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Numerical Experiments for Finding Roots of the Polynomials in Chebyshev Basis
Get PDFRoot finding for a function or a polynomial that is smooth on the interval [a; b], but otherwise arbitrary, is done by the following procedure. First, approximate it by a Chebyshev polynomial series. Second, find the zeros of the truncated Chebyshev series. Finding roots of the Chebyshev polynomial is done by eigenvalues of a nXn matrix such as companion or comrade matrices. There are some methods for finding eigenvalues of these matrices such as companion matrix and chasing procedures.We derive another algorithm by second kind of Chebyshev polynomials.We computed the numerical results of these methods for some special and ill-conditioned polynomials
Application of Kudryashov method for the Ito equations
Get PDFIn this present work, the Kudryashov method is used to construct exact solutions of the (1+1)- dimensional and the (1+2)-dimensional form of the generalized Ito integro-differential equation. The Kudryashov method is a powerful method for obtaining exact solutions of nonlinear evolution equations. This method can be applied to non-integrable equations as well as integrable ones
Mathematical modelling of Stoneley wave in a transversely isotropic thermoelastic media
Get PDFThis paper is concerned with the study of propagation of Stoneley waves at the interface of two dissimilar transversely isotropic thermoelastic solids without energy dissipation and with two temperatures. The secular equation of Stoneley waves is derived in the form of the determinant by using appropriate boundary conditions i.e. the stresses components, the displacement components, and temperature at the boundary surface between the two media are considered to be continuous at all times and positions . The dispersion curves giving the Stoneley wave velocity and Attenuation coefficients with wave number are computed numerically. Numerical simulated results are depicted graphically to show the effect of two temperature and anisotropy on resulting quantities. Copper material has been chosen for the medium and magnesium for the medium Some special cases are also deduced from the present investigation
On Circulant-Like Rhotrices over Finite Fields
Get PDFCirculant matrices over finite fields are widely used in cryptographic hash functions, Lattice based cryptographic functions and Advanced Encryption Standard (AES). Maximum distance separable codes over finite field GF2 have vital a role for error control in both digital communication and storage systems whereas maximum distance separable matrices over finite field GF2 are used in block ciphers due to their properties of diffusion. Rhotrices are represented in the form of coupled matrices. In the present paper, we discuss the circulant- like rhotrices and then construct the maximum distance separable rhotrices over finite fields
On the qualitative behaviors of a functional differential equation of second order
Get PDFThe aim of this paper is first to investigate the stability of the zero solution to a new Liénard type equation with multiple variable delays by two different methods. The methods to be used in the proofs involve the Lyapunov-Krasovskiĭ functional approach and the fixed point technique under an exponentially weighted metric, respectively. We make a comparison between the applications of these methods with the established conditions on the same stability problems. Then, we obtain three new results for uniformly stability and boundedness/ uniformly boundedness of the solutions to the considered equation by the Lyapunov-Krasovskiĭ functional approach. An example is given to verify the results obtained by the Lyapunov-Krasovskiĭ functional approach. Our results complement and improve some recent ones in the literature
Biotechnological induction of shikimate-based antioxidant accumulation in Phyla dulcis
No full textBackground: Medicinal phytochemicals have been used as dietary supplements in Asia and Africa for thousands of years. Biologically active antioxidants are very diverse and low in their chemical compositions thereby limiting their efficacies. The present study focuses on the enhanced accumulation of closely related dietary antioxidants: shikimate, quinate, salicylate and tocopherol in Phyla dulcis, the Central American herb known for its anti-inflammatory medicinal properties; but its polyphenolic antioxidants had not been studied. Methods: Phyla dulcis stem cuttings were planted in the greenhouse, and in field plots and treated with solutions of stoichiometric mixes of mineral salts known to double crop biomass and yield. Controls were treated with water. At maturity, P. dulcis shoots and flowers were harvested per treatment, immediately frozen in liquid nitrogen, and submitted to metabolomic analyses by gas chromatography-time-of-flight mass spectrometry. Results: Field plot P. dulcis treated with KKS-mineral salts combination induced increased shikimate accumulation of 1.59 g per 100 g from the 0.799 g per 100 g in the untreated control. Similarly salicylate, quinate, and tocopherols increased in accumulation by many orders of magnitude in the stoichiometric mixes of mineral salts-treated P. dulcis compared with the untreated controls. Conclusion: The accumulated polyphenolic antioxidants permitted the deduction of the unique biosynthetic pathway of the shikimate, with a massive inhibition at the enzyme steps of dehydroquinate dehydratase and shikimate dehydrogenase
Childhood emotional abuse, self/other attachment, and hopelessness in African-American women
No full textThere is evidence that individuals emotionally abused as children endorse more hopelessness, a precursor of suicidal behavior in adulthood. However, there has been little focus on this association among African-Americans or on factors that may mediate the childhood emotional abuse (CEA)–adult hopelessness link. The present study examined whether CEA is linked to hopelessness in adulthood in African-American women suicide attempters and if adult self and other attachment models mediate this association. Participants included 116 African-American women recruited from a large, urban hospital. Results revealed that CEA had no direct effect on hopelessness in adulthood, but did have an indirect effect on hopelessness through attachment models. Bootstrapping analyses showed that higher levels of CEA were related to more negative self and other attachment models, which were then linked to higher levels of hopelessness. Implications for targeting attachment in suicide intervention programs are discussed
Study on TiO2 nanoparticles distribution in electrospun polysulfone/TiO2 composite nanofiber
No full textComposite nanofibers composed of an organic polymer and inorganic nanomaterials have huge potential to be used in different industrial applications. However, the main concern on the use of composite nanofibers is the distribution properties of nanomaterials in the polymeric matrix. The effect of the capillary tip charge on the additive distribution in the electrospun nanofiber has been previously studied and can be found in the literature. In this study, the focus is placed on the investigation of TiO2 nanoparticles (TiO2 NPs) distribution in the Polysulfone (PSF) nanofiber. X-ray Photoelectron Spectroscopy (XPS) was conducted to measure the percentage of TiO2 on the surface of the prepared PSF/TiO2 composite nanofiber. The results showed that there was no TiO2 NPs on the surface of the nanofiber for up to 10 nm in depth. TiO2 nanoparticles were mainly found in the center of the nanofiber due to the accumulation of the hydrophobic PSF at the surface of the composite nanofiber. The findings of this work can provide better interpretation of the impact of the interfacial tension on the distribution of the inorganic nanomaterials in the electrospun nanofiber
Optimal Control of Investments in Old and New Capital Under Improving Technology
No full textAn optimal control problem for nonlinear integral equations of special kind is analyzed. It considers a firm’s investment into age-dependent capital under improving technology and limited substitutability among capital of different ages. We prove the existence of solutions and analyze their structure. It is shown that the initially bang-bang optimal investment switches to an interior one and eventually converges to a steady-state trajectory that represents balanced economic growth. The obtained analytic outcomes contribute to better understanding of investment policies under technological change