbert conjecture. Useful formulas are available for continuous eigenvalue problems with general boundary conditions as well as for discrete eigenvalue problems with Dirichlet boundary condition. The purpose of this paper is the construction of asymptotic formulas for discrete eigenvalue problems with general boundary conditions. The motivation is the computation of uniformly valid eigenvalue approximations. It is now widely accepted that the algebraic correction procedure, first proposed by Paine et al.,13 is one of the simplest methods for computing uniformly valid approximations to a sequence of eigenvalues of a continuous eigenvalue problem in Liouville normal form.8 This relates to the fact that, for Liouville normal forms with Dirichlet boundary conditions, it is not too difficult to prove that such procedures yield, under quite weak regularity conditions, uniformly valid O(h2) approximations. For Liouville normal forms with general boundary conditions, the corresponding error analysis is technically more challenging. Now it is necessary to have, for such Liouville normal forms, higher order accurate asymptotic formulas for the eigenvalues and eigenfunctions of their continuous and discrete counterparts. Assuming that such asymptotic formulas are available, it has been shown1 how uniformly valid O(h2) results could be established for the application of the algebraic correction procedure to Liouville normal forms with general boundary conditions. Algorithmically, this methodology represents an efficient procedure for determining uniformly valid approximations to sequences of eigenvalues, even though it is more complex than for Liouville normal forms with Dirichlet boundary conditions. As well as giving a brief review of the subject for general (Robin) boundary conditions, this paper sketches proofs for the asymptotic formulas, for Robin boundary conditions, which are required in order to construct the mentioned O(h2) results.

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31

Greenberg, Leon. "Sturm Sequences for Nonlinear Eigenvalue Problems." SIAM Journal on Mathematical Analysis 20, no. 1 (January 1989): 182–99. http://dx.doi.org/10.1137/0520015.

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32

Albrecht, James T., Cy P. Chan, and Alan Edelman. "Sturm Sequences and Random Eigenvalue Distributions." Foundations of Computational Mathematics 9, no. 4 (November 5, 2008): 461–83. http://dx.doi.org/10.1007/s10208-008-9037-x.

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33

DAHLQVIST, PETER. "Late Ordovician (Hirnantian) depositional pattern and sea-level change in shallow marine to shoreface cycles in central Sweden." Geological Magazine 141, no. 5 (September 2004): 605–16. http://dx.doi.org/10.1017/s0016756804009446.

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The Upper Ordovician Kyrkås Quartzite Formation at the Nifsåsen Quarry (Jämtland, Sweden) exhibits c. 90 m of siliciclastic sedimentary rocks deposited on a shallow shelf at the craton-attached part of the Caledonian foreland basin. Five lithologies are distinguished, including claystone, mudstone, siltstone, subarkose and sublitharenite. Based on these five lithologies, sedimentary structures and biota, three marine facies associations are defined: the Mudstone association (FA1) deposited close to storm wave base, the Sandstone/mudstone association (FA2) formed between storm and fair-weather wave bases, and the Sandstone association (FA3) accumulated above fair-weather wave base. The facies associations are arranged in two sequences, c. 50 and 40 m thick, separated by a transgressive surface, indicating repeated shoreline progradation. Both sequences commence with marine heterolithic shales and siltstones, with upwardly increasing frequency of tempestites. Continued shoaling is indicated by a dominance of hummocky and trough (locally tabular) cross-stratified sandstone beds in the upper part of each sequence. Sand beds are increasingly amalgamated up-sequence, reflecting progressively diminishing accommodation space. The depositional style and sedimentary structures indicate that the study area was storm-dominated with an abundant supply of siliciclastic material. Biostratigraphic data tie the depositional changes to the globally recognized Late Ordovician (Hirnantian) glacial interval. These data suggest that the first sequence was formed during the initial phase of regression in the earliest Hirnantian. The lowermost part of the overlying sequence contains elements of a typical Hirnantia fauna followed by beds yielding Normalograptus persculptus, suggesting a second regressive cycle in the Jämtland basin during the early N. persculptus Biozone.

