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The aim of the paper is to provide a simple and reliable hysteresis model for prediction of magnetization curves of a resistance spot welding transformer (RSWT) core, operating in a wide range of flux densities and excitation frequencies.

The hysteresis model considered in the paper is the T(x) description advanced by J. Takács. Three options to extend the model to the dynamic magnetization conditions are considered. The excitation conditions differ from those prescribed by international standards.

The quasi‐static Takács model combined with a fractional viscosity equation similar to that proposed by S.E. Zirka outperforms other considered options. The effect of eddy currents may be considered as a disturbance factor to the frequency‐independent quasi‐static hysteresis loop.

The combined approach yields in most cases a satisfactory agreement between theory and experiment. For highest frequency considered in the paper (1 kHz) excessive “heels” were observed in the modelled loops. This artifact may be reduced by the introduction of a more complicated relationship for the viscous term. Future work shall be devoted to this issue.

The combined Takács‐Zirka model is a useful tool for prediction of magnetization curves of a RSWT core in a wide range of flux densities and excitation frequencies.

The usefulness of the Takács description has been verified in a practical application. The model is able to predict magnetization curves under non‐standard excitation conditions.

The paper aims to take a critical view of the Wholfarth's assumption and the Henkel plots as the measure of molecular mean‐field interaction in magnetic materials. At the same time it seeks to formulate the effect of the molecular field interaction on the anhysteretic remanence.

Based on the recently verified Bosorth's original definition of anhysteretic state, the paper verifies Wohlfarth's conjecture. By including the molecular field interaction into the effective field expression it formulates the hysteretic and anhysteretic remanent behavior of the magnetic material.

The hysteretic and anhysteretic character of the material can be formulated up to and beyond the Barkhausen jump. The paper also points out that, the now verified, Wholfarth's conjecture is applicable to not only major hysteresis loops but also to symmetrical minor loops as well, within the same set. By doing so it removes the uncertainty surrounding its mathematical formulation.

In the light of these findings the conjecture's relation to multi‐phase magnetic materials has to be investigated in the future.

The formulation of the hyteretic and anhysteretic remanent character can provide a graphical interpretation of the materials behavior. The paper demonstrate how the Henkel plots, based on the Wholfarth's conjecture, used as an indicator of the magnitude of the molecular interaction, can be simplified to the benefit of the theoretical and practical users.

The paper sets out to formulate the intermolecular forces leading to Barkhausen instability. In the approach the known concept of effective field is used within the framework of the T(x) model. The aim is to provide a mathematical tool to theoreticians and applied scientists in magnetism that is easier to use than those of other models. At the same time to demonstrate the easy applicability of the T(x) model to hysteretic phenomena.

With the combination of the effective and the external field the model is applied to hysteresis loops as well as to the anhysteretic state showing in both cases the local development of unstable conditions at beyond a critical point, leading to local hysteresis loops.

The paper formulates the critical conditions for the hysteretic and the anhysteretic process and calculates the susceptibility as the functions of magnetisation and the applied field.

Experimental verification will be required to prove the applicability to the various magnetic materials and to the accuracy of the model.

The paper provides an easy mathematical and visual method to show the conditions before and after the Barkhausen instability sets in during the magnetisation process.

The paper provides an easy mathematical tool for theoreticians and experimental scientists with a visual presentation of processes leading to Barkhausen instability and magnetic behaviour beyond that by using the T(x) model.

An efficient device simulation method is presented, which has been derived from mapping the results of a complete two‐dimensional (2‐D) analysis onto an equivalent lumped element network. The method is currently being used to predict latch‐up sensitivities of CMOS process design.

We chose to analyse Hungarian childlessness in order to map whether there is any voluntary childlessness at all in a society which is characterised by strong traditional family values and the widely accepted social norm that everyone should become a parent.

To answer to this question, we applied both quantitative and qualitative methods. First, we analysed the first three waves of the Hungarian panel survey ‘Turning Points of the Life Course’ conducted in 2001, 2004 and 2008. The focus is on men and women who were childless in 2001 and were still childless in 2008. To have a better understanding of the background of the quantitative results, we have also analysed 55 life-history interviews conducted with heterosexual men and women, who were recruited by using chain-referral sampling.

According to the qualitative findings the categorisation of childless people is quite fluid. For example, postponers became definitely childless while some originally voluntarily childless respondents became parents. However, the qualitative analysis allowed us to understand the mechanism behind this. In addition, using mixed methods also highlighted some inconsistencies between the qualitative and quantitative results.

The mathematical complexity of the B_J(x) Brillouin function makes it unsuitable for most calculations and its application difficult for computer programming in magnetism. Here, its approximation with the tanh function is proposed to ease the mathematical operations for most cases. The approximation works with good accuracy, acceptable in practical calculations. This approximation has already formed the foundation of the “hyperbolic model” in magnetism for the study of hysteretic phenomena. The reversal of the Brillouin function is an important but difficult mathematical problem for practical purposes. Here, a proposal has been put forward for an easy approximation using an analytical expression. This provides a good workable solution for the B_J(x)⁻¹ function dependent on J, the angular momentum quantum number of the material used. The proposed approximation is applicable within the working range of practical applications. The paper aims to discuss these issues.

