Search results for: functional equations

Authors: Olusola Ezekiel Abolarin, Gift E. Noah

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This research work considered an innovative procedure to numerically approximate higher-order Initial value problems (IVP) of ordinary differential equations (ODE) using the Legendre polynomial as the basis function. The proposed method is a half-step, self-starting Block integrator employed to approximate fourth and fifth order IVPs without reduction to lower order. The method was developed through a collocation and interpolation approach. The basic properties of the method, such as convergence, consistency and stability, were well investigated. Several test problems were considered, and the results compared favorably with both exact solutions and other existing methods.

Keywords: initial value problem, ordinary differential equation, implicit off-grid block method, collocation, interpolation

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Authors: Mohammadreza Akbari, Leila Abdollahpour, Sara Akbari, Pooya Soleimani

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Transferring thermo at the field of solid materials for instance tube-shaped structures, causing dynamical vibration at them. Majority of thermal and fluid processes are done engineering science at solid materials, for example, thermo-transferred pipes, fluids, chemical and nuclear reactors, include thermal processes, so, they need to consider the moment solid-fundamental structural strength unto these thermal interactions. Fluid and thermo retentive materials in front of external force to it like thermodynamical force, hydrodynamical force and static force continuously according to a function of time vibrated, and this action causes relative displacement of the structural materials elements, as a result, the moment resistance analysis preservation materials in thermal processes, the most important parameters for design are discussed. Including structural substrate holder temperature and fluid of the administrative and industrial center, is a cylindrical tube that for vibration analysis of cylindrical cells with heat and fluid transfer requires the use of vibration differential equations governing the structure of a tubular and thermal differential equations as the vibrating motive force at double-glazed cylinders.

Keywords: heat transfer, elements in cylindrical coordinates, analytical solving the governing equations, structural vibration

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Authors: Giovanni Incerti

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In this paper the dynamic behavior of a synchronous belt drive during start-up is analyzed and discussed. Besides considering the belt elasticity, the mathematical model here proposed also takes into consideration the electrical behaviour of the DC motor. The solution of the motion equations is obtained by means of the modal analysis in state space, which allows to obtain the decoupling of all equations of the mathematical model without introducing the hypothesis of proportional damping. The mathematical model of the transmission and the solution algorithms have been implemented within a computing software that allows the user to simulate the dynamics of the system and to evaluate the effects due to the elasticity of the belt branches and to the electromagnetic behavior of the DC motor. In order to show the details of the calculation procedure, the paper presents a case study developed with the aid of the abovementioned software.

Keywords: belt drive, vibrations, startup, DC motor

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Authors: Xuezhang Hou

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A control problem of a flexible Lamina formulated by partial differential equations with viscoelastic boundary conditions is studied in this paper. The problem is written in standard form of linear infinite dimensional system in an appropriate energy Hilbert space. The semigroup approach of linear operators is adopted in investigating wellposedness of the closed loop system. A variable structural control for the system is proposed, and meanwhile an equivalent control method is applied to the thin plate system. A significant result on control theory that the thin plate can be approximated by ideal sliding mode in any accuracy in terms of semigroup approach is obtained.

Keywords: partial differential equations, flexible lamina, variable structural control, semigroup of linear operators

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Authors: Sergio Mauricio Pérez López, Luis Rodrigo Valencia Pérez, Juan Manuel Peña Aguilar, Adelina Morita Alexander

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The culture of continuous improvement in organizations is very important as it represents a source of competitive advantage. This article discusses the transfer of knowledge between companies which formed cross-functional teams and used a dynamic model for knowledge creation as a framework. In addition, the article discusses the structure of cognitive assets in companies and the concept of "stickiness" (which is defined as an obstacle to the transfer of knowledge). The purpose of this analysis is to show that an improvement in the attitude of individual members of an organization creates opportunities, and that an exchange of information and knowledge leads to generating continuous improvements in the company as a whole. This article also discusses the importance of creating the proper conditions for sharing tacit knowledge. By narrowing gaps between people, mutual trust can be created and thus contribute to an increase in sharing. The concept of adapting knowledge to new environments will be highlighted, as it is essential for companies to translate and modify information so that such information can fit the context of receiving organizations. Adaptation will ensure that the transfer process is carried out smoothly by preventing "stickiness". When developing the transfer process on cross-functional teams (as opposed to working groups), the team acquires the flexibility and responsiveness necessary to meet objectives. These types of cross-functional teams also generate synergy due to the array of different work backgrounds of their individuals. When synergy is established, a culture of continuous improvement is created.

