**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**174

# Search results for: recursive algebra

##### 174 A Generalised Relational Data Model

**Authors:**
Georgia Garani

**Abstract:**

**Keywords:**
nested relations,
recursive algebra,
recursive nested operations,
relational data model.

##### 173 Two-Dimensional Symmetric Half-Plane Recursive Doubly Complementary Digital Lattice Filters

**Authors:**
Ju-Hong Lee,
Chong-Jia Ciou,
Yuan-Hau Yang

**Abstract:**

This paper deals with the problem of two-dimensional (2-D) recursive doubly complementary (DC) digital filter design. We present a structure of 2-D recursive DC filters by using 2-D symmetric half-plane (SHP) recursive digital all-pass lattice filters (DALFs). The novelty of using 2-D SHP recursive DALFs to construct a 2-D recursive DC digital lattice filter is that the resulting 2-D SHP recursive DC digital lattice filter provides better performance than the existing 2-D SHP recursive DC digital filter. Moreover, the proposed structure possesses a favorable 2-D DC half-band (DC-HB) property that allows about half of the 2-D SHP recursive DALF’s coefficients to be zero. This leads to considerable savings in computational burden for implementation. To ensure the stability of a designed 2-D SHP recursive DC digital lattice filter, some necessary constraints on the phase of the 2-D SHP recursive DALF during the design process are presented. Design of a 2-D diamond-shape decimation/interpolation filter is presented for illustration and comparison.

**Keywords:**
All-pass digital filter,
doubly complementary,
lattice structure,
symmetric half-plane digital filter,
sampling rate conversion.

##### 172 New Recursive Representations for the Favard Constants with Application to the Summation of Series

**Authors:**
Snezhana G. Gocheva-Ilieva,
Ivan H. Feschiev

**Abstract:**

**Keywords:**
Effective summation of series,
Favard constants,
finite recursive representations,
Fourier series

##### 171 A Novel Recursive Multiplierless Algorithm for 2-D DCT

**Authors:**
V.K.Ananthashayana,
Geetha.K.S

**Abstract:**

**Keywords:**
DCT,
Multilplerless,
Ramanujan Number,
Recursive.

##### 170 On the Invariant Uniform Roe Algebra as Crossed Product

**Authors:**
Kankeyanathan Kannan

**Abstract:**

The uniform Roe C*-algebra (also called uniform translation)C^*- algebra provides a link between coarse geometry and C^*- algebra theory. The uniform Roe algebra has a great importance in geometry, topology and analysis. We consider some of the elementary concepts associated with coarse spaces.

**Keywords:**
Invariant Approximation Property,
Uniform Roe algebras.

##### 169 Design of Two-Channel Quincunx Quadrature Mirror Filter Banks Using Digital All-Pass Lattice Filters

**Authors:**
Ju-Hong Lee,
Chong-Jia Ciou

**Abstract:**

This paper deals with the problem of two-dimensional (2-D) recursive two-channel quincunx quadrature mirror filter (QQMF) banks design. The analysis and synthesis filters of the 2-D recursive QQMF bank are composed of 2-D recursive digital allpass lattice filters (DALFs) with symmetric half-plane (SHP) support regions. Using the 2-D doubly complementary half-band (DC-HB) property possessed by the analysis and synthesis filters, we facilitate the design of the proposed QQMF bank. For finding the coefficients of the 2-D recursive SHP DALFs, we present a structure of 2-D recursive digital allpass filters by using 2-D SHP recursive digital all-pass lattice filters (DALFs). The novelty of using 2-D SHP recursive DALFs to construct a 2-D recursive QQMF bank is that the resulting 2-D recursive QQMF bank provides better performance than the existing 2-D recursive QQMF banks. Simulation results are also presented for illustration and comparison.

**Keywords:**
All-pass digital filter,
doubly complementary,
lattice structure,
symmetric half-plane digital filter,
quincunx QMF bank.

##### 168 Genetic-Based Planning with Recursive Subgoals

**Authors:**
Han Yu,
Dan C. Marinescu,
Annie S. Wu,
Howard Jay Siegel

**Abstract:**

**Keywords:**
Planning,
recursive subgoals,
Sliding-tile puzzle,
subgoal interaction,
genetic algorithms.

##### 167 Explicit Chain Homotopic Function to Compute Hochschild Homology of the Polynomial Algebra

**Authors:**
Z. Altawallbeh

**Abstract:**

In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra, by providing certain homotopic function.

