Multi-Rate Data Fusion for State and Parameter Estimation in (Bio-)Chemical Process Engineering

For efficient operation, modern control approaches for biochemical process engineering require information on the states of the process such as temperature, humidity or chemical composition. Those measurement are gathered from a set of sensors which differ with respect to sampling rates and measurement quality. Furthermore, for biochemical processes in particular, analysis of physical samples is necessary, e.g., to infer cellular composition resulting in delayed information. As an alternative for the use of this delayed measurement for control, so-called soft-sensor approaches can be used to fuse delayed multirate measurements with the help of a mathematical process model and provide information on the current state of the process. In this manuscript we present a complete methodology based on cascaded unscented Kalman filters for state estimation from delayed and multi-rate measurements. The approach is demonstrated for two examples, an exothermic chemical reactor and a recently developed model for biopolymer production. The results indicate that the the current state of the systems can be accurately reconstructed and therefore represent a promising tool for further application in advanced model-based control not only of the considered processes but also of related processes.

Designing Standards-Setting for Levels of Mathematical Proficiency in Measurement and Geometry: Multidimensional Item Response Model

This study intends to design and verify the quality of a model that measures mathematical proficiency and aims to set the standards in measuring levels of proficiency in the subjects of measurement and geometry. Construct modeling was employed to design a mathematical proficiency measurement model which consists of the mathematical process and the dimensions of a conceptual structure. A total of 517 Secondary Year 1 students were selected from the big data to participate as test-takers. Design-based research encompassing four phases was used to verify the quality of the mathematical proficiency measurement model. A Multidimensional Random Coefficient Multinomial Logit model was used to examine the standards-setting of the mathematical proficiency measurement model. The results indicated that the two dimensions of mathematical proficiency can be further divided into five levels, from non-response/irrelevance to strategic/extended thinking and extended abstract structure for mathematical process and conceptual structural dimensions, respectively. The assessment tool covers 18 items with 15 multiple-choice items and three subjective items in measurement and geometry. Moreover, the results also demonstrated that the validity evidence associated with the internal structure of the multidimensional model is fit. Besides, reliability evidence, as well as item fit, is compliance with the quality of the mathematical proficiency measurement model as illustrated in analysis of the standard error of measurement and infit and outfit of the items. Finally, the researchers managed to set standards for the mathematical proficiency measurement model based on the assessment criterion results from the Wright Map. In conclusion, the standards-setting of the mathematical proficiency measurement model provides substantial information, particularly for measuring those students who are above the lowest level of mathematical proficiency because the error for estimating proficiency was low.

High Pressure Liquid Chromatographic Method for the Determination of Mobocertinib in Pharmaceutical Dosage Form and Study of Its Degradation

Aims: New validated method for the estimation of Mobocertinib using HPLC and study of its degradation. Place and Duration of Study: Department of Chemistry, RVR & JC College of Engineering, Chowdavaram, Guntur, Andhra Pradesh, between February 2021 and August 2021. Methodology: Using an X-bridge phenyl column (150 mm x 4.6 mm, 3.5 µ), acetonitrile, and 0.1 percent ortho phosphoric acid (OPA) (60:40 v/v) as a mobile phase, the proposed method successfully achieved effective chromatographic separation with a flow rate of 1 mL/min and a wave length of 224 nm. Mobocertinib had a retention time of 2.271 minutes. The isocratic chromatography was performed at room temperature and took approximately five minutes to complete. Results: Analysis was achieved within 5 min over an honest linearity within the concentration range from 6-90 µg/ml of Mobocertinib. Using a mathematical process, the suitability parameters of the system were investigated, and the results were found to be in acceptable limits. In a linear analysis, stages with regression coefficients of 0.999 were used. LOD and LOQ values were 0.075μg/ml and 0.248 g/ml for Mobocertinib. The drug was recovered at a rate of 98-102 percent, which means that the recovery is within reasonable limits. Conclusion: The validation results were satisfactory, and the approach was found to be suitable for bulk and formulation analysis. The recommended procedure was found to be warranted according to ICH guidelines.

Aggregation of Weak Fuzzy Norms

Aggregation is a mathematical process consisting in the fusion of a set of values into a unique one and representing them in some sense. Aggregation functions have demonstrated to be very important in many problems related to the fusion of information. This has resulted in the extended use of these functions not only to combine a family of numbers but also a family of certain mathematical structures such as metrics or norms, in the classical context, or indistinguishability operators or fuzzy metrics in the fuzzy context. In this paper, we study and characterize the functions through which we can obtain a single weak fuzzy (quasi-)norm from an arbitrary family of weak fuzzy (quasi-)norms in two different senses: when each weak fuzzy (quasi-)norm is defined on a possibly different vector space or when all of them are defined on the same vector space. We will show that, contrary to the crisp case, weak fuzzy (quasi-)norm aggregation functions are equivalent to fuzzy (quasi-)metric aggregation functions.