Keywords: knowledge transfer, continuous improvement, teamwork, cognitive assets

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Authors: Siddharth Deshpande, Nihar Masurkar, Vallerinteavide Mavelli Girish, Malan Desai, Chester Drum

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Folding and stabilization of recombinant proteins remain a consistent challenge for industrial and therapeutic applications. Proteins derived from thermophilic bacteria often have superior expression and stability qualities. To develop a generalizable approach to protein folding and stabilization, we tested the hypothesis that wrapping a thermostable exoshell around a protein substrate would aid folding and impart thermostable qualities to the internalized substrate. To test the effect of internalizing a protein within a thermostable exoshell (tES), we tested in vitro folding and stability using green fluorescent protein (GFPuv), horseradish peroxidase (HRP) and renilla luciferase (rLuc). The 8nm interior volume of a thermostable ferritin assembly was engineered to accommodate foreign proteins and either present a positive, neutral or negative interior charge environment. We further engineered the tES complex to reversibly assemble and disassemble with pH titration. Template proteins were expressed as inclusion bodies and an in vitro folding protocol was developed that forced proteins to fold inside a single tES. Functional yield was improved 100-fold, 100-fold and 150-fold with use of tES for GFPuv, HRP and rLuc respectively and was highly dependent on the internal charge environment of the tES. After folding, functional proteins could be released from the tES folding cavity using size exclusion chromatography at pH 5.8. Internalized proteins were tested for improved stability against thermal, organic, urea and guanidine denaturation. Our results demonstrated that thermostable exoshells can efficiently refold and stabilize inactive aggregates into functional proteins.

Keywords: thermostable shell, in vitro folding, stability, functional yield

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Authors: Esmaeil Bahmyari

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The natural frequency analysis of the functionally graded (FG) rotating cylindrical shells subjected to thermal loads is studied based on the three-dimensional elasticity theory. The temperature-dependent assumption of the material properties is graded in the thickness direction, which varies based on the simple power law distribution. The governing equations and the appropriate boundary conditions, which include the effects of initial thermal stresses, are derived employing Hamilton’s principle. The initial thermo-mechanical stresses are obtained by the thermo-elastic equilibrium equation’s solution. As an efficient and accurate numerical tool, the differential quadrature method (DQM) is adopted to solve the thermo-elastic equilibrium equations, free vibration equations and natural frequencies are obtained. The high accuracy of the method is demonstrated by comparison studies with those existing solutions in the literature. Ultimately, the parametric studies are performed to demonstrate the effects of boundary conditions, temperature rise, material graded index, the thickness-to-length and the aspect ratios for the rotating cylindrical shells on the natural frequency.

Keywords: free vibration, DQM, elasticity theory, FG shell, rotating cylindrical shell

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Authors: M. Salmanzadeh

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In paper, we will deal with incompressible Couette flow, which represents an exact analytical solution of the Navier-Stokes equations. Couette flow is perhaps the simplest of all viscous flows, while at the same time retaining much of the same physical characteristics of a more complicated boundary-layer flow. The numerical technique that we will employ for the solution of the Couette flow is the Crank-Nicolson implicit method. Parabolic partial differential equations lend themselves to a marching solution; in addition, the use of an implicit technique allows a much larger marching step size than would be the case for an explicit solution. Hence, in the present paper we will have the opportunity to explore some aspects of CFD different from those discussed in the other papers.

Keywords: incompressible couette flow, numerical method, partial differential equation, Crank-Nicolson implicit

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Authors: U. L. Fulco, E. L. Albuquerque, José X. Lima Neto, L. R. Da Silva

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The binding of the nonsteroidal anti-inflammatory drug ibuprofen (IBU) to human serum albumin (HSA) is investigated using density functional theory (DFT) calculations within a fragmentation strategy. Crystallographic data for the IBU–HSA supramolecular complex shows that the ligand is confined to a large cavity at the subdomain IIIA and at the interface between the subdomains IIA and IIB, whose binding sites are FA3/FA4 and FA6, respectively. The interaction energy between the IBU molecule and each amino acid residue of these HSA binding pockets was calculated using the Molecular Fractionation with Conjugate Caps (MFCC) approach employing a dispersion corrected exchange–correlation functional. Our investigation shows that the total interaction energy of IBU bound to HSA at binding sites of the fatty acids FA3/FA4 (FA6) converges only for a pocket radius of at least 8.5 °A, mainly due to the action of residues Arg410, Lys414 and Ser489 (Lys351, Ser480 and Leu481) and residues in nonhydrophobic domains, namely Ile388, Phe395, Phe403, Leu407, Leu430, Val433, and Leu453 (Phe206, Ala210, Ala213, and Leu327), which is unusual. Our simulations are valuable for a better understanding of the binding mechanism of IBU to albumin and can lead to the rational design and the development of novel IBU-derived drugs with improved potency.

