Search results for: polynomial constitutive equation

Authors: Giselle Maggie Fer Castañeda, Diego Iván González

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The objective of this work was to study the autoshaped choice behavior in the Donahoe, Burgos and Palmer (DBP) neural network model and analyze it under the matching law. Autoshaped choice can be viewed as a form of economic behavior defined as the preference between alternatives according to their relative outcomes. The Donahoe, Burgos and Palmer (DBP) model is a connectionist proposal that unifies operant and Pavlovian conditioning. This model has been used for more than three decades as a neurobehavioral explanation of conditioning phenomena, as well as a generator of predictions suitable for experimental testing with non-human animals and humans. The study consisted of different simulations in which, in each one, a ratio of reinforcement was established for two alternatives, and the responses (i.e., activations) in each of them were measured. Choice studies with animals have demonstrated that the data generally conform closely to the generalized matching law equation, which states that the response ratio equals proportionally to the reinforcement ratio; therefore, it was expected to find similar results with the neural networks of the Donahoe, Burgos and Palmer (DBP) model since these networks have simulated and predicted various conditioning phenomena. The results were analyzed by the generalized matching law equation, and it was observed that under some contingencies, the data from the networks adjusted approximately to what was established by the equation. Implications and limitations are discussed.

Keywords: matching law, neural networks, computational models, behavioral sciences

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Authors: Mustafa Ekici

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Natural convection is a basic process which is important in a wide variety of practical applications. In essence, a heated fluid expands and rises from buoyancy due to decreased density. Numerous papers have been written on natural or mixed convection in vertical ducts heated on the side. These equations have been proved to be valuable tools for the modelling of many phenomena such as fluid dynamics. Finding solutions to such equations or system of equations are in general not an easy task. We propose a method, which is called differential transform method, of solving a non-linear equations and compare the results with some of the other techniques. Illustrative examples shows that the results are in good agreement.

Keywords: differential transform method, momentum, energy equation, boundry value problem

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Authors: Ayan Chakraborty, BV. Rathish Kumar

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Off-late many models in viscoelasticity, signal processing or anomalous diffusion equations are formulated in fractional calculus. Tempered fractional calculus is the generalization of fractional calculus and in the last few years several important partial differential equations occurring in the different field of science have been reconsidered in this term like diffusion wave equations, Schr$\ddot{o}$dinger equation and so on. In the present paper, a time-dependent tempered fractional diffusion equation of order $\gamma \in (0,1)$ with forcing function is considered. Existence, uniqueness, stability, and regularity of the solution has been proved. Crank-Nicolson discretization is used in the time direction. B spline finite element approximation is implemented. Generally, B-splines basis are useful for representing the geometry of a finite element model, interfacing a finite element analysis program. By utilizing this technique a priori space-time estimate in finite element analysis has been derived and we proved that the convergent order is $\mathcal{O}(h²+T²)$ where $h$ is the space step size and $T$ is the time. A couple of numerical examples have been presented to confirm the accuracy of theoretical results. Finally, we conclude that the studied method is useful for solving tempered fractional diffusion equations.

Keywords: B-spline finite element, error estimates, Gronwall's lemma, stability, tempered fractional

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Authors: K. I. M. Guerra, L. A. P. Silva, J. C. Leal

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This study aims to understand with more amplitude and clarity the behavior of a porous medium where a pressure wave travels, translated into relative displacements inside the material, using mathematical tools derived from topology and symplectic geometry. The paper starts with a given partial differential equation based on the continuity and conservation theorems to describe the traveling wave through the porous body. A solution for this equation is proposed after all boundary, and initial conditions are fixed, and it’s accepted that the solution lies in a manifold U of purely spatial dimensions and that is embedded in the Real n-dimensional manifold, with spatial and kinetic dimensions. It’s shown that the U manifold of lower dimensions than IRna, where it is embedded, inherits properties of the vector spaces existing inside the topology it lies on. Then, a second manifold (U*), embedded in another space called IRnb of stress dimensions, is proposed and there’s a non-degenerative function that maps it into the U manifold. This relation is proved as a transformation in between two corresponding admissible solutions of the differential equation in distinct dimensions and properties, leading to a more visual and intuitive understanding of the whole dynamic process of a stress wave through a porous medium and also highlighting the dimensional invariance of Terzaghi’s theory for any coordinate system.

