Search results for: Pythagorean triplets

Authors: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

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The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation

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Authors: Anthony Overmars, Sitalakshmi Venkatraman

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This paper presents a method for determining all of the co-prime right angle triangles in the Euclidean field by looking at the intersection of the Pythagorean and Platonic right angle triangles and the corresponding lattice that this produces. The co-prime properties of each lattice point representing a unique right angle triangle are then considered. This paper proposes a conjunction between these two ancient disparaging theorists. This work has wide applications in information security where cryptography involves improved ways of finding tuples of prime numbers for secure communication systems. In particular, this paper has direct impact in enhancing the encryption and decryption algorithms in cryptography.

Keywords: Pythagorean triples, platonic triples, right angle triangles, co-prime numbers, cryptography

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Authors: Vahdetti̇n Sariyel, Bi̇rol Dağ

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In this research, growth and development parameters in Konya, a private company in Saanen kids reared in intensive conditions in the province were examined. Average birth weights were 3.42, 2.96, 3.57, 3.23 and 2.77 kg for male, female, single, twins and triplets kids. Average weaning weights (three months of age) were 12.65, 12.09, 12.80, 12.65 and 11.68 kg for male, female, single, twins and triplets kids. Average body weights at seven months of age were 20.55, 18.98, 20.12, 20.12 and 19.05 kg for male, female, single, twins and triplets kids respectively. Considering the gender of the live weight factors birth control and rule in favor of the first en ( P <0.01), the second control finally it disappeared statistically significant ( P> 0.05). Main age and the effect of birth weight in the first month, while significant (P < 0.01); The effect of the second month following the live weight of the kid was not significant.

Keywords: Saanen kids, growth, development, body weight

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Authors: Luiz G. Véras, Felipe L. Medeiros, Lamartine F. Guimarães

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This work approaches the automatic planning of paths for Unmanned Aerial Vehicles (UAVs) through the application of the Rapidly Exploring Random Tree Star-Smart (RRT*-Smart) algorithm. RRT*-Smart is a sampling process of positions of a navigation environment through a tree-type graph. The algorithm consists of randomly expanding a tree from an initial position (root node) until one of its branches reaches the final position of the path to be planned. The algorithm ensures the planning of the shortest path, considering the number of iterations tending to infinity. When a new node is inserted into the tree, each neighbor node of the new node is connected to it, if and only if the extension of the path between the root node and that neighbor node, with this new connection, is less than the current extension of the path between those two nodes. RRT*-smart uses an intelligent sampling strategy to plan less extensive routes by spending a smaller number of iterations. This strategy is based on the creation of samples/nodes near to the convex vertices of the navigation environment obstacles. The planned paths are smoothed through the application of the method called quintic pythagorean hodograph curves. The smoothing process converts a route into a dynamically-viable one based on the kinematic constraints of the vehicle. This smoothing method models the hodograph components of a curve with polynomials that obey the Pythagorean Theorem. Its advantage is that the obtained structure allows computation of the curve length in an exact way, without the need for quadratural techniques for the resolution of integrals.

Keywords: path planning, path smoothing, Pythagorean hodograph curve, RRT*-Smart

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Authors: Amar Partap Singh Pharwaha, Balkrishan Jindal

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In this paper, a new method is developed for hiding image in a digital image with multilayer security. In the proposed method, the secret image is encrypted in the first instance using a flexible matrix based symmetric key to add first layer of security. Then another layer of security is added to the secret data by encrypting the ciphered data using Pythagorean Theorem method. The ciphered data bits (4 bits) produced after double encryption are then embedded within digital image in the spatial domain using Least Significant Bits (LSBs) substitution. To improve the image quality of the stego-image, an improved form of pixel adjustment process is proposed. To evaluate the effectiveness of the proposed method, image quality metrics including Peak Signal-to-Noise Ratio (PSNR), Mean Square Error (MSE), entropy, correlation, mean value and Universal Image Quality Index (UIQI) are measured. It has been found experimentally that the proposed method provides higher security as well as robustness. In fact, the results of this study are quite promising.