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34

Baake, Michael. "Small Oscillations, Sturm Sequences, and Orthogonal Polynomials." Zeitschrift für Naturforschung A 49, no. 3 (March 1, 1994): 445–57. http://dx.doi.org/10.1515/zna-1994-0301.

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Abstract The relation between small oscillations of one-dimensional mechanical n-particle systems and the theory of orthogonal polynomials is investigated. It is shown how the polynomials provide a natural tool to determine the eigenfrequencies and eigencoordinates completely, where the existence of a specific two-termed recurrence formula is essential. Physical and mathematical statements are formulated in terms of the recurrence coefficients which can directly be obtained from the corresponding secular equation. Several results on Sturm sequences and orthogonal polynomials are presented with respect to the treatment of small oscillations. The relation to the numerical treatment of the generalized eigenvalue problem is discussed and further applications to physical problems from quantum mechanics, statistical mechanics, and spin systems are briefly outlined.

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35

Greenberg, L., and I. Babuška. "A Continuous Analogue of Sturm Sequences in the Context of Sturm–Liouville Equations." SIAM Journal on Numerical Analysis 26, no. 4 (August 1989): 920–45. http://dx.doi.org/10.1137/0726051.

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36

Pride, Walker, Alexander Smith, and Ryan Joseph. "Thyroid storm following rapid sequence intubation." American Journal of Emergency Medicine 36, no. 12 (December 2018): 2338.e5–2338.e6. http://dx.doi.org/10.1016/j.ajem.2018.09.006.

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37

Sun, X. W. "PREDICTION OF CARBONATE RESERVOIRS AND TRAPS BY APPLYING SEQUENCE STRATIGRAPHY IN THE EASTERN WARBURTON BASIN, SOUTH AUSTRALIA." APPEA Journal 38, no. 1 (1998): 380. http://dx.doi.org/10.1071/aj97018.

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The Early Palaeozoic eastern Warburton Basin unconformably underlies the Cooper and Eromanga Basins. Four seismic sequence sets (I−IV) are interpreted. Among them, sequence set II is subdivided into four Cambro-Ordovician depositional sequences. Sequence 1, the oldest, is a shallow shelf deposit that occurs only in the Gidgealpa area. Sequences 2 and 3 were deposited in a wider area; from west to east, environments varyied from deep siliciclastic ramp, carbonate inner-shelf, peritidal, shelf edge, and slope-to-basin. Their seismic reflection configurations are high-amplitude, regionally parallel-continuous, layered patterns, locally mounded geometry, as well as divergent-fill patterns. Sequence 4, the youngest, was deposited in a mixed siliciclastic and carbonate, storm-dominate shelf. Its seismic reflection configurations are moderate amplitude, parallel-layered patterns, decreasing in amplitude upwards.Boundaries between the four sequences generated good secondary porosity in the carbonates. Karst development is interpreted to have generated much of this porosity in shelf and peritidal carbonates, and carbonate build-ups. Shoal-water sandy limestone and calcareous sandstone of Sequence 4 may be other potential reservoir rocks. Potential source rocks comprise mudstone and shale of slope and basin lithofacies. There are two kinds of stratigraphic trap. One is in Sequences 2 and 3, associated with high-relief carbonate build-ups encased in lagoonal mudstone and shelf edge sealed by transgressive siltstone and shale. The other is a transgressive marine shale enclosing porous dolostone of the karstified Sequence 1. In addition, petroleum may have migrated from Permian source rocks of the Cooper Basin to karstified carbonate reservoirs of the Warburton Basin at unconformities.

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38

Röbenack, Klaus, and Rick Voßwinkel. "On Real Stable Pole Placement for Structured Systems Using Sturm and Sturm-Habicht Sequences." IFAC-PapersOnLine 53, no. 2 (2020): 4546–52. http://dx.doi.org/10.1016/j.ifacol.2020.12.475.

