Stan's Library

Stan's Library (ISSN 2421-1230)

Publisher: Extra Byte di Sykora Stanislav, Via Raffaello Sanzio 22c, Castano Primo (Mi), Italy 20022.

Each article published here is assigned a DOI (Digital Object Identifier).
Stan's Library adheres to the Budapest Open Access Initiative.

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To link to a Stan's Library article, use its URL, or its DOI (listed under the authors affiliation), or follow this format:
Sykora S., Generalized Heronian means, Stan's Library III, July 2009, DOI 10.3247/SL3Math09.002.
To cite a Stan's Library article in your own work, use the following format:
Sykora S., Generalized Heronian means, Stan's Library III, July 2009, DOI 10.3247/SL3Math09.002.

Contributors: This Library is an open forum for the thematic categories listed below and everybody is welcome to contribute. Get published for free and your work will receive immediate attention! Considering the dangers of the Internet, however, the Editor reserves the right to refuse any improper material and/or suggest editorial changes. For more details, contact the Editor.

Cumulative, reverse chronological Index of Volumes (indicated in the first column of each entry):

I: 2004-2006, II: 2007-2008, III: 2009-2010, IV: 2011-2013, V: 2014-2015, VI: 2016-2017, VII: 2018-

CATEGORIES

Research & educational articles on physics

Research & edu articles, books & references, datasets, posters and talks, ...

Math research & educational articles, references

Notes, algorithms, code SNIPPETS, ...

Scientific/technical databases and Collections of References

Notes on electronics

Essays about Science, epistemology, etc...

F Books Lists:	Popular Science	F Mathematics	F Physics	F Chemistry
Patents+IP	F Electronics \| DSP \| Tinkering	F Computing	Spintronics	F Materials
WWW issues	F Instruments / Measurements	Quantum Computing	F NMR \| ESR \| MRI	F Spectroscopy
Hint: the F symbols above, where present, are links to free online texts (books, courses, theses, ...)

