Mathematical Arithmetic Research Articles

A Novel Method of On-Line Coal-Rock Interface Characterization Using THz-TDs

The core problem in unmanned/intelligent working face of coal mining is the automatic adjustment of shearer arm where the coal-rock interface detection is the key. The cutting location of shearer drum affect the proportion of coal and rock powder around the cutting teeth of shearer drum. Therefore, the method of on-line coal rock interface characterization using Terahertz Time Domain spectroscopy (THz-TDs) we proposed aims to estimate the ratio of rock by Terahertz response. Firstly, anthracite and quartz sandstone were uniformly mixed according to 39 different ratios in this study, the samples' responses were obtained by terahertz system, and then the obtained time domain data was converted into frequency domain data by fast Fourier transform. The absorption coefficient spectrum and the refractive index profile of the 39 samples were calculated by optical parametric model. Secondly, corresponding quantitative model between mixed coal/rock powder and THz signal was built by using back propagation neural network (BPNN) and least squares support vector machine (LSSVM). We expected to use the ratio of rock powder detected by the model to estimate the depth of shearer drum teeth embedded in the rock layer. Finally, we found that both two mathematical arithmetic is feasible to quantitatively detect different proportion of coal and rock mixtures. The results show that the depth of shearer drum teeth embedded in the rock layer could be estimated by the novel method, which means the coal-rock interface could be on-line characterized by using THz-TDs and the height of the drum could be adjusted in time.

A concise handbook of mathematics, physics, and engineering sciences

MATHEMATICS Arithmetic and Elementary Algebra Elementary Functions Elementary Geometry Analytic Geometry Algebra Limits and Derivatives Integrals Series Functions of Complex Variables Integral Transforms Ordinary Differential Equations Partial Differential Equations Special Functions and Their Properties Probability Theory PHYSICS Physical Foundations of Mechanics Molecular Physics and Thermodynamics Electrodynamics Oscillations and Waves Optics Quantum Mechanics. Atomic Physics Quantum Theory of Crystals Elements of Nuclear Physics ELEMENTS OF APPLIED AND ENGINEERING SCIENCES Dimensions and Similarity Mechanics of Point Particles and Rigid Bodies Elements of Strength of Materials Hydrodynamics Mass and Heat Transfer Electrical Engineering Empirical and Engineering Formulas and Criteria for Their Applicability SUPPLEMENTS Integrals Integral Transforms Orthogonal Curvilinear Systems of Coordinates Ordinary Differential Equations Some Useful Electronic Mathematical Resources Index References appear at the end of each chapter.

On the stability of the difference scheme in the self-memorization model

In light of irreversibility of atmospheric motion, the memory function obtained by utilizing the previous information fully obtained from the observational data is introduced. The selfmemorization equation of the heat conduction equation is induced, and the stability and characteristics of which are studied, taking respectively Richardson scheme (RS) and DuFort-Frankel scheme (DS) as the retrospective order p=1. The calculation results indicate that the numerical integral is diffused sometimes in the multi-time model, due to the fact that the memory function is determined by the observational data via the special mathematics arithmetic, which makes the difference scheme designed previously change, and is a smooth time factor in itself.

Charles Watkins Merrifield, F.R.S.

MR. CHARLES WATKINS MERRIFIELD, F.R.S., who died at Hove on the 1st inst., at the comparatively early age of fifty-six, was a native of Brighton. Having entered for the Bar, he in 1847 received from the then Marquis of Lansdowne an appointment in the Education Department of the Privy Council Office. Though called to the Bar in due course, he never practised, but was speedily promoted to the office of an Examiner, the duties of which he discharged with marked attention and success, while finding time for other work which made for him a name among men of science. Though well versed in Greek and Latin, as well as in the classic authors in French and Italian, both of which languages he wrote well and spoke fluently, the bent of his mind was decidedly towards the more exact sciences. He was an early member of the Royal Institute of Naval Architects, of which he was for many years Honorary Secretary, receiving a handsome testimonial on his retirement in 1875. Some mathematical papers he had contributed to the Transactions of some of the learned societies, and especially some memoirs on the calculation of elliptic integrals in the Philosophical Transactions, led to his election as a Fellow of the Royal Society in 1863. In 1867 the Government established the Royal School of Naval Architecture and Marine Engineering at South Kensington, and Mr: C. W. Merrifield, at the request of the authorities, accepted the office of Vice-Principal. He only intended to take this as a temporary measure, but as the result of the lamented death of Mr. Purkiss, who was to have been Principal, Mr. Merrifield was appointed to that office. On the transfer of the Institution to Greenwich in 1873, he resumed his office of Examiner in the Education Department. Mr. Merrifield was a frequent attendant at the annual meetings of the British Association, and filled the office of Vice-President of its Section of Mechanical Science at the Brighton meeting in 1875, and was President of the same Section at the Glasgow meeting in the following year. He served on many important committees of that Association; one of these was the committee whose report on the stability, propulsion, and seagoing qualities of ships in 1869 was drawn up by him, and another was the committee for reporting on Babbage's celebrated analytical machine. Mr. Merrifield was a member, and in due course became President, of the London Mathematical Society, and he held the office of Treasurer until he was compelled by his health to resign it in 1882. To some of the leading scientific journals and periodical publications his contributions, extending from 1853, have been very numerous; they may be found in the publications of the Royal Society, the Philosophical Magazine, the Assurance Magazine, the Messenger of Mathematics, &c. His acquaintance with mathematical arithmetic, methods of interpolation, and tabular work in general, was very wide and complete. Mr. Merrifield edited many of the works in the Textbooks of Science published by Messrs. Longman, and himself wrote a successful treatise on arithmetic and mensuration as one of that series. Some of his papers on the difficult and scientifically interesting subject of sea waves were translated into Italian for the Rivista Marittima, in which they appear, and a footnote to one of them, after bearing testimony to the author's extensive knowledge and excellence of style, expresses the satisfaction of the editor at his adding to these qualifications that of “writing correctly our language.” He was closely connected with the Association for the Improvement of Geometrical Teaching from its foundation, and took an active and leading part in the work of the Association. Mr. Merrifield served on several important Royal Commissions, including one on the seaworthiness of ships, of which the Duke of Edinburgh was President. During the last few years he frequently sat as scientific assessor to Mr. Rothery in the Wreck Court. A part of his unofficial work consisted of the conduct for many years of the mathematical part of the May examinations of the Science and Art Department. All his arrangements for this purpose were completed in 1882, when, in April of that year, he was prostrated by an attack of apoplexy. He had so far recovered as to give hopes that his life might be spared for some years, but on October 18 last he was seized with a third attack, from which he never rallied.