Search results for: symbolic order

Authors: Kittipong Tripetch

Abstract:

This paper proposes studies of input impedance of two types of the CMOS active inductor. It derives two input impedance formulas. The first formula is the input impedance of a grounded active inductor. The second formula is an input impedance of floating active inductor. After that, these formulas can be used to simulate magnitude and phase response of input impedance as a function of current consumption with MATLAB. Common mode rejection ratio (CMRR) of a fully differential bandpass amplifier is derived based on superposition principle. CMRR as a function of input frequency is plotted as a function of current consumption

Keywords: grounded active inductor, floating active inductor, fully differential bandpass amplifier

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Authors: E. Olmos-Raya, A. Cascales Martínez, N. Minto de Sousa, M. Alcañiz Raya

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The late detection and subjectivity of the assessment of Autism Spectrum Disorder (ASD) imposed a difficulty for the children’s clinical and familiar environment. The results showed in this paper, are part of a research project about the assessment and training of social skills in children with ASD, whose overall goal is the use of virtual environments together with physiological measures in order to find a new model of objective ASD assessment based on implicit brain processes measures. In particular, this work tries to contribute by studying the differences and changes in the Skin Conductance Response (SCR) and Eye Tracking (ET) between a typical development group (TD group) and an ASD group (ASD group) after several combined stimuli using a low cost Immersive Virtual Environment (IVE). Subjects were exposed to a virtual environment that showed natural scenes that stimulated visual, auditory and olfactory perceptual system. By exposing them to the IVE, subjects showed natural behaviors while measuring SCR and ET. This study compared measures of subjects diagnosed with ASD (N = 18) with a control group of subjects with typical development (N=10) when exposed to three different conditions: only visual (V), visual and auditory (VA) and visual, auditory and olfactory (VAO) stimulation. Correlations between SCR and ET measures were also correlated with the Autism Diagnostic Observation Schedule (ADOS) test. SCR measures showed significant differences among the experimental condition between groups. The ASD group presented higher level of SCR while we did not find significant differences between groups regarding DF. We found high significant correlations among all the experimental conditions in SCR measures and the subscale of ADOS test of imagination and symbolic thinking. Regarding the correlation between ET measures and ADOS test, the results showed significant relationship between VA condition and communication scores.

Keywords: autism, electrodermal activity, eye tracking, immersive virtual environment, virtual reality

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Authors: Elhadj Bounadja, Mohand Oulhadj Mahmoudi, Abdelkader Djahbar, Zinelaabidine Boudjema

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In this paper we present a novel fuzzy second-order sliding mode control (FSOSMC) for wind energy conversion system based on a doubly-fed induction generator (DFIG). The proposed control strategy combines a fuzzy logic and a second-order sliding mode for the DFIG control. This strategy presents attractive features such as chattering-free, compared to the conventional first and second order sliding mode techniques. The use of this method provides very satisfactory performance for the DFIG control. The overall strategy has been validated on a 1.5-MW wind turbine driven a DFIG using the Matlab/Simulink.

Keywords: doubly fed induction generator, fuzzy second-order sliding mode controller, wind energy

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Authors: Ramandeep Behl, S. S. Motsa

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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: Pardeep Singh, Kamlesh Dutta

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Many languages have fixed sentence structure and others are free word order. The accuracy of anaphora resolution of syntax based algorithm depends on structure of the sentence. So, it is important to analyze the structure of any language before implementing these algorithms. In this study, we analyzed the sentence structure exploiting the case marker in Hindi as well as some special tag for subject and object. We also investigated the word order for Hindi. Word order typology refers to the study of the order of the syntactic constituents of a language. We analyzed 165 news items of Ranchi Express from EMILEE corpus of plain text. It consisted of 1745 sentences. Eight file of dialogue based from the same corpus has been analyzed which will have 1521 sentences. The percentages of subject object verb structure (SOV) and object subject verb (OSV) are 66.90 and 33.10, respectively.

