Search results for: multidimensional Hardy operator

Authors: Kairat T. Mynbaev, Elena N. Lomakina

Abstract:

We consider a Hardy-type operator generated by a family of open subsets of a Hausdorff topological space. The family is indexed with non-negative real numbers and is totally ordered. For this operator, we obtain two-sided bounds of its norm, a compactness criterion, and bounds for its approximation numbers. Previously, bounds for its approximation numbers have been established only in the one-dimensional case, while we do not impose any restrictions on the dimension of the Hausdorff space. The bounds for the norm and conditions for compactness earlier have been found using different methods by G. Sinnamon and K. Mynbaev. Our approach is different in that we use domain partitions for all problems under consideration.

Keywords: approximation numbers, boundedness and compactness, multidimensional Hardy operator, Hausdorff topological space

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Authors: Wedad Albalawi

Abstract:

The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is defined as a closed subset contains real numbers. Then the inequalities of time scales version have received a lot of attention and has had a major field in both pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on double integrals to obtain new time-scale inequalities of Copson driven by Steklov operator. They will be applied in the solution of the Cauchy problem for the wave equation. The proof can be done by introducing restriction on the operator in several cases. In addition, the obtained inequalities done by using some concepts in time scale version such as time scales calculus, theorem of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of Hardy, inequality of Coposon, Steklov operator

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Authors: Wedad Albalawi

Abstract:

The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques, and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then, dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is an arbitrary nonempty closed subset of the real numbers. Then, the dynamic inequalities on time scales have received a lot of attention in the literature and has become a major field in pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on Hardy and Coposon inequalities, using Steklov operator on time scale in double integrals to obtain special cases of time-scale inequalities of Hardy and Copson on high dimensions. The advantage of this study is that it uses the one-dimensional classical Hardy inequality to obtain higher dimensional on time scale versions that will be applied in the solution of the Cauchy problem for the wave equation. In addition, the obtained inequalities have various applications involving discontinuous domains such as bug populations, phytoremediation of metals, wound healing, maximization problems. The proof can be done by introducing restriction on the operator in several cases. The concepts in time scale version such as time scales calculus will be used that allows to unify and extend many problems from the theories of differential and of difference equations. In addition, using chain rule, and some properties of multiple integrals on time scales, some theorems of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of hardy, inequality of coposon, steklov operator

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Authors: Chih-Chun Tang

Abstract:

Nostalgia, to some people, may seem foolhardy in a way. However, nostalgia is a completely and intensely private but social, collective emotion. It has continuing consequence and outgrowth for our lives as social actions. It leads people to hunt and explore remembrance of persons and places of our past in an effort to confer meaning of persons and places of present. In the ‘Poems of 1912-13’ Thomas Hardy, a British poet, composed a series of poems after the unexpected death of his long-disaffected wife, Emma. The series interprets the cognitive and emotional concussion of Emma’s death on Hardy, concerning his mind and real visit to the landscape in Cornwall, England. Both spaces perform the author’s innermost in thought to his late wife and to the landscape. They present an apparent counterpart of the poet and his afflicted conscience. After Emma had died, Hardy carried her recollections alive by roaming about in the real visit and whimsical land (space) they once had drifted and meandered. This paper highlights the nostalgias and feds that seem endlessly to crop up.

Keywords: Thomas Hardy, remembrance, psychological, poems 1912-13, Fred Davis, nostalgia

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Authors: Mehdi Jafari Matehkolaee

Abstract:

In this paper, we have obtained the adjoint of an arbitrary operator (linear and nonlinear) in Hilbert space by introducing an n-dimensional Riemannian manifold. This general formalism covers every linear operator (non – differential) in Hilbert space. In fact, our approach shows that instead of using the adjoint definition of an operator directly, it can be obtained directly by relying on a suitable generalized space according to the action of the operator in question. For the case of nonlinear operators, we have to change the definition of the linear operator adjoint. But here, we have obtained an adjoint of these operators with respect to the definition of the derivative of the operator. As a matter of fact, we have shown one of the straight applications of the ''Frechet derivative'' in the algebra of the operators.

