The purpose of the research is to investigate the unique solvability of a nonlocal boundary value problem for a loaded equation of parabolic-hyperbolic type in a special domain. Methods: Using representations of a general regular solution, the existence and uniqueness of the problem posed is proved. Results: A new method for proving the unique solvability of nonlocal boundary value problems for one loaded equation of mixed type in a special domain has been formed and developed. Conclusions: The obtained results make it possible to solve some problems of genetics, immunology, transonic gas dynamics and thermal physics, which are associated with displacement.

In this paper, the functional variable method is used to establish solitary wave solutions and periodic wave solutions of the loaded quadratic non-linear Klein-Gordon equation, the loaded cubic non-linear Klein-Gordon equation and the loaded coupled non-linear Klein-Gordon equation. All solutions of these equations have been examined and three dimensional graphics of the obtained solutions have been drawn by using the Matlab software. The main advantage of the proposed functional variable method over other methods is that it provides more new exact traveling wave solutions along with additional free parameters. The graphical representations of the soliton solutions and the periodic wave solutions by using distinct values of random parameter are demonstrated to better understand their physical features. The exact solutions have its great importance to reveal the internal mechanism of the physical phenomena.

Phyllanthus emblica (P. emblica) has been described in many studies to have multiple therapeutic activities and is considered an important part of Ayurvedic and Unani medicinal systems. This study successfully synthesized P. emblica loaded polyvinylalcohol/gelatin based cryogels (PVA/Gel/P.emblica) to examine their potential in wound dressing applications. Swelling tests, Brunauer-Emmett-Teller (BET) and morphology analysis were conducted within the scope of characterization studies. In vitro cell culture studies were performed using HaCaT cells to illustrate the suitability of the synthesized cryogels as wound dressing material. The swelling tests and BET analysis results showed that swelling and surface area properties of cryogels increased with increasing P. emblica amounts. Morphological results displayed that the cryogels had a dense, interconnected pore morphology and a macroporous structure. 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT), trypan blue exclusion and live-dead assay results revealed that adding of P. emblica into cryogels led to enhanced cell proliferation, increased cell number, and improved cell viability. Based on the phase contrast microscope, scanning electron microscope (SEM), immunofluorescence and giemsa staining images, it was observed that P. emblica promoted cell attachment, proliferation and penetration. In conclusion, it has been shown that PVA/Gel/P.emblica cryogels are suitable for use as wound dressing materials and can be developed with further studies.

Periodontitis is a chronic inflammatory disease which results in the destruction of the tooth’ s supporting tissues and the alveolar bone resorption. The complement becomes a major link between infection and inflammatory pathology including periodontitis. Gingipians as important virulence factors of P. gingivalis have the activity of C5 convertase, could cleave C5 into fully functional C5a to activate C5aR. The above process could be blocked by the C5aR antagonist (PMX-53) to suppress local periodontal inflammation, and then achieves the purpose of treatment of periodontitis. Nanoparticles incorporated within gelatin are promising carrier system for drug delivery in recent years. This study aimed to investigate whether gelatin nanoparticles loaded with PMX-53 prevents alveolar bone resorption in miniature swines model of periodontitis. Four miniature swines were placed ligatures around the maxillary and mandibular fourth premolar and first molar on both sides for seven weeks to induce periodontitis. Then, animals were assigned randomly to four groups: minocycline-treated group, gelatin with PMX53-treated group, gelatin-treated group and a sham control group. They were treated with 1ml related drugs respectively, into gingival sulcusl for 4 times at one-week intervals. We showed that local treatments with gelatin nanoparticles loaded with PMX-53 could inhibit alveolar bone loss of periodontitis. Our study revealed that gelatin nanoparticles loaded with PMX-53 prevented alveolar bone resorption miniature swines model of periodontitis. In addition, provided proof-of-concept for local targeting of gelatin nanoparticles loaded with PMX-53 as a powerful candidate for the treatment of periodontitis.

For the last two decades, an increasing demand for low-cost adsorbents for drinking water treatment has been challenged in the rural areas of developing countries that have problems with arsenic (As) contamination. In this work, spent bleaching earth (SBE), a residual material that is formed during the process of refining vegetable oil, has been utilized to prepare the new magnetic adsorbent Fe-SBE/C by modifying its surface area through calcination and co-precipitation with iron. The experimental results demonstrate that Fe-SBE/C exhibits a substantial adsorption capacity towards both arsenite (As(III)) and arsenate (As(V)). Optimal pH conditions were found to be pH 10 for As(III) and pH 3 for As(V), resulting in adsorption percentages of 76.7% and 94.1%, respectively. Other experimental parameters such as calcination conditions, adsorbent dosage, iron-loading ratio, and the presence of co-existing ions were thoroughly investigated. The kinetic study revealed that the adsorption processes follow the Elovich and intraparticle diffusion models, suggesting a combined adsorption mechanism of boundary layer control and chemisorption. Furthermore, the isotherm followed the Langmuir model with a maximum adsorption capacity of 202.61 μg g-1 for As(III) and 187.61 μg g-1 for As(V). Through thermodynamic analysis and reinforcement by activation energy data, this research validates that the observed adsorption process is indicative through chemisorption. The regeneration study revealed the potential for multiple cycles of arsenic removal, highlighting the practical applicability of Fe-SBE/C in environmental contexts. In conclusion, the findings of this study underscore the efficacy of Fe-SBE/C in arsenic removal and present it as a promising and environmentally friendly solution for mitigating arsenic pollution.

Today, polymeric Drug Delivery Systems (DDS) appear as an interesting solution against bacterial resistance, having great advantages such as low toxicity, biocompatibility, and biodegradability. In this work, two polyketones (PK) have been post-functionalized with taurinate (PKT) or sulfanilate (PKSK) and employed as biocompatible carriers for Vancomycin against bacterial infections. Mod-ified PKs were easily prepared by Paal-Knorr reaction and loaded with Vancomycin at variable pH. All polymers were characterized by FT-IR, DSC, TGA, SEM and elemental analysis. Antimicrobial activity was tested against Gram positive Staphylococcus aureus ATCC 25923 and correlated to the different pH used for its loading (between 2.3 and 8.8). Distinctively, minimum inhibitory con-centrations achieved with PKT and PKSK loaded with Vancomycin are similar, 0.23μg/mL and 0.24μg/mL respectively, i.e. six times lower that Vancomycin alone. The use of post-functionalized aliphatic polyketones has thus been demonstrated to be a promising way to obtain very efficient polymeric DDS.

By introducing environmental mediator, for avoiding randomness in selecting indicators and subjectivity in deciding interaction path coefficients to reveal interaction mechanism among forest industry, ecology and environmental capacity, structural Pressure–State–Impact–Response (PSIR) and quantitative Structural Equation Modeling (SEM) are utilized with data on thirty–one provinces of China. We can find that: (i) forest industry has a negative influence on ecology, whereas ecology has a positive influence on industry; (ii) the destructive influence that industry has on ecology is much greater than the positive effect ecology has on industry; and (iii) environmental capacity plays a partial mediating role between industry and ecology. According to these results we can conclude that: (i) forest industry and ecology are not in a symbiotic relationship and have not reached a level of ecological security; (ii) the interaction between industry and ecology is in a period of transition from antagonistic to beneficial; and (iii) industry dominates ecology. However, we prospect the following advice: (i) methods of forest industry should be changed; (ii) new modes of industrial integration and circular economy should be developed; and (iii) the ability of the environment to sustain itself should be enhanced. The level of forest ecological security to discuss the symbiotic mechanism of industry and ecology will propose to be measured in future.

Calcium sulphate (CS) is currently used as a bioabsorbable, completely synthetic and sterile material in the management of infected tissues and dead spaces (DS) mainly resulting from surgical procedures. Residual DS in the postoperative, may create an environment where hematomas fill up and bacteria can proliferate, leading to a high incidence of postoperative infections. Considering the available reviews in the literature, CS has been mainly studied in orthopedic surgery mostly giving brilliant results and low complication rates. Nowadays, orthopedists avail it in the form of pearls both as a bone void filler and as an “off-label” delivery agent for antibiotics in arthroplasty, chronic osteomyelitis and open fractures, paving the way of its application in many other contexts given its natural dis-position to biodegradation. In the last years, CS beads have been gaining ground in the general, vascular and endocrinological surgical specialties. Despite its clear potential and the increasing number of scientific evidences on the safety and effectiveness of CS application in the prophylaxis and treatment of infections, there are not many studies reporting on its application in fields other than orthopedics, with a substantial paucity in plastic and reconstructive surgery literature. This is some-how surprising, since reconstructive surgery often deals with complex wounds secondary to bone and soft tissue exposure, suture dehiscence, trauma, and surgical site infections. As far as we know this is the first updated systematic review assessing the state of the art, indications and new perspectives on the application of CS beads in plastic and reconstructive surgery.

The fractional advection-dispersion equation FADE plays an important role, especially in explaining the process of solute-transport in natural porous media with different degrees of heterogeneity. However, studies of the flow and transport of contaminants in the underground environment are based on the knowledge of many functional parameters of the subsoil. The delay factor caused by nonlinear absorption is one of these parameters inheriting significant ambiguities in its estimation in heterogeneous media. In the study, a fractional advection-dispersion FADE model was developed by the implicit Euler method, based on a Grunwald and Caputo-Liousville approximation to explicitly evaluate and simulate the transport mechanism of contaminants in media with unsaturated porous materials subjected to a nonlinear sorption model. Better solute mass retention was observed for fractional advection-dispersion FADE model. Moreover, the absorption parameter of the retardation coefficient has a better impact on the motion of the solute in a saturated porous medium. In other words, it has a significant effect on the dispersion of pollutants in aquifers. This study highlights the need to characterize the aquifer to predict solute transport in porous media.

Inverse Sumudu transform multiple shifting properties are used to design methodology for solving ordinary differential equations. Then algorithm applied to solve Whittaker and Zettl equations to get their new exact solutions and profiles which shown through Maple complex graphicals. Table of inverse Sumudu transforms for elementary functions given for supporting the differential equations solving using inverse Sumudu transform.

We developed an ovarian cancer-targeted drug delivery system based on a follicle-stimulating hormone receptor (FSHR) peptide. The lipophilic chemotherapeutic drug SN38 and the photosensitizer IR820 were loaded into the phospholipid bilayer of liposomes. Near-infrared laser irradiation stimulated the generation of reactive oxygen species, causing short-term reactive molecular species and spatial-temporal restricted photodamage to the biological targets. The reactive molecular species and spatial-temporal restricted photodamage enhanced the release and uptake of chemotherapy drugs and increased the sensitivity to chemotherapy drugs in ovarian cancer cells. FSH liposomes loaded with SN38 and IR820 (SN38/IR820-Lipo@FSH) were prepared using thin-film hydration-sonication. FSH peptide binding was analyzed using 1H NMR spectrum and Maldi-Tof. The average size and zeta potential of SN38/IR820-Lipo@FSH were 105.1 ± 1.15 nm (PDI: 0.204 ± 0.03) and −27.8 ± 0.42 mV, respectively. SN38/IR820-Lipo@FSH exhibited good drug-loading properties and the in vitro release was slow. FSH significantly increased the uptake of liposomes, inhibited cell proliferation, and induced apoptosis in A2780 cells. Moreover, SN38/IR820-Lipo@FSH exhibited good tumor-targeting ability and anti-ovarian cancer activity in vivo. The SN38/IR820-Lipo@FSH exhibited specific targeting to A2780 ovarian cancer cells. The combination of chemotherapy and photodynamic treatment based on an FSH peptide-targeted delivery system may be an effective approach to treating ovarian cancer.