Keywords: Pythagorean theorem, pixel adjustment, ciphered data, image hiding, least significant bit, flexible matrix

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Authors: Berna Istegun, Erkan Celebi

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The main objective of this experimental study is to assess the shear strength and the crack behavior of the triplets built of perforated brickwork masonry elements. In order to observe the influence of shear resistance and energy dissipating before and after retrofitting applications by using the reinforcing system, static-cyclic shear tests were employed in the structural mechanics laboratory of Sakarya University. The reinforcing system is composed of hybrid multiaxial seismic fabric consisting of alkali resistant glass and polypropylene fibers. The plaster as bonding material used in the specimen’s retrofitting consists of expanded glass granular. In order to acquire exact measuring data about the failure behavior of the two mortar joints under shear stressing, vertical load-controlled cylinder having force capacity of 50 kN and loading rate of 1.5 mm/min. with an internal inductive displacement transducers is carried out perpendicular to the triplet specimens. In this study, a total of six triplet specimens with textile reinforcement were prepared for these shear bond tests. The three of them were produced as single-sided reinforced triplets with seismic fabric, while the others were strengthened on both sides. In addition, three triplet specimens without retrofitting and plaster were also tested as reference samples. The obtained test results were given in the manner of force-displacement relationships, ductility coefficients and shear strength parameters comparatively. It is concluded that two-side seismic textile applications on masonry elements with relevant plaster have considerably increased the sheer force resistance and the ductility capacity.

Keywords: expanded glass granular, perforated brickwork, retrofitting, seismic fabric, triplet shear tests

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Authors: Peter J. Riley

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Introductory courses in High Energy Physics (HEP) can be extended with the Tri-Preon (TP) model to both supplements and challenge the Standard Model (SM) theory. TP supplements by simplifying the tracking of Conserved Quantum Numbers at an interaction vertex, e.g., the lepton number can be seen as a di-preon current. TP challenges by proposing extended particle families to three generations of particle triplets for leptons, quarks, and weak bosons. There are extensive examples discussed at an introductory level in six arXiv publications, including supersymmetry, hyper color, and the Higgs. Interesting exercises include pion decay, kaon-antikaon mixing, neutrino oscillations, and K+ decay to muons. It is a revealing exercise for students to weigh the pros and cons of parallel theories at an early stage in their HEP journey.

Keywords: HEP, particle physics, standard model, Tri-Preon model

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Authors: Ana Paula Soares, Alexandrina Lages, Helena Oliveira, Francisco-Javier Gutiérrez-Domínguez, Marisa Lousada

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From an early age, exposure to a spoken language allows us to implicitly capture the structure underlying the succession of the speech sounds in that language and to segment it into meaningful units (words). Statistical learning (SL), i.e., the ability to pick up patterns in the sensory environment even without intention or consciousness of doing it, is thus assumed to play a central role in the acquisition of the rule-governed aspects of language and possibly to lie behind the language difficulties exhibited by children with development language disorder (DLD). The research conducted so far has, however, led to inconsistent results, which might stem from the behavioral tasks used to test SL. In a classic SL experiment, participants are first exposed to a continuous stream (e.g., syllables) in which, unbeknownst to the participants, stimuli are grouped into triplets that always appear together in the stream (e.g., ‘tokibu’, ‘tipolu’), with no pauses between each other (e.g., ‘tokibutipolugopilatokibu’) and without any information regarding the task or the stimuli. Following exposure, SL is assessed by asking participants to discriminate between triplets previously presented (‘tokibu’) from new sequences never presented together during exposure (‘kipopi’), i.e., to perform a two-alternative-forced-choice (2-AFC) task. Despite the widespread use of the 2-AFC to test SL, it has come under increasing criticism as it is an offline post-learning task that only assesses the result of the learning that had occurred during the previous exposure phase and that might be affected by other factors beyond the computation of regularities embedded in the input, typically the likelihood two syllables occurring together, a statistic known as transitional probability (TP). One solution to overcome these limitations is to assess SL as exposure to the stream unfolds using online techniques such as event-related potentials (ERP) that is highly sensitive to the time-course of the learning in the brain. Here we collected ERPs to examine the neurofunctional correlates of SL in preschool children with DLD, and chronological-age typical language development (TLD) controls who were exposed to an auditory stream in which eight three-syllable nonsense words, four of which presenting high-TPs and the other four low-TPs, to further analyze whether the ability of DLD and TLD children to extract-word-like units from the steam was modulated by words’ predictability. Moreover, to ascertain if the previous knowledge of the to-be-learned-regularities affected the neural responses to high- and low-TP words, children performed the auditory SL task, firstly, under implicit, and, subsequently, under explicit conditions. Although behavioral evidence of SL was not obtained in either group, the neural responses elicited during the exposure phases of the SL tasks differentiated children with DLD from children with TLD. Specifically, the results indicated that only children from the TDL group showed neural evidence of SL, particularly in the SL task performed under explicit conditions, firstly, for the low-TP, and, subsequently, for the high-TP ‘words’. Taken together, these findings support the view that children with DLD showed deficits in the extraction of the regularities embedded in the auditory input which might underlie the language difficulties.