PHYSICS (except NMR / MRI)
V	Talk	by Sykora S. Molecular Spins: a New Frontier Conjecture of persistent currents in acyclic molecules and molecular fragments.
V	Talk	by Sykora S. Fitting of spin system parameters to NMR spectra, revisited Proposal of a new, very fast, algorithm for simulations of spin systems spectra.
IV	Poster	by Sykora S. Molecular Spins: a new Frontier of Chemical Physics and Magnetic Resonance? A molecular-physics conjecture presented at 53rd ENC as a Poster and a Talk.
IV	Article	by Sýkora S., Phononian Science: current state and perspectives A mildly speculative and humorous reflection for Physicists.
III	Biography	Edited by S.Sykora, The Life of Professor Fuchun Yu Biography of a great physicists and co-discoverer of NMR chemical shifts.
II	Edu	by Sýkora S., The Hebel-Slichter effect Summary of a historic milestone in field-cycling NMR relaxometry.
I	Article	by Sýkora S., *Is every* finite-dimensional Hilbert space a spin-space ?** An unconventional way of introducing the basic formulae of spin-algebras.
I	Edu	by Sykora S., Ad Astra Ltd and Early History of Gravity Engineering A simple and amusing example of variational calculus applied to physics.
I	DataBase	edited by Sykora S., Constants of physics and mathematics Latest CODATA values. Customary & root SI dimensions.
I	DataBase	edited by Sykora S., SI dimensions of various quantities Alphabetic list of SI dimensions of over 200 quantities.
I	DataBase	edited by Sykora S., SI dimensions of various quantities listed by category Over 200 physical quantities in 22 categories.
I	DataBase	edited by Sykora S., Tables of SI units and prefixes Includes basic, derived, accepted and deprecated units.
		Collections of Physics Books and References:
V	Books list	Books about Spintronics, including its theory, physics, engineering, materials, and applications A large and continuously updated list.
III	Free texts	Online Texts about Spectroscopy List and Repository of free, downloadable Spectroscopy Books, Courses and Theses.
III	Books list	Spectroscopy Books A large and continuously updated list.
III	Free texts	Online Texts about Physics List and Repository of free, downloadable Physics Books, Courses and Theses.
II	Books list	Physics Books A large and continuously updated list.
II	References	Constants of Physics and Mathematics A large and continuously updated list.
I	References	Systems of Units of Measurements A large and continuously updated list .
		Reprints of hard-to-find physics articles:
I	Reprint	Sykora S., Vogt J., Experimental Noise in Data Acquisition and Evaluation, Parts I and II Bruker Report 2/1979.
I	Reprint	Sykora S., Raman Bandshapes and Rotational Diffusion of Molecules US Clearinghouse Fed.Sci.Tech.Inf. 724330, 20 (1971).
MAGNETIC RESONANCE (NMR, MRI, ESR and NQR) Fast jumps: Educational, Books & References, Datasets, Posters & Talks, Old reprints, Application notes
V	Review	by Cobas C., NMR Data Evaluation: Review of Covariance Applications Review of an important new NMR technique requiring special data evaluation.
IV	Tutorial	by Sykora S., From Spin Hamiltonian to Spectra Know Thy Spins series: A lecture on spin hamiltonian and NMR spectra simulation.
III	Eulogy	by William C. Stevens, Eulogy of the late Roy H. Bible A recollection of an early NMR enthusiast who passed away.
III	Biography	Edited by S.Sykora, The Life of Professor Fuchun Yu Biography of a great physicists and co-discoverer of NMR chemical shifts.
II	Article	by Sykora S., The Geometry and some General Characteristics of the Isotropic AB Quartet Know Thy Spins series: A recreational NMR essay.
II	Article	by Zeman V., Vzpomínky na NMR v Brnênské Tesle In Czech [Recollections of NMR development and production in Tesla Brno].
II	Article	by Cobas C., Wavelet-based filtering applied to the diagonal suppression of 2D NMR data sets A novel 2D-NMR data-evaluation algorithm.
II	Article	by Sýkora S., Suppression of receiver recovery time in NMR Extention of the classical Lowe-Tarr circuit.
II	Article	by Hornak J.P., MRI Hardware: A two decade retrospective An interesting reflection on the evolution of the routine MRI scanner
I	Article	by Sykora S., Field noise effects on NMR signals: Hahn echoes and CPMG Analysis of the propagation of magnetic field noise into spin echoes
I	Article	by Sykora S., Field noise effects on NMR signals: FID's and 1D spectra Analysis of the propagation of magnetic field noise into FID's and 1D spectra
I	Article	by Sykora S., NMR Sensitivity: Novel Approaches and Perspectives Review of things lurking behind the corner.
I	Article	by Warren G. Proctor, Reminiscences of the Early Days of NMR at Stanford A fascinating 1967 document, edited by S.Sykora.
