Mathematical analysis of the pulse coincidence process for applications on frequency sensors after the use of variable references

In most cases, sensors are the means that enable a computer to get information from a process of interest. This requires that the information generated by the sensor can be processed by the computer in a timely manner. However, if accurate data from the sensor is required, an appropriate transduction process is required. There are sensors that generate a frequency-domain output. Since these sensors typically have a short response time, it is required to get the best approximation to their frequency within the shortest time possible. There are different methods for obtaining the frequency value generated by the sensor. Although such methods can be applied, their functioning characteristics are not suitable for application in sensors. The principle of rational approximations is a method that has proven plenty of improvements in comparison to other frequency measurement methods. In this work, the functioning of the principle of rational approximations is explored when different time references are used.  After the computational analysis of the principle of rational approximations, it was found out how the reference frequency value affects the measurement process. It was found that if the magnitude of reference and unknown frequencies have an increment in their difference, then the relative error decreases

A New Approach to Measurement of Frequency Shifts Using the Principle of Rational Approximations

When a frequency domain sensor is under the effect of an input stimulus, there is a frequency shift at its output. One of the most important advantages of such sensors is their converting a physical input parameter into time variations. In consequence, changes of an input stimulus can be quantified very precisely, provided that a proper frequency counter/meter is used. Unfortunately, it is well known in the time-frequency metrology that if a higher accuracy in measurements is needed, a longer time for measuring is required. The principle of rational approximations is a method to measure a signal frequency. One of its main properties is that the time required for measuring decreases when the order of an unknown frequency increases. In particular, this work shows a new measurement technique, which is devoted to measuring the frequency shifts that occur in frequency domain sensors. The presented research result is a modification of the principle of rational approximations. In this work a mathematical analysis is presented, and the theory of this new measurement method is analysed in detail. As a result, a new formalism for frequency measurement is proposed, which improves resolution and reduces the measurement time

Textile Functionalization Using LTA and FAU Zeolitic Materials

COVID-19 has drawn worldwide attention to the need for personal protective equipment. Face masks can be transformed from passive filters into active protection. For this purpose, it is sufficient to apply materials with oligodynamic effect to the fabric of the masks, which makes it possible to destroy infectious agents that have fallen on the mask with aerosol droplets from the air stream. Zeolites themselves are not oligodynamic materials, but can serve as carriers for nanoparticles of metals and/or compounds of silver, zinc, copper, and other materials with biocidal properties. Such a method, when the particles are immobilized on the surface of the substrate, will increase the lifetime of the active oligodynamic material. In this work, we present the functionalization of textile materials with zeolites to obtain active personal protective equipment with an extended service life. This is done with the aim to extend the synthesis of zeolitic materials to polymeric fabrics beyond cotton. The samples were characterized using XRD, SEM, and UV-Vis spectroscopy. Data of physicochemical studies of the obtained hybrid materials (fabrics with crystals grown on fibers) will be presented, with a focus on the effect of fabrics in the growth process of zeolites

Study of Electric and Magnetic Properties of Iron-Modified MFI Zeolite Prepared by a Mechanochemical Method

Zeolites are materials of undeniable importance for science and technology. Since the properties of zeolites can be tuned after the inclusion of additional chemical species into the zeolitic framework, it is necessary to study the nature of zeolites after modification with transition metals to understand the new properties that were obtained, and with this information, novel applications can be proposed. This paper reports a solvent-free approach for the rapid synthesis of zeolites modified with iron and/or iron oxide particles. The samples were characterized, and their electrical and magnetic properties were investigated

Frequency Response Analysis of FAU, LTA and MFI Zeolites Using UV-Vis and Electrochemical Impedance Spectroscopy

Zeolites are porous materials that have cavities interconnected by channels. These crystalline materials are composed of Si-O tetrahedral structures, and according to the assembly of such tetrahedral structures, specific crystalline structures are obtained. Until now, it has been said that there are more than 245 different zeolitic frameworks, and since each one has a specific distribution of pores and cavities, each kind of zeolite has a specific area-to-volume ratio. As a result of the type of zeolite structure, the zeolite can exhibit specific properties, i.e., electrical or optical. Moreover, the physical properties of zeolites can be modified after the inclusion of another chemical species in their structure or in their voids, which can result in tuning a zeolite for specific applications. In this work, synthetic zeolites of types LTA, FAU and MFI are characterized by a number of methods. In particular, the data from UV-Vis spectroscopy are analyzed, and the effect of crystalline structure on properties such as optical bandgap, refractive index, absorption coefficient, incident photon frequency, and extinction coefficient is studied

Local Structures of Two-Dimensional Zeolites—Mordenite and ZSM-5—Probed by Multinuclear NMR

Mesostructured pillared zeolite materials in the form of lamellar phases with a crystal structure of mordenite (MOR) and ZSM-5 (MFI) were grown using CTAB as an agent that creates mesopores, in a one-pot synthesis; then into the CTAB layers separating the 2D zeolite plates were introduced by diffusion the TEOS molecules which were further hydrolyzed, and finally the material was annealed to remove the organic phase, leaving the 2D zeolite plates separated by pillars of silicon dioxide. To monitor the successive structural changes and the state of the atoms of the zeolite framework and organic compounds at all the steps of the synthesis of pillared MOR and MFI zeolites, the nuclear magnetic resonance method (NMR) with magic angle spinning (MAS) was applied. The 27Al and 29Si MAS NMR spectra confirm the regularity of the zeolite frameworks of the as synthetized materials. Analysis of the 1H and 13C MAS NMR spectra and an experiment with variable contact time evidence a strong interaction between the charged “heads” –[N(CH3)3]+ of CTAB and the zeolite framework at the place of [AlO4]− location. According to 27Al and 29Si MAS NMR the evacuation of organic cations leads to a partial but not critical collapse of the local zeolite structure

Mathematical Modeling for Robot 3D Laser Scanning in Complete Darkness Environments to Advance Pipeline Inspection

This paper introduces an autonomous robot designed for in-pipe structural health monitoring of oil/gas pipelines. This system employs a 3D Optical Laser Scanning Technical Vision System (TVS) to continuously scan the internal surface of the pipeline. This paper elaborates on the mathematical methodology of 3D laser surface scanning based on dynamic triangulation. This paper presents the mathematical framework governing the combined kinematics of the Mobile Robot (MR) and TVS. It discusses the custom design of the MR, adjusting it to use of robustized mathematics, and incorporating a laser scanner produced using a 3D printer. Both experimental and theoretical approaches are utilized to illustrate the formation of point clouds during surface scanning. This paper details the application of the simple and robust mathematical algorithm RANSAC for the preliminary processing of the measured point clouds. Furthermore, it contributes two distinct and simplified criteria for detecting defects in pipelines, specifically tailored for computer processing. In conclusion, this paper assesses the effectiveness of the proposed mathematical and physical method through experimental tests conducted under varying light conditions