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# Correlated signal inference by free energy exploration [CL]

The inference of correlated signal fields with unknown correlation structures is of high scientific and technological relevance, but poses significant conceptual and numerical challenges. To address these, we develop the correlated signal inference (CSI) algorithm within information field theory (IFT) and discuss its numerical implementation. To this end, we introduce the free energy exploration (FrEE) strategy for numerical information field theory (NIFTy) applications. The FrEE strategy is to let the mathematical structure of the inference problem determine the dynamics of the numerical solver. FrEE uses the Gibbs free energy formalism for all involved unknown fields and correlation structures without marginalization of nuisance quantities. It thereby avoids the complexity marginalization often impose to IFT equations. FrEE simultaneously solves for the mean and the uncertainties of signal, nuisance, and auxiliary fields, while exploiting any analytically calculable quantity. Finally, FrEE uses a problem specific and self-tuning exploration strategy to swiftly identify the optimal field estimates as well as their uncertainty maps. For all estimated fields, properly weighted posterior samples drawn from their exact, fully non-Gaussian distributions can be generated. Here, we develop the FrEE strategies for the CSI of a normal, a log-normal, and a Poisson log-normal IFT signal inference problem and demonstrate their performances via their NIFTy implementations.

T. Ensslin and J. Knollmuller
Wed, 28 Dec 16
31/46

Comments: 19 pages, 5 figures, submitted

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# Real-time kinematic positioning of LEO satellites using a single-frequency GPS receiver [IMA]

Due to their low cost and low power consumption, single-frequency GPS receivers are considered suitable for low-cost space applications such as small satellite missions. Recently, requirements have emerged for real-time accurate orbit determination at sub-meter level in order to carry out onboard geocoding of high-resolution imagery, open-loop operation of altimeters and radio occultation. This study proposes an improved real-time kinematic positioning method for LEO satellites using single-frequency receivers. The C/A code and L1 phase are combined to eliminate ionospheric effects. The epoch-differenced carrier phase measurements are utilized to acquire receiver position changes which are further used to smooth the absolute positions. A kinematic Kalman filter is developed to implement kinematic orbit determination. Actual flight data from China small satellite SJ-9A are used to test the navigation performance. Results show that the proposed method outperforms traditional kinematic positioning method in terms of accuracy. A 3D position accuracy of 0.72 m and 0.79 m has been achieved using the predicted portion of IGS ultra-rapid products and broadcast ephemerides, respectively.

P. Chen, J. Zhang and X. Sun
Wed, 16 Nov 16
32/64

Comments: 27 pages, 8 figures, ready for publication in GPS Solutions

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# Sparse image reconstruction on the sphere: analysis vs synthesis [CL]

We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems, and combinations thereof, are considered as examples. Inverse problems are solved in both the analysis and synthesis settings, with a number of different sampling schemes. The most effective approach is that with the most restricted solution-space, which depends on the interplay between the adopted sampling scheme, the selection of the analysis/synthesis problem, and any weighting of the l1 norm appearing in the regularisation problem. More efficient sampling schemes on the sphere improve reconstruction fidelity by restricting the solution-space and also by improving sparsity in wavelet space. We apply the technique to denoise Planck 353 GHz observations, improving the ability to extract the structure of Galactic dust emission, which is important for studying Galactic magnetism.

C. Wallis, Y. Wiaux and J. McEwen
Thu, 22 Sep 16
24/62

Comments: 11 pages, 6 Figures

# Autonomous Orbit Determination via Kalman Filtering of Gravity Gradients [IMA]

Spaceborne gravity gradients are proposed in this paper to provide autonomous orbit determination capabilities for near Earth satellites. The gravity gradients contain useful position information which can be extracted by matching the observations with a precise gravity model. The extended Kalman filter is investigated as the principal estimator. The stochastic model of orbital motion, the measurement equation and the model configuration are discussed for the filter design. An augmented state filter is also developed to deal with unknown significant measurement biases. Simulations are conducted to analyze the effects of initial errors, data-sampling periods, orbital heights, attitude and gradiometer noise levels, and measurement biases. Results show that the filter performs well with additive white noise observation errors. Degraded observability for the along-track position is found for the augmented state filter. Real flight data from the GOCE satellite are used to test the algorithm. Radial and cross-track position errors of less than 100 m have been achieved.

X. Sun, P. Chen, C. Macabiau, et. al.
Tue, 20 Sep 16
71/74

Comments: 29 pages, 15 figures, Ready for Publication in IEEE Transactions on Aerospace and Electronic Systems

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# Gravity Gradient Tensor Eigendecomposition for Spacecraft Positioning [IMA]

In this Note, a new approach to spacecraft positioning based on GGT inversion is presented. The gravity gradient tensor is initially measured in the gradiometer reference frame (GRF) and then transformed to the Earth-Centered Earth-Fixed (ECEF) frame via attitude information as well as Earth rotation parameters. Matrix Eigen-Decomposition is introduced to directly translate GGT into position based on the fact that the eigenvalues and eigenvectors of GGT are simplespecific functions of spherical coordinates of the observation position. without the need of an initial position. Unlike the strategy of inertial navigation aiding, no prediction or first guess of the spacecraft position is needed. The method makes use of the J2 gravity model, and is suitable for space navigation where higher frequency terrain contributions to the GGT signals can be neglected.

P. Chen, X. Sun and C. Han
Fri, 12 Aug 16
1/38

Comments: 18 pages, 9 figures

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# Low-Earth Orbit Determination from Gravity Gradient Measurements [IMA]

An innovative orbit determination method which makes use of gravity gradients for Low-Earth-Orbiting satellites is proposed. The measurement principle of gravity gradiometry is briefly reviewed and the sources of measurement error are analyzed. An adaptive hybrid least squares batch filter based on linearization of the orbital equation and unscented transformation of the measurement equation is developed to estimate the orbital states and the measurement biases. The algorithm is tested with the actual flight data from the European Space Agency Gravity field and steady-state Ocean Circulation Explorer. The orbit determination results are compared with the GPS-derived orbits. The radial and cross-track position errors are on the order of tens of meters, whereas the along-track position error is over one order of magnitude larger. The gravity gradient based orbit determination method is promising for potential use in GPS-denied spacecraft navigation.

X. Sun, P. Chen, C. Macabiau, et. al.
Fri, 12 Aug 16
20/38

Comments: 34 pages, 8 figures

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# Sparse image reconstruction on the sphere: analysis vs synthesis [CL]

We develop techniques to solve ill-posed inverse problems on the sphere by sparse regularisation, exploiting sparsity in both axisymmetric and directional scale-discretised wavelet space. Denoising, inpainting, and deconvolution problems, and combinations thereof, are considered as examples. Inverse problems are solved in both the analysis and synthesis settings, with a number of different sampling schemes. The most effective approach is that with the most restricted solution-space, which depends on the interplay between the adopted sampling scheme, the selection of the analysis/synthesis problem, and any weighting of the l1 norm appearing in the regularisation problem. More efficient sampling schemes on the sphere improve reconstruction fidelity by restricting the solution-space and also by improving sparsity in wavelet space. We apply the technique to denoise Planck 353 GHz observations, improving the ability to extract the structure of Galactic dust emission, which is important for studying Galactic magnetism.

C. Wallis, Y. Wiaux and J. McEwen
Tue, 2 Aug 16
20/80

Comments: 11 pages, 6 Figures

# Second-Generation Curvelets on the Sphere [CL]

Curvelets are efficient to represent highly anisotropic signal content, such as local linear and curvilinear structure. First-generation curvelets on the sphere, however, suffered from blocking artefacts. We present a new second- generation curvelet transform, where scale-discretised curvelets are constructed directly on the sphere. Scale-discretised curvelets exhibit a parabolic scaling relation, are well-localised in both spatial and harmonic domains, support the exact analysis and synthesis of both scalar and spin signals, and are free of blocking artefacts. We present fast algorithms to compute the exact curvelet transform, reducing computational complexity from $\mathcal{O}(L^5)$ to $\mathcal{O}(L^3\log_{2}{L})$ for signals band-limited at $L$. The implementation of these algorithms is made publicly available. Finally, we present an illustrative application demonstrating the effectiveness of curvelets for representing directional curve-like features in natural spherical images.

J. Chan, B. Leistedt, T. Kitching, et. al.
Thu, 19 Nov 15
59/73

Comments: 10 pages, 7 figures, Code available at this http URL

# Directional spin wavelets on the sphere [CL]

We construct a directional spin wavelet framework on the sphere by generalising the scalar scale-discretised wavelet transform to signals of arbitrary spin. The resulting framework is the only wavelet framework defined natively on the sphere that is able to probe the directional intensity of spin signals. Furthermore, directional spin scale-discretised wavelets support the exact synthesis of a signal on the sphere from its wavelet coefficients and satisfy excellent localisation and uncorrelation properties. Consequently, directional spin scale-discretised wavelets are likely to be of use in a wide range of applications and in particular for the analysis of the polarisation of the cosmic microwave background (CMB). We develop new algorithms to compute (scalar and spin) forward and inverse wavelet transforms exactly and efficiently for very large data-sets containing tens of millions of samples on the sphere. By leveraging a novel sampling theorem on the rotation group developed in a companion article, only half as many wavelet coefficients as alternative approaches need be computed, while still capturing the full information content of the signal under analysis. Our implementation of these algorithms is made publicly available.

J. McEwen, B. Leistedt, M. Buttner, et. al.
Thu, 24 Sep 15
10/60

Comments: 11 pages, 7 figures. Code available on http://www.s2let.org

# 3D weak lensing with spin wavelets on the ball [CEA]

We construct the spin flaglet transform, a wavelet transform to analyse spin signals in three dimensions. Spin flaglets can probe signal content localised simultaneously in space and frequency and, moreover, are separable so that their angular and radial properties can be controlled independently. They are particularly suited to analysing of cosmological observations such as the weak gravitational lensing of galaxies. Such observations have a unique 3D geometrical setting since they are natively made on the sky, have spin angular symmetries, and are extended in the radial direction by additional distance or redshift information. Flaglets are constructed in the harmonic space defined by the Fourier-Laguerre transform, previously defined for scalar functions and extended here to signals with spin symmetries. Thanks to various sampling theorems, both the Fourier-Laguerre and flaglet transforms are theoretically exact when applied to band-limited signals. In other words, in numerical computations the only loss of information is due to the finite representation of floating point numbers. We develop a 3D framework relating the weak lensing power spectrum to covariances of flaglet coefficients. We suggest that the resulting novel flaglet weak lensing estimator offers a powerful alternative to common 2D and 3D approaches to accurately capture cosmological information. While standard weak lensing analyses focus on either real or harmonic space representations (i.e., correlation functions or Fourier-Bessel power spectra, respectively), a wavelet approach inherits the advantages of both techniques, where both complicated sky coverage and uncertainties associated with the physical modelling of small scales can be handled effectively. Our codes to compute the Fourier-Laguerre and flaglet transforms are made publicly available.

