Search results for: generalized anti-reflexive matrix

Authors: Xing-Jian Li, Shen Qu

Abstract:

The Smith arithmetic determinant is investigated in this paper. By using two different methods, we derive the explicit formula for the Smith arithmetic determinant.

Keywords: Elementary row transformation, Euler function, Matrix decomposition, Smith arithmetic determinant.

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Authors: G.Mehdiyeva, M.Imanova, V.Ibrahimov

Abstract:

Beginning from the creator of integro-differential equations Volterra, many scientists have investigated these equations. Classic method for solving integro-differential equations is the quadratures method that is successfully applied up today. Unlike these methods, Makroglou applied hybrid methods that are modified and generalized in this paper and applied to the numerical solution of Volterra integro-differential equations. The way for defining the coefficients of the suggested method is also given.

Keywords: Integro-differential equations, initial value problem, hybrid methods, predictor-corrector method

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Authors: Alireza Gholami, Amir H. D. Markazi

Abstract:

In this paper, an observer-based direct adaptive fuzzy sliding mode (OAFSM) algorithm is proposed. In the proposed algorithm, the zero-input dynamics of the plant could be unknown. The input connection matrix is used to combine the sliding surfaces of individual subsystems, and an adaptive fuzzy algorithm is used to estimate an equivalent sliding mode control input directly. The fuzzy membership functions, which were determined by time consuming try and error processes in previous works, are adjusted by adaptive algorithms. The other advantage of the proposed controller is that the input gain matrix is not limited to be diagonal, i.e. the plant could be over/under actuated provided that controllability and observability are preserved. An observer is constructed to directly estimate the state tracking error, and the nonlinear part of the observer is constructed by an adaptive fuzzy algorithm. The main advantage of the proposed observer is that, the measured outputs is not limited to the first entry of a canonical-form state vector. The closed-loop stability of the proposed method is proved using a Lyapunov-based approach. The proposed method is applied numerically on a multi-link robot manipulator, which verifies the performance of the closed-loop control. Moreover, the performance of the proposed algorithm is compared with some conventional control algorithms.

Keywords: Adaptive algorithm, fuzzy systems, membership functions, observer.

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Authors: Dhairya Partap Sing, Vikram Singh, Sudhir Kumar

Abstract:

This investigation proposes Friction stir welding technique to solve the fusion welding problems. Objectives of this investigation are fabrication of AA7075-10%wt. Silicon carbide (SiC) aluminum metal matrix composite and optimization of optimal process parameters of friction stir welded AA7075-10%wt. SiC Composites. Composites were prepared by the mechanical stir casting process. Experiments were performed with four process parameters such as tool rotational speed, weld speed, axial force and tool geometry considering three levels of each. The quality characteristics considered is joint efficiency (JE). The welding experiments were conducted using L₂₇ orthogonal array. An orthogonal array and design of experiments were used to give best possible welding parameters that give optimal JE. The fabricated welded joints using rotational speed of 1500 rpm, welding speed (1.3 mm/sec), axial force (7 k/n) of and tool geometry (square) give best possible results. Experimental result reveals that the tool rotation speed, welding speed and axial force are the significant process parameters affecting the welding performance. The predicted optimal value of percentage JE is 95.621. The confirmation tests also have been done for verifying the results.

Keywords: Metal matrix composite, axial force, joint efficiency, rotational speed, traverse speed, tool geometry.

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Authors: Chiung-Hui Chen

Abstract:

With advancements in science and technology, the concept of the Internet of Things (IoT) has gradually developed. The development of the intelligent environment adds intelligence to objects in the living space by using the IoT. In the smart environment, when multiple users share the living space, if different service requirements from different users arise, then the context-aware system will have conflicting situations for making decisions about providing services. Therefore, the purpose of establishing a communication and negotiation mechanism among objects in the intelligent environment is to resolve those service conflicts among users. This study proposes developing a decision-making methodology that uses “Event Agents” as its core. When the sensor system receives information, it evaluates a user’s current events and conditions; analyses object, location, time, and environmental information; calculates the priority of the object; and provides the user services based on the event. Moreover, when the event is not single but overlaps with another, conflicts arise. This study adopts the “Multiple Events Correlation Matrix” in order to calculate the degree values of incidents and support values for each object. The matrix uses these values as the basis for making inferences for system service, and to further determine appropriate services when there is a conflict.