Keywords: ibuprofen, human serum albumin, density functional theory, binding energies

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Authors: Jin Liang, James H. Liu, Ti-Jun Xiao

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It is known that there exist many physical phenomena where abrupt or impulsive changes occur either in the system dynamics, for example, ad-hoc network, or in the input forces containing impacts, for example, the bombardment of space antenna by micrometeorites. There are many other examples such as ultra high-speed optical signals over communication networks, the collision of particles, inventory control, government decisions, interest changes, changes in stock price, etc. These are impulsive phenomena. Hence, as a combination of the traditional initial value problems and the short-term perturbations whose duration can be negligible in comparison with the duration of the process, the systems with impulsive conditions (i.e., impulsive systems) are more realistic models for describing the impulsive phenomenon. Such a situation is also suitable for the delay systems, which include some of the past states of the system. So far, there have been a lot of research results in the study of impulsive systems with delay both in finite and infinite dimensional spaces. In this paper, we investigate the periodicity of solutions to the nonautonomous impulsive evolution equations with infinite delay in Banach spaces, where the coefficient operators (possibly unbounded) in the linear part depend on the time, which are impulsive systems in infinite dimensional spaces and come from the optimal control theory. It was indicated that the study of periodic solutions for these impulsive evolution equations with infinite delay was challenging because the fixed point theorems requiring some compactness conditions are not applicable to them due to the impulsive condition and the infinite delay. We are happy to report that after detailed analysis, we are able to combine the techniques developed in our previous papers, and some new ideas in this paper, to attack these impulsive evolution equations and derive periodic solutions. More specifically, by virtue of the related transition operator family (evolution family), we present a Poincaré operator given by the nonautonomous impulsive evolution system with infinite delay, and then show that the operator is a condensing operator with respect to Kuratowski's measure of non-compactness in a phase space by using an Amann's lemma. Finally, we derive periodic solutions from bounded solutions in view of the Sadovskii fixed point theorem. We also present a relationship between the boundedness and the periodicity of the solutions of the nonautonomous impulsive evolution system. The new results obtained here extend some earlier results in this area for evolution equations without impulsive conditions or without infinite delay.

Keywords: impulsive, nonautonomous evolution equation, optimal control, periodic solution

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Authors: Farideh Tabatabei-Yazdi, Fereshteh Falah, Alireza Vasiee

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Nowadays, production of functional foods has become very essential. Inulin is one of the most functional hydrocolloid compounds used in such products. In the present study, the production of a synbiotic yogurt containing 1, 2.5, and 5% (w/v) inulin has been investigated. The yogurt was fermented with Lactobacillus brevis PML1 derived from Tarkhineh, an Iranian cereal-dairy fermented food. Furthermore, the physicochemical properties, antioxidant activity, sensory attributes, and microbial viability properties were investigated on the 0th, 7th, and 14th days of storage after fermentation. The viable cells of L. brevis PML1 reached 108 CFU/g, and the product resisted to simulated digestive juices. Moreover, the synbiotic yogurt impressively increased the production of antimicrobial compounds and had the most profound antimicrobial effect on S. typhimurium. The physiochemical properties were in the normal range, and the fat content of the synbiotic yogurt was reduced remarkably. The antioxidant capacity of the fermented yogurt was significantly increased (p<0:05), which was equal to those of DPPH (69:18±1:00%) and BHA (89:16±2:00%). The viability of L. brevis PML1 was increased during storage. Sensory analysis showed that there were significant differences in terms of the impressive parameters between the samples and the control (p<0:05). Addition of 2.5% inulin not only improved the physical properties but also retained the viability of the probiotic after 14 days of storage, in addition to the viability of L. brevis with a viability count above 6 log CFU/g in the yogurt. Therefore, a novel synbiotic product containing L. brevis PML1, which can exert the desired properties, can be used as a suitable carrier for the delivery of the probiotic strain, exerting its beneficial health effects.

Keywords: functional food, lactobacillus brevis, symbiotic yogurt, physiochemical properties

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Authors: Wilhelmina van den Berg

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Through intentionally developing the Register Continuum and the Functional Model of Language in the secondary history classroom, teachers can effectively build a teaching and learning cycle geared towards literacy improvement and EAL differentiation. Developing an understanding of and engaging students in the field, tenor, and tone of written and spoken language, allows students to build the foundation for greater academic achievement due to integrated literacy skills in the history classroom. Building a variety of scaffolds during lessons within these models means students can improve their academic language and communication skills.

