This paper deals with some questions that have received a lot of attention since they were raised by Hejhal and Rackner in their 1992 numerical computations of Maass forms. We establish sharp upper and lower bounds for the L2-restrictions of these forms to certain curves on the modular surface. These results, together with the Lindelof Hypothesis and known subconvex L∞-bounds are applied to pro...

Adrian Stoica, “Toward Evolvable Hardware Chips: Experiments with a Programmable Transistor Array,” IEEE, Apr. 1999, pp. 1-7.* Zebulum et al, “Eiolvable Hardware: on the Automatic Synthesis of Analog Control Systems,” IEEE, Mar. 2000, pp. 451-463.* August0 et al, “Analog Fault Diagnostic in Nonlinear DC Circuits with an Evolutionaly Algorithm,” IEEE, Jul. 2000, pp. 609-616.* Stoica et al, “Evol...

Given a graph H on vertex set {1, 2, · · · , n} and a function f : [0, 1] → R, define ‖f‖H := ∣∣∣∣∣ ∫ ∏ ij∈E(H) f(xi, xj)dμ |V (H)| ∣∣∣∣∣ 1/|E(H)| , where μ is the Lebesgue measure on [0, 1]. We say that H is norming if ‖·‖H is a semi-norm. A similar notion ‖·‖r(H) is defined by ‖f‖r(H) := ‖|f |‖H and H is said to be weakly norming if ‖·‖r(H) is a norm. Classical results show that weakly normin...

In this present paper, by utilizing ij−δ semi open sets, we introduce ij−∧δ, ij−∨δ, g− ij−∧δ, g− ij−∨δ sets and investigate some of their properties in bitopological spaces. Also, we present and study the notions of ij − T∨sδ space, ij−∧δ continuous, ij−∧δ irresolute, ij−∧δ open and ij−∧δ homeomorphism functions.

where <£fc(X)=2w=i dk(ri)e^ +residue term. Hopefully, one could expand the k integral and estimate the resulting infinite series. This does not seem feasible, however, unless k{z) satisfies a certain approximate functional equation (AFE); see [5, p. 147] and [6, p. 42]. This is one reason why only k=l, k=2 are known. However, Bellman [2] has shown that, if the e~ in k(z) are replaced b...

With the discovery of some hidden-charm pentaquark resonances by LHCb Collaboration, investigations states containing heavy quarks have aroused interest theorists. We study herein $qqq\bar{q}Q$ ($q = u$ or $d$, $Q=c$ $b$) system, in framework chiral quark model. In consequence, charmed and bottomed pentaquarks are considered to exist five-body dynamical calculations. charm sector, $\Sigma_c\pi(...