B. Leistedt, J. McEwen, T. Kitching, et. al.
Thu, 24 Sep 15
11/60

Comments: 24 pages, 4 figures

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# Localisation of directional scale-discretised wavelets on the sphere [CL]

Scale-discretised wavelets yield a directional wavelet framework on the sphere where a signal can be probed not only in scale and position but also in orientation. Furthermore, a signal can be synthesised from its wavelet coefficients exactly, in theory and practice (to machine precision). Scale-discretised wavelets are closely related to spherical needlets (both were developed independently at about the same time) but relax the axisymmetric property of needlets so that directional signal content can be probed. Needlets have been shown to satisfy important quasi-exponential localisation and asymptotic uncorrelation properties. We show that these properties also hold for directional scale-discretised wavelets on the sphere and derive similar localisation and uncorrelation bounds in both the scalar and spin settings. Scale-discretised wavelets can thus be considered as directional needlets.

J. McEwen, C. Durastanti and Y. Wiaux
Thu, 24 Sep 15
16/60

Comments: 29 pages, 8 figures

# A novel sampling theorem on the rotation group [CL]

We develop a novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) by associating the rotation group with the three-torus through a periodic extension. Our sampling theorem requires $4L^3$ samples to capture all of the information content of a signal band-limited at $L$, reducing the number of required samples by a factor of two compared to other equiangular sampling theorems. We present fast algorithms to compute the associated Fourier transform on the rotation group, the so-called Wigner transform, which scale as $O(L^4)$, compared to the naive scaling of $O(L^6)$. For the common case of a low directional band-limit $N$, complexity is reduced to $O(N L^3)$. Our fast algorithms will be of direct use in speeding up the computation of directional wavelet transforms on the sphere. We make our SO3 code implementing these algorithms publicly available.

J. McEwen, M. Buttner, B. Leistedt, et. al.
Fri, 14 Aug 15
33/49

Comments: 5 pages, 2 figures

# Complementary Lattice Arrays for Coded Aperture Imaging [CL]

In this work, we consider complementary lattice arrays in order to enable a broader range of designs for coded aperture imaging systems. We provide a general framework and methods that generate richer and more flexible designs than existing ones. Besides this, we review and interpret the state-of-the-art uniformly redundant arrays (URA) designs, broaden the related concepts, and further propose some new design methods.

J. Ding, M. Noshad and V. Tarokh
Tue, 9 Jun 15
41/56

Comments: N/A

# Meta learning of bounds on the Bayes classifier error [CL]

Meta learning uses information from base learners (e.g. classifiers or estimators) as well as information about the learning problem to improve upon the performance of a single base learner. For example, the Bayes error rate of a given feature space, if known, can be used to aid in choosing a classifier, as well as in feature selection and model selection for the base classifiers and the meta classifier. Recent work in the field of f-divergence functional estimation has led to the development of simple and rapidly converging estimators that can be used to estimate various bounds on the Bayes error. We estimate multiple bounds on the Bayes error using an estimator that applies meta learning to slowly converging plug-in estimators to obtain the parametric convergence rate. We compare the estimated bounds empirically on simulated data and then estimate the tighter bounds on features extracted from an image patch analysis of sunspot continuum and magnetogram images.

K. Moon, V. Delouille and A. Hero
Tue, 28 Apr 15
36/70

Comments: 6 pages, 3 figures

# The NIFTY way of Bayesian signal inference [IMA]

We introduce NIFTY, “Numerical Information Field Theory”, a software package for the development of Bayesian signal inference algorithms that operate independently from any underlying spatial grid and its resolution. A large number of Bayesian and Maximum Entropy methods for 1D signal reconstruction, 2D imaging, as well as 3D tomography, appear formally similar, but one often finds individualized implementations that are neither flexible nor easily transferable. Signal inference in the framework of NIFTY can be done in an abstract way, such that algorithms, prototyped in 1D, can be applied to real world problems in higher-dimensional settings. NIFTY as a versatile library is applicable and already has been applied in 1D, 2D, 3D and spherical settings. A recent application is the D3PO algorithm targeting the non-trivial task of denoising, deconvolving, and decomposing photon observations in high energy astronomy.

M. Selig
Wed, 24 Dec 14
18/37

Comments: 6 pages, 2 figures, refereed proceeding of the 33rd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2013), software available at this http URL and this http URL

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# A Novel, Fully Automated Pipeline for Period Estimation in the EROS 2 Data Set [IMA]

We present a new method to discriminate periodic from non-periodic irregularly sampled lightcurves. We introduce a periodic kernel and maximize a similarity measure derived from information theory to estimate the periods and a discriminator factor. We tested the method on a dataset containing 100,000 synthetic periodic and non-periodic lightcurves with various periods, amplitudes and shapes generated using a multivariate generative model. We correctly identified periodic and non-periodic lightcurves with a completeness of 90% and a precision of 95%, for lightcurves with a signal-to-noise ratio (SNR) larger than 0.5. We characterize the efficiency and reliability of the model using these synthetic lightcurves and applied the method on the EROS-2 dataset. A crucial consideration is the speed at which the method can be executed. Using hierarchical search and some simplification on the parameter search we were able to analyze 32.8 million lightcurves in 18 hours on a cluster of GPGPUs. Using the sensitivity analysis on the synthetic dataset, we infer that 0.42% in the LMC and 0.61% in the SMC of the sources show periodic behavior. The training set, the catalogs and source code are all available in this http URL

P. Protopapas, P. Huijse, P. Estevez, et. al.
Mon, 8 Dec 14
5/61

Comments: N/A

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# On spin scale-discretised wavelets on the sphere for the analysis of CMB polarisation [IMA]

A new spin wavelet transform on the sphere is proposed to analyse the polarisation of the cosmic microwave background (CMB), a spin $\pm 2$ signal observed on the celestial sphere. The scalar directional scale-discretised wavelet transform on the sphere is extended to analyse signals of arbitrary spin. The resulting spin scale-discretised wavelet transform probes the directional intensity of spin signals. A procedure is presented using this new spin wavelet transform to recover E- and B-mode signals from partial-sky observations of CMB polarisation.

J. McEwen, M. Buttner, B. Leistedt, et. al.
Thu, 4 Dec 14
3/82

Comments: 4 pages, Proceedings IAU Symposium No. 306, 2014 (A. F. Heavens, J.-L. Starck, A. Krone-Martins eds.)

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# Application of Lossless Data Compression Techniques to Radio Astronomy Data flows [CL]

The modern practice of Radio Astronomy is characterized by extremes of data volume and rates, principally because of the direct relationship between the signal to noise ratio that can be achieved and the need to Nyquist sample the RF bandwidth necessary by way of support. The transport of these data flows is costly. By examining the statistical nature of typical data flows and applying well known techniques from the field of Information Theory the following work shows that lossless compression of typical radio astronomy data flows is in theory possible. The key parameter in determining the degree of compression possible is the standard deviation of the data. The practical application of compression could prove beneficial in reducing the costs of data transport and (arguably) storage for new generation instruments such as the Square Kilometer Array.

T. Natusch
Fri, 23 May 14
12/44

Comments: In preparation for submission

# Slepian Spatial-Spectral Concentration on the Ball [CL]

We formulate and solve the Slepian spatial-spectral concentration problem on the three-dimensional ball. Both the standard Fourier-Bessel and also the Fourier-Laguerre spectral domains are considered since the latter exhibits a number of practical advantages (spectral decoupling and exact computation). The Slepian spatial and spectral concentration problems are formulated as eigenvalue problems, the eigenfunctions of which form an orthogonal family of concentrated functions. Equivalence between the spatial and spectral problems is shown. The spherical Shannon number on the ball is derived, which acts as the analog of the space-bandwidth product in the Euclidean setting, giving an estimate of the number of concentrated eigenfunctions and thus the dimension of the space of functions that can be concentrated in both the spatial and spectral domains simultaneously. Various symmetries of the spatial region are considered that reduce considerably the computational burden of recovering eigenfunctions, either by decoupling the problem into smaller subproblems or by affording analytic calculations. The family of concentrated eigenfunctions forms a Slepian basis that can be used be represent concentrated signals efficiently. We illustrate our results with numerical examples and show that the Slepian basis indeeds permits a sparse representation of concentrated signals.

Z. Khalid, R. Kennedy and J. McEwen
Mon, 24 Mar 14
49/50

# On the art and theory of self-calilbration [IMA]

Calibration is the process of inferring how much measured data depend on the signal one is interested in. It is essential for any quantitative signal estimation on the basis of the data. Here, we investigate the “art” of self-calibration that augments an external calibration solution using a known reference signal with an internal calibration on the unknown measurement signal itself. Contemporary self-calibration schemes try to find a self-consistent solution for signal and calibration. This can be understood in terms of maximizing their joint probability. Thus, the full uncertainty structure of this probability around its maximum is not taken into account by these schemes. Therefore better schemes — in sense of minimal square error — can be designed that also reflect the uncertainties of signal and calibration reconstructions. We argue that at least the signal uncertainty should not be neglected in typical measurement situations, since the calibration solutions suffer from a systematic bias otherwise, which consequently distorts the signal reconstruction. Furthermore, we argue that non-parametric, signal-to-noise filtered calibration should provide more accurate reconstructions than the common bin averages and provide a new, improved self-calibration scheme. We illustrate our findings with a simplistic numerical example.

Fri, 6 Dec 13
27/55

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# D3PO – Denoising, Deconvolving, and Decomposing Photon Observations [IMA]

The analysis of astronomical images is a non-trivial task. The D3PO algorithm addresses the inference problem of denoising, deconvolving, and decomposing photon observations. The primary goal is the simultaneous reconstruction of the diffuse and point-like photon flux from a given photon count image. In order to discriminate between these morphologically different signal components, a probabilistic algorithm is derived in the language of information field theory based on a hierarchical Bayesian parameter model. The signal inference exploits prior information on the spatial correlation structure of the diffuse component and the brightness distribution of the spatially uncorrelated point-like sources. A maximum a posteriori solution and a solution minimizing the Gibbs free energy of the inference problem using variational Bayesian methods are discussed. Since the derivation of the solution does not dependent on the underlying position space, the implementation of the D3PO algorithm uses the NIFTY package to ensure operationality on various spatial grids and at any resolution. The fidelity of the algorithm is validated by the analysis of simulated data, including a realistic high energy photon count image showing a 32 x 32 arcmin^2 observation with a spatial resolution of 0.1 arcmin. In all tests the D3PO algorithm successfully denoised, deconvolved, and decomposed the data into a diffuse and a point-like signal estimate for the respective photon flux components.

