Logical derivation search with assumption traceability

In this paper authors research the problem of traceability of assumptions in logical derivation. The essence of this task is to trace which assumptions from the available knowledge base of assumptions are necessary to derive a certain conclusion. The paper presents a new derivation procedure for propositional logic, which ensures traceability feature. For the derivable conclusion formula derivation procedure also returns the smallest set of assumptions those are enough to get derivation of the conclusion formula. Verification of the procedure were performed using authors implementation.

Compiling Textbook of Elastic-plastic Mechanics for Major of Oil and Gas Storage and Transportation Engineering

"Elastic-plastic mechanics" is a required course for engineering postgraduates in petroleum colleges and universities, such as students who major in oil and gas storage and transportation engineering. It is the basis for personnel engaged in structural safety assessment. In the past teaching process, the teaching effects of this course were unsatisfactory. There are many reasons for this phenomenon, such as the strong theoretical nature of this course, the need for a large number of formula derivation, the high requirements for students' mechanical foundation and mathematical foundation, the lack of appropriate teaching materials and the slackness of students' minds. Based on years of teaching experience, the teaching team has reformed the existing teaching materials of “Elastic-plastic mechanics” to meet the needs of petroleum colleges and universities. In this reform, we have referred to a large number of published textbooks of “Elasticplastic mechanics” and the experience of textbook construction at home and abroad. The newly compiled textbook of “Elastic-plastic mechanics” plays a certain role in improving the teaching quality of “Elastic-plastic mechanics” in petroleum colleges and universities.

The Use Of STEM Approaches To Widen Formula Derivation Steps In Material Science And Engineering Programmes At Higher Education Institutions

Many complex formula derivation steps found within material science and engineering programmes are essential skill-developing activities that enhance students’ learning. However, most students lack the required mathematical knowledge to fully comprehend some of those derivation steps. This work developed a framework of clarifying some of the formula derivations steps by adding further mathematical steps that support the students’ constructive and cognitive learning. Some derivation steps were added to the derivations of the theoretical tensile strength model as well as the Maxwell’s and the Voigt-Kelvin models. The idea was not to disrupt students’ constructive or cognitive learning processes but to facilitate their learning since their ultimate aim is not to derive but to apply the steps of the modified derivations in solving other material science and engineering problems. The students benefited from the activities in two folds; firstly, they understood the reasons behind each derivation step and secondly, it improved their self-study activities by reducing their study periods. These activities provide a platform to widen STEM activities at higher education institutions. The ongoing work will look at other important formula derivation steps within material science and engineering that can enhance students’ learning.

A feature learning-based method for impact load reconstruction and localization of the plate-rib assembled structure

Impact load is the load that machines frequently experienced in engineering applications. Its time-history reconstruction and localization are crucial for structural health monitoring and reliability analysis. However, when identifying random impact loads, conventional inversion methods usually do not perform well because of complex formula derivation, infeasibility of nonlinear structure, and ill-posed problem. Deep learning methods have great ability of feature learning and nonlinear representation as well as comprehensive regularization mechanism. Therefore, a new feature learning-based method is proposed to conduct impact load reconstruction and localization. The proposed method mainly includes two parts. The first part is designed to reconstruct impact load, named convolutional-recurrent encoder–decoder neural network (ED-CRNN). The other part is constructed to localize impact load, called deep convolutional-recurrent neural network (DCRNN). The ED-CRNN utilizes the one-dimensional (1-D) convolutional encoder–decoder to obtain low-dimension feature representations of input signals. Two long short-term memory (LSTM) layers and a bidirectional LSTM (BiLSTM) layer are uniformly distributed in this network to learn the relationship between input features and the output load in time steps. The DCRNN is constructed mainly by two 1-D convolutional neural network (CNN) layers and two BiLSTM layers to learn high-hidden-level spatial as well as temporal features. The fully connected layers are placed at the end to localize an impact load. The effectiveness of the proposed method was demonstrated by two numerical studies and two experiments. The results reveal that the proposed method has the ability to accurately and quickly reconstruct and localize the impact load of complex assembled structure. Furthermore, the performance of the DCRNN is related to the number of sensors and the architecture of the network. Meanwhile, the strategy of alternating layout is proposed to reduce the number of training locations.

