Reflective teaching, which has gained the status of an integral element of teacher pedagogy, is still an elusive concept, probably because it is merely attainable when teachers are provided with opportunities for building professional knowledge and for showing reflective teaching practices. The present study aimed at examining the English language teachers’ perception of their level of reflecti...

It is proved that, if F (x) be a cubic polynomial with integral coefficients having the property that F (n) is equal to a sum of two positive integral cubes for all sufficiently large integers n, then F (x) is identically the sum of two cubes of linear polynomials with integer coefficients that are positive for sufficiently large x. A similar result is proved in the case where F (n) is merely a...

The present paper deals with the mixed mode fracture analysis of a weakened orthotropic half-plane with multiple cracks propagation. The orthotropic half-plane contains Volterra type glide and climb edge dislocations. It is assumed that the medium is under in-plane loading conditions. The distributed dislocation technique is used to obtain integral equations for the dynamic problem of multiple ...

The concept of semicopula plays a fundamental role in the definition of a universal integral. We present an extension of semicopula to the case of symmetric interval [−1,1]. We call this extension bipolar semicopula. The last definition can be used to obtain a simplified definition of the bipolar universal integral. Moreover bipolar semicopulas allow for extension of theory of copulas to the in...

Sudoku graphs have only 5 or 6 distinct eigenvalues and all of them are integers. Moreover, the associated eigenspaces admit bases with entries from the set {0, 1,−1}.

In this paper, on 4-spheres equipped with Riemannian metrics we study some integral conformal invariants, the sign and size of which under Ricci flow characterize standard 4-sphere. We obtain a gap theorem, for Yamabe positive scalar curvature $L^2$ norm Weyl tensor metric suitably small, establish monotonic decay $L^p$ certain $p>2$ reduced along normalized flow, converging exponentially to

Quadrotor control has been noted for its trouble as the consequence of the high maneuverability, system nonlinearity and strongly coupled multivariable. This paper deals with the simulation depend on proposed controller of a quadrotor that can overcome this trouble. The mathematical model of quadrotor is determined using a Newton-Euler formulation. Fractional Order Proportional Integral Derivat...

We define a higher spin alternating sign matrix to be an integer-entry square matrix in which, for a nonnegative integer r, all complete row and column sums are r, and all partial row and column sums extending from each end of the row or column are nonnegative. Such matrices correspond to configurations of spin r/2 statistical mechanical vertex models with domain-wall boundary conditions. The c...

This paper concerns equilibrium problems in real metric linear spaces. Considering a modified notion of  upper sign property for bifunctions, we obtain the relationship between the solution sets of the local Minty equilibrium problem and the equilibrium problem, where the technical conditions on $f$ used in the literature are relaxed. The KKM technique is used to generalize and unify some exist...

This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...