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Purpose To evaluate the effect of a new-generation positional device, the sleep position trainer (SPT), in non-apneic position-dependent snorers. Methods Non-apneic position-dependent snorers with an apnea–hypopnea index (AHI)

A construction method of infinite families of quasi-exactly solvable position-dependent mass Schr\"odinger equations with known ground and first excited states is proposed in a deformed supersymmetric background. Such families correspond to extensions of known potentials endowed with a deformed shape invariance property. Two different approaches are combined. The first one is a generating function method, which enables to construct the first two superpotentials of a deformed supersymmetric hierarchy, as well as the first two partner potentials and the first two eigenstates of the first potential, from some generating function $W_+(x)$ [and its accompanying function $W_-(x)$]. The second approach is the conditionally deformed shape invariance method, wherein the deformed shape invariance property of the starting potentials is generalized to their extensions by adding some constraints on the parameters and by imposing compatibility conditions between sets of constraints. Detailed results are given for some extensions of the linear and radial harmonic oscillators, as well as the Kepler-Coulomb and Morse potentials., Comment: 28 pages, 8 figures, changes in introduction, conclusion, and references. arXiv admin note: text overlap with arXiv:1712.00329

We consider quantum walks with position dependent coin on 1D lattice $\mathbb{Z}$. The dispersive estimate $\|U^tP_c u_0\|_{l^\infty}\lesssim (1+|t|)^{-1/3} \|u_0\|_{l^1}$ is shown under $l^{1,1}$ perturbation for the generic case and $l^{1,2}$ perturbation for the exceptional case, where $U$ is the evolution operator of a quantum walk and $P_c$ is the projection to the continuous spectrum. This is an analogous result for Schr\"odinger operators and discrete Schr\"odinger operators. The proof is based on the estimate of oscillatory integrals expressed by Jost solutions., Comment: 28 pages

We present the Fokker-Planck equation (FPE) for an inhomogeneous medium with a position-dependent mass particle by making use of the Langevin equation, in the context of a generalized deformed derivative for an arbitrary deformation space where the linear (nonlinear) character of the FPE is associated with the employed deformed linear (nonlinear) derivative. The FPE for an inhomogeneous medium with a position-dependent diffusion coefficient is equivalent to a deformed FPE within a deformed space, described by generalized derivatives, and constant diffusion coefficient. The deformed FPE is consistent with the diffusion equation for inhomogeneous media when the temperature and the mobility have the same position-dependent functional form as well as with the nonlinear Langevin approach. The deformed version of the H-theorem permits to express the Boltzmann-Gibbs entropic functional as a sum of two contributions, one from the particles and the other from the inhomogeneous medium. The formalism is illustrated with the infinite square well and the confining potential with linear drift coefficient. Connections between superstatistics and position-dependent Langevin equations are also discussed.

The solution of integro-differential Schrodinger equation (IDSE) which was introduced by physicists has a great role in the fields of science. The purpose of this paper comes in two parts. First, studying the relationship between integro-differential Schrodinger equation with a symmetric non-local potential and one-dimensional Schrodinger equation with a position-dependent effective mass. Second, we show that the quantum Hamiltonian for a particle with position-dependent mass after applying Liouville–Green transformations will be converted to a quantum Hamiltonian for a particle with constant mass.

Strain wave gears are frequently used in small and medium size industrial robots. In order to describe and quantify friction effects in gearboxes of such type, a structurally simple, yet powerful model is proposed taking into account both speed-and load-dependent friction effects. Moreover, position-dependent disturbances in a robotic joint are considered. An identification procedure is presented that allows to separate the individual components of the model and identify them subsequently. The effectiveness of the model and identification procedure is validated using experimental data gathered from four different robotic joints of varying size. Furthermore, the benefits of improved friction modeling are shown by means of different applications, including smooth lead-through programming and sensorless force control.

