CONDITIONS OF DISCRETE CONVERGENCE OF STRUCTURES SYNTHESIS MODELS IN METAL AND NON-METALS COMPOSITIONS

The set-theoretical convergence of models of continuous and discrete synthesis processes in the compositions of metals and non-metals at the action of ray sources is shown. The non-metal density function obtained by the IDS thermal impulses on the temperature axis projection has a periodic view with fi xed stationary temperatures. They coincide with the boundaries of diff erent areas of change in the speeds of metal heating. This convergence of models to the general periodic operator is possible under four conditions of beam scanning: separation, compactness, property of states, stability. Then the current reciprocity ratios of the system (metals/non-metals) allow the use of the temperature of stationary non-metals as support for metals and serves to determine the parameters of ray sources when synthesizing structures in the compositions of the volume of the material.

Analisis Produktivitas Mesin Filling Auto Cup Sealer 1 dengan Metode Overall Equipment Effectiveness pada PT. Prima Kemasindo

The high level of downtime on the ACS 1 filling machine at PT. Prima Kemasindo causes the production process to be not optimal on the machine. The purpose of this study is to identify the maintenance system on the ACS 1 filling machine and measure the productivity level of the ACS 1 filling machine in the period from January to March 2021. This research is applied research using the Overall Equipment Effectiveness (OEE) method. The data used in this study are primary and secondary data obtained from company reports as well as interviews and observations. The results obtained in this study are the Overall Equipment Effectiveness (OEE) value of the ACS 1 filling machine for the period January 98.0%, February 98.5%, March 95.2%, and the average OEE value for the January-March period is 97.2 %. Then from the analysis of Six Big Loses, it is known that the highest loss elements are Idling and Mirror Stoppages and Reduced Speed. Based on the results of the fishbone diagram, it is known that the cause of Idling and Mirror Stoppages and Reduced Speed consists of several factors, namely humans, machines, materials, and methods. Several efforts can be made to increase the effectiveness of the use of machines, namely periodic replacement of machine maintenance, periodic operator training, and training on operator self-awareness, the importance of supervision, and operators must always supervise machine parts.

Bloch wave homogenisation of quasiperiodic media

Quasiperiodic media is a class of almost periodic media which is generated from periodic media through a ‘cut and project’ procedure. Quasiperiodic media displays some extraordinary optical, electronic and conductivity properties which call for the development of methods to analyse their microstructures and effective behaviour. In this paper, we develop the method of Bloch wave homogenisation for quasiperiodic media. Bloch waves are typically defined through a direct integral decomposition of periodic operators. A suitable direct integral decomposition is not available for almost periodic operators. To remedy this, we lift a quasiperiodic operator to a degenerate periodic operator in higher dimensions. Approximate Bloch waves are obtained for a regularised version of the degenerate operator. Homogenised coefficients for quasiperiodic media are obtained from the first Bloch eigenvalue of the regularised operator in the limit of regularisation parameter going to zero. A notion of quasiperiodic Bloch transform is defined and employed to obtain homogenisation limit for an equation with highly oscillating quasiperiodic coefficients.

Optimal Parameter Estimation in Activated Sludge Process Based Wastewater Treatment Practice

Activated sludge models (ASMs) are often used in the simulation of the wastewater treatment process to evaluate whether the effluent quality parameters of a wastewater treatment plant meet the standards. The premise of successful simulation is to choose appropriate dynamic parameters for the model. A niche based adaptive invasive weed optimization (NAIWO) algorithm is proposed in this paper to find the appropriate kinetic parameters of activated sludge model 1 (ASM1). The niche idea is used to improve the possibility of convergence to the global optimal solution. In addition, the adaptive mechanism and periodic operator are introduced to improve the convergence speed and accuracy of the algorithm. Finally, NAIWO is used to optimize the parameters of ASM1. Comparison with other intelligent algorithms such as invasive weed optimization (IWO), genetic algorithm (GA), and bat algorithm (BA) showed the higher convergence accuracy and faster convergence speed of NAIWO. The results showed that the ASM1 model results agreed with measured data with smaller errors.

Integrally Small Perturbations of Semigroups and Stability of Partial Differential Equations

Let be a generator of an exponentially stable operator semigroup in a Banach space, and let be a linear bounded variable operator. Assuming that is sufficiently small in a certain sense for the equation , we derive exponential stability conditions. Besides, we do not require that for each , the “frozen” autonomous equation is stable. In particular, we consider evolution equations with periodic operator coefficients. These results are applied to partial differential equations.

Zeroes of the spectral density of the periodic Schrödinger operator with Wigner–von Neumann potential

We consider the Schrödinger operator α on the half-line with a periodic background potential and the Wigner–von Neumann potential of Coulomb type: csin(2ωx + δ)/(x + 1). It is known that the continuous spectrum of the operator α has the same band-gap structure as the free periodic operator, whereas in each band of the absolutely continuous spectrum there exist two points (so-called critical or resonance) where the operator α has a subordinate solution, which can be either an eigenvalue or a “half-bound” state. The phenomenon of an embedded eigenvalue is unstable under the change of the boundary condition as well as under the local change of the potential, in other words, it is not generic. We prove that in the general case the spectral density of the operator α has power-like zeroes at critical points (i.e., the absolutely continuous spectrum has pseudogaps). This phenomenon is stable in the above-mentioned sense.