Four-Step One Hybrid Block Methods for Solution of Fourth Derivative Ordinary Differential Equations

We consider developing a four-step one offgrid block hybrid method for the solution of fourth derivative Ordinary Differential Equations. Method of interpolation and collocation of power series approximate solution was used as the basis function to generate the continuous hybrid linear multistep method, which was then evaluated at non-interpolating points to give a continuous block method. The discrete block method was recovered when the continuous block was evaluated at all step points. The basic properties of the methods were investigated and said to be converge. The developed four-step method is applied to solve fourth derivative problems of ordinary differential equations from the numerical results obtained; it is observed that the developed method gives better approximation than the existing method compared with.

Metaphor in the Speech of Achilles (Iliad 9.308–429)

This article offers an analysis of the conceptual metaphors lodged within a continuous block of Homeric text, Achilles’s famous speech in Iliad 9. It argues for the productivity of applying Conceptual Metaphor Theory (CMT) to Homer, while also contributing to the debate concerning the diachronic roots of modern conventional metaphors. Topics considered include (1) Achilles’s extension, confirmation, and modification of the metaphors used elsewhere in the epics, (2) the different layers of metaphorical usage found in Homer, and (3) the hero’s questioning of one prevalent Homeric metaphor in his rejection of Agamemnon’s gifts as a motivation to fight.

Mastication Muscle Suppression by the Mandibular Branch of Trigeminal Nerve Catheter-Based, Ultrasound-Guided Block: A Case Report

Introduction: Ultrasound-guided nerve blocks have enhanced our abilities to selectively and effectively suppress certain nerves to accomplish specific goals, including blockade a localized seizure muscle movement without affecting the seizure threshold or level of the consciousness. Case Presentation: This is a case report of the blockade of the movement of a chewing muscle by the continuous (catheter-based) mandibular nerve block in a 27 years old man with high-frequency partial seizures in facial muscles who was a candidate for seizure focus ablation. An out-of-plane approach was used to insert a catheter near the mandibular nerve to provide intermittent or continuous peripheral nerve block. This report demonstrated that a continuous block of the mandibular nerve could effectively facilitate the seizure focus mapping and ablation. Conclusions: We can selectively suppress the contractures of a certain muscle in partial seizures by a continuous block of the responsible nerve. This blockade can facilitate seizure focus mapping and ablation.

An Efficient Seven-Step Block Method for Numerical Solution of SIR and Growth Model

In this article, a new implicit continuous block method is developed using the interpolation and collocation techniques via Power series as the basis function. A constant step length within a seven-step interval of integration was adopted. The selected grid points were evaluated to get a continuous linear multistep method. The evaluation of the continuous method at the non-interpolation points produces the discrete schemes which form the block. The basic properties of the block method were investigated and found to be consistent, zero stable and hence convergent. The new method was tested on real life problems namely: SIR and Growth model. The results were found to compare favourably with the existing methods in terms of accuracy and efficiency. Keywords: Block method, Growth Model, implicit, power series and SIR model.

Algebraic basis of the algebra of block-symmetric polynomials on $\ell_1 \oplus \ell_{\infty}$

We consider so called block-symmetric polynomials on sequence spaces $\ell_1\oplus \ell_{\infty}, \ell_1\oplus c, \ell_1\oplus c_0,$ that is, polynomials which are symmetric with respect to permutations of elements of the sequences. It is proved that every continuous block-symmetric polynomials on $\ell_1\oplus \ell_{\infty}$ can be uniquely represented as an algebraic combination of some special block-symmetric polynomials, which form an algebraic basis. It is interesting to note that the algebra of block-symmetric polynomials is infinite-generated while $\ell_{\infty}$ admits no symmetric polynomials. Algebraic bases of the algebras of block-symmetric polynomials on $\ell_1\oplus \ell_{\infty}$ and $\ell_1\oplus c_0$ are described.