Keywords: development language disorder, statistical learning, transitional probabilities, word segmentation

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Authors: Jayson Wau, David Timi, Anthony Harakuwe, Bruce Bowden, Cherie Motti, Harry Sakulas, Rag Gubag-Sipou

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The latex of F. botryocarpa fruit is applied on sores, wounds and other skin infections in Papua New Guinea ethnotherapeutic practices. Systematic bioassay guided separation and isolation of subsequent fractions of latex extracts resulted in three bioactive fractions active against Staphylococcus aureus and Escherichia coli. This study reports structural elucidation of the three isolates. Structures were determined by physical (M.pt and Rf values) and spectroscopic (1D-1H NMR, 2D-HSQC NMR, 2D-HMBC NMR) and MS ESI-POS. The two methylene protons (2H-1) and (2H-3) resonate as triplets at δ 3.59 and δ 4.99 respectively. Electron dense δ 4.99 (2H-3) on (C-3) depicts the strong electron-withdrawing component, quaternary nitrogen (=N= +). Protons resonating at δ 3.88 and 3.89 are singlets depicting two methoxy groups. Both δ 3.88 and δ 3.89 are para-aryls substituents. The methines δ 9.13 and 8.60 are singlets depicting two lone protons on the indolizidinium aryl component. All isolates, (1), (2) and (3) were identified to be ficuseptine by comparing 1D-NMR assignments. 2D-NMR and MS of (2) found it to be ficuseptine chloride '2, 3-dihydro-6, 8-bis (4-methoxyphenyl)-, 1H-indolizinium chloride'. Their counter ions of the ficuseptines were not established and provide promising lead for the further investigation.

Keywords: Ficus botryocarpa, antimicrobial activity, ficuseptine, sores

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Authors: Alan S. Weber

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This contribution reviews the current biomedical and qualitative arts research on arts-in-health interventions to improve both individual and population health outcomes. Arts therapies–for example, music therapy with roots in Aristoxenus’s Ἁρμονικὰ στοιχεῖα and the Pythagorean sect–have long been employed in therapeutic contexts. However, the 20th century witnessed the increasing use of the visual and plastic arts (drawing, painting, sculpting), performing arts (drama and dance), and other expressive arts modalities into occupational therapy, well-being medicine, and psychological and psychiatric counselling, diagnosis, and treatment. A significant body of peer-reviewed evidence in the medical and neurological sciences on the role of arts-in-health has developed, and specifically, research on music and art therapy has led to their inclusion within the current biomedical paradigm of evidence-based practice. The arts cannot only aid in public and population health promotion (promoting healthy behaviors and lifestyles, preventing disease onset) but also in addressing psychological issues (regulation of emotion; stress, anxiety, and depression reduction), behavioural issues (basic life skills, coping), and physiological response (immune system function, hormonal regulation, homeostatis). Working as a cross-disciplinary researcher in the arts in an American medical college, the author has developed several successful arts-in-health programs at the national and international level.