In this paper, we analyze the effects of the positions of a millimeter-wave (mmWave) antenna on a vehicle for typical vehicle-to-vehicle (V2V) scenarios. Propagation does neither effectively penetrate nor diffract around vehicles as the wavelength becomes shorter, the positions of an antenna on a vehicle is a crucial question. Path loss measurement was performed at 28 GHz in an open space to minimize the effect of the surrounding objects. Based on the measurement, we investigated path loss characteristics for various transmitter and receiver positions.

This article discusses a method to identify targets in the raw data collected by a 2-dimensional radar array. A series of target simulations, in frequency space, are correlated against experimental data and these correlations are used to identify the target in the different data snippets. In each case, the target whose simulation correlates most strongly with the experimental data positively identifies the target in the data. We furthermore find that the two strongest cross-correlations between any particular experimental data sample and all target simulations has a 42% mean difference across all experimental data. From this exploratory study we conclude that this approach positively identifies all targets in our data set but that a more thorough study is necessary to determine its robustness.

Silicon nanopyramids with the excellent ability of light absorption have been mostly reported in solar cells. Here, we report an obviously enhanced lateral photovoltaic effect (LPE) in copper-nanoparticle-covered random Si nanopyramids (Cu@Si-pyramid). Remarkable photoelectric responses are achieved in broadband from 405 to 780 nm. Furthermore, a prominent LPE is double-enhanced from 74.0 to 157.9 mV mm-1 when the linear region decreases from 3 to 1 mm. Finite-difference time-domain simulation is applied to investigate the origin of the exceptional results. This work declares a position-sensitive property of Si-nanopyramid systems and proposes promising applications to photodetections based on LPE.

Mosheiov [4] and Fiszman and Mosheiov [2] studied flowshop scheduling problems with position dependent job processing times and proposed algorithms which employ solving an assignment problem as a subroutine. This subroutine needs a correction. We describe such a correction. The running times of the corrected algorithms match the best known running times for the studied problems.

We show that the results and conclusions of the paper “Study on the optical rectification and second-harmonic generation with position-dependent mass in a quantum well” [Journal of Physics and Chemistry of Solids, 119, (2018) 50–55] are incorrect.

Co(III) and Ga(III) complexes of 5,10-bis(pentafluorophenyl)corrole and 5,15-bis(pentafluorophenyl)corrole were synthesized by metalations with Co(OAc)2 •4H2O and GaCl3, respectively. The structures of these complexes have been all unambiguously revealed by X-ray diffraction analysis. Their optical and electrochemical properties have been studied, which reveals small but distinctly different substituent effects depending upon the substitution positions.

This study presents the Fisher information for the position-dependent mass Schrodinger equation with hyperbolic potential V ( x ) = − V 0 csch 2 ( a x ) . The analysis of the quantum-mechanical probability for the ground and exited states ( n = 0 , 1 , 2 ) has been obtained via the Fisher information. This controls both chemical and physical properties of some molecular systems. The Fisher information is considered only for x > 0 due to the singular point at x = 0 . We found that Fisher-information-based uncertainty relation and the Cramer–Rao inequality holds. Some relevant numerical results are presented. The results presented show that the Cramer–Rao and the Heisenberg products in both spaces provide a natural measure for anharmonicity of − V 0 csch 2 ( a x ) .

In this paper we consider two types of the generalized damped oscillator. One is governed by a single frictional force which has a position dependent frictional coecient and is proportional to the N-th power of the velocity. Another is a quadratically damped harmonic oscillator. For two models, we construct two independent constants of motion.

In this letter, the two-dimensional (2D) spatial-dependent of probe absorption based on biexciton coherence is investigated by monitoring the probe absorption spectra in a Quantum Dot (QD) Nanostructure. We find that due to the quantum interference which is set up by two control pulses that couples to a resonance of the biexciton, the 2D spatial distribution of probe absorption spectrum can be controlled via adjusting the system parameters. We study the effect of controlling parameters of the QD system on spatial distribution of the probe field absorption for two different cases in which the QD interacts with the standing-wave laser fields; first, when two laser fields which couple to a biexciton state, correspond to the two orthogonal standing-wave fields and couple the different transitions. Second, when only one of laser fields correspond to the combination of two orthogonal standing-wave fields, while the other one corresponds to a traveling-wave field. Results exhibit different interesting 2D absorption patterns.