Keywords: academic language, EAL, functional model of language, international baccalaureate, literacy skills

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Authors: Jamal A. Gledan, Othman A. Azzeidani

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During the last decade, Libya established a new Geodetic Datum called Libyan Geodetic Datum 2006 (LGD 2006) by using GPS, whereas the ground traversing method was used to establish the last Libyan datum which was called the Europe Libyan Datum 79 (ELD79). The current research paper introduces ELD79 to LGD2006 coordinate transformation technique, the accurate comparison of transformation between multiple regression equations and the three-parameters model (Bursa-Wolf). The results had been obtained show that the overall accuracy of stepwise multi regression equations is better than that can be determined by using Bursa-Wolf transformation model.

Keywords: geodetic datum, horizontal control points, traditional similarity transformation model, unconventional transformation techniques

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Authors: Halil Baris Cit, Mert Durmaz

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Subsequent to the design of the compact centrifugal compressor, which is specifically intended to be used in aviation platforms, the process has been evaluated within the context of this study. A trade-off study matrix for future studies has been formed after making comparison between the design and the previous studies taking part in literature. While the power consumption of the designed compressor will be approximately 25 kW, the working fluid will be refrigerant. Properties such as thermodynamic properties and Global Warmin Potential(GWP)-Ozone Depletion Potential(ODP) Values of the fluid have been taken into consideration during the selection process of the refrigerant. Concepts NREC and ANSYS Vista CCD software have been used in the part of conceptual design, and R1233ZD has been selected as the refrigerant. Real-gas Computational Fluid Dynamic(CFD) analysis has been carried out with different cubic equations of state in the ANSYS CFX solver so as to figure out the most suitable solution method. These equations are named as “The Redlich Kwong”, “Soave Redlich Kwong”, “Augnier Redlick Kwong,” and “Peng Robinson.” By being used the mentioned solution equations in the same compressor configuration, analysis also have been carried out with two gases having different characteristics. As a result of the 12 analysis carried out with three different refrigerants—R11, R134A, and R1233zd—and four different solution equations mentioned above, the most accurate solution method has been selected by comparing the densities of the gases at different pressure and temperature points. The results have been analyzed within two titles following to the completion of the design with the selected equation. The first one is a trade-off study matrix presenting a comparison regarding the compact centrifugal compressor operating with the refrigerant to be designed. This comparison is between some dimensionless and dimensional parameters determined before the design and their values in the literature. Second one will show the differences between the actual density and the density in the design software in each real gas analysis method, along with the effects of it on the design.

Keywords: turbocompressor, refrigerant, aviation, aerospace compressor

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Authors: Amal Shehata

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Low back pain related to disc prolapse is localized in the lumbar area and it may be radiated to the lower extremities, starting from neurons near or around the spinal canal. Most of the population may be affected with disc prolapse within their lifetime and leads to lost productivity, disability and loss of function. The study purpose was to examine the effect of rehabilitative nursing program on pain intensity and functional status among patients with discectomy. Design: Aquasi experimental design was utilized. Setting: The study was carried out at neurosurgery department and out patient's clinic of Menoufia University and Teaching hospitals at Menoufia governorate, Egypt. Instrument of the study: Five Instruments were used for data collection: Structured interviewing questionnaire, Functional assessment instrument, Observational check list, Numeric rating Scale and Oswestry low back pain disability questionnaire. Results: There was an improvement in mean total knowledge score about disease process, discectomy and rehabilitation program in study group (25.32%) than control group (7.32%). There was highly statistically significant improvement in lumbar flexibility among study group (80%) than control group (30%) after rehabilitation program than before. Also there was a decrease in pain score in study group (58% no pain) than control group (28% no pain) after rehabilitation program. There was an improvement in total disability score of study group (zero %) regarding effect of pain on the activity of daily living after rehabilitation program than control group (16%). Conclusion: Application of rehabilitative nursing program for patient with discectomy had proven a positive effect in relation to knowledge score, pain reduction, activity of daily living and functional abilities. Recommendation: A continuous rehabilitative nursing program should be carried out for all patients immediately after discectomy surgery on regular basis. Also A colored illustrated booklet about rehabilitation program should be available and distributed for all patients before surgery.

Keywords: discectomy, rehabilitative nursing program, pain intensity, functional status

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Authors: Arun Goel

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The present paper attempts to investigate the prediction of air entrainment rate and aeration efficiency of a free over-fall jets issuing from a triangular sharp crested weir by using regression based modelling. The empirical equations, support vector machine (polynomial and radial basis function) models and the linear regression techniques were applied on the triangular sharp crested weirs relating the air entrainment rate and the aeration efficiency to the input parameters namely drop height, discharge, and vertex angle. It was observed that there exists a good agreement between the measured values and the values obtained using empirical equations, support vector machine (Polynomial and rbf) models, and the linear regression techniques. The test results demonstrated that the SVM based (Poly & rbf) model also provided acceptable prediction of the measured values with reasonable accuracy along with empirical equations and linear regression techniques in modelling the air entrainment rate and the aeration efficiency of a free over-fall jets issuing from triangular sharp crested weir. Further sensitivity analysis has also been performed to study the impact of input parameter on the output in terms of air entrainment rate and aeration efficiency.

