A graceful labeling of a graph $G=(V,E)$ with $m$ edges is aninjection $f: V(G) rightarrow {0,1,ldots,m}$ such that the resulting edge labelsobtained by $|f(u)-f(v)|$ on every edge $uv$ are pairwise distinct. For natural numbers $n$ and $k$, where $n > 2k$, a generalized Petersengraph $P(n, k)$ is the graph whose vertex set is ${u_1, u_2, cdots, u_n} cup {v_1, v_2, cdots, v_n}$ and its edge set...

  The clustering problem under the criterion of minimum sum of squares is a non-convex and non-linear program, which possesses many locally optimal values, resulting that its solution often falls into these trap and therefore cannot converge to global optima solution. In this paper, an efficient hybrid optimization algorithm is developed for solving this problem, called Tabu-KM. It gathers the ...

Objective(s): Antibacterial materials are so significant in the textile industry, water disinfection, medicine, and food packaging. Unfortunately, organic compounds for sterilization show toxicity to the human body; therefore, the interest in inorganic disinfectants such as metal oxide nanoparticles (NPs) is increasing. Materials and Methods: Nickel and nickel hydroxide nanoparticles (NiNPs ...

Given a standard set δ of a finite size r, we show that the functor associating to a k-algebra B the set of all reduced Gröbner bases with standard set δ is representable. We show that the representing scheme Hilb′ δ k[x]/k is a locally closed stratum in the punctual Hilbert scheme Hilbrk[x]/k. Moreover, we cover the punctual Hilbert scheme by open affine subschemes attached to all standard set...

BACKGROUND Many patients with atrial fibrillation who are at moderate to high risk of stroke do not receive anticoagulation with vitamin K antagonists (VKAs) in accordance with recommendations. OBJECTIVE To determine (1) why Canadian patients with atrial fibrillation who are potentially eligible for VKA do not receive this therapy, (2) why Canadian primary care physicians discontinue VKA ther...

Closed formulas are known for S(k, 0; n), the number of standard Young tableaux of size n and with at most k parts, where 1 ≤ k ≤ 5. Here we study the analogous problem for S(k, ℓ; n), the number of standard Young tableaux of size n which are contained in the (k, ℓ)-hook. We deduce some formulas for the cases k + ℓ ≤ 4.

1. When the Ringer's solution applied to isolated frog sciatic nerve contains K(+) in concentrations greater than 2 x standard, the height of the spike and of the after-potential is decreased, as is the duration of the after-potential; recovery of height and of excitability following response is delayed; degree and duration of supernormal excitability are decreased; postcathodal depression and ...