Management of chronic inflammation and wounds has always been a key issue in the pharmaceutical and healthcare sector. Curcumin (CCM) is an active ingredient extracted from turmeric rhizomes that has antioxidant, anti-inflammatory, and antibacterial activities, thus showing significant effectiveness toward wound healing. However, its shortcomings such as poor water solubility, poor chemical stability and fast metabolic rate limit its bioavailability and long-term use. In this context, hydrogels appear to be a versatile matrix for carrying and stabilizing drugs due to the biomimetic structure, soft porous microarchitecture, and pleasant biomechanical properties. The drug loading/releasing efficiencies can also be controlled by use of highly crystalline and porous metal organic frameworks (MOFs). Here, a flexible hydrogel composed of sodium alginate (SA) matrix and CCM-loaded MOFs was constructed for long-term drug release and antibacterial activity. The morphology and physicochemical properties of composite hydrogels were analyzed by scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FT-IR), X-ray diffraction (XRD), ultraviolet visible spectroscopy (UV-Vis), Raman spectroscopy and mechanical property tests. The results showed that the composite hydrogel was highly twistable and bendable to mechanically comply with human skin. The as-prepared hydrogel could capture efficient CCM for slow drug release as well as effective killing of bacteria. Therefore, such composite hydrogel is expected to provide a new management system for chronic wound dressings.

By using Modified simple equation method, we study the Cahn Allen equation which arises in many scientific applications such as mathematical biology, quantum mechanics and plasma physics. As a result, the existence of solitary wave solutions of the Cahn Allen equation is obtained. Exact explicit solutions interms of hyperbolic solutions of the associated Cahn Allen equation are characterized with some free parameters. Finally, the variety of structure and graphical representation make the dynamics of the equations visible and provides the mathematical foundation in mathematical biology, quantum mechanics and plasma physics.

In this paper, we consider a fourth-order suspension bridge equation with nonlinear damping term |u_t|^m-2u_t and source term |u|^p-2u. We give necessary and sufficient condition for global existence and energy decay results without considering the relation between m and p. Moreover, when p>m, we give sufficient condition for finite time blow-up of solutions. The lower bound of the blow-up time T_max is also established. It worth to mention that our obtained results extend the recent results of Wang (J. Math. Anal. Appl., 2014) to the nonlinear damping case.

The stability properties of the Hill equation are discussed, and especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu equation for a trapped ion are characterized by using the Floquet theory and Hill's Method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters $a$ and $q$ that are real. Characteristic curves are introduced naturally by the Sturm-Liouville problem for the well known even and odd Mathieu equations $ce_m(z,q)$ and $se_m(z,q)$. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for axial and radial motion. In case of a Paul trap the stable solution corresponds to a superposition of harmonic motions. The problem of evaluating the maximum amplitudes of stable oscillations for the ideal conditions (taken into consideration) is also approached. Anharmonic corrections are discussed within the frame of the perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter. The results apply to 2D and 3D ion traps used for different applications in quantum engineering, among which optical clocks, quantum logic and quantum metrology, but not restricted only to these.

Preventing the occurrence of secondary caries serves as one of the significant issues in dental clinic, thus make it indispensable to improving the properties of conventional composite resin (CR) by developing a novel CR. In present study, two groups of experimental CRs loaded with different contents of fluoride-doped nano-zirconia fillers (25 wt% and 50 wt%) were fabricated. The surface topography, mechanical performance, fluoride release, antibacterial effect, aging property and cytotoxicity of the experimental CRs were evaluated subsequently. A uniform distribution of the F-zirconia fillers over the whole surface of resin matrix could be observed. The experimental CRs showed continuous fluoride release within 28 days, which was positively correlated with the content of F-zirconia fillers. Moreover, the amount of fluoride release increased in the acidic buffer. Addition of F-zirconia fillers could improve the color stability, wear resistance and microhardness of the experimental CRs, without reducing the flexure strength. Furtherly, the fluoride ions released continuously from the experimental CRs resulted in effective contact and antibacterial properties, while they showed no cytotoxicity. As a consequence, considerations can be made to employ this new kind of composite resin loaded with fluoride-doped nano-zirconia fillers to meet clinical requirements when the antimicrobial benefits are desired.

A typical halogen-free flame-retardant (HFFR) formulation for electric cables may contain polymers, various additives, and fire-retardant fillers. In this study, composites are prepared by mixing natural magnesium hydroxide (n-MDH) with linear low-density polyethylene (LLDPE) and a few types of ethylene-octene copolymers (C₈-POE). Depending on the content of LLDPE and C₈-POE, we obtained composites with different crystallinity that affected the final mechanical properties. The nucleation effect of the n-MDH and the variations in crystallinity caused by the blending of C₈-POE/LLDPE/n-MDH were investigated. In the C₈-POE/LLDPE blend, we found a decrease in the crystallization temperature of LLPDE compared to pure LLDPE and an increase in the crystallization temperature of C₈-POE compared to pure C₈-POE. On the contrary, the addition of n-MDH led to an increase in the crystallization temperature of LLDPE. As expected, the increase in the crystallinity of the polyolefin matrix of composites led to higher elastic modulus, higher tensile strength, and lower elongation at break. Overall, these results show how to obtain the required mechanical features for halogen-free flame-retardant compounds for electric cable applications depending on the quantities of the two miscible components in the final blend.

In this work, zinc oxide (ZnO)/ granular activated carbon (GAC) composites at different ZnO concentration (0.25M-ZnO@GAC, 0.5M-ZnO@GAC, and 0.75M-ZnO@GAC) were prepared by an in-situ hydrothermal method and demonstrated synergistic photocatalytic degradation and ad-sorption of Rhodamine B (RhB). The thermal stability, morphological structure, elemental com-position, crystallographic structure, and textural properties of developed catalysts were charac-terized by thermal gravimetric analysis (TGA/DTG), scanning electron microscopy equipped with energy dispersive-x-ray (SEM-EDS), x-ray diffraction (XRD), and Brunauer–Emmett–Teller (BET) analysis. Successful loading of ZnO onto GAC was confirmed by SEM-EDS and XRD analysis. The BET surface areas of GAC, 0.25M-ZnO@GAC, 0.5M-ZnO@GAC, and 0.75M-ZnO@GAC were 474 m2/g, 450 m2/g, 453 m2/g, and 421 m2/g, respectively. The decrease in GAC could be attributed to the successful loading of ZnO on the GAC surface. Notably, 0.5M-ZnO@GAC exhibited the best photocatalytic degradation efficiency of 82% and 97% under UV-A and UV-C light over 120 min, attributed to improved crystallinity and visible light absorption. The photocatalytic degradation parameters revealed that lowering the RhB concentration, raising the catalyst dosage and pH be-yond the point of zero charge (PZC) would favor the RhB degradation. Photocatalytic reusability was demonstrated over 5 cycles. Scavenger tests revealed that the hydroxyl radicals (•OH), su-peroxide radicals (O2−•), and photoinduced hole (h+) radicals play a major role during the RhB degradation process. Based on the TOC results, the RhB mineralization efficiency of 79.1% was achieved by 0.5M-ZnO@GAC. Additionally, GAC exhibited a strong adsorptive performance towards RhB with adsorption capacity and RhB removal of 487.1 mg/g and 99.5% achieved within 90 min equilibrium time. The adsorption characteristics were best described by pseu-do-second-order kinetics, suggesting chemical adsorption. This research offers a new strategy for the development of effective photocatalyst materials with potential for wider wastewater treat-ment applications.

Modern physics is situated on the fine line between scientific research and an attempt to answer metaphysical questions. Contemporary scholars such as Henry Stapp and Roger Penrose attempt to create an ontological interpretation of Schrödinger's equation in superposition state and its reduction or collapse to classical state. In this short essay I will try to explore how Immanuel Kant's metaphysics and the concept of noumena can be possibly integrated with quantum physics and Schrödinger's equation.

To improve efficacy and safety of sunscreen emulsions, UV‐filter skin permeation could be kept as low as possible by reducing UV‐filter content or changing emulsion composition. In this work, different lipid phase ratio (12, 14 and 16% w/w) were assessed for their ability to affect the technological and sensory properties of O/W emulsions in which bemotrizinol (BMTZ), a broad spectrum sunscreen agent, was incorporated free or loaded into nanostructured lipid nanocarriers (NLC) to reduce its release from the vehicle and, hence, its skin permeation. The following technological properties were evaluated in vitro by suitable methodologies: spreadability, viscosity, pH, occlusion factor, BMTZ release, sun protection factor (SPF). Sensory attributes were assessed by trained panelists in three different phases: before/during pick‐up, rub‐in, after application. Raising the lipid phase ratio led to an increase of viscosity and to a corresponding drop of spreadability while the incorporation of BMTZ‐loaded NLC determined a decrease of occlusion factor and an increase of SPF. No BMTZ release was observed from all emulsions. Sensory attributes were mainly affected by lipid phase ratio. These results suggest that lipid phase ratio and BMTZ incorporation into NLC could contribute to determine technological and sensory properties of O/W emulsions.

We apply utilized the extended form of the auxiliary equation method to obtain extensively reliable exact travelling wave solutions of perturbed Gerdjikov–Ivanov equation (GIE) that is widely used as a model in the field theory of quanta and non-linear optics. The method is based on a simple first order second degree ODE. The new form of the approach gives more solutions to the governing equation efficiently.

This paper deals with miniaturization technique based on frequency reduction using top loaded dielectric discs. In contrast to a simple monopole, the resonant frequency of monopole loaded with two dielectric discs changes from 1.98 to 1.29 GHz, resulting 34.84% reduction in resonant frequency keeping the antenna length (36.00 mm) unaltered. It is well-known fact that dielectric material can trap the energy to be delivered from source to antenna and as a result, it is unable to radiate efficiently. Then any approach to use the dielectric material for miniaturization process must, therefore, antenna coupled in such a way that it can radiate efficiently. The dielectric disc on top of monopole creates an inductive situation in a similar way to oppositely directed wire loop compensate the capacitive effect present at monopole causes the reduction in resonant frequency. This concept is implemented without sacrificing any desired features like bandwidth, radiation characteristics and efficiency (more than 98%) and analyzed with an equivalent circuit model. Experimental results illustrate good agreement with simulation results. This monopole antenna in car can be designed for GPS system, car to car communication, GSM or CDMA operation.

A proof is given showing the Collatz Conjecture is true for all positive integers. The proof was possible once the perspective of the proof was changed from looking at the pattern of the positive integers to looking at the conjecture rules. The conjecture rule for even numbers organizes all positive integers into unique sets and the rule for odd numbers interconnects the unique sets into dendritic pathways to “1.” Infinite loops, other than the minor 4-2-1 loop after reaching “1,” and pathways to infinity are shown to be mathematically impossible. The proof predicted a general equation that shows all positive integers ultimately reach a final value of “1," and calculates the values and locations of the odd positive integers during the iterations for each tested positive integer.

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an electron wave in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.

