Academic literature on the topic 'Padovan numbers'

Padovan numbers were defined by Stewart (1996) in honor of the modern architect Richard Padovan (1935) and were first discovered in 1924 by Gerard Cordonnier. Padovan numbers are a special status of Tribonacci numbers with initial conditions and general terms. The ratio between Padovan numbers is one of the important algebraic numbers because it produces plastic numbers. Up to now, various studies have been conducted on Padovan numbers and Padovan polynomial sequences. In this study, Padovan vectors are defined for the first time by using the Padovan Binet-like formula and reduction relation. Then, geometric properties of Padovan vectors such as inner product, norm, and vector products are analyzed. In the last part of the study, Padovan vectors were calculated with Binet formulas in the Geogebra program. In addition, the first ten Padovan numbers and Padovan vectors were calculated using the Binet formulas and shown as points and vectors in three-dimensional space. According to the Padovan vectors found, the Padovan curve was drawn in space for the first time by using the curve fitting feature of the Geogebra program. Thus, with our study, a geometric approach to Padovan number sequences was brought for the first time.

In this paper, we define the complex-type Padovan-p sequence and then give the relationships between the Padovan-p numbers and the complex-type Padovan-p numbers. Also, we provide a new Binet formula and a new combinatorial representation of the complex-type Padovan-p numbers by the aid of the nth power of the generating matrix of the complex-type Padovan-p sequence. In addition, we derive various properties of the complex-type Padovan-p numbers such as the permanental, determinantal and exponential representations and the finite sums by matrix methods.

In this paper, we find new relations involving the Pell-Padovan sequence which arise as determinants of certain families of Toeplitz-Hessenberg matrices. These determinant formulas may be rewritten as identities involving sums of products of Pell-Padovan numbers and multinomial coefficients. In particular, we establish four connection formulas between the Pell-Padovan and the Fibonacci sequences via Toeplitz-Hessenberg determinants.

In this paper, we define the Fibonacci–Jacobsthal, Padovan–Fibonacci, Pell–Fibonacci, Pell–Jacobsthal, Padovan–Pell and Padovan–Jacobsthal sequences which are directly related with the Fibonacci, Jacobsthal, Pell and Padovan numbers and give their structural properties by matrix methods. Then we obtain new relationships between Fibonacci, Jacobsthal, Pell and Padovan numbers.

Generalized Padovan Sequences are more general class of sequences which are viewed as general form of the classical Padovan sequences named after English mathematician Richard Padovan. Figurate numbers are special class of numbers which occur in various problems in number theory. In this paper, we discuss the limiting ratio of the recurrence relation formed by generalizing Padovan sequence and considering Figurate numbers as coefficients in two possible cases. We find very interesting numbers turning out to be limiting ratios under our assumptions.

In this paper, the Gaussian Padovan and Gaussian Perrin numbers are defined. Then Binet formula and generating functions of these numbers are given. Also, some summation identities for Gaussian Padovan and Gaussian Perrin numbers are obtained by using the recurrence relation satisfied by them. Then two relations are given between Gaussian Padovan and Gaussian Perrin numbers.

The hypercube is one of the best models for the network topology of a distributed system. Recently, Padovan cubes and Lucas–Padovan cubes have been introduced as new interconnection topologies. Despite their asymmetric and relatively sparse interconnections, the Padovan and Lucas–Padovan cubes are shown to possess attractive recurrent structures. In this paper, we determine the cube polynomial of Padovan cubes and Lucas–Padovan cubes, as well as the generating functions for the sequences of these cubes. Several explicit formulas for the coefficients of these polynomials are obtained, in particular, they can be expressed with convolved Padovan numbers and Lucas–Padovan numbers. In particular, the coefficients of the cube polynomials represent the number of hypercubes, a symmetry inherent in Padovan and Lucas–Padovan cubes. Therefore, cube polynomials are very important for characterizing these cubes.

