Let G be a graph. A subset X of V(G) is said to be dependent if X is not independent. We say that X is doubly dependent if both X and V (G) \ X are dependent. Let dk(G) denote the number of doubly dependent sets in G of cardinality k. In this paper, we show that the sequence {dk(G)} is unimodal and, in particular, if G has r vertices then maxk{ dk ( G)} = dLr/2J (G). We also show that the parti...

Values for printed circuit board (PCB) laminate dielectric constant (Dk) and dissipation factor (Df) used in circuit design and signal integrity (SI) modeling are typically those presented on laminate maker datasheets. In most cases, these values are derived from measurements on samples which have not been exposed to thermal stresses representative of the printed circuit board (PCB) assembly pr...

Studies on the alterations of liver and kidney function parameters in patients with diabetic ketoacidosis (DKA) and diabetic ketosis (DK) were limited. Participants with DKA, DK, non-DK, and healthy controls were enrolled in the current study. Parameters of liver and kidney function were measured and evaluated. The patients with DKA had higher levels of plasma glucose, hemoglobin A1c (HbA1c), u...

Let d n pn the n th prime for n and let dk n jdk n dk n j for k n A well known conjecture usually ascribed to Gilbreath but actually due to Proth in the th century says that dk for all k This paper reports on a computation that veri ed this conjecture for k It also discusses the evidence and the heuristics about this conjecture It is very likely that similar conjectures are also valid for many ...

Let F=∪i=1kSdi be the union of pairwise vertex-disjoint k stars order d1+1,…,dk+1, respectively, where k≥2 and d1≥⋯≥dk≥1. In this paper, we present two sharp upper bounds for spectral radius F-free (bipartite) graphs characterize all corresponding extremal graphs. Moreover, minimum least eigenvalue adjacency matrix an graph are obtained.

BACKGROUND Dexmedetomidine as a sole agent showed limited use for painful procedures due to its insufficient sedative/analgesic effect, pronounced hemodynamic instability and prolonged recovery. The aim of this study was to compare the effects of dexmedetomidine-ketamine (DK) versus dexmedetomidine-midazolam-fentanyl (DMF) combination on the quality of sedation/analgesia and recovery profiles f...

The aboveground growth, physiological and biochemical parameters of two clones of the cosmopolitan wetland grass Phragmites australis, grown at four treatment combinations of temperature and CO2, were investigated to elucidate whether their climate response differed due to inherent differences in their ecological adaptation. The two phylogeographically distinct P. australis clones (DK clone, Eu...

The rate of urine secretion by insect Malpighian tubules (MTs) is regulated by multiple diuretic and antidiuretic hormones, often working either synergistically or antagonistically. In the Drosophila melanogaster MT, only diuretic factors have been reported. Two such agents are the biogenic amine tyramine (TA) and the peptide drosokinin (DK), both of which act on the stellate cells of the tubul...

Diffusional kurtosis imaging (DKI) is a new technique based on non-Gaussian water diffusion analysis. However, the original DKI protocol (six b values and 30 motion-probing gradient (MPG) directions) requires more than 10 min of scanning time, which is too long for daily clinical use. We aimed to find suitable b value, MPG direction, and diffusion time settings for faster DKI. Four normal healt...