Proof. Proceed by contradiction. Suppose that f has more than one root in (0,∞). Let r1 and r2, with r1 < r2, be two consecutive such roots (note that we can always find two consecutive roots r1 and r2 because f (r) > 0 for any root r). From the hypothesis, we have f (r1) > 0 and f (r2) > 0. Since f ′ is continuous at r1, there exists an 0 < 2 < (r2− r1) such that f (x) > 0 in the interval (r1,...

(1) Let X be a real linear space and R1, R2 be finite sequences of elements of X. If lenR1 = lenR2, then ∑ (R1 +R2) = ∑ R1 + ∑ R2. (2) Let X be a real linear space and R1, R2, R3 be finite sequences of elements of X. If lenR1 = lenR2 and R3 = R1−R2, then ∑ R3 = ∑ R1− ∑ R2. (3) Let X be a real linear space, R1, R2 be finite sequences of elements of X, and a be an element of R. If R2 = aR1, then ...

The nonselective human corticotropin-releasing factor receptor 1 (hCRF-R1) and the ligand-selective Xenopus CRF-R1 (xCRF-R1) were compared. To understand the interactions of sauvagine and ovine CRF, both high-affinity ligands for hCRF-R1 but surprisingly weak ligands for xCRF-R1, chimeric receptors of hCRF-R1 and xCRF-R1 followed by double or multiple point mutations were constructed. Binding s...

The goal of this paper is to investigate the Generalized Hyers - Ulam Rassias (HUR) stability generalquartic functional equation (GQFE) fq(kr1 + (k -1)r2) = 2k4fq(r1) 2(k -1)4fq(r2) +6k2(k -1)2[fq(r1 r2) fq(r1 r2)] 12k2(k 1)2[fq(r1) fq(r2)] in fuzzy normed spaces (F.N. spaces). proved by using direct method. sense and Ulam- Gavruta also studied.

ARCHITECTING PROTOCOLS TO ENABLE MOBILE APPLICATIONS IN DIVERSE WIRELESS NETWORKS

In this paper, we consider the perfonnance of a cellular radio, : direct sequence, code division multiple access system. We analyze the performance of the mobile-to-base link, and we use a model corresponding to independent flat Rayleigh fading of each user.

Base stations represent the main contributor to the energy consumption of a mobile cellular network. Since traffic load in mobile networks significantly varies during a working or weekend day, it is important to quantify the influence of these variations on the base station power consumption. Therefore, this paper investigates changes in the instantaneous power consumption of GSM (Global System...