Gaussian Jacobsthal-Padovan numbers have been the central focus of this paper and firstly this number sequence has defined. Later, we have given the proof of the generating function of the Gaussian Jacobsthal-Padovan sequence. After that by using generating function, we have given the proof of the Binet formula for this number sequence. Additionally, we have investigated some properties such as Simson identity, summation formulas of this sequence. Finally, we have obtained some matrices whose elements are Gaussian Jacobsthal-Padovan numbers.

Padovan numbers and Perrin numbers belong to the family of numbers of the Fibonacci type and they are well described in the literature. In this paper, by studying independent (1,2)-dominating sets in paths and cycles, we obtain new binomial formulas for Padovan and Perrin numbers. As a consequence of graph interpretation, we propose a new dependence between Padovan and Perrin numbers. By studying special independent (1,2)-dominating sets in a composition of two graphs, we define Padovan polynomials of graphs. By the fact that every independent (1,2)-dominating set includes the set of leaves as a subset, in some cases a symmetric structure of the independent (1,2)-dominating set can be used.

The first main idea of this paper is to develop thematrix sequencesthat represent Padovan and Perrin numbers. Then, by taking into account matrix properties of these new matrix sequences, some behaviours of Padovan and Perrin numbers will be investigated. Moreover, some important relationships between Padovan and Perrin matrix sequences will be presented.

Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-28T11:10:07Z No. of bitstreams: 1 arquivototal.pdf: 800250 bytes, checksum: 42e76ab05ea580b4fd24a3312b9b4212 (MD5)<br>Made available in DSpace on 2016-03-28T11:10:07Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 800250 bytes, checksum: 42e76ab05ea580b4fd24a3312b9b4212 (MD5) Previous issue date: 2015-04-30<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>Morphic numbers are numbers related to the form and, somehow, they establish a conception of beauty, aesthetics and harmony. These numbers have important of applications in various branches of knowledge, such as geometry, arithmetic, architecture, and engineering. There are only two morphic numbers, the golden number and the plastic number. The rst one has been studied since ancient Greece, and the second one has only become a subject of interest in the twentieth century, what makes the plastic number a relatively new branch of research. In this work, we will analyze a data collection concerning arithmetic, algebraic or geometric properties of these numbers, by establishing a straight relation between the morphic numbers and the Fibonacci and Padovan sequences.<br>Os números mór cos são números relacionados à forma e que, de alguma maneira, estabelecem uma concepção de beleza, estética e harmonia. Esses números possuem uma série de aplicações em vários ramos do conhecimento, como geometria, aritmética, arquitetura e engenharia. Existem apenas dois números mór cos, o número de ouro e o número plástico, o primeiro deles é estudado desde a antiga Grécia e o segundo passou a ser estudado no século XX, o que torna o assunto relativamente novo. Traremos neste trabalho uma coleção de informações acerca desses números, sejam propriedades aritméticas, algébricas ou geométricas, estabelecendo um paralelo muito forte entre os mesmos e também como eles se relacionam com as sequências de Fibonacci e Padovan.

In 1480 publisher and bookseller Antonio Moretto delivered a total of over 900 incunabula to be sold in his shop in Padua. The details of this business transaction survive in a small paper gathering of 8 leaves, known as Quaderneto, in which the titles of the books, the number of copies available, and the sale prices fixed by Moretto himself are listed. It is an important source for our knowledge of Italian Renaissance book-trade and – thanks to a comparison with the Zornale of Francesco de Madiis – provides valuable information about book prices and sales towards the end of the 15th century.