We describe a method to separate, measure, and compensate for position-independent and position-dependent geometric errors in the rotary axes of a five-axis machine tool with a tilting rotary table using double ball-bar measurements. The measurement paths require control of a single rotary axis, and they are not affected by the accuracy of the linear axes. The positions of the balls of the double ball-bar are modeled as the nominal positions, with geometric errors considered via a kinematic analysis to represent the measurement configuration. The method is applied to measure both position-independent and position-dependent geometric errors, and the results are verified via measurements with compensation for the geometric errors. Furthermore, the possible range of the measured geometric errors is determined by analyzing the contributors.

The honing tool is often assumed to have an ideal behaviour, meaning that there is no difference between the forces or positions measured at the honing spindle and those measured directly at the honing tool. In reality the normal force at the honing stone is influenced by the behaviour of the honing tool: a tangential tolerance at the honing stone can enable a yawing of the stone. Friction between the tool components influences the forces at the tool and can lead to self-locking. Also the outer diameter of the honing tool can be influenced by several perturbations: elastic deformation of the tool can cause a difference between the feeding position at the honing spindle and at the honing stone. Axial tolerance at the honing stone can make the feeding position dependent on the direction and value of the axial stroke velocity. Varying feeding positions of the honing stone influence the process forces and consequently the material removal mechanism during the honing process. In this paper an analytical model of the honing tool will be used to investigate and estimate the real tool behaviour. The model uses geometric and algebraic methods to estimate the state, forces and lengths during the honing process. Two different tools from the industrial application will be used as an example to show the impacts on the process forces.

The leakage power has become a vital downside in modern VLSI technology, with the advent in the area of high performance chips and portable electronics. Thus it is necessarily to invest more time and effort in designing low power chip without sacrificing its high performance. This paper describes a steady state gate leakage based on position and biasing states. As a basic reference universal gates are selected and compared the gate leakage of conventional NAND and NOR gate using 180nm TSMC technology. It is shown that the overall leakage in a NAND -gate is smaller than in a NOR gate if equal size transistors are used. It also compares the leakage value of proposed leakage reduction techniques with conventional NAND gate. Simulation results shows up to 88% in average gate leakage reduction with modified techniques.

In this paper we solve analytical the position-dependent effective mass Klein–Gordon equation for modified Eckart potential plus Hulthen potential with unequal scalar and vector potential for l≠0. The Nikiforov-Uvarov (NU) method is used to obtain the energy eigenvalues and wave functions. We also discuss the energy eigenvalues and wave functions for the constant-mass case. The wave functions of the system are taken in the form of the Laguerre polynomials. The results are the exact analytical. The energy eigenvalues and wave functions are interesting for experimental physicists. Key words: Klein–Gordon equation, modified Eckart potential plus Hulthen potential, Nikiforov-Uvarov (NU) method, position-dependent mass.

The paper contributes to the topic of optimal utilization of spatially distributed renewable resources. Namely, a problem of "sustainable" optimal cyclic exploitation of a renewable resource with logistic law of recovery is investigated. The resource is distributed on a circle and is collected by a single harvester moving along the circle. The recovering and harvesting rates are position dependent, and the latter depends also on the velocity of the harvester, which is considered as a control. The existence of an optimal solution is proved, as well as necessary optimality conditions for the velocity of the harvester. On this base, a numerical approach is proposed, and some qualitative properties of the optimal solutions are established. The results are illustrated by numerical examples, which reveal some economically meaningful features of the optimal harvesting.