NEEDS ANALYSIS OF THE DEVELOPMENT STUDENT WORKSHEET BASED BLENDED LEARNING TO ENCOURAGE MATHEMATICAL LITERACY

Mathematical literacy is the ability of students to carry out activities formulate, apply, and interpret & evaluate mathematics in various contexts. This study aims to analyze the needs of student worksheet development which can stimulate students' mathematical literacy. This type of research is a qualitative descriptive study involving 15 students of class XI MIPA and 2 mathematics teachers of SMA Negeri 1 Gresik. This needs analysis includes material analysis, curriculum analysis, and student analysis. The results showed that one of the difficult mathematics materials for class XI MIPA was linear program, mathematics learning was carried out according to the 2013 Curriculum with the application of Blended Learning in the new normal era, and students still had difficulty solving problems on indicators of interpreting & evaluating mathematical process abilities. Therefore, Student Worksheet based Blended Learning will be developed which is more focused on activities that prioritize the interpretation and analysis of problem solving results according to the limitations and context of the problem in the Linear Program material.

Novel Lanthanum Doped Magnetic Teff Straw Biochar Nanocomposite and Optimization Its Efficacy of Defluoridation of Groundwater Using RSM: A Case Study of Hawassa City, Ethiopia

The problem extent of the large concentration of fluoride ions in drinking water is still a central health issue. In the present study, lanthanum doped magnetic Teff straw biochar (LDMTSB) was developed as a novel adsorbent for removing fluoride ions in the groundwater in Rift-Valley regions, especially Hawassa city, Ethiopia. The synthesized LDMTBC was characterized via FTIR, XRD, SEM, and BET. And, this analysis proposed that multiadsorption techniques such as ligand exchange, precipitations, and electrostatic interaction could be evinced throughout the fluoride ions adsorption process by LDMTSB. The constraints that influence the adsorption efficacy, namely, a dosage of LDMTSB, contact time, pH of the solution, and rotational speed, were analyzed and optimized using the response surface methodology approach. Under the optimum situations, LDMTSB dosage: 3.97 g, contact time: 56.36 min, rotational speed: 591.19 rpm, and pH: 3.968 demonstrate high efficacy of LDMTSB with 98.89% fluoride removal capacity. Further, the quadratic model (R2 = 0.9841) was designated for governing the mathematical process. The LDMTSB was successful in the removal of fluoride ions in the groundwater. This study provides a valuable economical solution for the application of Teff straw.

Stability Demonstrating Validated High Pressure Liquid Chromatographic Method for the Determination of Trilaciclib in Bulk and Pharmaceutical Formulation

Aims: New validated method for the estimation of Trilaciclib using HPLC and study of its degradation Place and Duration of Study: Department of Chemistry, RVR & JC College of Engineering, Chowdavaram, Guntur, Andhra Pradesh, between February 2021 and August 2021. Methodology: Using an inertsil ODS column (150 mm x 4.6 mm, 3.5 µ), acetonitrile, and 0.1 percent ortho phosphoric acid (OPA) (50:50 v/v) as a mobile phase, the proposed method successfully achieved effective chromatographic separation with a flow rate of 1 mL/min and a wave length of 220 nm. Trilaciclib had a retention time of 4.358 minutes. The isocratic chromatography was performed at room temperature and took approximately six minutes to complete. Results: Analysis was achieved within 6 min over an honest linearity within the concentration range from 3-45 µg/ml of Trilaciclib. Using a mathematical process, the suitability parameters of the system were investigated, and the results were found to be in acceptable limits. In a linear analysis, stages with regression coefficients of 0.999 were used. LOD and LOQ values were 0.038 μg/ml and 0.124 g/ml for trilaciclib. The drug was recovered at a rate of 98-102 percent, which means that the recovery is within reasonable limits. Conclusion: The validation results were satisfactory, and the approach was found to be suitable for bulk and formulation analysis. The recommended procedure was found to be warranted according to ICH guidelines.

Sixth-grade students’ experiences of a digital game-based learning environment: A didactic analysis

Students' conceptual understanding and mathematical process skills can be improved through digital games in mathematics education. The starting point of this study is the idea of having students encounter this kind of environment. The study didactically describes the process of 6th-grade students’ experiences of a digital game-based learning environment. A combination of the Theory of Didactical Situations (TDS) and Digital Game-Based Learning (DGBL) was used in the design of the digital game. The research focused on knowledge-based interactions (teacher-student-game) during the implementation of the game called Race with Numbers, designed in line with this synthesis. The case study, one of the qualitative research methods, was used in the study. Research participants consist of 16 middle secondary school students studying in the 6th grade in a public school. The research data were collected with a video camera and two voice recorders. The research application lasted 75 minutes. The data analysis related to the application was carried out by describing the interaction between the students and the game at stages of TDS. The study findings indicated that TDS has significant potential in designing DGBL environments. However, strong evidence is presented that such environments enable students to realize their own learning and encourage them to use mathematical process skills (such as problem-solving, reasoning, proving, and transfer). Finally, the study highlights the importance of the digital game-based learning approach in mathematics teaching for students.