Keywords: air entrainment rate, dissolved oxygen, weir, SVM, regression

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Authors: Anyeres N. Atehortua Jimenez, J. David Lambraño, Juan Carlos Muñoz

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Navier-Stokes equations (NSE), which describe the dynamics of a fluid, have an important application on modeling waves used for data inversion techniques as full waveform inversion (FWI). In this work a linearized version of NSE and its variables, neglecting deviatoric terms of stress tensor, is presented. In order to get a theoretical modeling of pressure p(x,t) and wave velocity profile c(x,t), a wave equation of visco-acoustic medium (VAE) is written. A change of variables p(x,t)=q(x,t)h(ρ), is made on the equation for the VAE leading to a well known Klein-Gordon equation (KGE) describing waves propagating in variable density medium (ρ) with dispersive term α^2(x). KGE is reduced to a Poisson equation and solved by proposing a specific function for α^2(x) accounting for the energy dissipation and dispersion. Finally, an integral form solution is derived for p(x,t), c(x,t) and kinematics variables like particle velocity v(x,t), displacement u(x,t) and bulk modulus function k_b(x,t). Further, it is compared this visco-acoustic formulation with another form broadly used in the geophysics; it is argued that this formalism is more general and, given its integral form, it may offer several advantages from the modern parallel computing point of view. Applications to minimize the errors in modeling for FWI applied to oils resources in geophysics are discussed.

Keywords: Navier-Stokes equations, modeling, visco-acoustic, inversion FWI

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Authors: K. Pandey

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The present study is a functional analysis of the relationship between castes which indicates the dynamics of the caste structure in the rural setting. The researcher has tried to show both the cooperation and competition on important ceremonial and social occasions. The real India exists in the villages, so we need to know about their solidarity and also what the village life is and has been shaping into. We need to emphasize a microcosmic study of Indian rural life. Furthermore, caste integration is an acute problem country faces today. To resolve this we are required to know the dynamics of behavior of the people of different castes and for the study of the caste dynamics a study of caste relations are needed. The present study is an attempt in this direction.

Keywords: hierarchial groups, jajmani system, functional dependence, commensalities

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Authors: Getachew T. Sedebo, Stephan V. Joubert, Michael Y. Shatalov

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Conventional configuration of the vibratory disc gyroscope is based on in-plane non-axisymmetric vibrations of the disc with a prescribed circumferential wave number. Due to the Bryan's effect, the vibrating pattern of the disc becomes sensitive to the axial component of inertial rotation of the disc. Rotation of the vibrating pattern relative to the disc is proportional to the inertial angular rate and is measured by sensors. In the present paper, the authors investigate a possibility of making a 3D sensor on the basis of both in-plane and bending vibrations of the disc resonator. We derive equations of motion for the disc vibratory gyroscope, where both in-plane and bending vibrations are considered. Hamiltonian variational principle is used in setting up equations of motion and the corresponding boundary conditions. The theory of thin shells with the linear elasticity principles is used in formulating the problem and also the disc is assumed to be isotropic and obeys Hooke's Law. The governing equation for a specific mode is converted to an ODE to determine the eigenfunction. The resulting ODE has exact solution as a linear combination of Bessel and Neumann functions. We demonstrate how to obtain an explicit solution and hence the eigenvalues and corresponding eigenfunctions for annular disc with fixed inner boundary and free outer boundary. Finally, the characteristics equations are obtained and the corresponding eigenvalues are calculated. The eigenvalues are used for the calculation of tuning conditions of the 3D disc vibratory gyroscope.