P-band radar remote sensing applied during the Airborne Microwave Observatory of Subcanopy and Subsurface (AirMOSS) mission has shown great potential for estimation of root zone soil moisture. When retrieving the soil moisture profile (SMP) from P-band radar, a mathematical function describing the vertical moisture distribution is required. Because only a limited number of observations are available, the number of free parameters of the mathematical model must not exceed the number of observed data. For example, a second order polynomial that contains 3 free parameters was presumed based on in-situ SMP data. The polynomial is currently parameterized based on 3 backscatter observations provided by AirMOSS (i.e. one frequency at three polarizations of HH, VV and HV). In this paper, a more realistic, physically-based SMP model containing 3 free parameters is derived based on a solution to Richards’ equation for unsaturated flow in soils. Evaluation of the new SMP model based on both numerical simulations and measured data revealed that it exhibits greater flexibility for fitting measured and simulated SMPs than the currently applied polynomial. It is also demonstrated that the new SMP model can be reduced to a second order polynomial at the expense of fitting accuracy.

The study aimed to analyze thoracic and lumbar erector spinae muscle activations during 3D elongation exercises in individuals with adolescent idiopathic scoliosis (AIS). Participants included 24 adolescents, meeting specific criteria such as a Cobb angle between 10° and 20°, and not having undergone surgical or brace treatments. EMG data were collected to evaluate muscle activations. The study found no significant interaction between exercise type and the side of the curve, but a significant main effect of exercise type on muscle activation, irrespective of Cobb angle. Different exercise types significantly affected muscle activity, with the highest activations in the TheraBand exercise, followed by manual and without equipment conditions. This suggests that exercise type significantly impacts muscle engagement in AIS patients, providing valuable insights for targeted exercise program design. The study, however, focused on short-term muscle activation, not long-term Cobb angle progression, pointing to the need for further research in this area.

Tryptanthrin has not been widely applied in clinical practice due to its poor solubility and low bioavailability in spite of possessing several biological and pharmacological activities. Here, to improve the solubility of tryptanthrin, two types of novel tryptanthrin-loaded micelles were prepared. One was tryptanthrin physically encapsulated by distearoyl phosphatidylethanolamine polyethylene glycol (DSPE-PEG) and the other was pegylated tryptanthrin synthesized by acid-sensitive hydrazone bond and further prepared as micelles. Molecular imprinting technology was used to separate pegylated tryptanthrin and free mPEG-COOH in the preparation of PEGylated tryptanthrin micelles with considerably high separation efficiency. The solubility of tryptanthrin-loaded DSPE-PEG micelles (TDMs) and PEGylated tryptanthrin micelles (PTMs) was increased by 300 and 1493 fold compared with that of tryptanthrin, respectively. The PTMs increased the solubility of tryptanthrin more effectively and 95% of tryptanthrin was released from PTMs at pH 5.5 in 12 h. The cytotoxicity of PTMs decreased under physiological conditions compared with that of tryptanthrin, whereas at pH 5.5, the PTMs showed comparable cytotoxicity with that of tryptanthrin, indicating successful drug release from the carrier in response to tumor cell pH. Overall, we elucidated an efficient method to improve water solubility of tryptanthrin and indicated pegylated tryptanthrin is a promising prodrug.

The fast-paced evolution of artificial intelligence (AI), machine learning (ML), natural language processing (NLP), large language model (LLM) applications, and generative pre-trained transformer (GPT) have set the stage for improved and autonomous project scheduling models. This study demonstrates how project scheduling can be enhanced by employing building information modeling (BIM) to predict reliable schedules for each project element. The research is based on design science research (DSR) methodology and focus group discussion. The proposed system consists of six components: project analyzer, data warehouse, activity identifier and sequencing, activity magnitude and direct cost calculator, activity duration calculator, and schedule analyzer. Unlike other solutions, the proposed solution sequences activities based on an ML model rather than constraint matrices. The proposed solution thus enhances project performance through proactive planning and risk management. Integrating the autonomous project scheduling solution with the other components of an autonomous project management system would surmount schedule challenges and would result in greater cost efficiency and fewer delays.

Current physiology attributes the mechanism of membrane potential generation to transmembrane ion transport, but ion adsorption could just as well play this fundamental role. The evidence shows that the ion adsorption mechanism accurately reproduces the experimentally measured membrane potential. The Goldman-Hodgkin-Katz equation (GHK eq.) and the Nernst equation (Nernst eq.) are the typical mathematical formulas representing the membrane potential in current physiology. However, the authors were able to show that the potential formulas by ion adsorption mechanism give identical results to GHK eq. and Nernst. eq. Our experimental and theoretical analyses suggest that there is a special relationship between the membrane potential and the membrane surface charge density, and this unique equation inevitably leads to the establishment of a GHK eq and/or a Nernst eq. The authors found that the unique equation is the foundation of thermodynamics “Boltzmann distribution”. Thus, the GHK eq. and the Nernst eq. are simply the natural consequence of thermodynamics from the view of the ion adsorption mechanism.

In this paper, we revisit the two theoretical approaches for the formulation of the tachyonic Dirac equation. The first approach works within the theory of restricted relativity, starting from a Lorentz invariant Lagrangian consistent with a spacelike four-momentum. The second approach uses the theory of relativity extended to superluminal motions and works directly on the ordinary Dirac equation through superluminal Lorentz transformations. The equations resulting from the two approaches show mostly different, if not opposite, properties. In particular, the first equation violates the invariance under the action of the parity and charge conjugation operations. Although it is a good mathematical tool to describe the dynamics of a space-like particle, it also shows that the mean particle velocity is subluminal. In contrast, the second equation is invariant under the action of parity and charge conjugation symmetries, but the particle it describes is consistent with the classical dynamics of a tachyon. This study shows that it is not possible with the currently available theories to formulate a covariant equation that coherently describes the neutrino in the framework of the physics of tachyons, and depending on the experiment, one equation rather than the other should be used.

The effects on Raychaudhuri's equation of an intrinsically discrete or particle nature of spacetime are investigated, through consideration of null congruences emerging from, or converging to, a generic point of spacetime, i.e. in geometric circumstances somehow prototypical of singularity issues. This is done from an effective point of view, meaning through a (continuous) description of spacetime modified to embody the existence of an intrinsic discreteness on the small scale, adding to previous results for non-null congruences. Various expressions for the effective rate of change of expansion are derived. They in particular provide finite values for the limiting effective expansion and its rate of variation when approaching the focal point; this on top of resulting non vanishing the limiting cross-sectional area itself of the congruence.

The production, processing of agricultural products results in massive generation of waste, which has an environmental impact. In current study on the node of valorisation of the processed waste, orange and banana peel waste are utilized for the production of biscuits. The fortified biscuits were analysed for proximate and sensory analysis. The fibre content of the fortified biscuits increases several folds. From the sensory score the proportion of biscuits with 7.5% and 10% has undesirable quality parameters, whereas up to 5% concentration all the parameters are more desirable. Fortifying biscuits with orange and banana peel powder may be an excellent source of dietary fibre and an enhanced valorisation technique.

In this paper, I investigate Hyers-Ulam-Rassias stabilities of the general quintic functional equation and the general sextic functional equation.

The design of multifunctional microcarriers has attracted significant attention because they combine various functions within a single system. In this study, we developed a set of multi-layered hydrogel microcarriers, which were first loaded with chemotherapeutic curcumin (CUR), then using the layer-by-layer (LbL) technique, coated through a polyelectrolyte shell consisting of chitosan (CHIT) or poly(allylamine hydrochloride) (PAH). As an outer layer with antimicrobial function, newly synthesised alkylene quaternary ammonium salt functionalised polyelectrolytes (A-QAS-PEs) were applied. For this purpose, poly(acrylic acid) (PAA) was decorated with dif-ferent hydrophobic side chains (n-hexane and n-dodecane side entities) and different degrees of substitution (m) of quaternary ammonium groups (abbreviated as PAA-C(O)O-(CH2)n-N+(CH3)3(m); n=6,12; m=8-14%). The grafting approach of PAA with the al-kylene quaternary ammonium salt moiety was performed under mild reaction conditions using Steglich esterification followed by quaternisation. The structure of antimicrobial decorated PAA was confirmed by 1H NMR and FTIR, and the mean diameter of all multifunctional microparticles was characterised by SEM. The viscoelastic properties of the functional layers were studied using QCM-D. The release of CUR from the microcarriers was described using a hybrid model, i.e., a combination of first-order kinetics and the Korsmeyer-Peppas model. The antimicrobial activity of functionalised PAA and multilayered CUR-loaded hydrogel microcarriers with quaternary am-monium function was assessed against Staphylococcus aureus and Serratia marcescens by the agar diffusion assay method. Only a limited inhibition zone of PAA was observed, but in the case of both antimicrobial decorated PAA and the corresponding multilayered nanocarriers, the inhibi-tory activity increase was achieved against both strains of bacteria.

An adequate representation of the water infiltration process in the soil allows improving the efficiency in application and the uniformity in surface irrigation. The Green and Ampt model has shown a good representation of the process, and researchers from the United States Department of Agriculture (USDA) determined the values of their parameters for soils of that country, which are shown in tables or through functional relationships and this information is used as reference in several parts of the world, although there is no certainty that they are representative of the soils in Mexico. In this study, the parameters of the Green & Ampt equation were determined and evaluated in some soils of agricultural importance in Mexico. The parameters were obtained in four ways: one of them applied a methodology adapted from Brooks and Corey to quantify the wetting front capillary pressure head and used an permeameter under constant hydraulic head to determine the saturated hydraulic conductivity, and the other three consisted in taking them from three studies reported by the USDA. The values of the parameters suggested in Mexico drastically underestimated the results with relative errors (RE) in a range of -49.0 to -94.0% and the most representative were those obtained with the methodology proposed in this research with RE of -15.0 to 6.0%.

Defining integrals over volume element in curved spacetime together with the mass and energy densities within that region of spacetime is apparently equivalent to the given energy and mass of that body or particle. With this in mind equations involving energies and mass can be rewritten in terms of their densities and the integral over the volume element. The idea find its place in the Hamiltonian formulations, and can be carried over into quantum mechanical frameworks systematically accounting for the effect of spacetime volume structures and gravity on dynamics of quantum systems. This article briefly explores this concept and runs through various frameworks and equations relevant to this idea, particularly the schrodinger-Newton equation and discusses the cosmological constant as a vacuum energy density.

In this paper, we introduce a way of representing a given mapping as the sum of odd and even mappings. Then, by using this representation, we investigate the stability of various forms for the general nonic functional equation.

Electrically charged particles such as Electrons and Protons carry electric, E, and magnetic, B, fields. In addition to these fields, Quantum Mechanics (QM) endows these particles with an `arcane and spooky' field --- the wavefunction. This wavefunction of QM is not only assumed to be separate but distinct from the electromagnetic field. We herein upend this view by demonstrating otherwise. That is, we demonstrate that the four components of the Dirac wavefunction, can be shown to not only be an intimate, but, a direct function of the electromagnetic field carried by the particle in question. Insofar as unity, depth in our understanding and insight into both Dirac and Maxwell's equations as major pillars of Modern Physics, we believe that this work may very well inch us one-step-closer to the truth.