**Keywords:**
Exterior algebra,
free resolution,
free and projective
modules,
Hochschild homology,
homotopic function,
symmetric
algebra.

##### 166 Deduction of Fuzzy Autocatalytic Set to Omega Algebra and Transformation Semigroup

**Authors:**
Liew Siaw Yee,
Tahir Ahmad

**Abstract:**

**Keywords:**
Fuzzy autocatalytic set,
omega algebra,
semigroup,
transformation semigroup.

##### 165 Adaptive MPC Using a Recursive Learning Technique

**Authors:**
Ahmed Abbas Helmy,
M. R. M. Rizk,
Mohamed El-Sayed

**Abstract:**

A model predictive controller based on recursive learning is proposed. In this SISO adaptive controller, a model is automatically updated using simple recursive equations. The identified models are then stored in the memory to be re-used in the future. The decision for model update is taken based on a new control performance index. The new controller allows the use of simple linear model predictive controllers in the control of nonlinear time varying processes.

**Keywords:**
Adaptive control,
model predictive control,
dynamic matrix control,
online model identification

##### 164 Recursive Least Squares Adaptive Filter a better ISI Compensator

**Authors:**
O. P. Sharma,
V. Janyani,
S. Sancheti

**Abstract:**

Inter-symbol interference if not taken care off may cause severe error at the receiver and the detection of signal becomes difficult. An adaptive equalizer employing Recursive Least Squares algorithm can be a good compensation for the ISI problem. In this paper performance of communication link in presence of Least Mean Square and Recursive Least Squares equalizer algorithm is analyzed. A Model of communication system having Quadrature amplitude modulation and Rician fading channel is implemented using MATLAB communication block set. Bit error rate and number of errors is evaluated for RLS and LMS equalizer algorithm, due to change in Signal to Noise Ratio (SNR) and fading component gain in Rician fading Channel.

**Keywords:**
Least mean square (LMS),
Recursive least squares(RLS),
Adaptive equalization,
Bit error rate (BER),
Rician fading channel,
Quadrature Amplitude Modulation (QAM),
Signal to noiseratio (SNR).

##### 163 How are Equalities Defined, Strong or Weak on a Multiple Algebra?

**Authors:**
Mona Taheri

**Abstract:**

For the purpose of finding the quotient structure of multiple algebras such as groups, Abelian groups and rings, we will state concepts of ( strong or weak ) equalities on multiple algebras, which will lead us to research on how ( strong or weak) are equalities defined on a multiple algebra over the quotients obtained from it. In order to find a quotient structure of multiple algebras such as groups, Abelian groups and loops, a part of this article has been allocated to the concepts of equalities (strong and weak) of the defined multiple functions on multiple algebras. This leads us to do research on how defined equalities (strong and weak) are made in the multiple algebra on its resulted quotient.

**Keywords:**
Multiple algebra,
mathematics,
universal algebra.

##### 162 1−Skeleton Resolution of Free Simplicial Algebras with Given CW−Basis

**Authors:**
Ali Mutlu,
Berrin Mutlu

**Abstract:**

In this paper we use the definition of CW basis of a free simplicial algebra. Using the free simplicial algebra, it is shown to construct free or totally free 2−crossed modules on suitable construction data with given a CW−basis of the free simplicial algebra. We give applications free crossed squares, free squared complexes and free 2−crossed complexes by using of 1(one) skeleton resolution of a step by step construction of the free simplicial algebra with a given CW−basis.

**Keywords:**
Free crossed square,
Free 2−crossed modules,
Free
simplicial algebra,
Free square complexes,
Free 2−crossed complexes
CW−basis,
1−skeleton.
A. M. S.Classification:[2000] 18D35,
18G30,
18G50,
18G55,
55Q05,
55Q20.

