In this work, an improved collocation method based on the Bernoulli polynomials is presented to solve the Volterra integral equation (VIE) of the second kind. The main idea of the proposed method is to improve the results of the classic Bernoulli collocation method (BCM) by dividing the interval into some sub-intervals and considering the collocation points on each of them. Here, the zeros of the shifted Chebyshev polynomials (SCPs) are considered as collocation points. Then, BCM is applied step by step from the first sub-interval to the last one. By this process, a system of algebraic equations is attained for each sub-interval that could be easily solved. Convergence of the scheme is analyzed. For the purpose of demonstrating the validity, applicability, and efficiency of the suggested scheme several numerical examples are provided. Numerical results illustrate that the accuracy of the improved Bernoulli collocation method (IBCM) is more than BCM.

In this paper, we report orthogonal fuzzy versions of some celebrated iterative mappings. We provide various concrete conditions on the real valued functions J,S:(0,1]→(−∞,∞) for the existence of fixed-points of (J,S)-fuzzy iterative mappings. We obtain many fixed point theorems in orthogonal fuzzy metric spaces. We apply (J,S)-fuzzy version of Banach fixed point theorem to show the existence and uniqueness of the solution. We support these results with several non-trivial examples and applications to Volterra-type integral equations and fractional differential equations.

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%.

Wave energy converter (WEC) arrays deployed in coastal regions may create physical disturbances potentially resulting in environmental stresses. Presently, limited information is available on the nature of these physical disturbance or the resultant effects. A quantitative Spatial Environmental Assessment Tool (SEAT) for evaluating potential effects of wave energy converter (WEC) arrays on nearshore hydrodynamics and sediment transport is presented for the central Oregon coast (USA) through coupled numerical model simulations of an array of WECs. Derived climatological wave conditions were used as inputs to the model to allow for the calculation of risk metrics associated with various hydrodynamic and sediment transport variables such as maximum shear stress, bottom velocity, and change in bed elevation. The risk maps provided simple, quantitative, and spatially-resolved means of evaluating physical changes in the vicinity of a hypothetical WEC array in response to varying wave conditions. Near-field risk of sediment mobility was determined to be moderate in the lee of the densely spaced array, where the potential for increased sediment deposition could result in benthic habitat alteration. Modifications to the nearshore sediment deposition and erosion patterns were observed near headlands and topographic features, which could have implications for littoral sediment transport. The results illustrate the benefits of a risk evaluation tool for facilitating coastal resource management at early market marine renewable energy sites.

Soft pneumatic actuators/robotics have received significant interest in the medical and health fields, due to their intrinsic elasticity and simple control strategies enabling desired interaction. However, current soft hand pneumatic exoskeletons often exhibit uniform deformation, mismatch the profile of the interacted objects, and seldom quantify the assistive effects during activities of daily life (ADL), such as extension angle and joint stiffness predicted. The lack of quantification poses challenges to the effective and sustainable advancement of rehabilitation technology. This paper introduces the design, modeling, and testing of pneumatic bioinspired Segmented Composite Proprioceptive Bending Actuators (SCPBAs) for hand rehabilitation in ADL tasks. The actuator’s soft-joint/rigid-bone segmented structure, inspired by the human finger anatomy, provides a superior fit compared to traditional continuous structures. A quasi-static model is established to predict the bending angles based on geometrical parameters. The SCPBAs also include a quantitative evaluation of joint stiffness and extension angle utilizing proprioceptive bending information. Additionally, a soft under-actuated hand exoskeleton equipped with SCPBAs demonstrates its potential in ADL rehabilitation scenarios.

In this paper, a generic fractional derivative is defined as a set of the linear operators left-inverse to the Riemann-Liouville fractional integral. Then the theory of the left-invertible operators developed by Przeworska-Rolewicz is applied for derivation of its properties. In particular, we characterize its domain, null-space, and projector operator, establish the interrelations between its different realisations, and present a generalized fractional Taylor formula involving the generic fractional derivative. Then we consider the fractional relaxation equation containing the generic fractional derivative, derive a closed form formula for its unique solution, and study its complete monotonicity.

In this paper, several classes of rough Marcinkiewicz integral operators along surfaces of revolution on product spaces are investigated. We prove the Lp boundedness of these operators when their kernels functions belong to a class of functions related to a class of functions introduced by Grafakos-Stefanov. The results in this paper extend and improve several known results on Marcinkiewicz integrals.

The field of smart materials is attaining global industrial importance rapidly. The ionic polymer metal metaIl composites withheld there importance in this field. They are not only used as biocompatible devices but also in the field of thin and conformal bio coatings. The nafion 117 is unstable at elevated temperatures and its water intake resistance is low, so the nafion 117 is coated with the noble material to increase its thermal stability and water resistant property. The high cost of noble metal make its too costly to use in day to day applications so parylene has been used as substitute for noble metal in order to reduce the cost. The high thermal stability and water intake property if parylene make its suitable for the same. Multiple chemical treatments like plasma ionization and others have been done on the parylene coated nafion to increase its desirable properties considerably. The low adhesion rate between parylene and nafion 117 has been increased upto the certain extend by the use of ionized plasma. This paper reviewed the plasma chemical treatment of paryelene coatings for the biocompatible devices and provides an insight knowledge on classification, structure and thermal stability of the parylene coatings.

Background: beta blockers of three generations are first-line drugs in the treatment of chronic heart failure (CHF). However, to date there is no clear understanding of the effect of beta blockers on myocardial energy metabolism disorders in CHF. The aim of the study: to conduct a study of beta-blockers of different generations on myocardial energy metabolism in the experimental CHF. Methods: CHF was modeled in white outbred rats by administering doxorubicin. The study drugs were administered intragastrically – new drug Hypertril (1-(β-phenylethyl)-4-amino-1,2,4-triazolium bromide)-3.5 mg/kg, metoprolol - 15 mg/kg, Nebivolol -10 mg/kg, Carvedilol 50 mg/kg, Bisoprolol, 10 mg/kg. In the myocardium, the main indices of energy metabolism were determined - ATP, ADP, AMP, malate, lactate, pyruvate, succinate dehydrogenase (SDH) activity, NAD-dependent malate dehydrogenase (NAD-MDH) activity. Results: traditional second-generation beta-blockers (Metoprolol and Bisoprolol) did not affect the studied indices of energy metabolism, and third-generation beta-blockers with additional properties - Carvedilol and, especially, Nebivalol and Hypertril improved myocardial energy metabolism. Conclusions: obtained results will help to expand our understanding of the effect of beta-blockers of various generations used to treat cardiovascular diseases on energy metabolism, and are also an experimental justification for the practical choice of these drugs in the complex therapy of CHF.

This article utilizes the Canny edge extraction algorithm based on contour curvature and the cross-correlation template matching algorithm to extensively study the impact of high-repetition-rate CO2 pulsed Laser on the target extraction and tracking performance of the infrared imaging detector. It establishes a quantified dazzling pattern for lasers on infrared imaging systems. By conducting laser dazzling and damage experiments, a detailed analysis of the normalized correlation between target and dazzling images is performed to quantitatively describe laser dazzling effects. Simultaneously, an evaluation system, including target distance and laser power evaluation factors, is established to determine the dazzling level and whether the target is recognizable. The research results reveal that laser power and target position are crucial factors affecting the detection performance of infrared imaging-guided weapon systems under laser dazzling. Different laser powers are required to successfully interfere with the recognition algorithm of infrared imaging-guided weapons at different distances. And laser dazzling will produce a lot of false edge information, which seriously affects the performance of pattern recognition algorithm. In laser damage experiments, the detector experienced functional damage, with a quarter of the image displaying as completely black. The energy density threshold required for functional damage to the detector is approximately 3 J/cm2. The dazzling assessment conclusions also apply to evaluating damage results. Finally, the proposed evaluation formula aligns with experimental results, objectively reflecting the actual impact of laser dazzling on the target extraction and tracking performance of infrared imaging systems. This study provides an in-depth and accurate analysis for understanding the influence of lasers on the performance of infrared imaging-guided weapons.

The study of biologically active substances from natural sources shows the prospect of obtaining a new type of antimicrobial agents, highly effective against pathogenic microorganisms and non-toxic to humans. Our study reveals for the first time that Cornu aspersum mucus has the potential to act as a source of antibacterial agents against bacterial pathogens such as Bacillus cereus 1085, Propionibacterium acnes 1897, Salmonella enterica 8691, Enterococcus faecalis 3915, and Enterococcus faecium 8754. Both mucus fractions with MW<20 kDa and MW>20 kDa showed antimicrobial activity and antioxidant properties that’s why they can be turned into an alternative agent to expensive synthetic antibacterial compounds. Using de novo sequencing 16 novel peptides with potential antibacterial activity were identified by in a fraction with MW<20 kDa. The results of electrophoretic and proteomic analysis of mucus fraction with MW >20 kDa presented proteins with potential antibacterial activity highly homologous to hemocyanins, mucus protein Aspernin, lectins, L-amino acid oxidase-like protein, and mucins (mucin-5AC, mucin-5B, mucin-2 and mucin-17). Thanks to the synergistic action of the bioactive components, the mucus fraction with MW > 20 kDa in low concentrations per 8–2 µg/mL showed promising antimicrobial activity against the tested bacteria, comparable to Vancomycin and without unwanted cytotoxic effects against non-target cells. Additionally, C. aspersum mucus fractions were found to have a positive effect on eukaryotic organisms by reducing the levels of intracellular oxidative damage and increasing the antioxidant capacity of the cell. These findings could serve as a basis for the development of a potent non-cytotoxic antibacterial agent to replace conventional antibiotics and avoid the development of antibiotic resistance.

