• Parasites, Hosts and Diseases
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• v.56 no.5
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• pp.453-461
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• 2018

The aim of this study is to delineate 'admixed hybrid' and 'introgressive' Fasciola genotypes present in the Fasciola population in Vietnam. Adult liver flukes collected from ruminants in 18 Provinces were morphologically sorted out by naked eyes for small (S), medium (M) and large (L) body shapes; and human samples (n=14) from patients. Nuclear ribosomal (rDNA) ITS1 and ITS2, and mitochondrial (mtDNA) nad1 markers were used for determination of their genetic status. Total 4,725 worm samples of ruminants were tentatively classified by their size: 6% (n=284) small (S)-, 13% (n=614) medium (M)-, and 81% (n=3,827) large (L)-forms. All the representative (n=120, as 40 each group) and 14 human specimens, possessed maternal mtDNA of only F. gigantica and none of F. hepatica. Paternally, all (100%) of the L-(n=40) and 77.5% (n=31) of the M-flukes had single F. gigantica rDNA indicating 'pure' F. gigantica. A majority (90%, n=36) of the S- and 15% (n=6) of the M-worms had single F. hepatica rDNA, indicating their introgressive; the rest (10%, n=4) of the S- and 7.5% (n=3) of the M-flukes had mixture of both F. gigantica and F. hepatica rDNAs, confirming their admixed hybrid genetic status. Fourteen human samples revealed 9 (64%) of pure F. gigantica, 3 (22%) of introgressive and 2 (14%) of admixed hybrid Fasciola spp. By the present study, it was confirmed that the small worms, which are morphologically identical with F. hepatica, are admixed and/or introgressive hybrids of Fasciola spp., and able to be the pathogens of human fascioliasis.

• The Pure and Applied Mathematics
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• v.23 no.2
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• pp.163-179
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• 2016

Let $M_1f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$, $M_2f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$ Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) $N(M_1f(x,y)-{\rho}M_2f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ and (0.2) $N(M_2f(x,y)-{\rho}M_1f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$ in fuzzy Banach spaces, where ρ is a fixed real number with ρ ≠ 1.

• The Pure and Applied Mathematics
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• v.23 no.2
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• pp.145-153
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• 2016

In this paper, we solve the quadratic ρ-functional inequalities (0.1) ${\parallel}f(x+y)+f(x-y)-2f(x)-2f(y){\parallel}$ $\leq$ ${\parallel}{\rho}(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)){\parallel}$, where $\rho$ is a fixed complex number with $\left|{\rho}\right|$ < 1, and (0.2) ${\parallel}4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y){\parallel}$ $\leq$ ${\parallel}{\rho}(f(x+y)+f(x-y)-2f(x)-2f(y)){\parallel}$, where ρ is a fixed complex number with |ρ| < $\frac{1}{2}$. Furthermore, we prove the Hyers-Ulam stability of the quadratic ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces.

• The Pure and Applied Mathematics
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• v.13 no.1 s.31
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• pp.11-18
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• 2006

Let f : (X, A) ${\rightarrow}$ (Y, B) be a map of pairs of compact polyhedra. A surplus Nielsen root number $SN(f;X\;{\backslash}\;A,\;c)$ is defined which is lower bound for the number of roots on X \ A for all maps in the homotopy class of f. It is shown that for many pairs this lower bound is the best possible one, as $SN(f;X\;{\backslash}\;A,\;c)$ can be realized without by-passing condition.

• The Pure and Applied Mathematics
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• v.20 no.1
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• pp.51-57
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• 2013

In this paper, we introduce asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces and consider approximating common fixed points of a sequence of asymptotically quasi-$f-g$-nonexpansive mappings in convex normed vector spaces.

• The Pure and Applied Mathematics
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• v.24 no.3
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• pp.171-178
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• 2017

In this paper, we define $C^*-ternary$ quadratic 3-Jordan homomorphisms associated with the quadratic mapping f(x + y) + f(x - y) = 2f(x) + 2f(y), and prove the Hyers-Ulam stability of $C^*-ternary$ quadratic 3-Jordan homomorphisms.

• The Pure and Applied Mathematics
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• v.11 no.4
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• pp.323-335
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• 2004

In this paper, we solve the general solution of a modified additive and quadratic functional equation f(χ + 3y) + 3f(χ-y) = f(χ-3y) + 3f(χ+y) in the class of functions between real vector spaces and obtain the Hyers-Ulam-Rassias stability problem for the equation in the sense of Gavruta.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.193-198
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• 2012

We show that every unbounded approximate Pexiderized exponential type function has the exponential type. That is, we obtain the superstability of the Pexiderized exponential type functional equation $$f(x+y)=e(x,y)g(x)h(y)$$. From this result, we have the superstability of the exponential functional equation $$f(x+y)=f(x)f(y)$$.

• The Pure and Applied Mathematics
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• v.1 no.1
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• pp.19-24
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• 1994

Let P be a probability measure on the real line with Lebesque-density f. The usual estimator of the distribution function (≡df) of P for the sample $\chi$$_1$,…, $\chi$$\_$n/ is the empirical df: F$\_$n/(t)=(equation omitted). But this estimator does not take into account the smoothness of F, that is, the existence of a density f. Therefore, one should expect that an estimator which is better adapted to this situation beats the empirical df with respect to a reasonable measure of performance.(omitted)

• The Pure and Applied Mathematics
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• v.16 no.3
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• pp.283-296
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• 2009

Let f(x) = $x^n\;+\;a$ be a binomial polynomial in Z[x] and $f_m(x)$ be the m-th iterate of f(x). In this work we study a necessary condition to be the Galois group of $f_m(x)$ is isomorphic to a wreath product group $[C_n]^m$ where $C_n$ is a cyclic group of order n.