Search results for: generalized mean-field theory
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1933

Search results for: generalized mean-field theory

1033 Positive Solutions of Second-order Singular Differential Equations in Banach Space

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for the boundary value problem of second-order singular differential equations in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular equation.

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1032 Failure to Replicate the Unconscious Thought Advantages

Authors: Vladimíra Čavojová, Eva Ballová Mikušková

Abstract:

In this study we tried to replicate the unconscious thought advantage (UTA), which states that complex decisions are better handled by unconscious thinking. We designed an experiment in e-prime using similar material as the original study (choosing between four different apartments, each described by 12 attributes). A total of 73 participants (52 women (71.2%); 18 to 62 age: M=24.63; SD=8.7) took part in the experiment. We did not replicate the results suggested by UTT. However, from the present study we cannot conclude whether this was the case of flaws in the theory or flaws in our experiment and we discuss several ways in which the issue of UTA could be examined further.

Keywords: Decision making, unconscious thoughts, UTT.

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1031 Improving Topic Quality of Scripts by Using Scene Similarity Based Word Co-Occurrence

Authors: Yunseok Noh, Chang-Uk Kwak, Sun-Joong Kim, Seong-Bae Park

Abstract:

Scripts are one of the basic text resources to understand broadcasting contents. Topic modeling is the method to get the summary of the broadcasting contents from its scripts. Generally, scripts represent contents descriptively with directions and speeches, and provide scene segments that can be seen as semantic units. Therefore, a script can be topic modeled by treating a scene segment as a document. Because scene segments consist of speeches mainly, however, relatively small co-occurrences among words in the scene segments are observed. This causes inevitably the bad quality of topics by statistical learning method. To tackle this problem, we propose a method to improve topic quality with additional word co-occurrence information obtained using scene similarities. The main idea of improving topic quality is that the information that two or more texts are topically related can be useful to learn high quality of topics. In addition, more accurate topical representations lead to get information more accurate whether two texts are related or not. In this paper, we regard two scene segments are related if their topical similarity is high enough. We also consider that words are co-occurred if they are in topically related scene segments together. By iteratively inferring topics and determining semantically neighborhood scene segments, we draw a topic space represents broadcasting contents well. In the experiments, we showed the proposed method generates a higher quality of topics from Korean drama scripts than the baselines.

Keywords: Broadcasting contents, generalized P´olya urn model, scripts, text similarity, topic model.

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1030 Automated Ranking of Hints

Authors: Sylvia Encheva

Abstract:

The importance of hints in an intelligent tutoring system is well understood. The problems however related to their delivering are quite a few. In this paper we propose delivering of hints to be based on considering their usefulness. By this we mean that a hint is regarded as useful to a student if the student has succeeded to solve a problem after the hint was suggested to her/him. Methods from the theory of partial orderings are further applied facilitating an automated process of offering individualized advises on how to proceed in order to solve a particular problem.

Keywords: Decision support services, uncertainty management, partial orderings.

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1029 The Ombudsman: Different Terminologies Same Missions

Authors: Khodr Fakih

Abstract:

The Ombudsman is a procedural mechanism that provides a different approach of dispute resolution. The ombudsman primarily deals with specific grievances from the public against governmental injustice and misconduct. The ombudsman theory is considered an important instrument to any democratic government. This is true since it improves the transparency of the governmental activities in a world in which executive power are rising. Many countries have adopted the concept of Ombudsman but under different terminologies. This paper will provide the different types of Ombudsman and the common activities/processes of fulfilling their mandates.

Keywords: Administration, Citizens, Government, Mediator, Ombudsman, Presidential Mediator.

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1028 Migrant Women English Instructors’ Transformative Workplace Learning Experiences in Post-Secondary English Language Programs in Ontario, Canada

Authors: Justine Jun

Abstract:

This study aims to reveal migrant women English instructors' workplace learning experiences in Canadian post-secondary institutions in Ontario. Migrant women English instructors in higher education are an understudied group of teachers. This study employs a qualitative research paradigm. Mezirow’s Transformative Learning Theory is an essential lens for the researcher to explain, analyze, and interpret the research data. It is a collaborative research project. The researcher and participants cooperatively create photographic or other artwork data responding to the research questions. Photovoice and arts-informed data collection methodology are the main methods. Research participants engage in the study as co-researchers and inquire about their own workplace learning experiences, actively utilizing their critical self-reflective and dialogic skills. Co-researchers individually select the forms of artwork they prefer to engage with to represent their transformative workplace learning experiences about the Canadian workplace cultures that they underwent while working with colleagues and administrators in the workplace. Once the co-researchers generate their cultural artifacts as research data, they collaboratively interpret their artworks with the researcher and other volunteer co-researchers. Co-researchers jointly investigate the themes emerging from the artworks. They also interpret the meanings of their own and others’ workplace learning experiences embedded in the artworks through interactive one-on-one or group interviews. The following are the research questions that the migrant women English instructor participants examine and answer: (1) What have they learned about their workplace culture and how do they explain their learning experiences? (2) How transformative have their learning experiences been at work? (3) How have their colleagues and administrators influenced their transformative learning? (4) What kind of support have they received? What supports have been valuable to them and what changes would they like to see? (5) What have their learning experiences transformed? (6) What has this arts-informed research process transformed? The study findings implicate English language instructor support currently practiced in post-secondary English language programs in Ontario, Canada, especially for migrant women English instructors. This research is a doctoral empirical study in progress. This study has the urgency to address the research problem that few studies have investigated migrant English instructors’ professional learning and support issues in the workplace, precisely that of English instructors working with adult learners in Canada. While appropriate social and professional support for migrant English instructors is required throughout the country, the present workplace realities in Ontario's English language programs need to be heard soon. For that purpose, the conceptualization of this study is crucial. It makes the investigation of under-represented instructors’ under-researched social phenomena, workplace learning and support, viable and rigorous. This paper demonstrates the robust theorization of English instructors’ workplace experiences using Mezirow’s Transformative Learning Theory in the English language teacher education field. 

Keywords: English teacher education, professional learning, transformative learning theory, workplace learning.

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1027 Periodic Solutions for a Delayed Population Model on Time Scales

Authors: Kejun Zhuang, Zhaohui Wen

Abstract:

This paper deals with a delayed single population model on time scales. With the assistance of coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Furthermore, the better estimations for bounds of periodic solutions are established.

Keywords: Coincidence degree, continuation theorem, periodic solutions, time scales

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1026 Positive Solutions for Systems of Nonlinear Third-Order Differential Equations with p-Laplacian

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point theory, we study the existence and multiplicity of the positive solutions for systems of nonlinear third-order differential equations with p-laplacian, which improve and generalize the result of related paper.

Keywords: p-Laplacian, cone, fixed point theorem, positive solution.

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1025 Multiple Criteria Decision Making Analysis for Selecting and Evaluating Fighter Aircraft

Authors: C. Ardil, A. M. Pashaev, R.A. Sadiqov, P. Abdullayev

Abstract:

In this paper, multiple criteria decision making analysis technique, is presented for ranking and selection of a set of determined alternatives - fighter aircraft - which are associated with a set of decision factors. In fighter aircraft design, conflicting decision criteria, disciplines, and technologies are always involved in the design process. Multiple criteria decision making analysis techniques can be helpful to effectively deal with such situations and make wise design decisions. Multiple criteria decision making analysis theory is a systematic mathematical approach for dealing with problems which contain uncertainties in decision making. The feasibility and contributions of applying the multiple criteria decision making analysis technique in fighter aircraft selection analysis is explored. In this study, an integrated framework incorporating multiple criteria decision making analysis technique in fighter aircraft analysis is established using entropy objective weighting method. An improved integrated multiple criteria decision making analysis method is utilized to aggregate the multiple decision criteria into one composite figure of merit, which serves as an objective function in the decision process. Therefore, it is demonstrated that the suitable multiple criteria decision making analysis method with decision solution provides an effective objective function for the decision making analysis. Considering that the inherent uncertainties and the weighting factors have crucial decision impacts on the fighter aircraft evaluation, seven fighter aircraft models for the multiple design criteria in terms of the weighting factors are constructed. The proposed multiple criteria decision making analysis model is based on integrated entropy index procedure, and additive multiple criteria decision making analysis theory. Hence, the applicability of proposed technique for fighter aircraft selection problem is considered. The constructed multiple criteria decision making analysis model can provide efficient decision analysis approach for uncertainty assessment of the decision problem. Consequently, the fighter aircraft alternatives are ranked based their final evaluation scores, and sensitivity analysis is conducted.

