Abstract:
The coupling reaction of
aryl bromide and aryl boronic acid in water/DMF as solvent was studied using a
palladium-complex as a catalyst in the presence of ultrasound at room
temperature. The effect on the reaction of a base and a solvent was also
studied with and without ultrasound and was found to increase the speed of the
reaction. In this regard, we propose reaction mechanisms that could explain the
results obtained.

Abstract:
In this paper we tried to condense the determinant of n square matrix to the determinant of (n - 1) square matrix with the mathematical proof.

Abstract:
This article modifies the traditional functional leadership model to accommodate contemporary needs in healthcare leadership based on two findings. First, the article argues that it is important that the ideal healthcare leadership emphasizes the outcomes of the patient care more than processes and structures used to deliver such care; and secondly, that the leadership must strive to attain effectiveness of their care provision and not merely targeting the attractive option of efficient operations. Based on these premises, the paper reviews the traditional Functional Leadership Model and the three elements that define the type of leadership an organization has namely, the tasks, the individuals, and the team. The article argues that concentrating on any one of these elements is not ideal and proposes adding a new element to the model to construct a novel Functional Result-Oriented healthcare leadership model. The recommended Functional-Results Oriented leadership model embosses the results element on top of the other three elements so that every effort on healthcare leadership is directed towards attaining excellent patient outcomes.

Abstract:
We present a new model for the propagation of polarized light in a random birefringent medium. This model is based on a decomposition of the higher order statistics of the reduced Stokes parameters along the irreducible representations of the rotation group. We show how this model allows a detailed description of the propagation, giving analytical expressions for the probability densities of the Mueller matrix and the Stokes vector throughout the propagation. It also allows an exact description of the evolution of averaged quantities, such as the degree of polarization. We will also discuss how this model allows a generalization of the concepts of reduced Stokes parameters and degree of polarization to higher order statistics. We give some notes on how it can be extended to more general random media.

Abstract:
This paper deals with the Schr{\"o}dinger equation $i\partial_s u({\bf z},t;s)-\cal L u({\bf z}, t;s)=0,$ where $\cal L$ is the sub-Laplacian on the Heisenberg group. Assume that the initial data $f$ satisfies $| f({\bf z},t)| \leq C q_a({\bf z},t),$ where $q_s$ is the heat kernel associated to $\cal L.$ If in addition $ |u({\bf z},t;s_0)|\leq C q_b({\bf z},t),$ for some $s_0\in \R^*,$ then we prove that $u({\bf z},t;s)=0$ for all $s\in \R $ whenever $ab

Abstract:
In this paper we give a mathematical proof of Dodgson algorithm [1]. Recently Zeilberger [2] gave a bijective proof. Our techniques are based on determinant properties and they are obtained by induction.

Abstract:
We construct a two-parameter family of actions \omega_{k,a} of the Lie algebra sl(2,R) by differential-difference operators on R^N \setminus {0}. Here, k is a multiplicity-function for the Dunkl operators, and a>0 arises from the interpolation of the Weil representation of Mp(N,R) and the minimal unitary representation of O(N+1,2) keeping smaller symmetries. We prove that this action \omega_{k,a} lifts to a unitary representation of the universal covering of SL(2,R), and can even be extended to a holomorphic semigroup \Omega_{k,a}. In the k\equiv 0 case, our semigroup generalizes the Hermite semigroup studied by R. Howe (a=2) and the Laguerre semigroup by the second author with G. Mano (a=1). One boundary value of our semigroup \Omega_{k,a} provides us with (k,a)-generalized Fourier transforms F_{k,a}, which includes the Dunkl transform D_k (a=2) and a new unitary operator H_k (a=1), namely a Dunkl-Hankel transform. We establish the inversion formula, and a generalization of the Plancherel theorem, the Hecke identity, the Bochner identity, and a Heisenberg uncertainty inequality for F_{k,a}. We also find kernel functions for \Omega_{k,a} and F_{k,a} for a=1,2 in terms of Bessel functions and the Dunkl intertwining operator.

Abstract:
We introduce a family of differential-reflection operators $\Lambda_{A, \varepsilon}$ acting on smooth functions defined on $\mathbb R.$ Here $A$ is a Strum-Liouville function with additional hypotheses and $\varepsilon\in \mathbb R.$ For special pairs $(A,\varepsilon),$ we recover Dunkl's, Heckman's and Cherednik's operators (in one dimension). The spectral problem for the operators $\Lambda_{A, \varepsilon}$ is studied. In particular, we obtain suitable growth estimates for the eigenfunctions of $\Lambda_{A, \varepsilon}$. As the operators $\Lambda_{A, \varepsilon}$ are mixture of $d/dx$ and reflection operators, we prove the existence of an intertwining operator $V_{A,\varepsilon}$ between $\Lambda_{A, \varepsilon}$ and the usual derivative. The positivity of $V_{A,\varepsilon}$ is also established. Via the eigenfunctions of $\Lambda_{A,\varepsilon},$ we introduce a generalized Fourier transform $\mathcal F_{A,\varepsilon}.$ An $L^p$-harmonic analysis for $\mathcal F_{A,\varepsilon}$ is developed when $0

Abstract:
The metal loading is sometimes regarded as a means of curing the manufacturing defects or the damage of the cast parts. In this direction and taking into account the high percentage of carbon, the parts out of pig iron and cast iron with graphite spheroid constitutes a rather difficult case. The principal objective of this study is the influence of the parameters of the annealing of softening on the mechanical characteristics and structure transformations of the samples into nodular cast iron, subjected to an assembly by welding with the oxyacetylene torch.

Abstract:
Two-phase (water and air) flow in the forced-air mechanically-stirred Dorr-Oliver machine has been investigated using computational fluid dynamics (CFD). A 6 m 3 model is considered. The flow is modeled by the Euler-Euler approach, and transport equations are solved using software ANSYS-CFX5. Unsteady simulations are conducted in a 180-degree sector with periodic boundary conditions. Air is injected into the rotor at the rate of 2.63 m 3/min, and a uniform bubble diameter is specified. The effects of bubble diameter on velocity field and air volume fraction are determined by conducting simulations for three diameters of 0.5, 1.0, and 2.0 mm. Air volume fraction contours, velocity profiles, and turbulent kinetic energy profiles in different parts of the machine are presented and discussed. Results have been compared to experimental data, and good agreement is obtained for the mean velocity and turbulent kinetic energy profiles in the rotor-stator gap and in the jet region outside stator blades.