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39

Bossé, Michael J., William J. Cook, and Joseph M. Castonguay. "Finding Real Roots of Polynomials Using Sturm Sequences." PRIMUS 30, no. 1 (April 8, 2019): 36–49. http://dx.doi.org/10.1080/10511970.2018.1501626.

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40

Briganti, Riccardo, Rosaria Ester Musumeci, Jentsje Van der Meer, Alessandro Romano, Laura Maria Stancanelli, Matthias Kudella, Rizki Akbar, et al. "LARGE SCALE TESTS ON FORESHORE EVOLUTION DURING STORM SEQUENCES AND THE PERFORMANCE OF A NEARLY VERTICAL STRUCTURE." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 13. http://dx.doi.org/10.9753/icce.v36.papers.13.

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This work presents the results of an experimental investigation on the effects of a sequence of storms on wave overtopping at a nearly vertical battered seawall at the back of a sandy foreshore. The experiments were carried out in the Large Wave Flume (GWK) at Leibniz UniversitÃ¤t Hannover (Germany), as part of the research project ICODEP (Impact of Changing fOreshore on flood DEfence Performance), within the European Union programme Hydralab+. The layout consisted of a 10/1 battered seawall and a natural sandy foreshore with an initial 1:15 slope. The beach sand had a nominal diameter of 0.30 mm. Three storm sequences were simulated, where each consisted of three individual storms. Each storm was divided into six steps in which the wave conditions and still water level were varied to represent the peak of an actual storm. The six sea states were based on a JONSWAP spectral shape, with wave heights roughly between 0.6 m and 0.8 m. Two still water levels were tested. For the central two steps the level was such that the freeboard was only 0.14 m and almost all waves were overtopping. In the remaining steps low still water levels were employed, leaving a narrow swash zone. Two storm profiles were considered, the first one with a lower level of energy and the second one with a higher one. These were combined in the three different sequences. All the tested wave conditions were designed to be erosive for the beach, with no recovery in between. Each sequence started from a plain beach configuration and the beach was not restored in between storms. The measurements included waves, pressure and forces, sediment concentrations and flow velocity together with overtopping. The profile of the beach was measured after each sea state tested.

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41

Krim, Nesma, Cédric Bonnel, Nicolas Tribovillard, Patrice Imbert, Charles Aubourg, Armelle Riboulleau, Viviane Bout-Roumazeilles, Guilhem Hoareau, and Bertrand Fasentieux. "Paleoenvironmental evolution of the southern Neuquèn basin (Argentina) during the Tithonian-Berriasian (Vaca Muerta and Picún Leufú Formations): a multi-proxy approach." Bulletin de la Société géologique de France 188, no. 5 (2017): 34. http://dx.doi.org/10.1051/bsgf/2017196.

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The Tithonian-Berriasian interval in the southern part of the Neuquén Basin is represented by the Vaca Muerta and the Picún Leufú Formations. Facies analysis and correlation of the Vaca Muerta Formation and the lower part of the Picún Leufú Formation in the Picún Leufú Anticline allow us to characterize the evolution of successive facies belts representing siliciclastic shelf and mixed ramp environments. Shoreface and offshore facies are developed on the siliciclastic shelf in the western and southern parts of the Picún Leufú Anticline. The offshore transition domain is characterized by storm beds and slump features, whereas the offshore domain corresponds to black to grey shales and turbidites. The mixed siliciclastic-carbonate ramp is characterized by the development of a lagoon and high-energy shoal in the proximal part of the inner ramp, whereas the distal part comprises a tidal complex. The mid-ramp zone is characterized by storm influence and the outer ramp by fine-grained deposits. Two major transgressive-regressive sequences and five high-frequency transgressive-regressive sequences are recognized. The high-frequency transgressive-regressive sequences make up three progradational sequences, an aggradational-progradational sequence and an aggradational sequence. The geochemical characteristics and clay mineralogy of the Tithonian-Berriasian interval in the southern Neuquén Basin indicate that (1) climate played a key role in the evolution of the sedimentary environment, (2) a “normal marine” depositional environment with oxic sea water and sediment pore waters, rapidly changing to suboxic conditions at shallow depth below the seabed and (3) the occurrence of episodically restricted water-mass circulation at the onset of deposition of the Vaca Muerta Formation.