I	Article	by Sykora S., NMR Relaxometry of Solid Urea, I Experimental obstacles due to strong piezoelectricity.
		Educational NMR / MRI Texts:
III	Edu	by Sýkora S., A Primer on Scalar Relaxation in NMR Reviews the concept, including order-of magnitude estimates for organic molecules.
II	Edu	di Gambaro S., Risonanza Magnetica Nucleare: Appunti di Lezione Introduzione alla spettroscopia NMR in lingua italiana.
II	Edu	by Shoolery J., A Basic Guide to NMR 3rd Edition of the famous Jim Shoolery's booklet.
II	Edu	by Sýkora S., The Hebel-Slichter effect Summary of a historic milestone in field-cycling NMR relaxometry.
II	Edu	by Sýkora S., Antenna Reciprocity Theorem in Magnetic Resonance A phenomenological summary of the topic.
II	Edu	by Sýkora S., p-Quantum Transitions and a Combinatorial Identity A combinatorial identity related to transitions in coupled n-spin systems
I	Edu	by Sýkora S., One-Page MR Primer for newcomers, busy managers, laywers, and other outsiders
I	Edu	by Sýkora S., NMR Math: Pulse and Delay Operators Basis for simulation of LR-NMR / MRI sequences. With free Matlab utilities
I	Edu	by Sýkora S., K-space formulation of MRI Principles of MRI image formation and of the k-space formalism. Errata: The 2D sinc function plot in Fig.2 was wrong until corrected on Jan.3, 2006.
I	Edu	by Sýkora S., Transformation Properties of Probability Density Functions Math article written after a discussion on T1 distributions in NMR.
		Collections of NMR / MRI Books and References:
III	Free texts	Online Texts about Magnetic Resonance List and Repository of free, downloadable MR Books, Courses and Theses.
II	References	Early MRI physics (PDF, 2267 KBytes) Collection of 270 titled, historic references up to the spring of 1984.
II	References	Early MRI instrumentation (PDF, 399 KBytes) Collection of 76 titled, historic references up to the spring of 1984.
I	Books list	Books about ESR (Electron Spin Resonance, EPR) The most complete list of ESR/EPR monographs available anywhere.
I	References	Works about the History of NMR / MRI Includes also many web links relevant to the history of NMR and MRI.
I	References	Early History of NMR A huge list of references: Part I (up to 1955) and Part II (1956-1959).
I	Books list	Books about NMR (excluding medical MRI) The most complete list of NMR monographs available anywhere.
I	Books list	Books about MRI (Magnetic Resonance Imaging) A large and continuously updated list .
I	References	Physical principles of MRI A large list from the early days of MRI.
		Collections of NMR Data:
III	DataSet	Varian Associates 1978 Varian EM360/A/L 60 MHz Spectra Set Historic collection of CW HR-NMR spectra acquired on the EM360 instrument.
		NMR Posters and Talks:
VII	Talk	by Sykora S., Realistic simulated MR data (virtual phantoms) and the development of IP algorithms To develop Inverse-Problems algorithms one needs access to expertly simulated data.
VII	Talk	by Sykora S., Vasini E.M. FFC Relaxometry of Poly-Dispersed Samples: some Special Aspects Part of an investigation of nuclear magnetization evolution in variable magnetic fields.
VII	Tutorial	by Sykora S. Tutorial on Spin Systems in Magnetic Resonance A 40' introduction to a topic that would require a book!
VII	Poster	by Vasini E.M., Cobas C., Sykora S. In-vivo spectra pre-conditioning using PcBc Automatic phase and baseline conditioning of in-vivo NMR spectra.
VII	Poster	by Vasini E.M., Cobas C., Sykora S. Metabolomic spectra pre-conditioning using PcBc Automatic phase and baseline conditioning of metabolomic NMR spectra.
VII	Poster	by Vasini E.M., Sykora S., Cobas C. PcBc - Novel Automatic Phase & Baseline Correction Algorithm Update of a recent algorithm for a basic evaluation of NMR and other spectra.
VII	Poster	by Vasini E.M. and Sykora S. Nuclear Magnetization Evolution During the Switching Time in Field Cycling NMR Part of a more general investigation of magnetization evolution in a variable field.
VI	Talk	by Vasini E.M., Cobas C., Sykora S. PcBc - A Novel Automatic Phase and Baseline Correction Algorithm Progress in the development of the novel algorithm.
VI	Talk	by Sykora S. The Unbearable Fuzziness of NMR Data A reflection and illustration of how experimental data are always fuzzy.
VI	Poster	by Vasini E.M., Cobas C., Sykora S. Automatic Concurrent Phase & Baseline Correction in 1D NMR Spectra A novel algorithm, nicknamed PcBc.
VI	Poster	by Vasini E.M., Bortolotti V., Fantazzini P. and Sykora S. PERFIDI Filters: A Summary Work done so far on the PERFIDI T₁filters so far, with focus on MRI