Mon, 11 Nov 13
31/39

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1. (Department of Electronics and Information Engineering, Jeonbuk National University, Jeonju 54896, Korea {wes7845@naver.com, felipe.p.vista.iv@gmail.com} )
2. (Advances Electronics & Information Research Center, Jeonbuk National University, Jeonju 54896, Korea )

GPS working set, ECU, ISO 11783, CAN bus, Virtual terminal, Precision agriculture

## 1. Introduction

Microprocessors (MPUs) and microcomputers are manufactured by a wide range of vendors, and electronic control units (ECUs) equipped with MPUs are installed in vehicles. A network and communication bus connect measuring and control units. Until recently, it has been difficult for these interconnected components to exchange information due to MPUs’ different internal structures and operation principles. To address this problem, standardization of computer communication has been actively pursued, and one example has been set up by the Society of Automotive Engineers (SAE) and the International Organization for Standardization [1].

The evolution of agriculture has led to uncertainty in production and instability in both supply and demand. To address such problems, extensive research has been conducted on mechanization and automation over the past 20 years. As a result, up to 80 percent of agricultural machines on the market include precision-agriculture components. The term precision agriculture'' (also known as precision farming) was officially adopted at an international conference in June 1997 at the University of Minnesota, USA [2]. In one study, Ünal proposed the integration of ZigBee communication and a controller area network (CAN) bus to reduce wire usage in precision farming [3].

Farmers are able to use a variety of systems economically and easily thanks to integrated management systems that monitor and analyze data to control farming equipment and implements. One such system is the Farm Management Information System (FMIS), which calculates the draft forces needed for pulling an implement to determine tractor power requirements and corresponding fuel consumption [4]. Another is an Agricultural Process-Data Service (APDS) prototype, which is part of the infrastructure in information-driven production [5]. Yet another type is an information management system for automated operation of a tractor-implement setup for managing information relevant to a task at hand [6]. An integral component for each of these systems is working sets, which consist of ECUs that handle data gathering and transmission.

In this study, a GPS ECU was designed for receiving and processing GPS data so that a tractor can receive and process essential GPS data. The algorithm structure is shown in Fig. 1. An analysis of experimental data shows that the implemented embedded system for the GPS working set complies with the required standard. The communication process was successfully implemented while providing the required GPS data. Plug-and-play functionality is also available, even if machines and implements may originate from different manufacturers and countries.

The contributions of this study are as follows:

· An ISOBUS compliant GPS working set

· Plug-and-play functionality regardless of farm-equipment source

· A device that is not specific to Global Navigation Satellite Systems (GNSSs) that can be used with any system that uses the standard data format of the National Marine Electronics Association (NMEA)

· Implementation of ISOAgLib in an embedded system

The proposed working set is presented in Section 2, followed by a description of the working set components in Section 3. The resulting system is then presented in Section 4, followed by a discussion in Section 5 and then the concluding remarks.

Fig. 1. Algorithm structure of proposed agricultural GPS ECU example.

### 1.2 Related Works

Tractors are the most common mechanical equipment used in modern agriculture and are powerful prime-mover work vehicles. The interface between a tractor and a farm implement is crucial since the tractor usually powers the implement in addition to controlling the work being done, whether stationary or in motion. A robust interface facilitates the task of connecting agricultural machinery or implements from one manufacturer to a tractor produced by a different manufacturer.

The advantage of this interface is that it makes mounting agricultural machinery and implements from different manufacturers a relatively straightforward process. Ultimately, farmers will be able to make a variety of choices, while manufacturers will benefit from the development of innovative products. However, until recently, it has been very difficult to use electronic systems in everyday farm works due to the absence of any standard for interfacing the electronic systems of a tractor with those of implements from other manufacturers.

This need has led to the formulation of the international standard ISO 11783, Tractors and machinery for agriculture and forestry — Serial control and communications data network'' [7,8]. ISO 11783 has been developed and now extends beyond the signal interface to virtual terminals, file servers, diagnostic interfaces, work area controllers, and domains. Although there are numerous manufacturers of agricultural machinery in Korea, only a few companies develop and produce ECUs that are compliant with the ISO 11783 protocol. For this reason, this research was carried out to address the important need to develop an ECU for agricultural machinery in Korea that complies with ISO 11783 [8].

Pereira $\textit{et al}$. worked on remote access to a CAN-based distributed control system (DCS) using several computers with ECU VTs, which use the IsoAgLib open library [9]. Backman $\textit{et al}$. discuss the use of ISO 11783 in the combined navigation and control of a tractor and an implement. They reported that the ISO 11783 network can transmit and receive all measurement data and control signals [10]. Oksanen $\textit{et al}$. presented a method of providing a development and run-time environment for designing an embedded system controller for a tractor and implements that is ISO 11783 compatible through software integration [11].

Sarker $\textit{et al}$. designed an embedded system ECU that uses GPS with IAR and IsoAgLib for agricultural tractors and follows the most important requirements of ISO 11783 [12]. Ham $\textit{et al}$. developed hardware and software aspects of GPS, light control, and sprayer ECUs according to the ISOBUS standard via the IsoAgLib library [13]. Stoll developed a CAN data logger system called SCANGate for recording auxiliary sensor data. It integrated several components, including an ECU, through messages transmitted over the tractor’s ISOBUS [14].

Rijanto’s logger went a bit further with a real-time maintenance embedded system that communicates with other ECUs through a CAN bus, which are then recorded to a secure digital card and then sent to an internet of things (IoT) server [15]. It must be noted that IoT entails the utilization of online systems security aspects [16].

GNSSs use satellites to calculate the position, elevation, and velocity of moving objects around the globe. They include a wide range of systems, including GPS (USA), GLONASS (Russia), Galileo (Europe), and Beidou (China). GPS data are an essential component of many applications, including simultaneous localization and mapping (SLAM) [17], autonomous driving [18], and heading for navigation [19].

## 2. Proposed Working Set Design

We will begin by describing the software and hardware implementation of GPS data for enabling precision agricultural equipment to perform CAN communication (CAN bus) using the ISOBUS 11783 protocol. Communication between different types of agricultural equipment and implements using the ISOBUS 11783 protocol is also analyzed to verify the effectiveness of the proposed method. The hardware development environment for the GPS working set is provided in Fig. 2.

The ARM version of IAR Embedded Workbench was used as the development environment for implementing GPS ECUs, and an STM32F107 ARM 32-bit Cortex-M3 board was used for the ECU hardware. A CAN bus was used for communicating via ISOBUS, and the UART communication function was used for retrieving data from the GPS receiver. In addition to ISOAgLib, the virtual terminal required a new library that included APIs to provide additional functionality.

Tractors and machine implements that comply with the ISO 11783 standard transmit and receive messages via CAN communication. All the interconnected ECUs communicating via CAN inside agricultural machines are microcontroller devices with a design based on international-standard computer network protocols and CAN bus standards. For the purposes of this study, the GPS working set was designed and implemented using the open-source ISOAgLib library, which is based on the ISO 11783 standard. The ISOAgLib library is an essential component in the development of an ISOBUS protocol-compliant GPS ECU. The GPS working set consists of a master and one member. The GPS ECU acts as the controller for the set member and complies with the ISO 11783 standard when transmitting position and time data to the CAN bus. The procedure for developing an ISOAgLib-based GPS working set is shown in Fig. 3.

Fig. 2. Hardware setup.

Fig. 3. Development process.

## 3. Working Set Components

### 3.1 ISOBUS

The International Organization for Standardization has merged SAE 1989 and DIN 9683 to establish ISO 11783 (ISOBUS). ISO 11783 describes an international standard data communication protocol and bus based on CAN2.0B. It is derived from a document from the Society of Automotive Engineers (SAE), J 1939, and was developed jointly for trucks, buses, construction, and agriculture [1].

The purpose of ISO 11783 is to provide an open and interconnected system for onboard electronic systems that enables ECUs to communicate with each other via a standardized system. The main components of the ISO 11783 standard that play an important part in the design of the working set are the physical layer [20, p. 2], datalink layer [21, p. 3], network layer [22, p. 4], virtual terminal [23], implement-messages application layer [24], tractor ECU [25], task controller and management information system data interchange [26], file server [27], and diagnostic services module [28]. Tractors and implements that comply with the ISO 11783 standard transmit and receive messages via the CAN specification, by which ECUs are interconnected to the CAN bus. They contain micro-controllers and devices that are compliant with the international standard for the computer network protocol and bus standards.

Fig. 4. VT-Designer.

### 3.2 ISOAgLib

Spangler and Wodok [7] have utilized an application development methodology using ISOAgLib. Tumenjargal [13,29,30] and Sarker [12] have conducted research on the development of ECUs that can be used in precision agricultural machinery, drawing on Spangler and Wodok’s application development methodology. The ISOAgLib library, which includes the vast ISO 11783 standard protocols, is an essential component in the development of GPS ECUs based on the ISOBUS protocol [25]. It is an open-source programming library that includes all of the functions built into the communications system in accordance with standard ISO 11783, including the user interface, virtual terminals, or task controllers [1, p. 1].

The ISOAgLib library consists of several parts, including communications, a scheduler, driver extensions, a hardware abstraction layer (HAL), and hardware drivers. All functions involving the compliance of machine interface and functions with standard protocols are already implemented in ISOAgLib, making it easier to develop ISOBUS applications. ISOAgLib is currently in active use in fields such as agriculture, forestry, construction, and special vehicle systems. Conveniently, an API (application programming interface) for an ECU has already been developed that uses the ISOAgLib library [12,31].

For the present study, each soft key was configured to correspond with information from the GPS, ECU, and firmware so that each key could be allocated its corresponding Data Mask and be properly displayed in the virtual terminal. In the case of data from ISOAgLib, both a CAN server and a VT client-server PC version were required to utilize ISOAgLib. In this study, however, programs were coded to enable implementing ISOAgLib in an embedded system.

### 3.3 XML Object Pool

A file in an IOP format (ISO 11783 ObjectPool) is required when the Cortex-M3 ARM-based ECU API is configured. The file includes library files with various functions in the data mask of the virtual terminal. The ISOAgLib library examples include XML files that are needed to create *.IOP files. These XML files need to be modified to customize the data mask with additional buttons, soft keys, and graphics to be included in the VT data mask.

The IOP file can be obtained from vt2iso.exe'' as provided by ISOAgLib, as well as the library files (*.inc, *.h) required to create applications. The XML file for IOP production is created using markup language. Users unfamiliar with XML may encounter some difficulty when writing code, but the task is made easier by VT-Designer, whose graphical interface enables object pools to be organized visually.

Lastly, ISOAgLib can also be used to create API and IOP files for desired functions to be implemented in the ECU. These functions are the parts of the application that transmit longitude and latitude coordinates and time data from the GPS to the GPS parser and then the VT. The design process using VT-Designer is shown in Fig. 4. It is possible to create an XML file and configure files in IOP format using the drag-and-drop feature of VT-designer.

### 3.4 CAN Communication

There are three separate CAN standards: CAN 1.0, 2.0A (standard CAN), and 2.0B (extended CAN). The main difference between them is the length of the identifier prepended to each message. Version 2.0B extended frames contain a 29-bit message identifier (Bosch, 1991). More information on CAN buses is available from Bosch (1991).