Keywords: arts-in-health, evidence based medicine, arts for health, expressive arts therapies

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Authors: Garba Yusuf, Ibrahim Rakson Muhammad, Bashir Fagge Muhammad, Shehu Ahmad Maigandi

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On-farm data were collected to evaluate reproductive performance of Red Sokoto does reared under small-holder agro-pastoral production system within metropolitan Kano, semi-arid, Nigeria. The effects of age of dams, parity, litter size(s) and sex of kid(s) on pre-weaning growth rate were investigated. Data was obtained from semi-intensively managed herds of twenty four households for a period of six months. Pregnant does were ear tagged and age determined through dentition. Upon kidding, litter size, parity of dam and sex of kid(s) were recorded. Subsequently, daily liveweight changes of kids was monitored and recorded. Results obtained revealed average weight at birth to be 3.18 kg and 2.87 kg for female and male kids with average daily weight gain of 0.11 and 0.13 kg, respectively. Result also showed that male kids gained higher liveweight from 21st day to weaning and single or twin births had higher liveweight changes relative to triplets. Does at third parity produced kids with higher weight gain. From the results of this study, it is concluded that male kids at 21 days of age (single or twin) or dam at third parity or three years of age be selected for a sound breeding programme.

Keywords: agro-pastoral, goats, parity, reproductive, semi-intensive

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Authors: Manendra Singh Parihar, Sandip Ghosh Chowdhury

Abstract:

Austenitic stainless steels are widely used and give a good combination of properties. When this steel is plastically deformed, a phase transformation of the metastable Face Centred Cubic Austenite to the stable Body Centred Cubic (α’) or to the Hexagonal close packed (ԑ) martensite may occur, leading to the enhancement in the mechanical properties like strength. The work was based on variant selection and corresponding texture analysis for the strain induced martensitic transformation during deformation of the parent austenite FCC phase to form the product HCP and the BCC martensite phases separately, obeying their respective orientation relationships. The automated method for reconstruction of the parent phase orientation using the EBSD data of the product phase orientation is done using the MATLAB and TSL-OIM software. The method of triplets was used which involves the formation of a triplet of neighboring product grains having a common variant and linking them using a misorientation-based criterion. This led to the proper reconstruction of the pre-transformation phase orientation data and thus to its microstructure and texture. The computational speed of current method is better compared to the previously used methods of reconstruction. The reconstruction of austenite from ԑ and α’ martensite was carried out for multiple samples and their IPF images, pole figures, inverse pole figures and ODFs were compared. Similar type of results was observed for all samples. The comparison gives the idea for estimating the correct sequence of the transformation i.e. γ → ε → α’ or γ → α’, during deformation of AISI 304 austenitic stainless steel.

Keywords: variant selection, reconstruction, EBSD, austenitic stainless steel, martensitic transformation

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Authors: Manendra Singh Parihar, Sandip Ghosh Chowdhury

Abstract:

Austenitic stainless steels are widely used and give a good combination of properties. When this steel is plastically deformed, a phase transformation of the metastable Face Centred Cubic Austenite to the stable Body Centred Cubic (α’) or to the Hexagonal close packed (ԑ) martensite may occur, leading to the enhancement in the mechanical properties like strength. The work was based on variant selection and corresponding texture analysis for the strain induced martensitic transformation during deformation of the parent austenite FCC phase to form the product HCP and the BCC martensite phases separately, obeying their respective orientation relationships. The automated method for reconstruction of the parent phase orientation using the EBSD data of the product phase orientation is done using the MATLAB and TSL-OIM software. The method of triplets was used which involves the formation of a triplet of neighboring product grains having a common variant and linking them using a misorientation-based criterion. This led to the proper reconstruction of the pre-transformation phase orientation data and thus to its micro structure and texture. The computational speed of current method is better compared to the previously used methods of reconstruction. The reconstruction of austenite from ԑ and α’ martensite was carried out for multiple samples and their IPF images, pole figures, inverse pole figures and ODFs were compared. Similar type of results was observed for all samples. The comparison gives the idea for estimating the correct sequence of the transformation i.e. γ → ε → α’ or γ → α’, during deformation of AISI 304 austenitic stainless steel.