Keywords: Bryan’s effect, bending vibrations, disc gyroscope, eigenfunctions, eigenvalues, tuning conditions

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Authors: Muhammad Rizwan Tariq, Muhammad Issa Khan, Zulfiqar Ahmad, Muhammad Adnan Nasir, Muhammad Sameem Javed, Sheraz Ahmed

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Functional foods may be a good tool that can be simply utilized in reducing community health expenses. Regular consumption of rabbit meat can offer patrons with bioactive components because the manipulation in rabbit feed is much successful to raise the levels of conjugated linoleic acid, ecosapentaenoic acid, decosahexaenoic acid, polyunsaturated fatty acids, selenium, tocopherol etc. and to reduce the ω-3/ω-6 ratio which is performing a major role in curing of cardiovascular and several other diseases. In comparison to the meats of other species, rabbit meat has higher amounts of protein with essential amino acids, especially in the muscles and low cholesterol contents that also have elevated digestibility. The present study was carried out to develop the functional rabbit meat by modifying feed ingredient of rabbit diet. Thirty-day old rabbits were fed with feeds containing 2 % and 4 % oat. The feeding trial was carried out for eight weeks. Rabbits were divided into three different groups and reared for the period of two months. T0 rabbits were considered control group while T1 rabbits were reared on 4% oat, and T2 were on 2% oat in the feed. At the end of the 8 weeks, the rabbits were slaughtered. Results presented in this study concluded that 4 % oat seed supplementation enhanced n-3 PUFA in meat. It was observed that oat seed supplementation also reduced fat percentage in the meat. Utilization of oat in the feed of rabbits significantly affected the pH, protein, fat, textural and concentration of polyunsaturated fatty acids. A study trial was conducted in order to examine the impact of functional meat on the blood lipid profile of human subjects. They were given rabbit meat in comparison to the chicken meat for the period of one month. The cholesterol, triglycerides and low density lipoprotein were found to be lower in blood serum of human subject group treated with 4 % oat meat.

Keywords: functional food, functional rabbit meat, meat quality, rabbit

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Authors: Bahatti̇n Ki̇mençe, Uğur Ki̇mençe

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In this study, the purpose of obtaining the influence functions of the displacement discontinuity in an anisotropic elastic medium is to produce the boundary element equations. A Displacement Discontinuous Method formulation (DDM) is presented with the aim of modeling two-dimensional elastic fracture problems. This formulation is found by analytical integration of the fundamental solution along a straight-line crack. With this purpose, Kelvin's fundamental solutions for anisotropic media on an infinite plane are used to form dipoles from singular loads, and the various combinations of the said dipoles are used to obtain the influence functions of displacement discontinuity. This study introduces a technique for coupling Fictitious Stress Method (FSM) and DDM; the reason for applying this technique to some examples is to demonstrate the effectiveness of the proposed coupling method. In this study, displacement discontinuity equations are obtained by using dipole solutions calculated with known singular force solutions in an anisotropic medium. The displacement discontinuities method obtained from the solutions of these equations and the fictitious stress methods is combined and compared with various examples. In this study, one or more crack problems with various geometries in rectangular plates in finite and infinite regions, under the effect of tensile stress with coupled FSM and DDM in the anisotropic environment, were examined, and the effectiveness of the coupled method was demonstrated. Since crack problems can be modeled more easily with DDM, it has been observed that the use of DDM has increased recently. In obtaining the displacement discontinuity equations, Papkovitch functions were used in Crouch, and harmonic functions were chosen to satisfy various boundary conditions. A comparison is made between two indirect boundary element formulations, DDM, and an extension of FSM, for solving problems involving cracks. Several numerical examples are presented, and the outcomes are contrasted to existing analytical or reference outs.

Keywords: displacement discontinuity method, fictitious stress method, crack problems, anisotropic material

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Authors: Joseph Wolff, Jeffrey Eilbott

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Autism Spectrum Disorders (ASD) are a spectrum of social disorders characterized by deficits in social communication, verbal ability, and interaction that can vary in severity. In recent years, researchers have used magnetic resonance imaging (MRI) to help detect how neural patterns in individuals with ASD differ from those of neurotypical (NT) controls for classification purposes. This study analyzed the classification of ASD within males and females using functional MRI data. Functional connectivity (FC) correlations among brain regions were used as feature inputs for machine learning algorithms. Analysis was performed on 558 cases from the Autism Brain Imaging Data Exchange (ABIDE) I dataset. When trained specifically on females, the algorithm underperformed in classifying the ASD subset of our testing population. Although the subject size was relatively smaller in the female group, the manual matching of both male and female training groups helps explain the algorithm’s bias, indicating the altered sex abnormalities in functional brain networks compared to typically developing peers. These results highlight the importance of taking sex into account when considering how generalizations of findings on males with ASD apply to females.

