Discretization and Associated Asymptotic Behavior for the Lax Equation with Skew-symmetry

The computation of matrix eigenvalues is vital for understanding various scientific phenomena. The QR method, which is based on the QR factorization of a matrix, is a common approach in numerical linear algebra. In integrable systems, the one-step process of the QR method is related to the time evolution of the Lax equation. In this paper, we clarify the relationship between the QR method, which incorporates an origin shift parameter, and the Lax equation with skew-symmetry. Furthermore, we show the asymptotic convergence of discretization based on matrix factorization of the Lax equation with skew-symmetry as discrete time approaches infinity

An Algorithm to Construct a Tridiagonal Matrix Factored by Bidiagonal Matrices with Prescribed Eigenvalues and Specified Entries

This paper presents an algorithm to construct a tridiagonal matrix factored by bidiagonal matrices with prescribed eigenvalues and specified matrix entries. The proposed algorithm addresses inverse eigenvalue problems (IEPs) constrained by LR decomposition. Using techniques from discrete soliton theory, we derive recurrence relations that connect matrix entries and eigenvalues. The algorithm systematically computes unknown entries in the matrix from given spectrum data and partial matrix information. Several examples, including cases with real, complex, and multiple eigenvalues, demonstrate the efficiency of the proposed algorithm. Additionally, we provide conditions under which the algorithm successfully solves the IEP

On the Interaction between Trichogramma chilonis and Jatiroto Flies with Stem Borer Pests in Sugarcane Plantation

Pests in sugarcane plantations are a major cause of damage, which could lead to severe damage to the crop, reduction of sugar quality, and significant economic loss. One of the major pests known in sugarcane plantations is stem borer (Chilo sacchriphagus), which attacks the canes. Two primary parasitoids, Trichogramma chilonis, which predates the stem borer eggs, and the Jatiroto fly (Diatraeophaga striatalis), which predates the stem borer larvae, are discussed here. This paper presents a time-dependent ten-dimensional dynamical mathematical model consisting of four-stage stem borer compartments, three-stage Trichogramma compartments, and three-stage Jatiroto compartments. Simulations are presented to describe the phenomenon of Trichogramma predation, Jatiroto predation, and simultaneous predation of both predators. It is shown that the release rate of each predator and a combined release of two predators can significantly reduce the infestation levels to a tolerable level for sugarcane production. The oscillatory dynamics of the stem borers and the Jatiroto flies affected the release timing strategy based on the level of infestation in the field. The results are expected to help us better understand the predator-prey phenomenon in the field and improve the forecasting of infestations in the field

Density Functional Theory Investigation on Muon Hyperfine Interaction in Methylated Guanine-Cytosine Double-Strand DNA

The aims of this study were to determine the most likely Mu trapping sites based on total energy consideration as well as identifying the associated muon hyperfine coupling constant of 1, 2, and 3 methylated guanine-cytosine base pair double-strand DNA. The Density Functional Theory method was used at B3LYP/6-31G level of theory to accomplish the objectives of the investigation. The relative energy in the 3 methylated guanine-cytosine base pair double-strand DNA molecule showed that N7 sites in the guanine base have the lowest energy, followed by N3, and C8 sites. It was found that the addition of a methyl group at the C5 atom in the cytosine base does change the stability of the C8 sites in the 3 methylated guanine-cytosine base pair double-strand DNA molecule, but the associated muon hyperfine coupling constant (HFCC) is not affected. The results of this study indicate that there will be no overlaps in the resonance dips due to N7, N3, and all C8 sites of the guanine bases and N3, C5, and C6 sites of the cytosine bases in the Avoided Level Crossing Muon Spin Resonance spectrum

Molecular Docking and In Vitro Studies of Synthesized Oxadiazole Derivatives as Urease Inhibitors

A novel sequence of 1,3,4-oxadiazoles (7a–h) was synthesized. The compounds were characterized by IR, ¹H NMR, and MS analyses. They were also examined to determine whether they could prevent urease from functioning.  Molecular docking was done with AutoDock Vina, and the findings were visualized in Discovery Studio. The H NMR spectra showed peaks at δ 10.20 to 10.69 ppm for NH protons, δ 7.16 to 8.01 ppm for aromatic protons, and δ 4.21 to 4.37 ppm for 2H and CH₂ groups, confirming the structural details. The EI-MS spectra showed molecular ion peaks at 337 m/z with an intensity of 14-67%. Among the bioactivity-tested compounds, 7d resulted in robust activity with IC50 values of 161.6 ± 5.8 µM; compound 7e exhibited the weakest activity, at 453.6 ± 5.8 µM; and no inhibition was discovered by the 7a, 7f, and 7h compounds when compared to the Thiourea, at 21.8 ± 1.51 µM. Molecular dockings confirmed compound 7d as the best-docked complex, with a minimum energy of -7.4 kcal/mol, an RMSD value of 1.573 Å, and hydrogen interactions at His593 with the active site residue, confirming the experimental results. It was determined that 1,3,4-oxadiazoles can be employed as urease inhibitors

