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8: Back to Power Series


  • 8.1: Uniform Convergence
    We will now draw our attention back to the question that originally motivated these definitions, “Why are Taylor series well behaved, but Fourier series are not necessarily?” More precisely, we mentioned that whenever a power series converges then whatever it converged to was continuous. Moreover, if we differentiate or integrate these series term by term then the resulting series will converge to the derivative or integral of the original series. This was not always the case for Fourier series.
  • 8.2: Uniform Convergence- Integrals and Derivatives
    We saw in the previous section that if f(n) is a sequence of continuous functions which converges uniformly to f on an interval, then f must be continuous on the interval as well. This was not necessarily true if the convergence was only pointwise, as we saw a sequence of continuous functions defined on (−∞,∞) converging pointwise to a Fourier series that was not continuous on the real line. Uniform convergence guarantees some other nice properties as well.
  • 8.3: Radius of Convergence of a Power Series
    We’ve developed enough machinery to look at the convergence of power series.
  • 8.4: Boundary Issues and Abel’s Theorem
    The integrations we performed in Chapter 2 are legitimate due to the Abel's theorem which extends uniform convergence to the endpoints of the interval of convergence even if the convergence at an endpoint is only conditional. Abel did not use the term uniform convergence, as it hadn’t been defined yet, but the ideas involved are his.

Thumbnail: Niels Henrik Abel. (public domain).


8: Back to Power Series

No claims of absolute originality are made for this material. As one man said, "I milk a lot of cows, but I churn my own butter." Please use these sermons as the Lord leads, but nothing on this site may be used for profit without my expressed, written permission!

Sermon Series

The Riches Of God's Grace

An Expository Series From The Book Of Ephesians

Dawning Of A New Day
(An Expositional Series From The Book Of Joshua)

Loser, Laymen and Leaders

A Study of the Judges of Israel

Home Improvement

01 - One Plus One Equals One - Mathew 19:4-6
02 - A Firm Family Foundation - Genesis 2:18-25
03 - Let's Talk - Ephesians 4:25-5:2
04 - The Case For Godly Manhood - Ephesians 5:21-6:4
05 - Putting A Woman In Her Place - 1 Timothy 2:9-15
06 - Parenting By The Book - Deuteronomy 6:1-9
07 - Growing Up Together - Ephesians 6:1-4

Biblical Worship:
What It Is And Why It Matters

Joseph: God Meant It For Good

The Baptist Deacon Series

Jesus: The Suffering Servant

Back To The Future
(51 Expository Sermons On the Book of Revelation)

Great Invitations Of The Bible
(12 Expository Sermons on the Great Invitations in the Bible.)

The Prison Experiences Of The Bible

David: A Man After God's Own Heart
(24 Expository Sermons on the Life of King David)

The Bible: God's Perfect Word

Behold The Lamb

Moments With The Master

God's Lost And Found Department

Abraham: Following in the Footsteps of Faith

The Decalogue: The Ten Commandments

Joshua: Claiming Your Canaan

The Book of Ruth: Pursued by Grace

Elijah The Prophet of Confrontation and Courage

Portrais of Jesus in John's Gallery

The Book of Romans

The Book of Revelation

(To give credit where credit is due, this series draws heavily upon the work of Dr. Jerry Vines. This sermon series was prepared back in the late 1980's. I was a very young and busy bivocational preacher. As I collected materials to use in this series, someone gave me a set of sermons on tape that Dr. Vines had preached while he was Pastor at West Rome Baptist Church in Rome, GA in the early 1970's. His skill, research and work in the biblical text formed much of the basis for this series. Thank you Dr. Vines.)

A Biblical View of the End Times

Basic Bible Doctrines

(Please note: This series of sermons was first preached by Dr. Adrian Rogers, when he was the Pastor of Bellevue Baptist Church in Memphis, TN. Dr. Rogers' outlines can be found at this link: http://www.bellevue.org/)

Home and Family Series

A Marriage Made In Paradise - Genesis 2:18-25 (Marriage)
The World's Greatest Undertaking - Deuteronomy 6:1-9 (Child Raising)
From Dreadlock To Wedlock - Ephesians 5:22-33 (Marriage)
God's Word To Married Couples - 1 Corinthians 7:1-5 (Marriage)
God's Word To Singles - 1 Corinthians 7:6-9 (Single Life)
God's Word To The Separated - 1 Corinthians 7:10-16 (Marriage, Divorce and Remarriage)
God's Word About Your Money - Mark 12:41-44 (Finances and Giving)

Prayer Series

Meetings and Travels

I will be preaching at New Prospect Baptist Churchin Horton, AL, July 23-27, 2018. The Pastor is Kenneth Shelton.