A combination of Poloxamer 407 (P407) and hydroxypropyl methylcellulose (HPMC) hydrosols is proposed as an in situ thermo-gelling vehicle for the nasal drug delivery of chlorhexidine-silver nanoparticles conjugates (SN-CX). Varying ratios of P407 and HPMC were applied in the presence and absence of SN-CX in order to optimize the gelation temperature (Tg) to values close to the physiological nasal such (30–34°C). Mechanisms for the observed gelation phenomena were suggested based on viscosimetry, texture analysis, and dynamic light scattering. Tests were carried out for sprayability, washout time, in vitro drug release, ex vivo permeation, and antimicrobial activity. When applied separately, HPMC was found to lower the P407 gelation temperature, whereas SN-CX increased it. However, in the presence of HPMC, SN-CX interfered with the P407 micellar organization in a principally contrasting way, while leading to an even further decrease in Tg. SN-CX-loaded nasal formulation composed of P407 16% and HPMC 0.1% demonstrated a desired gelation at 31.9 °C, good sprayability (52.95% coverage of the anterior nasal cavity), mucoadhesion for 70 min under simulated nasal clearance, expedient release and permeation, and preserved anti-infective activity against seasonal Influenza virus and beta-coronavirus, Pseudomonas aeruginosa, Klebsiella pneumoniae, Staphylococcus aureus and other pathogens. Our findings suggest that the current development could be considered a potential formulation of a protective nasal spray against respiratory infections.

In this short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

Maxwell equation for the electric field has been solved for any medium by suggesting the wavenumber and angular frequency be complex quantities. This accounts for the field decay by interaction with the medium.This expression for the time and special decay of the electric field in a medium is used to construct a new wave function sensitive to the medium physical properties. This new wave function, unlike the conventional one, differentiates between a beam of particles in a vacuum and that enters a medium which is an attenuated due to the scattering effect.Another expression for time decaying electric field was obtained using Newton’s laws for frictional medium. This expression shows that the electric field diminishes due to friction.Fortunately, this time decaying part of the electric field is typical to that derived from Maxwell’s equations. Finally, a new Schrodinger equation sensitive to the medium properties was derived. This equation, fortunately, describes some scattering processes for Protein scattering, scattering of x-rays, opto-acoustic phonons, and Raman scattering for some materials successfully .

Keywords: FTY720, self-assembled nanoparticles, intracerebral hemorrhage, neuroprotection

The SBA-15 loaded with methylene blue was successfully prepared by sample adsorption of methylene blue in SBA-15 and is characterized by an XRD, SEM, FTIR, and BET. The photocatalytic activity for methyl orange (MO) degradation was investigated under visible light irradiation under LEDs. Experimental results demonstrate that the SBA-15-MB exhibited higher photocatalytic activity than SBA-15 under visible light irradiation. The degradation efficiency of MO (50 ppm) by SBA-15-MB could reach 80% within 180 min under 25W LED visible light. The photocatalytic activity of SBA-15 could be attributed to the excitation of methylene blue by visible light, the transfer of electrons from methylene blue to SBA-15, and the production of radicals at the surface of SBA-15.

Proposed in 1889 by Svante Arrhenius, the Arrhenius equation is an important result in physical chemistry which aims to find the relationship between temperature and reaction rates. It is also an essential equation for analytic chemistry which helps to determine the energy barrier for a given reaction. In this article, we will go through a detailed derivation of the exponential factor in the Arrhenius Equation based on the Boltzmann distribution of particle energy probability. Then, we will attempt to model the pre-exponential factor in accordance with the principles of collision theory for bi-molecular reaction with gaseous reactants. Understanding the basic principles of chemical reaction provides valuable tools to analyze complex reaction mechanisms in the perspective of optimizing existing industrial processes.

Single-fluid electrospinning creates nanofibers from molten polymer solutions with active ingredients. The study utilized a combination of a fractional factorial design and a Box-Behnken design to examine crucial factors among a multitude of parameters and to optimize the electrospinning conditions that impact the fiber mats' morphology and entrapment efficiency of the Senna alata leaf extract. The findings indicated that the shellac content had the greatest impact on both fiber diameter and bead formation. The optimum electrospinning conditions were identified as a voltage of 24 kV, a solution feed rate of 0.8 mL/h, and a shellac-extract ratio of 38.5:3.8. These conditions produced nanosized fibers with a diameter of 306 nm, a low bead-to-fiber ratio of 0.29, and an extract entrapment efficiency of 96% within the fibers. The biphasic profile of optimized nanofibers was confirmed through an in vitro release study. This profile consisted of an initial burst release of 88% within the first hour, which was succeeded by a sustained release pattern surpassing 90% for the next 12 h, as predicted by zero-order release kinetics. The optimized nanofibers demonstrated antimicrobial efficacy against diverse pathogens, suggesting promising applications in wound dressings and protective textiles.

Recently quantum cosmology in tomographic representation was considered. as an important tool to analyze the quantum states of the early universe in relation with the subsequent classical evolution. Given a wave function the correspondent tomogram is defined proportional to the square modulus of its fractional Fourier transform. The classical limit obtained by taking the limit ℏ→0 can be compared with the classical tomogram obtained from the classical hamiltonian formalism. In this paper we show that a set of tomograms can be derived as exact solutions of a third order equation when a de Sitter quantum universe is considered. We finally discuss the limits of this approach to quantum cosmology because the extension to equations with arbitrary potentials can become extremely complicated for potentials given by algebraic polynomials of degree greater than two and therefore also for potentials expressible by arbitrary functions.

This article is devoted to Feller's diffusion equation which arises naturally in probabilities and physics (e.g. wave turbulence theory). If discretized naively, this equation may represent serious numerical difficulties since the diffusion coefficient is practically unbounded and most of its solutions are weakly divergent at the origin. In order to overcome these difficulties we reformulate this equation using some ideas from the Lagrangian fluid mechanics. This allows us to obtain a numerical scheme with a rather generous stability condition. Finally, the algorithm admits an elegant implementation and the corresponding Matlab code is provided with this article under an open source license.

Recently concluded, large-scale cancer genomics studies involving multiregion sequencing of primary tumors and paired metastases appear to indicate that many or most cancer patients have one or more “clonal" mutations in their tumors. Clonal mutations are those that are present in all of a patient’s cancer cells. Achilles Therapeutics is currently the only company specifically targeting clonal mutations. However, they are doing so with tumor-derived T cells. To address the potential limitations of immunotherapy, I have devised another approach for exploiting clonal mutations, which I call “Oncolytic Vector Efficient Replication Contingent on Omnipresent Mutation Engagement” (OVERCOME). The ideal version of OVERCOME would likely employ a bioengineered facultative intracellular bacterium. The bacterium would initially be attenuated, but (transiently) reverse its attenuation upon clonal mutation detection.

A study was conducted to predict failure stresses, failure locations, and their paths of initiation of perforated polymethyl methacrylate (PMMA) specimens as they were loaded using pins inserted into the holes. First, a series of experiments were conducted for perforated PMMA coupons. There were six different types of coupons. The test specimens had three different widths with a circular hole of a diameter of 8 mm, which was placed at two different locations along the specimen length. All the specimens were loaded using a pin inserted into the hole with three different pins of nominal diameters of 8 mm, 6 mm, and 5 mm, respectively. To predict the failure and compare the results against the experimental data, the recently proposed universal failure criterion was used in the study using finite element analyses. The failure criteria gave acceptable results as compared to the experimental data.

Nisin is a 3.4 kDa antimicrobial peptide, produced by Lactococcus lactis (ATCC 11454). This bacteriocin can inhibit spores gemination and gram-positive bacteria development and has gained visibility in therapeutic use. The bacterial cellulose (CB) has been considered an ideal material and with high quality applied in food and medical-pharmaceutical inputs. Because of all this benefits, it is important to know the system proceeding of CB with nisin. Therefore, it was realize nisin release profile analysis of CBs was performed; analysis of the minimum inhibitory concentration (MIC) of nisin against Escherichia coli ATCC 25922, Pseudomonas aeuroginosa ATCC 9721 and Staphylococus aureus ATCC 10390; antimicrobial stability test, for 100 days at different temperatures of 4º, 25º and 37 ° C against microorganisms: S. aureus e L. sakei. The results show that nisin is released by the CB in 4 hours of contact with medium and the MIC of nisin is 78 µg/mL for S. aureus, doesn’t have gram-negative inhibition. It had stability until 100 days against L. sakei and 60 days for S. aureus. The system proved to be efficient and CB potentiated the antimicrobial action of nisin, acting as a selective barrier for other compounds present in the standard solution, serving as protection of the peptide at different temperatures. The CB loading system can be an ideal antimicrobial stability system for nisin.

Biphasic oily/water nanoemulsions have been proposed as delivery systems for the intranasal administration of curcumin (CUR) and quercetin (QU), due to their high drug entrapment efficiency, the possibility of simultaneous drug administration and protection of the encapsulated compounds from the degradation. To better understand the physicochemical and biological performance of the selected formulation simultaneously co-encapsulating CUR and QU, a stability test of the compounds mixture was firstly carried out using X-ray powder diffraction and thermal analyses, such as differential scanning calorimetry (DSC) and thermogravimetric analyses (TGA). The determination and quantification of the encapsulated active compounds was then required being an essential tool for the development of innovative nanomedicines. Thus, a new HPLC–UV/Vis method for the simultaneous determination of CUR and QU in the nanoemulsions and their evaluation in stability studies in simulated biological fluids was developed and validated. The X-ray diffraction analyses demonstrated that no interaction between the mixture of active ingredients, if any, is strong enough to take place in the solid state. Moreover, the thermal analysis demonstrated that the CUR and QU are stable in the nanoemulsion production temperature range. The proposed analytical method for the simultaneous quantification of the two actives was selective and linear for both compounds in the range of 0.5 – 12.5 µg/mL (R2 > 0.9997), precise (RSD below 3%), robust and accurate (recovery 100 ± 5 %). The method was validated in accordance with ICH Q2 R1 “Validation of Analytical Procedures” and CDER-FDA 2validation of chromatographic methods” guideline. Furthermore, the low detection (LOD < 0.005 µg/mL for CUR and <0.14 µg/mL for QU) and quantification limits (LOQ < 0.017 µg/mL for CUR and < 0.48 µg/mL for QU) of the method were suitable for the application to drug release and permeation studies planned for the development of the nanoemulsions. The method was then applied for the determination of nanoemulsions CUR and QU encapsulation efficiencies (> 99%), as well as for the stability studies of the two compounds in simulated biological fluids over time. The proposed method represents, to our knowledge, the only method for the simultaneous quantification of CUR, and QU in nanoemulsions.

The present work is concerned with the study of the generalized Langevin equation and its link to the physical theories of statistical mechanics and scale relativity. It is demonstrated that the form of the coefficients of Langevin equation depend critically on the assumption of continuity of the reconstructed trajectory. This in turn demands for the fluctuations of the diffusion term to be discontinuous in time. This paper further investigates the connection between the scale-relativistic and stochastic mechanics approaches, respectively, with the study of the Burgers equation, which in this case appears as a stochastic geodesic equation. By further demanding time reversibility of the drift the Langevin equation can also describe equivalent quantum-mechanical systems in a path-wise manner. The resulting statistical description obeys the Fokker-Plank equation of the probability density of the differential system, which can be readily estimated from Monte Carlo simulations of the random paths. Based on the Fokker-Plank formalism a new derivation of the transient probability densities is presented. Finally, stochastic simulations are compared to the theoretical results.

