In this study, we define the unrestricted Pell and Pell-Lucas quaternions. We give generating functions, Binet formulas and some generalizations of well-known identities such as Vajda’s, Catalan’s, Cassini’s d’Ocagne’s identities.

This article describes a classification tool to cluster SARAL/AltiKa waveforms. The tool was made using Python scripts. Radar altimetry systems (e.g., SARAL/AltiKa) measures the distance from the satellite centre to a target surface by calculating the satellite-to-surface round-trip time of a radar pulse. An altimeter waveform represents the energy reflected by the earth’s surface to the satellite antenna with respect to time. The tool clusters the altimetric waveforms data into desired groups. For the clustering, we used evolutionary minimize indexing function (EMIF) with k-means cluster mechanism. The idea was to develop a simple interface which takes the altimetry waveforms data from a folder as inputs and provides single value (using EMIF algorithm) for each waveform. These values are further used for clustering. This is a simple light weighted tool and user can easily interact with it.

Introduction: the presence of anti-CCP is an important prognostic tool for rheumatoid arthritis (RA), but its relationship with the activity of the disease and functional capacity is still being investigated. Objectives: to study the relationship between anti-CCP and the indices of disease activity, functional capacity and structural damage, by means of conventional radiography (CR) and magnetic resonance imaging (MRI), in stabilized RA. Methods: cross-sectional study of RA patients with one to 10 years of disease. The participants were subjected to clinical evaluation with anti-CCP screening. Disease activity was assessed by means of the Clinical Disease Activity Index (CDAI) and functional capacity by means of the Health Assessment Questionnaire (HAQ). CR was analyzed by the Sharp van der Heijde index (SmvH) and MRI by the Rheumatoid Arthritis Magnetic Resonance Image Scoring System (RAMRIS). Results: 56 patients were evaluated, with median (IIq) of 55 (47.5–60.0) years, 50 (89.3%) were female among whom 37 (66.1%) were positive for anti-CCP. The median (IIq) of CDAI, HAQ, SmvH and RAMRIS were 14.75 (5.42–24.97), 1.06 (0.28–1.75), 2 (0–8) and 15 (7–35), respectively. There was no association between anti-CCP and CDAI, HAQ, SmvH and RAMRIS. Conclusion: our results did not establish the association of anti-CCP with the severity of the disease. So far, we cannot corroborate the anti-CCP as a prognostic tool in RA established.

Based on the characteristics of liquid lens sparse aperture imaging, a radiative multiplet array structure is proposed; a simplified model of sparse aperture imaging is given, and the analytical expression of the modulation transfer function is derived from the optical pupil function of the multiplet array structure; the specific distribution form of this multiplet array structure is given, and the structure parameters are approximated by the dimensionless method; the two types of radiative multiplet array structures are discussed, and the filling factor, redundancy, modulation transfer function and other characteristic parameters are calculated. The physical phenomena exhibited by the parametric scan are discussed, and the structural features and imaging characteristics of these two arrays are compared. The results show that the type-II structure with larger actual equivalent aperture and actual cutoff frequency and lower redundancy is selected when the average modulation transfer function and the IF characteristics of the modulation transfer function of the two structures are close to each other; the type-II structure has certain advantages in imaging; the conclusion is suitable for arbitrary enclosing circle size because the liquid lens-based multiplet array structure adopts dimensionless approximation parameters; compared with the composite toroidal structure, the radiative multiplet mirror structure has a larger actual cut-off frequency and actual equivalent aperture when the filling factor is the same.

Attempts were made in the present study to design and develop skeletally modified ether linked tetraglycidyl epoxy resin (TGBAPSB), which is subsequently reinforced with different weight percentages of amine functionalized mullite fiber (F-MF). The F-MF was synthesized by reacting mullite fiber with 3-aminopropyltriethoxysilane (APTES) as coupling agent and the F-MF structure was confirmed by FT-IR. TGBAPSB reinforced with F-MF formulation was cured with 4,4’-diamino diphenyl methane (DDM) to obtain nanocomposite. The surface morphology of TGBAPSB-F-MF epoxy nanocomposites was investigated by XRD, SEM and AFM studies. From the study, it follows that these nanocomposite materials offer enhancement in mechanical, thermal, thermo-mechanical, dielectric properties compared to neat (TGBAPSB) epoxy matrix. Hence we recommend these nanocomposites for a possible use in advanced engineering applications that require both toughness and stiffness.

In older adults with disabilities, muscle weakness reduces mobility and causes postural issues. Electrical muscle stimulation (EMS) training is effective for increasing strength by inducing involuntary skeletal muscle contractions. Thus, this study aimed to examine changes in lumbar movement, muscle activity during walking, and maximum muscle strength of lower-limb joints based on an 8-week EMS exercise program for older adults with physical disabilities. Sixteen older adults (aged 56–78 years) with physical disabilities were selected and randomly assigned to either the exercise group (EG, n = 8) or the control group (CG, n = 8). EG participants were instructed to wear EMS suits and participate in an elastic band and bare-body exercise program, whereas CG participants performed the exercise program without the EMS suits. Lumbar range of motion (ROM), body circumference, partial volume, maximum muscle strength, and muscle activity were measured. Statistical analysis was performed using SPSS 28.0 for Windows, with the critical value of α = 0.05. Compared to CG participants, EG participants had a superior ROM, body volume, partial volume, maximum muscle strength (knee joints), and muscle activity while walking. These positive outcomes highlight the efficacy of combining EMS with an exercise program for strength and rehabilitation training in older adults with physical disabilities.