Let k be a finite field and let E be an elliptic curve over k. In this paper we describe, for each finite extension l of k, the structure of the group E(l) of points of E over l as a module over the ring R of endomorphisms of E that are defined over k. If the Frobenius endomorphism ? of E over k does not belong to the subring Z of R, then we find that E(l)$R R(?&1), where n is the degree of l o...

MOTIVATION Many biological data processing problems can be formalized as clustering problems to partition data points into sensible and biologically interpretable groups. RESULTS This article introduces densityCut, a novel density-based clustering algorithm, which is both time- and space-efficient and proceeds as follows: densityCut first roughly estimates the densities of data points from a ...

Offering business services is widely considered a means for superior value creation. Increasing research activities in the emerging disciplines of Service Sciences and Service Science Management and Engineering (SSME) can be ascertained. Even so, the integration of service processes and their virtualization with suitable IT artifacts is seldom focused in SSME. Building on the Process Virtualiza...

Let E/k(T ) be an elliptic curve defined over a rational function field of characteristic zero. Fix a Weierstrass equation for E. For points R ∈ E(k(T )), write xR = AR/D2 R with relatively prime polynomials AR(T ), DR(T ) ∈ k[T ]. The sequence {DnR}n≥1 is called the elliptic divisibility sequence of R. Let P, Q ∈ E(k(T )) be independent points. We conjecture that deg ( gcd(DnP , DmQ) ) is boun...

t h e s p e c i a l c o n c e n t r i c a l l y b r a c e d f r a m e (s c b f) i s a c o m m o n t y p e o f s t e e l s t r u c t u r a l s y s t e m f o r r e s i s t i n g l a t e r a l l o a d i n g. t h i s t y p e o f s y s t e m p r o v i d e s t h e r e q u i r e d s t i f f n e s s a n d s t r e n g t h a t r e l a t i v e l y l o w c o s t. d e s i g n c o d e s, b a s e d o n p a s ...

Given integers r ⩾ 2 $r\geqslant 2$ and n , t 1 $n,t\geqslant 1$ we call families F ⋯ ⊆ P ( [ ] ) $\mathcal {F}_1,\dots ,\mathcal {F}_r\subseteq \mathcal {P}([n])$ $r$ -cross $t$ -intersecting if for all i ∈ $F_i\in {F}_i$ $i\in [r]$ have | ∩ $\vert \bigcap _{i\in [r]}F_i\vert \geqslant t$ . We obtain a strong generalisation of the classic Hilton–Milner theorem on cross-intersecting families. I...

The outer mitochondrial membrane protein mitoNEET was discovered as a binding target of pioglitazone, an insulin-sensitizing drug of the thiazolidinedione class used to treat type 2 diabetes (Colca, J. R., McDonald, W. G., Waldon, D. J., Leone, J. W., Lull, J. M., Bannow, C. A., Lund, E. T., and Mathews, W. R. (2004) Am. J. Physiol. 286, E252-E260). We have shown that mitoNEET is a member of a ...

The goal of the article is to introduce an order on a simple closed curve. To do this, we x two points on the curve and devide it to two arcs. We prove that such a decomposition is unique. Other auxiliary theorems about arcs are proven for preparation of the proof of the above. For simplicity, we use the following convention: a, b, c, s, r are real numbers, n is a natural number, p, q are point...

For any lacunary sequence $theta = (k_{r})$, we define the concepts of $S_{theta}-$limit point and $S_{theta}-$cluster point of a sequence of fuzzy numbers $X = (X_{k})$. We introduce the new sets  $Lambda^{F}_{S_{theta}}(X)$, $Gamma^{F}_{S_{theta}}(X)$ and prove some inclusion relaions between these and the sets $Lambda^{F}_{S}(X)$, $Gamma^{F}_{S}(X)$ introduced in ~cite{Ayt:Slpsfn} by Aytar [...

This paper deals with the multiple ellipse fitting problem based on a given set of data points in a plane. The presumption is that all data points are derived from k ellipses that should be fitted. The problem is solved by means of center-based clustering, where cluster centers are ellipses. If the Mahalanobis distance-like function is introduced in each cluster, then the cluster center is repr...