##### 161 Capital Mobility in Savings and Investment across China and the ASEAN-5: Evidence from Recursive Cointegration

**Authors:**
Chang Lee Shu-Jung,
Mei-Se Chien,
Chien-Chiang Lee,
Hui-Ting Hu

**Abstract:**

**Keywords:**
Investment,
savings,
recursive cointegration test,
ASEAN,
China.

##### 160 Online Estimation of Clutch Drag Torque in Wet Dual Clutch Transmission Based on Recursive Least Squares

**Authors:**
Hongkui Li,
Tongli Lu ,
Jianwu Zhang

**Abstract:**

This paper focuses on developing an estimation method of clutch drag torque in wet DCT. The modelling of clutch drag torque is investigated. As the main factor affecting the clutch drag torque, dynamic viscosity of oil is discussed. The paper proposes an estimation method of clutch drag torque based on recursive least squares by utilizing the dynamic equations of gear shifting synchronization process. The results demonstrate that the estimation method has good accuracy and efficiency.

**Keywords:**
Clutch drag torque,
wet DCT,
dynamic viscosity,
recursive least squares.

##### 159 Implementation of the Recursive Formula for Evaluation of the Strength of Daniels’ Model

**Authors:**
Václav Sadílek,
Miroslav Vořechovský

**Abstract:**

**Keywords:**
Daniels bundle model,
equal load sharing,
Python,
mpmath.

##### 158 Query Algebra for Semistuctured Data

**Authors:**
Ei Ei Myat,
Ni Lar Thein

**Abstract:**

**Keywords:**
Algebra,
Semistructured data,
Query Algebra.

##### 157 Optimal Design of Two-Channel Recursive Parallelogram Quadrature Mirror Filter Banks

**Authors:**
Ju-Hong Lee,
Yi-Lin Shieh

**Abstract:**

This paper deals with the optimal design of two-channel recursive parallelogram quadrature mirror filter (PQMF) banks. The analysis and synthesis filters of the PQMF bank are composed of two-dimensional (2-D) recursive digital all-pass filters (DAFs) with nonsymmetric half-plane (NSHP) support region. The design problem can be facilitated by using the 2-D doubly complementary half-band (DC-HB) property possessed by the analysis and synthesis filters. For finding the coefficients of the 2-D recursive NSHP DAFs, we appropriately formulate the design problem to result in an optimization problem that can be solved by using a weighted least-squares (WLS) algorithm in the minimax (*L _{∞}*) optimal sense. The designed 2-D recursive PQMF bank achieves perfect magnitude response and possesses satisfactory phase response without requiring extra phase equalizer. Simulation results are also provided for illustration and comparison.

**Keywords:**
Parallelogram Quadrature Mirror Filter Bank,
Doubly Complementary Filter,
Nonsymmetric Half-Plane Filter,
Weighted Least Squares Algorithm,
Digital All-Pass Filter.

##### 156 The Study of the Discrete Risk Model with Random Income

**Authors:**
Peichen Zhao

**Abstract:**

In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function. First, a mathematically recursive formula is derived for non ruin probability, and then, we examine the expected discounted penalty function, satisfy a defect renewal equation. Third, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give two examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function.

**Keywords:**
Discounted penalty function,
compound binomial process,
recursive formula,
discrete renewal equation,
asymptotic estimate.

##### 155 Simulation using the Recursive Method in USN

**Authors:**
Tae Kyung Kim,
Hee Suk Seo

**Abstract:**

**Keywords:**
Data filtering,
recursive CNP,
simulation.

##### 154 Recursive Wiener-Khintchine Theorem

**Authors:**
Khalid M. Aamir,
Mohammad A. Maud

**Abstract:**

Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (Wiener-Khintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this problem becomes even more prominent where computation of PSD is required after every shift in the window under analysis. In this paper, recursive version of the Wiener-Khintchine theorem has been derived by using the sliding DFT approach meant for computation of STFT. The computational complexity of the proposed recursive Wiener-Khintchine algorithm, for a window size of N, is O(N).

**Keywords:**
Power Spectral Density (PSD),
Wiener-KhintchineTheorem,
Periodogram,
Short Time Fourier Transform (STFT),
TheSliding DFT.