This paper is devoted to the study of multi-dimensional integral transform with Fox H-function in the kernel in weighted spaces integrable functions in the domain R+n with positive coordinates. Mapping properties such as the boundedness, the range, the representations of the considered transformation are established.

Currently, there is a tenacious need to find new ways to purify water by eliminating bacterial biofilms, textile dyes, and toxic water pollutants. These contaminants pose significant risks to both human health and the environment. To address this issue, in this study, we have developed an eco-friendly approach that involves synthesizing Cobalt-doped Cerium Iron Oxide (CCIO) nanocomposite (NC) using an aqueous extract of Gossypium arboreum L. stalks. The resulting nanoparticles can be used to effectively purify water and tackle the challenges associated with these harmful pollutants. Nanoparticles excel in water pollutant removal by providing high surface area for efficient adsorption, versatile design for simultaneous removal of multiple contaminants, catalytic properties for organic pollutant degradation, and magnetic features for easy separation, offering cost-effective and sustainable water treatment solutions. CCIO nanocomposite has been synthesized by green co-precipitation method due to biomolecules and co-enzymes present in the aqueous extract of Gossypium arboreum L. stalk; a single-step procedure completed in 5 h reaction time. Further, the synthesis of nanocomposites was confirmed by various characterization techniques such as Fourier-transform infrared (FT-IR) spectroscopy, X-ray diffraction (XRD), Field emission scanning electron microscopy (FE-SEM), Transmission electron microscopy (TEM), Thermogravimetric analysis (TGA), Dynamic light scattering (DLS), and Energy Dispersive X-Ray (EDX). CCIO NCs were discovered to have a spherical shape and an average size of 40 nm. Based on DLS zeta potential analysis, CCIO NCs were found to be anionic. Also, CCIO NCs showed significant antimicrobial and antioxidant activity. Overall, considering the physical and chemical properties, the application of CCIO NCs in the adsorption of various dyes (~91 %) and water pollutants (chromium = ~ 60 %) has been considered since they exhibit great adsorption capacity owing to their microporous structure which can be a step forward in water purification.

This work introduces a novel numerical method designed to address three-dimensional unsteady free surface flows incorporating integral viscoelastic constitutive equations, specifically, the K-BKZ-PSM (Kaye–Bernstein, Kearsley, Zapas - Papanastasiou, Scriven, Macosko) model. The new proposed methodology employs a second-order finite difference approach along with the deformation fields method to solve the integral constitutive equation, and the marker-particle method (known as \emph{Marker-and-Cell}) to accurately capture the evolution of the fluid's free surface. The newly developed numerical method has proven its effectiveness in handling complex fluid flow scenarios, including confined flows and extrudate swell simulations of Boger fluids. Furthermore, a new semi-analytical solution for velocity and stress fields is derived, considering fully developed flows of a K-BKZ-PSM fluid in a pipe.

This article presents a new input device for spastic patients and others with similar symptoms. The sensor consists of a disc used to determine positions and can replace standard joysticks in medical devices such as electric-powered wheelchairs. Using a standard joystick while operating a powered wheelchair can result in dangerous situations when spastic movements occur and extremities cramp making them uncontrollable. To avoid this, a disc was developed that can be controlled with any body part. By shifting weight (x- and y-axis) the disc can tilt in any direction creating a proportional output signal and can also be pushed down in the center (z-axis) to open a menu on a screen for example. When spasms occur it is impossible for users to get stuck on the input device because the disc is flat and can be mounted within a control panel. Body parts coming into contact with the disc would merely slide across the disc without triggering unintentional actions. The sensor presented here is also adaptive and can be adjusted to fit a user’s strength and range of motion. This proposal aims to develop an input device that enables spastic patients to operate sensitive systems safely.

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.

Hereditary hemochromatosis (HH) is the main genetic cause of iron overload and is regarded as metal-related human toxicosis. HH may result from HFE and non-HFE gene mutations causing hepcidin deficiency or hepcidin resistance. The disorder has a high biochemical penetrance, but a low clinical prevalence. Unfortunately, the majority of patients with HH remain undiagnosed at their disease-curable stage. The main aim of HH therapy is to prevent iron overload in the early-phase disease and elimination of excess iron from the body by phlebotomy in its late stage. Raising global awareness of HH among health professionals, their training to pay attention to early HH signs and symptoms, and strict patient monitoring are critical management strategies for preventing treatment delays, upgrading its efficacy, and improving patient prognosis.

Objective: To determine the effect of sandblasting before and after sintering on the surface roughness of zirconia and the micro-tensile bond strength of a pressable veneering ceramic to zirconia. Methods: Pre-sintered zirconia blocks (IPS e.max ZirCAD, Ivoclar Vivadent) were divided into a control group (CTR, no surface treatment) and four test groups of three specimens each: Pre-S-30, Pre-S-50, Pre-S-110 were sandblasted with 30µm SiO2, 50µm Al2O3 and 110µm Al2O3 particles respectively, before sintering, Post-S-30 was sandblasted with 30µm SiO2 after sintering. For each treatment, the surface roughness was measured (Ra, Perthometer M4P, Mahr Perthen). After sintering the zirconia blocks, a liner and a pressable ceramic (IPS e.max ZirPress, Ivoclar Vivadent) were fired. Sixteen micro-bars were obtained from each block and submitted to the micro-tensile bond strength (µTBS) test. Data were analyzed with one-way ANOVA. Any correlation between Ra and µTBS was evaluated (Sperman test). Results: Sandblasting before sintering with 110µm Al2O3 (Ra=3.44±0.44µm), 50µm Al2O3 (Ra=2.32±0.46µm), and 30µm SiO2 (Ra=1.22±0.22µm) resulted in significantly higher roughness than sandblasting after sintering with 30µm SiO2 (Ra=0.46±0.11µm). The highest µTBS was measured when the sintered zirconia was sandblasted with 30μm SiO2 (26.79±14.80 MPa), which was significantly different from that of specimens that were sandblasted before sintering (Pre-S-30=20.90±11.70; Pre-S-50=21.27±15.19; Pre-S-110=23.99±16.83) or were not treated (CTR=17.44±14.03). Conclusions: Sandblasting zirconia before sintering enhances the surface roughness proportionally to the particle size of the sand used. Sandblasting with 30µm SiO2 after sintering appeared to improve bonding between the veneering ceramic and zirconia. Clinical Significance: Sandblasting with 30µm SiO2 after sintering may improve bonding between veneering ceramics and zirconia, thus reducing ceramic fractures/chippings.

In this paper, we compile the fractional power series method and the Laplace transform to design a new algorithm for solving the fractional Volterra integro-differential equation. For that, we assume the Laplace power series (LPS) solution in terms of power q=1m,m∈Z+, where the fractional derivative of order α=qγ for which γ∈Z+. This assumption will help us to write the integral, the kernel, and the nonhomogeneous terms as a LPS with the same power. The recurrence relations for finding the series coefficients can be constructed using this form. To demonstrate the algorithm's accuracy, the residual error is defined and calculated for several values of the fractional derivative. Two strongly nonlinear examples are discussed to provide the efficiency of the algorithm. The algorithm gains powerful results for this kind of problem. Under Caputo meaning the obtained results are illustrated numerically, and graphically. Geometrically, the behavior of the solution declares that the changing of the fractional derivative parameter values' in their domain alters the style of the attained solution in a symmetrical meaning and fully coinciding to the ordinary derivative value'. From these simulations, the results report that the recommended novel algorithm is a straightforward, accurate, and superb tool to generate analytic-approximate solutions for Integral, and integro-differental equations of fractional order.

Antimicrobial peptides represent a promising alternative to traditional drugs in relation to cost, toxicity and, primarily, the growing problem of drug resistance. Here we report on the activity against HSV-1 and HSV-2 of a previously described wide-spectrum synthetic decapeptide, Killer Peptide (KP). As determined by plaque reduction assays, treatment with KP at 100 μg/mL resulted in a reduction in the viral yield titer of 3.5 Logs for HSV-1 and 4.1 Logs for HSV-2. Further evaluation of KP antiviral activity focused on the early stages of virus replicative cycle, including the determination of the residual infectivity of viral suspensions treated with KP. A direct effect of the peptide on viral particles, impairing virus absorption and penetration, was shown. The toxicity profile proved to be extremely good with a selectivity index of 29.6 for HSV-1 and 156 for HSV-2. KP was also active against an acyclovir (ACV)-resistant HSV-1 strain, while HSV-1 subcultures in the presence of sub-inhibitory doses of KP did not lead to the emergence of resistant strains. Finally, the antiviral action of KP proved to be synergistic with that of ACV. Overall, these results demonstrate that KP could represent an interesting addition/alternative to acyclovir for antiviral treatment.

In this note we prove that the Riemann hypothesis is false. The proof is by contradiction based on a criterion of Hu.

In the paper, the author presents explicit and unified expressions for a sequence of improper integrals in terms of the beta functions and the Wallis ratios. Hereafter, the author derives integral representations for the Catalan numbers originating from combinatorics.

This paper investigates the effects of various process parameters, specifically the substrate temperature, on weld track geometry in Directed Energy Deposition (DED) processes. A specialized experimental setup integrated within a DED machine facilitates controlled thermal conditioning of sample sheets. Through Design of Experiments (DoE) methods, individual weld marks are generated and analysed to assess geometric characteristics. Regression models are constructed to predict machine parameters for desired weld geometry at different substrate temperatures. Validation experiments confirm the accuracy and reliability of the regression models. Results show a consistent trend towards target geometric features across a broad range of substrate temperatures. Despite deviations in measured values, successful fabrication is achieved, demonstrating robust bonding between weld and substrate. Contact angle predictions exhibit precision within a partial temperature range for proper deposition. The developed model offers insights for optimizing DED process parameters to achieve desired weld characteristics, advancing the capabilities and reliability of additive manufacturing technology. Future work aims to refine the regression model and explore additional mathematical relationships for enhanced accuracy. An implication of this work is the potential to vary the local mechanical properties of parts by controlling the temperature profile while maintaining consistent geometric characteristics. By manipulating the substrate temperature, it may be possible to tailor the microstructure and mechanical properties of fabricated components in the future to meet specific requirements in different regions of the part.

