Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 8768

Search results for: finite group

8768 Characterization of Number of Subgroups of Finite Groups

Authors: Khyati Sharma, A. Satyanarayana Reddy


The topic of how many subgroups exist within a certain finite group naturally arises in the study of finite groups. Over the years, different researchers have investigated this issue from a variety of angles. The significant contributions of the key mathematicians over the time have been summarized in this article. To this end, we classify finite groups into three categories viz. (a) Groups for which the number of subgroups is less than |G|, (b) equals to |G|, and finally, (c) greater than |G|. Because every element of a finite group generates a cyclic subgroup, counting cyclic subgroups is the most important task in this endeavor. A brief survey on the number of cyclic subgroups of finite groups is also conducted by us. Furthermore, we also covered certain arithmetic relations between the order of a finite group |G| and the number of its distinct cyclic subgroups |C(G)|. In order to provide pertinent context and possibly reveal new novel areas of potential research within the field of research on finite groups, we finally pose and solicit a few open questions.

Keywords: abstract algebra, cyclic subgroup, finite group, subgroup

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8767 Noncommutative Differential Structure on Finite Groups

Authors: Ibtisam Masmali, Edwin Beggs


In this paper, we take example of differential calculi, on the finite group A4. Then, we apply methods of non-commutative of non-commutative differential geometry to this example, and see how similar the results are to those of classical differential geometry.

Keywords: differential calculi, finite group A4, Christoffel symbols, covariant derivative, torsion compatible

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8766 An Attack on the Lucas Based El-Gamal Cryptosystem in the Elliptic Curve Group Over Finite Field Using Greater Common Divisor

Authors: Lee Feng Koo, Tze Jin Wong, Pang Hung Yiu, Nik Mohd Asri Nik Long


Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.

Keywords: decryption, encryption, elliptic curve, greater common divisor

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8765 New High Order Group Iterative Schemes in the Solution of Poisson Equation

Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali


We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: explicit group iterative method, finite difference, fourth order compact, Poisson equation

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8764 A Comparative Study of High Order Rotated Group Iterative Schemes on Helmholtz Equation

Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping


In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: explicit group method, finite difference, helmholtz equation, rotated grid, standard grid

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8763 New Fourth Order Explicit Group Method in the Solution of the Helmholtz Equation

Authors: Norhashidah Hj Mohd Ali, Teng Wai Ping


In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two-dimensional Helmholtz equation. The formulation is based on the nine-point fourth-order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula

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8762 3 Dimensions Finite Element Analysis of Tunnel-Pile Interaction Scenarios Using Abaqus Software

Authors: Haitham J. M. Odeh


This paper introduced an analysis of the effect of tunneling near pile foundations. Accomplished by three-dimensional finite element modeling. The numerical simulation is conducted using Abaqus finite element software. By examining different Tunnel-pile scenarios. The paper presents the tunnel induced pile responses, Such as pile settlement, pile internal forces, and the comments made on changing the vertical and transversal location of the tunnel related to the piles, the study contains two pile-supported structure cases, single and a group of piles. A comprehensive comparison between real case study results and numerical simulation is presented. The results of the analysis reveal the critical and safe location of tunnel construction and the positive effect of a group of piles existing instead of single piles. Also, demonstrates the changes in pile responses by changing the tunnel location.

Keywords: pile responses, single pile, group of piles, pile-tunnel interaction

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8761 Sensitivity to Misusing Verb Inflections in Both Finite and Non-Finite Clauses in Native and Non-Native Russian: A Self-Paced Reading Investigation