VI	Poster	by Sykora S., Cobas C. Progress in Multi-Spectra Automatic Structure Verification (MS-ASV) Frank report on the problems encountered so far.
VI	Talk	by Sykora S. NMR in XXI Century: 30 selected things to do and explore A technologist's view of the many open roads to innovate Magnetic Resonance.
VI	Talk	by Sykora S. Is NMR Stuck? A frank personal view of the current state of NMR (though not of MRI).
V	Talk	by Sykora S. Molecular Spins: a New Frontier Conjecture of persistent currents in acyclic molecules and molecular fragments.
V	Talk	by Cobas C., Seoane F., Sykora S. Introducing GSD-2D An extension of GSD (Global Spectral Deconvolution) to two dimensions.
V	Talk	by Sykora S. Fitting of spin system parameters to NMR spectra, revisited Proposal of a new, very fast, algorithm for simulations of spin systems spectra.
IV	Poster	by Cobas C., Seoane F., Sykora S. Automatic Structure Verification (ASV) as an AI wizard: the milestones met and the challenges looming ahead Performance reached so far and perspectives.
IV	Poster	by Mari S., Righi V., Nocetti L., Valentini A., Schenetti L., Marchioro C., Sykora S., Cobas C. Toward direct application of multivariate statistical analysis to MRS Datasets A new approach to in-vivo and in-vitro Magnetic Resonance Spectroscopy in medicine.
IV	Poster	by Sykora S. Molecular Spins: a new Frontier of Chemical Physics and Magnetic Resonance? A molecular-physics conjecture presented at 53rd ENC as a Poster and a Talk.
IV	Poster	by Cobas C., Bernstein M., Vaz E., Seoane F., Sordo M., Domínguez S., Pérez M., Sykora S. An Expert System for the Auto Assignment of 1H NMR Spectra of Small Molecules 2012 ENC report on the performance of the new Mnova software feature.
IV	Poster	by Mari S., Fontana F., Manteiga J.G., Gaude E., Cenci S., Caneva E., Musco G., et al Metabolomic of Intact Tissues: Discrimination Between Different Osteolytic Lesion Regions from a Multiple Myeloma Patient 1H HRMAS NMR spectra A nice and novel application of NMR in clinical medicine.
IV	Poster	by Cobas C., Seoane F., Vaz E., Sykora S., Bernstein M. Automated QC with Compound Structure Verification and Quantitation 2012 ENC report on quality-control using NMR spectra and Mnova software.
III	Poster	by Bortolotti V., Fantazzini P., Gombia M., Greco D., Rinaldin G., Sykora S. Performance of two-sequence, two-inversion pulse PERFIDI filters to suppress and/or quantify relaxation time components in multicomponent systems A practical application of a simple PERFIDI pulse-sequence preamble.
III	Poster	by Mari S., Mannella V., Quilici G., Musco G., Seoane F., Cobas C., Sykora S. GSD in Metabolomics: Absolute Quantification and GSD Binning The first reported application of GSD to metabolomics.
III	Poster	by Cobas C., Sykora S. Progress in Bayesian DOSY and ROSY Transforms Report on improvements made possible by combining GSD with the BDT algorithm.
III	Poster	by Cobas C., Sykora S. The Bumpy Road towards Automatic Global Spectral Deconvolution (GSD) With GSD finally operative, the lessons we have learned.
II	Poster	by Cobas C., Seoane F., Sykora S. Global Spectral Deconvolution (GSD) of 1D-NMR spectra An approach to extracting all significant information from an HR-NMR spectrum.
II	Poster	by Cobas C., Sykora S. Bayesian DOSY: A New Approach to Diffusion Data Processing Bayesian Data Transform (BDT) algorithm and its further improvements.
II	Poster	by Gombia M., Sykora S., Bortolotti V., Vacchelli E., Fantazzini P. A numerical method to optimize presaturation sequences on multiexponential samples Introduction of the LAPSR pulse sequence.
II	Poster	by Sykora S. Spin Radiation: Properties and Suggested Experiments Discussion of the nature of radiation emitted/absorbed by spin-systems.
II	Poster	by Cobas C., Sykora S. New algorithms aiming at automatic analysis of ¹H-NMR spectra Steps towards automatic molecular structure verification and elucidation.
II	Poster	by Cobas C., Monje P., Fraga S., Sykora S. Novel Data Evaluation Algorithms: J-Correlator^TM An efficient aid for establishing proton-proton connectivity from 1D HR-NMR spectra.
II	Poster	by Cobas C., Larin N., Iglesias I., Seoane F., Sykora S. Novel Data Evaluation Algorithms: 1D and 2D Resolution Booster^TM A striking tool for disentangling high-resolution NMR spectra.
II	Poster	by Cobas C., Sordo M., Larin N., Sykora S. Novel Data Evaluation Algorithms: Bayesian DOSY and ROSY Transforms A natural way to display DOSY or ROSY data.
II	Poster	by C.Cobas, S.Sykora Extended DISPersion-Absorption (eDISPA) approach to Automatic Phasing of HR-NMR Spectra Advances in automatic evaluation of high-resolution NMR spectra.
