Functionals of random mappings: exact and asymptotic results

1991 ◽  
Vol 23 (3) ◽  
pp. 437-455 ◽  
Author(s):  
P. J. Donnelly ◽  
W. J. Ewens ◽  
S. Padmadisastra
Keyword(s):  
Frequency Spectrum ◽  
Exact Results ◽  
Asymptotic Results ◽  
Number Of Components ◽  
Random Mapping ◽  
Random Mappings ◽  
Simulation Results ◽  
Central Tool

A random mapping partitions the set {1, 2, ···, m} into components, where i and j are in the same component if some functional iterate of i equals some functional iterate of j. We consider various functionals of these partitions and of samples from it, including the number of components of ‘small' size and of size O(m) as m → ∞the size of the largest component, the number of components, and various symmetric functionals of the normalized component sizes. In many cases exact results, while available, are uniformative, and we consider various approximations. Numerical and simulation results are also presented. A central tool for many calculations is the ‘frequency spectrum', both exact and asymptotic.

Functionals of random mappings: exact and asymptotic results

1991 ◽  
Vol 23 (03) ◽  
pp. 437-455 ◽  
Author(s):  
P. J. Donnelly ◽  
W. J. Ewens ◽  
S. Padmadisastra
Keyword(s):  
Frequency Spectrum ◽  
Exact Results ◽  
Asymptotic Results ◽  
Number Of Components ◽  
Random Mapping ◽  
Random Mappings ◽  
Simulation Results ◽  
Central Tool

A random mapping partitions the set {1, 2, ···,m} into components, whereiandjare in the same component if some functional iterate ofiequals some functional iterate ofj. We consider various functionals of these partitions and of samples from it, including the number of components of ‘small' size and of sizeO(m) asm→ ∞the size of the largest component, the number of components, and various symmetric functionals of the normalized component sizes. In many cases exact results, while available, are uniformative, and we consider various approximations. Numerical and simulation results are also presented. A central tool for many calculations is the ‘frequency spectrum', both exact and asymptotic.

Factorial moments for random mappings by means of indicator variables

1993 ◽  
Vol 30 (1) ◽  
pp. 167-174 ◽  
Author(s):  
Brian J. English
Keyword(s):  
Factorial Moments ◽  
Number Of Components ◽  
Random Mapping ◽  
Indicator Variables ◽  
Random Mappings

A simple identity for the incomplete factorial of sums of zero-one variables is exploited to provide the factorial moments of the number of components and the number of cyclical elements of the random mapping (T, {pi}) considered by Ross (1981).

Factorial moments for random mappings by means of indicator variables

1993 ◽  
Vol 30 (01) ◽  
pp. 167-174
Author(s):  
Brian J. English
Keyword(s):  
Factorial Moments ◽  
Number Of Components ◽  
Random Mapping ◽  
Indicator Variables ◽  
Random Mappings

A simple identity for the incomplete factorial of sums of zero-one variables is exploited to provide the factorial moments of the number of components and the number of cyclical elements of the random mapping (T, {pi }) considered by Ross (1981).

Design of a high-gain dual-band antipodal Vivaldi antenna array for 5G communications

2021 ◽  
pp. 1-9
Author(s):  
Sumit Kumar ◽  
Amruta S. Dixit
Keyword(s):  
Frequency Spectrum ◽  
Impedance Matching ◽  
High Gain ◽  
Dual Band ◽  
Dual Frequency ◽  
Band Frequency ◽  
Dielectric Lens ◽  
Bottom Side ◽  
Simulation Results ◽  
Vivaldi Antenna

Abstract This paper presents a dual-band 1 × 4 antipodal Vivaldi antenna (AVA) array with high gain to operate over a dual-frequency band that covers the 5G frequency spectrum. The gain is enhanced by employing a dielectric lens (DL). The AVA array consists of four radiating patch elements, corrugations, DL, and array feeding network on the top side. The bottom side contains four radiating patches which are the mirror images of top radiating patches. The designed AVA contains 1 × 4 array antenna elements with a DL that is operating in the ranges of 24.59–24.98 and 27.06–29 GHz. The dimensions of the designed antenna are 97.2 mm × 71.2 mm × 0.8 mm. For the improvement in gain and impedance matching at the dual-band frequency, corrugation and feeding network techniques are used. The gain obtained is about 8–12 dBi. AVA array is tested after fabrication and the measured results are reliable with the simulation results.