The church is located at: 1393 County Highway 38 Horton, AL.

Please join uis for meeting if you can. Please pray regardless.

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Power: Starz Announces Three New Sequel TV Series

Power aired its finale on Starz on Sunday, but fans have not seen the last of the Power universe on the cable network. One sequel series was already announced, and three more were announced on Sunday.

Fans will see Power Book II: Ghost, Power Book III: Raising Kanan, Power Book IV: Influence and Power Book V: Force on Starz at some point in the future. Mary J. Blige is set to star in Power Book II: Ghost.

Starz revealed more about the the expansion of the Power universe in a press release. Check that out below.

Power has been one of the most successful series in premium pay television during its six-year run, garnering more than 10 million multiplatform views in its last two seasons.

With the launch of the expanded Power Universe, all of the new Power series will be available exclusively across Starz’ global footprint on its international platform STARZPLAY, giving subscribers worldwide access to episodes day and date with the U.S. for the first time.

“In television history, only a select few shows have inspired four consecutive series extensions, launched into active production and development at the same time,” said Jeffrey Hirsch, President and CEO of Starz. “These new and exciting chapters will continue the journey of some of Power’s most controversial characters while featuring a growing ensemble of complex, distinct characters along with the high-octane drama that set Power in a class of its own.”

In addition to the previously announced POWER BOOK II: GHOST, which will pick up where the original series leaves off, starring world-renowned recording artist and Oscar(R) nominee Mary J. Blige, Method Man and several members of the original “Power” cast, a prequel and two spinoff sequels have been greenlit. All four series will be produced by Lionsgate Television.

POWER BOOK III: RAISING KANAN – the prequel story that takes viewers back to the 󈨞s and the early years of iconic “Power” character Kanan Stark.

POWER BOOK IV: INFLUENCE which follows Rashad Tate (played by Larenz Tate) in his ruthless pursuit of political power.

POWER BOOK V: FORCE in which fans will ride along with Tommy Egan (played by Joseph Sikora) after he cuts ties and puts New York in his rearview mirror for good.

The Power series are executive produced by series creator and showrunner Courtney A. Kemp through her company End of Episode, and Curtis 󈬢 Cent” Jackson through his G-Unit Film and Television. Also serving as executive producers on the series are Mark Canton through his Atmosphere Entertainment MM, End of Episode’s Chris Salek and Danielle DeJesus, Shana Stein and Bart Wenrich. Lionsgate TV produces the series for STARZ.”

Starz also released a trailer for Power Book II: Ghost, which teases the expansion of the universe. Check that out now.

What do you think? Are you happy to see the Power universe expanding?


Berkshire Hathaway Offers to Spend $8.3 Billion on Emergency Power Plants in Texas

Russell Gold

Katherine Blunt

Warren Buffett’s Berkshire Hathaway Inc. is pitching Texas lawmakers on a plan to spend $8.3 billion to build power plants that would run during electricity emergencies, a month after the state suffered devastating blackouts.

Chris Brown, the chief executive of Berkshire Hathaway Energy Infrastructure, said it could build 10 large natural-gas plants that would only operate during times of extreme need, and not otherwise compete in the state’s power market. He said the plants could be operational by November 2023.

“The state and its residents should have a reliable source of backup power generation during emergencies to protect residents and businesses,” said Mr. Brown. “This is a break-the-glass-in-case-of-emergency plan.”

In February, half of the state’s power plants failed during a severe cold snap, forcing the grid operator to institute widespread blackouts that lasted for four days.

The Texas legislature would need to approve changes to its laws to allow for a new regulated utility to provide emergency backup power.

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Cisco Nexus 5600 Platform 10-Gbps Switches Data Sheet

In today’s data centers, virtualization deployments have become commonplace, and this trend is increasing rapidly with the availability of 10 Gigabit Ethernet servers at attractive prices. The combination of increased adoption of these servers and applications with higher bandwidth requirements is increasing the need for dense 10 and 40 Gigabit Ethernet switching. Moreover, data center architectures are changing as application environments create new demands for IT infrastructure. Application workloads are deployed across a mix of virtualized and nonvirtualized server and storage infrastructure, requiring a network infrastructure that provides consistent connectivity, security, and visibility across a range of bare-metal, virtualized, and cloud computing environments.

