• Nonlinear Functional Analysis and Applications
• /
• v.28 no.4
• /
• pp.1069-1086
• /
• 2023

The natural transform is represented by two (p, q)-analogues, and their comparative characteristics are established. To resolve some (p, q)-difference and functional equations, applications are carried out.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.1
• /
• pp.141-148
• /
• 2022

Let p(z) be a polynomial of degree n having no zero in |z| < k, k ≤ 1, then Govil proved $$\max_{{\mid}z{\mid}=1}{\mid}p^{\prime}(z){\mid}{\leq}{\frac{n}{1+k^n}}\max_{{\mid}z{\mid}=1}{\mid}p(z){\mid}$$, provided |p'(z)| and |q'(z)| attain their maximal at the same point on the circle |z| = 1, where $$q(z)=z^n{\overline{p(\frac{1}{\overline{z}})}}$$. In this paper, we extend the above inequality to polar derivative of a polynomial. Further, we also prove an improved version of above inequality into polar derivative.

• Journal of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.915-929
• /
• 2007

The main result of this paper is to construct the derivative twisted p-adic (h, q)-L-functions at s = 0. We obtain twisted version of Theorem 4 in [17]. We also obtain twisted (h, q)-extension of Proposition 1 in [3].

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.1
• /
• pp.133-138
• /
• 2020

It is shown that each sequence lying sufficiently close in the hyperbolic sense to a Q^#_p-sequence for a meromorphic function f in the unit disc is also a Q^#_p-sequence for f.

• Clinical and Experimental Pediatrics
• /
• v.51 no.11
• /
• pp.1241-1244
• /
• 2008

We report on 2 siblings with a partial trisomy of 7q ($7q22{\rightarrow}qter$) and concomitant partial monosomy of 8p ($8p23.3{\rightarrow}pter$), which were shown by FISH using probes located at the telomere region of each chromosome. All the balanced translocation carriers (father and a sister) in this family had a normal phenotype. The 2 siblings with the same abnormal karyotype had similar multiple congenital anomalies and dysmorphic features. During the follow-up, the first male patient died in the neonatal period, but the female sibling is still alive at 2 years and 6 months of age.

• East Asian mathematical journal
• /
• v.21 no.1
• /
• pp.123-135
• /
• 2005

We have extended the $H^p$ space and estabilished the derivative of inner functions, Blaschke product on weighted Hardy spaces for the unit disc in complex plane.

• Journal of Microbiology and Biotechnology
• /
• v.26 no.9
• /
• pp.1620-1628
• /
• 2016

In this study, we investigated colistin resistance mechanisms associated with the regulation of the pbgP operon in Klebsiella pneumoniae, using four isogenic pairs of colistin-susceptible strains and their colistin-resistant derivatives and two colistin-resistant clinical isolates. Amino acid sequence alterations of PhoPQ, PmrAB, and MgrB were investigated, and mRNA expression levels of phoQ, pmrB, pmrD, and pbgP were measured using quantitative real-time PCR. The phoQ and pmrB genes were deleted from two colistin-resistant derivatives, 134R and 063R. We found that phoQ, pmrD, and pbgP were significantly upregulated in all colistin-resistant derivatives. However, pmrB was significantly upregulated in only two colistin-resistant derivatives and one clinical strain. pmrB was not overexpressed in the other strains. The minimum inhibitory concentration of colistin was drastically lower in both phoQ- and pmrB-deleted mutants from a colistin-resistant derivative (134R) that was overexpressing phoQ and pmrB. However, colistin susceptibility was restored only in a phoQ-deleted mutant from a colistin-resistant derivative (063R) without overexpression of pmrB. In conclusion, two different regulations of the pbgP operon may associate with the development of colistinresisant K. pneumoniae.

• East Asian mathematical journal
• /
• v.36 no.1
• /
• pp.13-24
• /
• 2020

The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius-Genocchi numbers and polynomials of order α and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations. We also obtain integral representations, implicit and explicit formulas and relations for these polynomials and numbers. Furthermore, we consider some relationships for Apostol type (p, q)-Frobenius-Genocchi polynomials of order α associated with (p, q)-Apostol Bernoulli polynomials, (p, q)-Apostol Euler polynomials and (p, q)-Apostol Genocchi polynomials.

• Journal of applied mathematics & informatics
• /
• v.37 no.3_4
• /
• pp.295-305
• /
• 2019

In the present paper, we introduce (p, q)-Frobenius-Genocchi numbers and polynomials and investigate some basic identities and properties for these polynomials and numbers including addition theorems, difference equations, derivative properties, recurrence relations and so on. Then, we provide integral representations, implicit and explicit formulas and relations for these polynomials and numbers. We consider some relationships for (p, q)-Frobenius-Genocchi polynomials of order ${\alpha}$ associated with (p, q)-Bernoulli polynomials, (p, q)-Euler polynomials and (p, q)-Genocchi polynomials.

• Korean Journal of Mathematics
• /
• v.31 no.2
• /
• pp.229-242
• /
• 2023

In this paper, we investigate the [p, q] - φ order and [p, q] - φ type of f₁ + f₁, ${\frac{f_1}{f_2}}$ and f₁ f₁, where f₁ and f₁ are analytic or meromorphic functions with the same [p, q]-φ order and different [p, q]-φ type in the unit disc. Also, we study the [p, q]-φ order and [p, q]-φ type of different f and its derivative. At the end, we investigate the relationship between two different [p, q] - φ convergence exponents of f. We extend some earlier precedent well known results.