We still do not have satisfactory answers about the inflationary and accelerating expansions of the universe, the missing mass problem, and the origins of the four fundamental forces and the quantum phenomena. Here, we introduce a new model of matter and space and a postulate on a constant of motion, and then show that an equation of motion derived from the constant of motion could provide new understandings of the above problems. For example, we show that there is a natural inflation scenario and that the co-moving distance to the closest accelerating supernova is clearly given as $c/(\sqrt{3} H)$ ($\sim$8.1 billion ly). In addition, we show that, in a system including a proton and an electron, the equation of motion has eight acceleration terms, some of which are suspected to be responsible for the four fundamental forces and the galaxy rotation anomaly. From further discussion, we conjecture that in order to understand the gravitational and strong interactions and the quantum phenomena, it is necessary to consider the expansion of the universe. The lensing mass distribution is explained, based on another postulate on a method of representing superposition.

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.

This article aims to discuss, the stability and boundedness character of the solutions of the rational equation of the form \begin{equation}\label{eql21.1} y_{t+1}=\frac{\nu\epsilon^{-y_t}+\delta\epsilon^{-y_{t-1}}}{\mu+\nu y_t+\delta y_{t-1}},\quad t\in N(0). \end{equation} Here, $\epsilon>1, \nu,\delta,\mu\in (0,\infty)$ and $y_0, y_1$ are taken as arbitrary non-negative reals and $N(a)=\{a,a+1,a+2,\cdots \}$. Relevant examples are provided to validate our results. The exactness is tested using MATLAB.

This paper secures the analytical soliton solutions of the perturbed NLSE gives to (1). The existence criteria have been demonstrated and the wave speed of the soliton befall out. To achieve all the results obtained we used the mathematical technique. In view of the results obtained, some new additional one have been reported in left-handed metamaterials.

The aim of this study was to synthesize and optimize polylactide-co-glycolide (PLGA) nanoparticles loaded with rifampicin (RIF), with a given size and high loading rate, using the central composite design (CCD) method. CCD was used to investigate the influence of independent factors such as PLGA:RIF ratio, type of PLGA, type and concentration of surfactants, power and duration of homogenization, and type of organic solvent and its ratio to the aqueous phase on the dependent physicochemical characteristics of the nanoparticles. The optimized nanoparticles were investigated using scanning electron microscope (SEM), Fourier transform infrared spectroscopy (FTIR), thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). Comparative evaluation of the drug release kinetics was carried out using different pH and different setups: flow cuvette (USP 4 apparatus) and Franz diffusion cuvette. In addition, the mucoadhesive properties and mycobacterial activity of PLGA-RIF NPs were studied.

Physical processes are usually described using four-dimensional vector quantities - coordinate vector, momentum vector, current vector. But at the fundamental level they are characterized by spinors - coordinate spinors, impulse spinors, spinor wave functions. The propagation of fields and their interaction takes place at the spinor level, and since each spinor uniquely corresponds to a certain vector, the results of physical processes appear before us in vector form. For example, the relativistic Schrödinger equation and the Dirac equation are formulated by means of coordinate vectors, momentum vectors and quantum operators corresponding to them. In the Schrödinger equation the wave function is represented by a single complex quantity, in the Dirac equation a step forward is taken and the wave function is a spinor with complex components, but still coordinates and momentum are vectors. For a closed description of nature using only spinor quantities, it is necessary to have an equation similar to the Dirac equation in which momentum, coordinates and operators are spinors. It is such an equation that is presented in this paper. Using the example of the interaction between an electron and an electromagnetic field, we can see that the spinor equation contains more detailed information about the interaction than the vector equations. This is not new for quantum mechanics, since it describes interactions using complex wave functions, which cannot be observed directly, and only when measured goes to probabilities in the form of squares of the moduli of the wave functions. In the same way spinor quantities are not observable, but they completely determine observable vectors.In Section 2 of the paper, we analyze the quadratic form for an arbitrary four-component complex vector based on Pauli matrices. The form is invariant with respect to Lorentz transformations including any rotations and boosts. The invariance of the form allows us to construct on its basis an equation for a free particle combining the properties of the relativistic wave equation and the Dirac equation. For an electron in the presence of an electromagnetic potential it is shown that taking into account the commutation relations between the momentum and coordinate components allows us to obtain from this equation the known results describing the interactions of the electron spin with the electric and magnetic field. In section 3 of the paper this quadratic form is expressed through momentum spinors, which makes it possible to obtain an equation for the spinor wave function in spinor coordinate space by replacing the momentum spinor components by partial derivative operators on the corresponding coordinate spinor component. At the end of the paper the question on a possibility of second quantization of the electron field in the spinor coordinate space is touch upon. The statement that the electron and positron have the same, and exactly positive energy, and have opposite signs of charge and opposite signs of mass is also justified. Accordingly, in the process of annihilation their total energy, momentum, charge and mass do not change. It is shown that if we take as an axiom the conservation at interaction of the total mass of the system of particles taking into account its sign, then it is possible to explain the difference between bosons and fermions in the statistics to which they obey.

This study was to designed to develop sorafenib-loaded polymeric nanoparticles, surface-modified with pluronic F-127 for the effective treatment of hepatocellular (HCC) and renal cell carcinomas (RCC). Poly lactic coglycolic acid (PLGA) was used to encapsulate different concentrations of sorafenib by a simple modified solvent evaporation method applying pluronic F-127 as a surfactant and coating agent. The preformulation and characterization studies were conducted to evaluate the incompatibilities among sorafenib, PLGA and pluronic F-127, and physicochemical properties of the formulations, respectively. The sizes of the coated and plain PLGA nanoparticles were ~140 ± 14.7 nm and ~ 120 ± 10.1 nm, respectively. It has been confirmed from the in vitro release studies that PLGA sustained the release of sorafenib, avoiding the initial burst release, while the in vivo studies demonstared that surface-modified nanoparticles have greater affinity in the target aorgans than plain PLGA nanoparticles and free drug keeping the dose constant (20 mg/kg body weight). The delivery of sorafenib-loaded polymeric PLGA nanoparticles into the target tissues and their pharmacokinetic parameters have been improved significantly compared to the reported formulations.

Bovine lactoferrin (bLf) is a milk-derived protein that exhibits multiple biological activities and has been explored towards different therapeutic applications. Since this molecule is susceptible to degradation and some of its properties depend on its tertiary structure, the encapsulation of bLf in stimuli-responsive therapeutic formulations provides an added value to potentiate its biological activities when administered. Plasmonic magnetoliposomes emerge as promising nanosystems for dual hyperthermia (magneto-photothermia) and local therapy, since the combination of magnetic and gold nanoparticles (NPs) in a single nanosystem (multifunctional liposomes) enables the targeting and controlled release of encapsulated drugs. In this work, plasmonic magnetoliposomes (PMLs) containing manganese ferrite nanoparticles (28 nm size) and gold nanoparticles (~ 5 nm size) functionalized with 11-mercaptoundecanoic acid or octadecanethiol, were synthesized and loaded with bLf. The structural, magnetic and optical properties of the nanoparticles were measured by TEM, SQUID and UV/vis/NIR absorption spectroscopy. Specific Absorption Rate was determined to assess the capabilities for magnetic and photothermal hyperthermia. Finally, Saccharomyces cerevisiae was used as an eukaryotic cellular model to assess the biological activity and the mechanism of entry of bLf-loaded PMLs, through counting of colony forming units and fluorescence microscopy, respectively. The results demonstrate that PMLs are mainly internalized through an energy- and temperature-dependent endocytic process, though the contribution of a diffusion component cannot be discarded. Most notably, only bLf-loaded PMLs exhibit cytotoxicity with an efficiency similar to free bLf, attesting their promising potential for bLf delivery in the context of therapeutic interventions.

The adsorption of supramolecular composites for Cs(I) in high level liquid waste (HLLW) are different due to different carriers. We chose 25,27-bis(ethyl)-calix[4]arene-26,28-crown-6 (EC[4]C6) as adsorbent, SiO2-P, XAD-7 and UiO-66 as carriers. The synthesis and characterization of supramolecular EC[4]C6 loaded with three different carriers were presented. SEM, N2 adsorption/desorption isotherms, TG-DSC spectra, FT-IR spectra results shown that EC[4]C6 was successfully introduced into the pores of carriers via physical intermolecular interactions. EC[4]C6/SiO2-P, EC[4]C6/XAD-7 and EC[4]C6/UiO-66 shown high efficiency, high selectivity towards Cs(I) over 18 typical fission or corrosion products in HNO3 solution. The adsorption properties of the three materials were investigated after electron irradiation. These results demonstrate that EC[4]C6/SiO2-P possess greater potential for highly efficient removal of Cs(I) from HLLW.

Green electrospun materials are gaining popularity in the quest for a more sustainable environment for human life. Bee pollen (BP) is a valuable apitherapeutic product, and has many beneficial features such as, antioxidant and antibacterial properties. Alginate is a natural and low-cost polymer. Both natural materials show good compatibility with human tissues for biomedical applications and have no toxic effect on the environment. In this study, bee pollen-loaded sodium alginate and polyvinyl alcohol (SA/PVA) nanofibrous mats were fabricated by the electrospinning technique. The green electrospun nanofibrous mats were analyzed by scanning electron microscopy (SEM), Fourier transforms infrared spectroscopy (FTIR), and differential scanning calorimeter (DSC). According to the findings of the study, the toxin-free electrospinning method is suitable for producing green nanomaterial. Because of the useful properties of the bee pollen and the favorable biocompatibility of the alginate fibers, the bee pollen-loaded SA/PVA electrospun mats have the potential for use in a variety of biomedical applications

We show how the Poincar\'e--Riemann--Hilbert boundary-value problem enables us to construct effective estimates of the potential in the Schr\"odinger equation. The apparatus of the three-dimensional inverse problem of quantum scattering theory is developed for this. It is shown that the unitary scattering operator can be studied as a solution of the Poincar\'e--Riemann--Hilbert boundary-value problem. This allows us to go on to study the potential in the Schr\"odinger equation

Multi-parameter families of Lax pairs for the modified Korteweg-de Vries (mKdV) equation are defined by applying a direct method developed in the present study. The gauge transformations converting the defined Lax pairs to some simpler forms and reducing the variety of the Lax pairs this way are found. The direct method and its possible applications to other types of evolution equations are discussed.

Mesoporous silica nanoparticles (MSNs) can be used as carrier materials for the controlled release of pesticides while reducing their negative environmental impact. In this study, we screened an active ingredient, p-cymene (PC), with an excellent inhibitory effect on rice bacterial blight. Subsequently, the PC was successfully loaded onto MSNs via physisorption(PC@MSNs). PC@MSNs, characterized by a regular spherical shape, smooth surface, and an MSN average size of 262.9 nm, achieved an 8.6 % drug loading capacity. The release kinetics of the PC from the PC@MSNs demonstrated a sustained release (288 h) pattern influenced by drug diffusion. The efficacy of the PC@MSNs against Xanthomonas oryzae pv. Oryzae paralleled those of PC. Acute toxicity assays re-vealed that the PC@MSNs were less toxic to aquatic life (LC50=257.867 mg/L) and that the formu-lation showed no adverse effects on rice seedling growth. In summary, these results suggest that PC@MSNs can broaden PC's application scope in managing rice diseases.