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42

La Fontaine, Nathan, and Michael Hofmann. "Quantifying the stratigraphic and spatial facies distribution in an ancient mixed-influence delta." Mountain Geologist 56, no. 1 (February 2019): 19–44. http://dx.doi.org/10.31582/rmag.mg.56.1.19.

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Analysis of the sedimentology and stratigraphic architecture of tightly spaced three dimensional outcrops reveals that the Turonian (Upper Cretaceous) Wall Creek Member of the Frontier Formation in the western Powder River Basin, Wyoming, USA, is not composed of one continuous coarsening upward succession but of a complex stacked delta system containing three distinct sequences (S1-S3), each with a unique facies distribution and architectural heterogeneity. The basal sequence S1 consists of a fluvial dominated delta with two distinct lobes. These lobes are spatially constrained to the northeastern study area and show a rapid facies transition from trough crossbedded mouthbar deposits to lower delta front turbidites. Low angle clinoforms suggest a low accommodation setting with main sediment transport to the south. The middle S2 sequence is common throughout the study area and contains an abundance of storm-derived deposits, including hummocky cross stratification, suggesting the transition to a wave and storm-dominated delta setting. Sediment transport is largely to the south controlled by wind induced shear stresses. Lastly, heterolithic trough crossbedded sandstones with flaser bedding and abundant thin mudstones and rip-up clasts are characteristic for sequence S3. These deposits are interpreted as tidal bars in a tidal influenced delta. Quantitative evaluation of facies in the Wall Creek Member sequences shows that the dimensions and connectivity (baffle or barrier competence) of fine-grained thin beds varies systematically within the three delta types. The S1 fluvial delta is largely composed of laterally continuous delta front turbidites with continuous fine-grained thin beds (mean length 21.1 m or 69.2 ft, max length 83.9 m or 275.2 ft) separating individual sandstone beds. Conversely, abundant bioturbation and intense scouring by storms results in high amalgamation of sandy beds in sequence S2 and a limited length of fine-grained thin beds (mean 8.5 m or 27.9 ft) in the wave-dominated delta sequence. Tidally influenced deposits of sequence S3 are largely composed of heterolithic trough crossbedded sandstones and mudstones with low bioturbation, resulting in an intermediate fine-grained thin bed deposit (mean 12.1 m or 39.7 ft).

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De Gracia, Luis, Naoki Osawa, Hitoi Tamaru, and Toichi Fukasawa. "A Comparative Study on Fatigue Damage using a Wave Load Sequence Model." KnE Engineering 3, no. 1 (February 11, 2018): 160. http://dx.doi.org/10.18502/keg.v3i1.1422.

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Despite that ships get the approval of classification societies and structural members are designed to survive random environmental conditions for twenty or twenty-five years, fatigue crack damage still occurs. Nowadays, the operation based on weather routing programs has become important, not only to avoid adverse sea conditions that can cause damage, time loss or significant speed reduction but also to improve the crew safety. In this paper, S-N based fatigue assessment of a welded joint in an ocean going is performed. It is assumed that the ship sails following a planned route and a route based on weather conditions. Short sea sequences are generated by a storm model called “4G Storm Model”, proposed by one of the co-authors (De Gracia et al., 2017). Stress histories are generated considering the stochastical nature of the wave direction variation. Cumulative fatigue damage is performed following a classification society rule. Based on these results, the effect of ship routing and headings model on the S-N fatigue assessment is discussed. Keywords: Weather routing, fatigue, cumulative damage, storm model, wave sequence model.