Authors: Yang Cao


Analyzing the oral production of Chinese-speaking learners of English as a second language (L2), we can find a large variety of verb inflections – Why does it seem so hard for them to use consistent correct past morphologies in obligatory past contexts? Failed Functional Features Hypothesis (FFFH) attributes the rather non-target-like performance to the absence of [±past] feature in their L1 Chinese, arguing that for post puberty learners, new features in L2 are no more accessible. By contrast, Missing Surface Inflection Hypothesis (MSIH) tends to believe that all features are actually acquirable for late L2 learners, while due to the mapping difficulties from features to forms, it is hard for them to realize the consistent past morphologies on the surface. However, most of the studies are limited to the verb morphologies in finite clauses and few studies have ever attempted to figure out these learners’ performance in non-finite clauses. Additionally, it has been discussed that Chinese learners may be able to tell the finite/infinite distinction (i.e. the [±finite] feature might be selected in Chinese, even though the existence of [±past] is denied). Therefore, adopting a self-paced reading task (SPR), the current study aims to analyze the processing patterns of Chinese-speaking learners of L2 Russian, in order to find out if they are sensitive to misuse of tense morphologies in both finite and non-finite clauses and whether they are sensitive to the finite/infinite distinction presented in Russian. The study targets L2 Russian due to its systematic morphologies in both present and past tenses. A native Russian group, as well as a group of English-speaking learners of Russian, whose L1 has definitely selected both [±finite] and [±past] features, will also be involved. By comparing and contrasting performance of the three language groups, the study is going to further examine and discuss the two theories, FFFH and MSIH. Preliminary hypotheses are: a) Russian native speakers are expected to spend longer time reading the verb forms which violate the grammar; b) it is expected that Chinese participants are, at least, sensitive to the misuse of inflected verbs in non-finite clauses, although no sensitivity to the misuse of infinitives in finite clauses might be found. Therefore, an interaction of finite and grammaticality is expected to be found, which indicate that these learners are able to tell the finite/infinite distinction; and c) having selected [±finite] and [±past], English-speaking learners of Russian are expected to behave target-likely, supporting L1 transfer.

Keywords: features, finite clauses, morphosyntax, non-finite clauses, past morphologies, present morphologies, Second Language Acquisition, self-paced reading task, verb inflections

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8760 Finite Element Analysis of Rom Silo Subjected to 5000 Tons Monotic Loads at an Anonymous Mine in Zimbabwe

Authors: T. Mushiri, K. Tengende, C. Mbohwa, T. Garikayi


This paper introduces finite element analysis of Run off Mine (ROM) silo subjected to dynamic loading. The proposed procedure is based on the use of theoretical equations to come up with pressure and forces exerted by Platinum Group Metals (PGMs) ore to the silo wall. Finite Element Analysis of the silo involves the use of CAD software (AutoCAD) for3D creation and CAE software (T-FLEX) for the simulation work with an optimization routine to minimize the mass and also ensure structural stiffness and stability. In this research an efficient way to design and analysis of a silo in 3D T-FLEX (CAD) program was created the silo to stay within the constrains and so as to know the points of failure due dynamic loading.

Keywords: reinforced concrete silo, finite element analysis, T-FLEX software, AutoCAD

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8759 Circular Raft Footings Strengthened by Stone Columns under Dynamic Harmonic Loads

Authors: R. Ziaie Moayed, A. Mahigir


Stone column technique has been successfully employed to improve the load-settlement characteristics of foundations. A series of finite element numerical analyses of harmonic dynamic loading have been conducted on strengthened raft footing to study the effects of single and group stone columns on settlement of circular footings. The settlement of circular raft footing that improved by single and group of stone columns are studied under harmonic dynamic loading. This loading is caused by heavy machinery foundations. A detailed numerical investigation on behavior of single column and group of stone columns is carried out by varying parameters like weight of machinery, loading frequency and period. The result implies that presence of single and group of stone columns enhanced dynamic behavior of the footing so that the maximum and residual settlement of footing significantly decreased. 

Keywords: finite element analysis, harmonic loading, settlement, stone column

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8758 A United Nations Safety Compliant Urban Vehicle Design

Authors: Marcelo R. G. Duarte, Marcilio Alves


Pedestrians are the fourth group among road traffic users that most suffer accidents. Their death rate is even higher than the motorcyclists group. This gives motivation for the development of an urban vehicle capable of complying with the United Nations Economic Commission for Europe pedestrian regulations. The conceptual vehicle is capable of transporting two passengers and small parcels for 100 km at a maximum speed of 90 km/h. This paper presents the design of this vehicle using the finite element method specially in connection with frontal crash test and car to pedestrian collision. The simulation is based in a human body FE.