Keywords: adjoint operator, non-linear operator, differentiable operator, manifold

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Authors: Shams Alyusof

Abstract:

This work is to enrich the studies of the frames due to their prominent role in pure mathematics as well as in applied mathematics and many applications in computer science and engineering. Recently, there are remarkable studies of operators that preserve frames on some spaces, and this research could be considered as an extension of such studies. Indeed, this paper is to we characterize weighted composition operators that preserve frames in weighted Hardy spaces on the open unit disk. Moreover, it shows that this characterization does not apply to generalized weighted composition operators on such spaces. Nevertheless, this study could be extended to provide more specific characterizations.

Keywords: frames, generalized weighted composition operators, weighted Hardy spaces, analytic functions

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Authors: Ahmed Emad Ahmed, Zeyad Ahmed Hussein, Mohamed Salama Afifi, Ahmed Mohammed Eid

Abstract:

Water has a great importance in life. In order to deliver water from resources to the users, many procedures should be taken by the water engineers. One of the main procedures to deliver water to the community is by designing pressurizer pipe networks for water. The main aim of this work is to calculate the water demand of a small town and then design a simple water network to distribute water resources among the town with the smallest losses. Literature has been mentioned to cover the main point related to water distribution. Moreover, the methodology has introduced two approaches to solve the research problem, one by the iterative method of Hardy-cross and the other by water software Pipe Flow. The results have introduced two main designs to satisfy the same research requirements. Finally, the researchers have concluded that the use of water software provides more abilities and options for water engineers.

Keywords: looping pipe networks, hardy cross networks accuracy, relative error of hardy cross method

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Authors: Rohana Abdullah, Md Nizam Abd Rahman, Seri Rahayu Kamat

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Operator efficiency aspect is gaining importance in ensuring optimized usage of resources especially in the semi-automated manufacturing environment. This paper addresses a case study done to solve operator efficiency and line balancing issue at a semiconductor assembly and test manufacturing. A Man-to-Machine (M2M) work study technique is used to study operator current utilization and determine the optimum allocation of the operators to the machines. Critical factors such as operator activity, activity frequency and operator competency level are considered to gain insight on the parameters that affects the operator utilization. Equipment standard time and overall equipment efficiency (OEE) information are also gathered and analyzed to achieve a balanced and optimized production.

Keywords: operator efficiency, optimized production, line balancing, industrial and manufacturing engineering

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Authors: Jin Liang, Guanghua Shi

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In this paper, we are concerned with the further refinements of the Heinz operator inequalities in Hilbert spaces. Our purpose is to derive several new Heinz-type operator inequalities. First, with the help of the Taylor series of some hyperbolic functions, we obtain some refinements of the ordering relations among Heinz means defined by Bhatia with different parameters, which would be more suitable in obtaining the corresponding operator inequalities. Second, we present some generalizations of Heinz operator inequalities. Finally, we give a matrix version of the Heinz inequality for the Hilbert-Schmidt norm.

Keywords: Hilbert space, means inequality, norm inequality, positive linear operator

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Authors: Irina Peterburgsky

Abstract:

Let T be a unit circumference of a complex plane, E be a Banach space, E* and E** be its conjugate and second conjugate, respectively. In general, a Hardy space Hp(E), p ≥1, where functions act from the open unit disk to E, could contain a function for which even weak nontangential (angular) boundary value in the space E** does not exist at any point of the unit circumference T (C. Grossetete.) The situation is "better" when certain restrictions to the Banach space of values are applied (more or less resembling a classical case of scalar-valued functions depending on constrains, as shown by R. Ryan.) This paper shows that, nevertheless, in the case of a Banach space of a general type, the following positive statement is true: Proposition. For any function f(z) from Hp(E), p ≥ 1, there exists a function F(eiθ) on the unit circumference T to E** whose Poisson (in the Pettis sense) is integral regains the function f(z) on the open unit disk. Some characteristics of the function F(eiθ) are demonstrated.

