170 research outputs found
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
Generalized Cauchy means
Given two means M and N, the operator MM,NMM,N assigning to a given mean μ the mean MM,N(μ)(x,y)=M(μ(x,N(x,y)),μ(N(x,y),y)) was defined in Berrone and Moro (Aequationes Math 60:1–14, 2000) in connection with Cauchy means: the Cauchy mean generated by the pair f, g of continuous and strictly monotonic functions is the unique solution μ to the fixed point equation MA(f),A(g)(μ)=μ, where A(f) and A(g) are the quasiarithmetic means respectively generated by f and g. In this article, the operator MM,NMM,N is studied under less restrictive conditions and a general fixed point theorem is derived from an explicit formula for the iterates MnM,NMM,Nn . The concept of class of generalized Cauchy means associated to a given family of mixing pairs of means is introduced and some distinguished families of pairs are presented. The question of equality in these classes of means remains a challenging open problem.Fil: Berrone, Lucio Renato. Universidad Nacional de Rosario. Facultad de Ciencias Exactas, Ingeniería y Agrimensura; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
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
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
Norditerpenoids with selective anti-cholinesterase activity from the roots of Perovskia atriplicifolia Benth
Inhibition of cholinesterases remains one of a few available treatment strategies for neurodegenerative dementias such as Alzheimer's disease and related conditions. The current study was inspired by previous data on anticholinesterase properties of diterpenoids from Perovskia atriplicifolia and other Lamiaceae species. The acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) inhibition by the three new natural compounds-(1R,15R)-1-acetoxycryptotanshinone (1), (1R)-1-acetoxytanshinone IIA (2), and (15R)-1-oxoaegyptinone A (3)-as well as, new for this genus, isograndifoliol (4) were assessed. Three of these compounds exhibited profound inhibition of butyrylcholinesterase (BChE) and much weaker inhibition of acetylcholinesterase (AChE). All compounds (1-4) selectively inhibited BChE (IC(50) = 2.4, 7.9, 50.8, and 0.9 µM, respectively), whereas only compounds 3 and 4 moderately inhibited AChE (IC(50) 329.8 µM and 342.9 µM). Molecular docking and in silico toxicology prediction studies were also performed on the active compounds. Natural oxygenated norditerpenoids from the traditional Central Asian medicinal plant P. atriplicifolia are selective BChE inhibitors. Their high potential makes them useful candidate molecules for further investigation as lead compounds in the development of a natural drug against dementia caused by neurodegenerative diseases
On a functional equation involving iterates and powers
We present a complete list of all continuous solutions f : (0,+∞)→(0,+∞) of the equation f 2(x) = γ [f (x)]αxβ, where α, β and γ > 0 are given 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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