Keywords: Fighter Aircraft, Fighter Aircraft Selection, Multiple Criteria Decision Making, Multiple Criteria Decision Making Analysis, MCDMA

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1024 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (III)

Authors: Li Ge

Abstract:

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using Leray-Schauder theory:

Keywords: impulsive differential equations, impulsive integraldifferential equation, boundary value problems

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1023 H∞ Approach to Functional Projective Synchronization for Chaotic Systems with Disturbances

Authors: S. M. Lee, J. H. Park, H. Y. Jung

Abstract:

This paper presents a method for functional projective H∞ synchronization problem of chaotic systems with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) formulation, the novel feedback controller is established to not only guarantee stable synchronization of both drive and response systems but also reduce the effect of external disturbance to an H∞ norm constraint.

Keywords: Chaotic systems, functional projective H∞ synchronization, LMI.

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1022 Generalized Inverse Eigenvalue Problems for Symmetric Arrow-head Matrices

Authors: Yongxin Yuan

Abstract:

In this paper, we first give the representation of the general solution of the following inverse eigenvalue problem (IEP): Given X ∈ Rn×p and a diagonal matrix Λ ∈ Rp×p, find nontrivial real-valued symmetric arrow-head matrices A and B such that AXΛ = BX. We then consider an optimal approximation problem: Given real-valued symmetric arrow-head matrices A, ˜ B˜ ∈ Rn×n, find (A, ˆ Bˆ) ∈ SE such that Aˆ − A˜2 + Bˆ − B˜2 = min(A,B)∈SE (A−A˜2 +B −B˜2), where SE is the solution set of IEP. We show that the optimal approximation solution (A, ˆ Bˆ) is unique and derive an explicit formula for it.

Keywords: Partially prescribed spectral information, symmetric arrow-head matrix, inverse problem, optimal approximation.

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1021 Some Applications of Gröbner bases

Authors: Hassan Noori, Abdolali Basiri, Sajjad Rahmany

Abstract:

In this paper we will introduce a brief introduction to theory of Gr¨obner bases and some applications of Gr¨obner bases to graph coloring problem, automatic geometric theorem proving and cryptography.

Keywords: Gr¨obner bases, Application of Gr¨obner bases, Automatic Geometric Theorem Proving, Graph Coloring, Cryptography.

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1020 Revolutionizing Product Packaging: The Impact of Transparent Graded Lanes on Ketchup and Edible Oil Containers on Consumer Behavior

Authors: Saeid Asghari

Abstract:

The growing interest in sustainability and healthy lifestyles has stimulated the development of solutions that promote mindful consumption and healthier choices. One such solution is the use of transparent graded lanes in product packaging, which enables consumers to visually track their product consumption and encourages portion control. However, the influence of packaging on consumer behavior, trust, and brand loyalty, as well as the effectiveness of messaging on transparent graded lanes, is still not well understood. This research seeks to explore the effects of transparent graded lanes on consumer reactions of the Janbo chain supermarkets in Tehran, Iran, focusing on ketchup and edible oil containers. A representative sample of 720 respondents is selected using quota sampling based on sex, age, and financial status. The study assesses the effect of messaging on the graded lanes in enhancing consumer recall and recognition of the product at the time of purchase, increasing repeated purchases, and fostering long-term relationships with customers. Furthermore, the potential outcomes of using transparent graded lanes, including the promotion of healthy consumption habits and the reduction of food waste, are also considered. The findings and results can inform the development of effective messaging strategies for graded lanes and suggest ways to enhance consumer engagement with product packaging. Moreover, the study's outcomes can contribute to the broader discourse on sustainable consumption and healthy lifestyles, highlighting the potential role of packaging innovations in promoting these values. We used four theories (social cognitive theory, self-perception theory, nudge theory, and marketing and consumer behavior) to examine the effect of these transparent graded lanes on consumer behavior. The conceptual model integrates the use of transparent graded lanes, consumer behavior, trust and loyalty, messaging, and promotion of healthy consumption habits. The study aims to provide insights into how transparent graded lanes can promote mindful consumption, increase consumer recognition and recall of the product, and foster long-term relationships with customers. These innovative packaging designs not only encourage mindful consumption but also promote healthier choices. The communication on the categorized lanes is likewise discovered to be efficient in fostering remembrance and identification of the merchandise during the point of sale and stimulating recurrent acquisition. However, the impact of transparent graded lanes may be limited by factors such as cultural norms, personal values, and financial status. Broadly speaking, the investigation provides valuable insights into the potential benefits and challenges of using transparent graded lanes in product packaging, as well as effective strategies for promoting healthy consumption habits and building long-term relationships with customers.

