Search Results (32)

We present novel proofs of the Riemann hypothesis by extending the standard complex Riemann zeta function into a quaternionic algebraic framework. Utilizing λ-regularization, we construct a symmetrized form that ensures analytic continuation and restores critical-line reflection symmetry, a key structural property of the Riemann ξ(s) function. This formulation reveals that all nontrivial zeros of the zeta function must lie along the critical line Re(s) = 1/2, offering a constructive and algebraic resolution to this fundamental conjecture. Our method is built on convexity and symmetrical principles that generalize naturally to higher-dimensional hypercomplex spaces. We also explore the broader implications of this framework in quantum statistical physics. In particular, the λ-regularized quaternionic zeta function governs thermodynamic properties and phase transitions in Bose–Einstein condensates. This quaternionic extension of the zeta function encodes oscillatory behavior and introduces critical hypersurfaces that serve as higher-dimensional analogues of the classical critical line. By linking the spectral features of the zeta function to measurable physical phenomena, our work uncovers a profound connection between analytic number theory, hypercomplex geometry, and quantum field theory, suggesting a unified structure underlying prime distributions and quantum coherence. Full article

This research study investigated the production and properties of zinc oxide (ZnO) nanoparticles derived from corn husks and their priming effects on wheat plant proliferation and antioxidant mechanisms compared to the nutri-priming technique under regular irrigation and drought-stressed conditions. Transmission and scanning electron microscopy (TEM and SEM), energy-dispersive X-ray spectroscopy (EDAX), and X-ray diffraction confirmed the nanoparticles’ hexagonal morphology and typical dimensions of 51 nm. The size and stability of these nanoparticles were assessed through the size distribution and zeta potential analysis, indicating reasonable stability. Fourier-transform infrared spectroscopy (FTIR) detected the newly formed functional groups. This study emphasized the role of reactive oxygen species (ROS) and phenolic compounds in plant responses to nanoparticle treatment, particularly in detoxifying harmful radicals. The research also examined the activity of antioxidant enzymes, including peroxidase (POX), catalase (CAT), and glutathione reductase (GR), in alleviating stress caused by oxidation while subjected to various treatments, including micronutrient seed priming with DR GREEN fertilizer. Some biochemical compounds, such as total phenolics (TPCs), total flavonoids (TFCs), and total hydrolysable sugars, were estimated as well to show the effect of the different treatments on the wheat plants. The findings suggested that ZnO nanoparticles can enhance antioxidant enzyme activity under certain conditions while posing phytotoxic risks, underscoring the complexity of plant–nanoparticle interactions and the potential for improving crop resilience through targeted micronutrient applications. Full article

Nanoparticle-based formulations are considered valuable tools for diagnostic and treatment purposes. The surface decoration of nanoparticles with polyethyleneimine (PEI) is often used to enhance their targeting and functional properties. Here, we aimed at addressing the long-term fate in vivo and the potential “off-target” effects of PEI decorated iron oxide nanoparticles (PEI-MNPs) in individuals with low-grade and persistent systemic inflammation. For this purpose, we synthesized PEI-MNPs (core–shell method, PEI coating under high pressure homogenization). Further on, we induced a low-grade and persistent inflammation in mice through regular subcutaneous injection of pathogen-associated molecular patterns (PAMPs, from zymosan). PEI-MNPs were injected intravenously. Up to 7 weeks thereafter, the blood parameters were determined via automated fluorescence flow cytometry, animals were euthanized, and the organs analyzed for iron contents (atomic absorption spectrometry) and for expression of NF-κB associated proteins (p65, IκBα, p105/50, p100/52, COX-2, Bcl-2, SDS-PAGE and Western blotting). We observed that the PEI-MNPs had a diameter of 136 nm and a zeta-potential 56.9 mV. After injection in mice, the blood parameters were modified and the iron levels were increased in different organs. Moreover, the liver of animals showed an increased protein expression of canonical NF-κB signaling pathway members early after PEI-MNP application, whereas at the later post-observation time, members of the non-canonical signaling pathway were prominent. We conclude that the synergistic effect between PEI-MNPs and the low-grade and persistent inflammatory state is mainly due to the hepatocytes sensing infection (PAMPs), to immune responses resulting from the intracellular metabolism of the uptaken PEI-MNPs, or to hepatocyte and immune cell communications. Therefore, we suggest a careful assessment of the safety and toxicity of PEI-MNP-based carriers for gene therapy, chemotherapy, and other medical applications not only in healthy individuals but also in those suffering from chronic inflammation. Full article