I	Poster	by S.Sykora, E.Vacchelli, V.Bortolotti, P.Fantazzini New Universal NMR Sequences: PERFIDI and LAPSR Two ways of exploiting trains of inversion pulses.
I	Poster	by M.A.Cremonini, L.Venturi, S.Sykora, C.Cavani, G.Placucci, Reference Convolution of Low Resolution FIDs in the Presence of Poor Magnetic Field Homogeneity A simple approach to meaningful analysis of distorted NMR FIDs.
I	Poster	by D.Canina, A.Galkin, S.Sykora, G.M.Ferrante, Novel Approaches to Signal Acquisition and Accumulation in FFC-NMR experiments
I	Poster	by A.Galkin, D.Canina, S.Sykora, G.M.Ferrante, Novel Approaches to the Timing of FFC-NMR experiments
I	Poster	by M.Gombia, V.Bortolotti, P.Schembri, G.Ferrante, S.Sykora and P.Fantazzini, A dedicated NMR apparatus for non-invasive and non-destructive measurements of great dimension cores
I	Poster	by S.Sykora, Field-Noise Effects in NMR
I	Poster	by S.Sykora, M.A.Cremonini, L.Laghi, P.Fantazzini, 1H NMR relaxation dispersion profiles of solid BSA
I	Poster	by S.Sykora, G.Ferrante, Null-biased fast-field-cycling sequences
I	Poster	by V.Bortolotti, R.J.S.Brown, P.Fantazzini, G.Ferrante, S.Sykora, Field-dependence of relaxation time distributions in rock samples
I	Poster	by Cremonini M.A., Laghi L., Sykora S., Ferrante G., Franchini A., Placucci G., Field Cycling Relaxometry of Hen Egg Albumen
I	Poster	by Sykora S., Ferrante M., Galkin A., Measuring Fast Relaxing Samples on Current FFC-NMRD Relaxometers
I	Poster	by Sykora S., Segre A., Capitani D., Proietti N. 1H-NMRD Profiles of Polymers: A Preliminary Experimental Review
I	Poster	by Bray C.L., Lee D.Y., Hornak J.P., Satheesh V., Sykora S., Ferrante G., A Fast Field Cycling NMR Study of Soil
		Reprints of old & hard-to-find NMR / MRI articles:
II	Reprint	by Sýkora S., Doskocilová D., Teorie chemických posunù v Jaderné Magnetické Resonanci Czech-language review of the chemical shifts theory in Chemické Listy (1966).
I	Reprint	by Sýkora S., Vogt J., Experimental Noise in Data Acquisition and Evaluation, Parts I and II Bruker Report 2/1979. Properties and evaluation of noise in NMR Spectroscopy.
		FFC-NMR Application Notes written by S. Sykora:
I	AN040914	Computed T1MX in NMRD Profile Wizard Problems, solutions and a discussion of merits for Users of Stelar AcqNmr software.
I	AN040913	AcqNmr: User extensions of parameter capabilities A guide for advanced Users in AcqNmr.
I	AN040825	AcqNmr: Nesting Control Intervals in Pulse Sequences Guide to interval splitting/nesting for advanced Users of AcqNmr.
I	AN040824	AcqNmr: Direct Pulser-Channels Control Explains the control of pulser channels in sequences in AcqNmr.
I	AN030206	Estimates of mean signal offsets Explains the improved offset-estimate algorithm implemented in AcqNmr.
I	AN020815	Scripting of NMR Sequences in AcqNmr A guide for advanced Users of AcqNmr.
I	AN020805	XML format for an NMRD data base? A data-base proposal which did not catch-on so far.
I	AN020715	A brief note on FFC NMR relaxometry of soils written with G.Ferrante. A reflection on expected phenomena.
I	AN020703	Switching times and signal τ-dependence in FFC written with G.Ferrante. Proof that FFC NMRD results are correct.
I	AN010615	On-line evaluation of mono-exponential decays Explains how AcqNmr evaluates monoexponential decays.
I	AN010601	AcqNmr: Basic and Mute data accumulation modes Explains settings of the DAAM and DAAP parameters in AcqNmr.
MATHEMATICS Fast jumps: Educational texts and Reference collections
VI	Article	Sequences related to the differential equation f''= af'f Sequences whose egf's satisfy this equation form an interesting family.
VI	Article	Fixed points of the mappings exp(z) and -exp(z) in C Properties and 20-digit tables of complex fixed points of ±exp(z).
V	Article	On some number densities related to coprimes Densities of numbers m (non)coprime to [m\b] for various bases b.
V	Article	A Random Mapping Statistics and a Related Identity A new discrete statistic and new decompositions of unity and of n^n.
V	Article	On Neighbor-Property Cycles Counting round-table seatings where every neighbor pair has a certain property.
V	Article	On Canonical Gray Cycles Counting canonical cycles of Gray codes for various cycle lengths.
IV	Article	Blazys Expansions and Continued Fractions On a bijection of a subset of irrationals onto one of integer sequences.
IV	Article	Dawson Integral Approximations Rational approximations (plus exact code) for the Dawson integral function F(x).
III	Article	by Sýkora S., Mathematical Means and Averages: Hermean, alias Generalized Logarithmic Mean The limit of generalized Heronian means Her(k,a): existence and a closed formula.
III	Article	by Sýkora S., Generalized Heronian means III Proof that no generalized Heronian mean is ever smaller than geometric mean.