Keywords: poremechanics, soil dynamics, symplectic geometry, wave propagation

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Authors: K. Ebrahimi, Sh. Shahid, M. Mohammadi Ghaleni, M. H. Omid

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The longitudinal dispersion coefficient is a crucial parameter for 1-D water quality analysis of riverine flows. So far, different types of empirical equations for estimation of the coefficient have been developed, based on various case studies. The main objective of this paper is to develop an empirical equation for estimation of the coefficient for a riverine flow. For this purpose, a set of tracer experiments was conducted, involving salt tracer, at three sections located in downstream of a lengthy canal. Tracer data were measured in three mixing lengths along the canal including; 45, 75 and 100m. According to the results, the obtained coefficients from new developed empirical equation gave an encouraging level of agreement with the theoretical values.

Keywords: coefficients, dispersion, river, tracer, water quality

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Authors: Jorge Gonzalez Camus, Carlos Lizama

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In this work is proved the existence of at least one globally attractive mild solution to the Cauchy problem, for fractional evolution equation of neutral type, involving the fractional derivate in Caputo sense. An almost sectorial operator on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Hausdorff measure of noncompactness and fixed point theorems, specifically Darbo-type. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the analytic integral resolvent operator, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, each mild solution is globally attractive, a property that is desired in asymptotic behavior for that solution.

Keywords: attractive mild solutions, integral Volterra equations, neutral type equations, non-local in time equations

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Authors: Soumiya Bhattacharjee, P. K. Champati Ray, Shovan L. Chattoraj, Mrinmoy Dhara

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The entire Himalayan range is globally renowned for rainfall-induced landslides. The prime focus of the study is to determine rainfall based threshold for initiation of landslides that can be used as an important component of an early warning system for alerting stake holders. This research deals with temporal dimension of slope failures due to extreme rainfall events along the National Highway-58 from Karanprayag to Badrinath in the Garhwal Himalaya, India. Post processed 3-hourly rainfall intensity data and its corresponding duration from daily rainfall data available from Tropical Rainfall Measuring Mission (TRMM) were used as the prime source of rainfall data. Landslide event records from Border Road Organization (BRO) and some ancillary landslide inventory data for 2013 and 2014 have been used to determine Intensity Duration (ID) based rainfall threshold. The derived governing threshold equation, I= 4.738D^-0.025, has been considered for prediction of landslides of the study region. This equation was validated with an accuracy of 70% landslides during August and September 2014. The derived equation was considered for further prediction of landslides of the study region. From the obtained results and validation, it can be inferred that this equation can be used for initiation of landslides in the study area to work as a part of an early warning system. Results can significantly improve with ground based rainfall estimates and better database on landslide records. Thus, the study has demonstrated a very low cost method to get first-hand information on possibility of impending landslide in any region, thereby providing alert and better preparedness for landslide disaster mitigation.

Keywords: landslide, intensity-duration, rainfall threshold, TRMM, slope, inventory, early warning system

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Authors: Mohammad Mahmoud Mandurah

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The existence of InfoMiracles in scripture is evidence that the scripture has a divine origin. It is also evidence to the existence of God. An InfoMiracle is an information-based miracle. The basic component of an InfoMiracle is a piece of information that could not be obtained by a human except through a divine channel. The existence of a sufficient number of convincing InfoMiracles in a scripture necessitates the existence of the divine source to these InfoMiracles. A mathematical equation is developed to prove that the Qur’an has a divine origin, and hence, prove the existence of God. The equation depends on a single variable only, which is the number of InfoMiracles in the Qur’an. The Qur’an is rich with InfoMiracles. It is shown that the existence of less than 30 InfoMiracles in the Qur’an is sufficient proof to the existence of God and that the Qur’an is a revelation from God.

