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.

In this paper reliable computational methods (RCMs) based on the monomial stan-dard polynomials have been executed to solve the problem of Jeffery-Hamel flow (JHF). In addition, convenient base functions, namely Bernoulli, Euler and Laguerre polynomials, have been used to enhance the reliability of the computational methods. Using such functions turns the problem into a set of solvable nonlinear algebraic system that MathematicaⓇ12 can solve. The JHF problem has been solved with the help of Improved Reliable Computational Methods (I-RCMs), and a review of the methods has been given. Also, published facts are used to make comparisons. As further evidence of the accuracy and dependability of the proposed methods, the maximum error remainder

Some researchers are interested in using the flexible and applicable properties of quadratic functions as activation functions for FNNs. We study the essential approximation rate of any Lebesgue-integrable monotone function by a neural network of quadratic activation functions. The simultaneous degree of essential approximation is also studied. Both estimates are proved to be within the second order of modulus of smoothness.

The electric quadrupole moments for some nitrogen isotopes (12,14,15,16,18N) are
studied by shell model calculations with the proton-neutron formalism. Theoretical
calculations performed using the different set of effective charges due to the core
polarization effect. The effective charges in the p-shell nuclei are found to be
slightly different from those in the sd-shell nuclei. Most of the results we have
obtained are underestimated with the measured data for the isotopes considered in
this work.

The research deals with the topic of (formal formation and its semantic projections in the design interior spaces of daily newspapers buildings) including the research problem summarized by the following question: (does the formal formation do a semantic role in the design of the interior spaces?). The research objective has been evident in discovering strong and weak points in the formal formations and their semantic projections in the design of the interior spaces for the daily newspapers buildings, reaching at the best design foundations, and shedding light on the cognitive and scientific importance of the research, and the objective, temporal and spatial limits in addition to identifying the terms. The theoretical framework includes

The leaves and stems of the local Purslane plant ( Portulaca oleracea oleracea L. ) were used to preapare the extract of two types ( wet and dried extractions) the extracts were prepared by weighting of 60grams of the wet and the dried plant individually, then boiled in 500ml of distal water. Finally the volume was completed to1 liter, then we used these extracts to prepare of 8 types of the culture media contained basic, selective and enrichment media for growing a group of pathogenic bacteria. 8 types of bacteria were used for this purpose: Escherichia coli, Pseudomonas flouresence, Staphylococcus aureus , Staphylococcus epidermidis, Bacillus subtilis , Klebsiella pneumoniae , Proteus mirabilis and Proteus vulgaris. The stastica

In this paper, we give new results and proofs that include the notion of norm attainment set of bounded linear operators on a smooth Banach spaces and using these results to characterize a bounded linear operators on smooth Banach spaces that preserve of approximate - -orthogonality. Noting that this work takes brief sidetrack in terms of approximate - -orthogonality relations characterizations of a smooth Banach spaces.