Although Eulerian approaches are standard in computational acoustics, they are less effective for certain classes of problems like bubble acoustics and combustion noise. A different approach for solving acoustic problems is to compute with individual particles following particle motion. In this paper, a Lagrangian approach to model sound propagation in moving fluid is presented and implemented numerically, using three meshfree methods to solve the Lagrangian acoustic perturbation equations (LAPE) in the time domain. The LAPE split the fluid dynamic equations into a set of hydrodynamic equations for the motion of fluid particles and perturbation equations for the acoustic quantities corresponding to each fluid particle. Then, three meshfree methods, the smoothed particle hydrodynamics (SPH) method, the corrective smoothed particle (CSP) method, and the generalized finite difference (GFD) method, are introduced to solve the LAPE and the linearized LAPE (LLAPE). The SPH and CSP methods are widely used meshfree methods, while the GFD method based on the Taylor series expansion can be easily extended to higher orders. Applications to modeling sound propagation in steady or unsteady fluids in motion are outlined, treating a number of different cases in one and two space dimensions. A comparison of the LAPE and the LLAPE using the three meshfree methods is also presented. The Lagrangian approach shows good agreement with exact solutions. The comparison indicates that the CSP and GFD method exhibit convergence in cases with different background flow. The GFD method is more accurate, while the CSP method can handle higher Courant numbers.

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

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

The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudrayshov method for the exact analytical solution. The modified Kudrayshov method converts the nonlinear partial differential equation to algebraic equations, as a result of various steps, which on solving the so obtained equation systems yields the analytical solution. By this way various exact solutions including complex structures are found and drawn their behaviour in complex plane by Maple to compare the uniqueness of solutions.

The author demonstrates a stable Lagrangian solid modeling method, tracking the interactions of solid mass particles rather than using a meshed grid. This numerical method avoids the problem of tensile instability often seen with smooth particle applied mechanics by having the solid particles apply stresses expected with Hooke's law, as opposed to using a smoothing function for neighboring solid particles. This method has been tested successfully with a bar in tension, compression, and shear, as well as a disk compressed into a flat plate, and the numerical model consistently matched the analytical Hooke's law as well as Hertz contact theory for all examples. The solid modeling numerical method was then built into a 2-D model of a pressure vessel, which was tested with liquid water particles under pressure and simulated with smoothed particle hydrodynamics. This simulation was stable, and demonstrated the feasibility of Lagrangian specification modeling for fluid–solid interactions.

In this paper, we found a new model for compact star with charged anisotropic matter distribution considering an extended version of the Chaplygin equation of state. We specify a particular form of the metric potential Z(x) that allows us to solve the Einstein-Maxwell field equations. The obtained model satisfies all physical properties expected in a realistic star such that the expressions for the radial pressure, energy density, metric coefficients, measure of anisotropy and the mass are fully well defined and are regular in the interior of star. The solution obtained in this work can have multiple applications in astrophysics and cosmology.

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.

The second article in the series presents the application of the Smoothed Particle Hydrodynamics (SPH) method to modelling of batch crystallisation in stirred tanks. A methodology to integrate the population balance equations (PBE) in parallel and independently from the Navier-Stokes equations is demonstrated. The benefits of the proposed methodology in terms of computational requirements, accuracy and availability of the crystal size distribution are discussed. The specific formulation of the SPH equations where the resulting system of ordinary differential equations is solved using the weighted contributions rather than numerically by solving a linear system of equations allows for massive parallelisation and a very loose coupling of the population balance and the fluid dynamics. It has been demonstrated, that the population balance equations can be solved on a Shared Memory Architecture (SMA) system using the OpenMP interface while the fluid dynamics equations being computed independently on a General Purpose Graphics Processing Unit (GPGPU) using the NVidia CUDA technology. This way, a significant portion of the computational overhead due to the large number of additional transport equations resulting from the discretisation of the population balance was removed: the SPH simulation coupled with 200 population balance equations was only 40% slower compared to SPH-only simulation. Two methods for the solution of population balance equations that preserve full crystal size distribution were implemented: discretised population balance (DPB) and method of characteristics (MOCH). The DPB equations are solved using the high-resolution finite-volume method with flux limiter and the effect of a large number of different flux limiters have been investigated. Both methods were validated using the case studies from the literature where an analytical solution can be derived. The developed models were applied to a numerical solution of coupled computational fluid dynamics and population balance equations to model a batch crystallization process. The effect of the hydrodynamics on the local temperature/supersaturation and the resulting crystal size distribution was captured and compared to the ideal mixing case. The simulation results from the DPB and MOCH methods were compared in terms of computational requirements and accuracy and MOCH selected as computationally more efficient and accurate.

An expansion method based on time fractional Sine-Gordon equation is implemented to construct some real and complex valued exact solutions to the Korteweg-de Vries and modified Korteweg-de Vries equation in time fractional forms. Compatible fractional traveling wave transform plays a key role to be able to apply homogeneous balance technique to set the predicted solution. The relation between trigonometric and hyperbolic functions based on fractional Sine-Gordon equation allows to form the exact solutions with multiplication of powers of hyperbolic functions.

Besides the Lagrangian and the Eulerian descriptions, the motion of a body can also be expressed relative to the present configuration of the body, known as the relative motion description. It is interesting to consider such a relative motion description in general to formulate the basic system of field equations for solid bodies. In doing so, when the time increment from the present state is small enough, the nonlinear constitutive equations can be linearized relative to the present state so that the resulting system becomes linear. This will be done for thermoelastic materials with a brief comment on the exploitation of entropy principle in general. Relative Lagrangian formulation is based on the well-known ``small-on-large'' idea, and can be implemented for solving problems with large deformation in successive incremental manner. Some applications of such a formulation in numerical simulations are briefly reviewed.

Deterministic-stochastic empirical mode decomposition (EMD) is used to obtain low-frequency (non-diffusive, i.e., background velocity) and high-frequency (diffusive, i.e., eddies) components from a Lagrangian drifter‘s trajectory. Eddy characteristics are determined from the time series of eddy trajectories from individual Lagrangian drifter such as the eddy radial scale, eddy velocity scale, eddy Rossby number, and eddy-background kinetic energy ratio. A long-term dataset of the SOund Fixing And Ranging float time series obtained near the California coast by the Naval Postgraduate School from 1992 to 2004 at depth between 150 and 600 m (http://www.oc.nps.edu/npsRAFOS/) is used as an example to demonstrate the capability of the deterministic-stochastic EMD.