The CAN communication flow consists of large texts that provide the content of CAN messages and small text that provides PGN CAN message data with a size of 8 bytes. The VT status message is sent first with a PGN of E600 and a control byte of FE. This is omitted after the first message since the CAN bus protocol requires messages to be transmitted at a rate of once every second. The VT’s time/date (TD) message has a PGN of FEE6 and is transmitted continuously to all ECUs. Next is the address claim, in which each ECU claims ownership of an assigned address. If an ECU’s address is a duplicate of another’s, the working-set master with lower priority modifies its address according to the ISOBUS protocol. After receiving the PGN (EA00, 00EE00) through which address claims are conducted, each working-set master checks its own address and then displays the number of its members (FE0D, 01...).

Fig. 5. Experimental Setup.

Fig. 6. ECU-VT communication by CAN Analyzer.

## 4. Implemented System

Experimental and analytical data confirmed that the embedded GPS working set system observes the standard communication protocol when successfully transmitting the GPS data required by an agricultural machine. Standard time and position data were supplied separately to connected farm implements to perform precision agriculture tasks efficiently. The system architecture of the GPS working set has demonstrated its overall applicability to agricultural work. The system also complies with standard protocols for plug-and-play functionality for manufacturers from various countries, which is an additional convenience for users.

### 4.1 Experimental Setup

The experimental setup for the proposed system is shown in Fig. 5, where a uBlox M8 GNSS EV kit (EVK-M8T) was used as a GPS receiver with an ARM Cortex-M3 used as the controller for the system. CAN messages were analyzed using the KVASER PCIEcan HS, and an IntelliView IV virtual terminal was set as the communication target for verifying the system’s compliance with the ISO 11783 standard.

### 4.2 CAN Analysis

The GPS ECU complies with the VT and ISOBUS protocols, as shown in the CAN communication in Fig. 6. It is difficult to fully understand the message even though it is the actual data transmitted and received since only key information can be seen in the CAN analyzer, not original CAN 2.0B type data [7,12,31]. Hence, the results are presented in a much clearer manner in Fig. 7 as the flow of messages communicated during the experiment.

The analyzed data are presented as a flowchart of the entire communication flow of messages exchanged between the GPS ECU and the VT, beginning with the VT status message and real-time transmission of GPS data. In the flowchart, periodic and unnecessary messages are omitted to clearly show the data transmission/reception between the GPS and VT. The object pool remains in a transfer state until the entire object pool has been successfully transmitted and received via the CAN bus between the commercial VT and the GPS ECU without the GPS receiver. At the same time, the GPS working set with the GPS receiver transmits GPS data to VT.

Periodic and unnecessary messages are also omitted in the CAN message flow chart to show data transmission and reception between the VT and the GPS working-set master. Messages omitted after the initial message are VT status, time/date (TD), and working set maintenance messages. One example of these messages is the cap illumination (CL) message, which is sent from the VT to the tractor ECU (TECU). The CL message concerns the lighting in the driver’s seat. It is transmitted continuously and periodically until a response is received from the VT, but since the TECU is not present on the network, the message will continue to be transmitted.

Fig. 7. GPS ECU and VT CAN Communication Analysis (Detailed explanation of process explained in Sections 4.3 and 4.4).

### 4.3 Working Set

$\textbf{Part I:}$ The GPS working set consists of a working-set master and a working-set member, which comprise the basic units of an ISOBUS protocol working set. PGN (E700, FF ...) is a maintenance message that is sent by the working-set master separately from the VT status message in Fig. 7(a). This message is also omitted after the first message is transmitted to ensure that at least one message per second is transmitted.

The ECU then submits a request for information about which language is being used by the VT (EA00, 0F FE 00) [15]. The language of the VT used for the present experiment was English, so it returned a message (FE0F, 65 6E...) as part of the language command to the GPS working-set master, which indicated that the English setting should be used. Since the current ECU was set to little endian mode, the message was in PGN FEOF format. The first two bytes of the language command message after PGN FEOF refer to language converted to ASCII format (i.e., 65'' for e,'' and 6e'' for n''). The ECU then submits a query and receives information about the number of soft keys, fonts, hardware specifications, and memory requirements.

Fig. 8. Firmware with Korea time.

Fig. 9. Real-time latitude & longitude.

### 4.4 Object Pool Transmission: ECU to VT

When the explained preliminary steps are completed, the entire object pool is divided into ETP messages and transmitted from the ECU to the VT. The ETP sends and receives information regarding the number and size of the packages. ETP messages begin with sequence 1, and the maximum number of ETP packages is set at 30. The second byte of the get-memory message set is the international standard version of ISO 11783, with which the VT is compliant, and the third to the sixth bytes describe the memory requirement.

$\textbf{Part II:}$ The VT currently used is ISO 11783-compliant (second edition of 2010) with a required memory of $\textbf{00 80 FE}$ (hex, little endian) bytes, which is equal to 33,022 bytes. The second to the fifth bytes of ETP.CM$\backslash\_$RTS refer to the number of bytes that will be transmitted ($\textbf{80 89}$ hex; little endian; 32,905 bytes) (Fig. 7(b)).

$\textbf{Part III & Part IV:}$ The object pool of the GPS working set is sent via ETP, and the remaining small capacity is transferred to the VT via TP (Fig. 7(c), Fig. 7(d)). An End of Object Pool ($\textbf{E700}$,12 ...) message is then sent when the object pool transfer is complete.

$\textbf{Part V:}$ When the object pool to transfer to the VT is complete or a soft key is pressed, a corresponding message ($\textbf{E600}$, $\textbf{00}$ ...) is sent to the ECU (Fig. 7(e)). The seventh byte of the soft-key activation message ($\textbf{E600}$, $\textbf{00}$ ...) is a unique code that is assigned to the soft key and defined in the object pool. Three soft keys are activated in the object pool of the current GPS working set. The first (keycode 254) contains information about the current ECU software, the second (key code 255) includes GPS information, and the third (key code 256) is an auxiliary.

$\textbf{Part VI:}$ The GPS working-set master transmits three 15-byte packets and executes TP when the soft-key is released. VT receives a message indicating that TP has been completed when the operation is completed. Strangely, there are notification messages ($\textbf{E600}$, $\textbf{B3}$ ...) indicating that the string values have been updated (Fig. 7(f)). For this response message to be generated, a message that changes string values ($\textbf{E700}$, $\textbf{B3}$ ...) must first be transmitted. This message ($\textbf{E700}$, $\textbf{B3}$ ...) cannot be checked using the CAN bus and is transmitted as an 8-byte data message in the TP.

The data transmitted after the sequence byte ($\textbf{B3 40 9C}$ ...) were examined and verified for CM$\backslash\_$data transmission. $\textbf{B3}$ refers to $\textbf{E700 B3}$ and means the change of a string value (transport protocol), and $\textbf{40 9C}$ is an Object ID $\textbf{40000 i}$n little endian mode. The actual output string for the longitude object ID is 40,000. It can be seen that the output string of the latitude object ID (40001) is changed through the third and fourth data ($\textbf{419C}$) in the subsequent TP.CM$\backslash\_$Data Transfer message.

## 5. Discussion

It is difficult to fully understand the message even though it is the actual data transmitted and received since only key information can be seen in the CAN analyzer, not original CAN 2.0B type data [7,12,31]. The VT screen (Fig. 8) shows when the object pool is uploaded and the first soft-key (key code 254) is pressed. The data mask provides information about the ECU firmware updates, time data, and the second soft-key of the GPS receiver in real time. When the second soft key (keycode 255) is pressed, a new display is shown (Fig. 9).

The object pool’s limitations include memory and creating figure objects. Image data to be processed by the VT-designer can be represented only by a maximum of 8 bytes (256 bits). As shown in Fig. 9, the bitmap image uploaded to the VT has a lower resolution than the original, making it difficult for the image to display map data. It is difficult for ECU hardware with 256K of flash memory to accommodate even this low-resolution image data. Replacing the ECU with better hardware may be a workaround but is not a long-term solution. A better solution may be to ensure that there is a large amount of map data in the VT. Once this problem has been solved, the GPS ECU should require no further hardware configuration, and neither flash memory nor map resolution will be an issue.

There is currently an abundance of high-precision agricultural GNSS receivers and modules on the market to choose from. The designed ECU is not GNSS-specific as long as it can receive and process the GPS data that is eventually transmitted to the virtual terminal. The ECU is designed to process agricultural data by making use of GPS data, and the utility of the design method has been confirmed by experimental communication with a virtual terminal. The GPS ECU $\textbf{processes}$ longitude, latitude, and universal time-coordinated (UTC) data inputs from the GPS receiver and is responsible for CAN communication for the VT and related data transmission such as position, time, and bearing.

## 4. Conclusion

This paper has dealt with the design and implementation of an embedded system GPS working set based on the ISOBUS protocol for autonomous agricultural equipment, particularly for South Korea. Experimental analysis confirmed the successful communication between a VT and GPS ECU and implementation of plug-and-play functionality. Object-pool transmission, ECU response to VT commands, modification of the VT data mask, and analysis of transmitted and received messages during communication via the CAN analyzer have been discussed.

The GPS working set is only responsible for interworking, transmitting, and updating the VT for GPS-receiving data. In the case of farm equipment that is compliant with the ISOBUS protocol, a functional GPS working set in which plug-and-play functionality is executed is sufficient, regardless of the country and manufacturer. Since every manufacturer uses different hardware and software, a VT may not always be available, but GPS data alone is useless to farmers unless the user has access to a visual display of a map database. Therefore, future research on VT display of GPS data based on map data is an essential prerequisite to developing a fully functional precision agricultural GPS system.

### ACKNOWLEDGMENTS

This work was supported in part by the Brain Research Program of the National Research Foundation (NRF) funded by the Korean government (MSIT) (No. NRF-2017M3C7A1044816) and in part by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2019R1A6A3A01094685).