Keywords: InfoMiracle, God, mathematical proof, miracle, probability

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Authors: Massimiliano Nastri

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The study examines the façade systems according to the constitutive and typological characters, as well as the functional and applicative requirements such as the expressive, constructive, and interactive criteria towards the environmental, perceptive, and energy conditions. The envelope systems are understood as instruments of mediation, interchange, and dynamic interaction between environmental conditions. The façades are observed for the sustainable concept of eco-efficient envelopes, selective and multi-purpose filters, adaptable and adjustable according to the environmental performance.

Keywords: typologies of façades, environmental and energy sustainability, interaction and perceptive mediation, technical skins

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Authors: Pezhman Taghipour Birgani, Mehdi Shekarzadeh

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In this paper, the propagation of lamb waves in three-layer joints is investigated using global matrix method. Theoretical boundary value problem in three-layer adhesive joints with perfect bond and traction free boundary conditions on their outer surfaces is solved to find a combination of frequencies and modes with the lowest attenuation. The characteristic equation is derived by applying continuity and boundary conditions in three-layer joints using global matrix method. Attenuation and phase velocity dispersion curves are obtained with numerical solution of this equation by a computer code for a three-layer joint, including an aluminum repair patch bonded to the aircraft aluminum skin by a layer of viscoelastic epoxy adhesive. To validate the numerical solution results of the characteristic equation, wave structure curves are plotted for a special mode in two different frequencies in the adhesive joint. The purpose of present paper is to find a combination of frequencies and modes with minimum attenuation in high and low frequencies. These frequencies and modes are recognizable by transducers in inspections with Lamb waves because of low attenuation level.

Keywords: three-layer adhesive joints, viscoelastic, lamb waves, global matrix method

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Authors: Muhanad Al-Jubouri

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A local scour is the most important of the several scours impacting bridge performance and security. Even though scour is widespread in bridges, especially during flood seasons, the experimental tests could not be applied to many standard highway bridges. A computational fluid dynamics numerical model was used to solve the problem of calculating local scouring and deposition for non-cohesive silt and clear water conditions near single and double cylindrical piers with the effect of floating debris. When FLOW-3D software is employed with the Rang turbulence model, the Nilsson bed-load transfer equation and fine mesh size are considered. The numerical findings of single cylindrical piers correspond pretty well with the physical model's results. Furthermore, after parameter effectiveness investigates the range of outcomes based on predicted user inputs such as the bed-load equation, mesh cell size, and turbulence model, the final numerical predictions are compared to experimental data. When the findings are compared, the error rate for the deepest point of the scour is equivalent to 3.8% for the single pier example.

Keywords: local scouring, non-cohesive, clear water, computational fluid dynamics, turbulence model, bed-load equation, debris

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Authors: F. Maass, P. Martin, J. Olivares

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The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations.

Keywords: education, geogebra, ordinary differential equations, resonance

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Authors: Susana Marques

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Research on how store environment cues influence consumers’ store choice decision criteria, such as store operations, product quality, monetary price, store image and sales promotion, is sparse. Especially absent research on the simultaneous impact of multiple store environment cues. The authors propose a comprehensive store choice model that includes: three types of store environment cues as exogenous constructs; various store choice criteria as possible mediating constructs, and store patronage intentions as an endogenous construct. On the basis of testing with a sample of 561 customers of hypermarkets, the model is partially supported. This study used structural equation modelling to test the proposed model.