Ryan, M, Malone, S, Donnellan, A, and Collins, K. Acceleration profile of elite Gaelic football with special reference to position of play. J Strength Cond Res 34(6): 1750-1758, 2020-The current study aimed to characterize the positional match-play demands of elite Gaelic football players with special reference to acceleration using predetermined 5-minute periods (epochs). Thirty-five male Gaelic players (mean ± SD, age: 24 ± 6 years; height: 180 ± 7 cm; mass: 81 ± 7 kg) across 5 playing positions (full-back, half-back, midfield, half-forward, and full-forward) were monitored during the investigation. Player movement was recorded during 19 matches using 4-Hz global positioning system technology (VXSport, New Zealand) resulting in 154 player observations. Global positioning system was used to record total distance (m), (high-speed running; m; ≥17 km·h), (very high-speed running distance; m; ≥22 km·h), the number of accelerations (n), duration of accelerations (s), peak acceleration (m), and distance of accelerations (m). Acceleration profiles were position dependent with midfielders found to have a high accumulation of acceleration movements when compared with all other positions (p ≤ 0.05). Declines of -2 to -32% for acceleration distance (m) depending on positional line of play were observed during match-play. Less high-speed running and very high-speed running distance was performed by the full-back line (high-speed running; -39% and very high-speed running; -36%) and full-forward line (-35%; -29%) when compared with half-back, midfielders, and half-forwards (p = 0.01, d = 1.35-1.77). Similar trends were reported for peak acceleration distance (p = 0.01, d = 1.15-1.93). The current investigation provides a greater understanding of temporal differences in acceleration profiles of playing position. We show that half-back, midfield, and half-forwards have the highest acceleration movements; these data can assist coaches in appropriately preparing players for the required acceleration distances required during match-play.

We discuss a nanolocalization technique with sub-nanometer localization resolution based on position dependent transverse Kerker scattering, obtained via interference of tailored electric and magnetic dipole moments.

There are many sources affecting the time resolution of a large area single gap RPC, the dominant one being the position dependent gain. There are several reasons for this gain variation, e.g. variation in the gas composition due to improper flow and leakage of gas, variations in the thicknesses of glass, button and spacer, etc. In the current work, the technique of offline time correction is presented using which time resolution of better than one ns can be achieved. The technique has been applied on the cosmic ray data collected in the 1 m \(\times \) 1 m RPC stack at TIFR. A few alternate solutions to improve the time resolution during the operational phase of INO-ICAL experiment are also discussed in this work. All the results presented are not only valid for the INO, but for any experiment using the single gap large RPC detectors.

We study the $(1+1)$ dimensional generalized Dirac oscillator with a position-dependent mass. In particular, bound states with zero energy as well as non zero energy have been obtained for suitable choices of the mass function/oscillator interaction. It has also been shown that in the presence of an electric field, bound states exist if the magnitude of the electric field does not exceed a critical value., Comment: 5 pages, no figures. Typos in Eqs. (5), (34) and (35), and other typos corrected. Presentation Improved

Within the model of rectangular potential profile and continuous position-dependent effective mass of electron in the double-barrier open semiconductor plane nano-heterostructure, the exact solutions of Schrodinger equation are obtained. Using them, the transmission coefficient, resonance energies, and widths of sub-barrier quasi-stationary electron states are calculated for the structure with In0.53Ga0.47As wells and In0.52Al0.48As barriers. The transmission coefficient and spectral characteristics of electron states are analyzed as functions of the width of near-interface region where the effective mass linearly depends on coordinate. It is shown that the increasing width of near-interface region between wells and barriers does not change the heights of maxima of transmission coefficient peaks but shifts and broadens them.