The Cisco Nexus ® 5600 platform is the third generation of the Cisco Nexus 5000 Series Switches: the industry’s leading data center server access switches. The Cisco Nexus 5600 platform switches can be categorized into
10-Gbps and 40-Gbps switches. This data sheet focuses on the 10-Gbps switches only. Cisco Nexus 5600 platform 10-Gbps switches are the successors to the industry’s widely adopted Cisco Nexus 5500 platform switches. The switches maintain all the existing Cisco Nexus 5500 platform features, including LAN and SAN convergence (unified ports and Fibre Channel over Ethernet [FCoE]), fabric extenders, and Cisco ® FabricPath. In addition, the Cisco Nexus 5600 platform 10-Gbps switches bring integrated line-rate Layer 2 and 3 capabilities with true 40 Gigabit Ethernet support (on uplink and network-facing ports), Cisco programmable fabric innovations, Network Virtualization Using Generic Routing Encapsulation (NVGRE), Virtual Extensible LAN (VXLAN) bridging and routing, network programmability and visibility, large buffer capacity, and significantly greater scalability and performance for highly virtualized, automated, and cloud environments.

The Cisco Nexus 5600 platform 10-Gbps switches include both 1-Rack-Unit (1RU) and 2RU switches built to meet the challenges of today’s data centers with a flexible, agile, and energy-efficient design. These 10-Gbps switches are an important component of the Cisco Unified Data Center architecture, complementing existing Cisco Nexus switches. These energy-efficient switches offer 10 and 40 Gigabit Ethernet and FCoE, providing integrated Layer 2 and 3 features at wire speed and low latency of approximately 1 microsecond for any packet size. With a choice of port-side intake and fan-side intake airflow options to align with cold-aisle and hot-aisle placement in the data center, the 10-Gbps switches are designed for a broad range of traditional data center and large-scale virtualized cloud deployments.

The 10-Gbps switches together with the Cisco NX-OS Software operating system provides customers with features and capabilities that are widely deployed in data centers around the world. NX-OS is a purpose-built data center operating system designed for performance, resiliency, scalability, manageability, and programmability. It meets Ethernet and storage networking requirements, providing a robust and comprehensive feature set that can meet the demanding requirements of virtualization and automation in present and future data centers.

The Cisco Nexus 5600 platform 10-Gbps switches are designed for Top-of-Rack (ToR) and Middle-of-Row (MoR) deployment in data centers that support enterprise applications, service provider hosting, and cloud computing environments.

Models and Configurations

The Cisco 5600 platform 10-Gbps switches come in these configurations.

Cisco Nexus 5672UP Switch

● The Cisco Nexus 5672UP Switch (Figure 1) is a 10 and 40 Gigabit Ethernet (40-Gbps on uplink and network-facing ports) switch offering wire-speed performance for up to seventy-two 10 Gigabit Ethernet ports (using Quad Small Form-Factor Pluggable [QSFP] breakout cables). The Cisco Nexus 5672UP Switches are Layer 2 and 3 nonblocking 10 and 40 Gigabit Ethernet and FCoE-capable switches with up to 1.44 Terabits per second (Tbps) of internal bandwidth. The Cisco Nexus 5672UP offers 48 fixed 1 and 10 Gigabit Ethernet ports, of which the last 16 ports (highlighted in orange on the chassis for easy identification) are unified ports. All 48 fixed ports support classical Ethernet and FCoE. In addition, the 16 unified ports provide 8-, 4-, and 2-Gbps Fibre Channel, as well as 10 Gigabit Ethernet and FCoE connectivity options. The Cisco Nexus 5672UP also offers 6 ports of 40 Gbps using QSFP transceivers for Ethernet and FCoE support. The Cisco Nexus 5672UP has three fan modules and two power supplies. The Cisco Nexus 5672UP supports VXLAN in bridging and routing modes on all ports at line rate, enabling the migration of virtual machines between servers across Layer 3 networks. The switch also offers up to 15 buffer-to-buffer credits per port, helping provide SAN extension of up to 3.7 kilometers at 8-Gbps Fibre Channel speed assuming full Fibre Channel frame size of 2112 bytes.

The Cisco Nexus 5672UP is constructed with the components shown in Figure 2. The Cisco Nexus 5672UP has two 1+1 redundant, hot-swappable power supplies and three hot-swappable independent fans with support for 2+1 redundancy.

The Cisco Nexus 5672UP supports both port-side intake (red handle) and fan-side intake (blue handle) airflow options for flexible mounting.

Cisco Nexus 5672UP-16G Switch

● The Cisco Nexus 5672UP-16G Switch (Figure 3) is a 10 and 40 Gigabit Ethernet (40-Gbps on uplink and network-facing ports) switch offering wire-speed performance for up to seventy-two 10 Gigabit Ethernet ports (using QSFP breakout cables). The Cisco Nexus 5672UP-16G Switches are Layer 2 and 3 nonblocking 10 and 40 Gigabit Ethernet and FCoE-capable switches with up to 1.44 Tbps of internal bandwidth.

