The 20-60-20 Rule

In this paper we discuss an empirical phenomena known as the 20-60-20 rule. It says that if we split the population into three groups, according to some arbitrary benchmark criterion, then this particular ratio implies some sort of balance. From practical point of view, this feature often leads to efficient management or control. We provide a mathematical illustration, justifying the occurrence of this rule in many real world situations. We show that for any population, which could be described using multivariate normal vector, this fixed ratio leads to a global equilibrium state, when dispersion and linear dependance measurement is considered

A note on conditional covariance matrices for elliptical distributions

In this short note we provide an analytical formula for the conditional covariance matrices of the elliptically distributed random vectors, when the conditioning is based on the values of any linear combination of the marginal random variables. We show that one could introduce the univariate invariant depending solely on the conditioning set, which greatly simplifies the calculations. As an application, we show that one could define uniquely defined quantile-based sets on which conditional covariance matrices must be equal to each other if only the vector is multivariate normal. The similar results are obtained for conditional correlation matrices of the general elliptic case

Cyrenaican coinage from the beginning of Roman rule : new evidence from Ptolemais

Warsaw University Institute of Archaeology excavations at the so-called Villa with a View in Ptolemais, have contributed significantly to knowledge of town history and development. Numismatics is one field in which substantial verification as well as new evidence has been collected. Current finds by the Polish mission, have helped to rethink Cyrenaican coinage in both the Hellenistic and Roman periods, especially with regard to local issues from the beginning of Imperial rule, which are presented in the article.Agnieszka Uziębł

On Witt rings of funetion fields of real analytic surfaces and Curve

Sin resume

Negative curvature fibre optics for delivery of high-peak power light for manufacturing applications

This thesis covers investigations into high peak power short (nanosecond) and ultrashort (picosecond and femtosecond) pulse delivery through novel hollow-core microstructured silica fibres - the Negative Curvature Fibre (NCF) and the Free Boundary Anti-Resonant Fibre (FBARF) for manufacturing applications. Both types of fibres provide light guidance in the NIR and green spectral regions via the Anti- Resonant Reflecting Optical Waveguiding (ARROW) mechanism. NCFs exhibit extremely low attenuations of 0.04 dB/m and 0.15 dB/m at 1030 nm and 532 nm respectively, not achievable with photonic bandap hollow-core fibres. These fibres have been demonstrated to deliver NIR and green picosecond pulses with peak powers at the level of 15 MW and 5 MW respectively, which significantly exceeds the capabilities of commercially available singlemode fibres. Optimised NCFs for transmission in both spectral regimes provide singlemode, high quality output and maintain the spectral and temporal properties of the original laser pulse. Furthermore, these fibres exhibit a low sensitivity to bending with useful bend diameters ≥ 5 cm, which is sufficient for most beam delivery applications. This was further improved by developing and introducing a dynamic fibre delivered power stabilisation system which enables efficient compensations of bend-induced power fluctuations. Practical implementation of NCF delivered pulses in manufacturing applications has been demonstrated in the precision micro-machining of metals, crack-free micromilling of fused silica and waveguide writing in borosilicate glass. The FBARF structure is a modification of the NCF design aimed for an improvement in energy handling capacity, light confinement and further reduction of bending loss. However, the fibres reported in this thesis (fabricated for guidance at 1 μm and green wavelengths) are preliminary designs, and so their full potential e.g. their energy handling capacities could not be fully established. Nevertheless, initial tests performed within this work indicated that further development of this fibre design should result in a reduction of the intrinsic attenuation and bend loss to a level comparable with the NCFs while increasing the optical damage threshold

Use of cryotherapy in different diseases

Physiotherapy section - physicotherapy successfully applies frequent cryotherapy treatments in many different diseases. The paper presents a review of the literature on the basis of review papers as well as research papers from reputable scientific journals, which have been published over the last few years

Use of kinesiology taping in different diseases

Kinesiology taping, called in Poland more and more often dynamic plastering is a method with a very wide application. More and more often this method is noticed among patients. Currently, many studies have been conducted, in which the effectiveness of therapy with the use of tapes for kinesiology taping has been proven. What is more, no harmful effects of this form of therapy have been found. In addition, there is more and more research showing the effectiveness of cathodiology taping as a form of supporting the effects of the main therapy. The paper was written on the basis of review articles and research papers presented in reputable Polish magazines dealing with physiotherapy

Postural defects - kyphosis, lordosis, sway back, flat back. Part two

Posture defects are a serious social problem. It is very important to be able to distinguish between postural defects. A part of the second part of the paper presents a description of kyphosis, lordosis, sway back and flat back