The paper investigates the vacuum expectation value of the surface energy–momentum tensor (SEMT) for a scalar field with general curvature coupling in the geometry of two branes orthogonal to the boundary of anti-de Sitter (AdS) spacetime. For Robin boundary conditions on the branes, the SEMT is decomposed into the contributions corresponding to the self-energies of the branes and the parts induced by the presence of the second brane. The renormalization is required for the first parts only, and for the corresponding regularization the generalized zeta function method is employed. The induced SEMT is finite and is free from renormalization ambiguities. For an observer living on the brane, the corresponding equation of state is of the cosmological constant type. Depending on the boundary conditions and on the separation between the branes, the surface energy densities can be either positive or negative. The energy density induced on the brane vanishes in special cases of Dirichlet and Neumann boundary conditions on that brane. The effect of gravity on the induced SEMT is essential at separations between the branes of the order or larger than the curvature radius for AdS spacetime. In the considerably large separation limit, the decay of the SEMT, as a function of the proper separation, follows a power law for both massless and massive fields. For parallel plates in Minkowski bulk and for massive fields the fall-off of the corresponding expectation value is exponential. Full article

The aim of this investigation was to scrutinize the effects of a thermal treatment on the electrostatic complex formed between gum arabic (GA) and ε-polylysine (ε-PL), with the goal of improving the antibacterial properties and reducing the hygroscopicity of ε-PL. The heated complex with a ratio of 1:4 exhibited an encapsulation efficiency of 93.3%. Additionally, it had an average particle size of 350.3 nm, a polydispersity index of 0.255, and a zeta potential of 18.9 mV. The formation of the electrostatic complex between GA and ε-PL was confirmed through multispectral analysis, which demonstrated the participation of hydrogen bonding and hydrophobic and electrostatic interactions, as well as the enhanced effect of heat treatment on these forces within the complex. The complex displayed a core-shell structure, with a regular distribution and a shape that was approximately spherical, as observed in the transmission electron microscopy images. Additionally, the heated GA–ε-PL electrostatic composite exhibited favorable antibacterial effects on Salmonella enterica and Listeria monocytogenes, with reduced minimum inhibitory concentrations (15.6 μg/mL and 62.5 μg/mL, respectively) and minimum bactericidal concentrations (31.3 μg/mL and 156.3 μg/mL, respectively) compared to free ε-PL or the unheated electrostatic composite. Moreover, the moisture absorption of ε-PL reduced from 92.6% to 15.0% in just 48 h after being incorporated with GA and subsequently subjected to heat. This research showed a way to improve the antibacterial efficiency and antihygroscopicity of ε-PL, reducing its application limitations as an antimicrobial substance to some extent. Full article

Alcohol is a dangerous substance causing global mortality and health issues, including mental health problems. Regular alcohol consumption can lead to depression, anxiety, cognitive decline, and increased risk of alcohol-related disorders. Thus, monitoring ethanol levels in biological samples could contribute to maintaining good health. Herein, we developed an electrochemical sensor for the determination of ethanol in human salivary samples. Initially, the tetra-chloroauric acid (HAuCl₄) was chemically reduced using sparfloxacin (Sp) which also served as a stabilizing agent for the gold nanoparticles (AuNPs). As-prepared Sp-AuNPs were comprehensively characterized and confirmed by UV-visible spectroscopy, X-ray diffraction, field emission scanning electron microscopy (FE-SEM), energy-dispersive X-ray spectroscopy (EDS), and elemental mapping analysis. The average particle size (~25 nm) and surface charge (negative) of Sp-AuNPs were determined by using dynamic light scattering (DLS) and Zeta potential measurements. An activated screen-printed carbon electrode (A-SPE) was modified using Sp-AuNPs dispersion, which exhibited greater electrocatalytic activity and sensitivity for ethanol (EtOH) oxidation in 0.1 M sodium hydroxide (NaOH) as studied by cyclic voltammetry (CV) and differential pulse voltammetry (DPV). DPV showed a linear response for EtOH from 25 µM to 350 µM with the lowest limit of detection (LOD) of 0.55 µM. Reproducibility and repeatability studies revealed that the Sp-AuNPs/A-SPEs were highly stable and very sensitive to EtOH detection. Additionally, the successful electrochemical determination of EtOH in a saliva sample was carried out. The recovery rate of EtOH spiked in the saliva sample was found to be 99.6%. Thus, the incorporation of Sp-AuNPs within sensors could provide new possibilities in the development of ethanol sensors with an improved level of precision and accuracy. Full article

