When working with numbers such as real numbers x ∈ R or complex numbers z ∈ C, there is an unambiguous notion of a magnitude |x| or |z| of a number, with which to measure which numbers are large and which are small. One can also use this notion of magnitude to define a distance |x − y| or |z − w| between two real numbers x, y ∈ R, or between two complex numbers z, w ∈ C, thus giving a quantitat...

Let Pn,r(x) be the generalized weighted means: Pn,r(x) = ( ∑n i=1 qix r i ) 1/r , where Pn,0(x) denotes the limit of Pn,r(x) as r → 0+, x = (x1,x2, . . . ,xn) and qi > 0 (1 ≤ i ≤ n) are positive real numbers with ∑n i=1 qi = 1. In this paper, we let q = minqi and always assume n≥ 2, 0 ≤ x1 < x2 < ··· < xn. We defineAn(x) = Pn,1(x),Gn(x) = Pn,0(x),Hn(x) = Pn,−1(x), and we will write Pn,r for Pn,...

Let Mn,r(x) be the generalized weighted means Mn,r(x) = ( ∑n i=1 qix r i ) 1/r , where Mn,0(x) denotes the limit of Mn,r(x) as r → 0+, x = (x1,x2, . . . ,xn), and qi > 0 (1≤ i≤ n) are positive real numbers with ∑n i=1 qi = 1. In this paper, we let q =minqi and always assume n≥ 2, 0≤ x1 < x2 < ··· < xn. We define An(x)=Mn,1(x), Gn(x)=Mn,0(x),Hn(x)=Mn,−1(x) and we will writeMn,r forMn,r(x),An for...

The balancing numbers are natural numbers n satisfying the Diophantine equation 1 + 2 + 3 + · · · + (n − 1) = (n + 1) + (n + 2) + · · · + (n + r); r is the balancer corresponding to the balancing number n.The n balancing number is denoted by Bn and the sequence {Bn} ∞ n=1 satisfies the recurrence relation Bn+1 = 6Bn−Bn−1. The balancing numbers posses some curious properties, some like Fibonacci...

acquiring up-to-date information about stands is necessary for scientific management and planning of forest. remote sensing by its great capabilities in this way can be very useful. this study was done to investigate the capability of satellite data for gathering information about beech diameter specification. 21 plots of one hectare dimension were selected at experimental forest of kheyroud in...

In this paper, we prove that a graph G with no Ks,s-subgraph and twin-width d has r-admissibility r-coloring numbers bounded from above by an exponential function of r can construct graphs achieving such dependency in r.

ABSTRACT: This paper begins by using the Haar wavelet to analyze the cumulative distribution function of a stream of two-valued Bernoulli trials. We find that this function maps binary numbers in [0,1] into non-uniform binary numbers in [0,1]. More generally, for r-valued Bernoulli trials, the distribution function likewise maps usual base-r numbers into non-uniform base-r numbers. We also find...

Reasoning with domains containing continuous numeric change remains an open challenge in planning. In this paper, we discuss how an established temporal planner, CRIKEY3, can be adapted to plan in domains containing linear continuous numeric change. In particular, we discuss how an LP can be used to scheudule action choices, and how the LPRPG heuristic (hitherto for non-temporal planning) can b...

The Zarankiewicz number z(b; s) is the maximum size of a subgraph of Kb,b which does not contain Ks,s as a subgraph. The two-color bipartite Ramsey number b(s, t) is the smallest integer b such that any coloring of the edges of Kb,b with two colors contains a Ks,s in the rst color or a Kt,t in the second color.In this work, we design and exploit a computational method for bounding and computing...