Algebraic features of algorithm composition for calculating fractal structure

The construction methods analysis of known geometric fractals allows us to reveal algebraic features of fractal algorithms composition. The main concept of the analysis results is fractal operators which are basic operations for constructing fractals of a certain type. The result of using operators for geometric fractals is a structure with fractures of triangular, square, trapezoidal and similar forms. Multiplication and addition operations are introduced for operators, as well as the concept of the unit, null and inverse operator, which allows us to define periodic and quasiperiodic fractal structures. An algorithm for the formation of periodic and stochastic fractal structures is proposed, a distinctive feature of which is the implementation of the probabilistic choice of the basic geometric primitive on the current iterative cycle. The software implementation of the proposed algorithm confirmed the validity of the algebraic approach in studying and modeling fractal with a complex structure

Contractions dynamic of "fast" and "slow" rat muscle under spinal shock and modulators of contraction

Aim. To study the dynamics of neuromotor regulation of the contractile function of "fast" and "slow" muscles in rodents during spinal shock by spinal cord transection at the level Th11-Th12. Methods. The experiments were carried out on laboratory rats weighing 140-180 g. The animals were divided into two groups: "Control" (8 rats) and "Spinal shock" (6 rats). The lower leg muscles, m. soleus and m. extensor digitorum longus (m. EDL), were dissected by partially isolating without disrupting the connection with the body's circulatory system. The sciatic nerve was stimulated with single electrical impulses (10 V, 0.5 ms). Contractions of both muscles caused by electrical stimulation of the sciatic nerve before and after the injection of the substances into the femoral artery - tubocurarine (1 mM) or norepinephrine (10 mM) - were recorded in animals of both groups. After spinalization, muscle contractions were re-recorded during electrical stimulation of the sciatic nerve before and 10 minutes after the injection of tubocurarine or noradrenaline into the femoral artery in the same concentrations. Results. After spinalization of the animal, the contraction force of the muscle m. EDL fibers increased to 0.43±0.03 g (p=0.040), but the temporal parameters remained unchanged. M. soleus, on the contrary, showed a decrease in the contraction time to 0.053±0.005 s (p=0.045), and no change in the contraction force was observed under these conditions. Intra-arterial administration of norepinephrine in the control group resulted in an increase of m. soleus contractions up to 1.21±0.17 g (p=0.048), and m. EDL - up to 0.57±0.07 g (p=0.043). The administration of norepinephrine in spinalized animals caused an increase in the contraction of m. soleus up to 1.21±0.09 g (p=0.047), and m. EDL up to 0.66±0.05 g (p=0.043). The blocker of postsynaptic cholinergic receptors tubocurarine administration reduced the force of contraction of both muscle types in both control [m. soleus up to 0.39±0.03 g (p=0.039), m. EDL up to 0.11±0.02 g (p=0.042)] and spinalized [m. soleus up to 0.34±0.05 g (p=0.039), m. EDL up to 0.15±0.04 g (p=0.040)] animals. Conclusion. The data obtained demonstrate the presence of significant differences in the mechanisms of control of contractile activity in the "fast" and "slow" skeletal muscles of warm-blooded animals; the persistence of the similar effect of the basic modulators on the contraction of both muscles with such a striking reaction to spinalization highlights the contribution of neurotrophic control to the functioning of "fast" and "slow" motor units