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Advances in Pure Mathematics (APM) is an openly accessible journal published monthly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of ordered algebraic structures. All the manus…
Lili Song, Wei Chen, Zhenhui Xu, Hanlin Chen
In the paper, the homoclinic (hateroclinic) breather limit method (HBLM) is applied to seek rogue wave solution of the Benjamin Ono equation. We find that the rational breather wave solution is just a rogue wave solution. This result shows that rogue wave can…
Ramalingam Arul, Manvel Angayarkanni
In this paper, we study the oscillatory and asymptotic behavior of second order neutral delay difference equation with “maxima” of the form Examples are given to illustrate the main result.
Fengying Zhou, Xiaoyong Xu
This paper investigates the structure of general affine subspaces of <i>L</i><sup>2</sup>(R<i><sup>d</sup></i>) . For a d × d expansive matrix A , it shows that every affine subspace can be decomposed as an orthogonal sum of spaces each of which is generated…
Wolfgang Mueckenheim
It is widely held that irrational numbers can be represented by infinite digit-sequences. We will show that this is not possible. A digit sequence is only an abbreviated notation for an infinite sequence of rational partial sums. As limits of sequences, irrat…
Lixia Cao, Huijun Zheng
In this paper, we present and study a kind of Riemann boundary value problem of non-normal type for analytic functions on two parallel curves. Making use of the method of complex functions, we give the method for solving this kind of doubly periodic Riemann b…
Hatice Kusak Samanci, Ali Caliskan
This paper presents building one-parameter motion by complex numbers on a time scale. Firstly, we assumed that E and E ′ were moving in a fixed time scale complex plane and {0, e 1 ,e 2 } and {0', e' 1 ,e' 2 } were their orthonormal frames, respectively. By u…
Rex L. Agacy
The study of the confluences of the roots of a given set of polynomials—root-pattern problem— does not appear to have been considered. We examine the situation, which leads us on to Young tableaux and tableaux representations. This in turn is found to be an a…
Yongshun Liang
Fractional integral of continuous functions has been discussed in the present paper. If the order of Riemann-Liouville fractional integral is v, fractal dimension of Riemann-Liouville fractional integral of any continuous functions on a closed interval is no…
Ashish Pathak, Prabhat Yadav, Madan Mohan Dixit
In the present paper, we obtain asymptotic expansion of the wavelet transform for large value of dilation parameter a by using López technique. Asymptotic expansion of Shannon wavelet, Morlet wavelet and Mexican Hat wavelet transform are obtained as special c…
Antonio Granata
After studying finite asymptotic expansions in real powers, we have developed a general theory for expansions of type (*) , x → x 0 where the ordered n -tuple forms an asymptotic scale at x 0 , i.e . as x → x 0 , 1 ≤ i ≤ n – 1 , and is practically assumed to…
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Advances in Pure Mathematics (APM) is an openly accessible journal published monthly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of ordered algebraic structures. All the manus… All articles are open access under a CC BY 4.0 licence, with authors retaining copyright.
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