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• 53 Downloads • Abstract We study the asymptotic behaviour of N(α)—the number of negative eigenvalues of the operator (-τ) l -α V in L 2( R d) for an even d and 2l≥d. This is the only case where the previously known results were far from being complete. In order to describe our results we introduce an auxiliary ordinary differential operator (system) on the semiaxis. Depending on the spectral properties of this operator we can distinguish between three cases where N(α) is of the Weyl-type, N(α) is of the Weyl-order but not the Weyl-type coefficient and finally where N(α)= O(α q) with q>d/2l.

Power Usage Effectiveness (PUE) and its reciprocal Data Center infrastructure Efficiency (DCiE) are widely accepted benchmarking standards proposed by the Green Grid to help IT Professionals determine how energy efficient data centers are, and to monitor the impact of their efficiency efforts. The Uptime Institute also has a comprehensive benchmark it recommends named Corporate Average Data center Efficiency (CADE). At their February 2009 Technical Forum, the Green Grid introduced new benchmarks named Data Center Productivity (DCP) and Data Center energy Productivity (DCeP) which probe into the useful work produced by your data center. All benchmarks have their value, and when used correctly, they can be a useful and essential tool for improving your data center energy efficiency.

What is DCiE? PUE / DCiE are efficiency benchmarks comparing your data center’s infrastructure to your existing IT load.

The initial benchmarking of PUE / DCiE yields an efficiency score and sets a testing framework for the facility to repeat. Comparing initial and subsequent scores, data center managers can gauge the impact of what should be ongoing efficiency efforts. At any given time, they are comparing the power currently used for the IT equipment a company needs with the power used by the infrastructure which keeps that IT equipment cooled, powered, backed-up, and protected. PUE Example: Having a facility that uses 100,000 kW of total power of which 80,000 kW is used to power your IT equipment, would generate a PUE of 1.25.

The 100,000 kW of total facility power divided by the 80,000 kW of IT power. DCiE Example: Having that same facility that uses 100,000 kW of total power of which 80,000 kW is used to power your IT equipment, would generate a DCiE of.8. The 80,000 kW of IT power divided by the 100,000 kW of total facility power. Generating PUE / DCiE is only a start on your path to efficiency. For this benchmark to be meaningful it should be generated on a regular basis and preferably also on different days of the week and at different times of the day. The goal being to take actionable efficiency actions based on your actual data. By comparing your starting benchmark with benchmarks taken after implementing changes, you should be able to see noticeable improvements in your PUE/DCiE.

Reduce your operation costs by utilizing measurement, benchmarking, modeling, and analysis to improve your Data Center’s energy efficiency. PUE = Total Facility Power / IT Equipment Power DCiE = IT Equipment Power / Total Facility Power PUE DCiE Level of Efficiency 3.0 33% Very Inefficient 2.5 40% Inefficient 2.0 50% Average 1.5 67% Efficient 1.2 83% Very Efficient. DCiE and PUE Wars and Green Washing what PUE isn’t! You may have heard the terms “PUE Wars” or “PUE Marketing.” The Green Grid, the author of both PUE and DCiE, didn’t intend for either metric to compare one facility to another. Unfortunately that hasn’t stopped some people from publishing their PUE numbers in an attempt to market their facilities or design strategies. While their efforts to improve data center efficiency should be applauded, these metrics by themselves are not sufficient to determine data center efficiency.

The conversation must include productivity. Are you getting the most out of your servers and storage? Are you maximizing processing power? Retiring idle servers? Consolidating and Virtualizing? PUE and DCiE Benchmarking in Laymen’s Terms: Companies and organizations need IT equipment to provide their products and services, handle transactions, provide security, and to run and grow their businesses. The larger a company / organization grows, the greater the need to house their computer equipment in a secure environment.