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44

Xu, Guohui, Zhiqin Liu, Yongfu Sun, Xin Wang, Lin Lin, and Yupeng Ren. "Experimental characterization of storm liquefaction deposits sequences." Marine Geology 382 (December 2016): 191–99. http://dx.doi.org/10.1016/j.margeo.2016.10.015.

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45

Woolfenden, Wallace B., and Linah Ababneh. "Late Holocene vegetation in the Azraq Wetland Reserve, Jordan." Quaternary Research 76, no. 3 (November 2011): 345–51. http://dx.doi.org/10.1016/j.yqres.2011.08.007.

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AbstractShifts in aquatic and terrestrial vegetation associations and hydrology during the past > 3100 yr are indicated by the pollen and sediment sequences in a core retrieved from the Azraq wetland, Jordan. The pollen sequence provides evidence for a relatively stable wetland during the period of study until ca. AD 1400 when the wetland apparently declined as desert shrubland expanded. Springs continually supplied fresh water that maintained the shallow pools and marsh. In periods of increased winter precipitation, runoff from the surrounding wadis may have inundated the wetland and deposited silts and clays. During dryer episodes the influx of winter storm water would have been much less but the springs would have still provided water to the wetland and deposited peat. This is shown by the sequences of clay, silty and sandy clay loam, and peat in the core.

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46

Mondal, Saiful R., Kottakkaran Sooppy Nisar, and Thabet Abdeljawad. "On the Study of Trigonometric Polynomials Using Strum Sequence." Journal of Mathematics 2020 (November 21, 2020): 1–8. http://dx.doi.org/10.1155/2020/7068176.

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This article constructs trigonometric polynomials of the sine and cosine whose sums are nonnegative. As an application, those nonnegative trigonometric sums are used to study the geometric properties of complex polynomials in the unit disk. The Strum sequences are used to prove the main outcome.

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47

BOND, DAVID P. G., DIERK P. G. BLOMEIER, ANNA M. DUSTIRA, PAUL B. WIGNALL, DANIEL COLLINS, THOMAS GOODE, RALPH D. GROEN, WERNER BUGGISCH, and STEPHEN E. GRASBY. "Sequence stratigraphy, basin morphology and sea-level history for the Permian Kapp Starostin Formation of Svalbard, Norway." Geological Magazine 155, no. 5 (January 9, 2017): 1023–39. http://dx.doi.org/10.1017/s0016756816001126.

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AbstractBased on seven measured sections from Svalbard, the marine strata of the Permian Kapp Starostin Formation are arranged into seven transgressive–regressive sequences (TR1–TR7) ofc. 4–5 Ma average duration, each bound by a maximum regressive surface. Facies, including heterozoan-dominated limestones, spiculitic cherts, sandstones, siltstones and shales, record deposition within inner, middle and outer shelf areas. The lowermost sequence, TR1, comprises most of the basal Vøringen Member, which records a transgression across the Gipshuken Formation following a hiatus of unknown duration. Temperate to cold, storm-dominated facies established in inner to middle shelf areas between the latest Artinskian and Kungurian. Prolonged deepening during sequences TR2 and TR3 was succeeded by a long-term shallowing-upward trend that lasted until the latest Permian (TR4–TR7). A major depocentre existed in central and western Spitsbergen while to the north, Dickson Land remained a shallow platform, leading to a shallow homoclinal ramp in NE Spitsbergen and Nordaustlandet. The Middle Permian extinction (late Capitanian) is recorded near the base of TR6 in deeper parts of the basin only; elsewhere this sequence is not recorded. Likewise the youngest sequence, TR7, extending to the upper formational contact of latest Permian age, is found only in the basin depocentre. Comparison with age-equivalent strata in the Sverdrup Basin of Canada reveals a remarkably similar depositional history, with, for example, two (third-order) sea-level cycles recorded in the Late Permian of both regions, in keeping with the global record. Sequence stratigraphy may therefore be a powerful correlative tool for onshore and offshore Permian deposits across NW Pangaea.

