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1
Content available On the zeros of the MacDonald functions
Hamana Yuri, Matsumoto Hiroyuki, Shirai Tomoyuki
Opuscula Mathematica
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2019
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Vol. 39, no. 3
361--382
EN
We are concerned with the zeros of the Macdonald functions or the modified Bessel functions of the second kind with real index. By using the explicit expressions for the algebraic equations satisfied by the zeros, we describe the behavior of the zeros when the index moves. Results by numerical computations are also presented.
2
Content available Number of zeros of a polynomial in a specific region with restricted coefficients
Mir Abdullah, Ahmad Abrar, Malik Adil Hussain
Journal of Mathematics and Applications
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2019
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Vol. 42
135--146
EN
This paper focuses on the problem concerning the location and the number of zeros of polynomials in a specific region when their coefficients are restricted with special conditions. We obtain extensions of some classical results concerning the number of zeros of polynomials in a prescribed region by imposing the restrictions on the moduli of the coefficients, the real parts(only) of the coefficients, and the real and imaginary parts of the coefficients.
3
Content available Number of zeros of a polynomial (Lacunary-type) in a disk
Qasim I., Rasool T., Liman A.
Journal of Mathematics and Applications
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2018
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Vol. 41
181--194
EN
The problem of finding out the region which contains all or a prescribed number of zeros of a polynomial [wzór] has a long history and dates back to the earliest days when the geometrical representation of complex numbers was introduced. In this paper, we present certain results concerning the location of the zeros of Lacunary-type polynomials [wzór] in a disc centered at the origin.
4
Content available Location of zeros of Lacunary-type polynomials
Qasim I., Rasool T., Liman A.
Journal of Mathematics and Applications
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2018
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Vol. 41
171--180
EN
In this paper, we present some interesting results concerning the location of zeros of Lacunary-type of polynomial in the complex plane. By relaxing the hypothesis and putting less restrictive conditions on the coefficients of the polynomial, our results generalize and refines some classical results.
5
Content available remote Zeros of the Derivatives of L-functions Attached to Cusp Forms
Yashiro Y.
Bulletin of the Polish Academy of Sciences. Mathematics
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2016
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Vol. 64, no. 2/3
147--164
EN
Let f be a holomorphic cusp form of weight k with respect to SL2(Z) which is a normalized Hecke eigenform, and Lf(s) the L-function attached to f. We shall give a relation between the number of zeros of Lf(s) and of the derivatives of Lf(s) using Berndt’s method, and an estimate of zero-density of the derivatives of Lf(s) based on Littlewood’s method.
6
Content available remote On the zeros of an analytic function
Jain V.
Journal of Mathematics and Applications
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2014
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Vol. 37
51--58
7
Content available remote Analytic solution of transcendental equations
Górecki H.
International Journal of Applied Mathematics and Computer Science
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2010
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Vol. 20, no 4
671-677
EN
A decomposition technique of the solution of an n-th order linear differential equation into a set of solutions of 2-nd order linear differential equations is presented.
8
Content available Analityczne wyznaczanie ekstremów i zer równań różniczkowych n-tego rzędu
Górecki H.
Automatyka / Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie
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2009
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T. 13, z. 2
275-288
PL
W pracy przedstawiono metodę wyznaczania ekstremów rozwiązań równań różniczkowych liniowych o stałych współczynnikach, rzędu trzeciego i wyższych.
EN
A method for determination the extrema of solutions of linear differential equations with constant coefficients of the third and higher orders.
9
Content available remote Relationship between Smith zeros and invariant zeros in linear systems
Tokarzewski J.
Archives of Control Sciences
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2004
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Vol. 14, no. 1
15-26
EN
The question how the classical concept of the Smith zeros of a linear, time-invariant (LTI), multi-input, multi-output (MIMO) continuous-time singular system S (E, A, B, C, D) can be generalized and related to the stste-space methods is discussed. nothing is assumed about the relationship of the number of inputs to the number of outputs nor about the normal rank of the underlying system matrix. The aforementioned generalization treats zeros (called further the invariant zeros) as the triples . Such treatment is strictly connested with the output-zeroing problem and in that spirit the zeros can be easily interpreted even in the degenerate case.
10
Content available remote A note on zeros, output-nulling subspaces and zero-dynamics in MIMO LTI systems
Tokarzewski J.
Archives of Control Sciences
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2004
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Vol. 14, no. 2
179-199
EN
In a standard multi-input, multi-output linear time invariant (MIMO LTI) continuous-time system S9A,B,C) the classical notion of the Smith zeros does not characterize fully the output-zeroing problem nor the zero dynamics. The question how this notion can be extended and related to the state-space methods is discussed. Nothing is assumed about the ralationship of the number of inputs to the number of outputs nor about the normal rank of the underlying system matrix. The proposed extension treats multivariable zeros as the triples. Such a treatment is strictly connected with the output zeroing problem and in that spirit the zeros can be easily interpreted even in the degenerate case.
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