Keywords: hardy spaces, Banach space-valued function, boundary values, Pettis integral

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Authors: Sunil Bandaru, Suresh Yv, Srinivas Vanapalli

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Heavy machinery especially compactors has more vibrations induced from the compactor mechanism than the engines. Since the operator’s comfort is most important in any of the machines, this paper shows interest in studying the vibrations on the steering wheel for a double drum compactor. As there are no standard procedures available for testing vibrations on the steering wheel of double drum compactors, this paper tries to evaluate the vibrations on the steering wheel by considering most of the possibilities. In addition to the feasibility for the operator to adjust the steering wheel tilt as in the case of automotive, there is an option for the operator to change the orientation of the operator platform for the complete view of the road’s edge on both the ends of the front and rear drums. When the orientation is either +/-180°, the operator will be closer to the compactor mechanism; also there is a possibility for the shuffle in the modes with respect to the operator. Hence it is mandatory to evaluate the vibrations levels in both cases. This paper attempts to evaluate the vibrations on the steering wheel by considering the two operator platform positions and three steering wheel tilting angles.

Keywords: FEA, CAE, steering column, steering column orientation position

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Authors: Zouari Ezzeddine, Ghraieb Ikram

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From the results of the academic literature which evokes the limitations of previous studies, this article shows the reasons for multidimensionality Prediction of financial bubbles. A new framework for modeling study predicting financial bubbles by linking a set of variable presented on several dimensions dictating its multidimensional character. It takes into account the preferences of financial actors. A multicriteria anticipation of the appearance of bubbles in international financial markets helps to fight against a possible crisis.

Keywords: classical measures, predictions, financial bubbles, multidimensional, artificial neural networks

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Authors: Jianan Sun, Ziwen Ye

Abstract:

Multidimensional computerized adaptive testing (MCAT) is a popular research topic in psychometrics. It is important for practitioners to clearly know the item-trait patterns of administered items when a test like MCAT is operated. Item-trait pattern recognition refers to detecting which latent traits in a psychological test are measured by each of the specified items. If the item-trait patterns of the replenished items in MCAT item pool are well detected, the interpretability of the items can be improved, which can further promote the abilities of the examinees who attending the MCAT to be accurately estimated. This research explores to solve the item-trait pattern recognition problem of the replenished items in MCAT item pool from the perspective of statistical variable selection. The popular multidimensional item response theory model, multidimensional two-parameter logistic model, is assumed to fit the response data of MCAT. The proposed method uses the least absolute shrinkage and selection operator (LASSO) to detect item-trait patterns of replenished items based on the essential information of item responses and ability estimates of examinees collected from a designed MCAT procedure. Several advantages of the proposed method are outlined. First, the proposed method does not strictly depend on the relative order between the replenished items and the selected operational items, so it allows the replenished items to be mixed into the operational items in reasonable order such as considering content constraints or other test requirements. Second, the LASSO used in this research improves the interpretability of the multidimensional replenished items in MCAT. Third, the proposed method can exert the advantage of shrinkage method idea for variable selection, so it can help to check item quality and key dimension features of replenished items and saves more costs of time and labors in response data collection than traditional factor analysis method. Moreover, the proposed method makes sure the dimensions of replenished items are recognized to be consistent with the dimensions of operational items in MCAT item pool. Simulation studies are conducted to investigate the performance of the proposed method under different conditions for varying dimensionality of item pool, latent trait correlation, item discrimination, test lengths and item selection criteria in MCAT. Results show that the proposed method can accurately detect the item-trait patterns of the replenished items in the two-dimensional and the three-dimensional item pool. Selecting enough operational items from the item pool consisting of high discriminating items by Bayesian A-optimality in MCAT can improve the recognition accuracy of item-trait patterns of replenished items for the proposed method. The pattern recognition accuracy for the conditions with correlated traits is better than those with independent traits especially for the item pool consisting of comparatively low discriminating items. To sum up, the proposed data-driven method based on the LASSO can accurately and efficiently detect the item-trait patterns of replenished items in MCAT.

