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The purpose of this paper is to survey briefly how harmonic analyis started and developed throughout the centuries to reach its modern status and its surprisingly wide range of applications.

The author traces applications of harmonic analysis back to Mesopotamia, ancient Egypt and the Indus Valley, showing how the Greeks have applied trigonometry and influenced its birth, then the important developments in India in the sixth century laying the first brick to modern trigonometry with the definition of the sinus, then medieval India founding modern mathematical analysis. Trigonometry was developed further by the Arabs until the fourteenth century, then by the Europeans. The eighteenth century in France was particularly important when Bernoulli solved, with an infinite trigonometric series, the vibrating string problem, then Fourier, who studied these series extensively. The author goes on to harmonic analysis on locally compact groups, and ends up with a quick personal view on harmonic analysis nowadays. The last section of the paper presents some of the modern applications. Harmonic analysis is, of course, still used for navigation but also has many other very surprising applications such as signal processing, quantum mechanics, neuroscience, tomography, etc.

The power of harmonic analysis lies in giving the solutions to various problems as infinite series of basic functions, so to be able to produce algorithms for FFT boxes, it must be understood how these series came about and the convergence of these series.

The review should be useful to people interested in studying and/or applying harmonic analysis.

This paper aims to present an iterative path-following method with joint limits to solve the problem of large computation cost, movement exceeding joint limits and poor path-following accuracy for the path planning of hyper-redundant snake-like manipulator.

When a desired path is given, new configuration of the snake-like manipulator is obtained through a geometrical approach, then the joints are repositioned through iterations until all the rotation angles satisfy the imposed joint limits. Finally, a new arrangement is obtained through the analytic solution of the inverse kinematics of hyper-redundant manipulator. Finally, simulations and experiments are carried out to analyze the performance of the proposed path-following method.

Simulation results show that the average computation time is 0.1 ms per step for a hyper-redundant manipulator with 12 degrees of freedom, and the deviation in tip position can be kept below 0.02 mm. Experiments show that all the rotation angles are within joint limits.

Currently , the manipulator is working in open-loop, the elasticity of the driving cable will cause positioning error. In future, close-loop control based on real-time attitude detection will be used in in combination with the path-following method to achieve high-precision trajectory tracking.

Through a series of iterative processes, the proposed method can make the manipulator approach the desired path as much as possible within the joint constraints with high precision and less computation time.

To propose trigonometric interpolation in combination with the sliding‐surface technique for modeling rotation in electrical machine models discretised by the finite integration technique (FIT).

Locked‐step, linear and trigonometric interpolation techniques are developed for coupling the stator and rotor model parts of an electrical machine model.

Linear and trigonometric interpolation should be preferred over the locked‐step approach. Three‐machine models with sliding‐surface coupling discretised by the FIT result in efficient and reliable models.

The introduction of sliding‐surface techniques in the FIT, the trigonometric interpolation used in combination, the application of the FIT for simulating electrical machines.

Suddenly, in less than two years, a new high‐technology consumer product has swept world markets—the electronic pocket calculator. Such machines range from the relatively simple type that will add, subtract, multiply and divide up to six numerical digits, to the highly sophisticated ‘electronic slide‐rule’, with its instant calculation of square roots, logarithms, trig functions and other scientific esoterica.

Outlines some research on the effects of risk on portfolios for retirement planning and puts forward a method to help individuals “increase their chances of not outliving their retirement portfolios”. Uses numerical examples to show how calculations of the savings needed to achieve specific retirement incomes may prove inaccurate, and how regular portfolio assessment can be used to make any necessary adjustments during the accumulation and/or the retirement stage.

The purpose of this paper is the investigation of a new coordinated switching strategy to improve the transient performance of a fuel cell (FC)- supercapacitor (SC) electric vehicle. The proposed switching strategy protects FCs from large currents drawn during abrupt power variations. Furthermore, it compensates the poor FC transient response and suppresses the transient ripples occurring during power source switching instants.

Coordinated power source switching is achieved using three different transition functions. Vehicle model is fractioned into computational and console subsystems for its simulation using real time (RT) LAB simulator. Blocs containing coordination switching strategy, power sources models and their power electronics interface are placed in the computational subsystem that will be executed, in RT, on one of real time laboratory simulator central processing unit cores.

Coordination switching strategy resulted in reducing transient power ripples by 90% and direct current (DC) bus voltage fluctuations by 50%. Switching through transition functions compensated the difference between FC and SC transient responses responsible for transient power ripples. Among the three proposed transition functions, linear transition function resulted in the best transient performances.

The proposed coordinated switching strategy allows the control of the switching period duration. Furthermore, it enables the choice of adequate transition functions that fit the dynamics of power sources undergoing transition. Also, the proposed switching technique is simple and does not require the knowledge of system parameters or the complex control models.