### REFERENCES

1
Bosch , Dec. 2015, Part 1: Data link layer and physical signalling, Bosch, Standard
2
Kim Y. H., 2017, 정밀농업을 가능케 하는 위성·센서·빅데이터·드론 (Satellites, sensors, big data, and drones that enable precision farming), elec4: Agriculture turns into a industry, Sep. 02, 2016. Accessed
3
Ünal İ., 2020, Integration of ZigBee based GPS receiver to CAN network for precision farming applications, Peer-to-Peer Networking and Applications, pp. 1-12
4
Tsiropoulos Z., Fountas S., Gemtos T., Gravalos I., Paraforos D., 2013, Management information system for spatial analysis of tractor- implement draft forces, in Precision agriculture’13, pp. 349-356
5
Steinberger G., Rothmund M., Auernhammer H., Mar. 2009, Mobile farm equipment as a data source in an agricultural service architecture, Computers and Electronics in Agriculture, Vol. 65, No. 2, pp. 238-246
6
Pesonen L., Kaivosoja J., Virolainen V., Oittinen J., Kivipelto J., 2007, Remote assisted task management for ISOBUS equipped tractor-implement combination, Agricultural Engineering International: CIGR EJournal, Vol. IX
7
Spangler , Wodok M., 2010, IsoAgLib - Development of ISO 11783 Applications in an Object Oriented way, Accessed: Jun. 01, 2016
8
Park J., Huh M. Y., 2016, 스마트농업 국제 표준화 동향. 한국통신학회지 (정보와통신) (Trend of International Standardization of Smart Agriculture), The Journal of the Korean Institute of Communication Sciences(Information & Communication), Vol. 34, No. 1, pp. 70-75
9
Pereira R. R. D., Lopes W. C., Sousa R. V., Porto A. J. V., Inamasu R. Y., Dec. 2011, Object oriented C++ library IsoAgLib study and implementation from the remote CAN-Based Distributed Control System, in 2011 9th IEEE International Conference on Control and Automation (ICCA), pp. 744-749
10
Backman J., Oksanen T., Visala A., Mar. 2013, Applicability of the ISO 11783 network in a distributed combined guidance system for agricultural machines, Biosystems Engineering, Vol. 114, No. 3, pp. 306-317
11
Oksanen T., Kunnas A., Visala A., Jan. 2011, Development and Runtime Environment for Embedded Controller supporting ISO 11783 Standard, IFAC Proceedings Volumes, Vol. 44, No. 1, pp. 2895-2900
12
Sarker M. M. K., Park D., Ham W., Tumenjargal E., Lee J., Embedded Workbench Application of GPS Sensor for Agricultural Tractor, presented at the International Conference on Embedded Systems, Cyber-physical Systems, and Applications (ESCS), Las Vegas, USA, 2012
13
Ham W., Enkhbaatar T., Luubaatar B., Hyeokjae K., 2012, Implementation of ECU for Agricultural Machines Based on ISOAgLib Open Source
14
Stoll G. P., Luck J. D., Pitla S. K., Rohrer R. A., 2021, Integration of Auxiliary Sensor Data to ISOBUS for Agricultural Machinery Data Collection, Applied Engineering in Agriculture, Vol. 37, No. 1, pp. 157-162
15
Rijanto E., Adiwiguna E., Sadono A. P., Nugraha M. H., Mahendra O., Firmansyah R. D., 2020, A new design of embedded monitoring system for maintenance and performance monitoring of a cane harvester tractor, Journal of Mechatronics, Electrical Power, and Vehicular Technology, Vol. 11, No. 2, pp. 102-110
16
Bhati B. S., Rai C. S., Apr. 2020, Analysis of Support Vector Machine-based Intrusion Detection Techniques, Arabian Journal for Science and Engineering, Vol. 45, No. 4, pp. 2371-2383
17
Carlson J., 2010, Mapping large, urban environments with gps-aided slam, Carnegie Mellon University, Pittsburgh, Pennsylvania
18
Zein Y., Darwiche M., Mokhiamar O., Dec. 2018, GPS tracking system for autonomous vehicles, Alexandria Engineering Journal, Vol. 57, No. 4, pp. 3127-3137
19
Vista IV F. P., Chong K. T., 2019, Design and Real-Time Implementation of a 3-Stage CnW Heading System on an Ubuntu Linux-Embedded Board, Journal of Sensors, vol. 2019, pp. 13
20
ISOBUS Group in VDMA , Apr. 2002, Part 2: Physical layer, ISOBUS Group in VDMA, Standard
21
ISOBUS Group in VDMA , May 2014, Part 3: Data link layer, ISOBUS Group in VDMA, Standard
22
ISOBUS Group in VDMA , May 2001, Part 4: Network layer, ISOBUS Group in VDMA, Standard
23
ISOBUS Group in VDMA , Apr. 2014, Part 6: Virtual terminal, ISOBUS Group in VDMA, Standard
24
ISOBUS Group in VDMA , Mar. 2015, Part 7: Implement messages application layer, ISOBUS Group in VDMA, Standard
25
ISOBUS Group in VDMA , Jul. 2002, Part 9: Tractor ECU, ISOBUS Group in VDMA, Standard
26
ISOBUS Group in VDMA , Dec. 2009, Part 10: Task controller and management information system data interchange, ISOBUS Group in VDMA, Standard
27
ISOBUS Group in VDMA , May 2007, Part 13: File server, ISOBUS Group in VDMA, Standard
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ISOBUS Group in VDMA , Mar. 2009, Part 12: Diagnostics services, ISOBUS Group in VDMA, Standard
29
Tumenjargal E., Badarch L., Kwon H., Ham W., Mar. 2013, Embedded software and hardware implementation system for a human machine interface based on ISOAgLib, Journal of Zhejiang University SCIENCE C, Vol. 14, No. 3, pp. 155-166
30
Enkhbaatar T., Luubaatar B., Hyeokjae K., Ham W., 2012, Design and Implementation of Virtual Terminal Based on ISO11783 Standard for Agricultural Tractors, presented at the 11th Int. Conf. on Precision Agriculture, Indianapolis, Indiana, USA
31
Tumenjargal E., Badarch L., Kwon H., Ham W., 2012, Software Development Tool for Agricultural Machinery Based on IsoAgLib Open Source Library, presented at the 2012 Dallas, Texas, July 29 - August 1, 2012, St. Joseph, MI

## Author

##### JaYu Kim

JaYu Kim received his Master Degree in Electronic engineering from Jeonbuk National University, Jeonju, Korea, in 2017. His research interests are in the areas of Precision agricultural machinery, International standard protocol, Sensor fusion, Sensor network, Flying control & Optimization.

##### Felipe P. Vista IV

Felipe P. Vista IV got his Ph.D. degree in Electronic Engineering from Jeonbuk National University, Jeonju, Korea in 2013. He is a Research Assistant Professor fellow for Advances Electronics and Information Research Center and concurrently a lecturer at School of International Science and Engineering for Global Frontier College of JBNU. His research interests are in the field of Systems Design, Software Development, Fuzzy Logic, Sensor Fusion, Embedded Systems, Navigation Systems, Marine Information System, Signal Processing & Augmented Reality.

##### Dae-Young Lim

Dae-Young Lim got his Ph.D. degree in Electronic Engineering from Jeonbuk National University, Jeonju, Korea in 2018. Currently He is a post-doctoral fellow in Department of Electronic Engineering, Jeonbuk National University. His research interests include automatic control, neural networks and artificial intelligence.

##### Kil To Chong

Kil To Chong received the Ph.D. degree in Mechanical Engineering from Texas A&M University, College Station, USA in 1995. Currently, he is a Professor at the School of Electronic Engineering, Jeonbuk National University, South Korea and head of the Advanced Research Center of Electronics. His research interests are in the areas of Sensor network, Network system control, Motor fault detection, Time-delay systems, Neural network, Machine Learning, Artificial intelligence, and Bioinformatics.

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text:
# Partial derivatives and change of variables

## Homework Statement

Sorry I tried to use Latex but it didn't work out :/

Make the change of variables r = x + vt and s = x vt in the wave equation
partial^2y/partialx^2-(1/v^2)(partial^2y/partialt^2)=0

## Homework Equations

partialy/patialx=(partialy/partialr)(partialr/partialx)+(partialy/partials)(partials/partialx)
partialy/partialy=(partialy/partialr)(partialr/partialt)+(partialy/partials)(partials/partialy)

partialr/partialx=1
partials/partialx=1
partialr/partialt=v
partials/partialt=-v

## The Attempt at a Solution

I am a little bit confused about what to do. This is what I did:

Rearranging:
partial^2y/partialr^2(1-1/v)+partial^2y/partials^2(1+1/v)=0

I feel this is completely wrong, but I can't think of another way of doing it.

Related Calculus and Beyond Homework Help News on Phys.org
hunt_mat
Homework Helper
Start from the basics:

$$\begin{array}{ccc} \frac{\partial}{\partial x} & = & \frac{\partial r}{\partial x} \frac{\partial}{\partial r}+\frac{\partial s}{\partial x} \frac{\partial}{\partial s} \\ \frac{\partial}{\partial t} & = & \frac{\partial r}{\partial t} \frac{\partial}{\partial r}+\frac{\partial s}{\partial t} \frac{\partial}{\partial s} \end{array}$$

Computing these yields:

$$\begin{array}{ccc} \frac{\partial}{\partial x} & = & \frac{\partial}{\partial r}+\frac{\partial}{\partial s} \\ \frac{\partial}{\partial t} & = & v\frac{\partial}{\partial r}-v\frac{\partial}{\partial s} \end{array}$$

Then just apply these again to get the second order derivatives.

Yes, that is what i did and I got:

partial^2y/partialx^2=partial^2y/partialr^2+partial^2y/partials^2
partial^2y/partialt^2=vpartial^2y/partialr^2-v(partial^2y/partials^2)

Is that right? And then I just plugged that in the initial equation.

hunt_mat
Homework Helper
Just use:
$$\frac{\partial^{2}}{\partial x^{2}}=\left(\frac{\partial}{\partial r}+\frac{\partial }{\partial s}\right)\left(\frac{\partial}{\partial r}+\frac{\partial }{\partial s}\right)$$

Could you explain that ? And why what I did is wrong ? Can't I just take the partial derivative of partialy/partialx ?

hunt_mat
Homework Helper
Where dies y come into it, I thought the original variables were x and t which you were transforming into r and s?
Okay, you should know that:
$$\frac{\partial}{\partial x}=\left(\frac{\partial}{\partial r}+\frac{\partial }{\partial s}\right)$$

So just apply this operator twice.

Y comes from the original equation,

partial^2y/partialx^2-(1/v^2)(partial^2y/partialt^2)=0

I did what you said and I got

4partial^2y/(partialr * partials)

Is that right ?

hunt_mat
Homework Helper
That looks very good. set that equal to zero and you have your original equation which you have now reduced to:
$$\frac{\partial^{2}y}{\partial r\partial s}=0$$

Thank you very much !

How can I solve that equation ?

hunt_mat
Homework Helper
integrate once and what do you get?

do i get y=rs? I am confused...

hunt_mat
Homework Helper
Integrate once w.r.t. r say and you obtain:
$$\frac{\partial y}{\partial s}=f(s)$$
Now what would you do?

now Integrate with respect to s and I get: f(s)f(r)??

hunt_mat
Homework Helper
No, you're forgetting your basic integration:
$$y=\int f(s)ds+g(r)$$
The integral of f(s) w.r.t. s is just another function, call it h(s) amd trhat is your solution.

Oh okay ! thank you so much ! you were really helpful :)


text:
# Excluding a chapter from TOC

latexpdflatex

In my LaTeX document I've got a table of contents that is automatically generated by collecting everything that is of the form \chapter.

