258 research outputs found
A unitary test of the Ratios Conjecture
The Ratios Conjecture of Conrey, Farmer and Zirnbauer predicts the answers to
numerous questions in number theory, ranging from n-level densities and
correlations to mollifiers to moments and vanishing at the central point. The
conjecture gives a recipe to generate these answers, which are believed to be
correct up to square-root cancelation. These predictions have been verified,
for suitably restricted test functions, for the 1-level density of orthogonal
and symplectic families of L-functions. In this paper we verify the
conjecture's predictions for the unitary family of all Dirichlet -functions
with prime conductor; we show square-root agreement between prediction and
number theory if the support of the Fourier transform of the test function is
in (-1,1), and for support up to (-2,2) we show agreement up to a power savings
in the family's cardinality.Comment: Version 2: 24 pages, provided additional details, fixed some small
mistakes and expanded the exposition in place
On mixing and sparse ergodic theorems
We consider Bourgain's ergodic theorem regarding arithmetic averages in the
cases where quantitative mixing is present in the dynamical system. Focusing on
the case of the horocyclic flow, those estimates allows us to bound from above
the Hausdorff dimension of the exceptional set, providing evidence towards
conjectures by Margulis,Shah and Sarnak regarding equidistribution of
arithmetic averages in homogeneous spaces. We also prove the existence of a
uniform upper bound for the Hausdorff dimension of the exceptional set which is
independent from the spectral gap.Comment: Updated version, to appear in Journal of Modern Dynamic
Prioritization of service quality dimensions for healthcare sector using analytic hierarchy process
Due to the unique nature among the service industries, the overriding objective of the healthcare sector is to provide error free, impeccable services to their patients and clientele. It is not an option rather a norm for the healthcare sector to uphold and maintain the level of service that is quintessential and benchmark in the service industries. However, service quality has different meanings to different people. In this paper, SERVQUAL has been considered as the main tool to measure service quality and Analytic Hierarchy Process (AHP) has been applied to prioritize the five dimensions of SERVQUAL for healthcare sector. In addition to this, AHP has been applied to prioritize the various items representing each of the dimensions. The results show that Reliability and Assurance are the two most important service quality dimensions in the healthcare sector. The priorities of dimensions and their items are also determined with respect to a selected demographic factors on the part of the respondents
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