Keywords: Internet of things, intelligent object, event agents, negotiation mechanism, degree of similarity.

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Authors: Jai Raj, Jito Vanualailai, Bibhya Sharma, Shonal Singh

Abstract:

This paper proposes a solution to the motion planning and control problem of car-like mobile robots which is required to move safely to a designated target in a priori known workspace cluttered with swarm of boids exhibiting collective emergent behaviors. A generalized algorithm for target convergence and swarm avoidance is proposed that will work for any number of swarms. The control laws proposed in this paper also ensures practical stability of the system. The effectiveness of the proposed control laws are demonstrated via computer simulations of an emergent behavior.

Keywords: Swarm, practical stability, motion planning, emergent.

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Authors: Lv Yuhua

Abstract:

In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Cone, fixed point index, eigenvalue problem, p-Laplace operator, positive solutions.

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Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

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In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. Two numerical examples are presented to illustrate the validity of the main results.

Keywords: Gronwall-Bellman-Type integral inequalities, integrodifferential equation, p-exponentially stable, mixed delays.

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.

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Authors: Esma Gizem Daskiran, Mehmet Mustafa Daskiran, Mustafa Gencoglu

Abstract:

Textile reinforced cementitious composite (TRCC) is a development of a composite material where textile and fine-grained concrete (matrix) materials are used in combination. These matrices offer high performance properties in many aspects. To achieve high performance, polymer modified fine-grained concretes were used as matrix material which have high flexural strength. In this study, ten latex polymers and ten powder polymers were added to fine-grained concrete mixtures. These latex and powder polymers were added to the mixtures at different rates related to binder weight. Mechanical properties such as compressive and flexural strength were studied. Results showed that latex polymer and redispersible polymer modified fine-grained concretes showed different mechanical performance. A wide range of both latex and redispersible powder polymers were studied. As the addition rate increased compressive strength decreased for all mixtures. Flexural strength increased as the addition rate increased but significant enhancement was not observed through all mixtures.

Keywords: Textile reinforced composite, cement, fine grained concrete, latex, redispersible powder.

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Authors: Miin-Shen Yang, Yee-Shan Pan

Abstract:

Although there have been many researches in cluster analysis to consider on feature weights, little effort is made on sample weights. Recently, Yu et al. (2011) considered a probability distribution over a data set to represent its sample weights and then proposed sample-weighted clustering algorithms. In this paper, we give a sample-weighted version of generalized fuzzy clustering regularization (GFCR), called the sample-weighted GFCR (SW-GFCR). Some experiments are considered. These experimental results and comparisons demonstrate that the proposed SW-GFCR is more effective than the most clustering algorithms.

Keywords: Clustering; fuzzy c-means, fuzzy clustering, sample weights, regularization.

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Authors: Da-Xue Chen, Guang-Hui Liu

Abstract:

In this paper, we study the oscillation of a class of second-order nonlinear neutral damped variable delay dynamic equations on time scales. By using a generalized Riccati transformation technique, we obtain some sufficient conditions for the oscillation of the equations. The results of this paper improve and extend some known results. We also illustrate our main results with some examples.

Keywords: Oscillation theorem, second-order nonlinear neutral dynamic equation, variable delay, damping, Riccati transformation.

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Authors: Jui-Sheng Lin, Yi-Sung Yang, Meei-Ling Hung, Teh-Lu Liao, Jun-Juh Yan

Abstract:

The global chaos synchronization for a class of time-delayed power systems is investigated via observer-based approach. By employing the concepts of quadratic stability theory and generalized system model, a new sufficient criterion for constructing an observer is deduced. In contrast to the previous works, this paper proposes a theoretical and systematic design procedure to realize chaos synchronization for master-slave power systems. Finally, an illustrative example is given to show the applicability of the obtained scheme.