This paper presents for the first time the design of a microwave sensing setup for the potential monitoring and identification of red palm weevil (RPW) gender type. The microwave sensor consists of a planar two-port transmission line (TL) with a single complementary split-ring resonant (CSRR) inclusion etched from the bottom metallic layer. The CSRR sensor is placed on top of a customized non-conductive container. The microwave sensing setup has been designed, numerically demonstrated, fabricated and tested experimentally. Simulated results correlate quite well with the experimental data. Moreover, the sensitivity of the CSRR sensor when in close proximity to different RPW gender has been evaluated both numerically and experimentally. Based on the measured results from 15 RPW collected samples with different body sizes, different RPW gender types showed unique microwave signatures. Notable shift to the sensor's resonance frequency has been achieved, where on average a resonant frequency shift of 10% for adult RPWs was achieved, while 2.4% frequency change was obtained for larvae (young) RPWs. Hence, the proposed microwave sensing setup can be adopted in field trials to examine and differentiate between various RPW genders at various development stages.

Because of their high biocompatibility, stability, ability to negotiate biological barrier passage, and functionalization properties, biological nanoparticles have been actively investigated for many medical applications. Biological nanoparticles, including natural extracellular vesicles (EVs) and synthetic extracellular vesicle-mimetic nanovesicles (EMNVs) represent novel drug delivery vehicles that can accommodate different payloads. In this study, we investigated EVs and EMNVs for their physical, biological and delivery properties and we showed that EMNVs have similar delivery properties compared to EVs. In addition, these nanotherapeutics were analyzed for their cytostatic properties in combination with the FDA-approved drug hydroxychloroquine (HCQ), which increased their cytostatic thanks to its lysosome-destabilizing properties. Altogether, these data demonstrated that, at least in vitro, the use of synthetic biomimetic particles is comparable to the natural counterparts, while their synthesis is significantly faster and more cost effective. In addition, we highlighted the benefits of combining biological nanoparticles with a lysosome destabilizing agent that increased the delivery properties of the particles.

The concern about consuming eco-friendly products has motivated research in the development of new materials. Therefore, films based on natural polymers have been used to replace traditional polymers. This study consists of a production of films based on gelatin reinforced with black pepper essential oil-loaded nanoemulsions and Cloisite Na⁺. The films were characterized by water vapor permeability, mechanical and thermal properties, surface contact angle, X-ray diffraction and scanning electron microscopy. It was observed that the films containing the nanoemulsion have higher permeability values and an increase in their mechanical resistance. The addition of nanoclay contributed to an increase in the surface hydrophobicity of the film and an increase in the tensile strength at break by about 150%. The addition of essential oil nanoemulsions led to an increase in thermal stability. The presence of clay dispersion contributed to the formation of a surface that was slightly rougher and grainier. The addition of the black pepper essential oil nanoemulsion resulted in an increase in porosity of the gelatin matrix. Through X-ray diffraction analysis, it was possible to conclude that both the polymeric gelatin matrix and the essential oils nanoemulsion are intercalated with the clay dispersion.

Among the different ways to reduce the secondary effects of antineoplastic drugs in cancer treatment, the use of nanoparticles has demonstrated good results due to the protection of the drug and the possibility of releasing compounds to a specific therapeutic target. The α-isoform of folate receptor (FR) is overexpressed on a significant number of human cancers; therefore, folate-targeted crosslinked nanoparticles based on BSA and alginate mixtures and loaded with paclitaxel (PTX) have been prepared to maximizing the proven antineoplastic activity of the drug against solid tumors. Nanometric-range sized particles (169 ± 28nm - 296 ± 57nm), with negative Z-potential values (between -0.12 ± 0.04 and -94.1± 0.4), were synthesized. The loaded PTX (2.63±0.19 - 3.56 ±0.13 µg PTX/mg Np) was sustainably released along 23 and 27h. Three cell lines (MCF-7, MDA-MB-231 and HeLa) were selected to test the efficacy of the folate-targeted PTX-loaded BSA/ALG nanocarriers. The presence of FR on cell membrane led to a significant larger uptake of BSA/ALG-Fol nanoparticles regarding to the equivalent nanoparticles without folic acid on its surface. The cell viability results demonstrated a cytocompatibility of unloaded nanoparticle-Fol and a gradual decrease in cell viability after treatment with PTX-loaded nanoparticles-Fol due to the sustainable PTX release.

The ordinary 3D wave equation for nondissipative, homogeneous, isotropic media admits solutions where the point sources are permitted to move, but it does not admit solutions where the receiver is allowed to move. To overcome this limitation, the new wave equation is derived, permitting both the receiver and the source to move. This new wave equation is a generalization of the standard wave equation, and it reduces to the standard wave equation when the receiver is at rest. To derive this new wave equation, we first mathematically define a diverging spherical wave caused by the stationary point source. From this purely mathematical definition, the wave equation for the stationary source and the moving receiver is derived together with the corresponding free-space Green's function. Utilizing the derived Green's function, it was shown that this new wave equation also permits the solutions where both the receiver and the source are permitted to move. In conclusion, this paper demonstrates that, instead of an ordinary wave equation, the wave equation for the moving source and the moving receiver governs the waves emitted by the moving point sources and received by the moving receivers.

Let $S=\left(s_1, \ldots, s_n\right)$ be a finite sequence of integers. Then $S$ is a Gilbreath sequence of length $n$, $S\in\mathbb{G}_n$, iff $s_1$ is even or odd and $s_2, \ldots, s_n$ are respectively odd or even and $\min\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\leq s_{m+1}\leq\max\mathbb{K}_{\left(s_1, \ldots, s_m\right)}\forall m\in\left[\left.1, n\right)\right.$. This, applied to the order sequence of prime number $P$, defines Gilbreath polynomials and two integer sequences A347924 \cite{oeisA347924} and A347925 \cite{oeisA347925} which are used to prove that Gilbreath conjecture $GC$ is implied by $p_n-2^{n-1}\leqslant\mathcal{P}_{n-1}\left(1\right)$ where $\mathcal{P}_{n-1}\left(1\right)$ is the $n-1$-th Gilbreath polynomial at 1.

Coupling the Maxwell tensor to the Riemann-Christoffel curvature tensor is shown to lead to a geometricized theory of electrodynamics. While this geometricized theory leads directly to the classical Maxwell equations, it also extends their physical interpretation by giving charge density, mass density and the four-velocity that describes their motions geometric definitions. Assuming the existence of a conserved energy-momentum tensor, all solutions to the geometricized theory of electrodynamics developed here are shown to be consistent with the emergence of gravity obeying the General Relativity field equation augmented by a term that mimics the properties of dark matter and/or dark energy. Finally, due to the symmetries of the theory, the properties and phenomenology of antimatter emerge in solutions.

New proposals for the equation of state of four- and five-dimensional hard-hypersphere mixtures in terms of the equation of state of the corresponding monocomponent hard-hypersphere fluid are introduced. Such proposals (which are constructed in such a way so as to yield the exact third virial coefficient) extend, on the one hand, recent similar formulations for hard-disk and (three-dimensional) hard-sphere mixtures and, on the other hand, two of our previous proposals also linking the mixture equation of state and the one of the monocomponent fluid but unable to reproduce the exact third virial coefficient. The old and new proposals are tested by comparison with published molecular dynamics and Monte Carlo simulation results and their relative merit is evaluated.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

Soil erosion and sediment transport are quite complex processes as they depend on physical, biological, mechanical, and chemical processes within a particular catchment. Therefore, it is highly essential to better explain engaged physical processes and means of accounting for site-specific conditions, for soil loss and sediment yield estimation. This paper mainly focuses on physical explanations behind soil erosion and common soil erosion models like Universal or Revised Universal Soil Loss Equation(USLE/RUSLE) and Modified Universal Soil Loss Equation(MUSLE). Based on the physical explanations and overall limitations, the MUSLE is selected for the application of sediment yield estimation. The main objective of this paper is to estimate the best exponent of the MUSLE, and to estimate the best combination of the exponent and topographic factor of the MUSLE under hydro-climatic conditions of Ethiopia. For the sake of calibration procedure, the main parameters of the MUSLE which directly affect soil erosion process such as cover, conservation practice, soil erodibility, and topographic factors are estimated based on the past experiences from literature and comparative approaches, whereas the other parameters which do not directly affect the erosion process or which have no any physical meaning (i.e coefficient a and exponent b) are estimated through calibration. It is verified that the best exponent of the MUSLE is 1 irrespective of the topographic factor, which results in the maximum performance of the MUSLE (i.e approximately 100\%). For the best combination of the exponent and topographic factor, the performance of the MUSLE is greater than or equal to 80\% for all four watersheds under our consideration, we expect the same for other watersheds of Ethiopia.

Hemorrhagic shock is the primary cause of death in patients with severe trauma, and the development of rapid and efficient hemostatic methods is of great significance in promoting the life-saving of trauma patients. In this study, polycaprolactone (PCL) nanofiber membrane was prepared by electrospinning technology. The PCL-PDA loading system was developed by modifying the surface of polydopamine (PDA) inspired by mussel adhesion protein, and the efficient and stable loading of thrombin (TB) was realized on the premise of ensuring the bioactivity of TB. The new thrombin loading system overcomes the disadvantages of harsh storage conditions, poor strength, easy to fall off, and can use thrombin to start rapid coagulation cascade reaction, which has the characteristics of fast hemostasis, good biocompatibility, high safety and wide range of hemostasis. The physicochemical properties and biocompatibility of PCL-PDA-TB membrane were verified by scanning electron microscopy, cell proliferation test, cell adhesion test and extract cytotoxicity test. Red blood cell adhesion, platelet adhesion, dynamic coagulation time and animal models all verified the coagulation effect of PCL-PD-TB membrane. Therefore, PCL-PDA-TB membrane has great potential in wound hemostasis.

Biochar is a carbon allotrope obtained by pyrolysis of biomass, usually agro-waste. Owing to the demand for sustainable development, biochar is continuously raising much hope in the scientific community. However, in order to impart it with new properties, its modification is required, either in situ during pyrolysis, or after the carbonization process. Herein, we propose a new direct approach to obtain bimetallic copper/nickel nanoparticle-loaded on olive stone biochar. The bimetallic-coated biochar and the reference materials bare biochar, copper-loaded and nickel-loaded biochar were prepared at 400 °C under a stream of dinitrogen from olive pit powder particles impregnated first with citric acid (CA), and then with copper and nickel nitrates. We have employed citric acid in the process in order to check its effect on the structural and textural properties of biochar supporting the metallic nanoparticles. Surprisingly, citric acid induced the formation of agglomerated or even raspberry-shaped, bimetallic copper/nickel nanoparticles. Large 450-500 nm-sized agglomerates of ~80 nm bimetallic CuNi NPs were noted for B-CA@CuNi. Interestingly, for biochar material prepared with initial Cu/Ni=10 molar ratio (B-CA@CuNi10/1), the bimetallic NPs formed unusual nano-raspberries (1748 nm in size) which are agglomerates of individual 10-20 nm-sized CuNi10/1 nanoparticles. The B-CA@CuNi and reference materials were characterized by Raman spectroscopy, scanning electron microscopy (SEM)/energy-dispersive X-ray spectroscopy (EDX), X-ray diffraction (XRD) and magnetometry. The B-CA@CuNi and B-CA@Ni materials could be attracted efficiently with a magnet, but not B-CA@CuNi10/1 due to a low nickel loading. B-CA@CuNi was tested as a catalyst for the degradation of methyl orange (MO). Discoloration was noted within 10 min, much faster than a similar material prepared in the absence of CA. B-CA@CuNi could be recycled at least 3 times with exhibit as fast discoloration catalysis performance. This paper stresses the important role of citric acid in shaping the bimetallic nanoparticles loaded in situ on biochar during the slow pyrolysis process and to enable faster catalysed discoloration of organic dye solution.

