One-to-one functions on the positive integers

1970 ◽  
Vol 7 (2) ◽  
pp. 505-507 ◽  
Author(s):  
Gedalia Ailam ◽  
Mahabanoo N. Tata
Keyword(s):  
Random Functions ◽  
The Past ◽  
The Family ◽  
One To One ◽  
Image Position ◽  
Positive Integers

Let {an} be an increasing sequence of positive integers and let be the family of all functions from the positive integers into the positive integers, which satisfy Assume that are random functions with probabilities and for all n > 1 and 0 elsewhere, i.e., all permissible values of f, given the past, are equally likely.

One-to-one functions on the positive integers

1970 ◽  
Vol 7 (02) ◽  
pp. 505-507 ◽  
Author(s):  
Gedalia Ailam ◽  
Mahabanoo N. Tata
Keyword(s):  
Random Functions ◽  
The Past ◽  
The Family ◽  
One To One ◽  
Image Position ◽  
Positive Integers

Let {an } be an increasing sequence of positive integers and let be the family of all functions from the positive integers into the positive integers, which satisfy Assume that are random functions with probabilities and for all n > 1 and 0 elsewhere, i.e., all permissible values of f, given the past, are equally likely.

scholarly journals On the divisibility of r2(n)

1977 ◽  
Vol 18 (1) ◽  
pp. 109-111 ◽  
Author(s):  
E. J. Scourfield
Keyword(s):  
Modular Form ◽  
Algebraic Number ◽  
Modular Forms ◽  
Congruence Subgroup ◽  
Algebraic Number Field ◽  
The Past ◽  
Divisibility Property ◽  
Integral Weight ◽  
Image Position ◽  
Positive Integers

During the past few years, some papers of P. Deligne and J.-P. Serre (see [2], [9], [10] and other references cited there) have included an investigation of certain properties of coefficients of modular forms, and in particular Serre [10] (see also [11]) obtained the divisibility property (1) below. Letbe a modular form of integral weight k ≧ 1 on a congruence subgroup of SL2(Z), and suppose that each cn belongs to the ring RK of integers of an algebraic number field K finite over Q. For c ∈ RK and m ≧ 1 an integer, write c ≡ 0 (mod m) if c ∈ m RK and c ≢ 0 (mod m) otherwise. Then Serre showed that there exists α > 0 such thatas x → ∞, where throughout this note N(n ≦ x: P) denotes the number of positive integers n ≦ x with the property P.

An Overview on Phytochemical and Pharmacological Profile of Morus alba Linn.

2020 ◽  
Vol 16 ◽  
Author(s):  
Arpita Paul ◽  
Monami Rajiung ◽  
Kamaruz Zaman ◽  
Sushil Kumar Chaudhary ◽  
Hans Raj Bhat ◽  
...  
Keyword(s):  
Traditional Medicine ◽  
Morus Alba ◽  
Biologically Active ◽  
Pharmacological Profile ◽  
Pharmacological Activities ◽  
Significant Information ◽  
The Past ◽  
Comprehensive Information ◽  
The Family ◽  
White Mulberry

Background: Morus alba Linn. commonly known as white mulberry, belongs to the family Moraceae, is a promising traditional medicine. In Asia, besides its use in the preparation of delicacies, every part of this plant is utilized in traditional medicine. Over the past decade, studies related to identification and isolation of biologically active compounds, with flavonoids as the major class of phytoconstituents, from this plant has been reported. These phytoconstituents are not only found to be beneficial for the maintenance of general health but also are associated with a range of potential pharmacological activities such as antioxidant, anti-inflammatory, anti-diabetic, anticancer, hepatoprotective, cardioprotective, neuroprotective to name a few. Objective: This review aims to provide upgraded and comprehensive information regarding the phytochemical, ethnomedicinal use and pharmacological profile of the plant Morus alba Linn. Method: The significant information has been collected through various database viz. PubMed, Scopus, Web of Science, Science Direct based on the recent findings, using different terms of Morus alba. Results: The outcome of the study suggests that Morus alba is a multifunctional plant numerous phytochemicals, and possess a range of pharmacological activities. Conclusion: The data assembled on Morus alba will be beneficial to trigger research in various fields of pharmaceutical and allied science to explore the medicinal importance of this unique plant.