However, I've got an acknowledgements chapter before the table of contents and I don't want it to be automatically labelled "Chapter 1" or captured in the table of contents. Should I be avoiding \chapter altogether and use \section instead? I want to keep the font/formatting that other chapters have though.

#### Best Solution

The usual way to handle that kind of thing is with the \frontmatter command. Put it after the \begin{document}, and then put \mainmatter right before the \chapter you want to correspond to chapter 1. This may only work in the book class. If you're using \chapter in a report, then \chapter* should also create a chapter that has no number and won't show up in the table of contents.


text:
# zbMATH — the first resource for mathematics

On the product of semigroup valued measures. (English) Zbl 0917.28011
A version of Alexandroff’s theorem for measures defined on a ring and with values in a $$\sigma$$-complete commutative semigroup is proved. This result is applied to the existence of a product measure with values in a $$\sigma$$-distributive $$\ell$$-ring as well as to the existence of a joint observable on MV-algebras.
##### MSC:
 28B10 Group- or semigroup-valued set functions, measures and integrals 28B15 Set functions, measures and integrals with values in ordered spaces


text:
+0

# Math problem. Ty for the help!

+1
68
2
+155

Let a and b be the solutions to 5x^2 - 11x + 4 = 0 Find:
$$[\frac{1}{a} + \frac{1}{b}]$$

Feb 28, 2021

#1
+944
+2

sum of roots = -b/a = 11/5

product of roots = c/a = 4/5

$$\frac{1}{a} + \frac{1}{b} = \frac{a+b}{ab} = \frac{\frac{11}{5}}{\frac{4}{5}} = \boxed{\frac{11}{4}}$$

Feb 28, 2021
#2
+155
0

Tysm!

Mar 1, 2021


text:
• 2nd communication: from RERO Explore to swisscovery: Part of RERO's libraries joined the SLSP (Swiss Library Service Platform) network at the beginning of December 2020. See the implications (2nd communication in French / in German) of this change for you as a user.
This query concerns only resources held in libraries.
• Selected facet
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#### Selected facet

Expand to all references (without full text)
• Several versions

### Measurement of j/ production in pp collisions at = 2.76 and 7 tev with alice

Arnaldi, Roberta
Journal of Physics G: Nuclear and Particle Physics, 2011, Vol.38(12), p.124106 (4pp) [Peer Reviewed Journal]

• Several versions

### Experimental overview on quarkonium production

Arnaldi, Roberta
arXiv.org, Apr 11, 2016 [Peer Reviewed Journal]

• Article
Select

### The onset of the anomalous J/psi suppression in Pb-Pb collisions at the CERN SPS

Arnaldi, Roberta
Cornell University
Available
Title: The onset of the anomalous J/psi suppression in Pb-Pb collisions at the CERN SPS
Author: Arnaldi, Roberta
Subject: High Energy Physics - Experiment
Description: The J/psi suppression observed by the NA50 experiment is one of the most striking signatures for quark gluon plasma formation in Pb-Pb collisions at 158 AGeV. The J/psi production has been studied as a function of the centrality of the collision estimated via the forward energy EZDC released in a zero degree calorimeter (ZDC). The study of the correlation between the number of participant nucleons in the collisions, Npart, and EZDC allows to check whether the J/psi suppression pattern vs. EZDC is compatible with a sudden J/psi suppression mechanism expressed as a function of Npart. Comment: 4 pages, 3 figures, Proceedings of the "XXXVIth Rencontres de Moriond", Les Arcs, 4 pages, 3 figures, Proceedings of the "XXXVIth Rencontres de Moriond", Les Arcs, March 17-24 March 2001
Identifier: hep-ex/0106079 (ARXIV ID)
• Several versions


text:
# Why do we use 32.768 kHz crystals in most circuits?

Why do we use 32.768 kHz crystals in most circuits, for example in RTC circuits? What will happen if I use a 35 or 25 kHz crystal?

I assume because the IC internal Xin, Xout pin circuitry should be in CMOS/TTL/NMOS technology. Is it that true?

• And if you halve the frequency 15 times? – Ignacio Vazquez-Abrams Jun 29 '15 at 7:11
• @FEB1115: He (assuming) meant, what do you get if you multiply 2 for 15 times? – WedaPashi Jun 29 '15 at 7:18
• @FEB1115 I think Ignacio Vazquez-Abrams is hinting towards the fact that $2^{15}=32768$ – K. Rmth Jun 29 '15 at 18:34
• Bit OT... Another popular frequency for crystals was 4.43MHz (or there about). Early home micro-computers often used this. That's because crystals with this frequency was used to detect the color-signals in CRT color-TVs, so they were produced in large quantities (every color-TV needed one), and therefor very cheap (a concern for early home-computers). (It's possible USA and Europe used two different frequencies for color, but they'd both be in the 4 to 5MHz range.) – Baard Kopperud Jun 30 '15 at 11:22
• @BaardKopperud NTSC (previously used in North America and Japan and a few other countries) used a color burst crystal frequency of 3.579545 MHz, which is why there were a number of chips, including an NS 1pps chip, that used crystals of that frequency. – Spehro Pefhany Oct 20 '16 at 14:23

The frequency of a real time clock varies with the application. The frequency 32768 Hz (32.768 KHz) is commonly used, because it is a power of 2 (215) value. And, you can get a precise 1 second period (1 Hz frequency) by using a 15 stage binary counter.

Practically, in majority of the applications, particularly digital, the current consumption has to be as low as possible to preserve battery life. So, this frequency is selected as a best compromise between low frequency and convenient manufacture with market availability and real estate in term of physical dimensions while designing board, where low frequency generally means the quartz is physically bigger.

• one more doubt if some of the processors mostly used 27Mhz, it means because of the PLL input frequency require 27mhz to generate all other frequencies Am i right? – ramesh6663 Jun 29 '15 at 7:35
• @FEB1115: I doubt if I've comprehended your question neatly, but from what I can understand I'd say, many a processors have an internal oscillators and once it is stabilized, the external crustal oscillator is used with necessary configuration of multipliers and/or divisors to obtain a typical desired frequency. This multiplier and/or divisor values are used by the PLL to generate frequencies of your interest and requirement. – WedaPashi Jun 29 '15 at 9:08
• If you want to know why a processor uses an "odd" frequency, check to see if it has to deal with a signal at a multiple of that frequency. 27Mhz is useful for doing PAL & NTSC analog video. – joeforker Jun 29 '15 at 18:03
• Do you instead mean $32.768$ kilohertz, not hertz? (Many SE readers live in countries where comma is decimal separator.) – Ruslan Jun 30 '15 at 10:33
• @Ruslan: Yeah, valid point. I simply meant 2 to the power 15 = 32,768 Hz or 32.768 KHz. – WedaPashi Jun 30 '15 at 10:49

The number 32768 is a power of 2, i.e. it is 2^15. If you have a 32.768kHz clock frequency it is easy to divide it to an 1Hz frequency using binary frequency dividers, a.k.a. binary counters, i.e. chains of flip-flops.

Having a 1Hz frequency means you have a clock signal which provides 1s time resolution: count the seconds with a counter, do the math and you have a Real-Time Clock (RTC).

• thanks for your quick answer, so do we need 16bit counter? could you please help me to give any use full link to learn my own to understanding or please explain it here. – ramesh6663 Jun 29 '15 at 7:24
• I think you can use a 16bit counter and just use the most significant digit output as the clock signal output – tangrs Jun 29 '15 at 9:31
• Or you can just divide the 32768 by 2^15 which can be done by placing 15 divide-by-2 circuits in series. See for an example of a divide-by-2 this article: electronics-tutorials.ws/counter/count_1.html First schematic from the top ! – Bimpelrekkie Jun 29 '15 at 10:19
• I find it interesting that even devices with a 1/100-second readout still generally seem to use 32,768Hz crystals and bumping the count 25 times every 8192 pulses, rather than using a 32,000Hz crystal and dividing by 64, then 5, and then ten twice. – supercat Jun 29 '15 at 18:34
• @supercat: To divide by any number that's not a power of 2 like 5 or 10 (or 20) you need a divide circuit (or an ALU or CPU). To divide strictly by powers of 2 all you need is a D flip-flop (or several cascaded in series: a circuit better know as a counter) – slebetman Jun 30 '15 at 3:15

It's primarily due to cost. These particular crystals are dirt cheap due to the watch industry. This answer provides more detail, here's an excerpt:

There are 1.2 billion watches sold each year. The majority of them are inexpensive digital watches, requiring a small, 32kHz crystal. ...

As a result, these crystals are extraordinarily inexpensive... [Other crystals] cost 10 to 100 times more in quantity than these inexpensive watch crystals.

Further, these crystals are particularly well optimized for low power. Real time clocks are expected to run such an oscillator for 10 years on a CR2032 type cell. To get low frequency, low power, small crystals in other frequencies, you're looking at a substantial increase in cost.

In low volumes these crystals are still less expensive than even the normal or high power the 25kHz or 56kHz crystals, but cost the difference isn't large until you get into high volume manufacturing.

Choose what you need, but if you are going to produce a high volume product and can adjust your design to work with a 32kHz crystal, then there's a substantial financial incentive to do so.

• Do you think the 31.25 kHz rate for MIDI (based on dividing a common 1 MHz clock) was a mistake? Should MIDI have gone for 32.768? – Kaz Jun 29 '15 at 20:22
• @Kaz Most midi machines would need a faster clock anyway. 1MHz and multiples of it are cheap and easy to obtain. I don't think there was any reason to use a 32.768kHz timebase in midi - even the volumes were low, so there'd be no big cost savings. – Adam Davis Jun 29 '15 at 20:49
• @Kaz: Some UART designs require that the baud rate clock be synchronous with the main CPU cock and a multiple of 16x the desired baud rate. When MIDI was introduced, it was common for computers to use a clock derived from either a multiple of 1.0Mhz or 3.579545Mhz. Divide the former by 2 and then 16 to get 31250 precisely. Divide the latter by 7 and then 16 to get 31960Hz, which is about 2.2% fast. It might have been better to specify the MIDI rate as something like 31605Hz+/-1.2%, to make clear that any MIDI device should accept input at either rate. – supercat Sep 13 '16 at 17:21
• @Kaz: If a UART requires a 16x clock, the next faster speed one could get from a colorburst crystal would be 37287Hz, and the next faster speeds from a 4.0Mhz timebase would be 35714 and 41667Hz, which are substantially to either side of it. The 31250Hz rate is probably the best one if systems will need to be able to derive it from a multiple of either 1.0Mhz or 3.579545Mhz (BTW, PAL would use 4.433619MHz; dividing that by 9 and 16 yields 30789, which is about 1.5% slow; maybe 31250 was chosen as a compromise between PAL and NTSC)? – supercat Sep 13 '16 at 17:26

You can use any frequency you desire - provided your circuit is designed for it.

