let g be a (p, q) graph. let f : v (g) → {1, 2, . . . , k} be a map. for each edge uv, assign the label gcd (f(u), f(v)). f is called k-prime cordial labeling of g if |vf (i) − vf (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labeled with x, ef (1) and ef (0) respectively denote the number of edges labeled with 1 and not labeled with 1....

Let $M$ be a right module over a ring $R$, $tau_M$ a preradical on $sigma[M]$, and$Ninsigma[M]$. In this note we show that if $N_1, N_2in sigma[M]$ are two$tau_M$-lifting modules such that $N_i$ is $N_j$-projective ($i,j=1,2$), then $N=N_1oplusN_2$ is $tau_M$-lifting. We investigate when homomorphic image of a $tau_M$-lifting moduleis $tau_M$-lifting.

The aim of this short note is to introduce the concepts of prime and semiprime ideals in ordered AG-groupoids with left identity. These concepts are related to the concepts of quasi-prime and quasi-semiprime ideals, play an important role in studying the structure of ordered AG-groupoids, so it seems to be interesting to study them.

This note focuses on estimating the quantile function based on the kernel smooth estimator under a truncated dependent model. The Bahadurtype representation of the kernel smooth estimator is established, and from the Bahadur representation it can be seen that this estimator is strongly consistent.

The way super- and sub-additive transformations of aggregation functions are introduced involve suprema and infima taken over simplexes whose dimensions may grow arbitrarily. Exact values of such transformations may thus be hard to determine in general. In this note we discuss methods of algorithmic approximation of such transformations.

edge distance-balanced graphs are graphs in which for every edge $e = uv$ the number of edges closer to vertex $u$ than to vertex $v$ is equal to the number of edges closer to $v$ than to $u$. in this paper, we study this property under some graph operations.

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We reported a new approach of ABO genotyping by a polymerase chain reaction and restriction fragment length polymorphism method. Instead of amplifying the loci containing the positions of nucleotides 258 and 700 of cDNA of the A transferase separately, we successfully amplified these 2 loci together in one reaction mixture using 2 sets of primers. The amplified DNA products were digested at the...

Well known implementations for perspective correct rendering of planar polygons require a division per rendered pixel. Such a division is better to be avoided as it is an expensive operation in terms of silicon gates and clock cycles. In this paper we present a family of efficient midpoint algorithms that can be used to avoid division operators. These algorithms do not require more than a small...

Michael Darmady (1906–1989) is now largely forgotten, although he played a major role in several areas of Nephrology in the early days of the speciality, both as a clinician and as a pathologist. His contributions to the early understanding of acute renal failure and of the use of haemodialysis during the 1940s have been particularly neglected. His nephron microdissection work achieved some inf...