Keywords: store choice, store patronage, structural equation modelling, retailing

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Authors: Ali Safdari-Vaighani

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Pricing financial contracts on several underlying assets received more and more interest as a demand for complex derivatives. The option pricing under asset price involving jump diffusion processes leads to the partial integral differential equation (PIDEs), which is an extension of the Black-Scholes PDE with a new integral term. The aim of this paper is to show how basket option prices in the jump diffusion models, mainly on the Merton model, can be computed using RBF based approximation methods. For a test problem, the RBF-PU method is applied for numerical solution of partial integral differential equation arising from the two-asset European vanilla put options. The numerical result shows the accuracy and efficiency of the presented method.

Keywords: basket option, jump diffusion, ‎radial basis function, RBF-PUM

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Authors: B. Chetti, W. A. Crosby

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The work described in this paper is an investigation of the static and dynamic characteristics of two-lobe journal bearings taking into consideration the thermal effects. A thermo-hydrodynamic solution of a finite two-lobe journal bearing is performed by solving the generalized form Reynolds equation with the energy equation, taking into consideration viscosity variation across the film thickness. The static and dynamic characteristics were numerically obtained. The results are evaluated for different values of viscosity-temperature coefficient and Peclet number. The results show that considering the thermal effects in the solution of the two-lobe journal bearing has a marked on the study of its stability.

Keywords: two-lobe bearing, thermal effect, static, dynamic characteristics

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: A. Selmi

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Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.

Keywords: differential transformation method, functionally graded material, mode shape, natural frequency

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Authors: Yen-Hui Chen, Terry Walker

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As the world experiences an energy crisis, investing in sustainable energy resources is a pressing mission for many countries. Microalgae-derived biodiesel has attracted intensive attention as an important biofuel, and microalgae Chlorella protothecoides lipid is recognized as a renewable source for microalgae-derived biodiesel production. Supercritical carbon dioxide (SC-CO₂) is a promising green solvent that may potentially substitute the use of organic solvents for lipid extraction; however, the efficiency of SC-CO₂ extraction may be affected by many variables, including temperature, pressure and extraction time individually or in combination. In this study, response surface methodology (RSM) was used to optimize the process parameters, including temperature, pressure and extraction time, on C. protothecoides lipid yield by SC-CO₂ extraction. A second order polynomial model provided a good fit (R-square value of 0.94) for the C. protothecoides lipid yield. The linear and quadratic terms of temperature, pressure and extraction time—as well as the interaction between temperature and pressure—showed significant effects on lipid yield during extraction. The optimal lipid yield from the model was predicted as the temperature of 59 °C, the pressure of 350.7 bar and the extraction time 2.8 hours. Under these conditions, the experimental lipid yield (25%) was close to the predicted value. The principal fatty acid methyl esters (FAME) of C. protothecoides lipid-derived biodiesel were oleic acid methyl ester (60.1%), linoleic acid methyl ester (18.6%) and palmitic acid methyl ester (11.4%), which made up more than 90% of the total FAMEs. In summary, this study indicated that RSM was useful to characterize the optimization the SC-CO₂ extraction process of C. protothecoides lipid yield, and the second-order polynomial model could be used for predicting and describing the lipid yield very well. In addition, C. protothecoides lipid, extracted by SC-CO₂, was suggested as a potential candidate for microalgae-derived biodiesel production.

Keywords: Chlorella protothecoides, microalgal lipids, response surface methodology, supercritical carbon dioxide extraction

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Authors: R. Srinivas, K. V. Ramana

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This paper presents a novel method called VESTAL to label vertebrae and inter vertebral discs. Each vertebra has certain statistical features properties. To label vertebrae and discs, a new equation to model the path of spinal cord is derived using statistical properties of the spinal canal. VESTAL uses this equation for labeling vertebrae and discs. For each vertebrae and inter vertebral discs both posterior, interior width, height are measured. The calculated values are compared with real values which are measured using venires calipers and the comparison produced 95% efficiency and accurate results. The VESTAL is applied on 50 patients 350 MR images and obtained 100% accuracy in labeling.