III	Article	by Sýkora S., Generalized Heronian means II Proofs of Heronian means inequalities for two special cases.
III	Article	by Sýkora S., A convex functions inequality An inequality on means of convex function values at points evenly distributed over an interval.
III	Article	by Sýkora S., Mathematical Means and Averages: Generalized Heronian means A sweeping generalization of the Heronian mean to a parametrized family of means.
II	Article	by Nemes G., New asymptotic expansion for the Γ(x) function (an update) Adds estimates of the remainder for an asumptotic series published earlier.
II	Article	by Nemes G., Asymptotic expansion for log(n!) in terms of the reciprocal of a triangular number Presents a log-factorial expansion similar to Stirling's but using triangual numbers.
II	Article	by Nemes G., New asymptotic expansion for the Gamma function Presents two novel approximation formulas, a series and a closed-form.
II	Note	by Nemes G. and Sýkora S., A historic comment on ellipse perimeter approximations Contribution to the history of the Particularly Fruitful approximation
II	Article	by Sýkora S., Inequalities involving linear and cyclic sums of ratios Two inequalities for n-tuples of positive real numbers (+corollaries)
II	Article	by Sýkora S., K-Space Images of n-Dimensional Spheres and the Generalized Sinc Functions Extends the function sinc(x) = sin(x)/x to fit n-dimensional problems
II	Article	by Sýkora S., Advances in Approximations of Ellipse Perimeters and of the Complete Elliptic Integral S-class approximations, plus a report on Ahmadi 2006 and derivatives (error < 152 ppb)
I	Article	by Sýkora S., Algebraic Approximations of Ellipse Perimeters and of the Complete Elliptic Integral E(x) A-class approximations, some with relative errors below 1 ppm
I	Article	by Sýkora S., Finite and Infinite Sums of the Power Series (k^p)(x^k) Explicit formulas and some properties
I	Article	by Sýkora S., Binary Iterated Powers Introducing BIPs and a novel point of view on the hyperpower series and its cousins
I	Review	by Sýkora S., Approximations of Ellipse Perimeters and of the Complete Elliptic Integral E(x) Addendum to the 2005 Review
I	Article	by Sýkora S., *Is every* finite-dimensional Hilbert space a spin-space ?** An unconventional way of introducing the basic formulae of spin-algebras.
I	Review	by Sýkora S., Approximations of Ellipse Perimeters and of the Complete Elliptic Integral E(x) Includes a MATLAB utility.
I	Article	by Sýkora S., On the Circumference of Ellipses Two new approximations, applicable also to the complete elliptic integral E(x).
I	Article	by Sýkora S., Surface Integrals over n-Dimensional Spheres This is more tricky than it sounds ...
I	Article	by Sýkora S., Volume Integrals over n-Dimensional Ellipsoids This, of-course, includes multi-dimensional spheres ...
		Educational Math texts:
V	Edu	An Abel's Identity and its Corollaries A note on the huge family of Abel's combinatorial identities.
III	Edu	by Sýkora S., Mathematical Means and Averages: Basic Properties A primer on means, averages, and their properties with innovative definitions.
II	Edu	by Sýkora S., p-Quantum Transitions and a Combinatorial Identity A combinatorial identity related to transitions in coupled n-spin systems
I	Edu	by Sýkora S., Ad Astra Ltd and Early History of Gravity Engineering A simple and amusing example of applied variational calculus.
I	Edu	by Sýkora S., Exponential Transforms of Polygonal Functions Explicit Laplace and Fourier transforms of polygonal functions (this goes beyond education).
I	Edu	by Sýkora S., Taylor Traitor Functions Note on some counter-intuitive aspects of the Taylor series.
I	Edu	by Sýkora S., Transformation Properties of Probability Density Functions Math article written after a discussion on T1 distributions in NMR.
		Collections of Math Books and References:
III	Free texts	Online Texts about Mathematics List and Repository of free, downloadable Math Books, Courses and Theses.
II	DataBase	Mathematical Constants A growing collection of pure and applied mathematics constants.
I	Books list	Mathematics Books A large and continuously updated list .
PROGRAMMING
VII	Talk	by Sykora S., Realistic simulated MR data (virtual phantoms) and the development of IP algorithms To develop Inverse-Problems algorithms one needs access to expertly simulated data.
V	Article	by Sykora S., On Neighbor-Property Cycles Counting round-table seatings where every neighbor pair has a certain property.
V	Article	by Sykora S., On Canonical Gray Cycles Counting canonical cycles of Gray codes for various cycle lengths.