Factor X Deficiency Due to a Compound Heterozygosis Between a New Mutation (Gla72Asp) in Exon 2 and an Already Known one (Gly154Arg) in Exon 5: Factor X Mar Del Plata1)

2019 ◽  
Vol 19 (2) ◽  
pp. 169-173
Author(s):  
Antonio Girolami ◽  
Diana Noemi Garcia de Paoletti ◽  
Marcelo Leonardo Nenkies ◽  
Silvia Ferrari ◽  
Hugo Guglielmone
Keyword(s):  
Bleeding Tendency ◽  
Bleeding Disorders ◽  
Factor X ◽  
Substitution Therapy ◽  
New Mutation ◽  
Exon 2 ◽  
The Third ◽  
The Past ◽  
Factor X Deficiency ◽  
The Family

Background: Investigation of rare bleeding disorders in Latin-America. Objective: The report of a new case of FX deficiency due to a compound heterozygosis. Methods: Accepted clotting procedures were used. Sequencing of DNA was carried out by means of Applied Biosystems Instruments. Results: A compound heterozygote due to the association of a new mutation (Gla72Asp) with an already known mutation (Gly154Arg) of the FX gene is reported. The proposita is a 38 year old female who had a moderate bleeding tendency (menorrhagia, epistaxis, easy bruising). The proposita has never received substitution therapy but in the occasion of a uterine biopsy. The mother was asymptomatic but was a heterozygote for the new mutation. The father was asymptomatic but had deserted the family and could not be investigated. After this abandonment the mother of the proposita re-married with an asymptomatic man and she gave birth to a son who was asymptomatic but was also heterozygous for the new mutation (Gla72Asp). As a consequence it has to be assumed that the first husband of the mother of the proposita was heterozygous for the known mutation (Gly154Arg). Conclusion: This is the third case of a new mutation in the FX gene reported, during the past few years, in Argentina.

scholarly journals Adhesion GPCRs in Glioblastoma

2021 ◽  
Author(s):  
Gabriele Stephan ◽  
Niklas Ravn-Boess ◽  
Dimitris G Placantonakis
Keyword(s):  
G Protein ◽  
G Protein Coupled Receptors ◽  
The Past ◽  
Novel Treatment ◽  
The Family ◽  
Health And Disease ◽  
Basic Biology ◽  
G Protein Coupled ◽  
Potential Use ◽  
Receptor Family

Abstract Members of the adhesion family of G protein-coupled receptors (GPCRs) have received attention for their roles in health and disease, including cancer. Over the past decade, several members of the family have been implicated in the pathogenesis of glioblastoma. Here, we discuss the basic biology of adhesion GPCRs and review in detail specific members of the receptor family with known functions in glioblastoma. Finally, we discuss the potential use of adhesion GPCRs as novel treatment targets in neuro-oncology.

scholarly journals Sixty Years with the Chrysobalanaceae

2020 ◽  
Author(s):  
Ghillean T. Prance
Keyword(s):  
Economic Botany ◽  
Field Studies ◽  
Molecular Evidence ◽  
New Techniques ◽  
Conservation Ecology ◽  
The Past ◽  
New Findings ◽  
The Family ◽  
Molecular Studies ◽  
Economic Use

AbstractA review is given of the studies of Ghillean Prance and associates on the Chrysobalanaceae over the past sixty years. This has focussed on defining the generic boundaries in the family and on monographic work with a worldwide approach to this pantropical family. The importance of field studies for work on monographs and Floras is emphasized. Monographs are still the basis for much work on conservation, ecology and economic botany and are needed as a foundation for molecular studies. The importance of being open to experimenting with new techniques and as a result being willing to change the taxonomy in accordance with new findings is demonstrated and emphasized. The twelve genera of the Chrysobalanaceae at the beginning of this career-long study have now increased to twenty-eight in order to present a much better monophyletic and evolutionary arrangement based on recent molecular evidence. In particular it was necessary to divide and rearrange the originally large genera Parinari and Licania into a number of smaller segregate genera. All known species were included in a worldwide monograph published in 2003. A brief review of the economic use for the family is given.