A New Advanced Topology of Stacked Multicell Inverter

2014 ◽  
Vol 15 (4) ◽  
pp. 327-333 ◽  
Author(s):  
Mohamad R. Banaei ◽  
M. R. Jannati Oskuee ◽  
F. Mohajel Kazemi
Keyword(s):  
Frequency Spectrum ◽  
Output Voltage ◽  
Low Frequency ◽  
Experimental Results ◽  
The Novel ◽  
Stored Energy ◽  
Well Performance ◽  
Flying Capacitors ◽  
Voltage Frequency ◽  
Simulation Results

Abstract In this paper, a new advanced topology of stacked multicell inverter is proposed which is generally suitable for high number of steps associated with a low number of switches. Compared with traditional flying capacitor multicell and stacked multicell (SM) inverters, doubling the number of output voltage levels and the RMS value, ameliorating the output voltage frequency spectrum, decreasing the number and rating of components, stored energy and rating of flying capacitors are available with the proposed inverter. These improvements are achieved by adding only four low-frequency switches to the traditional SM inverter’s structure. The suggested topology is simulated using MATLAB/SIMULINK software, and simulation results are presented to indicate well-performance of the novel converter. In addition, the experimental results of proposed topology prototype have been presented to validate its practicability.

scholarly journals Predecessors and Successors in Random Mappings with Exchangeable In-Degrees

2013 ◽  
Vol 50 (3) ◽  
pp. 721-740 ◽  
Author(s):  
Jennie C. Hansen ◽  
Jerzy Jaworski
Keyword(s):  
Asymptotic Behaviour ◽  
Preferential Attachment ◽  
Degree Sequence ◽  
Discrete Distributions ◽  
Threshold Behaviour ◽  
Mapping Model ◽  
Random Mapping ◽  
Exact Distributions ◽  
Random Mappings ◽  
Expected Values

In this paper we characterise the distributions of the number of predecessors and of the number of successors of a given set of vertices, A, in the random mapping model, TnD̂ (see Hansen and Jaworski (2008)), with exchangeable in-degree sequence (D̂1,D̂2,…,D̂n). We show that the exact formulae for these distributions and their expected values can be given in terms of the distributions of simple functions of the in-degree variables D̂1,D̂2,…,D̂n. As an application of these results, we consider two special examples of TnD̂ which correspond to random mappings with preferential and anti-preferential attachment, and determine the exact distributions for the number of predecessors and the number of successors in these cases. We also characterise, for these two special examples, the asymptotic behaviour of the expected numbers of predecessors and successors and interpret these results in terms of the threshold behaviour of epidemic processes on random mapping graphs. The families of discrete distributions obtained in this paper are also of independent interest.

Exact results for a secretary problem

1996 ◽  
Vol 33 (03) ◽  
pp. 630-639 ◽  
Author(s):  
M. P. Quine ◽  
J. S. Law
Keyword(s):  
Markov Chain ◽  
Optimal Strategy ◽  
Secretary Problem ◽  
Exact Results ◽  
Asymptotic Results ◽  
Backwards Induction ◽  
Imbedded Markov Chain ◽  
Probability Of Success

We consider the following secretary problem: items ranked from 1 to n are randomly selected without replacement, one at a time, and to ‘win' is to stop at an item whose overall rank is less than or equal to s, given only the relative ranks of the items drawn so far. Our method of analysis is based on the existence of an imbedded Markov chain and uses the technique of backwards induction. In principal the approach can be used to give exact results for any value of s; we do the working for s = 3. We give exact results for the optimal strategy, the probability of success and the distribution of T, and the total number of draws when the optimal strategy is implemented. We also give some asymptotic results for these quantities as n → ∞.

SYSTEMATIC SYNTHESIS OF OTA-BASED T-T FILTERS USING NAME METHOD

2013 ◽  
Vol 22 (03) ◽  
pp. 1350002 ◽  
Author(s):  
YONG-AN LI
Keyword(s):  
Class Ii ◽  
Class I ◽  
Number Of Components ◽  
Simulation Results ◽  
Systematic Synthesis

According to the terminal relations of the DO-OTA, eight nullor–mirror models for the DO-OTA are presented in this paper, Moreover, the NAME method for two different classes of T-T filters is considered. The class I filters, employing three SISO-OTAs, have 16 different forms, and the class II filters, employing one SISO-OTA and one DISO-OTA or one SIDO-OTA, have eight different forms. Due to use of canonic number of components, the circuits are easy to be integrated and their parameters can be tuned electronically through tuning bias currents of the OTAs. The MULTISIM simulation results have been included to verify the workability of the derived circuit.

scholarly journals NEW METHOD FOR FAST IMAGE EDGE DETECTION BASED ON SUBBAND DECOMPOSITION

2011 ◽  
Vol 20 (1) ◽  
pp. 53 ◽  
Author(s):  
Chong-Yang Hao ◽  
Min Qi ◽  
U Heute ◽  
C Moraga
Keyword(s):  
Edge Detection ◽  
Frequency Spectrum ◽  
Spectrum Analysis ◽  
New Method ◽  
Subband Decomposition ◽  
Central Frequency ◽  
Spatial Methods ◽  
Image Edge Detection ◽  
Image Edge ◽  
Simulation Results

A new method of detection the edges of an image is presented in this article. The method uses a kind of twodimensional subband spectrum analysis (2D-SSA) filter that is based on subband decomposition, and it is very convenient to get the edge frequency spectrum of an image after certain preprocessing. Comparing with spatial methods, the method is less sensitive to noise. It is also superior to the conventional frequency methods. In conventional frequency methods, the bandwidth and central frequency of filter are fixed, and it needs to transform the whole image into frequency domain. While in this method, the bandwidth and central frequency can be adjusted flexibly, and it only uses a few pixels to implement FFT. So this method is a fast way to extract the edges of an image. The simulation results show its efficiency.

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