The classical and quantum mechanical correspondence for constant mass settings is used, along with some point canonical transformation, to find the position-dependent mass (PDM) classical and quantum Hamiltonians. The comparison between the resulting quantum PDM-Hamiltonian and the von Roos PDM-Hamiltonian implied that the ordering ambiguity parameters of von Roos are strictly determined. Eliminating, in effect, the ordering ambiguity associated with the von Roos PDM-Hamiltonian. This, consequently, played a vital role in the construction and identification of the PDM-momentum operator. The same recipe is followed to identify the form of the minimal coupling of electromagnetic interactions for the classical and quantum PDM-Hamiltonians. It turned out that whilst the minimal coupling may very well inherit the usual form in classical mechanics, it admits a necessarily different and vital form in quantum mechanics. Under our point transformation settings, only one of the two commonly used vector potentialsis found eligible and is considered for our Illustrative examples., Comment: 12 pages, minor amendments are done

In this paper, we consider a single machine no-wait scheduling model whereby job processing times are general functions of their position in the job sequence. We assume that the single machine must operate at a certain cycle, which can be determined by the scheduler. Furthermore, exactly one job has to be completed by the end of each cycle. Using different variations of the Linear Assignment Problem formulation, we develop polynomial time algorithms for minimizing the following objectives: makespan, total completion time, maximum earliness and total earliness.

Closely located multiple abasic sites or clustered abasic sites are highly mutagenic and potentially cytotoxic. They have been found to be repair resistant in several in vitro studies. We studied the efficiency of the repair of clustered abasic sites by the APE1 enzyme in nucleosome core particles (NCPs). Sequences having genomic importance as the core sequence of TATA box and CpG islands were used to assemble the NCPs where the abasic clusters are located around the A/T or G/C rich 0.5 positioning site of the NCPs. The thermodynamics of the binding and repair of the A/T or G/C encased clustered abasic sites in the NCPs by APE1 enzyme are reported herein for the first time that was monitored by Isothermal Titration Calorimetry (ITC). The A/T encased clustered abasic sites in the NCP showed greater binding affinity with APE1 than the G/C counterpart. A/T encased abasic sites are also cleaved faster to generate double strand breaks by APE1 enzyme as compared to the CpG island sequence in the NCP, albeit at much slower rate than the linear model. Although, the overall reactivity of the abasic sites is appreciably reduced in the NCPs, distinct differences exist in the processing of the abasic sites that are flanked by A/T or G/C rich sequence. Our study suggests that both sequence effect and nucleosomal positioning are important determinants for the repair efficiency of clustered abasic sites in NCPs.

In diesem Fachaufsatz wird die Entwicklung eines thermischen „Matlab Simscape“-Modells vorgestellt. Das geometrisch und zeitlich thermisch transiente Modell „SimTherm“ erlaubt die Berechnung der Erwärmung und Ausdehnung eines Kugelgewindetriebs. Das Modell wird anhand experimenteller Untersuchungen bezüglich der Temperaturverteilung validiert. Die Temperaturen der Kugelgewindetrieb-Spindel werden hierbei ortsvariabel mittels eines Infrarot (IR)-Sensors lokal auf der Spindeloberfläche ermittelt. This paper presents the development of a thermal “Matlab Simscape“ model. The geometrically and timewise thermal-transient model called “SimTherm“ makes it possible to calculate the temperature and the expansion of ball screws. The model is validated with experimental temperature tests. The temperature of the ball screw spindle is established locally on the spindle surface by using an infrared sensor.

ASA captures the degree of burial or surface accessibility of a protein residue. It is a very important indicator of the behavior of amino acids within a protein as well. It can be used to find protein interactions, interfaces, folding states, etc. Calculation of the ASA requires the presence of the structure of the protein. However, structure determination for proteins is expensive and requires significant technical effort. As a consequence, the prediction of ASA is a very important and fundamental problem in Bioinformatics and Proteomics. In this work, we have investigated self-taught machine learning methods along with deep neural network to predict the residue level accessible surface area (ASA) of a protein. We have found that deep learning neural networks can predict the ASA of the residues in a protein accurately. Furthermore, the proposed deep learning based method does not require the use of computationally demanding features such as the position specific scoring matrix (PSSM) which have been used in previous works. A simple Blosum62 matrix based position dependent representation of amino acids in a sequence window gives comparable performance. This is particularly attractive for proteome wide prediction of ASA. We have used various self-taught learning schemes for obtaining an optimal feature representation from unlabeled data. These include a sparse and regularized autoencoder neural network and a dictionary based learning scheme. We have used unlabeled data from the protein universe in an attempt to improve the feature representation. We have also evaluated the performance of a stochastic gradient based predictor of accessible surface area for different feature representations.