Keywords: variant selection, reconstruction, EBSD, austenitic stainless steel, martensitic transformation

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Authors: Davies Obaromi, Qin Yongsong, James Ndege

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To interpolate scattered or regularly distributed data, there are imprecise or exact methods. However, there are some of these methods that could be used for interpolating data in a regular grid and others in an irregular grid. In spatial epidemiology, it is important to examine how a disease prevalence rates are distributed in space, and how they relate with each other within a defined distance and direction. In this study, for the geographic and graphic representation of the disease prevalence, linear and biharmonic spline methods were implemented in MATLAB, and used to identify, localize and compare for smoothing in the distribution patterns of tuberculosis (TB) in Eastern Cape Province. The aim of this study is to produce a more “smooth” graphical disease map for TB prevalence patterns by a 3-D curve fitting techniques, especially the biharmonic splines that can suppress noise easily, by seeking a least-squares fit rather than exact interpolation. The datasets are represented generally as a 3D or XYZ triplets, where X and Y are the spatial coordinates and Z is the variable of interest and in this case, TB counts in the province. This smoothing spline is a method of fitting a smooth curve to a set of noisy observations using a spline function, and it has also become the conventional method for its high precision, simplicity and flexibility. Surface and contour plots are produced for the TB prevalence at the provincial level for 2012 – 2015. From the results, the general outlook of all the fittings showed a systematic pattern in the distribution of TB cases in the province and this is consistent with some spatial statistical analyses carried out in the province. This new method is rarely used in disease mapping applications, but it has a superior advantage to be assessed at subjective locations rather than only on a rectangular grid as seen in most traditional GIS methods of geospatial analyses.

Keywords: linear, biharmonic splines, tuberculosis, South Africa

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Authors: David Nogueiras Blanco, Amir Alwash, Arnaud Gaudinat, René Schneider

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At a time when the access to and the sharing of information are crucial in the world of research, the use of technologies such as persistent identifiers (PIDs), Current Research Information Systems (CRIS), and ontologies may create platforms for information sharing if they respond to the need of disambiguation of their data by assuring interoperability inside and between other systems. INCIPIT-CRIS is a continuation of the former INCIPIT project, whose goal was to set up an infrastructure for a low-cost attribution of PIDs with high granularity based on Archival Resource Keys (ARKs). INCIPIT-CRIS can be interpreted as a logical consequence and propose a research information management system developed from scratch. The system has been created on and around the Schema.org ontology with a further articulation of the use of ARKs. It is thus built upon the infrastructure previously implemented (i.e., INCIPIT) in order to enhance the persistence of URIs. As a consequence, INCIPIT-CRIS aims to be the hinge between previously separated aspects such as CRIS, ontologies and PIDs in order to produce a powerful system allowing the resolution of disambiguation problems using a combination of an ontology such as Schema.org and unique persistent identifiers such as ARK, allowing the sharing of information through a dedicated platform, but also the interoperability of the system by representing the entirety of the data as RDF triplets. This paper aims to present the implemented solution as well as its simulation in real life. We will describe the underlying ideas and inspirations while going through the logic and the different functionalities implemented and their links with ARKs and Schema.org. Finally, we will discuss the tests performed with our project partner, the Swiss Institute of Bioinformatics (SIB), by the use of large and real-world data sets.

Keywords: current research information systems, linked data, ontologies, persistent identifier, schema.org, semantic web

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Authors: Jutharat Attawet, Alex Y. Wang, Cindy M. Farquhar, Elizabeth A. Sullivan