scholarly journals The Divisibility of Divisor Functions

1961 ◽  
Vol 5 (1) ◽  
pp. 35-40 ◽  
Author(s):  
R. A. Rankin
Keyword(s):  
Positive Integer ◽  
Divisor Functions ◽  
Image Position ◽  
Positive Integers

For any positive integers n and v letwhere d runs through all the positive divisors of n. For each positive integer k and real x > 1, denote by N(v, k; x) the number of positive integers n ≦ x for which σv(n) is not divisible by k. Then Watson [6] has shown that, when v is odd,as x → ∞; it is assumed here and throughout that v and k are fixed and independent of x. It follows, in particular, that σ (n) is almost always divisible by k. A brief account of the ideas used by Watson will be found in § 10.6 of Hardy's book on Ramanujan [2].

scholarly journals Enduring Cell Lines: Parents’ Experiences of Postmortem Tumor Banking in Childhood Cancer

2021 ◽  
pp. 107484072110014
Author(s):  
Nancy J. Moules ◽  
Catherine M. Laing ◽  
Wendy Pelletier ◽  
Gregory M. T. Guilcher ◽  
Jennifer A. Chan
Keyword(s):  
Childhood Cancer ◽  
Pediatric Oncology ◽  
Common Factors ◽  
Living Cells ◽  
The Past ◽  
The Family ◽  
Deceased Donors ◽  
Cure Rates ◽  
The Impact ◽  
Parents Experiences

While cure rates in pediatric oncology have improved over the past 30 years, childhood cancer remains the second leading cause of death in children aged 1 to 14. Developing therapies often require using cancerous tissues, which may come from deceased donors. Tumor banks collect, store, and distribute these donated samples. While tumor banking is more common, factors that contribute to parents’ decision and the impact of it on the family are not well understood. The purpose of this hermeneutic study was to understand the meaning and impact of tumor banking for parents of children who have died from cancer. Findings suggest that parents donating their child’s tumors unexpectedly found a sense of meaning in their loss. They also found a legacy of their child’s life; the living cells in some ways assisted the parents with grief. Aspects of this sensitive conversation and decision are discussed from the perspective of the parents’ experiences.

scholarly journals Singular perturbations of the unicritical polynomials with two parameters

2016 ◽  
Vol 37 (6) ◽  
pp. 1997-2016 ◽  
Author(s):  
YINGQING XIAO ◽  
FEI YANG
Keyword(s):  
Julia Set ◽  
Dynamical Behavior ◽  
Rational Maps ◽  
Topological Properties ◽  
Fatou Set ◽  
The Family ◽  
Image Position ◽  
Two Parameters ◽  
Unicritical Polynomials

In this paper, we study the dynamics of the family of rational maps with two parameters $$\begin{eqnarray}f_{a,b}(z)=z^{n}+\frac{a^{2}}{z^{n}-b}+\frac{a^{2}}{b},\end{eqnarray}$$ where $n\geq 2$ and $a,b\in \mathbb{C}^{\ast }$. We give a characterization of the topological properties of the Julia set and the Fatou set of $f_{a,b}$ according to the dynamical behavior of the orbits of the free critical points.

scholarly journals A Markov model for Selmer ranks in families of twists

2014 ◽  
Vol 150 (7) ◽  
pp. 1077-1106 ◽  
Author(s):  
Zev Klagsbrun ◽  
Barry Mazur ◽  
Karl Rubin
Keyword(s):  
Markov Process ◽  
Markov Model ◽  
Elliptic Curve ◽  
Arbitrary Number ◽  
Equilibrium Distribution ◽  
Two Dimensional ◽  
Absolute Galois Group ◽  
Quadratic Twists ◽  
The Family ◽  
Positive Integers

AbstractWe study the distribution of 2-Selmer ranks in the family of quadratic twists of an elliptic curve $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}E$ over an arbitrary number field $K$. Under the assumption that ${\rm Gal}(K(E[2])/K) \ {\cong }\ S_3$, we show that the density (counted in a nonstandard way) of twists with Selmer rank $r$ exists for all positive integers $r$, and is given via an equilibrium distribution, depending only on a single parameter (the ‘disparity’), of a certain Markov process that is itself independent of $E$ and $K$. More generally, our results also apply to $p$-Selmer ranks of twists of two-dimensional self-dual ${\bf F}_p$-representations of the absolute Galois group of $K$ by characters of order $p$.

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