The evolution of human societal dynamics over the course of decades and centuries has led to an ever-increasingly complex digital modern life, one of the hallmark of which is the need for multi-tasking, inclusive of that with media. Is there an empirical mapping between this macroscopic (digital) evolution of the human societal dynamics (in terms of multi-tasking) and the microscopic evolution of the functional molecular units within cells (i.e., proteins) and their manifold cross-talks? Multi-tasking requires a certain degree of intrinsic or adapted flexibility which is as true at the bio-molecular level. Evolutionary diversification of structure-function relationship in proteins emphasizes the functional importance of intrinsically disordered entities (IDPs/IDRs) which are highly dynamic biological soft matters. Multi-functionality is favorably supported by their fluid-like shapes and other new malleable members of the protein family. The new wealth of knowledge coming from recent research on protein intrinsic disorder, fold-switching, moonlighting, hub proteins etc. has given us new insights into protein structure – functional relationship. This has led to a paradigm shift in protein science, clearly diverging from the traditional 'one structure – one function' model applicable to enzyme classes to a more complex understanding of protein functionality. This paradigm shift has caused scientists to delve deeper into the subject, exploring various evolutionary toys and tools to fit the cumulative multi-functional demands in higher organisms. This commentary covers the different evolutionary arsenals to achieve the growing multi-functionality and argues in favor of protein intrinsic disorder as probably the sharpest weapon of all.

Gaze tracking of high-speed moving targets is a novel application mode for low Earth orbit microsatellites. In this mode, small satellites are equipped with high-resolution narrow-field-of-view video cameras for stable gaze-tracking imaging of high-speed moving targets. This paper proposes a high-precision attitude adaptive integral sliding mode control method with a feedforward compensation disturbance observer to enhance the capability of a microsatellite attitude control system for gaze tracking of high-speed moving targets. Specifically, first, we present the attitude control system model for microsatellites and the calculation method for the desired attitude of target tracking based on image feedback. Then, an adaptive integral sliding mode attitude control algorithm with a feedforward compensation disturbance observer, which meets the requirements of high-precision tracking control, is designed. The developed algorithm utilizes the disturbance observer to observe the friction torque of the flywheel and compensates for it through feedforward control. It also employs the adaptive integral sliding mode control algorithm to reduce the impact of uncertain disturbances, decrease the steady-state error of the system, and enhance the attitude control precision. Simulation experiments demonstrated that the designed disturbance observer can successfully observe the frictional disturbance torque of the flywheel. The attitude Euler angle control precision for high-speed moving target tracking reached 0.009°, and the angular velocity control precision reached 0.005°/s, validating the effectiveness of the proposed approach.

Liver X receptors (LXR) are deemed as potential drug targets for atherosclerosis, whereas a role in adipose tissue expansion and its relation to insulin sensitivity remains unclear. To assess the metabolic effects of LXR activation, C57BL/6 mice on a high-fat diet (HFD) were treated with the dual LXRα/β agonist T0901317 (30 mg/kg per day) for 3 weeks. Differentiated 3T3-L1 was used for analysing the effect of T0901317 on glucose uptake.T0901317 reduced fat mass, accompanied by a massive fatty liver and lower adipokine levels in circulation of HFD mice. Increased adipocyte apoptosis and macrophage infiltration were found in epididymal fat of T0901317-treated HFD mice. In addition, T0901317 treatment promoted basal lipolysis, but blunted the anti-lipolytic action of insulin. Furthermore, LXR activation antagonized PPARγ target genes in epididymal fat and PPARγ-PPRE binding activity in 3T3-L1 adipocytes. Although the glucose tolerance was comparable to that in vehicle-treated HFD mice, the insulin tolerance was significantly decreased in T0901317-treated HFD mice, indicating decreased insulin sensitivity by T0901317 administration, and which was further supported by impaired insulin signalling found in epididymal fat and decreased insulin-induced glucose uptake in 3T3-L1 by T0901317administration. These findings reveal that LXR activation impairs adipose expansion which contributes to decreased insulin sensitivity.

The research was aimed at comparing the fire characteristics of different types of pepper in the context of designing explosion prevention. The following characteristics were studied: explosion pressure pmax and Kst at selected concentrations, ignition temperature of the deposited dust layer from the hot surface and minimum initiation energy. The comparison of the chemical properties of the used types of pepper was performed using TG/DSC. Results of the measurements suggest that different types of peppers exhibit different explosion characteristics. Each of the samples reached the maximum value of the explosion pressure, and their rate of pressure rise increased at different concentrations. The volume of the explosion chamber used also influenced the explosion characteristics. It is a consequence of the fact that the explosion characteristics strongly depend on the mechanism of action of a particular igniter. The minimum effect on the safety characteristics was observed when measuring the minimum initiation energy and the minimum ignition temperature of dust layer from the hot surface. The results of the measurements suggest that different types of peppers exhibit different explosion characteristics. This information should then be considered in explosion prevention.

For centuries, humans have relied on natural products to prevent and treat numerous health issues. However, biologically active compounds from natural sources, such as polyphenols, face significant challenges, including low solubility, rapid metabolism, and instability, which hinder their effectiveness. Advances in science and nanotechnology have provided solutions to overcoming these problems through the use of porous silica materials. These materials possess unique properties, such as a high specific surface area, adjustable particle and pore sizes, and a surface that can be easily and selectively modified. In this review, we summarize and discuss findings on how the pore and particle size, structure, and surface modification of silica materials influence the preparation of efficient delivery systems for biologically active polyphenols from natural sources. The available data demonstrate how parameters such as adsorption capacity, release and antioxidant properties, bioavailability, solubility, stability, etc. of the studied delivery systems could be affected by the structural and chemical characteristics of the porous silica carriers.

Sustainable continuous cover forestry is defined and analyzed in several ways. The differential equation representing growth of the basal areas of individual trees, motivated by fundamental biological production theory by Lohmander (2017a), is analyzed and extended in different directions. From the solution of the differential equation, the basal area and the tree diameter are obtained as explicit functions of time. The diameter is a strictly increasing function of time. In the absence of competitors, the diameter increment is shown to be a strictly decreasing function of time. Hence, the diameter increment can also be interpreted as a strictly decreasing function of the diameter. Alternative forms of adjustment of the differential equation, with consideration of competition, are defined. If the competition is strong, with large trees in the vicinity of a particular tree, then the basal area increment, and the diameter increment, are reduced. The growth of a large tree is less sensitive than the growth of a small tree, to competition from other trees. Under strong competition, the basal area increment, and the diameter increment, are strictly concave functions of the size of the tree. The unique maximum of the diameter increment occurs at a higher diameter, if the competition increases. In dynamic equilibrium, the tree size frequency distribution is stationary. If natural tree mortality can be avoided via the harvest strategy, the tree size frequency distribution is a function of the size and competition dependent growth function, and the harvest strategy. Empirical tree size frequency data are used to simultaneously estimate parameters of a size and competition dependent growth function and the applied harvest strategy, via nonlinear optimization. The properties of the estimated growth function are consistent with the corresponding properties of the production theoretically motivated hypothetical function, and the properties of the estimated harvest strategy confirm the corresponding hypotheses. The R2 of the nonlinear regression exceeds 0.97. With access to an empirically estimated equilibrium tree size distribution, it is possible to: 1. Estimate size frequency relevant parameters of tree size and competition dependent growth functions for individual trees. 2. Estimate the applied harvest strategy. 3. Explain and reproduce the empirically estimated tree size equilibrium distribution.

In this paper we establish some weighted integral inequalities of Ostrowski, Čebyšev and Lupaş type. Applications for continuous probability density functions supported on infinite intervals with two examples are also given.

Peptides, both natural and synthetic, are well suited for a wide range of purposes and offer versa-tile applications in different fields such as biocatalysts, injectable hydrogels, tumor treatment, and drug delivery. The rising prominence of therapeutic peptides encompasses anticancer, antiviral, antimicrobial, and anti-neurodegenerative properties. The metals Na, K, Mg, Ca, Fe, Mn, Co, Cu, Zn, and Mo are ten of the twenty elements that are considered essential for life. Crucial for under-standing the biological role of metals is the exploration of metal-bound proteins and peptides. Aside from essential metals, there are other, non-essential metals that also interact biologically, exhibiting either therapeutic or toxic effects. Irregularities in metal binding contribute to diseases like Alzheimer’s, neurodegenerative disorders, Wilson's, and Menkes disease. Certain metal com-plexes have potential applications as radiopharmaceuticals. The examination of these complexes was done by preforming UV-Vis, IR, EPR, NMR spectroscopy, and X-ray analysis.

In this paper, we establish the generalized Qi-type inequality involving conformable fractional integrals. The results presented here would provide extensions of those given in earlier works.

During pregnancy, profound physiological changes occur in the maternal body, including those affecting oral health. Dental stem cells (DSCs) have emerged as promising candidates for regenerative therapies in dentistry. This manuscript delves into the intricate interplay between DSC behavior and maternal oral health during pregnancy. We provide an overview of current knowledge concerning the impact of pregnancy on DSCs, highlighting their potential roles in maintaining oral homeostasis and responding to pathological conditions. Additionally, we identify key research gaps and propose future directions for investigating novel therapeutic strategies leveraging DSCs to improve maternal and fetal oral health outcomes. By elucidating this relationship, we aim to pave the way for innovative approaches in preventive and regenerative dentistry tailored to the unique needs of pregnant women.