In the present work report, the MgAl₂O₄and the Ag/MgAl₂O₄ samples were successfully synthesized by the modified hydrothermal and the isovolumetric impregnation methods, respectively. The structural properties of the prepared samples were systematically characterized by XRD, SEM, TEM, DRS, XPS and et al techniques. The photocatalytic degradation of methylene blue by the Ag/MgAl₂O₄ and MgAl₂O₄ samples was comparatively studied under UV lamp irradiation. The results revealed that the prepared Ag/MgAl₂O₄ (pH=6) samples were the most active among the samples in photocatalytic of methylene blue. Under UV lamp irradiation, the Ag/MgAl₂O₄ (pH=6) photodegradation of methylene blue reached to 89.6% within 120 min. And the Ag/MgAl₂O₄ (pH=6) complex photocatalysts displayed a high photochemical stability under repeated irradiation. Repeated irradiate the Ag/MgAl₂O₄ (pH=6) compound, which indicated it had a high photochemical stability.

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.

In this study we have investigated the effect of the addition of Nb2O5 (up to 5 mol%) on the structure and luminescent properties of ZnO-B2O3 glass doped with 0.5 mol % Eu2O3 by using of infrared (IR), Raman and photoluminescence (PL) spectroscopy. Physical properties as molar volume, oxygen packing density and glass transition temperature were determined using the results of differential thermal analyisis (DTA) and Archimedes principle for density. IR and Raman spectra revealed that niobium ions incorporate into the base zinc borate glass as NbO4 trtraherda and NbO6 octahedra. A strong red emission from the 5D0 level of Eu3+ ions was registered under near UV (392 nm) excitation using the sharp 7F0 - 5L6 transition of Eu3+. The integrated fluorescence intensity ratio R (5D0 → 7F2/5D0 → 7F1) was calculated to estimate the degree of asymmetry around the active ion, suggesting a location of Eu3+ in non-centrosymmetric sites. The higher Еu3+ luminescence emission observed in zinc borate glasses containing 1÷5 mol% Nb2O5 compared to the Nb2O5-free zinc borate glass evidences that Nb2O5 is suitable component for modification of host glass structure and improving the emission intensity.

Abstract Using the Pauli algebra version of the Dirac equation six symmetric but non-equivalent copies of the QED Lagrangian are constructed. The group of symmetries is the group of outer automorphisms of the finite quaternion group, isomorphic to the group of permutations on three letters. Solutions to corresponding Dirac equations form six sectors of fermion fields. The intersections between different sectors can only contain massless fields, implying that the sectors are distinct. If the symmetry could be extended to the full Standard Model Lagrangian it would predict the ratio of dark matter to ordinary matter of 5 : 1 which is close to the ratio of 5.2 : 1 according to current observations.

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.

Small interfering RNA (siRNA) holds significant therapeutic potential by silencing target genes through RNA interference. Current clinical applications of siRNA have been primarily limited to liver diseases, while achievements in delivery methods are expanding its applications to various organs, including the lungs. Cholesterol-conjugated siRNA emerges as a promising delivery approach due to its low toxicity and high efficiency. This study focuses on developing a cholesterol-conjugated anti-Il6 siRNA and the evaluation of its potency for the potential treatment of inflammatory diseases using the example of acute lung injury (ALI). The biological activities of different Il6-targeted siRNAs containing chemical modifications were evaluated in J774 cells in vitro. The lead cholesterol-conjugated anti-Il6 siRNA after intranasal instillation demonstrated dose-dependent therapeutic effects in a mouse model of ALI induced by lipopolysaccharide (LPS). The treatment significantly reduced Il6 mRNA levels, inflammatory cell infiltration, and the severity of lung inflammation. IL6 silencing by cholesterol-conjugated siRNA proves to be a promising strategy for treating inflammatory diseases, with potential applications beyond the lungs.

Self-organized criticality (SOC) is a universal mechanism for self-sustained critical behavior in large-scale systems evolving outside equilibrium. Our report explores a tentative link between SOC and Lagrangian field theory, with the long-term goal of bridging the gap between complex dynamics and the non-perturbative behavior of quantum fields.

Current numerical methods for simulating biophysical processes in aquatic environments are typically constructed in a grid-based Eulerian framework or as an individual-based model in a particle-based Lagrangian framework. Often, the biogeochemical processes and physical (hydrodynamic) processes occur at different time and space scales, and changes in biological processes do not affect the hydrodynamic conditions. Therefore, it is possible to develop an alternative strategy to grid-based approaches for linking hydrodynamic and biogeochemical models that can significantly improve computational efficiency for this type of linked biophysical model. In this work, we utilize a new technique which links hydrodynamic effects and biological processes through a property-carrying particle model (PCPM) in a Lagrangian/Eulerian framework. The model is tested in idealized cases and its utility is demonstrated in a practical application to Sandusky Bay. Results show the integration of Lagrangian and Eulerian approaches allows for a natural coupling of mass transport (represented by particle movements and random walk) and biological processes in water columns which is described by a nutrient-phytoplankton-zooplankton-detritus (NPZD) biological model. This method is far more efficient than traditional tracer based Eulerian biophysical models for 3-D simulation, particularly for a large domain and/or ensemble simulations.

The statistical bundle is the set of couples $(Q,W)$ of a probability density Q and a random variable W such that $\mathbb{E}$_Q [W] = 0. On a finite state space, we assume Q to be a probability density with respect to the uniform probability and give an affine atlas of charts such that the resulting manifold is a model for Information Geometry. Velocity and accelleration of a one-dimensional statistical model are computed in this set up. The Euler-Lagrange equations are derived from the Lagrange action integral. An example of Lagrangian using minus the entropy as potential energy is briefly discussed.

Local food has continued to become more popular in both the home and as featured ingredients in all segments of food service. Numerous studies have explored the motivating factors for consumer purchasing motivators. However, no known study has explored if there is a correlation between ego and intent to buy local foods. This study adopted a modified version of the Theory of Trying and surveyed a sample of 237 food service buying agents in South Carolina to examine their perceptions of buying local. Results suggest that ego is a predictor of trying to purchase local foods for restaurants. It was also found that the modified model is an acceptable model for predicting buyer intent. These findings support the majority of the studies looking at ego-centric behaviors with green purchases and could potentially help local food suppliers to better market their products to foodservice establishments. This study could also act as the foundation for future studies to explore the full extent of ego’s motivational effect on purchasing intentions in the food service industry.

