Search results for: inversion operator

Authors: Nastaran Moosavi, Mohammad Mokhtari

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Seismic inversion is a technique which has been in use for years and its main goal is to estimate and to model physical characteristics of rocks and fluids. Generally, it is a combination of seismic and well-log data. Seismic inversion can be carried out through different methods; we have conducted and compared post-stack and pre- stack seismic inversion methods on real data in one of the fields in the Persian Gulf. Pre-stack seismic inversion can transform seismic data to rock physics such as P-impedance, S-impedance and density. While post- stack seismic inversion can just estimate P-impedance. Then these parameters can be used in reservoir identification. Based on the results of inverting seismic data, a gas reservoir was detected in one of Hydrocarbon oil fields in south of Iran (Persian Gulf). By comparing post stack and pre-stack seismic inversion it can be concluded that the pre-stack seismic inversion provides a more reliable and detailed information for identification and prediction of hydrocarbon reservoirs.

Keywords: density, p-impedance, s-impedance, post-stack seismic inversion, pre-stack seismic inversion

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Authors: Mehdi Jafari Matehkolaee

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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: Shrey Sharma, Gunjan Kumar Verma

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High density electrical prospecting has been widely used in groundwater investigation, civil engineering and environmental survey. For efficient inversion, the forward modeling routine, sensitivity calculation, and inversion algorithm must be efficient. This paper attempts to provide a brief summary of the past and ongoing developments of the method. It includes reviews of the procedures used for data acquisition, processing and inversion of electrical resistivity data based on compilation of academic literature. In recent times there had been a significant evolution in field survey designs and data inversion techniques for the resistivity method. In general 2-D inversion for resistivity data is carried out using the linearized least-square method with the local optimization technique .Multi-electrode and multi-channel systems have made it possible to conduct large 2-D, 3-D and even 4-D surveys efficiently to resolve complex geological structures that were not possible with traditional 1-D surveys. 3-D surveys play an increasingly important role in very complex areas where 2-D models suffer from artifacts due to off-line structures. Continued developments in computation technology, as well as fast data inversion techniques and software, have made it possible to use optimization techniques to obtain model parameters to a higher accuracy. A brief discussion on the limitations of the electrical resistivity method has also been presented.

Keywords: inversion, limitations, optimization, resistivity

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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: Attaullah Khawaja, Amna Shabbir

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Channel inversion is one of the simplest techniques for multiuser downlink systems with single-antenna users. In this paper regularized channel inversion under equal power constraint in the multiuser multiple input multiple output (MU-MIMO) broadcast channels has been considered. Sum capacity with plain channel inversion also known as Zero Forcing Beam Forming (ZFBF) and optimum sum capacity using Dirty Paper Coding (DPC) has also been investigated. Analysis and simulations show that regularization enhances the system performance and empower linear growth in Sum Capacity and specially work well at low signal to noise ratio (SNRs) regime.

Keywords: broadcast channel, channel inversion, multiple antenna multiple-user wireless, multiple-input multiple-output (MIMO), regularization, dirty paper coding (DPC), sum capacity

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Authors: Meng Wu

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Motion planning is a common task required to be fulfilled by robots. A strategy combining Ant Colony Optimization (ACO) and gravity gradient inversion algorithm is proposed for motion planning of mobile robots. In this paper, in order to realize optimal motion planning strategy, the cost function in ACO is designed based on gravity gradient inversion algorithm. The obstacles around mobile robot can cause gravity gradient anomalies; the gradiometer is installed on the mobile robot to detect the gravity gradient anomalies. After obtaining the anomalies, gravity gradient inversion algorithm is employed to calculate relative distance and orientation between mobile robot and obstacles. The relative distance and orientation deduced from gravity gradient inversion algorithm is employed as cost function in ACO algorithm to realize motion planning. The proposed strategy is validated by the simulation and experiment results.

Keywords: motion planning, gravity gradient inversion algorithm, ant colony optimization

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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: Rais Yusoh, Rosli Saad, Mokhtar Saidin, Fauzi Andika, Sabiu Bala Muhammad

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Resistivity and seismic refraction profiling have become a common method in pre-investigations for visualizing subsurface structure. The integration of the methods could reduce an interpretation ambiguity. Both methods have their individual software packages for data inversion, but potential to combine certain geophysical methods are restricted; however, the research algorithms that have this functionality was existed and are evaluated personally. The interpretation of subsurface were improve by combining inversion data from both methods by influence each other models using closure coupling; thus, by implementing both methods to support each other which could improve the subsurface interpretation. These methods were applied on a field dataset from a pre-investigation for archeology in finding the ancient river. There were no major changes in the inverted model by combining data inversion for this archetype which probably due to complex geology. The combine data analysis provides an additional technique for interpretation such as an alluvium, which can have strong influence on the ancient river findings.