Keywords: anaphora resolution, free word order languages, SOV, OSV

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Authors: Eric Sanchis

Abstract:

Although there does not exist a definitive consensus on a precise definition of a complex system, it is generally considered that a system is complex by nature. The presented work illustrates a different point of view: a system becomes complex only with regard to the question posed to it, i.e., with regard to the problem which has to be solved. A complex system is a couple (question, object). Because the number of questions posed to a given object can be potentially substantial, complexity does not present a uniform face. Two types of complex systems are clearly identified: first-order complex systems and second-order complex systems. First-order complex systems physically exist. They are well-known because they have been studied by the scientific community for a long time. In second-order complex systems, complexity results from the system composition and its articulation that are partially unknown. For some of these systems, there is no evidence of their existence. Vagueness is the keyword characterizing this kind of systems. Autonomy and free will, two mental productions of the human cognitive system, can be identified as second-order complex systems. A classification based on the properties structure makes it possible to discriminate complex properties from the others and to model this kind of second order complex systems. The final outcome is an implementable synthetic property that distinguishes the solid aspects of the actual property from those that are uncertain.

Keywords: autonomy, free will, synthetic property, vaporous complex systems

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

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Authors: Henri Champliaud, Zhengkun Feng, Ngan Van Lê, Javad Gholipour

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In this article, a method is presented to effectively estimate the deformed shape of a thick plate due to line heating. The method uses a fifth order spline interpolation, with up to C3 continuity at specific points to compute the shape of the deformed geometry. First and second order derivatives over a surface are the resulting parameters of a given heating line on a plate. These parameters are determined through experiments and/or finite element simulations. Very accurate kriging models are fitted to real or virtual surfaces to build-up a database of maps. Maps of first and second order derivatives are then applied on numerical plate models to evaluate their evolving shapes through a sequence of heating lines. Adding an optimization process to this approach would allow determining the trajectories of heating lines needed to shape complex geometries, such as Francis turbine blades.

Keywords: deformation, kriging, fifth order spline interpolation, first, second and third order derivatives, C3 continuity, line heating, plate forming, thermal forming

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Authors: A. M. Sagir

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This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

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Authors: Mahdi Shamsi, Tohid Yousefi Rezaii, Siavash Eftekharifar

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Compressed sensing (CS) is a new powerful mathematical theory concentrating on sparse signals which is widely used in signal processing. The main idea is to sense sparse signals by far fewer measurements than the Nyquist sampling rate, but the reconstruction process becomes nonlinear and more complicated. Common dilemma in sparse signal recovery in CS is the lack of knowledge about sparsity order of the signal, which can be viewed as model order selection procedure. In this paper, we address the problem of sparsity order estimation in sparse signal recovery. This is of main interest in situations where the signal sparsity is unknown or the signal to be recovered is approximately sparse. It is shown that the proposed method also leads to some kind of signal denoising, where the observations are contaminated with noise. Finally, the performance of the proposed approach is evaluated in different scenarios and compared to an existing method, which shows the effectiveness of the proposed method in terms of order selection as well as denoising.

Keywords: compressed sensing, data denoising, model order selection, sparse representation

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Authors: Mohamed Suleiman, Zarina Bibi Ibrahim, Nor Ain Azeany, Khairil Iskandar Othman

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In this paper, a class of variable order fully implicit multistep Block Backward Differentiation Formulas (VOBBDF) using uniform step size for the numerical solution of stiff ordinary differential equations (ODEs) is developed. The code will combine three multistep block methods of order four, five and six. The order selection is based on approximation of the local errors with specific tolerance. These methods are constructed to produce two approximate solutions simultaneously at each iteration in order to further increase the efficiency. The proposed VOBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with single order Block Backward Differentiation Formula (BBDF). Numerical results shows the advantage of using VOBBDF for solving ODEs.

Keywords: block backward differentiation formulas, uniform step size, ordinary differential equations

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Authors: Parshanth Maroju, Ramandeep Behl, Sandile S. Motsa

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In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect.