Keywords: Packaging, customer behavior, purchase, brand loyalty, healthy consumption.

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1019 An Investigation into the Social Factors that Influence Sport Participation: A Case of Gymnastics in the Western Cape

Authors: W. C. Lucas, S. Titus, M. E. M. Young

Abstract:

Gymnastics is the umbrella term that represents seven different and unique disciplines of gymnastics. Men and women of all ages and abilities practice this sport, and participation in gymnastics can develop both gross and fine motor skills, strength, flexibility, coordination and balance. There are various social factors, such as a family’s socioeconomic status or accessibility to sports facilities that may play a role in affecting levels of participation. The aim of this study is to investigate the social factors that have an influence on gymnastics participation in the Western Cape. To this end, a qualitative approach is adopted to collect data. This study also adopts the ecological systems theory as the theoretical framework, and is used to analyze and interpret current social factors that directly or indirectly influence participation in gymnastics. The study’s objectives were to ascertain which social factors hinder participation, and which social factors promote participation, thus, coaches, parents and gymnasts participated in focus group discussions. Key informant interviews took place with experts in the field of gymnastics in the Western Cape. A thematic analysis was conducted on transcriptions from the focus group discussions and key informant interviews. Social factors investigated in this study occurred in the chronosystem, macrosystem, exosystem, mesosystem, and microsystem, and had both a direct and indirect influence on the gymnast’s continued participation. These systems are defined as the environment of the individual, in which they grow and develop. The research findings of this paper are used to draw conclusions and make specific recommendations for practice and further research. The information gathered in this study can assist all stakeholders within the field of gymnastics, such as parents, judges, coaches, gymnasts, and the supporting community which surround the participating gymnast.

Keywords: Developing child, ecological systems theory, facilities, federation, gymnastics, influence, participation, social factors, socioeconomic status, sport.

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1018 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (I)

Authors: Li Ge

Abstract:

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory:

Keywords: impulsive differential equations, impulsive integraldifferentialequation, boundary value problems

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1017 Existence of Solution for Four-Point Boundary Value Problems of Second-Order Impulsive Differential Equations (II)

Authors: Li Ge

Abstract:

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory:

Keywords: impulsive differential equations, impulsive integraldifferentialequation, boundary value problems

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1016 Identification of Outliers in Flood Frequency Analysis: Comparison of Original and Multiple Grubbs-Beck Test

Authors: Ayesha S. Rahman, Khaled Haddad, Ataur Rahman

Abstract:

At-site flood frequency analysis is used to estimate flood quantiles when at-site record length is reasonably long. In Australia, FLIKE software has been introduced for at-site flood frequency analysis. The advantage of FLIKE is that, for a given application, the user can compare a number of most commonly adopted probability distributions and parameter estimation methods relatively quickly using a windows interface. The new version of FLIKE has been incorporated with the multiple Grubbs and Beck test which can identify multiple numbers of potentially influential low flows. This paper presents a case study considering six catchments in eastern Australia which compares two outlier identification tests (original Grubbs and Beck test and multiple Grubbs and Beck test) and two commonly applied probability distributions (Generalized Extreme Value (GEV) and Log Pearson type 3 (LP3)) using FLIKE software. It has been found that the multiple Grubbs and Beck test when used with LP3 distribution provides more accurate flood quantile estimates than when LP3 distribution is used with the original Grubbs and Beck test. Between these two methods, the differences in flood quantile estimates have been found to be up to 61% for the six study catchments. It has also been found that GEV distribution (with L moments) and LP3 distribution with the multiple Grubbs and Beck test provide quite similar results in most of the cases; however, a difference up to 38% has been noted for flood quantiles for annual exceedance probability (AEP) of 1 in 100 for one catchment. This finding needs to be confirmed with a greater number of stations across other Australian states.

Keywords: Floods, FLIKE, probability distributions, flood frequency, outlier.

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1015 Intuitionistic Fuzzy Subalgebras (Ideals) with Thresholds (λ, μ) of BCI-Algebras

Authors: Shaoquan Sun, Qianqian Li

Abstract:

Based on the theory of intuitionistic fuzzy sets, the concepts of intuitionistic fuzzy subalgebras with thresholds (λ, μ) and intuitionistic fuzzy ideals with thresholds (λ, μ) of BCI-algebras are introduced and some properties of them are discussed.

