The pharmaceutical sector is one of the most profitable industries in the world, despite the very high proportion of the required research and development costs that determine the activity itself and the high risks involved in investing in them. In addition to a number of industry-specific characteristics, the innovation policies of each country might also have a significant impact on the efficiency of pharmaceutical companies. The primary aim of the research was to demonstrate this effect in the case of the Visegrád countries. The ROE seemed to best reflect the ownership interests and the combined effect of other profitability ratios and it was confirmed by analysis of variance. The analysis was based on the EMIS corporate database; multivariate statistical methods were applied to demonstrate the reaching of indicator trends, and from among those methods regression analysis was applied in particular. Based on the findings, it was concluded that primarily the more profitable pharmaceutical companies were able to utilize their assets more efficiently, while manufacturers in the latter category financed their operations with external capital to a lower extent. Although the indicators of the analysed companies showed a very high standard deviation in all four countries, the results of the regression were only outstanding in Slovakia, which had a very low number of cases. In addition, temporal tendencies have been almost the same in the entire region, which was also influenced by the fact that return on capital of the business entities within the sector decreased by 2016 throughout the region. JEL classification:C12, C21, C25, C55.

Objective:Saphenous venous grafts (SVGs) are established choices for coronary artery bypass grafting (CABG); however, their lumen patency is limited. Our goal was to investigate the risk factors of SVG degeneration.Methods:Seventy-five patients (mean age, 57.5±10.4 years) with 133 SVG conduits who had cardiac catheterization ≥1 year after CABG were selected; follow-up period was 67.6±36.8 months. Patients were divided into 3 groups according to angiographic status at follow up [intact: <20% (n=23); narrowed: 20–99% (n=24); and occluded (n=28)]. Baseline clinical conditions were evaluated in relation to follow-up angiography. As onset date of chronic total occlusions is usually uncertain, they arise typically from thrombotic lesions; thus, their value in evaluation is limited.Results:There were no significant differences between the 3 groups in clinical parameters. Linear correlation analysis found significant (p<0.01) positive connection of SVG disease (luminal diameter reduction 20–99%) with C-reactive protein (CRP) and homocysteine (Hcy), as well as between CRP and Hcy. Multiple regression analysis showed plasma Hcy level to be significantly related to graft diameter reduction normalized to time elapsed until angiography in narrowed grafts: 1 µmol/L increase of Hcy was associated with 0.053%/month decrease in lumen diameter (p<0.01; R2=0.428); extrapolating: +10 µmol/L higher Hcy level during 5 years is associated with 32.1% lumen reduction.Conclusion:Medium- to long-term SVG degeneration is related to elevated plasma total Hcy in patients with sub-occlusive graft stenosis, while in cases with intact SVGs, the beneficial local flow conditions may protect the grafts from degeneration.

Abstract. In our paper we find all functions f : R × R 3 → H and g : R 3 → H satisfying f (r, v)f (s, w) = − v, w + f (rs, svThese functional equations were motivated by the well-known identities for vector products and quaternions, which can be obtained from the solutions f (r, (v1, v2, v3) Mathematics Subject Classification (2010). 39B52, 16K20.Keywords. functional equation, vector product, quaternion. Quaternions and vector productsLet H = {r+v 1 i+v 2 j +v 3 k | r, v 1 , v 2 , v 3 ∈ R} be the skew field of quaternions with the basic relations i 2 = j 2 = k 2 = ijk = −1. We call r the real part and v 1 i + v 2 j + v 3 k the imaginary part of the quaternion r + v 1 i + v 2 j + v 3 k ∈ H. A quaternion is purely imaginary if its real part equals 0. The absolute value of the above quaternion is defined by r 2 + v 2 1 + v 2 2 + v 2 3 . It is well-known (see e.g. [1], [6], [9], [10]) that identifying the purely imaginary quaternion v 1 i+v 2 j +v 3 k with the vector (v 1 , v 2 , v 3 ) ∈ R 3 we have (r + v)(s + w) = (rs − v, w ) + (sv + rw + v × w) (r, s ∈ R, v, w ∈ R 3 ), and for purely imaginary quaternionswhere on the left-hand sides quaternionic products stand, v, w and v × w denote the standard inner product (dot product) and the cross product of v, w ∈ R 3 , respectively.

We prove strong consistency and asymptotic normality of least squares estimators for the subcritical Heston model based on continuous time observations. We also present some numerical illustrations of our results.

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