Direct Substitution Method Research Articles

Intranasal Radioiodinated Ferulic Acid Polymeric Micelles as the First Nuclear Medicine Imaging Probe for ETRA Brain Receptor.

The aim of this work was to prepare a selective nuclear medicine imaging probe for the Endothelin 1 receptor A in the brain. Ferulic acid (an ETRA antagonist) was radiolabeled using 131I by direct electrophilic substitution method. The radiolabeled ferulic acid was formulated as polymeric micelles to allow intranasal brain delivery. Biodistribution was studied in Swiss albino mice by comparing brain uptake of 131I-ferulic acid after IN administration of 131I-ferulic acid polymeric micelles, IN administration of 131I-ferulic acid solution and IV administration of 131I-ferulic acid solution. Successful radiolabeling was achieved with an RCY of 98 % using 200 μg of ferulic acid and 60 μg of CAT as oxidizing agents at pH 6, room temperature and 30 min reaction time. 131I-ferulic acid polymeric micelles were successfully formulated with the particle size of 21.63 nm and polydispersity index of 0.168. Radioactivity uptake in the brain and brain/blood uptake ratio for I.N 131I-ferulic acid polymeric micelles were greater than the two other routes at all periods. Our results provide 131I-ferulic acid polymeric micelles as a hopeful nuclear medicine tracer for ETRA brain receptor.

Element Free Galerkin (EFG) Formulation in Solving Kinematic Wave Equation for Hydrological Modelling

Meshfree methods such as Element Free Galerkin Method (EFG) are the cutting edge of numerical methods as it does not require user to perform meshing which often is time consuming and tedious. The method being "meshfree" for the user can theoretically generate more accurate models which follow more complex boundary conditions such as natural rivers etc. The time saving and potential of higher accuracy in modelling makes EFG formulation an interesting research topic. EFG formulation is used to solve kinematic wave equations which is detailed in this paper. Galerkin weighted residual method using EFG’s shape function parameters is used to discretize the partial differential equation (PDE) of kinematic wave equations. To discretize the equations, a forward difference scheme is used for temporal discretization and Picard direct substitution method is employed to solve the nonlinear system at each time step. The formulations are validated by making a comparison between well-established numerical techniques against actual recorded datasets. After which it is found that EFG method agrees with conventional established techniques, thus validating the formulations as useful. To further investigate the usefulness of this formulation, an optimal performance study was also conducted to determine the most optimal shape function parameters. The optimal shape function values improved the performance to where it was found that established methods such as FDM were surpassed and on par with FEM. This shows that EFG is a good alternative for hydrological modelling.

Acoustic emission of pulsating bubbles in viscous media

<sec>The classical single bubble’s acoustic emission equation has been used to describe the sound filed radiated by bubble for a long time. Because this formula does not consider the influence of the medium viscosity in the process of sound wave propagation, it is more reasonable to modify it in some special cases.</sec><sec>Based on the boundary condition of the bubbles, i.e. the vibration velocity of the bubble wall is equal to the particle vibration velocity of the external medium at the bubble boundary, the acoustic wave equation in spherical coordinate system in viscous medium is solved, and the modified acoustic emission formula of the bubble in the viscous medium is given.</sec><sec>The bubble radius <i>R</i>(<i>t</i>) is obtained numerically from the bubble dynamics equation by using the fourth-fifth order Runge-Kutta method. Then the bubble's radiation sound field is obtained by using the direct substitution method and the finite element (The pressure acoustics module; two-dimensional (2D) axisymmetric geometric model) method, respectively. The modified expression <i>p</i><sub>present</sub> given in this work is more accurate to describe the bubble’s radiation than the classical expression <i>p</i><sub>classical</sub> in the cases of high-viscosity, high-frequency and long-distance. In these cases, continuing to measure the acoustic emission of bubbles by using the classical expression may have an influence on the characteristics of cavitation, such as the inaccurate descriptions of parameters such as cavitation intensity and cavitation threshold.</sec>