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.

Three kinds of inorganic alkali are introduced into tetraethylenepentamine (TPEA) and polyethyleneimine (PEI) modified MCM-41 as the CO2 adsorbents. FT-IR and TGA are used to characterize the surface groups and the thermal stability of adsorbents. Chemical titration method is used to measure the alkali amounts of adsorbents. Thermo-gravimetric analysis with 10%CO2/N2 as the simulated flue gas is used to test the CO2 adsorption performance of adsorbents. The results show that all three kinds of inorganic alkali containing adsorbents exhibit promoted CO2 adsorption capability than traditional TPEA and PEI modified samples. Ca(OH)2 and PEI modified samples exhibit the highest adsorption capacity and stable regeneration property. The introduction of inorganic alkali changes the chemical adsorption mechanism between CO2 and increases the effective alkali amounts due to its hydroxyl groups. The CO2 adsorption capacities have a linear dependence relation with the alkali amounts of adsorbents, indicating that alkali amount is a critical factor for novel adsorbents exploring.

The Lagrangian and Eulerian structure and dynamics of a strong wind event in the Tokar Gap region are described using a WRF model hindcast for 2008. Winds in the Tokar Gap reach 25 m s-1 and remain coherent as a jet far out over the Red Sea, whereas equally strong wind jets occurring in neighboring gaps are attenuated abruptly by a jump-like hydraulic transition that occur just offshore of the Sudan coast. The transition is made possible by the supercritical nature of the jets, which are fed by air that spills down from passes at relatively high elevation. By contrast, the spilling flow in the ravine-like Tokar Gap does not become substantially supercritical and therefore does not undergo a jump, and also carries more total horizontal momentum. The Tokar Wind Jet carries some air parcels across the Red Sea and into Saudi Arabia, whereas air parcel trajectories in the neighboring jets ascend as they cross through the jumps, then veer sharply to the southeast and do not cross the Red Sea. The mountain parameter Nh/U is estimated to lie in the rage 1.0-4.0 for the general region, a result roughly consistent with a primary gap jet having a long extension, and supercritical jets spilling down from higher elevation passes. The strong event is marked by the formation of a cyclonic cell near the upstream entrance to the Tokar Gap, a feature absent from the more moderate events that occur throughout the summer. The cell contains descending air parcels that are fed into the primary and secondary jets. An analysis of the Bernoulli function along air parcel trajectories reveals an approximate balance between the loss of potential energy and gain of internal energy and pressure, with surprisingly little contribution from kinetic energy, along the path of the descending flow. All jets attain the critical wind speed nominally required to loft dust into the atmosphere, though only the Tokar Gap has a broad, delta region with plentiful deposits of silt.

Polyphenols are the most common organic compounds in wine. They improve both the sensory aspects of wine and human health by activating antioxidant systems. Therefore, there is a great need for a simple, fast and accessible method to determine the polyphenol content of wine. The aim of this study is to characterize polyphenolic compounds in natural wine samples using an electrochemical method and a modified carbon paste electrode with TiO2 nanoparticles. This work is motivated by the promising improvement of the sensing properties of a TiO2 nanoparticle-modified carbon paste electrode observed in the electrooxidation of different polyphenols. Since the voltammetric response of wine is largely irreversible, another motivation was the possibility of improving the processing of voltammograms to obtain data indicative of wine polyphenols, based on the approach described in the seminal work by Espinoza et al. The modified electrode studied provides an improved and reproducible voltammetric response of gallic acid in wine samples and provides a good basis for further development of an integrated sensor/data system with the possibility of wider application for the quantification of gallic acid as a flavor and visually relevant parameter in winemaking.

Meshfree particle method, which is always regarded as a pure Lagrangian approach, is easily represented complicated domain topologies, moving boundaries, and multiphase media. Solving acoustic problems with the mesfree particle method forms a branch of the acoustic wave modeling field, namely, particle-based computational acoustics (PCA). The aim of this paper is to improve the accuracy of using the PCA method to solve two-dimensional acoustic problems, and realize the particle representation with a hybrid meshfree and finite-difference time-domain (FDTD) method for acoustic boundary conditions at both the plane and curved surface. As a widely used Lagrangian meshfree method, the smoothed particle hydrodynamics (SPH) based on the support domain and the kernel function has developed rapidly in recent years. The traditional SPH method is easily implements parallel processing and has been applied in sound wave simulation. As a corrective method with higher accuracy than SPH, the acoustic propagation and scattering in the time domain is simulated with the corrective smoothed particle method (CSPM). Moreover, a hybrid meshfree-FDTD boundary treatment technique is utilized to represent different acoustic boundaries in the Lagrangian approach. In this boundary treatment technique, the parameter value of virtual particles is obtained with the FDTD method, which concerns truncation errors based on the Tayler series expansion. Soft, rigid, and Mur’s absorbing boundary conditions are developed to simulate sound waves in finite and infinite domain. Results of modeling acoustic propagation and scattering show that CSPM is accurate and convergence with exact solutions, and different acoustic boundaries are validated to be effective in the computation.

Here, we present a staged approach for an innovative repurposing of a portable infant humidicrib into a live cell growth, observation, and imaging system. Furthmore, humidicrib can support different variations of “umbilical” bioreactors, and can be used to conduct electrophysiology experiments and in situ immunohistochemistry. Modifications incorporate a closed loop carbon dioxide (CO₂) concentration control system with umbilical CO₂ and heating support for tailored bioreactors. The repurposing cost is inexpensive and allows for the continued observation and imaging of cells. This prototype unit has been used to continuously observe and image live primary neurons for up to 21 days. This demonstrates the repurposed units’ suitability for use in tissue culture based research, particularly where modifications to microscopes are required or where sensitive manipulation outside of a standard incubator is needed.

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

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.

