Existence and approximations of solutions to some fractional order functional integral equations

In this paper we shall study a fractional order functional integral equation. In the first part of the paper, we proved the existence and uniqueness of mile and global solutions in a Banach space. In the second part of the paper, we used the analytic semigroups theory oflinear operators and the fixed point method to establish the existence, uniqueness and convergence of approximate solutions of the given problem in a separable Hilbert space. We also proved the existence and convergence of Faedo-Galerkin approximate solution to the given problem. Finally, we give an example.

Synthesis, Structure, Spirocyclization Mechanism, and Glutathione Peroxidase-like Antioxidant Activity of Stable Spirodiazaselenurane and Spirodiazatellurane

The first examples of stable spirodiazaselenurane and spirodiazatellurane were synthesized by oxidative spirocyclization of the corresponding diaryl selenide and telluride and were structurally characterized. X-ray crystal structures of the spirodiazaselenurane and spirodiazatellurane suggest that the structures are distorted trigonal bipyramidal (TBP) with the electronegative nitrogen atoms occupying the apical positions and two carbon atoms and the lone pair of Se/Te occupying the equatorial positions. Interestingly, the spirodiazatellurane underwent spontaneous chiral resolution during crystallization, and the absolute configurations of its enantiomers were confirmed by single-crystal X-ray analyses. A detailed mechanistic study indicates that the cyclization to spirodiazaselenurane and spirodiazatellurane occurs via selenoxide and telluroxide intermediates. The chalcogenoxides cyclize to the corresponding spiro compounds in a stepwise manner via the involvement of hydroxyl chalcogenurane intermediates, and the activation energy for them spirocyclization reaction decreases in the order S > Se > Te. In addition to the synthesis, characterization, and mechanism of cyclization, the glutathione peroxidase (GPx) mimetic activity of the newly synthesized compounds was evaluated. These studies suggest that the tellurium compounds are more effective as GPx mimics than their selenium counterparts due to the fast oxidation of the tellurium center in the presence of peroxide and the involvement of an efficient redox cycle between the telluride and telluroxide intermediate.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

On the study of a third-order mechanical oscillator

In this paper, the study of a third-order mechanical oscillator is presented by demonstrating its equivalence to the well-known R.C. multivibrator with two additional reactive elements. The conditions for the oscillator's possession of periodic solutions are presented. It is also shown that under certain conditions, the study of the given third-order autonomous system can be reduced to the study of an equivalent second-order, non-autonomous system.

Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.

Future chemistry teachers use of knowledge dimensions and high-order cognitive skills in pre-laboratory concept maps

This poster describes a pilot case study, which aim is to study how future chemistry teachers use knowledge dimensions and high-order cognitive skills (HOCS) in their pre-laboratory concept maps to support chemistry laboratory work. The research data consisted of 168 pre-laboratory concept maps that 29 students constructed as a part of their chemistry laboratory studies. Concept maps were analyzed by using a theory based content analysis through Anderson & Krathwohls' learning taxonomy (2001). This study implicates that novice concept mapper students use all knowledge dimensions and applying, analyzing and evaluating HOCS to support the pre-laboratory work.

Word order and tonal shape in the production of focus in short Finnish utterances

This paper presents results from a study on the production of Finnish prosody. The effect of word order and the tonal shape in the production of Finnish prosody was studied as produced by 8 native Finnish speakers. Predictions formulated with regard to results from an earlier study pertaining to the perception of promi- nence were tested. These predictions had to do with the tonal shape of the utterances in the form of a flat hat pattern and the effect of word order on the so called top-line declination within an adver- bial phrase in the utterances. The results from the experiment give support to the following claims: the temporal domain of prosodic focus is the whole utterance, word order reversal from unmarked to marked has an effect on the production of prosody, and the pro- duction of the tonal aspects of focus in Finnish follows a basic flat hat pattern. That is the prominence of a word can be produced by an f 0 rise or a fall, depending on the location of the word in an utterance. The basic accentual shape of a Finnish word is then not a pointed rise/fall hat shape as claimed before since it can vary depending on the syllable structure and the position within an ut- terance.

Generation of Cationic Two-Coordinate Group-13 Ligand Systems by Spontaneous Halide Ejection: Remarkably Nucleophile-Resistant (Dimethylamino)borylene Complexes

Spontaneous ejection of chloride from a three-coordinate boron Lewis acid can be effected by employing very electron rich metal substituents and leads to the formation of a sterically unprotected terminal (dimethylamino)borylene complex that has a short metal-boron bond and remarkable resistance to attack by nucleophilic and protic reagents.

Organizing (with) Thirdness. A Dialogic Understanding of Bicultural Interactions in Organizations

This conceptual paper examines bicultural interactions in organizations as they are experienced by the involved individuals. Notions from Bakhtinian dialogism are used in order to conceptualize the sensemaking opportunities provided by the encounter with a cultural otherness. It is argued that in such bicultural situations, because of the lack of intimate understanding of the other culture, the third element in the dialogic relation - ‘thirdness’, i.e. the relation itself, without which there would be no sensemaking potential - may be lacking as a result of the distorting combination of projected similarity and stereotyping, added to certain counterproductive organizational dynamics. Therefore, it is suggested that, to make the bicultural work interaction the rewarding relation it could be, thirdness should be coordinated by management in a way that can transcend the spontaneous negative dynamics of the confrontational situation. If management was to fail to organize (with) thirdness appropriately, bringing in a third party could be a possible alternative in order to initiate the necessary mutual understanding that should eventually lead to a fruitful work interaction.

Design of first- and second-order sliding mode observers for induction motors using a stator-flux model

We extend current research in the area of 'sensorless' control of induction motors by presenting two observers based on first- and second-order sliding mode control theories for the simultaneous estimation of flux and speed. We base the observers on the stator-flux model of the motor instead of the usual rotor-flux model mainly because of the uncertain rotor resistance that plays a significant role in the latter. By designing the observers as if they are sliding mode controllers, we lend the properties of parameter insensitive closed-loop dynamics and finite time convergence to the stator flux and speed estimation schemes. We also present simulation and experimental results to validate the operation of the observers.

Charge-order driven multiferroic and magneto-dielectric properties of rare earth manganates

Charge-order driven magnetic ferroelectricity is shown to occur in several rare earth manganates of the general formula, Ln(1-x)A(x)MnO(3) (In = rare earth, A = alkaline earth). Charge-ordered manganates exhibit dielectric constant anomalies around the charge-ordering or the antiferromagnetic transition temperature. Magnetic fields have a marked effect on the dielectric properties of these compounds, indicating the presence of coupling between the magnetic and electrical order parameters. Magneto-dielectric properties are retained in small particles of the manganates. The observation of magneto-ferroelectricity in these manganates is in accordance with theoretical predictions.

Charge-order driven multiferroic and magneto-dielectric properties of rare earth manganates

Charge-order driven magnetic ferroelectricity is shown to occur in several rare earth manganates of the general formula, Ln(1-x)A(x)MnO(3) (In = rare earth, A = alkaline earth). Charge-ordered manganates exhibit dielectric constant anomalies around the charge-ordering or the antiferromagnetic transition temperature. Magnetic fields have a marked effect on the dielectric properties of these compounds, indicating the presence of coupling between the magnetic and electrical order parameters. Magneto-dielectric properties are retained in small particles of the manganates. The observation of magneto-ferroelectricity in these manganates is in accordance with theoretical predictions.