The multi-variant Brillouin function is closely approximated by the tanh function to ease calculations. Its mathematically unsolved reversed function is approximated by a simple analytical expression with a good working accuracy.

The Brillouin function and its reversal can be approximated for practical users mostly for professionals working in Magnetism.

Most if not all practical problems in Magnetism can be solved within the limitations of the two approximations.

Both proposed functions can ease the mathematical problems faced by researchers and other users in Magnetism.

Ease the frustration of most users working in the field of Magnetism.

The application of the tanh function for replacing the Brillouin function led to the creation of the hyperbolic model of hysteresis. To the author's knowledge, the reverse function was mathematically only solved in 2015 with a vastly complicated mathematics, and is hardly suitable for practical calculations in Magnetism. The proposed simple expression can be very useful for theorists and experimental scientists.

This paper aims to present an analytical way of formulating the vital parameters of an equivalent hysteresis loop of a composite, multi-component magnetic substance. By using the hyperbolic model, the only model, which separates the constituent parts of the composite magnetic materials, an equivalent loop can be composed analytically. So far, it was only possible to superimpose the tanh functions by numerical method. With this transformation, all multi-component composite substances can be treated mathematically as a single-phase material, as in the T(x) model, and include it in mathematical operations. The transformation works with good accuracy for major and minor loops and provides an easy analytical way to arrive to the vital parameters. This also shows an analytical way to the easy solution of some of the difficult problems in magnetism for multi-component ferrous materials, such as Fourier and Laplace transforms, accommodation and energy loss, already solved for the T(x) model.

The mathematical single loop formulation of hysteresis loop of a multi-phase substance shows the way in good approximation of the sum of constituent loops, described by tanh functions. That was so far only possible by numerical methods. By doing so, it becomes equivalent to the T(x) model for mathematical operations.

The described method gives an analytical formulation [identical to the T(x) model] of multi-component hysteresis loops described by hyperbolic model, leading to simple solution of difficult problems in magnetism such as loop reversal.

Although the method is an approximation, its accuracy is good enough for use in magnetic research and practical applications in industries engaged in application of magnetic materials.

The hyperbolic model is the only one which separates the magnetic substance, used in practice, to constituent components by describing its multi-component state. Superimposing the components was only possible so far by numerical means. The transformation shown is an analytical approximation applicable in mathematical calculations. The transformation described here enables the user to apply all rules applicable to the T(x) model.

This study equally helps researchers and practical users of the hyperbolic model.

This novel analytical approach to the problem provides an acceptable mathematical solution for practical problems in research and manufacturing. It shows a way to solutions of many difficult problems in magnetism.

A brief account of the exponential model introduces the reader to one of the mathematical descriptions of the double non‐linearity of the hysteretic phenomena. The model described here satisfies the requirement for calculating the Laplace transforms in closed form for excitation waveforms constructed of straight lines. The method is demonstrated by applying it to a triangular excitation in the hysteretic process. It is shown that the Laplace transform of the induction waveform can also be calculated when the same excitation waveform is being applied in an anhysteretic process. It is also shown that when the excitation is small and falls within the limits of the Rayleigh region the calculation becomes simpler. This is demonstrated by formulating the Laplace transform of the induction waveform that resulted from triangular excitation in the Rayleigh region for both the hysteretic and anhysteretic cases.

Examines the tenth published year of the ITCRR. Runs the whole gamut of textile innovation, research and testing, some of which investigates hitherto untouched aspects. Subjects discussed include cotton fabric processing, asbestos substitutes, textile adjuncts to cardiovascular surgery, wet textile processes, hand evaluation, nanotechnology, thermoplastic composites, robotic ironing, protective clothing (agricultural and industrial), ecological aspects of fibre properties – to name but a few! There would appear to be no limit to the future potential for textile applications.

The purpose of this paper is to examine the relationships between processing conditions and magnetic properties of cores made of Soft Magnetic Composite (SMC) Somaloy 500.

The effects of compaction pressure and hardening temperature may be combined considering SMC density. This quantity may be chosen for optimization of properties of ready-made cores. In order to describe hysteresis loops the phenomenological model based on hyperbolic tangent transformation is applied.

SMC density affects substantially the shape of hysteresis loop. The paper provides a number of charts useful for checking how the parameters of the hysteresis model are affected.

The present study considers just one composition of the SMC and one type of lubricant. Future research shall be devoted to verification of the approach on a wider class of SMCs.

Material density may be a relevant quantity in optimization of magnetic properties of ready-made SMC cores. The simple hysteresis model based on the, “effective field” concept and Takács’ idea of hyperbolic tangent transformation may be useful for description of hysteresis curves of SMC cores. Model parameters are sensitive against variations of material density.

The results of the analysis may be useful for designers of magnetic circuits made of SMCs.