Background: The modified Duke index derived from coronary computed tomography angiography (CCTA) was designed to predict cardiovascular outcomes based on the severity of coronary ste-nosis. However, it does not take into consideration the presence or severity of peri-coronary in-flammation. The peri-coronary fat attenuation index (FAI) is a novel imaging marker determined by CCTA which reflects the degree of inflammation in the coronary tree in patients with coronary artery disease. Purpose: To assess the association between the modified Duke index assessed by CCTA, cardiovascular risk factors and peri-coronary inflammation in the coronary arteries of pa-tients with coronary artery disease. Methods: One hundred seventy-two patients who underwent CCTA for typical angina were assigned into two groups based on the modified Duke index: group 1 – patients with low index ≤ 3 (n=107) and group 2 – patients with high index > 3 (n=65). Demo-graphic, clinical and CCTA data were collected for all patients, and FAI analysis of coronary in-flammation was performed. Results: Patients with increased values of the modified Duke index were significantly older compared to those with a low index (61.83 ± 9.89 vs. 64.78 ± 8.9; p = 0.002). No differences were found between the two groups in terms of gender distribution, hypertension, hypercholesterolemia or smoking history (all p > 0.5). The FAI score was significantly higher in patients from group 2, who presented a significantly higher score of inflammation compared to the patients in group 1, especially at the level of the right coronary artery (FAI score 20.85 ± 15.80 vs. 14.61 ± 16.66; p = 0.01 for the right coronary artery, 13.85 ± 8.04 vs. 10.91 ± 6.5; p = 0.01 for the circumflex artery, and 13.26 ±10.18 vs. 11.37 ± 8.84; p = 0.2 for the left anterior descending artery). CaRi-Heart® analysis identified a significantly higher risk of future events among patients with a high modified Duke index (34.84 % ± 25.86 % versus 16.87 % ± 15.80 %; p

The study assessed the trapping efficacy of locally-modified 1) Gravid Aedes Trap(GAT) lined with insecticide-treated net (ITN) as a killing agent, 2) Autocidal Gravid Ovitrap(AGO) with sticky board in the semi-field system (SFS) and field setting. Fully-balanced Latin square experiments were conducted to compare GAT lined with ITN vs AGO, both with either yeast or grass infusion. Biogents-Sentinel (BGS) with BG-Lure and no CO2 was used as standard trap for Aedes mosquitoes. In the SFS, GAT outperformed AGO in collecting both nulliparous (65% vs 49%,OR=2.22,[95%CI:1.89-2.60],p

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

This research paper examines a cosmological model in flat space-time via $f(R,G)$ gravity where $R$ and $G$ are respectively the Ricci scalar and Gauss-Bonnet invariant. Our model assumes that $f(R,G)$ is an exponential function of $G$ combined with a linear combination of $R$. We scrutinize the observational limitations under a power law cosmology that relies on two parameters - $H_0$, the Hubble constant, and $q$, the deceleration parameter, utilizing the 57-point $H(z)$ data, 8-point BAO data, 1048-point Pantheon data, joint data of $H(z)$ + Pantheon, and joint data of $H(z)$ + BAO + Pantheon. The outcomes for $H_0$ and $q$ are realistic within observational ranges. We have also addressed Energy Conditions, $Om(z)$ analysis and cosmographical parameters like Jerk, Lerk and Snap. Our estimate of $H_0$ is remarkably consistent with various recent Planck Collaboration studies that utilize the $\Lambda$CDM model. According to our study, the power law cosmology within the context of $f(R,G)$ gravity provides the most comprehensive explanation for the important aspects of cosmic evolution.

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

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

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%.

In this paper, carbon nanotubes modified screen-printed electrode (CNTs/SPE) was prepared and the CNTs/SPE was employed for the electrochemical determination of antioxidant substance Chlorogenic acids (CGAs). A pair of well-defined redox peak of CGA was observed at the CNTs/SPE in 0.10 mol∙L^-1 acetic acid-sodium acetate buffer (pH 6.2) and electrode process is adsorption-controlled. Cyclic voltammetry (CV) and differential pulse voltammetry (DPV) method for the determination of CGA were proposed based on the CNTs/SPE. Under the optimal conditions, the proposed method exhibited linear ranges from 4.73×10^-7 to 4.45×10^-5 mol∙L^-1, the linear regression equation was Ipa(µA) = 4.1993 C (mol∙L^-1)+1.1039 (r = 0.9976) and the detection limit for CGA could reach 3.25×10^-6 mol∙L^-1. The recovery of matrine was 94.74~106.65% (RSD = 2.92%) in coffe beans. The proposed method is quick, sensitive, reliable, and can be used for the determination of CGA.

At present there is a renewed interest in theories of ”modified” gravity. Here, under a more drastic modification enforced by Galilei group, we obtain a completely new gravitational structure, and which exists in addition to the already available general relativity of today. Correlated with this, we show that in addition, there is a new ”modified” quantum mechanics, in as much as it exists as an independent and new ”pure” non-relativistic quantum me- chanics, and which has no relativistic counterpart. This is in addition to the present quantum mechanics, where the relativistic and non-relativistic structures are counterparts of each other. The above holds, firstly due to the correlation between Galilei group and quantum mechanics. These math- ematical conclusions are consolidated by the fact that there exists a physical Majorana interaction between each neutron- proton pairs in nuclei. Galilei invariance of Majorana exchange in Majorana interaction, shows that the mass here is of pure gravitational nature, and which is immune to the other three forces. This makes an amazing connection between the gravitational force and the quantum mechanics. This pure gravitational mass would man- ifest itself as dark matter of the universe. It is our new modified gravity that generates the dark matter.

The aim of this study is to analyze the characteristics of drought such as intensity, cumulative curves and trends, based on SPEI (Standardized Precipitation Evapotranspiration Index) at 8 stations in Korea from 1981 to 2010. The traditional SPEI is based on Thornthwaite equation for estimating evapotranspiration; SPEI_th. However, a standard of agricultural water management in Korea suggests FAO Penman-Monteith equation; SPEI_pm. In this study, we analyzed the intensity and trends of drought using SPEI_th and SPEI_pm, respectively, and analyzed the relationship between them. Both of central and southern region, the SPEIs were below -1.0 (moderated drought) for the periods May-August in the representative drought year such as 1988, 2001, and 2008-09. The frequency of drought was higher in southern region than central region. In addition, SPEI_pm showed slightly more intensive drought rather than SPEI_th except for Chuncheon and Gwangju. In 5 stations except for Cheoncheon, Gwangju and Jinju, the cumulative probability that SPEI_pm is below -1.5 was significantly increased from 1981-1995 to 1996-2010. As the results of drought trends, the increasing trend of SPEIs was shown on fall season, and the cumulative probability that SPEI_pm is below -1.5 was also significantly increased.