Lanthanum chemical compound incorporates a sensible anionic complexing ability, however lacks stability at low pH scale. Biochar fibers will benefit of their massive space and plethoric useful teams on surface to support metal chemical compound. Herein, wet spinning technology was used to load La3+ onto sodium alginate fiber, and convert La3+ into La2O3 through carbonization. The La2O3 modified biochar (La-BC) fiber was characterized by SEM, XRD and XPS, etc. The adsorption experiment proved that La-BC showed excellent adsorption capacity for chromates, and its saturation adsorption capacity was about 104.93mg/g. The information suggested that the adsorption was in step with both Langmuir and Freundlich model, followed pseudo-second-order surface assimilation mechanics, which instructed that the Cr (VI) adsorption was characterized by single-phase and polyphase adsorption, mainly chemical adsorption. Thermodynamic parameter proved that the adsorption process was spontaneous and endothermic. The mechanistic investigation revealed that the mechanism of adsorption of Cr (VI) by La-BC may include electrostatic interaction, ligand exchange or complexation. Moreover, co-existing anions and regeneration experiments proved that La-BC was recyclable and had a good prospect in the field of chrome-containing wastewater removal.

Implantable drug-delivery systems provide new means for achieving therapeutic drug concentration over a prolonged time to achieve better tissue protection and enhanced recovery. The hypothesis of the current study was to test the antioxidant and anti-inflammatory effects of genistein and nanofibers on the spinal cord tissue following experimental spinal cord injury (SCI). Rats were treated post SCI with genistein loaded on chitosan/polyvinyl alcohol (CS/PVA) nanofibers as an implantable drug-delivery system. SCI caused marked oxidative damage and inflammation as evident by the reduction in the super oxide dismutase (SOD) activity and the level of interleukin-10 (IL-10) in injured spinal cord tissue, as well as, the significant increase in the levels of nitric oxide (NO), malondialdehyde (MDA) and tumor necrosis factor-alpha (TNF-α). Treatment of rats post SCI with genistein and CS/PVA nanofibers improved most of the above mentioned biochemical parameters and shifted them toward the control group values. Genistein induced an increase in the activity of SOD and the level of IL-10, while causing a decrease in the levels of NO, MDA and TNF-α in injured spinal cord tissue. Genistein and CS/PVA nanofibers provide a novel combination for treating inflammatory nervous tissue conditions, especially when combined as an implantable drug-delivery system.

This paper presents the perturbation theory for the double–sine–Gordon equation. We obtain a system of differential equations that shows the amplitude and phase modulation of the approximate solution.. In the particular case λ = 0 we get the well-known perturbation theory for the sine–Gordon equation. For a special value λ=-1/8, we derive a phase-locked solution with the same frequency of the linear case. In general we obtain both coherent (solitary waves, lumps and so on) solutions as well as fractal solutions. We can demonstrate the existence of envelope wobbling solitary waves, because of the phase modulation depending on the solution amplitude and on the position. The main conclusion is that it is too reductive focus only on coherent solutions for the double sine-Gordon equation, because of the very rich behavior for the DSG nonlinear equation, including wobbling chaotic and fractal solutions.

Although there is a common physiological notion that the origin of the membrane potential is attributed to transmembrane ion transport, it is theoretically possible to explain its generation by the mechanism of ion adsorption. It was previously suggested that the ion adsorption mechanism led even to the potential formulas which are even identical to either the famous Nernst equation or Goldman-Hodgkin-Katz equation. Our further analysis shown in this paper indicates that the potential formula based on the ion adsorption mechanism leads to one equation which is the function of material surface charge density and the material surface potential. Furthermore, we confirmed that the equation holds in all the different experimental systems we studied. Although we have not succeeded in elucidating why such an equation is established, the equation appears to be the key equation governing the characteristics of the membrane potential regardless of the systems in question.

HU is the Hypergeometrical Universe Theory (HU)[1-8], proposed in 2006, where the Universe is a Lightspeed Expanding Hyperspherical Hypersurface and Gravitation is an absolute-velocity-dependent, epoch-dependent force. Here we introduce the Big Pop Cosmogenesis and show our calculations associated with the Equation of State of the Universe. This article is the first in a series of articles[9-22] supporting the paradigm shift.

A solution for the Prandtl-Blasius equation is essential to all kinds of boundary layer problems. This paper revisits this classic problem and presents a general Maple code as its numerical solution. The solutions were obtained from the Maple code, using the Runge-Kutta method. The study also considers convergence radius expanding and an approximate analytic solution is proposed by curve fitting. Similarly, the study resolves some boundary layer related problems and provide relevant Maple codes for these.

Recent astronomical observations with respect to measurements in distant supernovas, cosmic microwave background and weak gravitational lensing confirm that the Universe is undergoing a phase of accelerated expansion and it has been proposed that this cosmological behavior is caused by a hypothetical dark energy which has a strong negative pressure that allows explain the expanding universe. Several theoretical ideas and models related dark the energy includes the cosmological constant, quintessence, Chaplygin gas, braneworld and tachyonic scalar fields. In this paper, we have obtained new relativistic stellar configurations considering an anisotropic fluid distribution with a charge distribution which could represents a potential model of a dark energy star. In order to investigate the effect of a quadratic equation of state in this anisotropic model we specify particular forms for the gravitational potential that allow solving the Einstein-Maxwell field equations. For these new solutions we checked that the radial pressure, metric coefficients, energy density, anisotropy factor, charge density , mass function are well defined and are regular in the interior of the star. The solutions found can be used in the development of dark energy stars models satisfying all physical acceptability conditions but the causality condition and strong energy condition are violated. We expect that these models have multiple applications in astrophysics and cosmology.

In this paper we study the initial boundary value problem for logarithmic Higher Order Wave equation. Introducing the Logarithmic Sobolev inequality and using the combination of Galerkin method, we consider the theorem of existence of a global weak solution to problem for the initial boundary value problem of the logarithmic wave equation. By constructing an appropriate Lyapunov function, we obtain the decay estimates of energy for logarithmic Higher Order Wave equation. The proof of the main theorem is given.

The Hamiltonian of a quantum mechanical system has an affiliated spectrum. If this spectrum is the sequence of prime numbers, a connection between quantum mechanics and the nontrivial zeros of the Riemann zeta function can be made. In this case, the Riemann zeta function is analogous to chaotic quantum systems, as the harmonic oscillator is for integrable quantum systems. Such quantum Riemann zeta function analogies have led to the Bender-Brody-Müller (BBM) conjecture, which involves a non-Hermitian Hamiltonian that maps to the zeros of the Riemann zeta function. If the BBM Hamiltonian can be shown to be Hermitian, then the Riemann Hypothesis follows. As such, herein we perform a symmetrization procedure of the BBM Hamiltonian to obtain a unique Hermitian Hamiltonian that maps to the zeros of the analytic continuation of the Riemann zeta function, and provide an analytical expression for the eigenvalues of the results. The holomorphicity of the resulting eigenvalues is examined. Moreover, a second quantization of the resulting Schrödinger equation is performed, and a convergent solution for the nontrivial zeros of the analytic continuation of the Riemann zeta function is obtained. Finally, from the holomorphicity of the eigenvalues it is shown that the real part of every nontrivial zero of the Riemann zeta function converges at σ = 1/2.

Addressing the growing need for effective and environmentally friendly fungicides in agricul-ture, this study explored the potential of alginate microparticles loaded with metal ions as a novel approach to combat fungal pathogens. Novel alginate microparticles (microspheres and microcapsules) loaded with zinc or simultaneously with zinc and silver ions were prepared and physicochemically characterized (microparticle size, morphology, topography, encapsulation efficiency, loading capacity, and swelling behavior). Investigation of molecular interactions in microparticles using FTIR-ATR spectroscopy exhibited complex interactions between all con-stituents. Fitting to the simple Korsmeyer-Peppas empirical model revealed the rate-controlling mechanism of zinc and silver ions release from microparticles is Fickian diffusion. Lower values of the release constant k imply a slower release rate of Zn or Ag ions from microcapsules com-pared to that of microspheres. The antimicrobial potential of the new formulations against the fungus Botrytis cinerea was evaluated. When subjected to tests against the fungus, microspheres and microparticles loaded with both zinc and silver ions effectively reduced its growth and al-tered the fungal hyphal structures well as exhibited superior antifungal activity. The results showed the potential of these novel microparticles as potent fungicides in agriculture.

One of the key pathogenetic links of type 2 diabetes mellitus (T2DM) is the formation of insulin resistance (IR). Besides a wide selection of synthetic antidiabetic drugs, various plant-origin extracts are also available to support the treatment of T2DM. This study aimed to investigate and gain knowledge of the chemical composition and potential IR correction effect of American cranberry (Vaccinium macrocarpon Aiton) leaf extracts and formulate novel 3D-printed oral dosage forms for such extracts. The bioactivity and IR of L-arginine-loaded cranberry leaf extracts were studied in vivo in rats. The cranberry leaf extracts consisted of quinic, 3-caffeoylquinic (chlorogenic), p-coumaroylquinic acids, quercetin 3-O-galactoside, quercetin-3-O-glucoside, quercetin-3-xyloside, quercetin-3-O-arabino-pyranoside, quercetin-3-O-arabinofuranoside, quercetin 3-O-rhamnoside and quercetin-O-p-coumaroyl-hexoside-2 identified by HPLC. In-vivo studies with rats showed that the oral administration of the cranberry leaf extracts had a positive effect on insulin sensitivity coefficients under ITT test, and affected HOMA-IR levels and liver lipid content with experimental IR. A novel 3D-printed immediate-release dosage form was developed for the oral administration of cranberry leaf extracts using polyethylene oxide (PEO) as a carrier gel in a semi-solid extrusion (SSE) 3D printing. In conclusion, American cranberry leaf extracts loaded with L-arginine could find uses in preventing health issues associated with IR.

Starch is a widespread natural polymer used in healthcare applications due to its low cost and antibacterial properties. The use of starch in its many forms and its sometimes combination with metallic nanoparticles have all contributed to the advancement of biomaterials. However, few studies have been conducted on biocomposites composed of jackfruit starch and silver nanopar-ticles (AgNPs). As a result, this research aims to study the physicochemical, morphological, and cytotoxic features of a Brazilian jackfruit (Artocarpus heterophyllus) starch-based scaffold loaded with AgNPs. Gelatinization and chemical reduction were used to synthesize the scaffold and AgNPs, respectively. X-ray diffraction (XRD), differential scanning calorimetry (DSC), scanning electron microscopy coupled with energy-dispersive spectroscopy (SEM-EDS), and Fourier transform infrared spectroscopy (FTIR) were utilized to explore the properties. The findings supported the development of anisotropic, stable, monodispersed AgNPs. The presence of AgNPs in the scaffold matrix was revealed by XRD and SEM-EDS. AgNPs were found to modify the crystallinity, roughness, and thermal stability of the scaffold while leaving its chemical and physical characteristics unchanged. Finally, the scaffolds did not show adverse effects on the L929 cells.

