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1
Content available remote Smooth blowup square for motives with modulus
Kelly Shane, Saito Shuji
Bulletin of the Polish Academy of Sciences. Mathematics
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2021
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Vol. 69, no. 2
97--106
EN
In this self-contained paper we prove that Voevodsky’s smooth blowup triangle of motives generalises to a smooth blowup triangle of motives with modulus.
2
Content available Invariance of reachability and observability for fractional positive linear electrical circuit with delays
Yuan Tong, Yang Hongli
Archives of Electrical Engineering
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2021
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Vol. 70, nr 3
513--530
EN
This paper focuses on the invariance of the reachability and observability for fractional order positive linear electrical circuits with delays and their checking methods. By derivation and comparison, it shows that conditions and checking methods of reachability and observability for integer and fractional order positive linear electrical circuits with delays are invariant. An illustrative example is presented at the end of the paper.
3
Content available Invariant properties of positive linear electrical circuits
Kaczorek Tadeusz
Poznan University of Technology Academic Journals. Electrical Engineering
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2019
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No. 97
109--123
EN
The invariant properties of the stability, reachability, and transfer matrices of positive linear electrical circuits with integer and fractional orders are investigated. It is shown that the stability, reachability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.
4
Content available Lie symmetries of first order neutral differential equations
Lobo Jervin Zen, Valaulikar Y.S.
Journal of Applied Mathematics and Computational Mechanics
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2019
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Vol. 18, nr 1
29--40
EN
In this paper we extend the method of obtaining symmetries of ordinary differential equations to first order non-homogeneous neutral differential equations with variable coefficients. The existing method for delay differential equations uses a Lie-Bäcklund operator and an Invariant Manifold Theorem to define the operators which are used to obtain the infinitesimal generators of the Lie group. In this paper, we adopt a different approach and use Taylor’s theorem to obtain a Lie type invariance condition and the determining equations for a neutral differential equation. We then split this equation in a manner similar to that of ordinary differential equations to obtain an over-determined system of partial differential equations. These equations are then solved to obtain corresponding infinitesimals, and hence desired equivalent symmetries. We then obtain the symmetry algebra admitted by this neutral differential equation.
5
Content available Invariant properties of positive linear electrical circuits
Kaczorek Tadeusz
Archives of Electrical Engineering
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2019
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Vol. 68, nr 4
875--890
EN
The invariant properties of the stability, reachability, observability and transfer matrices of positive linear electrical circuits with integer and fractional orders are investigated. It is shown that the stability, reachability, observability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.
6
Content available Periodic solutions in multivariate invariance arguments
Chudziak J., Wójcik S.
Opuscula Mathematica
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2013
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Vol. 33, no. 3
455--465
EN
Inspired by the recent results of A.E. Abbas we determine continuous multivariate utility functions invariant with respect to a wide family of transformations related to the shift transformations.
7
Content available Utility functions invariant with respect to some classes of transformations
Chudziak J.
Control and Cybernetics
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2013
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Vol. 42, no. 2
347--363
EN
Inspired by some relevant recent results of A. E. Abbas we determine utility functions invariant with respect to some classes of transformations.
8
Content available remote On stability in impulsive dynamical systems
Ciesielski K.
Bulletin of the Polish Academy of Sciences. Mathematics
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2004
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Vol. 52, nr 1
81-91
EN
Several results on stability in impulsive dynamical systems are proved. The first main result gives equivalent conditions for stability of a compact set. In particular, a generalization of Ura's theorem to the case of impulsive systems is shown. The second main theorem says that under some additional assumptions every component of a stable set is stable. Also, several examples indicating possible complicated phenomena in impulsive systems are presented.
9
Content available remote On an invariant Borel measure in Hilbert space
Pantsulaia G.
Bulletin of the Polish Academy of Sciences. Mathematics
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2004
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Vol. 52, nr 1
47-51
EN
An example of a nonzero [sigma]-finite Borel measure [my] with everywhere dense linear manifold I[my] of admissible (in the sense of invariance) translation vectors is constructed in the Hilbert space l[2] such that [my] and any shift [my]^[alpha] of [my] by a vector [alpha] is an element of l[2] \ I[my] are neither equivalent nor orthogonal. This extends a result established in [7].
10
Using place invariants to isolate faults in concurrent systems
Tabakow I.
Systems Science
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2003
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Vol. 29, nr 4
99-112
EN
A method of fault isolation in a given concurrent system is presented. First, the system considered is modelled by a live and bounded place-transition Petri net. Then the corresponding net place invariants are computed. The system k-distinguishability measure is obtained in an unique way from the place-invariant matrix. For a large value of k, the system model is extended by using some set of additional places called test points. This is in accordance with the practical requirements introduced. To obtain an 1-distinguishable net the notion of a marked graph component is used. Next, two different diagnosis test strategies are discussed, i.e., combinational and sequential fault diagnosis (assuming MTBF -> infinity and MTTR -> 0, respectively). The approach proposed can be extended for higher level Petri nets, e.g., such as coloured nets or also to design self-diagnosable circuit realisations of Boolean interpreted Petri nets. Several examples are given.
11
Content available remote Improvement and invariance analysis of Zernike moments using as a region-based shape descriptor
Ye B., Peng J.
Image Processing & Communications
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2002
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Vol. 8, no 3
11-20
EN
In order to retrieve an image from a large image database, the descriptor should be invariant to scale and rotation. It must, also have enough discriminating power and immunity to noise for retrieval from a large image database. The Zernike moment descriptor has manv desirable properties such as rotation invariance, robustness to noise, expression efficiency, fast computation and multi-level representation for describing the shapes of patterns, but it does not possess scale invariance. In this paper, we present an improved Zernike moment descriptor that not only has rotation invariance, but also has scale invariance. We apply the improved Zernike moments to image recognition using as an elective descriptor of global shape of an image in a large image database. The experimemtal results show that the improved Zernike moment has better invariant properties than unimproved Zernike moment using as region-based shape descriptor.
12
Content available remote On invariance of linear subspaces for stochastic evolution equations
Milian A.
Demonstratio Mathematica
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2001
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Vol. 34, nr 2
425-430
EN
In the paper we consider Ito equation on a Hilbert space. We give necessary and sufficient conditions ensuring the invariance property of linear subspaces of the state space by mild solutions to the equation.
13
Content available remote Reachability and Controlability of Positive Linear Systems with State Feedbacks
Kaczorek T.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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1999
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Vol. 47, nr 1
67-73
EN
It is shown that the reachability and controllability of positive linear systems is not invariant under the state-feedbacks.
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