Development of New Generalized Odd Fréchet-Exponentiated-G Family of Distribution

The study examines the limitations of existing parametric distributional models in accommodating various real-world datasets and proposes an extension termed the New Generalized Odd Fréchet-Exponentiated-G (NGOF-Et-G) family. Building upon prior work, this new distribution model aims to enhance flexibility across datasets by employing the direct substitution method. Mathematical properties including moments, entropy, moment generating function (mgf), and order statistics of the NGOF-Et-G family are analyzed, while parameters are estimated using the maximum likelihood technique. Furthermore, the study introduces the NGOF-Et-Rayleigh and NGOF-Et-Weibull models, evaluating their performance using lifetime datasets. A Monte Carlo simulation is employed to assess the consistency and accuracy of parameter estimation methods, comparing maximum likelihood estimation (MLE) and maximum product spacing (MPS). Results indicate the superiority of MLE in estimating parameters for the introduced distribution, alongside the enhanced flexibility of the new models in fitting positive data compared to existing distributions. In conclusion, the research establishes the potential of the proposed NGOF-Et-G family and its variants as promising alternatives in modelling positive data, offering greater flexibility and improved parameter estimation accuracy, as evidenced by Monte Carlo simulations and real-world dataset applications.

Integration of Rational Functions

A rational function can always be integrated, that is, the integral of such a function is always an elementary function. The integration procedure is complex and consists of four steps: elimination of the common zero-points of the numerator and denominator, reduction to a true rational function, decomposition into partial fractions and integration of the obtained expressions using direct integration, substitution method or partial integration method. Integrating rational functions is important because integrals of rational functions of trigonometric functions as well as integrals of some irrational functions are reduced to integrals of rational functions by appropriate transformations.

Using the product environmental footprint to strengthen the green market for sustainable feed ingredients; Lessons from a green biomass biorefinery in Denmark

Finding new and sustainable proteinaceous feed ingredients, especially those produced from locally available resources, is at the top of the agenda of many countries, including Denmark, to become feed protein self-sufficient. Protein concentrate (PC) production via the biorefining of green biomass has attracted considerable interest in recent years since they are more land efficient and productive than soybeans. The biorefining of clover-grass into protein concentrate (GPC) is a promising substitute for soybean and soybean meal, however, the environmental impacts of GPC have not been studied. The Product Environmental Footprint (PEF) method, developed by EU Joint Research Centre for the “Single Market for Green Products Initiative” was employed to assess the environmental footprints of organic GPC. The instructions, methodology, and guidelines detailed in Product Environmental Footprint Category Rules (PEFCR) Feed for Food-Producing Animals were followed to implement this PEF study. The results were intended for in-house management, process improvement, early guidance on the environmental footprint (EF) of compound feeds containing GPC, and the EF of livestock and animal production whose feed ration contains GPC. Our results showed that GPC would have a climate change impact of 1091.47 kg CO2,eq/t GPC. We found that farming/cultivation, more specifically direct emissions from manure slurry, dominated most impact categories, including acidification and eutrophication. The results were found sensitive to the choice of allocation method and very case-specific. For instance, the climate change impact of GPC was higher under economic allocation than direct substation, but the acidification impact was lower in economic allocation than direct substitution. However, the direct substitution method, showed that treating the process residues in biogas plants could result in GPC with lower EFs. The sensitivity analysis confirmed that increasing the clover-grass productivity and decreasing either manure slurry application or nitrogenous emissions from its application are the keys to further decreasing the overall environmental impacts.