With CMOS chips, frequency is related to power consumption. So a 25KHz clock would consume less power than a 32.768 KHz clock. 35 KHz clocking would comsume slightly more power. You should do the math to determine your proper minimum/ maximum clocking, coordinated with the actual chips you select.

There is a tradeoff between clock speed, power consumption, and the amount of work you can get done per clock cycle. This varies from circuit to circuit.

RTCs as a class, are most concerned with power consumption when the main power is off - and you are running on the back-up coin-cell battery, but also still need to be reasonably accurate clocks as well - within a few seconds per month typically.


text:
Compute Distance To:
 Documents Indexed: 68 Publications since 1995, including 1 Book Reviewing Activity: 20 Reviews Co-Authors: 43 Co-Authors with 62 Joint Publications 1,944 Co-Co-Authors
all top 5

all top 5

### Serials

 6 Journal of Pseudo-Differential Operators and Applications 5 Journal of Inequalities and Applications 4 Abstract and Applied Analysis 4 International Journal of Nonlinear Analysis and Applications 3 Chaos, Solitons and Fractals 3 Mathematical Inequalities & Applications 2 Kyungpook Mathematical Journal 2 Applied Mathematics Letters 2 Discrete Dynamics in Nature and Society 2 Mathematical Reports 2 International Journal of Geometric Methods in Modern Physics 2 Advances in Difference Equations 2 Journal of Mathematical Inequalities 2 Caspian Journal of Mathematical Sciences 1 Journal of Geometry and Physics 1 Glasgow Mathematical Journal 1 Le Matematiche 1 Pacific Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Bulletin of the Korean Mathematical Society 1 Bulletin of the Iranian Mathematical Society 1 Journal of Physics A: Mathematical and General 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Advances in Mathematical Sciences and Applications 1 Filomat 1 Scientific Bulletin. Series A. Applied Mathematics and Physics. Politehnica University of Bucharest 1 Journal of Computational Analysis and Applications 1 Journal of Applied Mathematics 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Miskolc Mathematical Notes 1 Journal of Concrete and Applicable Mathematics 1 Complex Variables and Elliptic Equations 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 Journal of Nonlinear Science and Applications 1 Afrika Matematika 1 Journal of Mathematical Extension 1 Tamsui Oxford Journal of Information and Mathematical Sciences 1 Journal of Nonlinear Analysis and Optimization: Theory & Applications 1 Iranian Journal of Numerical Analysis and Optimization 1 Sahand Communications in Mathematical Analysis 1 Springer Optimization and Its Applications
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### Fields

 32 Operator theory (47-XX) 25 Difference and functional equations (39-XX) 21 Functional analysis (46-XX) 15 Partial differential equations (35-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 General topology (54-XX) 5 Ordinary differential equations (34-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Nonassociative rings and algebras (17-XX) 2 Abstract harmonic analysis (43-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Statistical mechanics, structure of matter (82-XX)

### Citations contained in zbMATH Open

37 Publications have been cited 227 times in 167 Documents Cited by Year
On the stability of $$J^*$$-derivations. Zbl 1188.39029
Eshaghi Gordji, M.; Ghaemi, M. B.; Kaboli Gharetapeh, S.; Shams, S.; Ebadian, A.
2010
A fixed-point method for perturbation of higher ring derivations in non-Archimedean Banach algebras. Zbl 1251.39015
2011
An extension of Darbo fixed point theorem and its applications to coupled fixed point and integral equations. Zbl 1466.47040
2014
Lower bounds for the blow-up time in a semilinear parabolic problem involving a variable source. Zbl 1436.35252
2014
A study on the adjoint of pseudo-differential operators on $$\mathbb {S}^{1}$$ and $$\mathbb {Z}$$. Zbl 1317.47049
2015
Fixed and periodic points in the probabilistic normed and metric spaces. Zbl 1101.54042
Ghaemi, M. B.; Razani, Abdolrahman
2006
Generalized Hyers-Ulam-Rassias theorem in Menger probabilistic normed spaces. Zbl 1189.39029
Eshaghi Gordji, M.; Ghaemi, M. B.; Majani, H.
2010
Stability of the second order partial differential equations. Zbl 1280.35006
Gordji, M. Eshaghi; Cho, Y. J.; Ghaemi, M. B.; Alizadeh, B.
2011
Characterizations of nuclear pseudo-differential operators on $$\mathbb {S}^1$$ with applications to adjoints and products. Zbl 06818251
Ghaemi, M. B.; Jamalpour Birgani, M.; Wong, M. W.
2017
Generalized Ulam-Hyers stability of Jensen functional equation in Šerstnev PN spaces. Zbl 1192.39019
Eshaghi Gordji, M.; Ghaemi, M. B.; Majani, H.; Park, C.
2010
A study on pseudo-differential operators on $$\mathbb {S}^{1}$$ and $$\mathbb {Z}$$. Zbl 1353.47095
2016
Some inequalities involving operator monotone functions and operator means. Zbl 1372.47026
2016
The fibering map approach to a quasilinear degenerate $$p(x)$$-Laplacian equation. Zbl 1373.35144
2015
An extension of Darbo’s theorem and its application. Zbl 1473.47018
2014
Hyers-Ulam stability of exact second-order linear differential equations. Zbl 1291.34091
2012
An extension of Darbo’s theorem and its application to system of neutral differential equations with deviating argument. Zbl 1399.47137
Banaei, Sh.; Ghaemi, M. B.; Saadati, R.
2017
Fixed points and approximately octic mappings in non-Archimedean 2-normed spaces. Zbl 1280.39019
2012
On the Hyers-Ulam stability of sextic functional equations in $$\beta$$-homogeneous probabilistic modular spaces. Zbl 1292.39013
2013
Nearly ternary quadratic higher derivations on non-Archimedean ternary Banach algebras: a fixed point approach. Zbl 1252.39035
2011
Approximately quintic and sextic mappings on the probabilistic normed spaces. Zbl 1242.39039
Ghaemi, Mohammad Bagher; Majani, Hamid; Eshaghi Gordji, Majid
2012
A general system of Euler-Lagrange-type quadratic functional equations in Menger probabilistic non-Archimedean 2-normed spaces. Zbl 1227.39023
Eshaghi Gordji, M.; Ghaemi, M. B.; Cho, Y. J.; Majani, H.
2011
A common fixed point for operators in probabilistic normed spaces. Zbl 1198.47075
Ghaemi, M. B.; Lafuerza-Guillen, Bernardo; Razani, A.
2009
Eigenvalue inequalities related to the Ando-Hiai inequality. Zbl 1427.47008
2017
A generalization of the Meir-Keeler condensing operators and its application to solvability of a system of nonlinear functional integral equations of Volterra type. Zbl 1438.47089
2019
$$L^{p}$$-boundedness, compactness of pseudo-differential operators on compact Lie groups. Zbl 1368.47037
Ghaemi, M. B.; Jamalpour Birgani, M.
2017
A study on the adjoint of pseudo-differential operators on compact Lie groups. Zbl 1439.22020
Ghaemi, M. B.; Nabizadeh, E.; Jamalpour, M.; Kalleji, M. K.
2018
General system of cubic functional equations in non-Archimedean spaces. Zbl 1291.39051
Ghaemi, M. B.; Majani, H.; Gordji, M. E.
2012
A fixed point approach to superstability of generalized derivations on non-Archimedean Banach algebras. Zbl 1227.39022
2011
On the existence of positive solutions for a class of ($$p(x), q(x)$$)-Laplacian system. Zbl 1263.35092
Ghaemi, M. B.; Afrouzi, G. A.; Rasouli, S. H.; Choubin, M.
2013
A fixed point approach to stability of quintic functional equations in modular spaces. Zbl 1331.39020
2015
Hausdorff measure of noncompactness of matrix operators on some sequence spaces of a double sequential band matrix. Zbl 1330.47065
2015
On the reverse Young and Heinz inequalities. Zbl 1376.15011
Ghaemi, Mohammad Bagher; Gharakhanlu, Nahid; Furuichi, Shigeru
2017
Approximately quintic and sextic mappings form $$r$$-divisible groups into Šerstnev probabilistic Banach spaces: fixed point method. Zbl 1237.39031
Eshaghi Gordji, M.; Cho, Y. J.; Ghaemi, M. B.; Majani, H.
2011
Boolean algebras of projections and algebras of spectral operators. Zbl 1063.47027
Dowson, H. R.; Ghaemi, M. B.; Spain, P. G.
2003
Generalized reverse Young and Heinz inequalities. Zbl 1406.15021
Furuichi, Shigeru; Ghaemi, Mohammad Bagher; Gharakhanlu, Nahid
2019
A fixed point approach to the stability of Euler-Lagrange sextic $$(a,b)$$-functional equations in Archimedean and non-Archimedean Banach spaces. Zbl 1333.39035
Ghaemi, Mohammad Bagher; Choubin, Mehdi; Saadati, Reza; Park, Choonkil; Shin, Dong Yun
2016
A study on the inverse of pseudo-differential operators on $$\mathbb {S}^{1}$$. Zbl 06768757
2016
A generalization of the Meir-Keeler condensing operators and its application to solvability of a system of nonlinear functional integral equations of Volterra type. Zbl 1438.47089
2019
Generalized reverse Young and Heinz inequalities. Zbl 1406.15021
Furuichi, Shigeru; Ghaemi, Mohammad Bagher; Gharakhanlu, Nahid
2019
A study on the adjoint of pseudo-differential operators on compact Lie groups. Zbl 1439.22020
Ghaemi, M. B.; Nabizadeh, E.; Jamalpour, M.; Kalleji, M. K.
2018
Characterizations of nuclear pseudo-differential operators on $$\mathbb {S}^1$$ with applications to adjoints and products. Zbl 06818251
Ghaemi, M. B.; Jamalpour Birgani, M.; Wong, M. W.
2017
An extension of Darbo’s theorem and its application to system of neutral differential equations with deviating argument. Zbl 1399.47137
Banaei, Sh.; Ghaemi, M. B.; Saadati, R.
2017
Eigenvalue inequalities related to the Ando-Hiai inequality. Zbl 1427.47008
2017
$$L^{p}$$-boundedness, compactness of pseudo-differential operators on compact Lie groups. Zbl 1368.47037
Ghaemi, M. B.; Jamalpour Birgani, M.
2017
On the reverse Young and Heinz inequalities. Zbl 1376.15011
Ghaemi, Mohammad Bagher; Gharakhanlu, Nahid; Furuichi, Shigeru
2017
A study on pseudo-differential operators on $$\mathbb {S}^{1}$$ and $$\mathbb {Z}$$. Zbl 1353.47095
2016
Some inequalities involving operator monotone functions and operator means. Zbl 1372.47026
2016
A fixed point approach to the stability of Euler-Lagrange sextic $$(a,b)$$-functional equations in Archimedean and non-Archimedean Banach spaces. Zbl 1333.39035
Ghaemi, Mohammad Bagher; Choubin, Mehdi; Saadati, Reza; Park, Choonkil; Shin, Dong Yun
2016
A study on the inverse of pseudo-differential operators on $$\mathbb {S}^{1}$$. Zbl 06768757
2016
A study on the adjoint of pseudo-differential operators on $$\mathbb {S}^{1}$$ and $$\mathbb {Z}$$. Zbl 1317.47049
2015
The fibering map approach to a quasilinear degenerate $$p(x)$$-Laplacian equation. Zbl 1373.35144
2015
A fixed point approach to stability of quintic functional equations in modular spaces. Zbl 1331.39020
2015
Hausdorff measure of noncompactness of matrix operators on some sequence spaces of a double sequential band matrix. Zbl 1330.47065
2015
An extension of Darbo fixed point theorem and its applications to coupled fixed point and integral equations. Zbl 1466.47040
2014
Lower bounds for the blow-up time in a semilinear parabolic problem involving a variable source. Zbl 1436.35252
2014
An extension of Darbo’s theorem and its application. Zbl 1473.47018
2014
On the Hyers-Ulam stability of sextic functional equations in $$\beta$$-homogeneous probabilistic modular spaces. Zbl 1292.39013
2013
On the existence of positive solutions for a class of ($$p(x), q(x)$$)-Laplacian system. Zbl 1263.35092
Ghaemi, M. B.; Afrouzi, G. A.; Rasouli, S. H.; Choubin, M.
2013
Hyers-Ulam stability of exact second-order linear differential equations. Zbl 1291.34091
2012
Fixed points and approximately octic mappings in non-Archimedean 2-normed spaces. Zbl 1280.39019
2012
Approximately quintic and sextic mappings on the probabilistic normed spaces. Zbl 1242.39039
Ghaemi, Mohammad Bagher; Majani, Hamid; Eshaghi Gordji, Majid
2012
General system of cubic functional equations in non-Archimedean spaces. Zbl 1291.39051
Ghaemi, M. B.; Majani, H.; Gordji, M. E.
2012
A fixed-point method for perturbation of higher ring derivations in non-Archimedean Banach algebras. Zbl 1251.39015
2011
Stability of the second order partial differential equations. Zbl 1280.35006
Gordji, M. Eshaghi; Cho, Y. J.; Ghaemi, M. B.; Alizadeh, B.
2011
Nearly ternary quadratic higher derivations on non-Archimedean ternary Banach algebras: a fixed point approach. Zbl 1252.39035
2011
A general system of Euler-Lagrange-type quadratic functional equations in Menger probabilistic non-Archimedean 2-normed spaces. Zbl 1227.39023
Eshaghi Gordji, M.; Ghaemi, M. B.; Cho, Y. J.; Majani, H.
2011
A fixed point approach to superstability of generalized derivations on non-Archimedean Banach algebras. Zbl 1227.39022
2011
Approximately quintic and sextic mappings form $$r$$-divisible groups into Šerstnev probabilistic Banach spaces: fixed point method. Zbl 1237.39031
Eshaghi Gordji, M.; Cho, Y. J.; Ghaemi, M. B.; Majani, H.
2011
On the stability of $$J^*$$-derivations. Zbl 1188.39029
Eshaghi Gordji, M.; Ghaemi, M. B.; Kaboli Gharetapeh, S.; Shams, S.; Ebadian, A.
2010
Generalized Hyers-Ulam-Rassias theorem in Menger probabilistic normed spaces. Zbl 1189.39029
Eshaghi Gordji, M.; Ghaemi, M. B.; Majani, H.
2010
Generalized Ulam-Hyers stability of Jensen functional equation in Šerstnev PN spaces. Zbl 1192.39019
Eshaghi Gordji, M.; Ghaemi, M. B.; Majani, H.; Park, C.
2010
A common fixed point for operators in probabilistic normed spaces. Zbl 1198.47075
Ghaemi, M. B.; Lafuerza-Guillen, Bernardo; Razani, A.
2009
Fixed and periodic points in the probabilistic normed and metric spaces. Zbl 1101.54042
Ghaemi, M. B.; Razani, Abdolrahman
2006
Boolean algebras of projections and algebras of spectral operators. Zbl 1063.47027
Dowson, H. R.; Ghaemi, M. B.; Spain, P. G.
2003
all top 5