Keywords: basins of attraction, nonlinear equations, simple roots, Newton's method

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Authors: Thomas Ousterhout

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The purpose of this study was to investigate if incorporating meaningful pictures of gestures and facial expressions in short sentences of text could supplement the text with enough semantic information to produce and N400 effect when probe words incongruent to the picture were subsequently presented. Event-related potentials (ERPs) were recorded from a 14-channel commercial grade EEG headset while subjects performed congruent/incongruent reaction time discrimination tasks. Since pictures of meaningful gestures have been shown to be semantically processed in the brain in a similar manner as words are, it is believed that pictures will add supplementary information to text just as the inclusion of their equivalent synonymous word would. The hypothesis is that when subjects read the text/picture mixed sentences, they will process the images and words just like in face-to-face communication and therefore probe words incongruent to the image will produce an N400.

Keywords: EEG, ERP, N400, semantics, congruency, facilitation, Emotiv

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Authors: Sandeep Singh

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In this article, two classes of iterative schemes are proposed for approximating solutions of nonlinear systems of equations whose orders of convergence are six and eight respectively. Sixth order scheme requires the evaluation of two vector-functions, two first Fr'echet derivatives and three matrices inversion per iteration. This three-step sixth-order method is further extended to eighth-order method which requires one more step and the evaluation of one extra vector-function. Moreover, computational efficiency is compared with some other recently published methods in which we found, our methods are more efficient than existing numerical methods for higher and medium size nonlinear system of equations. Numerical tests are performed to validate the proposed schemes.

Keywords: Nonlinear systems, Computational complexity, order of convergence, Jarratt-type scheme

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Authors: B. S. Harish, M. B. Revanasiddappa

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Due to rapid growth of text documents in digital form, automated text classification has become an important research in the last two decades. The major challenge of text document representations are high dimension, sparsity, volume and semantics. Since the terms are only features that can be found in documents, selection of good terms (features) plays an very important role. In text classification, feature selection is a strategy that can be used to improve classification effectiveness, computational efficiency and accuracy. In this paper, we present a quantitative analysis of most widely used feature selection (FS) methods, viz. Term Frequency-Inverse Document Frequency (tf
idf ), Mutual Information (MI), Information Gain (IG), CHISquare (x2), Term Frequency-Relevance Frequency (tf
rf ), Term Strength (TS), Ambiguity Measure (AM) and Symbolic Feature Selection (SFS) to classify text documents. We evaluated all the feature selection methods on standard datasets like 20 Newsgroups, 4 University dataset and Reuters-21578.

Keywords: classifiers, feature selection, text classification

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Authors: Gubhinder Kundhi, Paul Rilstone

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Refined procedures for higher-order asymptotic theory for non-linear models are developed. These include a new method for deriving stochastic expansions of arbitrary order, new methods for evaluating the moments of polynomials of sample averages, a new method for deriving the approximate moments of the stochastic expansions; an application of these techniques to gather improved inferences with the weak instruments problem is considered. It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. In our application, finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap.

Keywords: edgeworth expansions, higher order asymptotics, saddlepoint expansions, weak instruments

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Authors: Ying Yi Wu

Abstract:

The study of finite groups is a central topic in algebraic structures, and one of the most fundamental questions in this field is the classification of finite groups up to isomorphism. In this paper, we investigate the cyclic property of groups of prime order, which is a crucial result in the classification of finite abelian groups. We prove the following statement: If p is a prime, then every group G of order p is cyclic. Our proof utilizes the properties of group actions and the class equation, which provide a powerful tool for studying the structure of finite groups. In particular, we first show that any non-identity element of G generates a cyclic subgroup of G. Then, we establish the existence of an element of order p, which implies that G is generated by a single element. Finally, we demonstrate that any two generators of G are conjugate, which shows that G is a cyclic group. Our result has significant implications in the classification of finite groups, as it implies that any group of prime order is isomorphic to the cyclic group of the same order. Moreover, it provides a useful tool for understanding the structure of more complicated finite groups, as any finite abelian group can be decomposed into a direct product of cyclic groups. Our proof technique can also be extended to other areas of group theory, such as the classification of finite p-groups, where p is a prime. Therefore, our work has implications beyond the specific result we prove and can contribute to further research in algebraic structures.