Keywords: BCI-algebra, intuitionistic fuzzy set, intuitionistic fuzzy subalgebra with thresholds (λ, μ), intuitionistic fuzzy ideal with thresholds (λ, μ).

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1014 Bifurcations of a Delayed Prototype Model

Authors: Changjin Xu

Abstract:

In this paper, a delayed prototype model is studied. Regarding the delay as a bifurcation parameter, we prove that a sequence of Hopf bifurcations will occur at the positive equilibrium when the delay increases. Using the normal form method and center manifold theory, some explicit formulae are worked out for determining the stability and the direction of the bifurcated periodic solutions. Finally, Computer simulations are carried out to explain some mathematical conclusions.

Keywords: Prototype model, Stability, Hopf bifurcation, Delay, Periodic solution.

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1013 The Differential Transform Method for Advection-Diffusion Problems

Authors: M. F. Patricio, P. M. Rosa

Abstract:

In this paper a class of numerical methods to solve linear and nonlinear PDEs and also systems of PDEs is developed. The Differential Transform method associated with the Method of Lines (MoL) is used. The theory for linear problems is extended to the nonlinear case, and a recurrence relation is established. This method can achieve an arbitrary high-order accuracy in time. A variable stepsize algorithm and some numerical results are also presented.

Keywords: Method of Lines, Differential Transform Method.

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1012 Arc Length of Rational Bezier Curves and Use for CAD Reparametrization

Authors: Maharavo Randrianarivony

Abstract:

The length  of a given rational B'ezier curve is efficiently estimated. Since a rational B'ezier function is nonlinear, it is usually impossible to evaluate its length exactly. The length is approximated by using subdivision and the accuracy of the approximation n is investigated. In order to improve the efficiency, adaptivity is used with some length estimator. A rigorous theoretical analysis of the rate of convergence of n to  is given. The required number of subdivisions to attain a prescribed accuracy is also analyzed. An application to CAD parametrization is briefly described. Numerical results are reported to supplement the theory.

Keywords: Adaptivity, Length, Parametrization, Rational Bezier

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1011 DNA Nanowires: A Charge Transfer Approach

Authors: S. Behnia, S. Fathizadeh

Abstract:

Conductivity properties of DNA molecule is investigated in a simple, but chemically specific approach that is intimately related to the Su-Schrieffer-Heeger (SSH) model. This model is a tight-binding linear nanoscale chain. We have tried to study the electrical current flowing in DNA and investigated the characteristic I-V diagram. As a result, It is shown that there are the (quasi-) ohmic areas in I-V diagram. On the other hand, the regions with a negative differential resistance (NDR) are detectable in diagram.

Keywords: Charge transfer in DNA, Chaos theory, Molecular electronics, Negative Differential resistance.

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1010 Closed-Form Solutions for Nanobeams Based On the Nonlocal Euler-Bernoulli Theory

Authors: Francesco Marotti de Sciarra, Raffaele Barretta

Abstract:

Starting from nonlocal continuum mechanics, a thermodynamically new nonlocal model of Euler-Bernoulli nanobeams is provided. The nonlocal variational formulation is consistently provided and the governing differential equation for transverse displacement is presented. Higher-order boundary conditions are then consistently derived. An example is contributed in order to show the effectiveness of the proposed model.

Keywords: Bernoulli-Euler beams, Nanobeams, nonlocal elasticity.

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1009 Project Selection by Using Fuzzy AHP and TOPSIS Technique

Authors: S. Mahmoodzadeh, J. Shahrabi, M. Pariazar, M. S. Zaeri

Abstract:

In this article, by using fuzzy AHP and TOPSIS technique we propose a new method for project selection problem. After reviewing four common methods of comparing alternatives investment (net present value, rate of return, benefit cost analysis and payback period) we use them as criteria in AHP tree. In this methodology by utilizing improved Analytical Hierarchy Process by Fuzzy set theory, first we try to calculate weight of each criterion. Then by implementing TOPSIS algorithm, assessment of projects has been done. Obtained results have been tested in a numerical example.

Keywords: Fuzzy AHP, Project Selection, TOPSIS Technique.