In this paper, we identify several relative ordering properties of the modified proportional hazard rate and modified proportional reversed hazard rate models. For this purpose, we use two well-known relative orderings, namely the relative hazard rate ordering and the relative reversed hazard rate ordering. The investigation is to see how a relative ordering between two possible base distributions for the response distributions in these models is preserved when the parameters of the underlying models are changed. We will give some examples to illustrate the results and the conditions under which they are obtained.

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

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

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

A rapid-response Lagrangian model for simulating the transport of a chemical pollutant in the Arabian/Persian Guls is described. The model is well suited to provide a fast response after an emergency due to an accident or a deliberate spill. Baroclinic circulation was obtained from HYCOM ocean model and tides were calculated using a barotropic model. The interactions of pollutants with sediments (uptake/release processes) were described using a dynamic approach based on kinetic transfer coefficients and a stochastic numerical method. Some examples of model applications are shown.

A controlled ammonia (NH₃) release experiment was performed at a grassland site to quantify the effect of dry deposition, at the field scale between the source and the receptors (NH₃ measurement locations), on the estimates of emission rates by means of inverse dispersion modelling. NH₃ was released for 3 hours at a constant rate of Q = 6.29 mg s⁻¹ from a grid of 36 orifices spread over an area of 250 m². The increase in line-integrated NH₃ concentration was measured with open-path optical miniDOAS devices at different locations downwind of the artificial source. Using a backward Lagrangian stochastic (bLS) dispersion model (bLSmodelR), the fraction of the modelled release rate to the emitted NH₃ (Q_bLS/Q) was calculated from the measurements of the individual instruments. Q_bLS/Q was found to be systematically lower than 1, on average between 0.69 and 0.91, depending on the location of the receptor. We hypothesized that NH₃ dry deposition to grass and soil surfaces was the main factor responsible for the observed depletion of NH₃ between source and receptor. A dry deposition algorithm based on a deposition velocity approach was included in the bLS modelling. Model deposition velocities were evaluated from a ‘big‑leaf’ canopy resistance analogy. Canopy resistances (generally termed Rc) that provided Q_bLS/Q = 1 ranged from 75 to 290 s m⁻¹, showing that surface removal of NH₃ by dry deposition can plausibly explain the original underestimation of Q_bLS/Q. The inclusion of a dry deposition process in dispersion modelling is crucial for emission estimates, which are based on concentration measurements of depositing tracers downwind of homogeneous area sources or heterogeneously distributed hot spots, such as e.g. urine patches on pastures in the case of NH₃.

Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu transform and investigate many properties and relations including modified Sumudu transforms of the power function, sine, cosine, hyperbolic sine, hyperbolic cosine, exponential function, and function derivatives. Moreover, we attain two shifting properties and a scale preserving theorem for the modified Sumudu transform. We give modified inverse Sumudu transform and investigate some relations and examples. Furthermore, we show that the modified Sumudu transform is the theoretical dual transform to the modified Laplace transform.

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

Modern organic synthesis is majorly focused on developing environmentally benign synthetic protocols by employing green chemistry principles. Accordingly, in our recent research work, we herein report the use of modified supramolecular host cyclodextrin as an effective solid based green catalyst for accessing structurally diverse and medicinally relevant pyrimidone architectures. The catalyst and the synthesized compounds 4 (a-r) were characterized using FT-IR, NMR and GC-Mass spectroscopy. Major highlights of the reported work include: atom economical process, extremely milder reaction conditions, operational simplicity, high isolated yields, and excellent catalyst turnover number. The molecular docking studies suggest that the compound 4n has the hydrogen bonding, hydrophobic and π-pair interactions with the active site of active sites of CXT M 15 receptor.

Abstract: Cancer cells are originated by normal cells and with those share the need to be fed. Metabolic reprogramming in cancer cells is not yet fully understood although there is a vast literature suggesting that huge amounts of both energy and substrates are require for synthesis of components of new neoplastic cells so that any macronutrient may be efficiently utilized. Recently, in vitro data show that EAA supplementation promoted colon cancer cells apoptosis by enhanced autophagy. Therefore, in this study we tested in vivo the effects of matched macronutrients standard laboratory diet (control) versus EAA rich modified diet (EAArmd) in mice injected with colon cancer cells. Results of the first set of 12 animals, 6 controls and 6 EAArmd-fed, showed that controls mice develop cancer volume cancers 5 times larger and heavier than EAArmd-fed. If confirmed, these results would open new scenarios for the cancer integrate therapies.

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

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

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

The space time fractional Korteweg-de Vries equation, modified Equal Width equation and Benney-Luke Equations are solved by using simple hyperbolic tangent Ansatz method. A simple compatible wave transformation in one dimension is employed to reduce the governing equations to integer ordered ODEs. Then, the ansatz approximation is used to derive exact solutions. Some illustrative examples are presented for some particular choices of parameters and derivative orders.

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

A viable radiation dominated era in the early universe is best described by the standard (FLRW) model of cosmology. In this short review, we demonstrate reconstruction of the forms of F(R) in the modified theory of gravity, and the metric compatible F(T) together with the symmetric F(Q) in alternative teleparallel theories of gravity from different perspectives, primarily rendering emphasis on a viable FLRW radiation era. Inflation has also been studied for a particular choice of the scalar potential. The inflationary parameters are found to agree appreciably with the recently released observational data.