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Background: Adverse maternal and perinatal outcomes of multiple pregnancies resulting from multiple embryo transfers (ET) has become significant concerns. This is particularly relevant for gestational carriers since they usually do not have infertility issues. Single embryo transfer (SET) therefore has been encouraged to assist reproductive technology (ART) practice in order to reduce multiple pregnancies. Objectives: This systematic review aims to investigate the pregnancy and birth outcomes of SET and multiple ET in surrogacy arrangements. Search methods: This study is a systematic review. Electronic databases were searched from CINAHL, Medline, Embase, Scopus and ProQuest for studies from 1980 to 2017. Cross-references and national ART reports were also manual searchings. Articles without restriction of English language and study types were accessed. Carrier cycles involving in SET and multiple ET were identified in database searching. The main outcome measures including clinical pregnancy, live delivery and multiple deliveries per gestational carrier cycle were compared between SET and multiple ET. Mantel-Haenzel risk ratios (RRs) with 95% confidence intervals (CIs), using the numbers of outcome events in SET and multiple ET of each study were calculated suing RevMan5.3. Outcomes: The search returned 97 articles of which 5 met the inclusion criteria. Approximately 50% of carrier cycles were transferred a single embryo and 50% were transferred more than one embryo. The clinical pregnancy rate (CPR) was 39% for SET and 53% for multiple ET, which was not significantly different with RR = 0.83 (95% CI: 0.67-1.03). The live delivery rate was 33% for SET and 57% for multiple ET which was not significantly different with RR = 0.78 (95% CI: 0.61-1.00). The multiple delivery rate per carrier was greater risks in the multiple ET carrier cycles (RR =0.4, 95% CI: 0.01-0.26). There were 104 sets of twins (including one set of twins selectively reduced from triplets to twins) and 1 set of triples in the multiple ET carrier cycle. In the SET carrier cycles, there were 2 sets of twins. Significance of the study: SET should be advocated among surrogate carriers to prevent multiple pregnancies and subsequent adverse outcomes for both carrier and baby. Surrogacy practice should be reviewed and surrogate carriers should be fully informed of the risk of adverse maternal and birth outcome of multiple pregnancies due to multiple embryo transfers.

Keywords: assisted reproduction, birth outcomes, carrier, gestational surrogacy, multiple embryo transfer, multiple pregnancy, pregnancy outcomes, single embryo transfer, surrogate mother, systematic review

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Authors: Soumava Boral, Sanjay K. Chaturvedi, Ian Howard, Kristoffer McKee, V. N. A. Naikan

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Due to strict regulations from government to enhance the possibilities of sustainability practices in industries, and noting the advances in sustainable manufacturing practices, it is necessary that the associated processes are also sustainable. Maintenance of large scale and complex machines is a pivotal task to maintain the uninterrupted flow of manufacturing processes. Appropriate maintenance practices can prolong the lifetime of machines, and prevent associated breakdowns, which subsequently reduces different cost heads. Selection of the best maintenance strategies for such machines are considered as a burdensome task, as they require the consideration of multiple technical criteria, complex mathematical calculations, previous fault data, maintenance records, etc. In the era of the fourth industrial revolution, organizations are rapidly changing their way of business, and they are giving their utmost importance to sensor technologies, artificial intelligence, data analytics, automations, etc. In this work, the effectiveness of several maintenance strategies (e.g., preventive, failure-based, reliability centered, condition based, total productive maintenance, etc.) related to a large scale and complex gearbox, operating in a steel processing plant is evaluated in terms of economic, social, environmental and technical criteria. As it is not possible to obtain/describe some criteria by exact numerical values, these criteria are evaluated linguistically by cross-functional experts. Fuzzy sets are potential soft-computing technique, which has been useful to deal with linguistic data and to provide inferences in many complex situations. To prioritize different maintenance practices based on the identified sustainable criteria, multi-criteria decision making (MCDM) approaches can be considered as potential tools. Multi-Attributive Ideal Real Comparative Analysis (MAIRCA) is a recent addition in the MCDM family and has proven its superiority over some well-known MCDM approaches, like TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and ELECTRE (ELimination Et Choix Traduisant la REalité). It has a simple but robust mathematical approach, which is easy to comprehend. On the other side, due to some inherent drawbacks of Intuitionistic Fuzzy Sets (IFS) and Pythagorean Fuzzy Sets (PFS), recently, the use of Fermatean Fuzzy Sets (FFSs) has been proposed. In this work, we propose the novel concept of FF-MAIRCA. We obtain the weights of the criteria by experts’ evaluation and use them to prioritize the different maintenance practices according to their suitability by FF-MAIRCA approach. Finally, a sensitivity analysis is carried out to highlight the robustness of the approach.

Keywords: Fermatean fuzzy sets, Fermatean fuzzy MAIRCA, maintenance strategy selection, sustainable manufacturing, MCDM

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