In recent years, natural polymers have replaced synthetic polymers for antibacterial orthopedic applications owing to their excellent biocompatibility and biodegradability. Zein is a biopolymer found in corn. The lacking mechanical stability of zein is overcome by incorporating bioceramics e.g. mesoporous bioactive glass nanoparticles (MBGNs). In present study, pure zein and zein/Zn-Mn MBGNs composite coatings were deposited via electrophoretic deposition (EPD) on 316L stainless steel (SS). Zn and Mn were co-doped in MBGNs in order to make use of their antibacterial and osteogenic potential, respectively. A Taguchi design of experiment (DoE) study was established to evaluate the effect of various working parameters on the morphology of the coatings. It was observed that coatings deposited at 20 V for 5 min with 4 g/L concentration (conc.) of Zn-Mn MBGNs showed highest deposition yield. Uniform coatings with highly dispersed MBGNs were obtained adopting these optimized parameters. Scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), X-Ray diffraction (XRD), and fourier transform infrared spectroscopy (FTIR) were employed to investigate the morphology and elemental composition of zein/Zn-Mn MBGNs composite coating. Surface properties i.e. coating roughness and wettability analysis concluded that composite coatings were appropriate for cell attachment and proliferation. For adhesion strength various techniques including tape test, bend test, pencil hardness test, and tensile test were performed. Wear and corrosion analysis highlighted the mechanical and chemical stability of coatings. Colony forming unit (CFU) test showed that zein/Zn-Mn MBGNs composite coating was highly effective against Staphylococcus aureus (S. aureus) and Escherichia coli (E. coli) due to the presence of Zn. The formation of hydroxyapatite (HA) like structure upon immersion in simulated body fluid (SBF) validated the in vitro bioactivity of the coating. It was concluded that zein/Zn-Mn MBGNs coating synthesized in this work can be used for bioactive and antibacterial orthopedic applications.

Biofilms play a crucial role in the development of Candida-associated denture stomatitis. Inhibition of microbial adhesion to PMMA and phosphate containing PMMA has been examined in this work. C. albicans and mixed salivary microbial biofilms were compared on naked and salivary pre-conditioned PMMA surfaces in the presence or absence of antimicrobials (cetyl pyridinium chloride [CPC], KSL-W, histatin 5 [his 5]). Polymers with varying amounts of phosphate (0-25%) were tested using four C. albicans oral isolates as well as mixed salivary bacteria and 24 h biofilms were assessed for metabolic activity and confirmed using Live/Dead staining and confocal microscopy. Biofilm metabolism was reduced as phosphate density increased (15%: P=0.004; 25%: P=0.001). Loading of CPC on 15% phosphated disks showed a substantial decrease (P=0.001) in biofilm metabolism in the presence or absence of a salivary pellicle. Salivary pellicle on uncharged PMMA enhanced the antimicrobial activity of CPC only. CPC also demonstrated remarkable antimicrobial activity on mixed salivary bacterial biofilms under different conditions displaying the potent efficacy of CPC (350 µg/ml) when combined with an artificial protein pellicle (Biotene half strength).

This study delves into the Schrödinger equation's new invariants, shedding light on their crucial implications for theoretical physics and beyond. Specifically, it explores the behavior of scattering amplitudes and bound states concerning the choice of coordinate systems. The research unveils that while the energy of bound states remains invariant under coordinate transformations, the phase of scattering amplitudes undergoes variations, underscoring its pivotal role in theories reliant on phase normalization. Moreover, these findings have played a pivotal role in constructing estimates for three-dimensional Navier-Stokes equations, enhancing our ability to model complex fluid dynamics with greater precision and reliability. Additionally, in seismic exploration, tomography, and ultrasound imaging, these properties allow researchers to optimize phase selection, facilitating the most effective interpretation of measurement results. This strategic phase manipulation ensures clearer insights into subsurface structures, tissue composition, and fluid dynamics, with the flexibility to seamlessly transition back to the original coordinate system post-interpretation. This interdisciplinary synergy underscores the profound impact of fundamental theoretical research on advancing practical applications across diverse scientific domains.

The mind-body problem is the central issue in both of philosophy and life science for several centuries. To date, there is still no conclusive theory to interpret the relation between the mind and the body, even just the mind alone. Here, we promote a novel model, a derived mathematic equation called the entropic system equation, to describe the innate characters of the mind and the mechanism of the mind-body coupling phenomenon. As the semi-open thermodynamic systems far from equilibrium, the living organisms could be logically considered as an entropic system. In the living organisms or the entropic systems, there also are three essential existing elements including mass, energy and information, in which the mind and the body are hypothetically coupled by free energy and entropic force.

An extension of the Stoney formula for the case of a back side metallized 8” silicon taiko wafer has been developed, in the elastic regime, within the frame of the theory of elasticity. A good correlation between the calculated warpage, determined by the stress released by a given back side metallization (BSM), and the corresponding experimental warpages of the same thick metal layers deposited on an 8” silicon taiko wafer provides evidences of the correctness of the developed theory. This development suggests the possibility to extend this approach to the case of 8” taiko wafers based on a wide band gap semiconductor such as silicon carbide (SiC).

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

Cellulose-based carbon (CBC) has been widely concerned with its porous structure, high specific surface area, and is liable to adsorb gas molecules and macromolecular pollutants. However, the application of CBC in gas sensing has been little studied. In this paper, ZnO/CBC heterojunction was formed by means of simple co-precipitation and high temperature carbonization. As a new ammonia sensor, the prepared ZnO/CBC sensor can detect ammonia compared with that of the previous pure ZnO ammonia sensor can not at room temperature. It has great gas sensing response, stability and selectivity to ammonia concentration at 200 ppm. This study provides a new idea for the design and synthesis of biomass carbon-metal oxide composites.

Accruing evidence on the influence of β-carotene regarding the prevention of several chronic diseases - in addition to its well-acknowledged role in vision has been a strong driver for developing alternative delivery systems. Though oral delivery is accepted as the most fitting, mild and safe path for delivering bioactive agents, β-carotene delivery via food items poses challenges due to its lipophilic nature, poor water-solubility, high chemical/photochemical instability and poor oral bioavailability. Nanotechnology has opened new windows for delivering bioactive agents. Their physiochemical characteristics, i.e. small size, high surface area, unique composition, biocompatibility and biodegradability make these nanomaterials an attractive tool for β-carotene delivery. Delivering β-carotene through nanoparticles does not only improve its bioavailability/bioaccumulation in target tissues, but also lessens its sensitivity against environmental factors during processing. Regardless of these benefits, nanocarriers inherit some limitations, such as variations in sensory quality, modification of the food matrix, increasing costs, as well as limited consumer acceptance and regulatory challenges. This research area has been rapidly evolved, with a plethora of innovative nano-engineered materials, including micelles, nano/microemulsion, liposomes, niosomes, solid-lipid nanoparticles and nanostructured lipid carriers. These nano-delivery systems make conventional delivery systems appear archaic and promise better solubilization, protection during processing, improved shelf-life, higher bioavailability as well as controlled and targeted release. This review provides information on the state of knowledge on β-carotene nano-delivery systems adopted for developing functional foods: depicting their classification, composition, preparation methods, challenges, release-and absorption of β-carotene in the GIT and possible risks and future prospects.

Polyhydroxyalkanoate (PHA) co-polymers show relatively higher in vivo degradation rate compared to other PHAs thus they received a great deal of attention for a wide range of medical applications. Nanoparticles (NPs) loaded with poorly water soluble anticancer drug docetaxel (DCX) were produced using poly 3-hydroxybutyrate-co-4-hydroxybutyrate, P(3HB-co-4HB), co-polymers biosynthesised from Cupriavidus sp. USMAA1020 isolated from Malaysian environment. Three co-polymers with different molar proportions of 4-hydroxybutirate (4HB) were used: 16% (PHB16), 30% (PHB30) and 70% (PHB70) 4HB-containing P(3HB-co-4HB). Blank and DCX loaded nanoparticles were then characterized for their size and size distribution, surface charge, encapsulation efficiency and drug release. Pre-formulation studies showed that an optimised formulation could be achieved through the emulsification/solvent evaporation method using PHB70 with the addition of 1.0% PVA, as stabilizer and 0.03% VitE-TPGS, as surfactant. DCX-loaded PHB70 nanoparticles (DCX-PHB70) gave the desired particle size distribution in term of average particles sizes around 150 nm and narrow particle size distribution (PDI below 0.100). The encapsulation efficiencies result showed that at 30% w/w drug-to-polymer ratio: DCX- PHB16 NPs were able to encapsulate up to 42% of DCX; DCX-PHB30 NPs encapsulated up to 46% of DCX and DCX-PHB70 NPs encapsulated up to 50% of DCX within the nanoparticles system. Approximately 60% of DCX was released from the DCX-PHB70 NPs within 7 days for 5%, 10% and 20% of drug to polymer ratio while for the 30% and 40% drug to polymer ratios, an almost complete drug release (98%) after 7 days of incubation was observed.

Drug delivery through Liposomes has shown tremendous potential in terms of the therapeutic application of nanoparticles. There are several drug-loaded liposomal formulations approved for clinical use that help mitigate harmful effects of life-threatening diseases. Developments in the field of liposomal formulations and drug delivery have made it possible for clinicians and researchers to find therapeutic solutions for complicated medical conditions. A key aspect in the development of drug-loaded liposomes is a careful review of optimization techniques to improve the overall formulation stability and efficacy. Optimization studies help in improving/modulating the various properties of drug-loaded liposomes and are vital for the development of this class of delivery systems. A comprehensive overview of the various process variables and factors involved in the optimization of drug-loaded liposomes is presented in this review. The influence of different independent variables on drug release and loading properties with the application of a statistical experimental design is also explained in this article.

The aim of the current study was to develop and evaluate the therapeutic potential of apocynin (APO) loaded pH-sensitive nanoparticles (NPs) based transdermal hydrogel for management of rheumatoid arthritis (RA). Slightly modified nanoprecipitation technique was used for preparation of polymeric nanoparticles. Optimization was done through design expert software. Optimized APO-NPs were loaded into carbopol-934 based hydrogel as final dosage form and further studied for physicochemical properties. Optimized APO-NPs formulation had a minimum particle size 63.44 nm, polydisperibility index 0.161, and zeta potential -15mV with a maximum encapsulation efficiency of 89%. In-vitro and ex-vivo studies of APO-NPs based hydrogel was performed at pH 5.5 (pH of normal skin) and 6.8 (pH of inflammed joint) showed a pH-responsive sustained drug release and increased penetration in comparison to free APO based hydrogel. The stability studies of APO-NPs based hydrogel were done to strengthen the potential use of the prepared formulation through transdermal route. Assessment and therapeutic efficacy of the prepared pH-sensitive nanocarriers system was evaluated in chronic inflammatory RA mice model. Parameters associated with chronic inflammation were investigated including behavioral changes and histopathological, and radiological x-rays images of joints of mice paws. In-vivo study depicts improvement in behavioral parameter, decline in synovial hyperplasia and bone structure restoration. In conclusion, APO loaded pH-sensitive NPs based transdermal is a promising carrier system that can effectively manage RA.