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 present study evaluated the effect of Prosthechea karwinskii leaves extract on antioxidant enzymes superoxide dismutase (SOD) and catalase (CAT) in a model of obese rats with insulin resistance to know its nutraceutical potential on insulin resistance and oxidative stress. Obesity and insulin resistance were induced in rats by administering 40% sucrose in water. Once the model was established, four groups were evaluated (control, obese, obese administered with extract, and obese administered with metformin), and the indices of insulin resistance and the activity of antioxidant enzymes were measured. In addition, compounds in the extract were identified with UHPLC-ESI-qTOF-MS/MS. The glucose, insulin, triglycerides, and insulin resistance indicators (HOMA-IR and TyG) increased in obese rats. The activity of the antioxidant enzymes evaluated increased in the obese group, apparently as an adaptive response to oxidative stress to inhibit reactive oxygen species formed by hyperglycemia. Administration of P. karwinskii extract and metformin reduced glucose, insulin, triglyceride levels, insulin resistance indicators and antioxidant enzymes to values like those of the control group. This study shows the nutraceutical potential of P. karwinskii extract as an ingredient in the formulation of food supplements or functional foods to help treat diseases related to insulin resistance and oxidative stress.

In physics, thought experiments are impressive heuristic tools. They are valuable instruments to help scientists find new results and to teach students the known ones. However, as we shall show, they should always be received with prudence, even when they are a shortcut to 'prove' well-established results. Here, we show that the most widely known thought experiments devised to derive the gravitational frequency shift from energy conservation are, in fact, problematic. When properly set and correctly read, those thought experiments reveal that the existence of the gravitational frequency shift is, in fact, at odds with energy conservation. We also propose two new simple thought experiments, one using the conservation of energy and the other the conservation of linear momentum, that corroborate that conclusion, showing that those conservation principles do not imply the gravitational frequency shift. We think that our results may be of some epistemological interest and could serve as a warning sign on how thought experiments should be received and trusted.

In this paper we establish some generalizations of Opial’s inequal- ities for Riemann-Stieltjes integral and for two functions. Applications related to trapezoid and Grüss’ ’type inequalities are also given.

Shrimp is the most important aquaculture industry. Therefore, we determined the effect of nitrifying-probiotic bacteria on water quality, growth, survival, immune response and intestinal microbiota of Litopenaeus vannamei cultured without water exchange. In vitro, only B. licheniformis used TAN, nitrites and nitrates since nitrogen bubbles were produced. TAN decreased significantly in the treatments with bacilli and LAB, but no differences were observed in nitrites. Nitrates were significantly higher in the treatments with bacteria. The final weight and survival of shrimp in the bacterial treatments increased significantly and superoxide anion increased significantly only in LAB treatment. The activity of phenoloxidase decreased significantly in the treatment with LAB and with the mixture of bacilli and LAB. Shrimp treated with bacilli in the water showed lower species richness. The gut bacterial community after treatments was significantly different from that of the control. Linoleic acid metabolism was positively correlated with final weight and superoxide anion, whereas quorum sensing was correlated with survival. Thus, bacilli and LAB in the water of hyperintensive culture systems act as nitrifers, modulate the intestinal microbiota and immune response, and improve the growth and survival of shrimp. This is the first report on Pediococcus pentosaceus and Leuconostoc mesenteroides as nitrifying bacteria.

In this paper, we have established Hermite-Hadamard inequalities for r-preinvex functions via fractional integrals.

Probiotics are living microbes that provide benefits to the host. The increasing data on health promotion following probiotics administration triggered growing interest among researchers and pharmaceutical companies looking for novel therapeutic or preventive tools. Infections of the lower genital tract in females are caused by a wide range of pathogens, they are widespread, and represent one of the main areas for the use of probiotics and postbiotics. Vulvovaginal candidiasis (VVC) affects 75% of women in their reproductive age at least once during their lifetime. Of these women 5-8% develop the recurrent form (RVVC). The disease onset is triggered by the overgrowth of Candida species on the vaginal mucosa. Here, we evaluated the beneficial properties of the Bacillus coagulans spore-producing LMG S-24828 against C. albicans and C. parapsilosis. Our results show that both alive B. coagulans and its Cell-Free-Supernatant (CFS) exerted antifungal activity against both fungi. Moreover, alive B. coagulans reduced hyphal formation, inhibited C. albicans adhesion to vaginal epithelial cells and showed co-aggregation capacity. Overall, B. coagulans LMG S-24828 exerted a protective effect on vaginal epithelial cells infected with C. albicans. These data suggest that B. coagulans LMG S-24828 may provide benefits in the context of Candida vaginal infections.

In this paper, the existence of optimal solutions for problems governed by differential equations involving feedback controls is established, when the problem must account for a Volterra-type distributed delay and is subject to the action of impulsive external forces. The problem is reformulated within the class of impulsive semilinear integro-differential inclusions in Banach spaces and is studied using topological methods and multivalued analysis. The paper concludes with an application to a population dynamics model.

This paper proposes a definition of fractional line integral, generalising the concept of fractional definite integral. The proposal replicates the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It is based on the concept of fractional anti-derivative used to generalise the Barrow formula. To define the fractional line integrals the Gr\"unwald-Letnikov and Liouville directional derivatives are introduced and their properties described. The integral is defined first for broken line paths and afterwards to any regular curve

Grating (moiré) interferometry is one of the well-known methods for full-field in-plane displacement and strain measurement. There are many design solutions for grating interferometers, including systems with a microinterferometric waveguide head. This article proposes a modification to the conventional waveguide interferometer head, enabling the implementation of a polarization fringe phase shift for automatic fringe pattern analysis. The article presents both the theoretical consideration of the proposed solution and its experimental verification, along with the concept of the in-plane displacement/strain sensor using the described head.

The classical Lotka-Volterra predator-prey model is globally stable and uniformly persistent. However, in real-life biosystems extinction of species due to stochastic effects is possible. In this paper, we consider the classical Lotka-Volterra predator-prey model under stochastic perturbations. For this model, using an analytical technique based on the direct Lyapunov method and a development of the ideas of R.Z. Khasminskii, we find the precise sufficient conditions for the stochastic extinction of one and both species and the precise necessary conditions for the stochastic system persistence. The stochastic extinction occurs via a process known as the stabilization by noise of the Khasminskii type, and, in order to establish the sufficient conditions for extinction, we found the conditions for the stabilization. The analytical results are illustrated by numerical simulations. {\bf Keywords:} stochastic perturbations, white noise, Ito's stochastic differential equation, the Lyapunov functions method, stability in probability, stabilization by noise, stochastic extinction, persistence.

Fatigue performance and self-repairing activity of asphalt binders are two properties that highly influence the fatigue cracking response of asphalt pavement. There are still numerous gaps of knowledge to fill linked with these two characteristics. For instance, current parameters fail to fully accommodate these two bitumen phenomena. This study aims to propose a new procedure to address this issue utilizing the linear amplitude sweep (LAS) test, LAS with rest period (RP) (LASH) test, and simplified viscoelastic continuum damage (S-VECD) model. This research work used four different types of asphalt binders: neat asphalt (NA), self-healing thermoplastic polyurethane (STPU)-modified bitumen (STPB), self-healing poly (dimethyl siloxane) crosslinked with urea bond (IPA1w)-modified bitumen (IPAB), and styrene–butadiene–styrene (SBS)-modified bitumen (SBSB). Before the testing process, all the materials were subjected to short-term and long-term aging. The new procedure showed a superior capacity to analyze and accommodate all bitumen fatigue performances and self-repairing activities compared to the current method. Another finding proved that asphalt binders with higher self-restoration behavior failed to show better fatigue performance. A breakthrough finding demonstrated that asphalt binder fatigue response augmented when the RP was applied at a higher damage intensity (S) value. STPBs and IPABs reached their highest increments of fatigue response, containing 1.0% of STPU and 0.5% of IPA1w, respectively. Those augmentations were 207.54% and 232.64%, respectively.

In this paper, we consider the Cauchy problem of a time fractional nonlinear diffusion equation. According to the Kaplan’s first eigenvalue method, we first prove the blow-up of the solutions in finite time for some sufficient conditions. We next give sufficient conditions for the existence of global solutions by using the result of Zhang and Sun. In conclusions, we find the second critical exponent for the existence of global and non-global solutions via the decay rates of the initial data at spatial infinity.

The unified Mittag-Leffler (ML) function is important factor in formulation of compact form of fractional integrals. In this paper estimations of integral operators, with the unified ML function as kernel are given. The Hadamard inequality in the form of fractional integrals is proved by considering refinement of convexities. These estimations provide various inequalities as refinements of recently published results.

The COVID-19 pandemic has led to the widespread use of face masks to reduce disease transmission, but one unintended consequence is that this may negatively impact sleep and arousal by altering the expression of yawning. Yawns are defined by an involuntary and powerful gaping of the jaw with inspiration, and the typical design of face masks may restrict and/or disrupt the mandibular jaw movement and counter-current heat exchange during this behavior. Face masks additionally impair the contagious nature of yawning by disrupting the recognition of yawning in others within social/community settings. Given that the neurophysiological consequences of yawning function in facilitating changes in state and arousal, and most notably transitions in waking and sleeping via thermoregulation, face mask usage could be an important variable to consider within sleep studies. We briefly outline these connections, highlight some important factors to consider, and discuss the implications for both prior and current research on sleep.