Keywords: autism spectrum disorder, machine learning, neuroimaging, sex differences

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Authors: Serdal Pamuk, Irem Cay

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Our model is based on the theory of reinforced random walks coupled with Michealis-Menten mechanisms which view endothelial cell receptors as the catalysts for transforming both tumor and macrophage derived tumor angiogenesis factor (TAF) into proteolytic enzyme which in turn degrade the basal lamina. The model consists of two main parts. First part has seven differential equations (DE’s) in one space dimension over the capillary, whereas the second part has the same number of DE’s in two space dimensions in the extra cellular matrix (ECM). We connect these two parts via some boundary conditions to move the cells into the ECM in order to initiate capillary formation. But, when does this movement begin? To address this question we estimate the thresholds that activate the transport equations in the capillary. We do this by using steady-state analysis of TAF equation under some assumptions. Once these equations are activated endothelial, pericyte and macrophage cells begin to move into the ECM for the initiation of angiogenesis. We do believe that our results play an important role for the mechanisms of cell migration which are crucial for tumor angiogenesis. Furthermore, we estimate the long time tendency of these three cells, and find that they tend to the transition probability functions as time evolves. We provide our numerical solutions which are in good agreement with our theoretical results.

Keywords: angiogenesis, capillary formation, mathematical analysis, steady-state, transition probability function

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Authors: Sidrah Ahmed

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The river and lakes flows are modeled mathematically by shallow water equations that are depth-averaged Reynolds Averaged Navier-Stokes equations under Boussinesq approximation. The temperature stratification dynamics influence the water quality and mixing characteristics. It is mainly due to the atmospheric conditions including air temperature, wind velocity, and radiative forcing. The experimental observations are commonly taken along vertical scales and are not sufficient to estimate small turbulence effects of temperature variations induced characteristics of shallow flows. Wind shear stress over the water surface influence flow patterns, heat fluxes and thermodynamics of water bodies as well. Hence it is crucial to couple temperature gradients with shallow water model to estimate the atmospheric effects on flow patterns. The Ripa system has been introduced to study ocean currents as a variant of shallow water equations with addition of temperature variations within the flow. Ripa model is a hyperbolic system of partial differential equations because all the eigenvalues of the system’s Jacobian matrix are real and distinct. The time steps of a numerical scheme are estimated with the eigenvalues of the system. The solution to Riemann problem of the Ripa model is composed of shocks, contact and rarefaction waves. Solving Ripa model with Riemann initial data with the central schemes is difficult due to the eigen structure of the system.This works presents the comparison of four different finite difference schemes for the numerical solution of Riemann problem for Ripa model. These schemes include Lax-Friedrichs, Lax-Wendroff, MacCormack scheme and a higher order finite difference scheme with WENO method. The numerical flux functions in both dimensions are approximated according to these methods. The temporal accuracy is achieved by employing TVD Runge Kutta method. The numerical tests are presented to examine the accuracy and robustness of the applied methods. It is revealed that Lax-Freidrichs scheme produces results with oscillations while Lax-Wendroff and higher order difference scheme produce quite better results.

Keywords: finite difference schemes, Riemann problem, shallow water equations, temperature gradients

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Authors: Adel Mohsen

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A direct method based on the good Broyden's updates for evaluating the inverse of a nonsingular square matrix of full rank and solving related system of linear algebraic equations is studied. For a matrix A of order n whose LU-decomposition is A = LU, the multiplication count is O (n3). This includes the evaluation of the LU-decompositions of the inverse, the lower triangular decomposition of A as well as a “reduced matrix inverse”. If an explicit value of the inverse is not needed the order reduces to O (n3/2) to compute to compute inv(U) and the reduced inverse. For a symmetric matrix only O (n3/3) operations are required to compute inv(L) and the reduced inverse. An example is presented to demonstrate the capability of using the reduced matrix inverse in treating ill-conditioned systems. Besides the simplicity of Broyden's update, the method provides a mean to exploit the possible sparsity in the matrix and to derive a suitable preconditioner.

Keywords: Broyden's updates, matrix inverse, inverse factorization, solution of linear algebraic equations, ill-conditioned matrices, preconditioning

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Authors: Mohammad Khazaei, Reza Rostami, Hassan Gharayagh Zandi, Ruhollah Basatnia, Mahboubeh Ghayour Najafabadi

Abstract:

