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1

A non-singular analytical technique for reinforced noncircular holes in orthotropic laminate

Mohan Pradeep, Kumar R. Ramesh

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 1

92--105

EN

The intricacy in Lekhnitskii’s available single power series solution for stress distribution around hole Edg for both circular and noncircular holes represented by a hole shape parameter ε is decoupled by introducing a new technique. Unknown coefficients in the power series in ε are solved by an iterative technique. Full field stress distribution is obtained by following an available method on Fourier solution. The present analytical solution for reinforced square hole in an orthotropic infinite plate is derived by completely eliminating stress singularity that depends on the concept of stress ratio. The region of validity of the present analytical solution on reinforcement area is arrived at based on a comparison with the finite element analysis. The present study will also be useful for deriving analytical solution for orthotropic shell with reinforced noncircular holes.

2

Korovkin-type approximation by operators in Riesz spaces via power series method

Chil Elmiloud, Assili Marwa

Demonstratio Mathematica

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2019

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Vol. 52, nr 1

490--495

EN

In this paper we prove an Ozguç, Yurdakadim and Taş version of the Korovkin-type approximation by operators in the sense of the power series method. That is, we try to extend the Korovkin approximation theorems, obtained by Ozguç and Taş in 2016, and Taş and Yurdakadim in 2017, for concrete classes of Banach spaces to the class of Riesz spaces. Some applications are presented.

3

Energy-optimal current distribution in an electrical network – controlling by the differential or the integral systems

Siwczyński M., Żaba S., Drwal A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2019

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Vol. 67, nr 3

613--620

EN

In the complex RLC network, apart from the currents flows arising from the normal laws of Kirchhoff, other distributions of current, resulting from certain optimization criteria, may also be received. This paper is the development of research on distribution that meets the condition of the minimum energy losses within the network called energy-optimal distribution. Optimal distribution is not reachable itself, but in order to trigger it off, it is necessary to introduce the control system in current-dependent voltage sources vector, entered into a mesh set of a complex RLC network. For energy-optimal controlling, to obtain the control operator, the inversion of R(s) operator is required. It is the matrix operator and the dispersive operator (it depends on frequency). Inversion of such operators is inconvenient because it is algorithmically complicated. To avoid this the operator R(s) is replaced by the R’ operator which is a?matrix, but non-dispersive one (it does not depend on s). This type of control is called the suboptimal control. Therefore, it is important to make appropriate selection of the R’ operator and hence the suboptimal control. This article shows how to implement such control through the use of matrix operators of multiple differentiation or integration. The key aspect is the distribution of a single rational function H(s) in a series of ‘s’ or ‘s1’. The paper presents a new way of developing a given, stable rational transmittance with real coefficients in power series of ‘s/s1. The formulas to determine values of series coefficients (with ‘s/s1’) have been shown and the conditions for convergence of differential/integral operators given as series of ‘s/s1’ have been defined.

4

Natural frequencies of axisymmetric vibrations of thin hyperbolic circular plates with clamped edges

Jaroszewicz J.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 2

451--457

EN

A free vibration analysis of homogeneous and isotropic circular thin plates with nonlinear thickness variation and clamped edges is considered. The limited independent solutions of differential Euler equation were expanded in the power series based on the properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations.

5

New inequalities of CBS-type for power series of complex numbers

Dragomir S. S.

Fasciculi Mathematici

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2016

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Nr 57

37--51

EN

Let [formula] be a function defned by power series with complex coefficients and convergent on the open disk D (0, R) C, R > 0. In this paper we show amongst other that, if α, z C are such that |α|, |α||z| < R, then [formula] where [formula]. Aplications for some fundamental functions defined by power series are also provided. be a function defned by power series with complex coefficients and convergent on the open disk D(0, R) C, R > 0. In this paper we show amongst other that, if α, z C are such that |α|, |α||z| < R, then [formula] where Applications for some fundamental functions defined by power series are also provided.

6

Modelling of simply supported circular diaphragm for touch mode capacitive sensors

Jindal S. K., Raghuwanshi S. K.

Journal of Theoretical and Applied Mechanics

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2015

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Vol. 53 nr 2

431--438

EN

This paper describes the power series solution for modelling of the simply supported circular diaphragm deflection under uniform load. The parameters such as touch point pressure and touch radius are defined. Moreover, these parameters are also computed by the algorithm proposed in the paper. Therefore, the power series solution can be applied for touch mode operation.

7

On the Behavior of Power Series with Completely Additive Coefficients

Petrushov O.

Bulletin of the Polish Academy of Sciences. Mathematics

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2015

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Vol. 63, no. 3

217--225

EN

Consider the power series A(z)=∑∞n=1 α (n) zn, where α(n) is a completely additive function satisfying the condition α(p) = o(lnp) for prime numbers p. Denote by e(l/q) the root of unity e2πil/q. We give effective omega-estimates for A(e(l/pk)r) when r→1−. From them we deduce that if such a series has non-singular points on the unit circle, then it is a zero function.

8

Power series solution of first order matrix differential equations

Kukla S., Zamorska I.

Journal of Applied Mathematics and Computational Mechanics

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2014

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Vol. 13, nr 3

123--128

EN

In the paper, the solution of second order differential equations with various coefficients is presented. The concerning equations are written as first order matrix differential equations and solved with the use of the power series method. Examples of application of the proposed method to the equations occurring in the technical problems are presented.

9

Useful approximation of discrete transcedent transfer function

Kukal J, Schmidt O.

Archives of Control Sciences

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2007

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Vol. 17, no. 1

5-13

EN

Linear systems with distributed parameters are described via linear partial differential equations. The application of Laplace transform comes to discrete transcendent transfer functions. When the response to unit step is aperiodic then the transfer function can be approximated by the system of second order with time delay. The role of sampling period is studied on four examples of heat and mass transfer systems. The methodology is based on inverse Laplace transform, sampling, Z transform and properties of power series. A new useful lemma was developed to help with error approximation. All the calculations were performed in the Matlab environment.

10

Reduction of power series in a polydisc with respect to a Gröbner basis

Szpond J.

Bulletin of the Polish Academy of Sciences. Mathematics

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2005

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Vol. 53, no 2

137-145

EN

We deal with a reduction of power series convergent in a polydisc with respect to a Gröbner basis of a polynomial ideal. The results are applied to proving that a Nash function whose graph is algebraic in a “large enough” polydisc, must be a polynomial. Moreover, we give an effective method for finding this polydisc.