Keywords: spine, vertebrae, inter vertebral disc, labeling, statistics, texture, disc

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Authors: Nilanjana Chanda, Rangeet Bhattacharyya

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Grover’s search algorithm is the fastest possible quantum mechanical algorithm to search a certain element from an unstructured set of data of N items. The algorithm can determine the desired result in only O(√N) steps. It has been demonstrated theoretically and experimentally on two-qubit systems long ago. In this work, we investigate the fidelity of Grover’s search algorithm by implementing it on an open quantum system. In particular, we study with what accuracy one can estimate that the algorithm would deliver the searched state. In reality, every system has some influence on its environment. We include the environmental effects on the system dynamics by using a recently reported fluctuation-regulated quantum master equation (FRQME). We consider that the environment experiences thermal fluctuations, which leave its signature in the second-order term of the master equation through its appearance as a regulator. The FRQME indicates that in addition to the regular relaxation due to system-environment coupling, the applied drive also causes dissipation in the system dynamics. As a result, the fidelity is found to depend on both the drive-induced dissipative terms and the relaxation terms, and we find that there exists a competition between them, leading to an optimum drive amplitude for which the fidelity becomes maximum. For efficient implementation of the search algorithm, precise knowledge of this optimum drive amplitude is essential.

Keywords: dissipation, fidelity, quantum master equation, relaxation, system-environment coupling

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Authors: Jean-Marie Vilaire, Ricardo Abreu-Blaya, Juan Bory-Reyes

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The classical Beltrami system of elliptic equations generalizes the Cauchy Riemann equation in the complex plane and offers the possibility to consider homogeneous system with no terms of zero order. The theory of Douglis-valued functions, called Hyper-analytic functions, is special case of the above situation. In this note, we prove an analogue of the N. Davydov theorem in the framework of the theory of hyperanalytic functions. The used methodology contemplates characteristic methods of the hypercomplex analysis as well as the singular integral operators and elliptic systems of the partial differential equations theories.

Keywords: Beltrami equation, Douglis algebra-valued function, Hypercomplex Cauchy type integral, Sokhotski-Plemelj formulae

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Authors: Muslim Malik, Avadhesh Kumar

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A stronger concept of exact controllability which is called Total Controllability is introduced in this manuscript. Sufficient conditions have been established for the total controllability of a control problem, governed by second order nonlinear differential equation with delay and non-instantaneous impulses in a Banach space X. The results are obtained using the strongly continuous cosine family and Banach fixed point theorem. Also, the total controllability of an integrodifferential problem is investigated. At the end, some numerical examples are provided to illustrate the analytical findings.

Keywords: Banach fixed point theorem, non-instantaneous impulses, strongly continuous cosine family, total controllability

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Authors: Jihye Jeon

Abstract:

This paper analyzes the conceptual framework of three statistical methods, multiple regression, path analysis, and structural equation models. When establishing research model of the statistical modeling of complex social phenomenon, it is important to know the strengths and limitations of three statistical models. This study explored the character, strength, and limitation of each modeling and suggested some strategies for accurate explaining or predicting the causal relationships among variables. Especially, on the studying of depression or mental health, the common mistakes of research modeling were discussed.

Keywords: multiple regression, path analysis, structural equation models, statistical modeling, social and psychological phenomenon

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Authors: Tokuei Sako

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Laser-induced current in a quasi-one-dimensional nanostructure has been studied by a model of a few electrons confined in a 1D electrostatic potential coupled to electrodes at both ends and subjected to a pulsed laser field. The time-propagation of the one- and two-electron wave packets has been calculated by integrating the time-dependent Schrödinger equation directly by the symplectic integrator method with uniform Fourier grid. The temporal behavior of the resultant light-induced current in the studied systems has been discussed with respect to the lifetime of the quasi-bound states formed when the static bias voltage is applied.

Keywords: pulsed laser field, nanowire, electron wave packet, quantum dots, time-dependent Schrödinger equation

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Authors: Debajyoti Choudhuri, Ratan Kumar Giri, Shesadev Pradhan

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The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed.