Keywords: item-trait pattern recognition, least absolute shrinkage and selection operator, multidimensional computerized adaptive testing, variable selection

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Authors: Pushpendra Kumar, Sanjeev Kumar, R. Balasubramanian

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Estimation of optical flow from a sequence of images using variational methods is one of the most successful approach. Discontinuity between different motions is one of the challenging problem in flow estimation. In this paper, we design a new anisotropic diffusion operator, which is able to provide smooth flow over a region and efficiently preserve discontinuity in optical flow. This operator is designed on the basis of intensity differences of the pixels and isotropic operator using exponential function. The combination of these are used to control the propagation of flow. Experimental results on the different datasets verify the robustness and accuracy of the algorithm and also validate the effect of anisotropic operator in the discontinuity preserving.

Keywords: optical flow, variational methods, computer vision, anisotropic operator

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Authors: Ouzayr Rabhi, Ibtissam Arrassen

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To provide a complete analysis of the organization and to help decision-making, leaders need to have relevant data; Data Warehouses (DW) are designed to meet such needs. However, designing DW is not trivial and there is no formal method to derive a multidimensional schema from heterogeneous databases. In this article, we present a Model-Driven based approach concerning the design of data warehouses. We describe a multidimensional meta-model and also specify a set of transformations starting from a Unified Modeling Language (UML) metamodel. In this approach, the UML metamodel and the multidimensional one are both considered as a platform-independent model (PIM). The first meta-model is mapped into the second one through transformation rules carried out by the Query View Transformation (QVT) language. This proposal is validated through the application of our approach to generating a multidimensional schema of a Balanced Scorecard (BSC) DW. We are interested in the BSC perspectives, which are highly linked to the vision and the strategies of an organization.

Keywords: data warehouse, meta-model, model-driven architecture, transformation, UML

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Authors: Guillermo Manuel Flores Figueroa, Juan Alejandro Vazquez Feijoo, Jose Navarro Antonio

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A continuous nonlinear system response may be obtained by an infinite sum of the so-called Volterra operators. Each operator is obtained from multidimensional convolution of nth-order between the nth-order Volterra kernel and the system input. These operators can also be obtained from the Associated Linear Equations (ALEs) that are linear models of subsystems which inputs and outputs are of the same nth-order. Each ALEs produces a particular nth-Volterra operator. As linear models a unitary impulse response can be obtained from them. This work shows the relationship between this unitary impulse responses and the corresponding order Volterra kernel.

Keywords: Volterra series, frequency response functions FRF, associated linear equations ALEs, unitary response function, Voterra kernel

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Authors: Rawhy Ismail

Abstract:

Applying fractional calculus in the field of electromagnetics shows significant results. The fractionalization of the conventional curl operator leads to having additional solutions to an electromagnetic problem. This work restudies the concept of the fractional curl operator considering fractional time derivatives in Maxwell’s curl equations. In that sense, a general scheme for the wave loss term is introduced and the degree of freedom of the system is affected through imposing the new fractional parameters. The conventional case is recovered by setting all fractional derivatives to unity.

Keywords: curl operator, fractional calculus, fractional curl operators, Maxwell equations

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Authors: Ramya Rachel S.

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For women in a developing country like India, poverty is an ever-clinging problem which has rooted itself without any trace of absolute abolition. Poverty is a deprivation of many imminent needs and must be measured accordingly. Therefore, it is important to study the dimensions of education, health, and standard of living to understand the true nature of the impoverished. The study focused on studying the deprivation on these aspects using the Alkire-Foster methodology to estimate the Multidimensional Poverty Index. The study has utilized the individual data of women aged 15 to 49 of the National Family Health Survey (NFHS) for the year 2015-16. Findings reveal that women in India still face extreme levels of deprivation in various dimensions. More than one-third of the total women aged 15 to 24 in India were multidimensionally poor. Dimensional breakdown of the levels of multidimensional poverty indicates that the dimension of Education is the highest contributor to poverty. Decomposition of the multidimensional poverty among various demographic sub-groups, reveals that the multidimensional poverty level increases with age. Results point out that deprivations were higher among widowed and married women, and among women who lived alone. There was also a huge rural-urban divide with respect to poverty. The basic needs of these women must be targeted and met so that they are withdrawn from all forms of poverty.