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48

Camargo Brunetto, M. A. O., D. M. Claudio, and V. Trevisan. "An algebraic algorithm to isolate complex polynomial zeros using Sturm sequences." Computers & Mathematics with Applications 39, no. 3-4 (February 2000): 95–105. http://dx.doi.org/10.1016/s0898-1221(99)00336-3.

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49

Piper, David J. W., Peta J. Mudie, Ali E. Aksu, and Philip R. Hill. "Late Quaternary sedimentation, 50° N, North-East Newfoundland shelf." Géographie physique et Quaternaire 32, no. 4 (January 25, 2011): 321–32. http://dx.doi.org/10.7202/1000331ar.

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Ten cores from the Northeast Newfoundland shelf and adjacent continental slope have correlable late Quaternary marine sequences. Late Holocene sediment is olive grey mud, with some ice-rafted debris. The early Holocene is characterised by warmer water microfossil assemblages, abundant ice-rafted carbonate debris, and pollen assemblages indicating open boreal woodland interspersed with tundra. Late and mid-Wisconsinan glacial stades show subarctic planktonic microfossil assemblages, regional sources of tundra pollen, storm reworking of earlier sediment, including till, and shallower water assemblages of benthonic foraminifera and diatoms. Two mid-Wisconsinan interstades are recognised, with marine microfossils similar to the early Holocene. This sequence rests disconformably on earlier (?lllinoian) pro-glacial muds which appear to overlie till.

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Arisan, Elif Damla, Alwyn Dart, Guy H. Grant, Serdar Arisan, Songul Cuhadaroglu, Sigrun Lange, and Pinar Uysal-Onganer. "The Prediction of miRNAs in SARS-CoV-2 Genomes: hsa-miR Databases Identify 7 Key miRs Linked to Host Responses and Virus Pathogenicity-Related KEGG Pathways Significant for Comorbidities." Viruses 12, no. 6 (June 4, 2020): 614. http://dx.doi.org/10.3390/v12060614.

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Severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) is a member of the betacoronavirus family, which causes COVID-19 disease. SARS-CoV-2 pathogenicity in humans leads to increased mortality rates due to alterations of significant pathways, including some resulting in exacerbated inflammatory responses linked to the “cytokine storm” and extensive lung pathology, as well as being linked to a number of comorbidities. Our current study compared five SARS-CoV-2 sequences from different geographical regions to those from SARS, MERS and two cold viruses, OC43 and 229E, to identify the presence of miR-like sequences. We identified seven key miRs, which highlight considerable differences between the SARS-CoV-2 sequences, compared with the other viruses. The level of conservation between the five SARS-CoV-2 sequences was identical but poor compared with the other sequences, with SARS showing the highest degree of conservation. This decrease in similarity could result in reduced levels of transcriptional control, as well as a change in the physiological effect of the virus and associated host-pathogen responses. MERS and the milder symptom viruses showed greater differences and even significant sequence gaps. This divergence away from the SARS-CoV-2 sequences broadly mirrors the phylogenetic relationships obtained from the whole-genome alignments. Therefore, patterns of mutation, occurring during sequence divergence from the longer established human viruses to the more recent ones, may have led to the emergence of sequence motifs that can be related directly to the pathogenicity of SARS-CoV-2. Importantly, we identified 7 key-microRNAs (miRs 8066, 5197, 3611, 3934-3p, 1307-3p, 3691-3p, 1468-5p) with significant links to KEGG pathways linked to viral pathogenicity and host responses. According to Bioproject data (PRJNA615032), SARS-CoV-2 mediated transcriptomic alterations were similar to the target pathways of the selected 7 miRs identified in our study. This mechanism could have considerable significance in determining the symptom spectrum of future potential pandemics. KEGG pathway analysis revealed a number of critical pathways linked to the seven identified miRs that may provide insight into the interplay between the virus and comorbidities. Based on our reported findings, miRNAs may constitute potential and effective therapeutic approaches in COVID-19 and its pathological consequences.

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