Incorporation and testing of refrigerant fluids (R-134a) in the subchannel analysis code CTF (COBRA-TF)

The subchannel codes such as COBRA-TF (CTF) are often used in the simulation of thermal hydraulic parameters in a reactor core. Use of these codes for safety analysis requires extensive validation against experimental data. While typically validation is performed on experiments in water, a large number of experiments using refrigerant are available in literature and may be used to expand the validation range of these codes. This research is focused on the subchannel code CTF which has been modified to incorporate Refrigerant-134a fluid properties. Subsequently the modified code was tested against several experimental results available for R-134a. Evaluation of the Heat Balance Method (HBM) and Direct Substitution Method (DSM) for CHF was carried out. In the case of the CHF Look-Up Table (LUT), fluid-to-fluid scaling was performed to predict the local CHF phenomena. Overall the HBM predictions show better agreement (with the exception of Katto's correlation when applied to test section with a cold-wall) as compared to the CHF LUT results which tended to significantly overpredict dryout under high qualities.

PERFORMANCE OF RADIAL POINT INTERPOLATION METHOD IN SOLVING KINEMATIC WAVE EQUATION FOR HYDROLOGIC MODELLING

This paper presents the solution of the kinematic wave equation using a meshless radial point interpolation method (RPIM). The partial differential equation is discretized using a Galerkin weighted residual method employing RPIM shape functions. A forward difference scheme is used for temporal discretization, while the direct substitution method is employed to solve the nonlinear system at each time step. The formulation is validated against solutions from conventional numerical techniques and physical observation. In all cases, excellent agreements are achieved and hence the validation of the proposed formulation. Optimum values of the multi-quadrics shape parameters were then determined before the assessment of the performance of the method. Based on the convergence rate, it has been shown that the proposed method performs better than the finite difference method and equivalent to the finite element method. This highlights the potential of RPIM as an alternative method for hydrologic modeling.

A phenomenological CHF model for mixing-vane spacers in a subchannel of a rod bundle

A phenomenological model to account for the effect of a grid spacer with mixing vanes on CHF has been developed. It takes into the account of the mixing vane configuration (i.e., angle, number, position, etc.) on the flow field, the turbulent mixing between subchannels and heat transfer. Changes in flow field, turbulent mixing and heat transfer have led to CHF enhancement in subchannels and hence the bundle. The model has been implemented into the subchannel code ATHAS and assessed against the bundle CHF at conditions of interest to Pressurized Water Reactors (PWRs). Prediction of CHF in subchannel is based on the 2006 CHF look-up table and the mixing-vane spacer model. The assessment applies the direct substitution method (DSM) and the heat balance method (HBM). At the same time, significant improvement in CHF prediction accuracy was found for 467 data points.

Direct-substitution method for studying second harmonic generation in arbitrary optical superlattices

In this paper, we present the direct-substitution (DS) method to study the second-harmonic generation (SHG) in arbitrary one-dimensional optical superlattices (OS). Applying this method to Fibonacci and generalized Fibonacci systems, we obtain the relative intensity of SHG and compare them with previous works. We confirmed the validity of the proposed DS method by comparing our results of SHG in quasiperiodic Fibonacci OS with previous works using analytical Fourier transform method. Furthermore, the three-dimension SHG spectra obtained by DS method present the properties of SHG in Fibonacci OS more distinctly. What’s more important, the DS method demands very few limits and can be used to compute directly and conveniently the intensity of SHG in arbitrary OS where the quasi-phase-matching (QPM) can be achieved. It shows that the DS method is powerful for the calculation of electric field and intensity of SHG and can help experimentalists conveniently to estimate the distributions of SHG in any designed polarized systems.