Keywords: deprivations, multidimensional poverty, sub-group decomposition, women

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Authors: Bidyadhar Dehury, Sanjay Kumar Mohanty

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According to the Right to Education Act of India, education is the fundamental right of all children of age group 6-14 year irrespective of their status. Using the unit level data from India Human Development Survey (IHDS), we tried to understand the inter-relationship between the level of poverty and the academic performance of the children aged 8-11 years. The level of multidimensional poverty is measured using five dimensions and 10 indicators using Alkire-Foster approach. The weighted deprivation score was obtained by giving equal weight to each dimension and indicators within the dimension. The weighted deprivation score varies from 0 to 1 and grouped into four categories as non-poor, vulnerable, multidimensional poor and sever multidimensional poor. The academic performance index was measured using three variables reading skills, math skills and writing skills using PCA. The bivariate and multivariate analysis was used in the analysis. The outcome variable was ordinal. So the predicted probabilities were calculated using the ordinal logistic regression. The predicted probabilities of good academic performance index was 0.202 if the child was sever multidimensional poor, 0.235 if the child was multidimensional poor, 0.264 if the child was vulnerable, and 0.316 if the child was non-poor. Hence, if the level of poverty among the children decreases from sever multidimensional poor to non-poor, the probability of good academic performance increases.

Keywords: multidimensional poverty, academic performance index, reading skills, math skills, writing skills, India

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Authors: Joseph Siani

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Over the last decades, dissatisfaction with global indicators of economic performance, such as GDP (Gross Domestic Product) per capita, has shifted the attention to what is now referred to as multidimensional poverty. In this framework, poverty goes beyond income to incorporate aspects of well-being not captured by income measures alone. This paper applies the totally fuzzy approach to estimate the fuzzy index of poverty (FIP) in fourteen Sub-Saharan African (SSA) countries using Demographic and Health Survey (DHS) data and explores whether pictures created by the standard headcount ratio at $1.90 a day and the fuzzy index of poverty tell a similar story. The results suggest that there is indeed considerable mismatch between poverty headcount and the fuzzy index of multidimensional poverty, meaning that the majority of the most deprived people (as identified by the fuzzy index of multidimensional poverty) would not be identified by the poverty headcount ratio. Moreover, we find that poverty is distributed differently by colonial heritage (language). In particular, the most deprived countries in SSA are French-speaking.

Keywords: fuzzy set approach, multidimensional poverty, poverty headcount, overlap, Sub-Saharan Africa

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Authors: Mohammed Husein Mohammed Rashid

Abstract:

Let Τ = U |Τ| be a polar decomposition of a bounded linear operator T on a complex Hilbert space with ker U = ker |T|. T is said to be class p-w A(s,t) if (|T*|ᵗ|T|²ˢ|T*|ᵗ )ᵗᵖ/ˢ⁺ᵗ ≥|T*|²ᵗᵖ and |T|²ˢᵖ ≥ (|T|ˢ|T*|²ᵗ|T|ˢ)ˢᵖ/ˢ⁺ᵗ with 0Keywords: class p-w A (s, t), normaloid, isoloid, finite, orthogonality

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Authors: Manal Azzidani

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This research consideres the extension of special functions called Positive Linear Operators. the bounded linear operator which defined from normed space to Banach space will extend to the closure of the its domain, And extend identified linear functional on a vector subspace by Hana-Banach theorem which could be generalized to the positive linear operators.

Keywords: extension, positive operator, Riesz space, sublinear function

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Authors: I. Khutsishvili, G. Sirbiladze, B. Ghvaberidze

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This work proposes a fuzzy methodology to support the investment decisions. While choosing among competitive investment projects, the methodology makes ranking of projects using the new aggregation OWA operator – AsPOWA, presented in the environment of possibility uncertainty. For numerical evaluation of the weighting vector associated with the AsPOWA operator the mathematical programming problem is constructed. On the basis of the AsPOWA operator the projects’ group ranking maximum criteria is constructed. The methodology also allows making the most profitable investments into several of the project using the method developed by the authors for discrete possibilistic bicriteria problems. The article provides an example of the investment decision-making that explains the work of the proposed methodology.