text:
# Studying Got an MS admission offer -- Have some questions

1. Feb 15, 2017

### random_soldier

I had applied to several universities and got a positive reply from the University of Florida for the program in MS Nuclear Engineering.

Anyway, these are my questions:

1. Is there anything I should be aware of in particular about the university or the program at this university? Whatever you guys know is fine. It would be too much of me to ask everybody detailed info on this.

2. My undergraduate background is in Electronics and Communications so that might make people a bit skeptical. However, I have this admission offer now. They must have seen something and regardless of what it is, if something trivial, I will not back off from any and all work it takes me to make the most of this opportunity and beyond that. What preemptive measures can I take prior to joining to ease myself to the greatest degree into my studies?

3. The letter says that I have to respond by April 15. Obviously, I am still waiting for other responses. It is not possible that they would rescind the offer prior to that date, would they?

4. What is the research scene like at the MS level? My thesis will be the most important, I have come to learn, but is there anything else I can or should do during my MS to improve my credentials as a researcher in this field? I am not particularly familiar with the process it takes to become a fully fledged and recognized researcher. I only know a few bits and pieces such as you have to work well with other recognized professionals in the field on research projects, internships during summers/after the program, perhaps submitting some papers of your own (though, you have to be affiliated with a recognized institute in my understanding). However, this is a bit vague, so is there anything that I should specifically be informed of?

5. How exactly does writing a thesis work? And how would I find a suitable topic to write one on? Or hot topics for research in general?

6. Given my background, is there an heavy obligation to draw from it at the university, in my studies or otherwise?

2. Feb 15, 2017

### Dr. Courtney

Have you only been admitted, or is there a significant financial aid package (fellowship, research assistantship, teaching assistandship)?

I wouldn't take too much confidence in merely being admitted, if you are going to have to pay six figures to attend. They admitted you, because they want your money.

3. Feb 15, 2017

No. $1500 tuition waiver per semester for 3 semesters currently. Anything I should note? 4. Feb 15, 2017 ### Dr. Courtney That's not much love in light of the in-state tuition of$12,470 per year and total expenses estimated at $30k per year. I encourage students to think of financial aid in that ballpark more as a discount coupon than as real aid. They want your money, not your mind. 5. Feb 15, 2017 ### random_soldier I get that. I am an international student, just so you know. What I was asking was is there some other serious problem it leads to? I really wish I could pass on the offer but circumstances are not in my favour. Besides, couldn't I attempt for a scholarship or assistantship midway? 6. Feb 15, 2017 ### Dr. Courtney Wow! So you likely have out of state tuition also. That's going to be expensive. Scholarships midway are unlikely (at least of the magnitude to make a significant dent in overall costs.) Assistantships depend on the relative supply and demand of research and teaching labor needs. I would not be optimistic unless you investigate it thoroughly and determine that you are well qualified for those and they are likely. But if that were the case, one wonders why that offer is not already on the table. Safer to assume they only want your money until they put the money on the table to prove they want your mind. 7. Feb 15, 2017 ### random_soldier I myself did not ask for assistantships. It's true my record isn't great so I just didn't ask for it in my application. Regardless, some help is better than no help, so I'll probably be on the lookout if opportunities arise for better aid. However, I still would like to know, perhaps they are after my money but does this also lead to other problems? As in do I not get a certain service everybody else does or do they not perform some duty they are supposed to generally? 8. Feb 15, 2017 ### Dr. Courtney It can. Since you are paying them, they do not have the same level of motivation for you to complete your degree as quickly as if they were paying you. One or two more semesters means more money for them. As a result, faculty may not be as eager to help you complete all your course and research requirements in a timely manner compared with how eager they would be if your tuition and stipend were coming out of a faculty member's research grant. Faculty tend to be more invested in the success and graduation of students they are paying. 9. Feb 15, 2017 ### random_soldier Any particular example? Do they purposely try to sabotage me or find stupid, petty reasons to hold me back from something or another? And which part of the faculty may be responsible for any such deeds? Teaching, administratve, others? 10. Feb 15, 2017 ### Dr. Courtney Nothing as bad as purposeful sabotage - more of being less willing to go out of their way to help you. More likely to cancel a course you might need due to low enrollment or less likely to get something you need approved in a timely manner. Being an RA or TA you have a built in advocate - the faculty member you are working for. 11. Feb 15, 2017 ### Vanadium 50 Staff Emeritus I have never seen a professor make that kind of calculus. I can't even imagine it - it's not like faculty are paid on commission. 12. Feb 15, 2017 ### Dr. Courtney No, not that kind of calculus. But I've seen professors decline to help students that were not "their" students dozens of times. Who can say what the intent was. But "no" means "no" regardless of intent. 13. Feb 16, 2017 ### random_soldier To be honest, I'm trying to get my foot in the door at this point. If it is nothing nearly as bad as open, rampant corruption, I can't really concern myself with it. I'll just have to find ways to mitigate all this, be on top of things from the get-go and you did say it was not impossible even if difficult to obtain assistantships during the course. Do you remember any examples or any times where it was particularly obvious and/or bad? 14. Feb 16, 2017 ### CalcNerd . If that is the case, you need to step back and look at the bigger picture. Are you prepared for their program? And as Dr. Courtney has stated, they ain't showing you a lot of love. You may be much better served by going to a school of your choice, chasing after a degree of your choosing, and initially paying your first semester (with savings and loans as required). . Chances are you may choose a school with lower tuition with a program that is more in line with your background or desire. Most mid-tier schools will welcome you aboard if you have a halfway decent GPA and an acceptable GRE. Most Grad students can receive some assistance once on board, certainly an amount comparable to$1500.

15. Feb 16, 2017

### random_soldier

Any particulars you have in mind when you think about preparation for the program?

Also, I don't understand what you mean by school or degree of my choosing. I would not have applied to this school in this program if it was not my choice.

Wait, how is that any different from me joining this school and proving my worth for assistantships or the like?

Anyway, I'll let you know more. I still have a few responses I am waiting for.

16. Feb 19, 2017

### random_soldier

Bumping because I believe I could benefit from the advice.

17. Feb 19, 2017

### Student100

I agree, you're paying the university not the professors.

I also dont see the conundrum, most Engineers in the US pay out pocket for a masters, less any finacial aid, at least all the ones I've met. If you want to find out ways to help pay for the program, email the admissions officer who you've been in contact with or better the schools finacial aid department/engineering department. You're an international student, so many avenues of aid are closed to you.

If you want to study there, study there. Your biggest concern should be with your lack of preparatory work. If I were you I'd look at the undergraduate courses in a comparable bachelors program in the US and see where you stand. Then self study those topics between now and when you start.

18. Feb 19, 2017

### random_soldier

Their course list is available on their website and the respective syllabus can be easily found. Can I use those to guide myself where necessary?

19. Feb 19, 2017

Yes.