Sensor network design for maximizing process efficiency: An algorithm and its application

Sensor network design (SND) is a constrained optimization problem requiring systematic and effective solution algorithms for determining where best to locate sensors. A SND algorithm is developed for maximizing plant efficiency for an estimator‐based control system while simultaneously satisfying accuracy requirements for the desired process measurements. The SND problem formulation leads to a mixed integer nonlinear programming (MINLP) optimization that is difficult to solve for large‐scale system applications. Therefore, a sequential approach is developed to solve the MINLP problem, where the integer problem for sensor selection is solved using the genetic algorithm while the nonlinear programming problem including convergence of the “tear stream” in the estimator‐based control system is solved using the direct substitution method. The SND algorithm is then successfully applied to a large scale, highly integrated chemical process. © 2014 American Institute of Chemical Engineers AIChE J, 61: 464–476, 2015

Fundamental issues in fluid modeling: Direct substitution and aliasing methods

It is shown how the accuracy of fluid models of charged particles in gases can be improved significantly by direct substitution of swarm transport coefficient data, rather than cross sections, into the average collision terms. This direct substitution method emerges in a natural way for fluid formulations in which the role of the mean energy is transparent, whatever the mass of the charged particles in equation (ions or electrons), and requires no further approximations. The procedure is illustrated by numerical examples for electrons, including the operational window of E/N for an idealized Franck-Hertz experiment. Using the same fluid formulation, we develop an aliasing method to estimate otherwise unknown mobility data for one type of particle, from known mobility data for another type of particle. The method is illustrated for muons in hydrogen, using tabulated data for protons in the same gas.

Multi-objective Short-term Hydrothermal Generation Scheduling Using Predator–Prey Optimization

In this article, a predator–prey-based optimization technique is applied to obtain the scheduling of a hydrothermal system with cascaded reservoirs, minimizing economic and gaseous pollutants and emission objectives. These objectives are mutually conflicting and are equally important. Predator–prey optimization is a stochastic optimization technique based on the particle swarm optimization concept having an additional predator effect that helps to explore the search area more efficiently due to the fear created by the predator. A heuristic search technique is applied for generating an initial feasible solution. The direct substitution method is implemented to handle the equality constraints, whereby dependent variables are determined from the equality constraint. Inequality constraints of dependent variables are taken care by incorporating an additional objective function represented by the fuzzy membership index, and other variables are set to their limits on violation. Fuzzy methodology has been exploited for solving a decision-making problem involving the multiplicity of objectives and selection criterion for the best compromised solution. The solutions obtained from the proposed technique are compared with other existing techniques, and results are found to be satisfactory. The proposed method has the capability to escape from local optimum solutions due to its predator effect, and it is easy to implement.

Synthesis, radioiodination and biological evaluation of novel dipeptide attached to triazole-pyridine moiety

A new dipeptide derivative, ethyl 2-(3-(4-hydroxyphenyl)-2-(2-(4-phenyl-5-((pyridin-4-ylamino)methyl)-4H-1,2,4-triazol-3-ylthio)acetamido)propanamido)-3-(1H-indol-3-yl)propanoate (EHPTIP) was successfully synthesized and radiolabeled with 125I by the direct electrophilic substitution method. The non radiolabeled compound (EHPTIP) was tested as an antimicrobial agent and the radiolabeled derivative was tested as a new imaging agent. The study results showed a good antimicrobial activity of EHPTIP and a good in vitro and in vivo stability of 125I-EHPTIP. The biodistribution of the radiolabeled compound showed a high brain uptake of 7.60 ± 0.01 injected activity/g tissue organ at 30 min post-injection and retention in brain remained high up to 1 h, whereas the clearance from the normal mice appeared to proceed via the renal system. Such brain uptake is better than that of currently used radiopharmaceuticals for brain imaging (99mTc-ECD and 99mTc-HMPAO). As a conclusion, EHPTIP is a newly synthesized dipeptide with a good antimicrobial activity and the radioiodinated EHPTIP which is labeled with 123I could be used as a novel agent for brain SPECT.