Keywords: Chaos, Synchronization, Quadratic stability theory, Observer

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Authors: Dursun Aydın, Bilgin Senel

Abstract:

In this paper, the sum of squares in linear regression is reduced to sum of squares in semi-parametric regression. We indicated that different sums of squares in the linear regression are similar to various deviance statements in semi-parametric regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the semi-parametric regression model. Then, it is made an application in order to support the theory of the linear regression and semi-parametric regression. In this way, study is supported with a simulated data example.

Keywords: Semi-parametric regression, Penalized LeastSquares, Residuals, Deviance, Smoothing Spline.

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Authors: Fotis N. Koumboulis, Michael G. Skarpetis, Maria P. Tzamtzi

Abstract:

The problem of robust disturbance rejection (RDR) using a proportional state feedback controller is studied for the case of Left Invertible MIMO generalized state space linear systems with nonlinear uncertain structure. Sufficient conditions for the problem to have a solution are established. The set of all proportional feedback controllers solving the problem subject to these conditions is analytically determined.

Keywords: System theory, uncertain systems, robust control, singular systems.

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.

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Authors: K. A. D. N. K Wimalawarne

Abstract:

In this paper we introduce a novel kernel classifier based on a iterative shrinkage algorithm developed for compressive sensing. We have adopted Bregman iteration with soft and hard shrinkage functions and generalized hinge loss for solving l1 norm minimization problem for classification. Our experimental results with face recognition and digit classification using SVM as the benchmark have shown that our method has a close error rate compared to SVM but do not perform better than SVM. We have found that the soft shrinkage method give more accuracy and in some situations more sparseness than hard shrinkage methods.

Keywords: Compressive sensing, Bregman iteration, Generalisedhinge loss, sparse, kernels, shrinkage functions

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Authors: Dezhi Liu

Abstract:

In the paper, based on stochastic analysis theory and Lyapunov functional method, we discuss the mean square stability of impulsive stochastic delay differential equations with markovian switching and poisson jumps, and the sufficient conditions of mean square stability have been obtained. One example illustrates the main results. Furthermore, some well-known results are improved and generalized in the remarks.

Keywords: Impulsive, stochastic, delay, Markovian switching, Poisson jumps, mean square stability.

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Authors: Takeru YOKOI, Hidekazu YANAGIMOTO, Sigeru OMATU

Abstract:

We have proposed an information filtering system using index word selection from a document set based on the topics included in a set of documents. This method narrows down the particularly characteristic words in a document set and the topics are obtained by Sparse Non-negative Matrix Factorization. In information filtering, a document is often represented with the vector in which the elements correspond to the weight of the index words, and the dimension of the vector becomes larger as the number of documents is increased. Therefore, it is possible that useless words as index words for the information filtering are included. In order to address the problem, the dimension needs to be reduced. Our proposal reduces the dimension by selecting index words based on the topics included in a document set. We have applied the Sparse Non-negative Matrix Factorization to the document set to obtain these topics. The filtering is carried out based on a centroid of the learning document set. The centroid is regarded as the user-s interest. In addition, the centroid is represented with a document vector whose elements consist of the weight of the selected index words. Using the English test collection MEDLINE, thus, we confirm the effectiveness of our proposal. Hence, our proposed selection can confirm the improvement of the recommendation accuracy from the other previous methods when selecting the appropriate number of index words. In addition, we discussed the selected index words by our proposal and we found our proposal was able to select the index words covered some minor topics included in the document set.

Keywords: Information Filtering, Sparse NMF, Index wordSelection, User Profile, Chi-squared Measure

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Authors: M. M. Morgham, A. A. Hameda, N. A. Zriba, H. A. Jawan

Abstract:

This paper aims to study the effect of cold work condition on the microstructure of Cu-1.5wt%Ti, and Cu-3.5wt%Ti and hence mechanical properties. The samples under investigation were machined, and solution heat treated. X-ray diffraction technique is used to identify the different phases present after cold deformation by compression and also different heat treatment and also measuring the relative quantities of phases present. The metallographic examination is used to study the microstructure of the samples. The hardness measurements were used to indicate the change in mechanical properties. The results are compared with the mechanical properties obtained by previous workers. Experiments on cold compression followed by aging of Cu-Ti alloys have indicated that the most efficient hardening of the material results from continuous precipitation of very fine particles within the matrix. These particles were reported to be β`-type, Cu4Ti phase. The β`-β transformation and particles coarsening within the matrix as well as long grain boundaries were responsible for the overaging of Cu-1.5wt%Ti and Cu-3.5wt%Ti alloys. It is well known that plate-like particles are β – type, Cu3Ti phase. Discontinuous precipitation was found to start at the grain boundaries and expand into grain interior. At the higher aging temperature, a classic Widmanstätten morphology forms giving rise to a coarse microstructure comprised of α and the equilibrium phase β. Those results were confirmed by X-ray analysis, which found that a few percent of Cu3Ti, β precipitates are formed during aging at high temperature for long time for both Cu- Ti alloys (i.e. Cu-1.5wt%Ti and Cu-3.5wt%Ti).

Keywords: Metallographic, hardness, precipitation, aging.

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Authors: J. Mahanta, P.K. Das

Abstract:

A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets. Alongwith the study of fundamental results of such closed sets, we define and characterize fuzzy weakly compact space and fuzzy weakly closed space.

Keywords: Fuzzy weakly-closed set, fuzzy weakly-closed space, fuzzy weakly-compactness, MSC: 54A40, 54D30.

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Authors: Muhammad Shahid, Muhammad Mansoor

Abstract:

Increasing demands of contemporary applications for high strength and lightweight materials prompted the development of metal-matrix composites (MMCs). After the discovery of carbon nanotubes (CNTs) in 1991 (revealing an excellent set of mechanical properties) became one of the most promising strengthening materials for MMC applications. Additionally, the relatively low density of the nanotubes imparted high specific strengths, making them perfect strengthening material to reinforce MMCs. In the present study, aluminum-multiwalled carbon nanotubes (Al-MWCNTs) composite was prepared in an air induction furnace. The dispersion of the nanotubes in molten aluminum was assisted by inherent string action of induction heating at 790°C. During the fabrication process, multifunctional fluxes were used to avoid oxidation of the nanotubes and molten aluminum. Subsequently, the melt was cast in to a copper mold and cold rolled to 0.5 mm thickness. During metallographic examination using a scanning electron microscope, it was observed that the nanotubes were effectively dispersed in the matrix. The mechanical properties of the composite were significantly increased as compared to pure aluminum specimen i.e. the yield strength from 65 to 115 MPa, the tensile strength from 82 to 125 MPa and hardness from 27 to 30 HV for pure aluminum and Al-CNTs composite, respectively. To recognize the associated strengthening mechanisms in the nanocomposites, three foremost strengthening models i.e. shear lag model, Orowan looping and Hall-Petch have been critically analyzed; experimental data were found to be closely satisfying the shear lag model.

Keywords: Carbon nanotubes, induction melting, nanocomposite, strengthening mechanism.

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Authors: R. AliMohammadzadeh, M. Rahgozar, A. Zarnani

Abstract:

The inherent flexibilities of XML in both structure and semantics makes mining from XML data a complex task with more challenges compared to traditional association rule mining in relational databases. In this paper, we propose a new model for the effective extraction of generalized association rules form a XML document collection. We directly use frequent subtree mining techniques in the discovery process and do not ignore the tree structure of data in the final rules. The frequent subtrees based on the user provided support are split to complement subtrees to form the rules. We explain our model within multi-steps from data preparation to rule generation.

Keywords: XML, Data Mining, Association Rule Mining.

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Authors: Sidharth Talan, Devendra Kumar Yadav, Yuvraj Singh Rajput, Subhajit Bhattacharjee

Abstract:

Mining industry is known for its appetite to spend sizeable capital on mine equipment. However, in the current scenario, the mining industry is challenged by daunting factors of non-uniform geological conditions, uneven ore grade, uncontrollable and volatile mineral commodity prices and the ever increasing quest to optimize the capital and operational costs. Thus, the role of equipment reliability and maintenance planning inherits a significant role in augmenting the equipment availability for the operation and in turn boosting the mine productivity. This paper presents the Risk Based Maintenance (RBM) planning conducted on mine loading equipment namely Load Haul Dumpers (LHDs) at Vedanta Resources Ltd subsidiary Hindustan Zinc Limited operated Sindesar Khurd Mines, an underground zinc and lead mine situated in Dariba, Rajasthan, India. The mining equipment at the location is maintained by the Original Equipment Manufacturers (OEMs) namely Sandvik and Atlas Copco, who carry out the maintenance and inspection operations for the equipment. Based on the downtime data extracted for the equipment fleet over the period of 6 months spanning from 1^st January 2017 until 30^th June 2017, it was revealed that significant contribution of three downtime issues related to namely Engine, Hydraulics, and Transmission to be common among all the loading equipment fleet and substantiated by Pareto Analysis. Further scrutiny through Bubble Matrix Analysis of the given factors revealed the major influence of selective factors namely Overheating, No Load Taken (NTL) issues, Gear Changing issues and Hose Puncture and leakage issues. Utilizing the equipment wise analysis of all the downtime factors obtained, spares consumed, and the alarm logs extracted from the machines, technical design changes in the equipment and pre shift critical alarms checklist were proposed for the equipment maintenance. The given analysis is beneficial to allow OEMs or mine management to focus on the critical issues hampering the reliability of mine equipment and design necessary maintenance strategies to mitigate them.

Keywords: Bubble matrix analysis, LHDs, OEMs, pareto chart analysis, spares consumption matrix, critical alarms checklist.

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Authors: A. Gürses, T. B. Barın, Ç. Doğar

Abstract:

Bitumen has been widely used as the binder of aggregate in road pavement due to its good viscoelastic properties, as a viscous organic mixture with various chemical compositions. Bitumen is a liquid at high temperature and it becomes brittle at low temperatures, and this temperature-sensitivity can cause the rutting and cracking of the pavement and limit its application. Therefore, the properties of existing asphalt materials need to be enhanced. The pavement with polymer modified bitumen exhibits greater resistance to rutting and thermal cracking, decreased fatigue damage, as well as stripping and temperature susceptibility; however, they are expensive and their applications have disadvantages. Bituminous mixtures are composed of very irregular aggregates bound together with hydrocarbon-based asphalt, with a low volume fraction of voids dispersed within the matrix. Montmorillonite (MMT) is a layered silicate with low cost and abundance, which consists of layers of tetrahedral silicate and octahedral hydroxide sheets. Recently, the layered silicates have been widely used for the modification of polymers, as well as in many different fields. However, there are not too much studies related with the preparation of the modified asphalt with MMT, currently. In this study, organo-clay-modified bitumen, and calcareous aggregate and organo-clay blends were prepared by hot blending method with OMMT, which has been synthesized using a cationic surfactant (Cetyltrymethylammonium bromide, CTAB) and long chain hydrocarbon, and MMT. When the exchangeable cations in the interlayer region of pristine MMT were exchanged with hydrocarbon attached surfactant ions, the MMT becomes organophilic and more compatible with bitumen. The effects of the super hydrophobic OMMT onto the micro structural and mechanic properties (Marshall Stability and volumetric parameters) of the prepared blends were investigated. Stability and volumetric parameters of the blends prepared were measured using Marshall Test. Also, in order to investigate the morphological and micro structural properties of the organo-clay-modified bitumen and calcareous aggregate and organo-clay blends, their SEM and HRTEM images were taken. It was observed that the stability and volumetric parameters of the prepared mixtures improved significantly compared to the conventional hot mixes and even the stone matrix mixture. A micro structural analysis based on SEM images indicates that the organo-clay platelets dispersed in the bitumen have a dominant role in the increase of effectiveness of bitumen - aggregate interactions.

Keywords: Hot mix asphalt, stone matrix asphalt, organo clay, Marshall Test, calcareous aggregate, modified bitumen.