This study focuses on the optimal deployment problem, and determines the optimal size of a military force to send to the battle field. The decision is optimized, based on an objective function, that considers the cost of deployment, the cost of the time it takes to win the battle, and the costs of killed and wounded soldiers with equipment. The cost of deployment is modeled as an explicit function of the number of deployed troops and the value of a victory with access to a free territory, is modeled as a function of the length of the time it takes to win the battle. The cost of lost troops and equipment, is a function of the size of the reduction of these lives and resources. An objective function, based on these values and costs, is optimized, under different parameter assumptions. The battle dynamics is modeled via the Lanchester differential equation system based on the principles of directed fire. First, the deterministic problem is solved analytically, via derivations and comparative statics analysis. General mathematical results are reported, including the directions of changes of the optimal deployment decisions, under the influence of alternative types of parameter changes. Then, the first order optimum condition from the analytical model, in combination with numerically specified parameter values, is used to determine optimal values of the levels of deployment in different situations. A concrete numerical case, based on documented facts from the Battle of Iwo Jima, during WW II, is analyzed, and the optimal US deployment decisions are determined under different assumptions. The known attrition coefficients of both armies, from USA and Japan, and the initial size of the Japanese force, are parameters. The analysis is also based on some parameters without empirical documentation, that are necessary to include to make optimization possible. These parameter values are motivated in the text. The optimal solutions are found via Newton- Raphson iteration. Finally, a stochastic version of the optimal deployment problem is defined. The attrition parameters are considered as stochastic, before the deployment decisions have been made. The attrition parameters of the two armies have the same expected values as in the deterministic analysis, are independent of each other, have correlation zero, and have relative standard deviations of 20%. All possible deployment decisions, with 5000 units intervals, from 0 to 150000 troops, are investigated, and the optimal decisions are selected. The analytical, and the two numerical, methods, all show that the optimal deployment level is a decreasing function of the marginal deployment cost, an increasing function of the marginal cost of the time to win the battle, an increasing function of the marginal cost of killed and wounded soldiers and lost equipment, an increasing function of the initial size of the opposing army, an increasing function of the efficiency of the soldiers in the opposing army and a decreasing function of the efficiency of the soldiers in the deployed army. With stochastic attrition parameters, the stochastic model also shows that the probability to win the battle is an increasing function of the size of the deployed army. When the optimal deployment level is selected, the probability of a victory is usually less than 100%, since it would be too expensive to guarantee a victory with 100% probability. Some of many results of relevance to the Battle of Iwo Jima, are the following: In the deterministic Case 0 analysis, the optimal US deployment level is 66200, the time to win the battle is 30 days and 14000 US soldiers are killed or wounded. If the marginal cost of the time it takes to win a victory doubles, the optimal deployment increases to 75400, the time to win a victory is reduced to 26 days, and less than 12000 soldiers are killed or wounded. In the stochastic Case 0 analysis, the optimal US deployment level is 65000, the expected time to win the battle is 46 days and almost 25000 US soldiers are expected to be killed or wounded. If the cost per killed or wounded soldier increases from 0 to 5 M $US, the optimal deployment level increases to 75000. Then, the victory is expected to appear after 35 days and 19900 US soldiers are expected to be killed or wounded.

The goal of this study is to create regression models estimating the daily Penman–Monteith reference evapotranspiration (PMR) using latitude–temperature data for the state of Sinaloa, Mexico. Daily series of minimum–maximum temperature (1979–2017) were obtained from seven weather stations in Sinaloa. The reference evapotranspiration was calculated by the methods of Penman–Monteith using empirical equations (PMC), Hargreaves (HAC), and PMR. Prior to calculating PMC, the incident solar radiation (SR) was calculated. From the Acaponeta station (2005–2008, 2011–2013 and 2015–2017), all complete observed variables were obtained: mean temperature, incident solar radiation (SRg), average relative humidity and average wind speed at a height of 10 m. The data from the eight weather stations were provided by the National Meteorological Service and the National Water Commission. The daily observed Penman–Monteith reference evapotranspiration (PMO) was calculated. For validation, three simple linear regressions (SLR) were applied: SR vs SRg, PMC vs PMO and PMR vs PMO. hypothesis tests were applied to each SLR: Pearson correlation (Pr) vs critical Pearson correlation (Pcr). All rP were significantly different from zero (&gt; |0.576|): SRg vs SR (Pr = 0.951), PMC vs PMO (Pr = 0.592), and PMR vs PMO (Pr = 0.625). This study provides new models that can motivate and support the design and implementation of intelligent irrigation in the state considered “the breadbasket of Mexico.”

This study delves into the intricate dynamics of sustainable fisheries through the lens of mathematical modeling, specifically employing the Lotka-Volterra equations. The Lotka-Volterra equations, originally conceived to understand predator-prey interactions, offer a potent framework to model and predict fish population dynamics within aquatic ecosystems. The aim of this research is to demonstrate the applicability and efficacy of the Lotka-Volterra equations in understanding the delicate balance of fish populations and aiding sustainable fisheries management. Through this mathematical approach, we seek to provide a structured methodology and present results that showcase the potential of this model in predicting and managing fish populations. In our analysis, we adjust the parameters of the Lotka-Volterra equations to simulate various scenarios, enabling a comprehensive understanding of sustainable fishing practices. Our findings underscore the significance of mathematical models, particularly the Lotka-Volterra equations, in informing strategies to maintain fish populations in a sustainable and ecologically balanced manner, thereby ensuring the longevity of marine ecosystems and the fisheries thatrely upon them.

In this paper, we consider a pursuit-evasion game of inertial players, where pursuer’s control is subject to integral constraint, and evader’s control is subject to geometric constraint. In the pursuit problem, the main tool is the strategy of parallel pursuit. Sufficient conditions are obtained for the solvability of pursuit-evasion problems. Also, the main lemma describing the monotonicity of an attainability domain of the evader is proved and an explicit analytical formula for this domain is given. As one of the important results of our paper, the Isaacs Life-line game is solved for a special case.

Previous control methods developed by our research team cannot satisfy the high-accuracy requirements of unmanned surface vessel (USV) path-tracking during bathymetric mapping because of the excessive overshoot and slow convergence speed. For this reason, this study developed an adaptive fuzzy integral-derivative line-of-sight (AFIDLOS) guidance law for USV path-tracking control. Integral and derivative terms were added to counteract the effect of the sideslip angle, with which the USV could be quickly guided to converge to the planned path for bathymetric mapping. To obtain a high-accuracy of the look-ahead distance, a fuzzy control method was proposed. The proposed method was verified using simulations and outdoor experiments. The results demonstrate that the AFIDLOS guidance law can reduce the overshoot by 79.85%, shorten the settling time by 55.32% in simulation experiments, and reduce the average cross-track error by 10.91%, and can ensure a 30% overlap of neighboring strips of bathymetric LiDAR outdoor mapping when compared with the traditional method.

In this article, we present a comparative study between the Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM). The study outlines the significant features of the two methods, for solving nonlinear Volterra-Fredholm integro-differential equations. From the computational viewpoint, the VIM is more efficient, convenient and easy to use. Moreover, we proved the existence and uniqueness results and convergence of the solution. Finally, an example is included to demonstrate the validity and applicability of the proposed techniques.

This study aims to focus on using the Volterra series and machine learning for forecasting random and chaotic wind speed regimes, since the calm weather is mostly noticed at the local site, making the dataset selection difficult. A novel method is proposed to predict Volterra kernels up to the third order, using a forward-back propagation neural network with 12-month measurements at Fujairah site (UAE). Both daily and monthly wind speed data sets are investigated for forecasting. The three dominant hourly and daily kernels are extracted for each day and each month. Predicted future Volterra kernels are estimated from past values using both statistical analysis and individual neuro networks for each of the Volterra kernel coefficients. Due to the random nature of wind speed at the local site, a two-layer with 4 neurons per layer neuro network is used to locate the most variable and intense speed during 8-hours in the day. Forecasted wind speed is determined with errors arising from different sources such as the utilization of only 3rd-order Volterra kernels and the difficulty of machine training of the employed shallow network. Nevertheless, this work depicts a useful algorithm to forecast chaotic and random wind speed regimes. Computational time is a trade of the complexity of Volterra mathematical analysis.

This paper deals with the study of the existence and non existence of solutions of a three parameter's family of nonlinear fractional differential equation with mixed-integral boundary value conditions. We consider the $\alpha$-Riemann-Liouville fractional derivative, with $\alpha \in (1,2]$. In order to deduce the existence and non existence results, we first study the linear equation, by deducing the main properties of the related Green's functions. We obtain the optimal set of parameters where the Green's function has constant sign. After that, by means of the index theory, the nonlinear boundary value problem is studied. Some examples, at the end of the paper, are showed to illustrate the applicability of the obtained results.

In this paper we provide some bounds for the error in approximating the Riemann-Stieltjes integral $\int_{a}^{b}f (t) du (t)$ by the generalized trapezoidal rule \begin{equation*} \left[ u\left( b\right) -u\left( x\right) \right] f\left( b\right) +\left[ u\left( x\right) -u\left( a\right) \right] f\left( a\right) \end{equation*} under various assumptions for the integrand $f$ and the integrator $u$ for which the above integral exists. Applications for continuous functions of selfadjoint operators and unitary operators in Hilbert spaces are provided as well.

Dual generalized commutative quaternions have broad application prospects in many fields. Additionally, the matrix equation AXB = C has important applications in mathematics and engineering, especially in control systems, economics, computer science, and other disciplines. However, research on the matrix equation AXB = C over the dual generalized commutative quaternions remains relatively insufficient. In this paper, we derive the necessary and sufficient conditions for the solvability of the dual generalized commutative quaternion matrix equation AXB = C. Furthermore, we provide the general solution expression for this matrix equation, when it is solvable. Finally, a numerical algorithm and an example are provided to confirm the reliability of the main conclusions.