Nanoencapsulation is widely considered as a highly effective strategy to enhance essential oils’ (EO) stability by protecting them from oxidative deterioration and evaporation. The present study aims to optimize and characterize an efficient technique for encapsulating Cinnamomum (C.) verum essential oil into chitosan nanoparticles using response surface methodology (RSM). Moreover, the optimized C. verum EO nanoparticle was investigated for its antibacterial (against Gram-positive and Gram-negative bacteria), antifungal (against Candida albicans), and antiparasitic activity (against Leishmania parasites). Five parameters were investigated using a Plackett–Burman and Box–Behnken statistical design: the chitosan molecular weight, TPP concentration, C. verum EO/chitosan ratio, mixing method, and the duration of the reaction. Encapsulation efficiency and anti-candida activity were considered as responses. The antibacterial, anticandidal, and anti-leishmanial activities were also assessed using a standard micro-broth dilution assay and the cytotoxicity assay was assessed against the macrophage cell line RAW 264.7. The optimized nanoparticles were characterized using Fourier transform infrared spectroscopy, Zeta potential, and scanning electron microscopy. The study results indicated that under optimal conditions, the nanoencapsulation of C. verum EO into chitosan nanoparticles resulted in an encapsulation efficiency of 92.58%, with a regular distribution, a nanoparticle size of 480 ± 14.55 nm, and a favorable Zeta potential of 35.64 ± 1.37 mV. The optimized C. verum EO/chitosan nanoparticles showed strong antifungal activity against C. albicans pathogens (CMI = 125 µg mL⁻¹), notable antibacterial activity against both Gram-positive and Gram-negative bacteria (ranging from 125 to 250 µg mL⁻¹), high leishmanicidal potential against the promastigotes form of L. tropica and L. major (IC50 = 10.47 and 15.09 µg mL⁻¹, respectively), and a four-fold cytotoxicity reduction compared to non-encapsulated essential oil. These results suggest that C. verum EO-loaded chitosan nanoparticles could be a promising delivery system for the treatment of cutaneous Candida albicans infections. Full article

A core–shell-derived structural magnetic zeolite imidazolate framework-67 (Fe₃O₄-COOH@ZIF-67) nanocomposite was fabricated through a single-step coating of zeolite imidazolate framework-67 on glutaric anhydride-functionalized Fe₃O₄ nanosphere for the magnetic solid-phase extraction (MSPE) of theophylline (TP). The Fe₃O₄-COOH@ZIF-67 nanocomposite was characterized through scanning electron microscopy, transmission electron microscopy, energy dispersive X-ray spectrometry, Fourier transform infrared spectroscopy, Zeta potential analysis, X-ray diffraction, Brunauer–Emmett–Teller, and vibrating sample magnetometer. The material has a high specific surface area and good magnetism, which maintains the regular dodecahedron structure of ZIF-67 without being destroyed by the addition of Fe₃O₄-COOH nanospheres. The Fe₃O₄-COOH@ZIF-67 can rapidly adsorb TP mainly through the strong coordination interaction between undercoordinated Co²⁺ on ZIF-67 and –NH from imidazole of TP. The adsorption and desorption conditions, such as the amount of adsorbent, adsorption time, pH value, and elution solvent, were optimized. The kinetics of TP adsorption on Fe₃O₄-COOH@ZIF-67 was found to follow pseudo-second-order kinetics. The Langmuir model fits the adsorption data well and the maximum adsorption capacity is 1764 mg/g. Finally, the developed MSPE-HPLC method was applied in the enrichment and analysis of TP in four tea samples and rabbit plasma. TP was not detected in oolong tea and rabbit plasma, and its contents in jasmine tea, black tea, and green tea are 5.80, 4.31, and 1.53 μg/g, respectively. The recoveries of spiked samples are between 74.41% and 86.07% with RSD in the range of 0.81–3.83%. The adsorption performance of Fe₃O₄-COOH@ZIF-67 nanocomposite was nearly unchanged after being stored at room temperature for at least 80 days and two consecutive adsorption–desorption cycles. The results demonstrate that Fe₃O₄-COOH@ZIF-67 nanocomposite is a promising magnetic adsorbent for the preconcentration of TP in complex samples. Full article