THERE is far too much talk and writing about book expenditure per authority or per 1,000 of population, which frankly does not get one very far. What matters is what books you buy or do not buy. I have picked, quite at random, one copy of the British National Bibliography, for May 7th, 1958, and made a list of all the books which I think every library authority ought to have, whether large or small, industrial, rural or urban. These titles would meet the needs of the inhabitants of any community and enlarge their vision, give them the materials for attempting an understanding of the world and its problems, arts and sciences, and enable them to improve their abilities and skills, and fit themselves physically, mentally and morally to be useful citizens. It sounds pompous, I know, but that is what we are trying to do. Here is part of the list: Irwin: Origins of the English Library. Jung: Undiscovered Self (a world famous psychologist on social problems). Mackenzie: Free Elections (textbook on matters of interest to all citizens). Finer: Anonymous Empire (lobbying, its faults and virtues). Roberts: Trade Union Congress. Pollard: Problem of Divorce. Stengel: Attempted Suicide. Railway Magazine Miscellany. Dunn: Teach Yourself Japanese. Trustram: Classbook of Arithmetic and Trigonometry. Calder: Electricity Grows Up. Morley and Hughes: Elementary Engineering Science (a standard work). Powell: Physics, Vol. 2 (textbook for National Certificate students). Bowen: Exploration of Time. Brown: How to Make a Home Nature Museum. Leithauser: Inventors of Our World. Meares and Neale: Electrical Engineering Practice. Lamberment and Pirie: Helicopters and Autogyros of the World. Spicer and Pegler: Practical Book‐keeping. Luker: School Craftwork in Wood. Goff: Further Guide to Long Play. Clark: Royal Albert Hall. Graveney: Cricket Through the Covers. Swift: Collected Poems. Bolt: Flowering Cherry. Austen: The Watsons. Hobbs: Maps and Regions. Richie: Hampshire Coastways. Winch: Introducing Germany. Cooper: Rainbow Comes and Goes. Cope: Florence Nightingale and the Doctors. Hudson: Sir Joshua Reynolds. Pitt: Zeebrugge. Cowles: Phantom Major. Grinnell‐Milne: Silent Victory. Pollock: Jervis Bay. Then add on some half‐a‐dozen novels.

The purpose of this paper is to present a combined scheme of active laser‐based triangulation and a morphological edge detection, to quantify features dimensions (width and depth) over smooth plastic surfaces. The inspected target is an automotive polyethylene, optically black fender, with average roughness of 1μm, while the sought features are mold sinks with depth variations of 0.3‐1.0 mm and a width of ∼3 mm.

Several non‐contact scanning and reconstruction optical modalities are discussed along with its associated noise for current application; such techniques include interferometry and triangulation. The proposed system projects a linear coherent illumination and scans its reflection profile to infer the reflected component position using trigonometry and its width using a Sobel morphological operator. The retrieved dimensions are then reconstructed into feature boundaries that enable a depth and width quantification.

The proposed setup and processing are validated through experimental scans of actual molded fenders with artificial deviations. The proposed system accuracy is then analyzed and its spatial resolution is found to be 0.14 mm using the current charge‐coupled device format of 640 × 480. Additionally the proposed system is benchmarked against a commercial 3D stereo‐based scanner; proposed system proved to be more accurate with faster scanning rates.

The post processor combines the predicted width and depth values in real‐time to synthesize a 3D surface profile for sought features, with a resolution of 0.14 mm, an accuracy of 0.09 mm, and a repeatability of 0.11 mm. The proposed scheme is customized to current laser illuminant and to the plastic surface profile, which further modifications for other illuminations and roughness values.

New image processing code is used to reduce the laser speckle effect and the moving mechanism vibration using a moving Gaussian illuminant and a double thresholding scheme coupled with sequential averaging, respectively.

Aerial Navigation has not yet conic into its own. It is a little doubtful if it ever will during this generation. Man is by nature prone to accept, and use, the line of least resistance, and those pilots who in their early stages are apt to follow railways in preference to keeping “red on red” are equally likely to demand wireless directional or homing devices in preference to the use of stars. However much we may be able to put aerial navigation in all its branches into effect on paper, when it comes to its practical application without the use of wireless it fails in its object. It is understood that even our record long‐distance flight pilots did not know where they were for some considerable time as “they had no means of checking earlier sights.” Hinkler used a thorough knowledge of air pilotage. The Mollisons presumably work on the same basis. Imperial Airways use wireless. The taxi‐pilot of the small machine uses a vast store of accumulated knowledge of air pilotage and takes a machine through weather the air liners go above. He has no wireless and no sextant, but he gets there because he understands the fundamentals and knows how to apply them.

The first official test of the AutoTutor teaching machine in this country has been completed by the RAF. Results show that trainees taught by Auto‐Tutors learned as much as those taught in classrooms by human instructors, in just 39 per cent of the time.