This chapter focuses on the recently rediscovered Padua, Biblioteca universitaria di Padova, MS 1647 and gives the first in-depth analysis of its contents. This manuscript, like MS Vat. lat. 4953, contains a number of refuted errors taken from a Latin translation of Marguerite Porete's The Mirror of Simple Souls but takes a decidedly canon-legal approach to its refutations and employs vitriolic rhetoric that paints the Mirror as diabolical. It is the only known polemic written against the Mirror and it represents the strongest attack against it outside of its condemnations in Valenciennes and Paris and, in its rhetoric and detail at least, surpasses even those iconic events in the Mirror's history. The uniqueness of the text becomes even more important when considered in the context of its origins. While it exists only in a fifteenth-century copy, it was very likely first composed in the early fourteenth century, quite close in time to—perhaps even contemporarily with or before—the Mirror's two condemnations and Marguerite Porete's execution.

Intermodal quantum key distribution (QKD) enables seamless integration of fiber networks and free-space channels, which are essential to create a global quantum network. Here we report on a recent field trial of an intermodal QKD system within a 3-node heterogeneous quantum network, that we presented in details in the work by F. Picciariello et al., arXiv:2310.17441. The network consists of two polarization-based transmitters and a single receiver, where the active channel is alternately switched between a 620-meter free-space link and a 17-kilometer deployed fiber link in the metropolitan area of Padova. The trial evaluates the performance of the free-space channel in relation to the atmospheric turbulence strength. Conducted over several hours during daylight, the trial confirms the interoperability between fiber and free-space channels, achieving a secret key rate on the order of kbps for both types of channels. Notably, the QKD hardware and software function consistently across both channels without requiring different strategies, despite the distinct characteristics of the links. This switching system offers a cost-effective solution for a trusted QKD network by minimizing the number of devices needed across different networks. The results underscore the feasibility of intermodal QKD systems for future quantum networks.

Alba CubeSat UniPD is a student team of University of Padova with the aim to participate to the ESA Fly Your Satellite! (FYS!) programme and to launch for the first time at University of Padova a CubeSat made by students.&#x0D; The proposed mission has three independent objectives: (1) to collect in-situ measurements of the sub-mm space debris environment in LEO, (2) to study the micro-vibration environment on the satellite throughout different mission phases, (3) to do precise orbit determination through laser ranging and evaluate procedures for fast satellite Pointing, Acquisition and Tracking (PAT) from ground. The proposed technological experiments aim to obtain data that will enrich the current knowledge of the space environment and will provide precious information useful for the further development of some research projects currently performed at University of Padova.&#x0D; In order to reach the objectives, in these years the activities of the teams aimed to develop a 2U CubeSat equipped with three payloads. The first payload is an impact sensor that will be placed on one of the outer faces of the satellite and will be able to count the number of debris impacting the spacecraft thus being able to measure the energy/momentum transferred to the satellite. The second one is a Commercial Off The Shelf (COTS) sensor that measures the micro-vibrations experienced by payloads in a CubeSat in different mission phases. The third one consists in a number of COTS Corner Cube Retroreflectors that will be placed onboard the satellite. Thanks to this, Satellite Laser Ranging (SLR) will be done to collect data on the satellite range and range rate using a facility currently under development at University.&#x0D; This paper presents the mission objectives and motivations. In addition, the mission phases and the preliminary design of the CubeSat reached during the activities of the project are shown. Particular attention is given to the payloads which are the most challenging aspect of this project.