Keywords: group theory, finite groups, cyclic groups, prime order, classification.

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Authors: Moh'd Alodat

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In this paper, we discuss the power function distribution and derive the maximum likelihood estimator of its parameter as well as the reliability parameter. We derive the large sample properties of the estimators based on the selective order statistic scheme. We conduct simulation studies to investigate the significance of the selective order statistic scheme in our setup and to compare the efficiency of the new proposed estimators.

Keywords: fisher information, maximum likelihood estimator, power function distribution, ranked set sampling, selective order statistics sampling

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Authors: Ellis D. Cooper

Abstract:

“Circularchy” is supposed to be an adjustable formal framework with enough expressive power to articulate biological theory about Earthly Life in the sense of multi-scale biological autonomy constrained by non-equilibrium thermodynamics. “Formal framework” means specifically a multi-sorted first-order-theorywithequality (for each sort). Philosophically, such a theory is one kind of “microlect,” which means a “way of speaking” (or, more generally, a “way of behaving”) for overtly expressing a “mental model” of some “referent.” Other kinds of microlect include “natural microlect,” “diagrammatic microlect,” and “behavioral microlect,” with examples such as “political theory,” “Euclidean geometry,” and “dance choreography,” respectively. These are all describable in terms of a vocabulary conforming to grammar. As aspects of human culture, they are possibly reminiscent of Ernst Cassirer’s idea of “symbolic form;” as vocabularies, they are akin to Richard Rorty’s idea of “final vocabulary” for expressing a mental model of one’s life. A formal microlect is presented by stipulating sorts, variables, calculations, predicates, and postulates. Calculations (a.k.a., “terms”) may be composed to form more complicated calculations; predicates (a.k.a., “relations”) may be logically combined to form more complicated predicates; and statements (a.k.a., “sentences”) are grammatically correct expressions which are true or false. Conclusions are statements derived using logical rules of deduction from postulates, other assumed statements, or previously derived conclusions. A circularchy is a formal microlect constituted by two or more sub-microlects, each with its distinct stipulations of sorts, variables, calculations, predicates, and postulates. Within a sub-microlect some postulates or conclusions are equations which are statements that declare equality of specified calculations. An equational bond between an equation in one sub-microlect and an equation in either the same sub-microlect or in another sub-microlect is a predicate that declares equality of symbols occurring in a side of one equation with symbols occurring in a side of the other equation. Briefly, a circularchy is a network of equational bonds between sub-microlects. A circularchy is solvable if there exist solutions for all equations that satisfy all equational bonds. If a circularchy is not solvable, then a challenge would be to discover the obstruction to solvability and then conjecture what adjustments might remove the obstruction. Adjustment means changes in stipulated ingredients (sorts, etc.) of sub-microlects, or changes in equational bonds between sub-microlects, or introduction of new sub-microlects and new equational bonds. A circularchy is modular insofar as each sub-microlect is a node in a network of equation bonds. Solvability of a circularchy may be conjectured. Efforts to prove solvability may be thwarted by a counter-example or may lead to the construction of a solution. An automated theorem-proof assistant would likely be necessary for investigating a substantial circularchy, such as one purported to represent Earthly Life. Such investigations (chains of statements) would be concurrent with and no substitute for simulations (chains of numbers).