In order to improve the properties and characteristics of rose clay composites with acai, hydroxyapatite (HA), and nanosilica, the systems were mechanically treated. This treatment provides the preparation of better nanostructured composites with natural and synthetic nanomaterials with improved properties. The materials were characterized using XRD, nitrogen adsorption and desorption, particle sizing, zeta potential, and surface charge density measurements. For the systems tested in the aqueous media, the pH value of the point of zero charge (pH_PZC) ranges from 8 to 9.9. However, the isoelectric point (pH_IEP) values for all composites are below pH 2. This large difference between pH_PZC and pH_IEP is due to the complexity of the electrical double layer (EDL) and the relation of these points to different layers of the EDL. The tested samples as composite/electrolyte solutions are colloidally unstable. The toxicity level of the ingredients and release of anthocyanins as bioactive substances from acai in the composites were determined. The composites demonstrate an enhanced release of anthocyanins. There are some regularities in the characteristics depending on the type of components, morphology, and textural features of solids. The morphological, electrochemical, and structural characteristics of the components have changed in composites. The release of anthocyanins is greater for the composites characterized by minimal confined space effects in comparison with rose clay alone. The morphological, electrochemical, and structural characteristics allow us to expect high efficiency of composites as bioactive systems that are interesting for practical applications in cosmetics. Full article

This paper presents a theoretical calculation of the vacuum energy density by summing the contributions of all quantum fields’ vacuum states, which turns out to indicate that there seems to be a missing bosonic contribution in order to match the predictions of the current cosmological models and all observational data to date. The basis for this calculation is a new Zeta function regularization method used to tame the infinities present in the improper integrals of power functions. The paper also presents a few other contributions in the area of vacuum energy. Full article

In this paper, we study quantum relativistic features of a scalar field around the Rindler–Schwarzschild wormhole. First, we introduce this new class of spacetime, investigating some energy conditions and verifying their violation in a region nearby the wormhole throat, which means that the object must have an exotic energy in order to prevent its collapse. Then, we study the behavior of the massless scalar field in this spacetime and compute the effective potential by means of tortoise coordinates. We show that such a potential is attractive close to the throat and that it is traversable via quantum tunneling by massive particles with sufficiently low energies. The solution of the Klein–Gordon equation is obtained subsequently, showing that the energy spectrum of the field is subject to a constraint, which induces a decreasing oscillatory behavior. By imposing Dirichlet boundary conditions on a spherical shell in the neighborhood of the throat we can determine the particle energy levels, and we use this spectrum to calculate the quantum revival of the eigenstates. Finally, we compute the Casimir energy associated with the massless scalar field at zero temperature. We perform this calculation by means of the sum of the modes method. The zero-point energy is regularized using the Epstein–Hurwitz zeta-function. We also obtain an analytical expression for the Casimir force acting on the shell. Full article

Essential oils have unique functional properties, but their environmental sensitivity and poor water solubility limit their applications. Therefore, we encapsulated oregano essential oil (OEO) in chitosan nanoparticles (CSNPs) and used tripolyphosphate (TPP) as a cross-linking agent to produce oregano essential oil chitosan nanoparticles (OEO-CSNPs). The optimized conditions obtained using the Box–Behnken design were: a chitosan concentration of 1.63 mg/mL, TPP concentration of 1.27 mg/mL, and OEO concentration of 0.30%. The OEO-CSNPs had a particle size of 182.77 ± 4.83 nm, a polydispersity index (PDI) of 0.26 ± 0.01, a zeta potential of 40.53 ± 0.86 mV, and an encapsulation efficiency of 92.90%. The success of OEO encapsulation was confirmed by Fourier transform infrared spectroscopy (FT-IR) and thermogravimetric analysis (TGA). The scanning electron microscope (SEM) analysis showed that the OEO-CSNPs had a regular distribution and spherical shape. The in vitro release profile at pH = 7.4 showed an initial burst release followed by a sustained release of OEO. The antibacterial activity of OEO before and after encapsulation was measured using the agar disk diffusion method. In conclusion, OEO can be used as an antibacterial agent in future food processing and packaging applications because of its high biological activity and excellent stability when encapsulated. Full article