Keywords: ancient river, combine inversion, resistivity, seismic refraction

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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: Rawhy Ismail

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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: Fofie Kokea Ariane Darolle, Gouet Daniel Hervé, Koumetio Fidèle, Yemele David

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The electrical resistivity method is successfully used in this paper in order to have a clearer picture of the subsurface of the North-East ofFiguil in northern Cameroon. It is worth noting that this method is most often used when the objective of the study is to image the shallow subsoils by considering them as a set of stratified ground layers. The problem to be solved is very often environmental, and in this case, it is necessary to perform an inversion of the data in order to have a complete and accurate picture of the parameters of the said layers. In the case of this work, thirty-three (33) Schlumberger VES have been carried out on an irregular grid to investigate the subsurface of the study area. The 1D inversion applied as a preliminary modeling tool and in correlation with the mechanical drillings results indicates a complex subsurface lithology distribution mainly consisting of marbles and schists. Moreover, the quasi-3D inversion with lateral constraint shows that the misfit between the observed field data and the model response is quite good and acceptable with a value low than 10%. The method also reveals existence of two water bearing in the considered area. The first is the schist or weathering aquifer (unsuitable), and the other is the marble or the fracturing aquifer (suitable). The final quasi 3D inversion results and geological models indicate proper sites for groundwaters prospecting and for mining exploitation, thus allowing the economic development of the study area.

Keywords: electrical resistivity method, 1D inversion, quasi 3D inversion, groundwaters, mining

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Authors: Ying Zhang

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Surface waves provide critical constraints about the earth's structure in the crust and upper mantle. However, different modes of Love waves with close group velocities often arrive at a similar time and interfere with each other. This problem is typical for Love waves at intermediate periods that travel through the oceanic lithosphere. Therefore, we developed a two-step inversion approach to separate the waveforms of the fundamental and first higher mode of Love waves. We first solve the phase velocities of the two modes and their amplitude ratios. The misfit function is based on the sum of phase differences among the station pairs. We then solve the absolute amplitudes of the two modes and their initial phases using obtained phase velocities and amplitude ratio. The separated waveforms of each mode from the two-step inversion method can be further used in surface wave tomography to improve model resolution.

Keywords: surface wave inversion, waveform separation, love waves, higher-mode interference

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Authors: Nicholas D. Assimakis

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In linear estimation, the traditional Kalman filter uses the Kalman filter gain in order to produce estimation and prediction of the n-dimensional state vector using the m-dimensional measurement vector. The computation of the Kalman filter gain requires the inversion of an m x m matrix in every iteration. In this paper, a variation of the Kalman filter eliminating the Kalman filter gain is proposed. In the time varying case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix and the inversion of an m x m matrix in every iteration. In the time invariant case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix in every iteration. The proposed Kalman filter gain elimination algorithm may be faster than the conventional Kalman filter, depending on the model dimensions.

Keywords: discrete time, estimation, Kalman filter, Kalman filter gain

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Authors: Fernando P. Silva, Valter J. S. Leite, Erivelton G. Nepomuceno

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In this paper, a nonlinear controller design for an omnidirectional mobile is presented. The robot controller consists of an inner-loop controller and an outer-loop controller, the first is designed using state feedback (robust allocation) and the second controller is designed based on Robust Multi Inversion (RMI) approach. The objective of RMI controller is rendering the robust inversion of the dynamic, when the model is affected by uncertainties. A model nonlinear MIMO of an omni-directional robot (small-league of Robocup) is used to simulate the RMI approach. The parameters of linear and nonlinear model are varied to cause modelling uncertainties among the model and the real model (real system) generating an error in inner-loop controller signal that must be compensated by RMI controller. The simulation test results show that the RMI is capable of compensating the uncertainties and keep the system stable and controlled under uncertainties.