Keywords: electric urban vehicle, finite element method, global human body model, pedestrian safety, road safety

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8757 Study on 3D FE Analysis on Normal and Osteoporosis Mouse Models Based on 3-Point Bending Tests

Authors: Tae-min Byun, Chang-soo Chon, Dong-hyun Seo, Han-sung Kim, Bum-mo Ahn, Hui-suk Yun, Cheolwoong Ko


In this study, a 3-point bending computational analysis of normal and osteoporosis mouse models was performed based on the Micro-CT image information of the femurs. The finite element analysis (FEA) found 1.68 N (normal group) and 1.39 N (osteoporosis group) in the average maximum force, and 4.32 N/mm (normal group) and 3.56 N/mm (osteoporosis group) in the average stiffness. In the comparison of the 3-point bending test results, the maximum force and the stiffness were different about 9.4 times in the normal group and about 11.2 times in the osteoporosis group. The difference between the analysis and the test was greatly significant and this result demonstrated improvement points of the material properties applied to the computational analysis of this study. For the next study, the material properties of the mouse femur will be supplemented through additional computational analysis and test.

Keywords: 3-point bending test, mouse, osteoporosis, FEA

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8756 Effect of pH-Dependent Surface Charge on the Electroosmotic Flow through Nanochannel

Authors: Partha P. Gopmandal, Somnath Bhattacharyya, Naren Bag


In this article, we have studied the effect of pH-regulated surface charge on the electroosmotic flow (EOF) through nanochannel filled with binary symmetric electrolyte solution. The channel wall possesses either an acidic or a basic functional group. Going beyond the widely employed Debye-Huckel linearization, we develop a mathematical model based on Nernst-Planck equation for the charged species, Poisson equation for the induced potential, Stokes equation for fluid flow. A finite volume based numerical algorithm is adopted to study the effect of key parameters on the EOF. We have computed the coupled governing equations through the finite volume method and our results found to be in good agreement with the analytical solution obtained from the corresponding linear model based on low surface charge condition or strong electrolyte solution. The influence of the surface charge density, reaction constant of the functional groups, bulk pH, and concentration of the electrolyte solution on the overall flow rate is studied extensively. We find the effect of surface charge diminishes with the increase in electrolyte concentration. In addition for strong electrolyte, the surface charge becomes independent of pH due to complete dissociation of the functional groups.

Keywords: electroosmosis, finite volume method, functional group, surface charge

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8755 Regularity and Maximal Congruence in Transformation Semigroups with Fixed Sets

Authors: Chollawat Pookpienlert, Jintana Sanwong


An element a of a semigroup S is called left (right) regular if there exists x in S such that a=xa² (a=a²x) and said to be intra-regular if there exist u,v in such that a=ua²v. Let T(X) be the semigroup of all full transformations on a set X under the composition of maps. For a fixed nonempty subset Y of X, let Fix(X,Y)={α ™ T(X) : yα=y for all y ™ Y}, where yα is the image of y under α. Then Fix(X,Y) is a semigroup of full transformations on X which fix all elements in Y. Here, we characterize left regular, right regular and intra-regular elements of Fix(X,Y) which characterizations are shown as follows: For α ™ Fix(X,Y), (i) α is left regular if and only if Xα\Y = Xα²\Y, (ii) α is right regular if and only if πα = πα², (iii) α is intra-regular if and only if | Xα\Y | = | Xα²\Y | such that Xα = {xα : x ™ X} and πα = {xα⁻¹ : x ™ Xα} in which xα⁻¹ = {a ™ X : aα=x}. Moreover, those regularities are equivalent if Xα\Y is a finite set. In addition, we count the number of those elements of Fix(X,Y) when X is a finite set. Finally, we determine the maximal congruence ρ on Fix(X,Y) when X is finite and Y is a nonempty proper subset of X. If we let | X \Y | = n, then we obtain that ρ = (Fixn x Fixn) ∪ (H ε x H ε) where Fixn = {α ™ Fix(X,Y) : | Xα\Y | < n} and H ε is the group of units of Fix(X,Y). Furthermore, we show that the maximal congruence is unique.

