In this paper, we study the extension of the Riemann zeta function to finite-dimensional commutative algebras and present examples of such extensions for several hypercomplex systems. We also investigate the zeros of the quaternionic zeta function and prove that its nontrivial zeros are spherical.

We develop fixed point and periodic point results for self-mappings on \(n\)-G-metric spaces. The definition is stated in a form compatible with the classical case \(n=3\), while the paper specializes to the genuinely higher-order case \(n\geq4\). The first result proves a sharp bound: a mapping satisfying an \(n\)-tuple contraction on pairwise distinct points has at most \(n-1\) periodic points, and hence at most \(n-1\) fixed points. This formulation makes clear the role of short periodic orbits, which are the natural obstruction to applying a distinct-tuple contraction along Picard blocks. Under \(d_G\)-completeness, orbital continuity and an \(n\)-orbit-separation condition, every Picard orbit either reaches a fixed point or converges to one. We also state direct \(n\)-ary Kannan- and Reich-type analogues and separate them from the standard consequences obtained from the associated metric. Finally, the total pairwise polygonal-length functional on normed spaces provides a concrete geometric model of the theory. To make the model computationally explicit, we add a Picard algorithm in \(n\)-G-metric spaces, pseudocode, convergence and error tables for several values of \(n\), \(\lambda\) and \(\rho\), and both linear and nonlinear discrete polygonal systems illustrating the comparison between the associated metric \(d_G\) and the pairwise polygonal-length dynamics.

An FR-PCM composite was produced for the development of an efficient material for thermal energy storage and fire protection through the incorporation of paraffin wax into a cassava starch-oil palm empty fruit bunch lignin-nano-bentonite-boric acid-based biopolymer-mineral matrix. Characterization of the material was done through FTIR, TGA/DTG, scanning electron microscopy (SEM), energy-dispersive spectroscopy (EDS), XRD, Brunauer–Emmett–Teller (BET) analysis, leakage test, thermal cycling, cone calorimetry, smoke-toxicity screening, mechanical properties assessment, and water uptake analysis. FTIR analysis revealed the presence of the C–H bands associated with paraffin wax as well as hydrogen bonding and borate interactions within the biopolymer-mineral matrix. TGA/DTG revealed the increase in the onset of decomposition from about 180 \(^\circ\)C for pure paraffin to about 245 \(^\circ\)C and the increase in residue at 600 \(^\circ\)C from about 15% for pure paraffin to about 30%. Cone-calorimetry smoke/toxicity screening test demonstrated the enhancement in fire performance attributes, such as the increase in time to ignition from 35 s for pure paraffin to 85 s, decrease in peak heat release rate from 900 to 380 kW m\(^{-2}\) and decrease in fire growth index from 2600 to 900 W s\(^{-1}\). Laboratory flame-spread testing revealed reduction in flame spread rate from 3.50 to 1.36 cm min\(^{-1}\) and increase in ignition delay to 97 s. SEM, EDS, XRD and BET analysis revealed the successful incorporation of biopolymer and mineral materials, maintenance of paraffin crystalline nature, control of mesoporosity and formation of cohesive protective char layer. Leakage and thermal cycling revealed the ability of the matrix to preserve 92% shape retention at 70 \(^\circ\)C and more than 90% latent heat retention after 100 thermal cycles. Mechanical and water-uptake properties assessment revealed improvement in the material structural characteristics together with introduction of mild moisture sensitivity. Overall, the FR-PCM composite provides a practical balance between latent heat storage, thermal transport, shape stability, and fire safety for energy-efficient building applications.

In selecting the suitable UAV for agricultural spraying, it is necessary to consider simultaneously the payload capacity, field productivity, endurance, spraying capacity, energy capacity, range of operation, weight, and charging requirement. In this paper, the authors have presented a multi-attribute decision analysis technique to rank alternative spraying UAVs based on a common set of criteria. The AHP method was used to evaluate the weights of criteria through reciprocal pairwise comparison, and then, the criterion weights are utilized to calculate the ranking orders of three spraying UAV alternatives using TOPSIS, MABAC, and ARAS methods. From AHP result, it can be seen that the weights of payload capacity, work efficiency, endurance time, and spraying flow performance are higher than other criteria. As a consequence, the results obtained from the above three ranking methods have been completely coincided and showed that the order of UAV alternatives are D-T5 > D-T4 > D-T2A. It shows that the decision is not affected by the choice of computational logic. In addition, sensitivity analysis on payload capacity and work efficiency criteria was performed, and there was no change in ranking order in considered intervals. Hence, the results revealed that D-T5 is superior alternative compared with other two alternatives in terms of capacity, efficiency, spray capability, and operational range while D-T4 and D-T2A are ranked in second and third positions, respectively. The study offers a transparent and technically consistent decision procedure for UAV selection in precision agriculture and related equipment-selection problems.