Keywords: autonomy, first-order theory, mathematics, thermodynamics

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

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This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: interpolation, approximate solution, collocation, differential system, half step, converges, block method, efficiency

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Authors: Samia Ait Ali Yahia

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Rock paintings and engravings in the Kabylia region of Algeria have been extensively studied, with 54 sites identified. These artworks were primarily discovered by Poyto and Musso in the mid-1960s. The paintings are predominantly adorned with red ochre ornaments, while some engravings can also be found on sandstone rocks. These artistic expressions can be found in various locations, such as shelters, rocks, and sandstone blocks in the northern part of Kabylia. These sites showcase a diverse range of decorations, including human figures, animal silhouettes, enigmatic designs, symbolic drawings, engravings, and Libyan characters. The research will involve conducting fieldwork at the Azru Imeyazen site to identify and study the different paintings and engravings present. This research aims to provide a detailed description of the rock paintings and engravings found in Kabylia, specifically focusing on the Azru Imeyazen (Tarihant) site.

Keywords: rock paintings, engraving, Kabylia, Tarihant, Azru Imayazen

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Authors: Salisu Ibrahim

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The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of MATLAB (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, analog control

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Authors: Salisu Ibrahim

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The paper studies the commutativity associated with fractional order linear time-varying systems (LTVSs), which is an important area of study in control systems engineering. In this paper, we explore the properties of these systems and their ability to commute. We proposed the necessary and sufficient condition for commutativity for fractional order LTVSs. Through a simulation and mathematical analysis, we demonstrate that these systems exhibit commutativity under certain conditions. Our findings have implications for the design and control of fractional order systems in practical applications, science, and engineering. An example is given to show the effectiveness of the proposed method which is been computed by Mathematica and validated by the use of Matlab (Simulink).

Keywords: fractional differential equation, physical systems, equivalent circuit, and analog control

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Authors: Huei Chu Weng

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This paper presents a study on the effect of second-order slip on forced convection through a long isoflux heated or cooled planar microchannel. The fully developed solutions of flow and thermal fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and local heat flux boundary conditions. Results reveal that when the average flow velocity increases or the wall heat flux amount decreases, the role of thermal creep becomes more insignificant, while the effect of second-order slip becomes larger. The second-order term in the Deissler slip boundary condition is found to contribute a positive velocity slip and then to lead to a lower pressure drop as well as a lower temperature rise for the heated-wall case or to a higher temperature rise for the cooled-wall case. These findings are contrary to predictions made by the Karniadakis slip model.

Keywords: microfluidics, forced convection, thermal creep, second-order boundary conditions

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Suhrita Saha

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Barbie is a fashion doll manufactured by the American toy company Mattel Inc and it made debut at the American International Toy Fair in New York in 9 March 1959. From being a fashion doll to a symbol of fetishistic commodification, Barbie has come a long way. A Barbie doll is sold every three seconds across the world, which makes the billion dollar brand the world’s most popular doll for the girls. The 11.5 inch moulded plastic doll has a height of 5 feet 9 inches at 1/6 scale. Her vital statistics have been estimated at 36 inches (chest), 18 inches (waist) and 33 inches (hips). Her weight is permanently set at 110 pounds which would be 35 pounds underweight. Ruth Handler, the creator of Barbie wanted a doll that represented adulthood and allowed children to imagine themselves as teenagers or adults. While Barbie might have been intended to be independent, imaginative and innovative, the physical uniqueness does not confine the doll to the status of a play thing. It is a cultural icon but with far reaching critical implications. The doll is a commodity bearing more social value than practical use value. The way Barbie is produced represents industrialization and commodification of the process of symbolic production. And this symbolic production and consumption is a standardized planned one that produce stereotypical ‘pseudo-individuality’ and suppresses cultural alternatives. Children are being subject to and also arise as subjects in this consumer context. A very gendered, physiologically dissected sexually charged symbolism is imposed upon children (both male and female), childhood, their social worlds, identity, and relationship formation. Barbie is also very popular among Indian children. While the doll is essentially an imaginative representation of the West, it is internalized by the Indian sensibilities. Through observation and questionnaire-based interview within a sample population of adolescent children (primarily female, a few male) and parents (primarily mothers) in Kolkata, an Indian metropolis, the paper puts forth findings of sociological relevance. 1. Barbie creates, recreates, and accentuates already existing divides between the binaries like male- female, fat- thin, sexy- nonsexy, beauty- brain and more. 2. The Indian girl child in her associative process with Barbie wants to be like her and commodifies her own self. The male child also readily accepts this standardized commodification. Definition of beauty is thus based on prejudice and stereotype. 3. Not being able to become Barbie creates health issues both psychological and physiological varying from anorexia to obesity as well as personality disorder. 4. From being a plaything Barbie becomes the game maker. Barbie along with many other forms of simulation further creates a consumer culture and market for all kind of fitness related hyper enchantment and subsequent disillusionment. The construct becomes the reality and the real gets lost in the play world. The paper would thus argue that Barbie from being an innocuous doll transports itself into becoming social construct with long term and irreversible adverse impact.