Keywords: intra-regular, left regular, maximal congruence, right regular, transformation semigroup

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8754 A Social Decision Support Mechanism for Group Purchasing

Authors: Lien-Fa Lin, Yung-Ming Li, Fu-Shun Hsieh


With the advancement of information technology and development of group commerce, people have obviously changed in their lifestyle. However, group commerce faces some challenging problems. The products or services provided by vendors do not satisfactorily reflect customers’ opinions, so that the sale and revenue of group commerce gradually become lower. On the other hand, the process for a formed customer group to reach group-purchasing consensus is time-consuming and the final decision is not the best choice for each group members. In this paper, we design a social decision support mechanism, by using group discussion message to recommend suitable options for group members and we consider social influence and personal preference to generate option ranking list. The proposed mechanism can enhance the group purchasing decision making efficiently and effectively and venders can provide group products or services according to the group option ranking list.

Keywords: social network, group decision, text mining, group commerce

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8753 The Different Ways to Describe Regular Languages by Using Finite Automata and the Changing Algorithm Implementation

Authors: Abdulmajid Mukhtar Afat


This paper aims at introducing finite automata theory, the different ways to describe regular languages and create a program to implement the subset construction algorithms to convert nondeterministic finite automata (NFA) to deterministic finite automata (DFA). This program is written in c++ programming language. The program reads FA 5tuples from text file and then classifies it into either DFA or NFA. For DFA, the program will read the string w and decide whether it is acceptable or not. If accepted, the program will save the tracking path and point it out. On the other hand, when the automation is NFA, the program will change the Automation to DFA so that it is easy to track and it can decide whether the w exists in the regular language or not.

Keywords: finite automata, subset construction, DFA, NFA

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8752 The Finite Element Method for Nonlinear Fredholm Integral Equation of the Second Kind

Authors: Melusi Khumalo, Anastacia Dlamini


In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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8751 Relevancy Measures of Errors in Displacements of Finite Elements Analysis Results

Authors: A. B. Bolkhir, A. Elshafie, T. K. Yousif


This paper highlights the methods of error estimation in finite element analysis (FEA) results. It indicates that the modeling error could be eliminated by performing finite element analysis with successively finer meshes or by extrapolating response predictions from an orderly sequence of relatively low degree of freedom analysis results. In addition, the paper eliminates the round-off error by running the code at a higher precision. The paper provides application in finite element analysis results. It draws a conclusion based on results of application of methods of error estimation.

Keywords: finite element analysis (FEA), discretization error, round-off error, mesh refinement, richardson extrapolation, monotonic convergence

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8750 A Finite Memory Residual Generation Filter for Fault Detection

Authors: Pyung Soo Kim, Eung Hyuk Lee, Mun Suck Jang


In the current paper, a residual generation filter with finite memory structure is proposed for fault detection. The proposed finite memory residual generation filter provides the residual by real-time filtering of fault vector using only the most recent finite observations and inputs on the window. It is shown that the residual given by the proposed residual generation filter provides the exact fault for noise-free systems. Finally, to illustrate the capability of the proposed residual generation filter, numerical examples are performed for the discretized DC motor system having the multiple sensor faults.

Keywords: residual generation filter, finite memory structure, kalman filter, fast detection

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8749 Disability, Stigma and In-Group Identification: An Exploration across Different Disability Subgroups

Authors: Sharmila Rathee


Individuals with disability/ies often face negative attitudes, discrimination, exclusion, and inequality of treatment due to stigmatization and stigmatized treatment. While a significant number of studies in field of stigma suggest that group-identification has positive consequences for stigmatized individuals, ironically very miniscule empirical work in sight has attempted to investigate in-group identification as a coping measure against stigma, humiliation and related experiences among disability group. In view of death of empirical research on in-group identification among disability group, through present work, an attempt has been made to examine the experiences of stigma, humiliation, and in-group identification among disability group. Results of the study suggest that use of in-group identification as a coping strategy is not uniform across members of disability group and degree of in-group identification differs across different sub-groups of disability groups. Further, in-group identification among members of disability group depends on variables like degree and impact of disability, factors like onset of disability, nature, and visibility of disability, educational experiences and resources available to deal with disabling conditions.