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.

Monogenity is a classical area of algebraic number theory that is very actively researched even today. This paper is a collection of the results obtained during the last few years in this area. Several of these results were presented at the series of online conferences "Monogenity and power integral bases".

In this study, the complex interactions between the well-known Mittag-Leffler functions with two, three, and four parameters are explored. We first study the integral forms of the Mittag-Leffler function $\mathsf{E}_{\alpha, \beta}^{\rho,\kappa}(z)$ with the goal of clarifying its mathematical behaviours and features. Moreover, we create relations between these functions and generalised hypergeometric functions and Fox-Wright functions, expanding the range of their use and comprehension. We explore a number of unique situations by in-depth examination, providing insight into the subtle characteristics of these functions. This investigation advances our theoretical knowledge and opens up possibilities for future applications in a number of scientific fields. As such, this study adds to the current conversation in mathematical analysis and is an important tool for both practitioners and researchers.

In this paper, the notion of θ∗-weak contraction is introduced, which is utilized to prove some fixed point results. These results are helpful to give a positive response to certain open question raised by Kannan [Amer. Math. Monthly 76:1969] and Rhoades [Contemp. Math. 72:1988] on the existence of contractive definition which does not force the mapping to be continuous at the fixed point. Some illustrative examples are also given to support our results. As applications of our result, we investigate the existence and uniqueness of a solution of non-linear matrix equations and integral equations of Volterra type as well.

In the paper, the authors generalize the notion "k-Mittag-Leffler function'', establish some integral transforms of the generalized k-Mittag-Leffler function, and derive several special and known conclusions in terms of the generalized Wright function and the generalized k-Wright function.

The authors propose a novel approach for a comprehensive evaluation of neuroprotective effects using both in vitro and in vivo methods. This approach allows for the initial screening of numerous newly synthesized chemical compounds and substances from plant and animal sources while preserving animal life. In vitro techniques, including mitochondrial suspensions and neuronal cell cultures, enable assessment of neuroprotective activity, which can be challenging in intact organisms. The preliminary methods help outline the neuroprotection mechanism depending on the neurodestruction agent. The authors have validated a model of acute cerebrovascular accident, which simulates key cerebrovascular phenomena such as reduced cerebral blood flow, energy deficit, glutamate-calcium excitotoxicity, oxidative stress, and early gene expression. A significant advantage of this model is its ability to reproduce the clinical picture of cerebral ischemia: impaired motor activity, signs of neurological deficits (paresis, paralysis, etc.), as well as disturbances in attention, learning, and memory. Crucial to this approach is the selection of biochemical, molecular, and cellular markers to evaluate nerve tissue damage and characterize potential neuroprotective agents. Additionally, a comprehensive set of molecular, biochemical, histological, and immunohistochemical methods is proposed for evaluating neuroprotective effects and underlying mechanisms of potential pharmaceutical compounds.

In contemporary construction, the prevalence of vibration serviceability issues in lightweight and slender structures has become increasingly common, owing to advancements in building materials and construction methods. While these structures often meet the criteria for ultimate limit states, they can still elicit complaints due to excessive vibrations induced by human activity. To address this challenge, the Integral Resonant Control (IRC) technique has emerged as a favored approach for actively damping vibrations in various systems. This study introduces a fresh perspective on implementing a multi-input multi-output (MIMO) IRC scheme for active vibration control (AVC) specifically tailored for pedestrian structures utilizing inertial mass actuators. Building upon a common framework and design methodology outlined in previous research, this work presents a novel application of MIMO IRC for AVC. The designed controller is rigorously tested and implemented on a laboratory floor structure to validate its efficacy.

Here we are concerning with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.

Systemic inflammation and coronary microvascular endothelial dysfunction are essential pathophysiological factors in heart failure with preserved ejection fraction (HFpEF) that support the use of statins. The pleiotropic properties of statins, such as anti-inflammatory, antihypertrophic, antifibrotic, and antioxidant effects, are generally accepted and may be beneficial in HF, especially in HFpEF. Numerous observational clinical trials have consistently shown a beneficial prognostic effect of statins in patients with HFpEF, while the results of two larger trials in patients with HFrEF have been controversial. Such differences may be related to a more pronounced impact of the pleiotropic properties of statins on the pathophysiology of HFpEF and pro-inflammatory comorbidities (arterial hypertension, diabetes mellitus, obesity, chronic kidney disease) that are more common in HFpEF. This review discusses the potential mechanisms of statin action that may be beneficial for patients with HFpEF, as well as clinical trials that have evaluated the statin effects on left ventricular diastolic function and clinical outcomes in patients with HFpEF.

In a multivariable system there are usually a number of relaxation times. When some of the relaxation times are shorter than others, the corresponding variables will decay to their equilibrium value faster than the others. After the fast variables have decayed, the system can be described with a smaller number of variables. From the theory of nonequilibrium thermodynamics, as formulated by Onsager, we know that the coefficients in the linear flux-force relations satisfy the so-called Onsager symmetry relations. The question we will address in this paper is how to eliminate the fast variables such that the coefficients in the reduced description for the slow variables still satisfy the Onsager relations. As the proof Onsager gave of the symmetry relations does not depend on the choice of the variables, it is equally valid for the subset of slow variables. Elimination procedures that lead to symmetry breaking are possible, but do not consider systems that satisfy the laws of nonequilibrium thermodynamics.

In this paper, we study nonlocal problems for a fractional diffusion equation and a degenerate hyperbolic equation with singular coefficients in the lower terms. The uniqueness of the solution to the problem is proved by the method of energy integrals. The existence of a solution is equivalently reduced to the question of the solvability of Volterra integral equations of the second kind and a fractional differential equation. For a particular solution of the proposed problem, its visualization is carried out for various values of the order of the fractional derivative. It is shown that the order of the derivative affects the intensity of the diffusion process (subdiffusion), as well as the shape of the wave front.

ACL instability poses a significant challenge in traumatology and orthopedic medicine, often requiring accurate diagnosis for appropriate treatment. While the pivot-shift test offers a crucial means of assessment, its reliance on subjective interpretation underscores the need for supplementary imaging studies. This study aims to address this limitation by developing a Bayesian classification algorithm tailored for integration into a mobile application. Using the built-in inertial sensors of smartphones, this new approach aims to dynamically evaluate rotational stability during knee examinations. Orthopedic specialists conducted knee evaluations on 52 subjects, with subsequent analysis revealing interesting insights. Intraobserver and interobserver analyses, as measured by ICC, demonstrated strong agreement both in terms of timing between maneuvers (ICC = 0.94) and signal amplitude (ICC = 0.71-0.66). Notably, the Bayesian algorithm successfully classified 95% of joint hypermobility cases, with an additional 7 cases of hyperlaxity identified by the Pivot-Shift Meter (PSM). These findings highlight the practicality and effectiveness of implementing a Bayesian classification algorithm within a mobile application for assessing and categorizing signals captured by smartphone inertial sensors during the pivot-shift test.

The resilience of towns and cities refers to their ability to adapt and recover when confronted with pressures or challenges. This study employs ten variables as indicators to assess the resilience of urban areas by analyzing official data and constructing a multilevel mixed-effects structural equation model. The empirical findings demonstrate that enhancing resilience significantly influ-ences urban service functions, such as strengthening healthcare systems, stabilizing the real estate market, and addressing socio-economic challenges. Specifically, factors such as healthcare re-sources, housing demand, population structure, and social security exhibit varying levels of resil-ience, which profoundly impact the spatial distribution of these factors and socio-economic de-velopment. Disparities in healthcare resource allocation, demographic aging trends, and shifts in the housing market closely correlate with resilience levels in different regions. Additionally, the study emphasizes that improving resilience not only boosts the reliability and security of urban services but also ensures that communities receive necessary support and protection during times of adversity. Consequently, policymakers should recognize the pivotal role of urban resilience in resource allocation and social equity, devising corresponding strategies to enhance the resilience of these areas.

Dual quaternions have wide applications in automatic differentiation, computer graphics, mechanics and others. Due to its application in control theory, the matrix equation AXB=C has been extensively studied. However, there is currently limited information on matrix equation AXB=C over the dual quaternion algebra. In this paper, we provide the necessary and sufficient conditions for the solvability of the dual quaternion matrix equation AXB=C, and present the expression for the general solution when it is solvable. As an application, we derive the ϕ-Hermitian solutions for the dual quaternion matrix equation AXAϕ=C, where the ϕ-Hermitian extends the concepts of Hermiticity and η-Hermiticity. Lastly, we present a numerical example to verify the main research results of this paper.

This article focuses on obtaining the analytical solutions for parabolic Volterra integro- differential equations in d-dimensional with different types frictional memory kernel. Based on theories of Laplace transform, Fourier transform, the properties of Fox-H function and convolution theorem, analytical solutions of the equations in the infinite domain are derived under three frictional memory kernel functions respectively. The analytical solutions are expressed by infinite series, the generalized multi-parameter Mittag-Leffler function, Fox-H function and convolution form of Fourier transform. In addition, the graphical representations of the analytical solution under different parameters are given for one-dimensional parabolic Volterra integro-differential equation with power-law memory kernel. It can be seen that the solution curves subject to Gaussian decay at any given moment.

In the paper, the authors survey integral representations of the Catalan numbers and the Catalan–Qi function, discuss equivalent relations between these integral representations, supply alternative and new proofs of several integral representations, collect applications of some integral representations, and present sums of several power series whose coefficients involve the Catalan numbers.

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.