##### 153 Blind Image Deconvolution by Neural Recursive Function Approximation

**Authors:**
Jiann-Ming Wu,
Hsiao-Chang Chen,
Chun-Chang Wu,
Pei-Hsun Hsu

**Abstract:**

This work explores blind image deconvolution by recursive function approximation based on supervised learning of neural networks, under the assumption that a degraded image is linear convolution of an original source image through a linear shift-invariant (LSI) blurring matrix. Supervised learning of neural networks of radial basis functions (RBF) is employed to construct an embedded recursive function within a blurring image, try to extract non-deterministic component of an original source image, and use them to estimate hyper parameters of a linear image degradation model. Based on the estimated blurring matrix, reconstruction of an original source image from a blurred image is further resolved by an annealed Hopfield neural network. By numerical simulations, the proposed novel method is shown effective for faithful estimation of an unknown blurring matrix and restoration of an original source image.

**Keywords:**
Blind image deconvolution,
linear shift-invariant(LSI),
linear image degradation model,
radial basis functions (rbf),
recursive function,
annealed Hopfield neural networks.

##### 152 Multiplicative Functional on Upper Triangular Fuzzy Matrices

**Authors:**
Liu Ping

**Abstract:**

**Keywords:**
Multiplicative functional,
triangular fuzzy matrix,
fuzzy addition operation,
fuzzy multiplication operation.

##### 151 Inverse Dynamic Active Ground Motion Acceleration Inputs Estimation of the Retaining Structure

**Authors:**
Ming-Hui Lee,
Iau-Teh Wang

**Abstract:**

**Keywords:**
Earthquake,
Fuzzy Estimator,
Kalman Filter,
Recursive Least Square Estimator.

##### 150 Algebraic Quantum Error Correction Codes

**Authors:**
Ming-Chung Tsai,
Kuan-Peng Chen,
Zheng-Yao

**Abstract:**

**Keywords:**
Quotient-Algebra Partition,
Codeword Spinors,
Basis
Codewords,
Syndrome Spinors

##### 149 Ruin Probabilities with Dependent Rates of Interest and Autoregressive Moving Average Structures

**Authors:**
Fenglong Guo,
Dingcheng Wang

**Abstract:**

**Keywords:**
Lundberg inequality,
NWUC,
Renewal recursive technique,
Ruin probability

##### 148 Convergence Analysis of a Prediction based Adaptive Equalizer for IIR Channels

**Authors:**
Miloje S. Radenkovic,
Tamal Bose

**Abstract:**

**Keywords:**
Adaptive blind equalizer,
Recursive leastsquares,
Adaptive Filtering,
Convergence analysis.

##### 147 Reliability Assessment of Bangladesh Power System Using Recursive Algorithm

**Authors:**
Nahid-Al-Masood,
Jubaer Ahmed,
Amina Hasan Abedin,
S. R. Deeba,
Faeza Hafiz,
Mahmuda Begum

**Abstract:**

An electric utility-s main concern is to plan, design, operate and maintain its power supply to provide an acceptable level of reliability to its users. This clearly requires that standards of reliability be specified and used in all three sectors of the power system, i.e., generation, transmission and distribution. That is why reliability of a power system is always a major concern to power system planners. This paper presents the reliability analysis of Bangladesh Power System (BPS). Reliability index, loss of load probability (LOLP) of BPS is evaluated using recursive algorithm and considering no de-rated states of generators. BPS has sixty one generators and a total installed capacity of 5275 MW. The maximum demand of BPS is about 5000 MW. The relevant data of the generators and hourly load profiles are collected from the National Load Dispatch Center (NLDC) of Bangladesh and reliability index 'LOLP' is assessed for the period of last ten years.

**Keywords:**
Recursive algorithm,
LOLP,
forced outage rate,
cumulative probability.

##### 146 An Algebra for Protein Structure Data

**Authors:**
Yanchao Wang,
Rajshekhar Sunderraman

**Abstract:**

**Keywords:**
Domain-Specific Data Management,
Protein
Algebra,
Protein Ontology,
Protein Structure Data.

##### 145 Fixed Point Equations Related to Motion Integrals in Renormalization Hopf Algebra

**Authors:**
Ali Shojaei-Fard

**Abstract:**

**Keywords:**
Birkhoff Factorization,
Connes-Kreimer Hopf Algebra of Rooted Trees,
Integral Renormalization,
Lax Pair Equation,
Rota- Baxter Algebras.