235 research outputs found
Mangiferin: A Promising Anticancer Bioactive
Of late, several biologically active antioxidants from natural products have been investigated by the researchers in order to combat the root cause of carcinogenesis, i.e., oxidative stress. Mangiferin, a therapeutically active C-glucosylated xanthone, is extracted from pulp, peel, seed, bark and leaf of Mangifera indica. These polyphenols of mangiferin exhibit antioxidant properties and tend to decrease the oxygen-free radicals, thereby reducing the DNA damage. Indeed, its capability to modulate several key inflammatory pathways undoubtedly helps in stalling the progression of carcinogenesis. The current review article emphasizes an updated account on the patents published on the chemopreventive action of Mangiferin, apoptosis induction made on various cancer cells, along with proposed antioxidative activities and patent mapping of other important therapeutic properties. Considering it as promising polyphenol, this paper would also summarize the diverse molecular targets of Mangiferin
New generalized fuzzy metrics and fixed point theorem in fuzzy metric space
In this paper, in fuzzy metric spaces (in the sense of Kramosil and Michalek (Kibernetika 11:336-344, 1957)) we introduce the concept of a generalized fuzzy metric which is the extension of a fuzzy metric. First, inspired by the ideas of Grabiec (Fuzzy Sets Syst. 125:385-389, 1989), we define a new G-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by M Grabiec). Next, inspired by the ideas of Gregori and Sapena (Fuzzy Sets Syst. 125:245-252, 2002), we define a new GV-contraction of Banach type with respect to this generalized fuzzy metric, which is a generalization of the contraction of Banach type (introduced by V Gregori and A Sapena). Moreover, we provide the condition guaranteeing the existence of a fixed point for these single-valued contractions. Next, we show that the generalized pseudodistance J:X×X→[0,∞) (introduced by Włodarczyk and Plebaniak (Appl. Math. Lett. 24:325-328, 2011)) may generate some generalized fuzzy metric NJ on X. The paper includes also the comparison of our results with those existing in the literature
Remark on globally Lipschitzian composition operators
Let I C R be an interval, f : I x R —> R a fixed two-place function, and J’(Z) the linear space of all the functions u : I —> R. The function F : F(I) —> F{I} given by the formula
(F(u))(x) := /(x,u(x)), x G I, u G F(Z),
is said to be a composition operator.
Let a G I be fixed. Denote by Lip(I) the Banach space of all the functions « E 7(f) with the norm
(1) IhllLip(l) := lu(°)l + sup | I Xi — X2 xi,x2 e I-,
In [2] it is proved that if a composition operator F mapping Lip(I) into itself is globally Lipschitzian with respect to the Lip(I)-norm, then /(x, y) = g(x)y + h(x), (x G I;y 6 R), for some g,h GLip(I) (Fragment tekstu)
Reducing the polynomial-like iterative equations order and a generalized Zoltan Boros' problem
We present a technique for reducing the order of polynomial-like iterative equations; in particular, we answer a question asked by Wenmeng Zhang and Weinian Zhang. Our method involves the asymptotic behaviour of the sequence of consecutive iterates of the unknown function at a given point. As an application we solve a generalized problem of Zoltán Boros posed during the 50th ISFE
Loss of estrogen receptor beta expression correlates with shorter overall survival and lack of clinical response to chemotherapy in ovarian cancer patients
Background: Estrogen receptor beta (ERβ) belongs to a large family of nuclear receptors. Recent studies have suggested that ERβ in contrast to ERα might act as a tumour suppressor in ovarian cancer (OVCA). Materials and Methods: Expression of ERβ was detected by immunocytochemistry in 11 OVCA cell lines and by immunohistochemistry in 43 (41 FIGO stage III) OVCA specimens prepared before chemotherapy and 30 specimens from the same group after chemotherapy. Cisplatin sensitivity in the 11 cell lines was also analysed. Results: No significant correlations between cisplatin-sensitivity and expression of ERβ was found in the cell lines. In the cases which responded well to chemotherapy (complete response) ERβ expression at preliminary laparotomy (PL) was significantly higher (p=0.0004) than in those with progressive disease. Kaplan-Meier analysis revealed that the patients with higher ERβ expression (>30% of cells) at PL had an increased overall survival time and progression-free time (p=0.00161 and p=0.03255, respectively) than the patients with lower ERβ espression. Significantly shorter overall survival time characterized the cases with lower immunoreactivity score of ERβ expression at secondary cytoreduction (SCR) (p=0.00346). Conclusion: The loss of ERβ expression in ovarian tumours may be a feature of malignant transformation
Translation Representations and Scattering By Two Intervals
Studying unitary one-parameter groups in Hilbert space (U(t),H), we show that
a model for obstacle scattering can be built, up to unitary equivalence, with
the use of translation representations for L2-functions in the complement of
two finite and disjoint intervals.
The model encompasses a family of systems (U (t), H). For each, we obtain a
detailed spectral representation, and we compute the scattering operator, and
scattering matrix. We illustrate our results in the Lax-Phillips model where (U
(t), H) represents an acoustic wave equation in an exterior domain; and in
quantum tunneling for dynamics of quantum states
A composite functional equation from algebraic aspect
In this paper we discuss the composite functional equation
f(x+2f(y))=f(x)+y+f(y)
on an Abelian group. This equation originates from Problem 10854 of the American Mathematical Monthly. We give an algebraic description of the solutions on uniquely 3-divisible Abelian groups, and then we construct all solutions f of this equation on finite Abelian groups without elements of order 3 and on divisible Abelian groups without elements of order 3 including the additive group of real numbers
Means and covariance functions for geostatistical compositional data: an axiomatic approach
This work focuses on the characterization of the central tendency of a sample
of compositional data. It provides new results about theoretical properties of
means and covariance functions for compositional data, with an axiomatic
perspective. Original results that shed new light on the geostatistical
modeling of compositional data are presented. As a first result, it is shown
that the weighted arithmetic mean is the only central tendency characteristic
satisfying a small set of axioms, namely continuity, reflexivity and marginal
stability. Moreover, this set of axioms also implies that the weights must be
identical for all parts of the composition. This result has deep consequences
on the spatial multivariate covariance modeling of compositional data. In a
geostatistical setting, it is shown as a second result that the proportional
model of covariance functions (i.e., the product of a covariance matrix and a
single correlation function) is the only model that provides identical kriging
weights for all components of the compositional data. As a consequence of these
two results, the proportional model of covariance function is the only
covariance model compatible with reflexivity and marginal stability
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