In the realm of metal steel and iron manufacturing, there is a constant drive to optimize production efficiency and enhance the quality of the final products. This abstract explores a paradigm shift in this industry through the utilization of Computational Fluid Dynamics (CFD) as a powerful tool for achieving these goals .The study focuses on various critical aspects of the manufacturing process. Firstly, it delves into three-phase processes such as slag and gas entrainment in liquid steel, which have a significant impact on the overall product quality. Understanding and optimizing these processes is crucial to ensure the desired chemical composition and physical properties of the final metal.The abstract investigates the role of CFD in vacuum degassing, a process that plays a pivotal role in removing impurities, such as hydrogen and oxygen, from the liquid steel. By leveraging CFD to simulate and analyze the fluid flow patterns, researchers and engineers can design more efficient vacuum degassing systems, leading to improved product purity and reduced waste.Another crucial aspect explored in this abstract is the alloy melt and mixing process. By employing CFD simulations, researchers can gain insights into the movement of different alloy components and optimize their distribution within the melt. This aids in achieving the desired alloy composition, ensuring uniformity, and enhancing the mechanical properties of the final product.In addition, the study delves into the movement and flotation of inclusions, which are unwanted impurities present in the metal. CFD can be utilized to model and analyze the behavior of these inclusions, enabling engineers to design efficient strategies for their removal, thereby enhancing the purity and integrity of the final product.Moreover, the abstract considers the impact of melt temperature losses, which can occur during different stages of the manufacturing process. By employing CFD, it becomes possible to understand and mitigate these temperature losses, leading to improved energy efficiency and better control over the manufacturing parameters.Part 1 of this abstract critically evaluates the use of CFD in iron making, analyzing its benefits and limitations. It highlights how CFD can aid in process optimization, improving the understanding of complex phenomena involved in iron making, and ultimately leading to enhanced production efficiency.Part 2 focuses on the application of CFD in steel making and steel operation. It explores the fluid flow dynamics during different stages of steel production, including refining, casting, and rolling. By leveraging CFD, engineers can optimize these processes, leading to improved product quality, reduced defects, and increased productivity.This abstract demonstrates the transformative potential of Computational Fluid Dynamics in metal, steel, and iron manufacturing. By utilizing CFD as a tool to model and analyze complex fluid flow phenomena, researchers and engineers can revolutionize the production process, maximizing efficiency, and ensuring high-quality end products.

The article presents the case of a 27-year-old female patient with idiopathic congenital complete heart block who was referred by her primary care physician for cardiological evaluation. The conduction disturbance was recognized at the age of 6 years and was asymptomatic. The disqualification from pacemaker implantation included detailed history of a patient’s symptoms, echocardiographic assessment of the heart, exercise testing and ECG Holter monitoring. The aid of salbutamol administered orally was also useful.

The goal was to model the irrigated (IBY) and rainfed (RBY) bean yields, as a function of essential climatic variables (ECVs), in the center (Culiacán) and south (Rosario) from Sinaloa. In Sinaloa, and for the period 1982–2013 (October–March), the following were calculated: a) temperatures. b) average degree days for the bean, c) cumulative potential evapotranspiration and d) cumulative effective precipitation. For ECVs, from the European Space Agency, e) daily soil moisture. f) IBY and RBY, from the Agrifood and Fisheries Information Service. Multiple linear regressions were applied, which modeled IBY–RBY (dependent variables), as a function of ECVs (independent variables). Then, to establish each Pearson correlation (PC) as significantly different from zero, a hypothesis test was applied: PC vs Pearson's critical correlation (CPC). The four models obtained were significantly predictive: IBY–Culiacán (PC = 0.590 > CPC = |0.349|), RBY–Culiacán (PC = 0.734 > CPC = |0.349|), IBY–Rosario (PC = 0.621 > CPC = |0.355|) and RBY–Rosario (PC = 0.532 > CPC = |0.349|). This study is the first in Sinaloa to predict IBY and RBY based on ECVs, contributing to the production of sustainable food.

Scientific, technical and bioinformatics advances have made it possible to establish analytics-based molecular biosimilarity for the approval of biosimilars. If the molecular structure and other product- and process-related attributes are comparable within the limits of testing then a biosimilar candidate would have safe safety and efficacy as its reference products. The current model of animal and human testing becomes redundant since all of these studies have much lower sensitivity and reproducibility in confirming biosimilarity. The recent AI-based protein structure prediction model has confirmed that the 3D structure can be predicted from the amino acid sequence, reducing the need for structural analysis; however, the new test methods based on MS are millions of times more sensitive and accurate. While the regulatory agencies have begun waiving animal testing and, in some cases, clinical efficacy testing, removing clinical pharmacology profiling brings a dramatic paradigm shift, reducing development costs without compromising safety and efficacy. Also shared is a list of 160+ products ready to enter as biosimilars. Major actions from regulatory agencies and developers are required to make this paradigm shift.

Diversity as well as temporal and spatial changes of the proportional abundances of different antibiotics (cycling, mixing or combinations thereof) have been hypothesised to be an effective administrative control strategy in hospitals to reduce the prevalence of antibiotic-resistant pathogens in nosocomial or community-acquired infections. However, a rigorous assessment of the efficacy of these control strategies is lacking. The main purpose here is to present a mathematical framework for the assessment of control stategies from a processual stance. To this end, we adopt diverse measures of heterogeneity and diversity of proportional abundances based on the concept of entropy from other fields and adapt them to the needs in assessing the impact of variations in antibiotic consumption on antibiotic resistance. Thereby, we derive a family of diversity measures whose members exhibit different degrees of complexity. Most important, we extent these measures such that they account for the assessment of temporal changes in heterogeneity including otherwise undetected diversity-invariant permutations of antibiotics consumption and prevalence of resistant pathogens. We apply a correlation analysis for the assessment of associations between changes of heterogeneities on the antibiotics and on the pathogen side. As a showcase, which serves as a proof-of-principle, we apply the derived methods to records of antibiotic consumption and prevalence of antibiotic-resistant germs from University Hospital Dresden. Besides the quantification of heterogeneities of antibiotics consumption and antibiotic resistance, we show that a reduction of prevalence of antibiotic-resistant germs correlates with a temporal change of similarity with respect to the first observation of antibiotics consumption, although heterogeneity remains approximately constant. Although an interventional study is pending, our mathematical framework turns out to be a viable concept for the assessment and optimisation of control strategies intended to reduce antibiotic resistance.

The research paper provides a mathematical framework for understanding phase shift in wave phenomena, bridging theoretical foundations with real-world applications. It emphasizes the importance of phase shift in physics and engineering, particularly in fields like telecommunications and acoustics. Key equations are introduced to explain phase angle, time delay, frequency, and wavelength relationships. The study also introduces the concept of time distortion due to a 1° phase shift, crucial for precise time measurements in precision instruments. The research also addresses infinitesimal wave energy loss related to phase shift, enriching our understanding of wave behavior, and impacting scientific and engineering disciplines.

Nutrigenetics concerns individual differences in the reaction to food based on the genetic factors. Nutrigenomics analyses direct influences of nutrients on gene expression. Both terms are explained in our review article. Nutrigenetics and nutrigenomics require a deep understanding of nutrition, genetics and biochemistry and of new ‘omic’ technologies. It is often difficult to appreciate their relevance in the practice of preventive approaches for optimizing health, delaying onset of disease and diminishing its severity. This paper represents a review about the current research on Nutrigenomics and Nutrigenetics, and provide scientific data for a new integrated clinical approach.

In the past few years, cloud-based additive manufacturing has shown its application and potential in industries. For this reason, when the demand for cloud-based additive products increases, efficient scheduling of related tasks becomes more important to achieve optimized duration. This research proposes a Heuristic Scheduling Algorithm (HSA) for use in Cloud-Based Additive Manufacturing (CBAM) with an approach to Critical Chain Buffer Management (CC/BM). This research aims to schedule and optimize the time in cloud-based additive manufacturing, in addition to the parts production process, it also includes the steps of receiving online orders and informing the manufacturing unit and sending them to the customer. The HSA proposed in this research consists of three phases 1- Buffer sizing, 2- Additive manufacturing and logistics scheduling, and 3- Buffer controlling. To evaluate, the performance of the algorithm is simulated. The finding shows that the proposed HAS can effectively solve the CBAM scheduling problem.

The intranasal route of drug administration is characterized by high bioavailability and is considered promising for rapid delivery of drugs with systemic action to the central nervous system, bypassing the blood-brain barrier. This is particularly important for the use of neuroprotective drugs in the treatment of brain tissue damage in infants caused by the effects of intrauterine hypoxia. Creation of new dosage forms for neonatology with the use of software and mathematical technologies in pharmaceutical development allows to create cerebroprotective drugs with controlled pharmaco-technological properties, thus reducing time and resources for necessary research. We developed a formulation of a new nasal gel formulation with Angiolin using Box-Benken experiment design for the therapy of prenatal CNS damage. It was found that the consistency properties of the nasal gel were significantly influenced by the gelling agent and mucoadhesive component - sodium salt of carboxymethylcellulose. We have optimized the composition of nasal gel formulation with Angiolin using the formed models and relationships between the factors. The optimized composition of the obtained nasal gel has satisfactory parameters of thixotropic properties. The developed 1% gel for neuroprotection with Angiolin meets all the requirements for harmlessness and safety to drug forms of this group - low toxicity, absence of local irritant and allergic effect.