Many-Electron QED with Redefined Vacuum Approach

The redefined vacuum approach, which is frequently employed in the many-body perturbation theory, proved to be a powerful tool for formula derivation. Here, we elaborate this approach within the bound-state QED perturbation theory. In addition to general formulation, we consider the particular example of a single particle (electron or vacancy) excitation with respect to the redefined vacuum. Starting with simple one-electron QED diagrams, we deduce first- and second-order many-electron contributions: screened self-energy, screened vacuum polarization, one-photon exchange, and two-photon exchange. The redefined vacuum approach provides a straightforward and streamlined derivation and facilitates its application to any electronic configuration. Moreover, based on the gauge invariance of the one-electron diagrams, we can identify various gauge-invariant subsets within derived many-electron QED contributions.

Many-Electron QED with Redefined Vacuum Approach

The redefined vacuum approach, which is frequently employed in the many-body perturbation theory, proved to be a powerful tool for formula derivation. Here, we elaborate this approach within the bound-state QED perturbation theory. In addition to general formulation, we consider the particular example of a single particle (electron or vacancy) excitation with respect to the redefined vacuum. Starting with simple one-electron QED diagrams, we deduce first- and second-order many-electron contributions: screened self-energy, screened vacuum polarization, one-photon exchange, and two-photon exchange. The redefined vacuum approach provides a straightforward and streamlined derivation and facilitates its application to any electronic configuration. Moreover, based on the gauge invariance of the one-electron diagrams, we can identify various gauge-invariant subsets within derived many-electron QED contributions.

Parameters to characterize the internal recirculation of an oxidation ditch

Mixed liquor circulates ceaselessly in the closed-loop corridor in an oxidation ditch (OD), which is significantly different from other wastewater treatment processes. The internal recirculation ratio (IRR), i.e., the ratio between circulation flow rate (QCC) and influent flow rate (QIn), and the circulatory period (T), i.e. the time consumed for the mixed liquor to complete one lap in the circular corridor, was used to quantify the internal recirculation characteristics of the OD system. In order to elucidate the characteristics and applicability of IRR and T, this study obtained the numerical relationship between IRR and T by formula derivation. It also discusses the factors influencing IRR and analyses the applications of IRR and T. The results showed that IRR = QCC/QIn = HRT/T = HRT ž IRF (HRT = hydraulic retention time of the mixed liquor in the circular corridor; IRF = internal recirculation frequency). Moreover, three kinds of parameters had an effect on IRR: QIn; reactor dimensions, i.e., length (Lmid), width (B), and height (H) of the circular corridor; and horizontal velocity of the mixed liquor in the circular corridor (v). QIn changed IRR by altering HRT. However, B, H, Lmid, and v changed IRR by altering IRF and T. Furthermore, the same IRR corresponded to many different HRT and IRF. Therefore, when QIn and QCC varied in the OD system, using HRT and IRF to evaluate the variation of QIn and QCC, respectively, was better than using IRR to evaluate their synthetical variation. IRF and T were useful for directly and precisely characterizing the circulation speed and circulation flow rate in the circular corridor, while IRR was more useful for evaluating the dilution effect of reflux on influent.

Quantum Fourier Transforms

Quantum Fourier transform (QFT) plays a key role in many quantum algorithms, but the existing circuits of QFT are incomplete and lacking the proof of correctness. Furthermore, it is difficult to apply QFT to the concrete field of information processing. Thus, this chapter firstly investigates quantum vision representation (QVR) and develops a model of QVR (MQVR). Then, four complete circuits of QFT and inverse QFT (IQFT) are designed. Meanwhile, this chapter proves the correctness of the four complete circuits using formula derivation. Next, 2D QFT and 3D QFT based on QVR are proposed. Experimental results with simulation show the proposed QFTs are valid and useful in processing quantum images and videos. In conclusion, this chapter develops a complete framework of QFT based on QVR and provides a feasible scheme for QFT to be applied in quantum vision information processing.