Keywords: robust multi inversion, omni-directional robot, robocup, nonlinear control

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Authors: Sheryl Avendaño, Miguel Ospina, Hebert Montegranario

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Full Wave Inversion (FWI) is a variant of seismic tomography for obtaining velocity profiles by an optimization process that combine forward modelling (or solution of wave equation) with the misfit between synthetic and observed data. In this research we are modelling wave propagation in a visco-acoustic medium in the frequency domain. We apply finite differences for the numerical solution of the wave equation with a mix between usual and rotated grids, where density depends on velocity and there exists a damping function associated to a linear dissipative medium. The velocity profiles are obtained from an initial one and the data have been modeled for a frequency range 0-120 Hz. By an iterative procedure we obtain an estimated velocity profile in which are detailed the remarkable features of the velocity profile from which synthetic data were generated showing promising results for our method.

Keywords: seismic inversion, full wave inversion, visco acoustic wave equation, finite diffrence methods

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Authors: Rezvan Ravanfar Haghighi, S. Chatterjee, Pratik Kumar, V. C. Vani, Priya Jagia, Sanjiv Sharma, Susama Rani Mandal, R. Lakshmy

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The dual energy computed tomography (DECT) aims at noting the HU(V) values for the sample at two different voltages V=V1, V2 and thus obtain the electron densities (ρe) and effective atomic number (Zeff) of the substance. In the present paper, we aim to obtain a numerical algorithm by which (ρe, Zeff) can be obtained from the HU(100) and HU(140) data, where V=100, 140 kVp. The idea is to use this inversion method to characterize and distinguish between the lipid and fibrous coronary artery plaques.With the idea to develop the inversion algorithm for low Zeff materials, as is the case with non calcified coronary artery plaque, we prepare aqueous samples whose calculated values of (ρe, Zeff) lie in the range (2.65×1023≤ ρe≤ 3.64×1023 per cc ) and (6.80≤ Zeff ≤ 8.90). We fill the phantom with these known samples and experimentally determine HU(100) and HU(140) for the same pixels. Knowing that the HU(V) values are related to the attenuation coefficient of the system, we present an algorithm by which the (ρe, Zeff) is calibrated with respect to (HU(100), HU(140)). The calibration is done with a known set of 20 samples; its accuracy is checked with a different set of 23 known samples. We find that the calibration gives the ρe with an accuracy of ± 4% while Zeff is found within ±1% of the actual value, the confidence being 95%.In this inversion method (ρe, Zeff) of the scanned sample can be found by eliminating the effects of the CT machine and also by ensuring that the determination of the two unknowns (ρe, Zeff) does not interfere with each other. It is found that this algorithm can be used for prediction of chemical characteristic (ρe, Zeff) of unknown scanned materials with 95% confidence level, by inversion of the DECT data.

Keywords: chemical composition, dual-energy computed tomography, inversion algorithm

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Authors: Mohammed Husein Mohammed Rashid

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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: Rezvan Ravanfar Haghighi, V. C. Vani, Suresh Perumal, Sabyasachi Chatterjee, Pratik Kumar

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X-ray attenuation coefficient [µ(E)] of any substance, for energy (E), is a sum of the contributions from the Compton scattering [ μCom(E)] and photoelectric effect [µPh(E)]. In terms of the, electron density (ρe) and the effective atomic number (Zeff) we have µCom(E) is proportional to [(ρe)fKN(E)] while µPh(E) is proportional to [(ρeZeffx)/Ey] with fKN(E) being the Klein-Nishina formula, with x and y being the exponents for photoelectric effect. By taking the sample's HU at two different excitation voltages (V=V1, V2) of the CT machine, we can solve for X=ρe, Y=ρeZeffx from these two independent equations, as is attempted in DECT inversion. Since µCom(E) and µPh(E) are both energy dependent, the coefficients of inversion are also dependent on (a) the source spectrum S(E,V) and (b) the detector efficiency D(E) of the CT machine. In the present paper we tabulate these coefficients of inversion for different practical manifestations of S(E,V) and D(E). The HU(V) values from the CT follow: <µ(V)>=<µw(V)>[1+HU(V)/1000] where the subscript 'w' refers to water and the averaging process <….> accounts for the source spectrum S(E,V) and the detector efficiency D(E). Linearity of μ(E) with respect to X and Y implies that (a) <µ(V)> is a linear combination of X and Y and (b) for inversion, X and Y can be written as linear combinations of two independent observations <µ(V1)>, <µ(V2)> with V1≠V2. These coefficients of inversion would naturally depend upon S(E, V) and D(E). We numerically investigate this dependence for some practical cases, by taking V = 100 , 140 kVp, as are used for cardiological investigations. The S(E,V) are generated by using the Boone-Seibert source spectrum, being superposed on aluminium filters of different thickness lAl with 7mm≤lAl≤12mm and the D(E) is considered to be that of a typical Si[Li] solid state and GdOS scintilator detector. In the values of X and Y, found by using the calculated inversion coefficients, errors are below 2% for data with solutions of glycerol, sucrose and glucose. For low Zeff materials like propionic acid, Zeffx is overestimated by 20% with X being within1%. For high Zeffx materials like KOH the value of Zeffx is underestimated by 22% while the error in X is + 15%. These imply that the source may have additional filtering than the aluminium filter specified by the manufacturer. Also it is found that the difference in the values of the inversion coefficients for the two types of detectors is negligible. The type of the detector does not affect on the DECT inversion algorithm to find the unknown chemical characteristic of the scanned materials. The effect of the source should be considered as an important factor to calculate the coefficients of inversion.

