Articles Articles and publications listed below are written by Visilab Signal Technologies's personnel. Some of them are scanned as PDF documents. Some of them are published elsewhere, some are unpublished. Use the local copy if
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is not available.Henrik Stenlund on ResearchGate Henrik Stenlund, Visilab Report #2022-11 The trigonometric polynomials are simple yet have lots of interest in theories of orthogonal polynomials and in numerical analysis. The elementary trigonometric polynomials are broken series of sin(x) and cos(x). Some of their important properties have been left unsolved. Their integral representations are derived and the polynomials can be generated with them. Their differential equations are solved and the generating functions are created with the help of their recursion relations. A correspondence was observed between the exponential and trigonometric polynomials in the form of a pair of equations. Henrik Stenlund, Visilab Report #2022-07 The basic exponential polynomial is simple but has no closed-form expression other than the polynomial itself. This polynomial is mostly studied in group theories and with prime numbers. However, some of its basic properties seem to have been ignored. In this paper are shown an integral representation for it with which one can generate the polynomial. It is based on both a recursion relation and a differential equation. By using them various generating functions are solved. Henrik Stenlund, Visilab Report #2021-07 In this paper it is shown that a function of the constant dot product of the gradient operator acting on an arbitrary function can be transformed to a double three-dimensional integral. The inner one of them is a Fourier transform of the operator function. The result converted to one-dimensional problems is also useful in transforming complex differential expressions. Henrik Stenlund, Visilab Report #2021-05 In this communication it is shown that a function of the Laplace operator acting on an arbitrary function can be transformed to a three-dimensional integral. The cases of the exponential function and of an arbitrary function expressible as a power series, are treated. Two special cases of radial functions are presented based on elementary observations made here. Henrik Stenlund, Visilab Report #2020-11 This study derives the connection between the functional power series and the inversion formula, both given in series form. The link is established by differentiation of the inversion formula showing an expression of a functional power series for the reciprocal of the derivative in terms of the function itself. Henrik Stenlund, Visilab Report #2020-04 This study handles the three-dimensional linear diffusion in a new way. A general solution is given without particular initial conditions. In addition, solutions are obtained for a source-sink as a constant in time but spatially varying in three dimensions and having an arbitrary time dependence. An auxiliary function for diffusion is given having an interesting relationship with the concentration. It appears that both the time derivative and the Laplacian of the concentration obey the diffusion equation. An integro-differential equation for diffusion is presented. Henrik Stenlund, Visilab Report #2020-03 This study handles spatial three-dimensional solution of the nonlinear diffusion equation without particular initial conditions. The functional behavior of the equation and the concentration have been studied in new ways. An auxiliary function for diffusion is given having an interesting relationship with the concentration. A set of new integro-differential equations is given for diffusion Henrik Stenlund, Visilab Report #2019-04 Four new relations have been found between the Stirling numbers of first and second kind. They are derived directly from recently published relations. Henrik Stenlund, Visilab Report #2019-03 The powers of the ordinary differential operator can be expanded in terms of the Cauchy-Euler differential operator and for the opposite case. The expansions involve the Stirling numbers of first and second kind as is well known. Two relations between the Stirling numbers of first and second kind will find their proof in this work, generated by the two expansions. A third relation is obtained by algebraic manipulation from the two known recursion relations. Henrik Stenlund, Visilab Report #2018-06 The critical line of the Riemann zeta function is studied from a new viewpoint. It is found that the ratio between the zeta function at any zero and the corresponding one at a conjugate point has a certain phase and its absolute value is unity. This fact is valid along the whole critical line and only there. The common functional equation is used with the aid of the function ratio between any zero and its negative side pair, a complex conjugate. As a result, an equation is obtained for solving the phase along the critical line. Henrik Stenlund, Visilab Report #2017-11 Henrik Stenlund, Visilab Report #2017-07 Henrik Stenlund, Visilab Report #2016-12 - We transformed the generalized exponential power series to another functional form suitable for further analysis. By applying the Cauchy-Euler differential operator in the form of an exponential operator, the series became a sum of exponential differential operators acting on a simple exponential (e(-x)). In the process we found new relations for the operator and a new polynomial with some interesting properties. Another form of the exponential power series became a nested