Brewery effluent may have dissolved heavy metals that remain in the receiving waters and affect both aquatic life and human health. This study explored the efficiency of the African pear seed activated carbon (APSAC) derived from Dacryodes edulis seed waste as a low-cost adsorbent for removing chromium ion (Cr²⁺) from brewery wastewater. APSAC was synthesized by the procedure involving drying and pulverization of the seed waste, carbonization at 600 °C for 2 h, 40% H₂SO₄ impregnation for 24 h, activation at 500 °C for 4 h, neutral washing, drying, and sieving into 250 \(\mu\)m fraction. Proximate analysis, Fourier-transform infrared spectroscopy, and scanning electron microscopy were employed for characterizing bulk properties, surface functional groups, and surface morphology. Batch experiments of the adsorption process were planned on the basis of central composite design to investigate the influence of contact time (15–75 min), initial Cr²⁺ concentration (0.005–0.025 mg L^\(-1\)), and adsorbent dosage (0.5–2.5 g). The maximum Cr²⁺ removal observed was 96% at 0.025 mg L^\(-1\), 1.5 g APSAC, and 45 min, while the maximum adsorption capacity of APSAC was 0.0048 mg g^\(-1\) at 0.015 mg L^\(-1\), 0.5 g APSAC, and 45 min. The developed model for the adsorption capacity response was statistically significant (\(F=13.94\), \(p=0.0049\)) and had high explanatory power (\(R^2=0.9617\)). The equilibrium data were better described by the Sips isotherm model (\(R^2=0.9849\)) indicating the heterogeneity of surface adsorption process. The kinetic and Boyd studies suggested that surface absorption and film diffusion controlled the process of chromium removal rate. The results confirm the effectiveness of APSAC as biomass-derived adsorbent for chromium removal from brewery effluent and the potential of valorization of the African pear seed waste in wastewater treatment.

Force regulation is one of the important requirements in robotics when objects being grasped are fragile, deformable, or vulnerable due to excessive contact forces. This paper describes the design, development, and experimental evaluation of an inexpensive force-controlled robotic gripper which allows to safely grasp fragile objects. The developed system includes screw drive mechanism, YZC-131 load cell, HX711 analog-to-digital conversion module, Arduino control unit, DRV8871 motor driver and GA25-370 DC geared motor. Measurement of gripping force is accomplished via the application of exponential moving average filter and the process of its regulation is realized by means of the Proportional-Derivative control law together with contact detection, deadzone logic and minimum pulse-width modulation compensation algorithm. The performance of the proposed prototype was analyzed in terms of force-sensor calibration, controller tuning, fingertips interface evaluation, repeatability tests and real grasping experiments. The calibration procedure revealed very high linearity of the dependence between applied force and digitized sensor readings, with \(R^2 = 0.99897\). Experimental results have confirmed the possibility of stable low-force regulation, minimal overshoot and satisfactory settling process, better contact stability using the silicon-coated fingertips interface, repeatable responses to applied force and successful grasp of a chicken egg without any shell damage.

In this paper, we develop an effective gauge-theoretic description of atmospheric electrical breakdown where the transition from weakly conducting air to a lightning channel is described via an order parameter instability. The formulation includes the interaction of the degree of ionization and the collective conducting amplitude with the electromagnetic potential. The key question is whether regularities found in lightning initiation, stepped leader propagation, channel confinement, and branching can be captured using topological invariants or just via threshold values of fields. Our model defines the critical field strength to be the point where the conducting order parameter becomes unstable, derives vortex channel solutions with a finite core and an effective flux increment, and connects branch geometry to symmetrically constrained weight vectors. We also describe the limited role played by instanton-like nucleation, anomalous transport terms, and dual confinement within the framework of an effective description rather than as a microscopically justified one. Predictions derived within our approach are formulated in terms of measurable quantities: vortex core length scales, branch angle clustering, field-temperature scaling, radio signals polarization dependence, and magnetic field increment near developing channels.

The steady magnetohydrodynamic boundary-layer flow of a conducting ferro-nanofluid over a permeable stretching sheet of variable thickness subject to Hall effect, thermal radiation, viscous dissipation, Brownian diffusion, thermophoresis and first order chemical reaction is analyzed. A uniform transverse magnetic field along with the consideration of the Hall effect produces an additional secondary fluid motion in association with the main stretching flow. Applying the similarity transformation technique, the governing equations of conservation of mass, momentum, energy and species concentrations are transformed into a nonlinear system of ordinary differential equations. The numerical solution of the similarity equation with proper boundary conditions is obtained using a fourth order Runge-Kutta shooting algorithm under appropriate convergence criteria. It is found that a higher magnetic parameter decreases the main flow velocity and increases the secondary velocity due to Hall effect. Thermal boundary layer thickness increases with increasing Brownian motion and thermophoresis but decreases with increasing chemical reaction rate and Lewis number. The wall gradient profiles reveal that an increase in the interaction between magnetic field and flow leads to enhance the magnitude of the primary shear as well as significantly changes the heat and mass transfer.

A privacy-based risk analysis demands a proper identification of whether a data element is private, non-private or potentially private. Though some of the personal characteristics may be inherently sensitive, others acquire sensitivity due to their statistical and semantic association with already known private variables. In this paper, we propose a feature-selection based technique to identify potentially private variables based on their relevance to known private variables. Our approach considers each feature as a target variable at a time, performs three different filter-based feature selection techniques: chi-square filter, correlation-based feature selection, fast correlation-based feature selection, generates feature-distance matrices based on the ranks obtained from these techniques and identifies relevant pairs based on the threshold distance. We have conducted experiments on the Adult dataset which shows that there are strong relations between workclass, occupation, marital-status, relationship, race, native-country, gender, income-class and age attributes. A relevant features subset for the income-class attribute that can predict as well as the complete feature set predicts with an 83% accuracy whereas the complete feature set predicts with an 85% accuracy. These findings show that feature selection can support privacy risk assessment by revealing implicit privacy dependencies that are not visible when variables are examined in isolation.