Linear and Nonlinear Electro-optic Response of MHPOCBC

This study investigated the linear and second-order electro-optic responses in chiral smectic liquid crystal 4-(1-methylheptyloxycarbonyl) phenyl 4-octylcarbonyloxybiphenyl-4-carboxylate (MHPOCBC). The result revealed a single Debye-type relaxation in the linear electro-optic frequency dispersion, with a relaxation frequency extending up to one hundred kHz. Conversely, the second-order electro-optic response exhibited intricate temperature-dependence, accurately depicted by a phenomenological Landau theory around the SmA–SmCa* phase transition point. Notably, in the SmCa* phase, critical slowing down of the amplitude mode occurred near the transition to the SmA phase, while at lower temperatures of the SmCa* phase, a distinct low-frequency relaxation mode emerged. Furthermore, the relaxation frequency of the antiferroelectric Goldstone mode in the SmCA* phase remained constant across the entire temperature range. These findings should significantly contribute to the understanding of dynamic behaviors in chiral smectic liquid crystals, shedding light on their complex phase transitions and electro-optic properties

Rapid Synthesis of Graphene Oxide Derived from Biomass with Atmospheric Plasma Technology

In this study, we explored a low-cost, green, and renewable approach utilizing biomass resources, i.e., coconut fronds, palm fronds, and rambutan stems, to rapidly synthesize graphene oxide via atmospheric plasma techniques. The plasma treatment, with argon gas as the plasma source and a power source of 960 W, lasted for 5 minutes. Graphene oxide (GO) was confirmed using SEM and TEM images with a C:O content ratio greater than 80% for all samples and the formation of graphene layers. The presence of a D-band and a G-band in Raman spectroscopy as well as O-H and C-O groups in the FTIR confirmed the existence of GO

Environmentally Friendly Graphene Oxide Production using Ultrasonication for Fiber Optic Coating as Humidity Sensor

Graphene oxide (GO) has many applications, such as energy storage, sensors, and polymer composites. This study aimed to produce environmentally friendly GO for use as a humidity sensor. The GO was synthesized using liquid phase exfoliation (LPE) with ultrasonication. The ultraviolet-visible (UV-Vis) test results showed an absorption peak at a wavelength of 227 nm and a shouldering peak at 270 nm. The Fourier transform infrared (FTIR) spectrum showed the presence of oxygen functional groups indicating hydrophilic material characteristics. The X-ray diffraction (XRD) patterns indicated that the GO had an amorphous phase, as evidenced by a broadened peak at 2θ ≅ 12.2°. The scanning electron microscope (SEM) images showed that the synthesized GO was in the form of indentations or sheets of planar hexagonal structures in single or multi-layers. Based on the energy dispersive X-ray (EDX) characterization, the GO consisted of 63.6% carbon (C) and 26.4% oxygen (O). The C/O ratio after sonication showed a reduction in oxygen with a ratio of 2.4. Interestingly, the humidity tests showed that the GO coated on polymer optical fiber (POF) significantly enhanced the gradient values from 0.0567 to 0.4042 compared to the POF without coating, confirming its potential as a humidity sensor.

Sedimentary Facies, Palynology, and Organic Geochemistry of Eocene Kalumpang Formation in Lariang and Karama Areas, West Sulawesi, Indonesia

The Kalumpang Formation was deposited in a delta plain setting. A Middle to Late Eocene age (Proxapertites operculatus zone) was inferred from palynological analysis, with a paleoenvironment in a coastal plain setting with a strong terrestrial influence. Samples from the Kalumpang Formation indicate a marginal to early mature stage for hydrocarbon generation. It is mostly composed of gas-prone to oil and gas-prone Type III kerogen facies. The biomarker character of both the rock and oil samples suggests a terrestrial origin, with a significant contribution of estuarine or bay organic material. The oil derives from a non-carbonate lithology, while the rock samples are from carbonate/calcareous shale origin. The abundance of oleanane compound and C30 resins suggests higher plant angiosperm input of Late Cretaceous or younger age for both the rock and the oil samples. The oil seep contains more abundant oleananes compared to the carbonaceous mudstone of the Kalumpang Formation. This suggests that the oil originated from more marine facies than the rock samples, which were deposited in a delta plain setting. This study demonstrated the agreement of depositional environment interpretation and age assessment between lithofacies, palynological, and organic geochemistry analysis

Synthesis and Characterization of Bi2S3 Deposited on TiO2 Nanotubes (TiO2NTAs) as Photoanode in the Tandem DSSC-PEC System for Hydrogen Evolution

TiO2NTAs is one of the most frequently used photoanodes. However, TiO2NTAs has a wide bandgap, so it is only active under UV light. Therefore, this study modified TiO2NTAs photoanode film to increase its efficiency. A simple method that successfully assists the Bi2S3 coating process on the surface of TiO2NTAs film is the Successive Ionic Layer Adsorption and Reaction (SILAR) method. In this research, modified Bi2S3 with TiO2NTAs was prepared using the SILAR method with variations of the number of synthesis cycles at 1, 2, 4, and 6. Based on the synthesis results, the number of deposition cycles greatly influences the performance of TiO2NTAs films. The synthesized TiO2NTAs/Bi2S3 results were characterized using SEM, XRD, FTIR, UV-Vis DRS, and photoelectrochemistry. The X-ray diffractogram showed that the composite compound was obtained successfully. The SEM images showed that Bi2S3 was deposited on the surface of the TiO2NTAs without blocking the nanotube holes. The constructed DSSC-PEC system could produce hydrogen with an STH (solar-to-hydrogen) efficiency of 0.02318% in an H-type reactor using anode irradiation for 6 hrs