In recent years, the number of applications of Multi-Temporal Interferometric Synthetic Aperture Radar (MT-InSAR) techniques for structural health monitoring (SHM) purposes has constantly raised. One of the main advantages that MT-InSAR can provide is the possibility to analyze wide areas, such as entire cities or archaeological sites. Thus, several interferometric algorithms have proven to be particularly valid when applied in urban contexts, considering the high reflectivity provided by the structures. In addition, the growing availability of high-resolution SAR satellite constellations, such as the Italian COSMO-SkyMed and the German TerraSAR-X, allows obtaining significantly accurate measures and detecting high density of Measurement Points (MP). Consequently, sufficiently detailed information on single structures can be recorded, permitting to perform both urban scale and local scale analyses. On the other hand, several drawbacks are still present, mostly related to the hardly post-processing processes needed. Indeed, beside the technical difficulties that can be encountered during the analysis (e.g. geocoding errors and noisiness in the time series), an expert interpretation of the results is still required to avoid misinterpretation of data. Anyway, considering both advantages and disadvantages of the technique, MT-InSAR undoubtedly represents a very cost-effective tool in the structural monitoring field. In this paper, MT-InSAR applications for structural monitoring on the Italian Cultural Heritage context are presented. The analyses have been conducted at both urban and local scale, processing images acquired by COSMO-SkyMed constellation in Stripmap mode (~3 meters resolution). First, spatial interpolation algorithms have been implemented to estimate the overall deformations at urban scale. Subsequently, the attention has focused on some of the main cultural assets of the case-study cities, investigating the MPs detected on the structures themselves. In this work, three cities are presented as case-studies: Verona, Padova (North Italy), and L’Aquila (central Italy). For each city, a specific Cultural Heritage structure has been selected for the local scale analysis, namely the Roman Arena in Verona, the Scrovegni Chapel in Padova, and the Civic Tower in L’Aquila. All these monuments have been monitored by traditional SHM techniques for years, with the possibility to correlate and validate onsite and satellite data.

Sound recordings have proven to be irreplaceable primary sources for disciplines like linguistics, musicology, ethnomusicology and sociology. Their fragile physical nature has activated a number of counter-actions aimed at prolonging the life expectancy of their content. Methodological issues have been raised in the past three decades, considering the relationship between the physical object and its (digitized) intangible content, which is not only complex but develops over time. This article re ects on the role of the emerging discipline known as ‘digital philology’ in the long- term preservation of audio documents, pointing out how some concepts (such as authenticity, reliability and accuracy) may require a ‘customized’ (as opposed to a ‘ready-made’) approach in the preservation work ow – mainly depending on the type of the archive: unique copies, eld recordings, electronic music, oral history, to name some representative cases. The set-up of the laboratory for sound preservation at the Centro di Sonologia Computazionale (CSC) of the University of Padova, Italy, represents one customized approach in which conscious methodological decisions support philologically informed digitization e orts. The methods affect the results, and ultimately the consequences are not merely technological but cultural.

Risk of having hypoglycemia is one of the biggest barriers preventing Type 1 Diabetes (T1D) patients from performing exercise. In addition, management of diet and exercise levels needs to be personalized for each patient to avoid hypoglycemia and to achieve a good glycemic control. In this paper, we developed a model-based diet and exercise recommender system that could be used to provide an (optimal) personalized intervention on diet and exercise for T1D patients. The recommender system makes prediction of blood glucose at each intervention time based on a patient-specific model of glucose dynamics, and then provides the optimal meal sizes, target heart rates during exercise, pre-exercise carbohydrate and bedtime snack by minimizing a clinical risk function under constraints. Patient-specific models of glucose dynamics were identified for 30 virtual subjects generated from a modified UVa/Padova simulator with an added exercise-glucose subsystem. The performance of the recommender system was then compared to two self-management schemes (the Starter and the Skilled). The latter represents an off-line optimal solution providing a lower bound on the risk index. The average clinical risk under the recommender system was reduced by 49% compared to that under the Starter, and it was comparable to the risk of the Skilled. In addition, the recommender system had less number of post-exercise/nocturnal hypoglycemia events occurred than that under the Starter or the Skilled. Such recommender system can be implemented as an “App” patient advisor to improve T1D patients’ self-management of glucose control.