Keywords: p-Laplacian, p-biharmonic, elliptic PDEs, Concentration lemma, Sobolev space

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Authors: Ahmad Moussavi

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In this paper, we are concerned with the Jacobson semisimple skew inverse Laurent series rings R((x−1; α, δ)) and the skew Laurent power series rings R[[x, x−1; α]], where R is an associative ring equipped with an automorphism α and an α-derivation δ. Examples to illustrate and delimit the theory are provided.

Keywords: skew polynomial rings, Laurent series, skew inverse Laurent series rings

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Authors: H. M. Al-Qassem, L. Cheng, Y. Pan

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In this paper we establish sharp bounds for oscillatory singular integrals with an arbitrary real polynomial phase P. Our kernels are allowed to be rough both on the unit sphere and in the radial direction. We show that the bounds grow no faster than log(deg(P)), which is optimal and was first obtained by Parissis and Papadimitrakis for kernels without any radial roughness. Among key ingredients of our methods are an L¹→L² estimate and extrapolation.

Keywords: oscillatory singular integral, rough kernel, singular integral, Orlicz spaces, Block spaces, extrapolation, L^{p} boundedness

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Authors: Mohammad Ahmad, Dayalan Kasilingam

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In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

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Authors: Lidija R. Jevrić, Sanja O. Podunavac-Kuzmanović, Strahinja Z. Kovačević

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Quantitative structure-retention relationship (QSRR) analysis was used to predict the chromatographic behavior of s-triazine derivatives by using theoretical descriptors computed from the chemical structure. Fundamental basis of the reported investigation is to relate molecular topological descriptors with chromatographic behavior of s-triazine derivatives obtained by reversed-phase (RP) thin layer chromatography (TLC) on silica gel impregnated with paraffin oil and applied ethanol-water (φ = 0.5-0.8; v/v). Retention parameter (RM0) of 14 investigated s-triazine derivatives was used as dependent variable while simple connectivity index different orders were used as independent variables. The best QSRR model for predicting RM0 value was obtained with simple third order connectivity index (3χ) in the second-degree polynomial equation. Numerical values of the correlation coefficient (r=0.915), Fisher's value (F=28.34) and root mean square error (RMSE = 0.36) indicate that model is statistically significant. In order to test the predictive power of the QSRR model leave-one-out cross-validation technique has been applied. The parameters of the internal cross-validation analysis (r2CV=0.79, r2adj=0.81, PRESS=1.89) reflect the high predictive ability of the generated model and it confirms that can be used to predict RM0 value. Multivariate classification technique, hierarchical cluster analysis (HCA), has been applied in order to group molecules according to their molecular connectivity indices. HCA is a descriptive statistical method and it is the most frequently used for important area of data processing such is classification. The HCA performed on simple molecular connectivity indices obtained from the 2D structure of investigated s-triazine compounds resulted in two main clusters in which compounds molecules were grouped according to the number of atoms in the molecule. This is in agreement with the fact that these descriptors were calculated on the basis of the number of atoms in the molecule of the investigated s-triazine derivatives.

Keywords: s-triazines, QSRR, chemometrics, chromatography, molecular descriptors

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Authors: Ralpian Randolian

Abstract:

Eighty-five Romanian teachers and principals participated on this study to examine their perspectives of different leadership styles. Demographic variables such as the source of degree (Romania, Europe institutes, USA institutes, etc.), gender, region, level taught, years of experience, and specialty were identified. The researcher developed a questionnaire that consisted of 4 leadership styles. The data were analyzed using structural equation modeling (SEM) to identify which of the variables best predict the leadership styles. Results indicated that the democracy style was the most preferred leadership style by Jordanian parents, while the authoritarian styles ranked second. The results also found statistically significant differences were found related to the study variables. This study ends by putting forward a number of suggestions and recommendation.

Keywords: teachers’ perspectives, leadership styles, gender, structural equation modeling

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