Effect of Linearization in a WNT Signaling Model.

A nonlinear model consisting of a system of coupled ordinary differential equations (ODE), describing a biological process linked with cancer development, is linearized using Taylor series and tested against different magnitudes of input perturbations, in order to investigate the extent to which the linearization is accurate. The canonical wingless/integrated (WNT) signaling pathway is considered. The linearization procedure is described, and special considerations for linearization validity are analyzed. The analytical properties of nonlinear and linearized systems are studied, including aspects such as existence of steady state and initial value sensitivity. Linearization is a useful tool for speeding up drug response computations or for providing analytical answers to problems such as required drug concentrations. A Monte Carlo-based error testing workflow is employed to study the errors introduced by the linearization for different input conditions and parameter vectors. The deviations between the nonlinear and the linearized system were found to increase in a polynomial fashion w.r.t. the magnitude of tested perturbations. The linearized system closely followed the original one for perturbations of magnitude within 10% of the base input vector which yielded the state-space fixed point used for the linearization.

[Inertial separation of dust particles in a direct-flow field]. / Inertsionno razdeliane na prakhovi chastichki v pravopotochno pole.

A description is given of a graphic-mathematical method for approximate finding the separation capacity of the forward directed flow separator. The differential equations for the movement of a particle in changeable air flow are used. The parameters of the air flow in the canal of the separator are established in a graphic way. The equations are solved after the numerical method of Runge-Kuta. The aim of the work is to project a separator in a theoretical way observing definite requirements of the respirable fraction of the total dust.

[Method and apparatus setup for preparing test dusts with a specified granulometric composition by air separation]. / Metod i ustanovka za prigotviane na opitni zeolitni prakhove s opredelen granulometrichen sustav chrez vuzdushna separatsiia.

A method is developed and apparatuses constructed for the preparation of zeolite dusts for biological experiments in vivo and in vitro with dimensions under 5 micron. The method includes autogenic grinding of rocky zeolite material and air separation of the fraction under 63 micron, by means of cyclone and experimentally chosen conditions of work. The received "respirable" dust very well imitates the dust of the air from the working environment. The preparation of different experimental dusts is possible when suitable conditions, for working with the equipment, are chosen and the density of the material for separation is considered.

[Basic work environment factors at the Kremikovtsi Coke Chemical Plant]. / Osnovni factori na rabotnata sreda v koksokhimichen zavod SMK "Kremikovtsi".

The investigations, carried out by the institute of Hygiene and Occupational Diseases, for the assessment of toxic-chemical and physical factors of the working environment in the metallurgical-chemical plant showed a high degree of air pollution with dust and high number of toxic substances, many of them manifestating an additive effect or effect of synergism. At certain working places the physical factors have manifested deleterious effect. On the base of the investigations carried out, recommendations are proposed for further investigations on proper assessment of the occupational risk and improvement of labour conditions.

[New high-capacity sampling device for controlling air dust content]. / Nov visokodebiten probovzemen ured za kontrol na zaprashenostta na vuzdukha.

The construction of a new high-capacity sample taking device, designed for dust pollution control, and furnished with an electric aspirator is described. The device can be used in weight analyses of dust pollution in the air of working rooms and atmosphere alike. The basic feature of the apparatus is the so-called sample taking head which fulfils the functions of measurer and regulator of the capacity within 50-200 dm3/min limits. The measurement filters are made of FPP-15 material with dimeter measuring 80 mm. Sample taking using the above device is conducted in compliance with the requirements of dust control standards adopted in this country.