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

MgAl oxide coatings containing MgO and MgAl2O4 phases were doped with CeO2 particles using plasma electrolytic oxidation (PEO) of AZ31 magnesium alloy in 5 g/L NaAlO2 water solution, with CeO2 particles added at concentrations up to 8 g/L. They underwent extensive inve-stigation into their morphology, chemical and phase compositions, and most importantly, photoluminescent (PL) properties and photocatalytic-activity (PA) in photodegradation of methyl orange (10 cm3 of 8 mg/L). The concentration of CeO2 particles in the aluminate electrolyte influences the amount of CeO2 particles incorporated into MgAl oxide coatings, but CeO2 particles have no signi-ficant effect on the surface morphology, thickness, or phase structure of the coatings. The PL emi- ssion spectrum of MgAl oxide coating is divided into two bands: one in the 350-600 nm range related to structural defects in MgO, and another much more intense in the 600-775 nm range attributed to F+ centres in MgAl2O4. Incorporated CeO2 particles do not have a significant effect on the PL intensity of the band in the red spectral region, but the PL intensity of the first band increases with the concentration of CeO2 particles. PA of MgAl/CeO2 oxide coatings is higher than that of pure MgAl oxide coatings. The highest PA was observed for MgAl/CeO2 oxide coatings formed in aluminate electrolytes with the addition of 2 g/L of CeO2 particles. The MgAl/CeO2 oxide coatings remained chemically and physically stable across multiple cycles, indicating their potential for applications.

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

In this work, we introduce a scalable and efficient GPU-accelerated methodology for volumetric particle advection and finite-time Lyapunov exponent (FTLE) calculation, focusing on the analysis of Lagrangian Coherent Structures (LCS) in large-scale Direct Numerical Simulation (DNS) datasets across incompressible, supersonic, and hypersonic flow regimes. LCS play a significant role in turbulent boundary layer analysis, and our proposed methodology offers valuable insights into their behavior in various flow conditions. Our novel owning-cell locator method enables efficient, constant-time cell search, and the algorithm draws inspiration from classical search algorithms and modern multi-level approaches in numerical linear algebra. The proposed method is implemented for both multi-core CPUs and Nvidia GPUs, demonstrating strong scaling up to 32,768 CPU cores and up to 62 Nvidia V100 GPUs. By decoupling particle advection from other problems, we achieve modularity and extensibility, resulting in consistent parallel efficiency across different architectures. Our methodology was applied to calculate and visualize the FTLE on four turbulent boundary layers at different Reynolds and Mach numbers, revealing that coherent structures grow more isotropic proportional to the Mach number, and their inclination angle varies along the streamwise direction. We also observed increased anisotropy and FTLE organization at lower Reynolds numbers, with structures retaining coherency along both spanwise and streamwise directions. Additionally, we demonstrated the impact of lower temporal frequency sampling by upscaling with an efficient linear upsampler, preserving general trends with only 10% of the required storage. In summary, we present a particle search scheme for particle advection workloads in the context of visualizing LCS via FTLE that exhibits strong scaling performance and efficiency at scale. Our proposed algorithm is applicable across various domains requiring efficient search algorithms in large structured domains. While this manuscript focuses on the methodology and its application to LCS, an in-depth study of the physics and compressibility effects in LCS candidates will be explored in a future publication.

Given the documented wave-induced damage of elevated coastal decks during extreme natural hazards (e.g. hurricanes) in the last two decades, it is of utmost significance to decipher the wave-structure-interaction of complex deck geometries and quantify the associated loads. Therefore, this study focuses on the assessment of solitary wave impact on open-girder decks that allow the air to escape from the sides. To this end, an arbitrary Lagrangian-Eulerian (ALE) numerical method with a multi-phase compressible formulation is used for the development of three-dimensional hydrodynamic models, which are validated against a large-scale experimental dataset of a coastal deck. Using the validated model as a baseline, a parametric investigation of different deck geometries with a varying number of girders Ng and three different widths, was conducted. The results reveal that the Ng of a superstructure has a complex role and that for small wave heights the horizontal and uplift forces increase with the Ng, while for large waves the opposite happens. If the Ng is small the wave particles accelerate after the initial impact on the offshore girder leading to a more violent slamming on the onshore part of the deck and larger pressures and forces, however, if Ng is large then unsynchronized eddies are formed in each chamber, which dissipate energy and apply out-of-phase pressures that result in multiple but weaker impacts on the deck. The decomposition of the total loads into slamming and quasi-static components, reveals surprisingly consistent trends for all the simulated waves, which facilitates the development of predictive load equations. These new equations, which are a function of Ng and are limited by the ratio of the wavelength to the deck width, provide more accurate predictions than existing empirical methods, and are expected to be useful to both engineers and researchers working towards the development of resilient coastal infrastructure.

Purpose: To improve numerical simulation of the non-contact tonometry test by using Arbitrary Eulerian-Lagrangian deforming mesh in the coupling between computational fluid dynamics model of an air jet and finite element model of the human eye. Methods: Computational fluid dynamics model simulated impingement of the air puff and consisted of 25920 wedge6 elements and employed Spallart-Allmaras model to simulate capture turbulence of the air jet. The time span of the jet wais 30 ms and maximum Reynolds number

In this study, we aim to evaluate how cyclodextrin molecules affect the hydrophilicity and selec-tivity of PVDF membrane. Herein, we prepared PVDF-PVP(1-x) β-CDx membranes, with x rang-ing from 0 to 1 wt%. The membranes were deeply characterized by means of X-ray diffraction (XRD), attenuated total reflectance infrared (ATR-IR), Raman spectroscopies, Thermal gravimet-ric analysis (TGA), Contact angle measurement (CA), scanning electron microscopy (SEM) and atomic force microscopy (AFM). The study unequivocally demonstrates the effectiveness of the addition of β-CD molecules on membranes' structural, morphological, and dielectric properties. Adding 0.25wt% β-CD enhanced hydrophilicity, with CA decreasing from 72.6° to 56° and roughness decreasing from 81 to 29 nm. The PVDF-PVP(1-x) β-CDx membranes were then fully characterized using electrochemical impedance spectroscopy (EIS) to determine their dielectric properties, which clearly showed that the presence of β-CD induced polarization of the mem-brane. The separation of various dyes with different sizes and charges was utilized. These dyes included methylene blue (MB, positive, 0.504 nm), methyl red (MR, neutral, 0.487 nm), rose Bengal (RB, negative, 0.588 nm), and brilliant blue (BB, negative, 0.798 nm). Based on our re-search, we found that the membrane's selectivity is determined by both exclusion factors (such as size and dielectric properties) and inclusion inside the β-CD cage. We found that using alpha-CD instead of beta-CD led to the disappearance of dye inclusion. These findings strongly sug-gest that β-CD molecules can be a viable solution for dye removal from wastewater.