IntroductionDigital assistant systems (DAS) can support tasks by mediating between complex data and users, promoting continuous learning and on-the-job training (Jwo et al., 2021; Longo et al., 2017; Prinz et al., 2017). Integrating a DAS into surgical instrument reprocessing, where instrument-specific and complex manual tasks need to be performed strictly according to the manufacturer's instructions, can be advantageous. In Germany, reprocessing by trained on-the-job personnel is common. In addition, human factors are often neglected in the instructions for instrument reprocessing (Choi et al., 2017). A cooperative robot can be a valuable addition to mitigate health risks associated with handling contaminated surgical instruments during reprocessing, resulting in a cyber-physical assistance system (Heibeyn et al., 2021). However, it is unclear how the transition from paper-based instructions to either a DAS or a DAS supplemented with a cooperative robot assistance (“cyber-physical assistance system” – CPAS) affects usability for complex and workpiece-specific tasks in instrument reprocessing. Therefore, this study aimed to investigate the differences in usability with different assistance systems for typical tasks in instrument reprocessing for untrained personnel.MethodsWe conducted an interaction-centered user study with 13 participants unfamiliar with the reprocessing tasks. The participants were asked to complete typical reprocessing tasks three times in a random order, using different assistance approaches each time. The reference process consisted of paper-based instructions that required stepping away from the workstation to retrieve information from the storage of guidelines, simulating common set-ups of current reprocessing processes. The first assistance approach presented digital instructions right at the workstation. The second assistant combined a cooperative robot with digital instructions. The robot performed simple processing steps, while the human operator focused on the complex tasks and verified the cleaning success. We measured the required time, counted user errors and rated the criticality, measured the perceived workload using the NASA-TLX questionnaire (NASA, 2020), and documented the remarks of the participants using the thinking-out-loud method for all assistance systems.Results The NASA-TLX did not reveal any significant differences among the three systems, however, the CPAS reduced the number of critical errors. The errors included omitted processing steps and deviations from required times, which could pose risks to patients. The DAS was perceived as a suitable way to check instructions, based on the participants’ comments. However, in the case of the CPAS, some participants missed or ignored messages provided by the user interface.Discussion and ConclusionIn summary, the CPAS improved usability the most, improving effectiveness (number of errors) while maintaining the same efficiency (total duration). Although our study found promising results for integrating a DAS or CPAS into on-the-job training assistance for novice personnel, future studies should compare the results obtained from inexperienced to those of experienced users to fully assess the usability of related approaches. This study contributes to the field of human factors by providing comparative data on usability across different levels of assistance for complex and workpiece-specific tasks in surgical instrument reprocessing.ReferencesChoi, J., Seraphina, S., &amp; Knudsen, K. (2017). The Clean and Dirty of Redesigning Reprocessing Instructions for Use. Proceedings of the International Symposium on Human Factors and Ergonomics in Health Care, 6(1), 150–153. https://doi.org/10.1177/2327857917061032Heibeyn, J., König, N., Domnik, N., Schweizer, M., Kinzius, M., Janß, A., &amp; Radermacher, K. (2021). Design and Evaluation of a Novel Instrument Gripper for Handling of Surgical Instruments. Current Directions in Biomedical Engineering, 7(1), 1–5. https://doi.org/10.1515/cdbme-2021-1001Jwo, J.‑S., Lin, C.‑S., &amp; Lee, C.‑H. (2021). An Interactive Dashboard Using a Virtual Assistant for Visualizing Smart Manufacturing. Mobile Information Systems, 2021, 1–9. https://doi.org/10.1155/2021/5578239Longo, F., Nicoletti, L., &amp; Padovano, A. (2017). Smart operators in industry 4.0: A human-centered approach to enhance operators’ capabilities and competencies within the new smart factory context. Computers &amp; Industrial Engineering, 113, 144–159. https://doi.org/10.1016/j.cie.2017.09.016NASA (Ed.). (2020, December 15). NASA TLX: Task Load Index. https://humansystems.arc.nasa.gov/groups/TLX/Prinz, C., Kreimeier, D., &amp; Kuhlenkötter, B. (2017). Implementation of a Learning Environment for an Industrie 4.0 Assistance System to Improve the Overall Equipment Effectiveness. Procedia Manufacturing, 9, 159–166. https://doi.org/10.1016/j.promfg.2017.04.004