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1008 First-Principles Investigation of the Structural and Electronic Properties of Mg1-xBixO

Authors: G. P. Abdel Rahim, M. María Guadalupe Moreno Armenta, Jairo Arbey Rodriguez

Abstract:

We investigated the structure and electronic properties of the compound Mg1-xBixO with varying concentrations of 0, ¼, ½, and ¾ x bismuth in the the cesium chloride (CsCl), zinc-blende (ZnS), nickel arsenide (NiAs) NaCl (rock-salt) and WZ (wurtzite) phases. We calculated. The calculations were performed using the first-principles pseudo-potential method within the framework of spin density functional theory (DFT).

Keywords: DFT, Mg1-xBixO, pseudo-potential, rock-salt and wurtzite.

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1007 Hardiness vs Alienation Personality Construct Essentially Explains Burnout Proclivity and Erroneous Computer Entry Problems in Rural Hellenic Hospital Labs

Authors: Angela–M. Paleologou, Aphrodite Dellaporta

Abstract:

Erroneous computer entry problems [here: 'e'errors] in hospital labs threaten the patients-–health carers- relationship, undermining the health system credibility. Are e-errors random, and do lab professionals make them accidentally, or may they be traced through meaningful determinants? Theories on internal causality of mistakes compel to seek specific causal ascriptions of hospital lab eerrors instead of accepting some inescapability. Undeniably, 'To Err is Human'. But in view of rapid global health organizational changes, e-errors are too expensive to lack in-depth considerations. Yet, that efunction might supposedly be entrenched in the health carers- job description remains under dispute – at least for Hellenic labs, where e-use falls behind generalized(able) appreciation and application. In this study: i) an empirical basis of a truly high annual cost of e-errors at about €498,000.00 per rural Hellenic hospital was established, hence interest in exploring the issue was sufficiently substantiated; ii) a sample of 270 lab-expert nurses, technicians and doctors were assessed on several personality, burnout and e-error measures, and iii) the hypothesis that the Hardiness vs Alienation personality construct disposition explains resistance vs proclivity to e-errors was tested and verified: Hardiness operates as a resilience source in the encounter of high pressures experienced in the hospital lab, whereas its 'opposite', i.e., Alienation, functions as a predictor, not only of making e-errors, but also of leading to burn-out. Implications for apt interventions are discussed.

Keywords: Hospital lab, personality hardiness/alienation, e-errors' cost, burnout.

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1006 A New Approach to Optimal Control Problem Constrained by Canonical Form

Authors: B. Farhadinia

Abstract:

In this article, it is considered a class of optimal control problems constrained by differential and integral constraints are called canonical form. A modified measure theoretical approach is introduced to solve this class of optimal control problems.

Keywords: control problem, Canonical form, Measure theory.

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1005 On the Positive Definite Solutions of Nonlinear Matrix Equation

Authors: Tian Baoguang, Liang Chunyan, Chen Nan

Abstract:

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δi are discussed. An algorithm that avoids matrix inversion with the case -1<-δi<0 is proposed.

Keywords: Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion

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1004 Profile Calculation in Water Phantom of Symmetric and Asymmetric Photon Beam

Authors: N. Chegeni, M. J. Tahmasebi Birgani

Abstract:

Nowadays, in most radiotherapy departments, the commercial treatment planning systems (TPS) used to calculate dose distributions needs to be verified; therefore, quick, easy-to-use and low cost dose distribution algorithms are desirable to test and verify the performance of the TPS. In this paper, we put forth an analytical method to calculate the phantom scatter contribution and depth dose on the central axis based on the equivalent square concept. Then, this method was generalized to calculate the profiles at any depth and for several field shapes regular or irregular fields under symmetry and asymmetry photon beam conditions. Varian 2100 C/D and Siemens Primus Plus Linacs with 6 and 18 MV photon beam were used for irradiations. Percentage depth doses (PDDs) were measured for a large number of square fields for both energies, and for 45º wedges which were employed to obtain the profiles in any depth. To assess the accuracy of the calculated profiles, several profile measurements were carried out for some treatment fields. The calculated and measured profiles were compared by gamma-index calculation. All γ–index calculations were based on a 3% dose criterion and a 3 mm dose-to-agreement (DTA) acceptance criterion. The γ values were less than 1 at most points. However, the maximum γ observed was about 1.10 in the penumbra region in most fields and in the central area for the asymmetric fields. This analytical approach provides a generally quick and fairly accurate algorithm to calculate dose distribution for some treatment fields in conventional radiotherapy.

Keywords: Dose distribution, equivalent field, asymmetric field, irregular field.

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