The microbial contamination in food packaging have been a major concern that paved the way for the search for natural based new anti-microbial agents, such as modified α-mangostin. In the present work, twelve synthetic analogs were obtained via semi-synthetic modification of α-mangostin by Ritter reaction, reduction by palladium-carbon (Pd-C), alkylation, and acetylation. The evaluation of the anti-microbial potential of the synthetic analogs showed higher therapeutic value than the parent molecule. The anti-microbial studies proved that I E showed higher antibacterial activity whereas I I showed most significant antifungal activity. Due to their microbial properties, modified α-mangostin can be utilized as active anti-microbial agents in food packaging.

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

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

The importance of frailty in older people is getting constant recognition as an important aspect both in terms of public health, as well in personal level for the appropriate management of an older person health condition. This is reflected by the continuously increasing number of research studies carried out in several settings across different countries. Sometimes this is very solid, but in other cases there is a considerable gap in terms of accurate and well grounded documentation of frailty status. This is the case in Greece, where we are missing clinically validated tools to approach frailty. We are missing frailty screening tools, such as for instance PRISMA 7, the gold standard tool of Fried criteria is somehow problematic since the question referring to physical activity originates from a questionnaire that has not been translated and validated, while Clinical Frailty Scale has been validated for the translation but not for the capacity to detect frailty. Aim of this study is to validate these tools for their accuracy to detect frailty by using a measurable index of frailty, previously proposed for use in clinical studies: the Short Physical Performance Battery (SPPB). 74 male and female participants have been evaluated for their frailty status using different tools. We observed that PRISMA 7 translation detects frailty only when one question is removed at a cut-off of ≥ 2 and indicated a sensitivity of 88.1%, and specificity of 99.9% with a good correlation with SPPB measurements (r = 0.858; p < 0.001). When CFS was validated using SPPB it demonstrated a very good correlation (r = -0.838; p < 0.001 respectively) as it was the case for the modified Fried Criteria (r = -0.725; p < 0.001). All items demonstrated a good correlation between them. We can here propose that we can accurately assess frailty status in the community setting by using a modified version of Fried criteria, Clinical Frailty Scale translation in Greek and we can screen for frailty by using the Greek translation of PRISMA 7 only after removing the item 6 of the questionnaire.

The three dimensional conformable time fractional Kadomtsev-Petviashvili and the conformable time fractional modified Kawahara equations are solved by implementing the Kudryashov's procedure. The corresponding wave transformation reduces both equations to some ODEs. Balancing the nonlinear and the highest order derivative terms gives the structure of the solutions in the finite series form. The useful symbolic tools are used to solve the resultant algebraic systems. The solutions are expressed in explicit forms.

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

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

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

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

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

A series of waterborne polyurethane (WBPU)/modified lignin amine (MLA) adhesives was prepared using modified lignin amine (MLA) as a chain extender by a prepolymer mixing process. A successful Mannich reaction was achieved during the synthesis of MLA by reacting lignin with bis(3-aminopropyl)amine. Higher tensile strength, Young’s modulus and thermal stability were recorded for WBPU/MLA adhesives with higher MLA contents. The WBPU/MLA adhesive materials were used to coat PVC substrates. The adhesive strength increased with increasing MLA content. More importantly, the MLA also enhanced the WBPU/MLA coating in terms of adhesive strength at moderately high temperatures as well as under natural weather exposed conditions. The adhesive strength was essentially unaffected with 6.48 mole% MLA in the WBPU/MLA coating after exposure to natural weather conditions for 180 days.

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

We have found a region in the northwestern Japan Sea near the Subpolar Front where mesoscale eddies regularly form and circulate. The anticyclonic eddy with a strong dynamic feature, vertically extended to the bottom (~3500 m), multilayer core structure and extreme values of temperature and salinity was sampled there in the cruise in May 2004. The altimetry-based eddy tracking showed that it had a life span of nine months with the size reaching 120 km. CTD observational data were used to explore the eddy’s features and vertical structure. The eddy had a multilayer core with different thermohaline characteristics which could be originated by eddy interaction with the surrounding waters during its life. The evolution of the eddy has been studied and analyzed with the help of altimetry-based Lagrangian indicators of water motion. Performing the particle-tracking numerical experiments, we computed the Lagrangian maps that contain information on the origin of water inside the eddy core and its ‘age’ on every day of the eddy’s life. Inspecting daily-computed Lagrangian maps, we documented the essential events in the evolution of the eddy including its formation, splitting, merger, entrainment and detrainment of water, erosion and eventual decay. All these observations have been verified with the infrared satellite images. The new Lagrangian technique has been applied to calculate day by day the content of water of various origin (coastal, subtropical and subarctic) entrained into the eddy core. It has been found that the surface core has been filled mainly with subtropical water originated in the southern flank of the Subpolar Front. The episodes with cardinal changes of ratio of different water types have been recorded and verified with the infrared satellite images and maps of the origin of water inside the eddy core.

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

In the present work we consider two modified Chevallier-Polarski-Linder (CPL) models in the background of homogeneous and isotropic FLRW space-time, namely (i) the generalized CPL model (Model I) and (ii) the logarithmic form of the the equation of state for the dark energy. From the observational data sets ((Pantheon+)+BAO+HST), we find that at the present epoch (redshift $z=0$), the equation of state for the dark energy converges almost at the same value $\omega_{fld}\approx -0.86$ and the variation of $\omega_{fld}(z)$ with respect to the redshift parameter is very small for both models. we also find that the present value of the Hubble parameter $H_0$ is almost same for both the models. Finally, we compare the models in the light of Akaike, Bayesian Information Criterion (BIC) and Bayesian Evidence. However, we find that Model II is better compared to the Model I from the estimated value of the deceleration parameter.