Introduction: This study delves into the influence of diverse interventions on brain functional connectivity among young male basketball players. Given the significance of understanding how interventions affect cognitive functions in athletes, particularly in the context of basketball, this research contributes to the growing body of knowledge in sports neuroscience. Methods: Three distinct groups were selected for comprehensive investigation: the Motivational Interview Group, Placebo Consumption Group, and Ritalin Consumption Group. The study involved assessing brain functional connectivity using various frequency bands (Delta, Theta, Alpha, Beta1, Beta2, Gamma, and Total Band) before and after the interventions. The participants were subjected to specific interventions corresponding to their assigned groups. Results: The findings revealed substantial differences in brain functional connectivity across the studied groups. The Motivational Interview Group exhibited optimal outcomes in PLI (Total Band) connectivity. The Placebo Consumption Group demonstrated a marked impact on PLV (Alpha) connectivity, and the Ritalin Consumption Group experienced a considerable enhancement in imCoh (Total Band) connectivity. Discussion: The observed variations in brain functional connectivity underscore the nuanced effects of different interventions on young male basketball players. The enhanced connectivity in specific frequency bands suggests potential cognitive and performance improvements. Notably, the Motivational Interview and Placebo Consumption groups displayed unique patterns, emphasizing the multifaceted nature of interventions. These findings contribute to the understanding of tailored interventions for optimizing cognitive functions in young male basketball players. Conclusion: This study provides valuable insights into the intricate relationship between interventions and brain functional connectivity in young male basketball players. Further research with expanded sample sizes and more sophisticated statistical analyses is recommended to corroborate and expand upon these initial findings. The implications of this study extend to the broader field of sports neuroscience, aiding in the development of targeted interventions for athletes in various disciplines.

Keywords: electroencephalography, Ritalin, Placebo effect, motivational interview

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Authors: Ramandeep Behl, S. S. Motsa

Abstract:

The main focus of this manuscript is to provide a highly efficient two-point sixth-order family of super-Halley type methods that do not require any second-order derivative evaluation for obtaining simple roots of nonlinear equations, numerically. Each member of the proposed family requires two evaluations of the given function and two evaluations of the first-order derivative per iteration. By using Mathematica-9 with its high precision compatibility, a variety of concrete numerical experiments and relevant results are extensively treated to confirm t he t heoretical d evelopment. From their basins of attraction, it has been observed that the proposed methods have better stability and robustness as compared to the other sixth-order methods available in the literature.

Keywords: basins of attraction, nonlinear equations, simple roots, super-Halley

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Authors: Beata Jackowska-Zduniak

Abstract:

We formulate and analyze a mathematical model describing dynamics of cancer growth under the influence of radiation therapy. The effect of this type of therapy is considered as an additional equation of discussed model. Numerical simulations show that delay, which is added to ordinary differential equations and represent time needed for transformation from one type of cells to the other one, affects the behavior of the system. The validation and verification of proposed model is based on medical data. Analytical results are illustrated by numerical examples of the model dynamics. The model is able to reconstruct dynamics of treatment of cancer and may be used to determine the most effective treatment regimen based on the study of the behavior of individual treatment protocols.

Keywords: mathematical modeling, numerical simulation, ordinary differential equations, radiation therapy

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Authors: Merouane Salhi, Mohamed Roudane, Abdelkader Kirad

Abstract:

In this work, we present a new form of characteristics method, which is a technique for solving partial differential equations. Typically, it applies to first-order equations; the aim of this method is to reduce a partial differential equation to a family of ordinary differential equations along which the solution can be integrated from some initial data. This latter developed under the real gas theory, because when the thermal and the caloric imperfections of a gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with the gas parameters. The gas doesn’t stay perfect. Its state equation change and it becomes for a real gas. The presented equations of the characteristics remain valid whatever area or field of study. Here we need have inserted the developed Prandtl Meyer function in the mathematical system to find a new model when the effect of stagnation pressure is taken into account. In this case, the effects of molecular size and intermolecular attraction forces intervene to correct the state equation, the thermodynamic parameters and the value of Prandtl Meyer function. However, with the assumptions that Berthelot’s state equation accounts for molecular size and intermolecular force effects, expressions are developed for analyzing the supersonic flow for thermally and calorically imperfect gas. The supersonic parameters depend directly on the stagnation parameters of the combustion chamber. The resolution has been made by the finite differences method using the corrector predictor algorithm. As results, the developed mathematical model used to design 2D minimum length nozzles under effect of the stagnation parameters of fluid flow. A comparison for air with the perfect gas PG and high temperature models on the one hand and our results by the real gas theory on the other of nozzles shapes and characteristics are made.

Keywords: numerical methods, nozzles design, real gas, stagnation parameters, supersonic expansion, the characteristics method

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Authors: N. N. Joshi, G. K. Singh

Abstract:

We present the stimuli implementation and verification of a Programmable Peripheral Interface (PPI) 8255. It involves a designing and verification of configurable intellectual property (IP) module of PPI protocol using Verilog HDL for implementation part and System Verilog for verification. The overview of the PPI-8255 presented then the design specification implemented for the work following the functional description and pin configuration of PPI-8255. The coverage report of design shows that our design and verification environment covered 100% functionality in accordance with the design specification generated by the Questa Sim 10.0b.

Keywords: Programmable Peripheral Interface (PPI), verilog HDL, system verilog, questa sim

Procedia PDF Downloads 513