Historic information regarding the appearence and creation of fundamentals of algebro-logical apparatus-"equivalental algebra" for description of neuro-nets paradigms and algorithms is considered which is unification of theory of neuron nets, linear algebra and the most generalized neurobiology extended for matrix case. A survay is given of"equivalental models" of neuron nets (NN) and associativememoryis suggested new, modified matrix-tenzor neurological equivalental models MTNLEMS) are offered with double adaptive -equivalental weighing (DAEW) for spatial -non-invariant recognition (SNIR) and spaceinvariant rrecognition (SIR) of2-D images (patterns). It is shown, that MTNLEMs DAEW are the most generalized, they can describe the processes in NN both within the frames of known paradigms and within new "equivalental" paradigm of noninteration type, and the computing process in NN under using the offered MTNLEMs DAEW is reduced to two-step and multistep algorithms and step-by-step matrix-tenzor procedures(for SNIR) and procedures ofdefining ofspace-dependent equivalental ftinctions fromtwo images (for SIR). Possible architectures ofNNand MTNLEMs DAEW SNIRare discussed on base of matrixtenzor equivalentors MTE), represented by two optical matrix-tenzor multiplicators. For realization ofMTNLEMs DAEW SIR its arhitecture is offered as modification of known correlators and convolution operation systems. The results of modelling are given which confirm the possibility ofincreasing the NN capacity with such MTNLEMs at least up to 1, 1 ammount of neurons! A successful recognition has been received ofboth large dimensional(from lOOxlOO up to 150x150 pixels) two level 2D images, and multilevel2D-images(49x7Sx8bit) in themodels DAEW SNIR(withthe numberofneurons from 3000 to 20000)and in models DAEW SIR.

Modified trim cut method with low level of invasion into the process is developed for visualization of laser cutting process. The method consists in high speed filming via transparent plate which slides with respect to the metal to allow visual access and simultaneously serves as the second missing wall of the kerf. The method is suitable for visualization in conditions equivalent to industrial cutting process in a wide range of plate thicknesses. High speed recordings are done for cutting of mild steel with oxygen and stainless steel with nitrogen. The effect of radiation wave length on the surface quality is studied by comparison of CO2 and fiber laser processing. The obtained results suggest that in case of oxygen assisted cutting, the combustion effects dominate on the surface quality and the effect of the radiation wavelength is moderate. In contrast, inert-gas-assisted cutting visualization reveals very high sensitivity to hydrodynamics of the melt flow which is strongly dependent on the radiation wavelength.

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The article deals with issues related to the development of seismological equipment and software, in relation to the study of seismic emission as a harbinger of destructive deformations of the side of a coal quarry. Examples of recordings of typical seismic impacts are given. The filtering and event selection algorithms used in the processing of records are shown.