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The purpose of this paper is to survey briefly how harmonic analyis started and developed throughout the centuries to reach its modern status and its surprisingly wide range of applications.

The author traces applications of harmonic analysis back to Mesopotamia, ancient Egypt and the Indus Valley, showing how the Greeks have applied trigonometry and influenced its birth, then the important developments in India in the sixth century laying the first brick to modern trigonometry with the definition of the sinus, then medieval India founding modern mathematical analysis. Trigonometry was developed further by the Arabs until the fourteenth century, then by the Europeans. The eighteenth century in France was particularly important when Bernoulli solved, with an infinite trigonometric series, the vibrating string problem, then Fourier, who studied these series extensively. The author goes on to harmonic analysis on locally compact groups, and ends up with a quick personal view on harmonic analysis nowadays. The last section of the paper presents some of the modern applications. Harmonic analysis is, of course, still used for navigation but also has many other very surprising applications such as signal processing, quantum mechanics, neuroscience, tomography, etc.

The power of harmonic analysis lies in giving the solutions to various problems as infinite series of basic functions, so to be able to produce algorithms for FFT boxes, it must be understood how these series came about and the convergence of these series.

The review should be useful to people interested in studying and/or applying harmonic analysis.

Before 2011, student performance rates in college algebra and trigonometry at North Carolina A&T State University (NCA&TSU) were consistently below 50%. To remedy this situation, the Mathematics Department implemented the math emporium model (MEM) instructional method. The underlying principle behind MEM is that students learn math by doing math (Twigg, 2011). The MEM requires students to work on math problems and spend more time on material that they do not understand while allowing them to spend less time on material that they do understand. Also, students receive immediate feedback on problems from teaching assistants as they work through their online assignments. After implementing the MEM, student pass rates improved for both the MEM and traditional sections. Data to date also show that female students outperform male students in both instructional models. Further study is needed to determine the factors that have caused improvement in pass rates in addition to the implementation of the MEM. Some important lessons learned by the NCA&TSU math faculty from implementing the MEM into the college algebra and trigonometry courses are that successful implementation requires a long-term commitment, internal and external collaborations, and the collective ability to determine what works for the local setting.

This paper aims to present an iterative path-following method with joint limits to solve the problem of large computation cost, movement exceeding joint limits and poor path-following accuracy for the path planning of hyper-redundant snake-like manipulator.

When a desired path is given, new configuration of the snake-like manipulator is obtained through a geometrical approach, then the joints are repositioned through iterations until all the rotation angles satisfy the imposed joint limits. Finally, a new arrangement is obtained through the analytic solution of the inverse kinematics of hyper-redundant manipulator. Finally, simulations and experiments are carried out to analyze the performance of the proposed path-following method.

Simulation results show that the average computation time is 0.1 ms per step for a hyper-redundant manipulator with 12 degrees of freedom, and the deviation in tip position can be kept below 0.02 mm. Experiments show that all the rotation angles are within joint limits.

Currently , the manipulator is working in open-loop, the elasticity of the driving cable will cause positioning error. In future, close-loop control based on real-time attitude detection will be used in in combination with the path-following method to achieve high-precision trajectory tracking.

Through a series of iterative processes, the proposed method can make the manipulator approach the desired path as much as possible within the joint constraints with high precision and less computation time.

To propose trigonometric interpolation in combination with the sliding‐surface technique for modeling rotation in electrical machine models discretised by the finite integration technique (FIT).

Locked‐step, linear and trigonometric interpolation techniques are developed for coupling the stator and rotor model parts of an electrical machine model.

Linear and trigonometric interpolation should be preferred over the locked‐step approach. Three‐machine models with sliding‐surface coupling discretised by the FIT result in efficient and reliable models.

The introduction of sliding‐surface techniques in the FIT, the trigonometric interpolation used in combination, the application of the FIT for simulating electrical machines.

This chapter highlights the creation of a STEM Center of Excellence for Active Learning (SCEAL) at North Carolina Agricultural and Technical State University. The overarching goal of the STEM Center is to transform pedagogy and institutional teaching and learning in order to significantly increase the production of high-achieving students who will pursue careers and increase diversity in the STEM workforce. Some of the STEM Center’s efforts to reach its goals included supporting active learning classroom and course redesign efforts along with providing professional development workshops and opportunities to garner funding to cultivate student success projects through the development of an Innovation Ventures Fund. Outcomes from this Center have led to several publications and external grant funding awards to continue implementation, assessment, and refinement of active learning innovations and interventions for STEM student success for years to come.

Suddenly, in less than two years, a new high‐technology consumer product has swept world markets—the electronic pocket calculator. Such machines range from the relatively simple type that will add, subtract, multiply and divide up to six numerical digits, to the highly sophisticated ‘electronic slide‐rule’, with its instant calculation of square roots, logarithms, trig functions and other scientific esoterica.

The purpose of this work is to explore the new possibilities enabled by the recent introduction of RDF-star, an extension that allows for statements about statements within the Resource Description Framework (RDF). Alongside Named Graphs, this approach offers opportunities to leverage a meta-level for data modeling and data applications.

In this extended paper, the authors build onto three modeling use cases published in a previous paper: (1) provide provenance information, (2) maintain backwards compatibility for existing models, and (3) reduce the complexity of a data model. The authors present two scenarios where they implement the use of the meta-level to extend a data model with meta-information.

The authors present three abstract patterns for actively using the meta-level in data modeling. The authors showcase the implementation of the meta-level through two scenarios from our research project: (1) the authors introduce a workflow for triple annotation that uses the meta-level to enable users to comment on individual statements, such as for reporting errors or adding supplementary information. (2) The authors demonstrate how adding meta-information to a data model can accommodate highly specialized data while maintaining the simplicity of the underlying model.

Through the formulation of data modeling patterns with RDF-star and the demonstration of their application in two scenarios, the authors advocate for data modelers to embrace the meta-level.

With RDF-star being a very new extension to RDF, to the best of the authors’ knowledge, they are among the first to relate it to other meta-level approaches and demonstrate its application in real-world scenarios.

Outlines some research on the effects of risk on portfolios for retirement planning and puts forward a method to help individuals “increase their chances of not outliving their retirement portfolios”. Uses numerical examples to show how calculations of the savings needed to achieve specific retirement incomes may prove inaccurate, and how regular portfolio assessment can be used to make any necessary adjustments during the accumulation and/or the retirement stage.

The purpose of this paper is the investigation of a new coordinated switching strategy to improve the transient performance of a fuel cell (FC)- supercapacitor (SC) electric vehicle. The proposed switching strategy protects FCs from large currents drawn during abrupt power variations. Furthermore, it compensates the poor FC transient response and suppresses the transient ripples occurring during power source switching instants.

Coordinated power source switching is achieved using three different transition functions. Vehicle model is fractioned into computational and console subsystems for its simulation using real time (RT) LAB simulator. Blocs containing coordination switching strategy, power sources models and their power electronics interface are placed in the computational subsystem that will be executed, in RT, on one of real time laboratory simulator central processing unit cores.

Coordination switching strategy resulted in reducing transient power ripples by 90% and direct current (DC) bus voltage fluctuations by 50%. Switching through transition functions compensated the difference between FC and SC transient responses responsible for transient power ripples. Among the three proposed transition functions, linear transition function resulted in the best transient performances.

The proposed coordinated switching strategy allows the control of the switching period duration. Furthermore, it enables the choice of adequate transition functions that fit the dynamics of power sources undergoing transition. Also, the proposed switching technique is simple and does not require the knowledge of system parameters or the complex control models.