Keywords: disability, stigma, in-group identification, social identity

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8748 Computation of Stress Intensity Factor Using Extended Finite Element Method

Authors: Mahmoudi Noureddine, Bouregba Rachid


In this paper the stress intensity factors of a slant-cracked plate of AISI 304 stainless steel, have been calculated using extended finite element method and finite element method (FEM) in ABAQUS software, the results were compared with theoretical values.

Keywords: stress intensity factors, extended finite element method, stainless steel, abaqus

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8747 Finite Element Method as a Solution Procedure for Problems in Tissue Biomechanics

Authors: Momoh Omeiza Sheidu


Finite element method as a method of providing solutions to problems in computational bio mechanics provides a framework for modeling the function of tissues that integrates structurally from cell to organ system and functionally across the physiological processes that affect tissue mechanics or are regulated by mechanical forces. In this paper, we present an integrative finite element strategy for solution to problems in tissue bio mechanics as a case study.

Keywords: finite element, biomechanics, modeling, computational biomechanics

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8746 A Weighted Group EI Incorporating Role Information for More Representative Group EI Measurement

Authors: Siyu Wang, Anthony Ward


Emotional intelligence (EI) is a well-established personal characteristic. It has been viewed as a critical factor which can influence an individual's academic achievement, ability to work and potential to succeed. When working in a group, EI is fundamentally connected to the group members' interaction and ability to work as a team. The ability of a group member to intelligently perceive and understand own emotions (Intrapersonal EI), to intelligently perceive and understand other members' emotions (Interpersonal EI), and to intelligently perceive and understand emotions between different groups (Cross-boundary EI) can be considered as Group emotional intelligence (Group EI). In this research, a more representative Group EI measurement approach, which incorporates the information of the composition of a group and an individual’s role in that group, is proposed. To demonstrate the claim of being more representative Group EI measurement approach, this study adopts a multi-method research design, involving a combination of both qualitative and quantitative techniques to establish a metric of Group EI. From the results, it can be concluded that by introducing the weight coefficient of each group member on group work into the measurement of Group EI, Group EI will be more representative and more capable of understanding what happens during teamwork than previous approaches.

Keywords: case study, emotional intelligence, group EI, multi-method research

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8745 Using ε Value in Describe Regular Languages by Using Finite Automata, Operation on Languages and the Changing Algorithm Implementation

Authors: Abdulmajid Mukhtar Afat


This paper aims at introducing nondeterministic finite automata with ε value which is used to perform some operations on languages. a program is created to implement the algorithm that converts nondeterministic finite automata with ε value (ε-NFA) to deterministic finite automata (DFA).The program is written in c++ programming language. The program inputs are FA 5-tuples from text file and then classifies it into either DFA/NFA or ε -NFA. For DFA, the program will get the string w and decide whether it is accepted or rejected. The tracking path for an accepted string is saved by the program. In case of NFA or ε-NFA automation, the program changes the automation to DFA to enable tracking and to decide if the string w exists in the regular language or not.

Keywords: DFA, NFA, ε-NFA, eclose, finite automata, operations on languages

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8744 Finite Element Analysis of RC Frames with Retrofitted Infill Walls

Authors: M. Ömer Timurağaoğlu, Adem Doğangün, Ramazan Livaoğlu


The evaluation of performance of infilled reinforced concrete (RC) frames has been a significant challenge for engineers. The strengthening of infill walls has been an important concern to enhance the behavior of RC infilled frames. The aim of this study is to investigate the behaviour of retrofitted infill walls of RC frames using finite element analysis. For this purpose, a one storey, one bay infilled and strengthened infilled RC frame which have the same geometry and material properties with the frames tested in laboratory are modelled using different analytical approaches. A fibrous material is used to strengthen infill walls and frame. As a consequence, the results of the finite element analysis were evaluated of whether these analytical approaches estimate the behavior or not. To model the infilled and strengthened infilled RC frames, a finite element program ABAQUS is used. Finally, data obtained from the nonlinear finite element analysis is compared with the experimental results.