In this manuscript, we present a general computational method for characterizing the molecular structure of liquid water interfaces as sampled from atomistic simulations. With this method, the interfacial structure is quantified based on the statistical analysis of the orientational configurations of interfacial water molecules. The method can be applied to generate position dependent maps of the hydration properties of heterogeneous surfaces. We present an application to the characterization of surface hydrophobicity, which we use to analyze simulations of a hydrated protein. We demonstrate that this approach is capable of revealing microscopic details of the collective dynamics of a protein hydration shell., 13 pages, 6 figures

This paper presents a method to design the contour control of the ball screw system. The friction is one of the main factors to deteriorate the positioning performance. There exists the nonlinearity in the friction such as the Stribeck effect and the hysteresis property. The friction has the position dependent and asymmetric characteristics which change the friction size depending on the position and the direction of object. In addition, the friction varies depending on temperature and wear. From the above, it is necessary to successively estimate the friction. In these conditions, we propose the method to estimate and compensate the friction in real time. The LuGre model is applied to describe the dynamics of friction, which is able to represent the characteristics by a few parameters. The unscented Kalman filter is used to estimate the friction which is applicable to nonlinear systems. The estimated variables are used to compensate the friction in real time. The effectiveness is illustrated by simulations and experiments.

Since the parity-time-(PT-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with PT-symmetric potentials have been investigated. However, previous studies of PT-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized $\mathcal{PT}$-symmetric Scarf-II potentials. The broken linear PT symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than PT-symmetric ones, but feature similar properties. Our results may suggest new experiments for PT-symmetric nonlinear waves in nonlinear nonuniform optical media., Comment: 22 pages, 14 figures (Scientific Reports, in press)

We give exact analytical results for diffusion with a power-law position dependent diffusion coefficient along the main channel (backbone) on a comb and grid comb structures. For the mean square displacement along the backbone of the comb we obtain behavior < x(2) (t)> similar to t(1/(2-alpha)), where alpha is the power-law exponent of the position dependent diffusion coefficient D (x) similar to |x|(alpha). Depending on the value of alpha we observe different regimes, from anomalous subdiffusion, superdiffusion, and hyperdiffusion. For the case of the fractal grid we observe the mean square displacement, which depends on the fractal dimension of the structure of the backbones, i.e., < x(2) (t)> similar to t((1+upsilon)/(2-alpha)), where 0 < upsilon< 1 is the fractal dimension of the backbones structure. The reduced probability distribution functions for both cases are obtained by help of the Fox H-functions. (C) 2017 Elsevier Ltd. All rights reserved.

Schrodinger’s equation for a position-dependent effective mass is successfully tackled using the De la Peña’s factorization technique Fil: Canderle, Luis. Universidad Nacional de La Pampa; Argentina Fil: Plastino, Ángel Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina

A majority of patients diagnosed with obstructive sleep apnea are position dependent whereby they are at least twice as severe when sleeping supine (POSA). This study evaluated the accuracy and efficacy of a neck-worn device designed to limit supine sleep. The study included nightly measurements of snoring, sleep/wake, time supine, and the frequency and duration of feedback to monitor compliance.Thirty patients between ages 18 and 75 years, BMI ≤ 35 with an overall apnea-hypopnea index (AHI) ≥ 5 and an overall AHI ≥ 1.5 times the non-supine AHI, and an Epworth score ≥ 5 were prospectively studied. Subjective reports and polysomnography were used to assess efficacy resulting from 4 weeks of in-home supine-avoidance therapy and to measure device accuracy. From 363 polysomnography reports, 209 provided sufficient positional data to estimate one site's prevalence of positional OSA.In 83% of participants exhibiting50% reduction in overall AHI, the mean and median reductions were 69% and 79%. Significant reductions in the overall and supine AHI, apnea index, percent time SpO290%, and snoring contributed to significant improvements in stage N1 and N2 sleep, reductions in cortical arousals and awakenings, and improved depression scores. Supine position was under-detected by5% in 3% of cases. Sleep efficiency by neck actigraphy was within 10% of polysomnography in 87% of the studies when position feedback was delivered. The prevalence of POSA was consistently70% when the overall AHI was60.The neck position therapy device is accurate and effective in restricting supine sleep, improving AHI, sleep architecture and continuity, and monitoring treatment outcomes.

This paper considers single machine scheduling and due date assignment problems in which the jobs need to be delivered to customers after processing. It is assumed that the delivery times are proportional to the length of the already processed jobs, and a job's processing time depends on its position in a sequence. The objective functions include total earliness, the weighted number of tardy jobs and the cost of due date assignment. We analyze the problems with two different due date assignment methods and conclude that the problems are polynomial time solvable. We provide a dynamic programming algorithm with O(n3) times for the problems.

To improve the accuracy of five-axis machine tools, the measurement and compensation of position-dependent geometric errors (PDGEs) for rotary axes are of great importance. A double ball bar-based measuring method is proposed to precisely calibrate PDGEs. For each rotary axis, five measuring patterns are designed, in which the ball bar is sensitive to one direction throughout the measuring process. In the measurement, the ball bar functions as a high-precision displacement sensor with a single degree of freedom. Based on the ball bar readings, analytical solutions for 10 PDGEs, except for two angular position errors, are simply deduced. Simulations are conducted to analyze the influence of PDGEs and setup errors on measuring patterns. The advantages of the proposed method are discussed by comparison with three other measuring schemes. Finally, experimental verification of this approach is conducted on a five-axis machine tool. The results confirm that the method provides precision results of PDGEs for rotary axes.

We demonstrate localization effect in a two-dimensional quantum walk architecture. With position-dependent phase defects, the symmetry of standard quantum walk is broken; the walker is trapped in a fixed position dynamically. We show how the factors such as the phase defect, initial state and coin flipping affect on the localization effect in the quantum walk architecture.

In many real-life scheduling situations, the jobs deteriorate at a certain rate while waiting to be processed. This study introduces a new deterioration model where the actual processing time of a job depends not only on the starting time of the job but also on its scheduled position. The objective is to find the optimal schedule such that the makespan or total completion time is minimised. This study first shows that both problems are solvable in On log n time. This study further shows that in both cases there exists an optimal schedule that is the shortest processing time, longest processing time, or V-shaped with respect to the job normal processing times, depending on the relationships between problem parameters.

Through the Kaluza–Klein theory, we investigate the quantum dynamics of a Klein–Gordon particle under the Aharonov–Bohm effect for bound states, where it is subject to the linear and Coulomb-type central potentials inserted in the Klein–Gordon equation by modification of the mass term. Then, we determine analytically solutions of bound states and the energy profile of the scalar particle in this background.

The primary purpose of this work is to reproduce the scenario composed of a charge-dyon system utilizing position-dependent effective mass (PDM) background in the non-relativistic and in the relativistic regimes. In the non-relativistic case we substitute the exact charge-dyon eigenfunction into PDM Schrödinger equation, in the Zhu-Kroemer parametrization, and then solve it for the mass distribution considering M = M(r). Analogously, in the relativistic case we study the Klein-Gordon equation for a position-dependent mass, and in this case, we are able to analytically solve the equation for M = M(r,θ).