(1) Background: In this work, a series of benzimidazole derivatives containing colchicine-like and cathechol-like moieties with methyl group substitution in the benzimidazole ring were evaluated for their in vitro antiproliferative, pro-apoptotic and antioxidative activity against highly invasive breast cancer cell line MDA-MB-231 and related impairment of tubulin dynamics; (2) Methods: MTT assay was used to evaluate the antiproliferative activity. In vitro tubulin polymerization assay as well as docking analysis was applied to prove the alterations in tubulin polymerization. Immunofluorescent and DAPI staining reveal the pro-apoptotic potential of benzimidazole derivatives and the effect on tubulin’s dynamics in living cells. The antioxidant activity was evaluated by scavenging of H2O2 and hypochlorite ion and ortho-phenanthroline tests; (3) Results: The compounds containing colchicine-like moiety displayed significant growth inhibitory effect against cancer cell line as was highlighted the role of methyl functional group on the tubulin aggregation and blockage of mitosis. All compounds showed an ability to scavenge H2O2, while the compounds with cathecol-like moiety were more effective against hypochlorite ion and chelation of iron; (4) Conclusions: The benzimidazole derivative containing colchicine-like moiety and methyl group substitution in benzimidazole ring is a potential antiproliferative and microtubule destabilizing agent.

This research work deals with the formulation of numerical scheme with algorithm to compute singularly perturbed partial differential equations(SP-PDEs) involving a significant negative shift. The problem involves small parameter which causes a rapidly changing boundary layers in the vicinity of a body, and the negative shift term causes interior layer. Such appearance of an abruptly varying layers causes difficulties to find the exact solution and it is not adequate to employ classical numerical methods. The technique presented in this research work simplifies these challenges and yields accurate numerical solution.The stability and convergence analyses of the methods are examined and proven. To test the developed technique, numerical experiments are carried out and confirmed with theoretical analysis.

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.

In this paper, the definition of information entropy of Smoluchowski coagulation equation for Brownian motion is introduced based on coagulation probability. The expression of entropy is the function of geometric average particle volume and standard deviation with lognormal distribution assumption. The asymptotic solution with moment method shows that the entropy is a monotone increasing function of time, which is equivalence to the entropy based on particle size distribution. the result reveals that the present definition of entropy of Smoluchowski coagulation equation are inadequate because the particle average volume at equilibrium cannot be determined from the principle of maximum entropy. This provides a basis for further exploring the global properties of Smoluchowski coagulation equation.

In the paper, by induction and recursively, the author proves that the generating function of multivariate logarithmic polynomials and its reciprocal are a Bernstein function and a completely monotonic function respectively, establishes a Lévy-Khintchine representation for the generating function of multivariate logarithmic polynomials, deduces an integral representation for multivariate logarithmic polynomials, presents an integral representation for the reciprocal of the generating function of multivariate logarithmic polynomials, computes real and imaginary parts for the generating function of multivariate logarithmic polynomials, derives two integral formulas, and denies the uniform convergence of a known integral representation for Bernstein functions.

The conformations of trifluoroacetyl triflate, CF3C(O)OSO2CF3, were investigated through vibrational experimental methods (gas-phase FTIR, liquid-phase Raman, and Ar-matrix FTIR spectroscopy) and Density Functional Theory (DFT) calculations. A potential energy surface was computed using the B3P86 /6-31+g(d) approximation as a function of the dihedral angles τ1 = CCOS and τ2 = COSC. The surface reveals three minima, which were further optimized using the B3LYP method with various basis sets (6-31++G(d), 6-311++G(d), tzvp and cc-pvtz). The global minimum corresponds to a syn-anti conformer (the CO double bound syn with respect the O−S single bond and the C−O single bond anti with respect to de S−C single bond). The other two minima represent enantiomeric syn-gauche forms. The Ar-matrix FTIR spectrum exhibited clear evidence of the presence of two conformers. Furthermore, the randomization process observed following broad-band UV-visible irradiation facilitated the identification of the IR absorption of each conformer. Based on the Ar-matrix FTIR experiments, the vapour phase of trifluoroacetyl triflate at room temperatures was composed of approximately 60-70% of the syn-anti conformer and 30-40% of the syn-gauche form.

In the paper, the authors survey integral representations (including the Lévy--Khintchine representations) and applications of some bivariate means (including the logarithmic mean, the identric mean, Stolarsky's mean, the harmonic mean, the (weighted) geometric means and their reciprocals, and the Toader--Qi mean) and the multivariate (weighted) geometric means and their reciprocals, derive integral representations of bivariate complex geometric mean and its reciprocal, and apply these newly-derived integral representations to establish integral representations of Heronian mean of power 2 and its reciprocal.

In the research we consider a structure-fluid interaction of oscillating piezodevice and acoustic liquid. Such problem requires finding resonance or anti-resonance frequencies of the solid structure to use them in the latter frequency-response analyses step. After finite element discretization of the issue, we need to solve a generalized eigenvalue problem (GEP). The most efficient numerical method for solving the partial GEP is the shift-and-invert Lanczos method. Each step of this algorithm requires solving a large scale system of linear algebraic equations (SLAEs) with special properties. Various ways of ordering grid nodes lead to coefficient matrices with different structure. Several methods are compared in terms of efficiency. The results of the numerical experiments are presented.

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.

We investigate solutions of the classical Mathieu-Hill (MH) equation which characterizes the dynamics of trapped ions, based on the Floquet theory and starting from a well known analytical model. The analytical model we introduce demonstrates that the equations of motion are equivalent to those of the harmonic oscillator (HO). Two independent approaches are used, based on two classes of complex solutions of the MH equation. The paper addresses both the damped HO and parametric oscillator (PO) for an ion confined in an electrodynamic (Paul) trap. Stability and instability regions for the periodic orbits associated to the MH equation which describes a HO (PO) confined in an electrodynamic trap are also discussed, depending on the values of the Floquet exponent, for very small values of the $q$ parameter. The main objective of the paper is to identify stable and bounded solutions for the dynamics of a HO levitated in an electrodynamic trap. This paper represents a follow-up of a recently published article in Photonics, 11 (6) 551.

In our previous papers, we demonstrated that inflammation and aging are the common roots of cancer and Alzheimer’s disease (AD). In both diseases, there is an inhibition of the mitochondria. In cancer, the alkaline intracellular pH (pHi) is associated with cell proliferation; acidic pHi causes apoptosis in AD. This difference is because cancer feeds on chemically neutral glucose, while neurons feed on acidic lactic acid. Increased uptake of lactic acid is responsible for acidic pH and cell death. Similarly, to AD, inflammation is responsible for metabolic shifts in age-related macular degeneration (AMD). In AD, there is hyperosmolarity responsible for increased lactic secretion by glial cells. Increased lactic secretion will cause neo-angiogenesis and neural cell death. Drugs increasing hyperosmolarity (Polyethylene Glycol) cause neo-angiogenesis and drusen-like structures in rodents. The link between AMD and inflammation is reinforced by the fact that treatments aiming at restoring mitochondrial activity, such as lipoic acid and/or methylene blue, have been experimentally shown to be effective in each set of diseases. The role of osmolarity has been demonstrated in the pathologies of the anterior segment of the eye, such as dry eye, corneal ulceration, cataracts, and glaucoma. The role of increased osmolarity in age-related macular degeneration (AMD) has been largely overlooked. We herein suggest that metabolic shift, inflammation, and hyperosmolarity are key players in the pathogenesis of AMD.

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.

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.

Prosthechea karwinskii is an orchid endemic to Mexico, threatened by the destruction of its habitat and the extraction of specimens to meet its demand for ornamental and religious use. Most of its populations, and the most locally abundant ones, are found in Oaxaca state. Variations in some floral traits have been observed in these populations. We implemented a morphometric analysis to assess their floral variation and identify the most significant characters in the morphological patterns of this orchid. Floral samples were collected from 17 populations of P. karwinskii in Oaxaca, as well as from specimens used as ornaments during Easter in a Oaxacan community (Zaachila), whose origin is unknown. Sampling of natural populations covered the environmental, geographic and morphological variation of the species. We performed an analysis of variance (ANOVA), principal component analysis (PCA), and canonical variate analysis (CVA), and cluster analysis including 185 individuals and 45 variables (13 of them were discarded in the multivariate analyzes due to high correlation). Characters of the column, lateral sepal, and labellum were most informative about the observed morphological patterns. Albarradas showed the greatest morphological differentiation, mainly due to the column. In general, individuals from the same locality tended to overlap more, especially the populations of Jaltianguis and Yahuiche, which were different from the geographically close population of Etla. Teposcolula presented the highest values in perianth characters, unlike Sola_Rancho Viejo. The specimens recovered from religious ornaments were morphologically more similar to those from the Mixtec region and surroundings of Etla. Our work encourages working on collaborative conservation strategies to ensure the long-term permanence of both the species and its traditional uses.

Clustering, or otherwise known as cluster analysis, is a learning problem that takes place without any human supervision. This technique has often been utilized, much efficiently, in data analysis, and serves for observing and identifying interesting, useful, or desired patterns in the said data. The clustering technique functions by performing a structured division of the data involved, in similar objects based on the characteristics that it identifies. This process results in the formation of groups, and each group that is formed, is called a cluster. A single said cluster consists of objects from the data, that have similarities among other objects found in the same cluster, and resemble differences when compared to objects identified from the data that now exist in other clusters. The process of clustering is very significant in various aspects of data analysis, as it determines and presents the intrinsic grouping of objects present in the data, based on their attributes, in a batch of unlabeled raw data. A textbook or otherwise said, good criteria, does not exist in this method of cluster analysis. That is because this process is so different and so customizable for every user, that needs it in his/her various and different needs. There is no outright best clustering algorithm, as it massively depends on the user’s scenario and needs. This paper is intended to compare and study two different clustering algorithms. The algorithms under investigation are k-mean and mean shift. These algorithms are compared according to the following factors: time complexity, training, prediction performance and accuracy of the clustering algorithms.