Magnetic nanoparticles (MNPs) are becoming important DNA nanocarriers for genetic engineering of industrial fungi. However, the biological effect of MNPs on industrial fungi remains unknown. In this study, we prepared three kinds of magnetic nanoparticles with different sizes (i.e., 10 nm, 20 nm, and 200 nm) to investigate their impact on the growth and sporulation of the important industrial fungus Aspergillus niger. Transmission electron microscopy, X-ray diffraction analysis and Zeta potential analysis revealed that the three kinds of MNPs, including MNP10, MNP20 and MNP200, had uniform size distribution, regular Fe₃O₄ X-ray diffraction (XRD) patterns and similar Zeta potentials. Interestingly, although the three kinds of MNPs did not obviously inhibit growth of the fungus, the MNP20 at 500 mg/L strongly attenuated sporulation, leading to a remarkable decrease in spore numbers on culturing plates. Further investigation showed that MNP20 at the high concentration led to drastic chitin accumulation in the cell wall, indicating cell wall disruption of the MNP20-treated fungal cells. Moreover, the MNPs did not cause unusual iron dissolution and reactive oxygen species (ROS) accumulation, and the addition of ferrous ion, ferric ion or the reactive oxygen species scavenger N-acetyl-L-cysteine (NAC) had no impact on the sporulation of the fungus, suggesting that both iron dissolution and ROS accumulation did not contribute to attenuated sporulation by MNP20. This study revealed the size-dependent effect of MNPs on fungal sporulation, which was associated with MNP-induced cell wall disruption. Full article

Dihydromyricetin (DHM) has garnered attention due to its promising antitumor activity, but its low bioavailability restricts its clinical application. Thus, developing nano-drug delivery systems could enhance its antitumor activity. We prepared DHM@ZIF-8 nanoparticles using the zeolite imidazole framework-8 (ZIF-8) as a carrier loaded with dihydromyricetin. A series of characterizations were performed, including morphology, particle size, zeta potential, X-single crystal diffraction, ultraviolet spectroscopy, infrared spectroscopy, and Brunauer–Emmett–Teller (BET). The in vitro release characteristics of DHM@ZIF-8 under pH = 5.0 and pH = 7.4 were studied using membrane dialysis. The antitumor activity and pro-apoptotic mechanism of DHM@ZIF-8 were investigated through CCK-8 assay, reactive oxygen species (ROS), Annexin V/PI double-staining, transmission electron microscopy, and Western blot. The results depicted that DHM@ZIF-8 possessed a regular morphology with a particle size of 211.07 ± 9.65 nm (PDI: 0.19 ± 0.06) and a Zeta potential of −28.77 ± 0.67 mV. The 24 h drug releasing rate in PBS solution at pH = 7.4 was 32.08% and at pH = 5.0 was 85.52% in a simulated tumor micro acid environment. DHM@ZIF-8 could significantly enhance the killing effect on HepG2 cells compared to the prodrug. It can effectively remove ROS from the tumor cells, promote apoptosis, and significantly affect the expression of apoptosis-related proteins within tumor cells. Full article

Microalgae peptides have many medical and industrial applications due to their functional properties. However, the rapid degradation of peptides not naturally present in biological samples represents a challenge. A strategy to increase microalgae peptide stability in biological samples is to use carriers to protect the active peptide and regulate its release. This study explores the use of gold nanoparticles (AuNPs) as carriers of the Chlorella microalgae peptide (VECYGPNRPQF). The potential of these peptide biomolecules as stabilizing agents to improve the colloidal stability of AuNPs in physiological environments is also discussed. Spectroscopic (UV-VIS, DLS) and Microscopic (TEM) analyses confirmed that the employed modification method produced spherical AuNPs by an average 15 nm diameter. Successful peptide capping of AuNPs was confirmed with TEM images and FTIR spectroscopy. The stability of the microalgae peptide increased when immobilized into the AuNPs surface, as confirmed by the observed thermal shifts in DSC and high zeta-potential values in the colloidal solution. By optimizing the synthesis of AuNPs and tracking the conferred chemical properties as AuNPs were modified with the peptide via various alternative methods, the synthesis of an effective peptide-based coating system for AuNPs and drug carriers was achieved. The microalgae peptide AuNPs showed lower ecotoxicity and better viability than the regular AuNPs. Full article