In this paper, we introduce new definitions of the - spaces  namely the    - spaces  Here,  and  are natural numbers that are not necessarily equal, such that . The space  refers to the n-dimensional Euclidean space,  refers to the quaternions set and  refers to the N-dimensional quaternionic space. Furthermore, we establish and prove some properties of their elements. These elements are quaternion-valued N-vector functions defined on , and the  spaces  have never been introduced in this way before.

The rotational model symmetry is a strong feature of 1d shell nuclei, where symmetry breaking spin-orbital force is rather weak. The binding energies and low-lying energy spectra of Mg (A=20,22,28 and 30) even-even isotopes have been calculated. The interaction used contains the monopole-monopole, quadrupole-quadrupole and isospin dependent terms. Interaction parameters are fixed so as to reproduce the binding of 8 nucleons in N=8 orbit for Z=12 isotope.
 

Recently, the environmental isotopes are adopted to figure out the hydrological processes, recharge areas, flow paths, groundwater origin and the interaction between different watery bodies. Currently, five samples of the rainwater have been collected since January to April 2012, as well as December 2011. Those sampling periods have highest amounts of precipitation events. Meantime, 25 samples of groundwater, 5 of the Lesser Zab River and 3 of overland flow have been picked up during the wet period. The dry sampling of groundwater and the Lesser Zab River has been achieved in summer 2011. The Local Meteoric Water Line lies between Global Meteoric Water Line (GMWL) and East Mediterranean Water Line (EMWL). The lowest, highest and

The proton momentum distributions (PMD) and the elastic
electron scattering form factors F(q) of the ground state for some
even mass nuclei in the 2p-1f shell for 70Ge, 72Ge, 74Ge and 76Ge are
calculated by using the Coherent Density Fluctuation Model (CDFM)
and expressed in terms of the fluctuation function (weight function)
|F(x)|2. The fluctuation function has been related to the charge
density distribution (CDD) of the nuclei and determined from the
theory and experiment. The property of the long-tail behavior at high
momentum region of the proton momentum distribution has been
obtained by both the theoretical and experimental fluctuation
functions. The calculated form factors F (q) of all nuclei under s

The inelastic C2 form factors and the charge density distribution (CDD) for ^58,60,62Ni and ^64,66,68Zn nuclei has been investigated by employing the Skyrme-Hartree-Fock method with (Sk35-Skzs*) parametrization. The inelastic C2 form factor is calculated by using the shape of Tassie and Bohr-Mottelson models with appropriate proton and neutron effective charges to account for the core-polarization effects contribution. The comparison of the predicted theoretical values was conducted with the available measured data for C2 and CDD form factors and showed very good agreement.

In this paper, we made comparison among different parametric ,nonparametric and semiparametric estimators for partial linear regression model users parametric represented by ols and nonparametric methods represented by cubic smoothing spline estimator and Nadaraya-Watson estimator, we study three nonparametric regression models and samples sizes  n=40,60,100,variances used σ²=0.5,1,1.5 the results  for the first model show that N.W estimator for partial linear regression model(PLM) is the best followed the cubic smoothing spline estimator for (PLM),and the results of the second and the third model show that the best estimator is C.S.S.followed by N.W estimator for (PLM) ,the

PC-based controller is an approach to control systems with Real-Time parameters by controlling selected manipulating variable to accomplish the objectives. Shell and tube heat exchanger have been identified as process models that are inherently nonlinear and hard to control due to unavailability of the exact models’ descriptions. PC and analogue input output card will be used as the controller that controls the heat exchanger hot stream to the desired temperature.
The control methodology by using four speed pump as manipulating variable to control the temperature of the hot stream to cool to the desired temperature.
In this work, the dynamics of cross flow shell and tube heat exchanger is modeled from step changes in cold water f