Effect of in-plane boundary conditions on forced vibration analysis of stiffened plates with a free edge

This paper undertakes a large amplitude forced vibration analysis of stiffened plates with free edges under harmonic excitation through a numerical method. The methodology adopted is an indirect one in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude. Free vibration analysis at the deflected configuration of the same system is also carried out separately to determine the backbone curves. The mathematical formulation is based on energy principles and the governing equations in both forced and free vibration cases are derived using Hamilton’s principle. The set of nonlinear governing equations is solved by employing an iterative direct substitution method with an appropriate relaxation technique. A multidimensional quasi-Newton method, known as Broyden’s method, is separately used when the system becomes computationally stiff. The results for a reduced system are validated with the published results of other researchers. For different combinations of boundary conditions including free edge results are furnished in the dimensionless amplitude-frequency plane. The effect of in-plane end conditions is studied by considering immovable and movable edges. Response in the vicinity of the second mode is also studied. Three dimensional operational deflection shape plots along with contour plots are also provided in a few cases.

Klein-Gordon Oscillator in Noncommutative Phase Space Under a Uniform Magnetic Field

Using a direct substitution method, Klein-Gordon oscillator in a uniform magnetic field is researched in the noncommutative phase space (NCPS), the corresponding exact energy is obtained, and the analytic eigenfunction is presented in terms of the confluent hypergeometric. It is shown that the Klein-Gordon oscillator in uniform magnetic field in noncommutative phase space has the similar behaviors to the Landau problem in commutative space. In addition, the non-relativistic limit of the energy spectrum is obtained.

Large Amplitude Forced Vibration Analysis of Stiffened Plates Under Harmonic Excitation

Large amplitude forced vibration behaviour of stiffened plates under harmonic excitation is studied numerically incorporating the effect of geometric non-linearity. The forced vibration analysis is carried out in an indirect way in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude. Large amplitude free vibration analysis of the same system is carried out separately to determine the backbone curves. The mathematical formulation is based on energy principles and the set of governing equations for both forced and free vibration problems derived using Hamilton’s principle. Appropriate sets of coordinate functions are formed by following the two dimensional Gram-Schmidt orthogonalization procedure to satisfy the corresponding boundary conditions of the plate. The problem is solved by employing an iterative direct substitution method with an appropriate relaxation technique and when the system becomes computationally stiff, Broyden’s method is used. The results are furnished as frequency response curves along with the backbone curve in the dimensionless amplitude-frequency plane. Three dimensional operational deflection shape (ODS) plots and contour plots are provided in a few cases.

Large amplitude forced vibration analysis of cross-beam system through energy method

Large amplitude forced vibration behaviour of cross-beam system under harmonic excitation is studied, incorporating the effect of geometric non-linearity. The forced vibration analysis is carried out in an indirect way, in which the dynamic system is assumed to satisfy the force equilibrium condition at peak load value, thus reducing the problem to an equivalent static case. The two beams of the system are solved individually either by a direct substitution method employing successive relaxation technique or a multi-dimensional secant method, known as Broyden’s method. An iterative scheme, based on the reaction force between the two beams of the system and equality of vibration amplitude at the contact of two beams, is developed to obtain the response of the system under external harmonic excitation. The present method is validated through results generated in ANSYS 11.0. The system response is studied for various loading type and contact location of the beams. The results are presented in terms of plots of vibration amplitude of the contact point versus frequency of forcing excitation in dimensional plane. Keywords: Cross-beam, Forced vibration, Geometric non-linearity, Variational methods, Harmonic excitation

Comment on ‘The Klein–Gordon equation with a generalized Hulthén potential in D dimensions’

The energy eigenvalues and the wavefunction of the D-dimensional Hulthén potential are obtained in terms of the hypergeometric function using the direct substitution method.

A Maple Package to Compute Lie Symmetry Groups and Symmetry Reductions of (1+1)-Dimensional Nonlinear Systems

Armed with the computer algebra system Maple, using a direct algebraic substitution method, we obtain Lie point symmetries, Lie symmetry groups and the corresponding symmetry reductions of one component nonlinear integrable and nonintegrable equations only by clicking the ‘Enter’ key. Abundant (1+1)-dimensional nonlinear mathematical physical systems are analysed effectively by using a Maple package LieSYMGRP proposed by us.