Keywords: attenuation coefficient, computed tomography, photoelectric effect, source spectrum

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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: Arka Roy, Chandra Prakash Dubey

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Inverse problem generally used for recovering hidden information from outside available data. Vertical component of gravity field we will be going to use for underneath density structure calculation. Ill-posing nature is main obstacle for any inverse problem. Linear regularization using Tikhonov formulation are used for appropriate choice of SVD and GSVD components. For real time data handle, signal to noise ratios should have to be less for reliable solution. In our study, 2D and 3D synthetic model with rectangular grid are used for gravity field calculation and its corresponding inversion for density reconstruction. Fine grid also we have considered to hold any irregular structure. Keeping in mind of algebraic ambiguity factor number of observation point should be more than that of number of data point. Picard plot is represented here for choosing appropriate or main controlling Eigenvalues for a regularized solution. Another important study is depth resolution plot (DRP). DRP are generally used for studying how the inversion is influenced by regularizing or discretizing. Our further study involves real time gravity data inversion of Vredeforte Dome South Africa. We apply our method to this data. The results include density structure is in good agreement with known formation in that region, which puts an additional support of our method.

Keywords: depth resolution plot, gravity inversion, Picard plot, SVD, Tikhonov formulation

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Authors: Kairat T. Mynbaev, Elena N. Lomakina

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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: 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: Kawalpreet Kalra, Alpana Goel

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The behaviour of the rotational bands should be smooth but due to large amount of inertia and decreased pairing it is not so. Many experiments have been done in the last few decades, and a large amount of data is available for comprehensive study in this region. Peculiar features like signature dependence, signature inversion, and signature reversal are observed in many two quasiparticle rotational bands of doubly odd and doubly even nuclei. At high rotational frequencies, signature and parity are the only two good quantum numbers available to label a state. Signature quantum number is denoted by α. Even-angular momentum states of a rotational band have α =0, and the odd-angular momentum states have α =1. It has been observed that the odd-spin members lie lower in energy up to a certain spin Ic; the normal signature dependence is restored afterwards. This anomalous feature is termed as signature inversion. The systematic of signature inversion in high-j orbitals for doubly odd rare earth nuclei have been done. Many unusual features like signature dependence, signature inversion and signature reversal are observed in rotational bands of even-even/odd-odd nuclei. Attempts have been made to understand these phenomena using several models. These features have been analyzed within the framework of the Two Quasiparticle Plus Rotor Model (TQPRM).

Keywords: rotational bands, signature dependence, signature quantum number, two quasiparticle

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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

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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: 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

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Authors: Mohammed Husein Mohammad Rashid

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For a bounded linear operator T acting on a complex infinite dimensional Hilbert space ℋ, we say that T is ∗-class A operator (abbreviation T∈A*) if |T²|≥ |T*|². In this article, we prove the following assertions:(i) we establish some conditions which imply the normality of ∗-class A; (ii) we consider ∗-class A operator T ∈ ℬ(ℋ) with reducing kernel such that TX = XS for some X ∈ ℬ(K, ℋ) and prove the Fuglede-Putnam type theorem when adjoint of S ∈ ℬ(K) is dominant operators; (iii) furthermore, we extend the asymmetric Putnam-Fuglede theorem the class of ∗-class A operators.

Keywords: fuglede-putnam theorem, normal operators, ∗-class a operators, dominant operators

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