IV	Article	by Sykora S., Dawson Integral Approximations Rational approximations (plus exact code) for the Dawson integral function F(x).
I	Edu	by Sykora S., Writing C/C++ Macros: Rules, Tricks and Hints What you should know before writing a macro. Updated March 22, 2007.
		Articles with CODE snippets
IV	Code	Integer Numbers C/C++ Macros Testing and handling of integer numbers.
III	Code	Three-point interpolation of a real function This C code includes coordinate estimates and reliability of local minima/maxima.
II	Code	ASCI Strings C/C++ Macros Testing and handling of plain ASCII strings (char*).
II	Code	ASCI Characters C/C++ Macros Testing and conversions of characters.
II	Code	Complex Metric C/C++ Macros Distances to / between elements of a set of complex numbers.
II	Code	Basic Metric C/C++ Macros Distances to / between set elements.
I	Code	Extrema C/C++ Macros Maximum & minimum values and/or their locations.
I	Code	Bits and Flags C/C++ Macros Management of single Bits and Bit-Flag Arrays.
I	Code	Relational and Sign C/C++ Macros Relations, Sorting and Sign management.
I	Code	General Purpose C/C++ Macros Data extraction, Shifts and Permutations.
		Data Bases
VI	Books list	Books about HDL's, FPGA's, and Silicon Programming A large, updated list covering modern digital hardware development.
VI	Books list	Books about Programming and Computing Tools A large and continuously updated list covering languages, libraries, OS, and more.
III	Books list	Books on Quantum Computing, Information and Entaglement A large and continuously updated list.
III	Free texts	Online Texts about Programming List and Repository of free, downloadable Programming Books, Courses and Theses.
II	CodeLib	by IBM (International Business Machines Corporation), System/360 Scientific Subroutine Package Programmer's Manual, Version III Free, online re-edition of the now historic 1968 document.
II	Books list	Books about Web Issues and Web Programming A large and continuously updated list.
I	Books list	Books about Software, Programming, Algorithms, ... A large and continuously updated list.
I	DataBase	HTML Character Sets Charset specification in the http-equiv meta. Includes code-pages.
I	DataBase	HTML Entities and their Glyphs W3C HTML 4.0 entities with corresponding glyphs.
DATA BASES edited by S. Sykora
II	DataBase	Mathematical Constants Huge, growing collection of pure and applied mathematics constants.
I	DataBase	HTML Character Sets Charset specification in the http-equiv meta. Includes code-pages.
I	DataBase	HTML Entities and their Glyphs W3C HTML 4.0 entities with corresponding glyphs.
I	DataBase	Constants of physics and mathematics Latest CODATA values. Customary & root SI dimensions.
I	DataBase	SI dimensions of various quantities Alphabetic list of SI dimensions of over 200 quantities.
I	DataBase	SI dimensions of various quantities listed by category Over 200 physical quantities in 22 categories.
I	DataBase	Tables of SI units and prefixes Includes basic, derived, accepted and deprecated units.
		Edited lists of BOOKS and REFERENCES:
VI	Books list	Books about HDL's, FPGA's, and Silicon Programming A large, updated list covering modern digital hardware development.
VI	Books list	Books about Programming and Computing Tools A large, updated list covering languages, libraries, OS, and more.
V	Books list	Books about Home and Classroom Electronics Tinkering, Hacking, Programming, and having fun with Raspberry Pi, Arduino, Intel Edison, Intel Galileo, BeagleBone, etc.
V	Books list	Books about Spintronics, including its theory, physics, engineering, materials, and applications A large and continuously updated list.
V	Books list	Books about Intellectual Property (IP), Patents, Copyright, and Self-publishing A large and continuously updated list.
V	Books list	Books about WWW development issues A large and continuously updated list.
IV	Books list	Popular Science Books (a reach-out collection) A large and continuously growing list.
IV	Books list	Books on Materials Science and Technology A large and continuously updated list.
IV	Books list	Books on Quantum Computing, Information and Entaglement A large and continuously updated list.
III	Free texts	Online Texts about Spectroscopy List and Repository of free, downloadable Spectroscopy Books, Courses and Theses.
III	Books list	Spectroscopy Books A large and continuously updated list.
III	Free texts	Online Texts about Chemistry List and Repository of free, downloadable Chemistry Books, Courses and Theses.
III	Books list	Chemistry Books A large and continuously updated list.
III	Free texts	Online Texts about Programming List and Repository of free, downloadable Programming Books, Courses and Theses.