Keywords: barbie, commodification, personality disorder, sterotype

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Authors: Zhanar Imanova

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Masses of real celestial bodies change anisotropically and reactive forces appear, and they need to be taken into account in the study of these bodies' dynamics. We studied the two-planet problem of three bodies with variable masses in the presence of reactive forces and obtained the equations of perturbed motion in Newton’s form equations. The motion equations in the orbital coordinate system, unlike the Lagrange equation, are convenient for taking into account the reactive forces. The perturbing force is expanded in terms of osculating elements. The expansion of perturbing functions is a time-consuming analytical calculation and results in very cumber some analytical expressions. In the considered problem, we obtained expansions of perturbing functions by small parameters up to and including the second degree. In the non resonant case, we obtained evolution equations in the Newton equation form. All symbolic calculations were done in Wolfram Mathematica.

Keywords: two-planet, three-body problem, variable mass, evolutionary equations

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Authors: Suheyla Saritas

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No matter who we are or where we live, our lives revolve around food, which is much more than a merely sustenance. As a part of the human culture, food carries complex significance and symbolic meanings. Turkish people attribute great value to food and its usage specifically tied to rites of passages of human life. Traditions, especially the ones practiced during rites of passages, such as birth, circumcisions, weddings and funerals, have always been accompanied by food in Turkish culture. Since food celebrates and symbolizes human progress in life in the culture, it also surrounds by aspects of belief, custom, magic, ritual and religion and has always been used in ceremonial context during such rites. Even though that context may be different depending on the religious, economic and social nuances of the various Turkish regions, like wheat, meat and bread, certain kinds of food play key roles during Turkish rites, generally upholding traditions. This paper highlights the sociocultural aspect of food in the rites of passages in the Turkish culture. The importance of this work also is how the ceremonial food represents the identity of Turkish people.

Keywords: food, culture, rites of passages, ritual and identity

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Authors: Guy Joseph Eyebe, Gambo Betchewe, Alidou Mohamadou, Timoleon Crepin Kofane

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In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that appearance of chaos in the system depends strongly on the fractional order parameter.

Keywords: chaos, fractional-order, Melnikov method, nanobeam

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Authors: Brando Vagenende, Marie-Anne Guerry

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For stochastic matrices of any order, the geometric description of the convex set of eigenvalues is completely known. The purpose of this study is to investigate the subset of the monotone matrices. This type of matrix appears in contexts such as intergenerational occupational mobility, equal-input modeling, and credit ratings-based systems. Monotone matrices are stochastic matrices in which each row stochastically dominates the previous row. The monotonicity property of a stochastic matrix can be expressed by a nonnegative lower-order matrix with the same eigenvalues as the original monotone matrix (except for the eigenvalue 1). Specifically, the aim of this research is to focus on the properties of eigenvalues of monotone matrices. For those matrices up to order 3, there already exists a complete description of the convex set of eigenvalues. For monotone matrices of order at least 4, this study gives, through simulations, more insight into the geometric description of their eigenvalues. Furthermore, this research treats in a geometric and algebraic way the properties of eigenvalues of monotone matrices of order at least 4.

Keywords: eigenvalues of matrices, finite Markov chains, monotone matrices, nonnegative matrices, stochastic matrices

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