sum of the new polynomial, thus isolating the main variable to a different functional dependence. We studied shortly the asymptotic behavior by using the dominant terms of the transformed series. New series expressions were created for common functions, like the trigonometric and exponential functions, in terms of the polynomial. Henrik Stenlund, Visilab Report #2016-11 - In this paper we present a new identity and some of its variants which can be used for finding solutions while solving fractional infinite and finite series. We introduce another simple identity which is capable of generating solutions for some finite series. We demonstrate a method for generation of variants of the identities based on the findings. The identities are useful for solving various infinite products.. Henrik Stenlund, Visilab Report #2016-08 Henrik Stenlund, Visilab Report #2016-01 - In this work we present new methods for transforming and solving finite series by using the Laplace transform. In addition we introduce both an alternative method based on the Fourier transform and a simplified approach. The latter allows a quick solution in some cases. Henrik Stenlund,
Visilab Report #2015-11 Henrik Stenlund, Visilab Report #2014-12 Henrik Stenlund, Visilab Report #2014-11 Henrik Stenlund, Visilab Report #2014-05 Henrik Stenlund,
Visilab Report #2014-02 Henrik Stenlund,
Visilab Report #2013-08
Henrik Stenlund, Henrik Stenlund, Henrik Stenlund, Henrik Stenlund,
"Inversion
Formula", arXiv:1008.0183v3[math.GM], 27th Jul 2010
(local copy)Visilab Report #2010-07 - This work introduces a new inversion formula for analytical functions. It is simple, generally applicable and straightforward to use both in hand calculations and for symbolic machine processing. It is easier to apply than the traditional Lagrange-Bürmann formula since no taking limits is required. This formula is important for inverting functions in physical and mathematical problems. Henrik Stenlund, - This study offers three solutions of the diffusion coefficient's dependence on concentration in general cases without any limitations by boundary conditions. They are all suitable for numerical analysis when the experimental concentration data and time series are available producing dependence functions. As they are also of general nature, the expressions can be used for further investigations and modeling and fitting. Two of the methods offer three-dimensional approaches to this problem and may prove useful when combined with present-day laser scanning volumetric sensors, atomic probe microscopes and high performance computers. This is particularly true in geometries more complex than the regular one consisting of two semi-infinite slabs. Henrik Stenlund, Henrik Stenlund, Henrik Stenlund, " Henrik Stenlund, " Henrik Stenlund, " Henrik Stenlund, " Abstract
The purpose of the TOFMS project was to develop a
prototype being feasible for manufacturing as a product, having sensible
spectrometric features. A compact structure for the instrument was designed
by making it in axial form. As a result we have two prototypes both having
mass resolution much better than R > 1500 and the useful mass range over
1200 amu. The original specification was to exceed R = 400. The system is
able to deliver 5000 spectra / s on the screen of an oscilloscope. The free
length of flight was about 1000 mm and the ion optical mechanical parts
required some 800 mm in the vacuum chamber. Henrik Stenlund, Karl Holmström, " Henrik Stenlund, " Henrik Stenlund, " Henrik Stenlund, " Henrik Stenlund, Department of Chemistry, University of Helsinki, " Time-of-Flight Mass Spectrometry", Finnish Physical Society
Meeting, Oulu, 2-8-1985 - A prototype of a reflection type TOFMS is presented. Henrik Stenlund, " Henrik Stenlund, " Henrik Stenlund, - Electron optical system design with magnetic lenses for an X-ray system. The spherical electron gun design is also described in detail. Henrik Stenlund,
"Quantum Theory of Interstitial Atomic Diffusion
of Light Impurities in Semiconductors", University of Helsinki, 1979, a
Ph.Lic thesis A quantum theory of atomic diffusion in solids is presented and applied to a particular problem of interstitial diffusion, Li in Ge and Si. The theory is based on transport in narrow bands using the relaxation time approximation. The bands are evaluated by a one-dimensional method and the interaction potential between the impurity atom and lattice atoms is examined through numerical calculations, where the lattice potential difference between the equilibrium site and saddle point, the potential barrier height, is fitted with experimental values. Henrik Stenlund,
"Quantum Theory of Interstitial Diffusion", University
of Helsinki, 1979, a private study A quantum theory of atomic diffusion in solids is presented and applied to a particular problem of interstitial diffusion, Li in Ge and Si. The theory is based on transport in allowed narrow bands using the relaxation time approximation. The bands were calculated by using a proper potential model through numerical methods. The relaxation time was taken from the theory of Kagan and Klinger [18] and the diffusion coefficients were calculated. For comparison, the result of the theory of Kagan and Klinger was put also in numerical form. All coefficients show relatively good agreement with experimental values (see table 3.).The isotopic effect was also studied and Do and Eo were found to have dependences of (m)**-1/2 and (m)**-1 + B, respectively. Comments and feedback are invited:
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