III	Free texts	Online Texts about Mathematics List and Repository of free, downloadable Math Books, Courses and Theses.
III	Free texts	Online Texts about Physics List and Repository of free, downloadable Physics Books, Courses and Theses.
III	Books list	Physics Books A large and continuously updated list.
III	Free texts	Online Texts about Electronics List and Repository of free, downloadable Electronics Books, Courses and Theses.
III	Free texts	Online Texts about Magnetic Resonance List and Repository of free, downloadable MR Books, Courses and Theses.
II	References	Early MRI physics (PDF, 2267 KBytes) A collection of 270 titled, historic references up to the spring of 1984.
II	References	Early MRI instrumentation (PDF, 399 KBytes) A collection of 76 titled, historic references up to the spring of 1984.
II	Books list	Books about Patents and Intellectual Property A large and continuously updated list.
II	Books list	Books about Web Issues and Web Programming A large and continuously updated list.
I	References	Constants of Physics and Mathematics A large and continuously updated list.
I	Books list	Books about Software, Programming, Algorithms, ... A large and continuously updated list.
I	Books list	Mathematics Books A large and continuously updated list.
I	Books list	Books about ESR (Electron Spin Resonance, EPR) The most complete list of ESR/EPR monographs available anywhere.
I	Books list	Books about Scientific Instruments, Measurements, and Sensors A large and continuously updated list.
I	Books list	Digital Signal Processing books A large and continuously updated list. Includes books on embedded systems.
I	Books list	Electronic and Electric Engineering books A large and continuously updated list.
I	References	Works about the History of NMR / MRI Includes also many web links relevant to the history of NMR and MRI.
I	References	Early History of NMR, Part II Covers years 1956-1959.
I	References	Early History of NMR, Part I From prior art up to 1955.
I	Books list	Books about NMR (excluding medical MRI) The most complete list of NMR monographs available anywhere.
I	Books list	Books about MRI (Magnetic Resonance Imaging) A large and continuously updated list.
I	References	Physical principles of MRI A large and continuously updated list.
I	References	Systems of Units of Measurements A large and continuously updated list.
ELECTRONICS
VI	Books list	Books about HDL's, FPGA's, and Silicon Programming A large, updated list covering modern digital hardware development.
V	Books list	Books about Home and Classroom Electronics Tinkering, Hacking, Programming, and having fun with Raspberry Pi, Arduino, Intel Edison, Intel Galileo, BeagleBone, etc.
III	Free texts	Online Texts about Electronics List and Repository of free, downloadable Electronics Books, Courses and Theses.
II	Edu	by Sykora S., Antenna Reciprocity Theorem in Magnetic Resonance A phenomenological summary of the topic.
II	Article	by Sykora S., Suppression of receiver recovery time in NMR Extention of the classical Lowe-Tarr circuit.
I	Edu	by Sýkora S., Noise Figure and Equivalent Input Noise Definitions of - and the relation between - the two concepts.
I	Edu	by Sýkora S., Passive Electronic Components: Standard Values Values of resistors, capacitors and inductors as defined by IEC 63.
I	Edu	by Sýkora S., Passive Electronic Components: Color Codes Color coding of resistors, inductors and capacitors as defined by IEC 62.
I	DataBase	SI dimensions of various quantities listed by category Includes a large section on electromagnetic physical quantities.
I	Books list	Electronic and Electric Engineering books A large and continuously updated list.
I	Books list	Digital Signal Processing books A large and continuously updated list. Includes books on embedded systems.
I	Books list	Books about Scientific Instrumentation and Measurements A large and continuously updated list.
I	Poster	by D.Canina, A.Galkin, S.Sykora, G.M.Ferrante, Novel Approaches to Signal Acquisition and Accumulation in FFC-NMR experiments
I	Poster	by A.Galkin, D.Canina, S.Sykora, G.M.Ferrante, Novel Approaches to the Timing of FFC-NMR experiments
About SCIENCE, EPISTEMOLOGY, ...
V	Article	by Sýkora S., On the Law of Diminishing Returns in R&D and Science A technical reflection about research and development management (including Science).
IV	Article	by Sýkora S., Phononian Science: current state and perspectives A mildly speculative and humorous reflection for Physicists.
I	Article	by Sýkora S., Quo Vadis, Science Effects of mass-production of Science (1970).

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