‎By the Mordell‎- ‎Weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎This paper studies the rank of the family Epq:y2=x3-pqx of elliptic curves‎, ‎where p and q are distinct primes‎. ‎We give infinite families of elliptic curves of the form y2=x3-pqx with rank two‎, ‎three and four‎, ‎assuming a conjecture of Schinzel ...

INTRODUCTION Optical techniques are routinely used to size and count extracellular vesicles (EV). For comparison of data from different methods and laboratories, suitable calibrators are essential. A suitable calibrator must have a refractive index (RI) as close to that of EV as possible but the RI of EV is currently unknown. To measure EV, RI requires accurate knowledge of size and light scatt...

The world population is increasing swiftly and expected to reach 109 billion by 2100. As compared increment, food resources feed a huge are not increasing. Similarly, in the future country having enough its inhabitants will be considered more powerful. There two main protein sources used living beings which from plant origin animal origin. Furthermore, crucial for humans due presence of essenti...

The biological relevance of extracellular vesicles (EV) in intercellular communication has been well established. Thus far, proteins and RNA were described as main cargo. Here, we show that EV released from human bone marrow derived mesenchymal stromal cells (BM-hMSC) also carry high-molecular DNA in addition. Extensive EV characterization revealed this DNA mainly associated with the outer EV m...

Enterovirus D68 (EV-D68) is an emerging pathogen that recently caused a large outbreak of severe respiratory disease in the United States and other countries. Little is known about the relationship between EV-D68 virus and host cells. In this study, we assessed the effect of the host cell cycle on EV-D68 viral production, as well as the ability of EV-D68 to manipulate host cell cycle progressio...

A classical R-matrix structure is described for the Lax representation of the integrable n-particle chains of Calogero-Olshanetski-Perelomov. This R-matrix is dynamical, non antisymmetric and non-invertible. It immediately triggers the integrability of the Type I, II and III potentials, and the algebraic structures associated with the Type V potential.

A new spectral parameter independent R-matrix (that depends on all of the dynamical variables) is proposed for the elliptic Calogero-Moser models. Necessary and sufficient conditions for this R-matrix to exist reduce to an equality between determinants of matrices involving elliptic functions. The needed identity appears new and is still unproven in full generality: we present it as a conjecture.

with constants C ;p1;p2 depending only on ; p1; p2 and p := p1p2 p1+p2 hold. The rst result of this type is proved in [4], and the purpose of the current paper is to extend the range of exponents p1 and p2 for which (2) is known. In particular the case p1 = 2, p2 =1 is solved to the a rmative. This was originally considered to be the most natural case and is known as Calderon's conjecture [3]. ...

This paper proves the reconstruction conjecture for graphs which are isomorphic to the cube of a tree. The proof uses the reconstructibility of trees from their peripheral vertex deleted subgraphs. The main result follows from (i) characterization of the cube of a tree (ii) recognizability of the cube of a tree (iii) uniqueness of tree as a cube root of a graph G, except when G is a complete gr...