Keywords: finite element analysis, infilled RC frames, infill wall, strengthening

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8743 A Study on Finite Element Modelling of Earth Retaining Wall Anchored by Deadman Anchor

Authors: K. S. Chai, S. H. Chan


In this paper, the earth retaining wall anchored by discrete deadman anchor to support excavations in sand is modelled and analysed by finite element analysis. A study is conducted to examine how deadman anchorage system helps in reducing the deflection of earth retaining wall. A simplified numerical model is suggested in order to reduce the simulation duration. A comparison between 3-D and 2-D finite element analyses is illustrated.

Keywords: finite element, earth retaining wall, deadman anchor, sand

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8742 Finite Sample Inferences for Weak Instrument Models

Authors: Gubhinder Kundhi, Paul Rilstone


It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. Finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap.

Keywords: bootstrap, Instrumental Variable, Edgeworth expansions, Saddlepoint expansions

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8741 Numerical Modelling of Dry Stone Masonry Structures Based on Finite-Discrete Element Method

Authors: Ž. Nikolić, H. Smoljanović, N. Živaljić


This paper presents numerical model based on finite-discrete element method for analysis of the structural response of dry stone masonry structures under static and dynamic loads. More precisely, each discrete stone block is discretized by finite elements. Material non-linearity including fracture and fragmentation of discrete elements as well as cyclic behavior during dynamic load are considered through contact elements which are implemented within a finite element mesh. The application of the model was conducted on several examples of these structures. The performed analysis shows high accuracy of the numerical results in comparison with the experimental ones and demonstrates the potential of the finite-discrete element method for modelling of the response of dry stone masonry structures.

Keywords: dry stone masonry structures, dynamic load, finite-discrete element method, static load

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8740 Quantum Algebra from Generalized Q-Algebra

Authors: Muna Tabuni


The paper contains an investigation of the notion of Q algebras. A brief introduction to quantum mechanics is given, in that systems the state defined by a vector in a complex vector space H which have Hermitian inner product property. H may be finite or infinite-dimensional. In quantum mechanics, operators must be hermitian. These facts are saved by Lie algebra operators but not by those of quantum algebras. A Hilbert space H consists of a set of vectors and a set of scalars. Lie group is a differentiable topological space with group laws given by differentiable maps. A Lie algebra has been introduced. Q-algebra has been defined. A brief introduction to BCI-algebra is given. A BCI sub algebra is introduced. A brief introduction to BCK=BCH-algebra is given. Every BCI-algebra is a BCH-algebra. Homomorphism maps meanings are introduced. Homomorphism maps between two BCK algebras are defined. The mathematical formulations of quantum mechanics can be expressed using the theory of unitary group representations. A generalization of Q algebras has been introduced, and their properties have been considered. The Q- quantum algebra has been studied, and various examples have been given.

Keywords: Q-algebras, BCI, BCK, BCH-algebra, quantum mechanics

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8739 The Control Illusion of Conditioned Superstition

Authors: Chia-Ching Tsai


The study examined the control illusion of conditioned superstition by using Taiwanese subjects. The study had a three-group experimental design, that is, conditioning group and a control group, and the conditioning group was further separated into superstitious and unsuperstitious groups. The results showed that conditioned superstition can significantly influence the control illusion. Further analysis showed that the control illusion in the superstitious conditioning group was significantly greater than in the control group or in the unsuperstitious conditioning group. Besides, there was no significant difference between the control group and the unsuperstitious conditioning group.

Keywords: Control illusion, Conditioned superstition, experimental design

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