In this study organic bulk heterojunction (BHJ) solar cell along with the spiro OMeTAD as a hole transport layer (HTL) and the PDINO as an electron transport layer (ETL) was simulated through the Solar Capacitance Simulator, one dimensional (SCAPS-1D) software to examine the performance of this type of polymer thin film organic solar cells. As an active layer the blend of polymer donor PBDB-T and non-fullerene acceptor ITIC-OE was used. Numerical simulation was performed by varying the thickness of HTL and active layer. Firstly, the HTL layer thickness was optimized to 50 nm, after that the active layer thickness varied up to 80 nm. These results of simulation demonstrated that the HTL thickness has rather little impact on efficiency while in the case of active layer thickness improves efficiency significantly. The temperature effect on the performance of solar cells was considered, by the simulation performed for temperature from 300 K up to 400 K and the efficiency of solar cell decreases with increasing temperature. Generally, polymer films usually are full of traps and defects, the density of defects (Nt) value was also introduced to the simulation, and it was confirmed that with the increasing of defect density (Nt), the efficiency of solar cell decreases. After thickness, temperature and defect density optimization, the reflection coating was also applied on it. It turned out that by introducing the reflection coating on the back side of solar cell, the efficiency increases by 2.5 %. Additionally, the positive effect of HTL and ETL doping on efficiency of this type of solar cells was demonstrated.

Kim-Kim ([9]) studied some properties of the degenerate gamma and degenerate Laplace transformation and obtained their properties. In this paper, we define modified degenerate gamma and modified degenerate Laplace Transformation and investigate some properties and formulas related to them.

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

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

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

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

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

A large number of physicists now admit that quantum mechanics is a non-local theory. EPR argument and the many experiences (including recent “loop-hole free” tests) showing the violation of Bell’s inequalities seem to have confirmed convincingly that quantum mechanics cannot be local. Nevertheless, this conclusion can only be drawn inside a standard realist framework assuming an ontic interpretation of the wave function and viewing the collapse of the wave function as a real change of the physical state of the system. We show that this standpoint is not mandatory and that if the collapse is no more considered as an actual physical change, it is possible to recover locality.

The production of biomass fly ash has been increasing every year in Europe, reaching 5.5 million tons in 2020. Biomass fly ash is not yet accepted in the standards as a substitute material for cement in mortar and concrete. In a first approach, the substitution limit of biomass fly ash is determined by comparing the mechanical strengths, fresh state properties and hardened properties of mortars produced with biomass fly ash to those of mortars produced with classical coal fly ash. Then, masonry and rendering mortars have been designed with different substitution rates of biomass fly ashes from wood combustion in thermal power plant. Although there is an overall decrease in performance, mortars made with biomass ash retain properties that make them suitable for use in masonry or rendering.

Egg white lysozyme was modified by chemical methods using organic acids. Caffeic acid and p-coumaric acid in organic acids were used as modifiers, and 1-Ethyl-3- (3-dimethylaminopropyl) carbodiimide hydrochloride and N-hydroxy succinimide were used as dehydration condensation agents during modification. A certain degree of modified lysozyme was obtained through appropriate modification conditions. The antibacterial properties and structure of the obtained two organic acid modified lysozymes were compared with natural enzymes. The results showed that compared with the natural enzyme, the activity of modified lysozyme decreased, but the inhibitory effect on Gram-negative bacteria was enhanced. The minimum inhibitory concentrations of caffeic acid modified enzyme and p-coumaric acid modified enzyme on Escherichia coli and Pseudomonas aeruginosa were 0.5 mg/mL and 0.75 mg/mL, respectively. However, the antibacterial ability of modified lysozyme to Gram-positive bacteria was lower than that of natural enzyme. The minimum inhibitory concentration of caffeic acid modified enzyme and p-coumaric acid modified enzyme to Staphylococcus aureus and Bacillus subtilis was 1.25 mg/mL. The peak fitting results of the amide-I band (1600 cm-1-1700 cm-1) absorption peak in the infrared spectroscopy showed that the content of the secondary structure of the two modified enzymes obtained after modification was different from that of natural enzymes.

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

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

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

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

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

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

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

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

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

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

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

In Tunisia, olive is the most cultivated fruit crop while in the north where rainfall exceeded 400mm.year-1, the olive growing area is in widely extension in marginal soil with high slope gradient. Thus, the inclusion of cover crops is a sustainable solution to increase the ecosystem productivity, improve the soil fertility and oil yields. But, in Tunisia a few study were investigated the effect of legumes cover crop on the olive productivity. Therefore, the aim of this study was to evaluate the short-term (two cropping seasons s 2021 and 2022) effects of different seeded cover crops and soil management practices on the cover crops and soil characteristics, as well as enzymes activities and related microbial diversity. Six intercropping were tested in rainfed olive orchards (cv.Chétoui): Spontaneous vegetation (Spont), Wheat, Vetch, Oat, Fenugreek, mixture Vetch-Oat and compared to control (3 periodic tillage/year without intercropping). During the first cropping season, cover crops were cut as animal feed and only residues were incorporated into the soil. While, during the second year, all cover crops biomass were incorporated into the soil. Results indicate that the dry biomass and carbon uptake were significantly higher in grasses species (Wheat and Oat). But, highest level of nitrogen was found in Fenugreek cover crops. As compared to control, all cover crops including spontaneous vegetation increased soil organic matter and macronutrient level, mainly phosphorus. The most activity of β-glucosidase, phosphatase and arysulphatase was found in the cover crops plot of wheat and oat. In addition, this study improve that the utilization of the carbon sources was dominated by amides, amine and amino-acids in the fenugreek plot; while it was dominated by polymers and carboxylic acids in the case of wheat and oat.

The objective of the present paper is to get a better understanding of the electrochemical properties of organoclays, which were prepared via solid-state intercalation of three cationic surfactants, such as dodecyltrimethylammonium, tetradecyltrimethylammonium, and hexadecyltrimethylammonium, as bromide salts, at different loading levels into the interlayers of two natural smectite clays (AH and DI). The electrochemical properties of the prepared organoclays were investigated by cyclic voltammetry. The cyclic voltammetry response of the electrochemical probe, 〖Fe(CN)〗_6^(3-)/〖Fe(CN)〗_6^(4-), shows that the intensities of the anodic and cathodic peaks don’t increase when the working electrode is based on carbon paste modified with the raw clays (AH or DI), whereas the peaks intensities increase significantly when the working electrode consists of carbon paste modified with organoclays. This increase in the intensity of the current indicates an improvement in the surface conductivity of the carbon paste electrode when they are modified with organoclays. When the working Electrode is based on organoclays modified carbon paste, the potential differences (ΔEp) are ranged between 140 and 170 mV, which are lower than those of the unmodified carbon paste electrode (330 mV) and those modified with raw clays (520 mV). This indicates an easy electron transfer process on the surface of the organoclays modified carbon paste electrodes.