Keywords: expert evaluations, investment decision making, OWA operator, possibility uncertainty

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Authors: Manju Pandey, Nilay Khare, S. C. Shrivastava

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This paper is the final in a series, which has defined two new classes of aggregation operators for triangular and trapezoidal fuzzy numbers based on the geometrical characteristics of their fuzzy membership functions. In the present paper, a new aggregation operator for trapezoidal fuzzy numbers has been defined. The new operator is based on the geometric mean of the membership lines to the left and right of the maximum possibility interval. The operator is defined and the analytical relationships have been derived. Computation of the aggregate is demonstrated with a numerical example. Corresponding arithmetic and geometric aggregates as well as results from the recent work of the authors on TrFN aggregates have also been computed.

Keywords: LR fuzzy number, interval fuzzy number, triangular fuzzy number, trapezoidal fuzzy number, apex angle, left apex angle, right apex angle, aggregation operator, arithmetic and geometric mean

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Authors: B. Schmid, C. Kexel, E. Djafarova

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Understanding consumers is elementary for practitioners in marketing. Consumers of sports events, the sports spectators, are a particularly complex consumer crowd. In order to identify and define their profiles different segmentation approaches can be found in literature, one of them being multidimensional segmentation. Multidimensional segmentation models correspond to the broad range of attitudes, behaviours, motivations and beliefs of sports spectators, other than earlier models. Moreover, in sports there are some well-researched disciplines (e.g. football or North American sports) where consumer profiles and marketing strategies are elaborate and others where no research at all can be found. For example, there is almost no research on athletics spectators. This paper explores the current state of research on sports spectators segmentation. An in-depth literature review provides the framework for a spectators segmentation in athletics. On this basis, additional potential consumer groups and implications for social media marketing will be explored. The findings are the basis for further research.

Keywords: multidimensional segmentation, social media, sports marketing, sports spectators segmentation

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Authors: Li Dan, Zhao Junsuo, Zhang Wenjun

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Aiming at the shortcomings of the Quantum Genetic Algorithm such as the multimodal function optimization problems easily falling into the local optimum, and vulnerable to premature convergence due to no closely relationship between individuals, the paper presents an Improved Many Worlds Quantum Genetic Algorithm (IMWQGA). The paper using the concept of Many Worlds; using the derivative way of parallel worlds’ parallel evolution; putting forward the thought which updating the population according to the main body; adopting the transition methods such as parallel transition, backtracking, travel forth. In addition, the algorithm in the paper also proposes the quantum training operator and the combinatorial optimization operator as new operators of quantum genetic algorithm.

Keywords: quantum genetic algorithm, many worlds, quantum training operator, combinatorial optimization operator

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Authors: Jessada Tariboon

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In this article, using distribution kernel, we study the nonlinear equations with n-dimensional telegraph operator iterated k-times.

Keywords: telegraph operator, elementary solution, distribution kernel, nonlinear equations

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Authors: Renkai Wang, Tingcun Wei

Abstract:

In this paper, a digital control algorithm based on delta-operator is presented for high-frequency digitally-controlled DC-DC switching converters. The stability and the controlling accuracy of the DC-DC switching converters are improved by using the digital control algorithm based on delta-operator without increasing the hardware circuit scale. The design method of voltage compensator in delta-domain using PID (Proportion-Integration- Differentiation) control is given in this paper, and the simulation results based on Simulink platform are provided, which have verified the theoretical analysis results very well. It can be concluded that, the presented control algorithm based on delta-operator has better stability and controlling accuracy, and easier hardware implementation than the existed control algorithms based on z-operator, therefore it can be used for the voltage compensator design in high-frequency digitally- controlled DC-DC switching converters.

Keywords: digitally-controlled DC-DC switching converter, digital voltage compensator, delta-operator, finite word length, stability

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Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

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This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.

Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions

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Authors: M. Berrehail, F. Benamira

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We study the quantum motion of a particle in the presence of a time- dependent linear potential using an operator invariant that is quadratic in p and linear in q within the framework of the Lewis-Riesenfeld invariant, The special invariant operator proposed in this work is demonstrated to be an Hermitian operator which has an Airy wave packet as its Eigenfunction

Keywords: airy wave packet, ivariant, time-dependent linear potential, unitary transformation

Procedia PDF Downloads 462