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Authors: Sunitha. S.L., V. Udayashankara

Abstract:

Background noise is particularly damaging to speech intelligibility for people with hearing loss especially for sensorineural loss patients. Several investigations on speech intelligibility have demonstrated sensorineural loss patients need 5-15 dB higher SNR than the normal hearing subjects. This paper describes Discrete Cosine Transform Power Normalized Least Mean Square algorithm to improve the SNR and to reduce the convergence rate of the LMS for Sensory neural loss patients. Since it requires only real arithmetic, it establishes the faster convergence rate as compare to time domain LMS and also this transformation improves the eigenvalue distribution of the input autocorrelation matrix of the LMS filter. The DCT has good ortho-normal, separable, and energy compaction property. Although the DCT does not separate frequencies, it is a powerful signal decorrelator. It is a real valued function and thus can be effectively used in real-time operation. The advantages of DCT-LMS as compared to standard LMS algorithm are shown via SNR and eigenvalue ratio computations. . Exploiting the symmetry of the basis functions, the DCT transform matrix [AN] can be factored into a series of ±1 butterflies and rotation angles. This factorization results in one of the fastest DCT implementation. There are different ways to obtain factorizations. This work uses the fast factored DCT algorithm developed by Chen and company. The computer simulations results show superior convergence characteristics of the proposed algorithm by improving the SNR at least 10 dB for input SNR less than and equal to 0 dB, faster convergence speed and better time and frequency characteristics.

Keywords: Hearing Impairment, DCT Adaptive filter, Sensorineural loss patients, Convergence rate.

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Authors: Minghui Wang, Shanrui Hu

Abstract:

An inverse problem of doubly center matrices is discussed. By translating the constrained problem into unconstrained problem, two iterative methods are proposed. A numerical example illustrate our algorithms.

Keywords: doubly center matrix, electric network theory, iterative methods, least-square problem.

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Authors: Hari Singh, Abhishek Kamboj, Sudhir Kumar

Abstract:

This investigation proposes a grey-based Taguchi method to solve the multi-response problems. The grey-based Taguchi method is based on the Taguchi’s design of experimental method, and adopts grey relational analysis (GRA) to transfer multi-response problems into single-response problems. In this investigation, an attempt has been made to optimize the drilling process parameters considering weighted output response characteristics using grey relational analysis. The output response characteristics considered are surface roughness, burr height and hole diameter error under the experimental conditions of cutting speed, feed rate, step angle, and cutting environment. The drilling experiments were conducted using L27 orthogonal array. A combination of orthogonal array, design of experiments and grey relational analysis was used to ascertain best possible drilling process parameters that give minimum surface roughness, burr height and hole diameter error. The results reveal that combination of Taguchi design of experiment and grey relational analysis improves surface quality of drilled hole. 

Keywords: Metal matrix composite, Drilling, Optimization, step drill, Surface roughness, burr height, hole diameter error.

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Authors: Khidir R. Sharaf, Didar A. Ali

Abstract:

The nullity η(G) of a graph is the occurrence of zero as an eigenvalue in its spectra. A zero-sum weighting of a graph G is real valued function, say f from vertices of G to the set of real numbers, provided that for each vertex of G the summation of the weights f(w) over all neighborhood w of v is zero for each v in G.A high zero-sum weighting of G is one that uses maximum number of non-zero independent variables. If G is graph with an end vertex, and if H is an induced subgraph of G obtained by deleting this vertex together with the vertex adjacent to it, then, η(G)= η(H). In this paper, a high zero-sum weighting technique and the endvertex procedure are applied to evaluate the nullity of t-tupple and generalized t-tupple graphs are derived  and determined for some special types of graphs,

 Also, we introduce and prove some important results about the t-tupple coalescence, Cartesian and Kronecker products of nut graphs.

Keywords: Graph theory, Graph spectra, Nullity of graphs.

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Authors: Ram Kumar Soni, Alok Jain, Rajiv Saxena

Abstract:

The tree structured approach of non-uniform filterbank (NUFB) is normally used in perfect reconstruction (PR). The PR is not always feasible due to certain limitations, i.e, constraints in selecting design parameters, design complexity and some times output is severely affected by aliasing error if necessary and sufficient conditions of PR is not satisfied perfectly. Therefore, there has been generalized interest of researchers to go for near perfect reconstruction (NPR). In this proposed work, an optimized tree structure technique is used for the design of NPR non-uniform filterbank. Window functions of Blackman family are used to design the prototype FIR filter. A single variable linear optimization is used to minimize the amplitude distortion. The main feature of the proposed design is its simplicity with linear phase property.

Keywords: Tree structure, NUFB, QMF, NPR.

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