The paper presents the development of a model for ozone treatment in a dynamic bed of different microorganisms (Bacillus subtilis, B. cereus, B. pumilus, Escherichia coli, Pseudomonas fluorescens, Aspergillus niger, Eupenicillium cinnamopurpureum) on a heterogeneous matrix (juniper berries, cardamom seeds) initially treated with numerous ozone doses during various contact times was studied. Taking into account various microorganism susceptibility to ozone, it was of great importance to develop a sufficiently effective ozone dose to preserve food products using different strains based on the microbial model. For this purpose, we have chosen the Weibull model to describe the survival curves of different microorganisms. Based on the results of microorganism survival modelling after ozone treatment and considering the least susceptible strains to ozone, we selected the critical ones. Among tested strains, those from genus Bacillus were recognized as the most critical strains. In particular, B. subtilis and B. pumilus possessed the highest resistance to ozone treatment because the time needed to achieve the lowest level of its survival was the longest (up to 17.04 min and 16.89 min for B. pumilus reduction on juniper berry and cardamom seed matrix, respectively). Ozone treatment allow inactivate microorganisms to achieving lower survival rates by ozone dose (20.0 g O3/m3 O2, with a flow rate of 0.4 L/min) and contact time (up to 20 min). The results demonstrated that a linear correlation between parameters p and k in Weibull distribution, providing an opportunity to calculate a fitted equation of the process.

Abstract. This paper presents new strategies for bond portfolio immunization which combine the time-honored duration with the M-Absolute measure defined by Nawalkha and Chambers (1996). The innovation consists in considering an average shock in a fixed time period as a random variable with mean µ or, alternatively, with normal distribution with mean µ and variance σ 2 . Additionally, an extension to arbitrage free models of polynomial shocks is provided. Moreover, the Fisher and Weil model, the M-Absolute strategy and a new one are compared empirically with respect to financial liquidity.Introduction. Management of interest rate risk, the control of changes in the value of a stream of future cash flows as a result of changes in interest rates are important issues for an investor. Therefore many academic researchers have examined the immunization problem for a bond portfolio (see Nawalkha and Chambers, 1999). They have proposed multiple-risk measure models (e.g. Fong and Vasicek, 1984, Balbás andIbáñez, 1998) or singlerisk measure models (e.g. Chambers, 1996, Kałuszka andKondratiuk-Janyska, 2004). We propose new strategies for bond portfolio immunization. One is called the duration-dispersion strategy (DD strategy for short) and combines the time-honored duration with the remarkable risk measure M-Absolute defined by Nawalkha and Chambers (1996). The other is named the modified DD strategy and includes, additionally, M-Squared of Fong and Vasicek (1984). We consider a wider set of shocks than examined by Fong and Vasicek (1984) and Nawalkha and Chambers (1996). A new class includes all parallel movements. Considering an average shock in a fixed time period as a random variable with mean µ or with normal distribution with mean µ and variance σ 2 is our innovation. Moreover, we generalize ar-2000 Mathematics Subject Classification: 62P20, 91B28.

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