The Cisco Nexus 5672UP-16G offers 48 10 Gigabit Ethernet ports, of which the first 24 ports are capable of doing 1/10G Ethernet and the last 24 ports (highlighted in orange on the chassis for easy identification) are unified ports that support 16-, 8-, 4-, and 2-Gbps Fibre Channel. All 48 fixed ports support classical Ethernet and FCoE.

The 24 unified ports provide 16-, 8-. 4-, and 2-Gbps Fibre Channel as well as 10 Gigabit Ethernet and FCoE connectivity options. The Cisco Nexus 5672UP-16G also offers 6 ports of 40 Gbps using QSFP transceivers for Ethernet and FCoE support. The Cisco Nexus 5672UP-16G has three fan modules and two power supplies and supports VXLAN in bridging and routing modes on all ports at line rate, enabling the migration of virtual machines between servers across Layer 3 networks. The switch also offers up to 128 buffer-to-buffer credits per port, helping provide SAN extension of up to 16 kilometers at 16-Gbps Fibre Channel speed assuming full Fibre Channel frame size of 2122 bytes.

The Cisco Nexus 5672UP-16G platform is constructed with the components shown in Figure 4. The Cisco Nexus 5672UP-16G has two 1+1 redundant, hot-swappable power supplies and three hot-swappable independent fans with support for 2+1 redundancy.

The Cisco Nexus 5672UP-16G supports both port-side intake (red handle) and fan-side intake (blue handle) airflow options for flexible mounting.

Cisco Nexus 56128P Switch

The Cisco Nexus 56128P Switch (Figure 5) is a 2RU switch that supports 2.56 Tbps of bandwidth across 48 fixed 1 and 10 Gigabit Ethernet SFP+ ports and four 40-Gbps QSFP+ ports. The 48 ports on the base chassis support 10 Gigabit Ethernet and FCoE. The 4 QSFP ports support 40 Gigabit Ethernet and FCoE.

The Cisco Nexus 56128P also offers two slots for a Generic Expansion Module (GEM). The GEM (Figure 6) for the Cisco Nexus 56128P provides 24 SFP+ ports for 10 Gigabit Ethernet and FCoE or 2-, 4-, and 8-Gbps Fibre Channel, and 2 QSFP+ ports for 40 Gigabit Ethernet and FCoE. The expansion module supports native 40 Gigabit Ethernet on the QSFP+ ports. The GEM is supported on the Cisco Nexus 56128P chassis only and can be populated in either of the two expansion slots.

The Cisco Nexus 56128P is constructed with the components shown in Figure 7. The Cisco Nexus 56128P has four 2+2 redundant, hot-swappable power supplies and four 3+1 redundant, hot-swappable independent fans. The Cisco Nexus 56128P supports both port-side intake (red handle) and fan-side intake (blue handle) airflow options.

The Cisco Nexus 56128P supports VXLAN bridging and routing modes on all ports at line rate, enabling the migration of virtual machines between servers across Layer 3 networks.

With the Cisco Nexus 5600 10-Gbps platform, organizations can quickly and easily upgrade existing data centers through advanced Cisco bidirectional (BiDi) optics, which enable the use of existing 10 Gigabit Ethernet fiber (a pair of multimode fiber strands) to carry 40 Gigabit Ethernet to the aggregation layer or to the spine (in a leaf-and-spine configuration) without requiring any change to the existing cabling infrastructure. Additionally, the platform can be deployed in MoR or EoR configurations to meet the 10 and 40 Gigabit Ethernet connectivity requirements of multiple racks or pods.

When used with Cisco Nexus 2000 Series Fabric Extenders, the Cisco Nexus 5600 platform 10-Gbps switches can support even more servers in a collapsed access- and aggregation-layer design, supporting 1 and 10 Gigabit Ethernet connectivity across multiple racks.

The following are some of the primary features of the Cisco Nexus 5600 10-Gbps platform switches:

Optimization for virtualization and cloud deployments: Today, high-performance servers deployed in the cloud can support many more virtual machines and workloads than ever before. The requirement to be able to deploy new servers on demand puts additional strain on the network fabric. The 10-Gbps switches address this challenge by providing scalability and performance, making it an excellent platform for meeting current and future needs.

Density and resilience: Built for today’s data centers, the switches are designed just like the servers they support. Ports and power connections are at the rear, close to server ports, helping keep cable lengths as short as possible and delivering to rack servers benefits traditionally offered only on blade servers. Hot-swappable power and fan modules can be accessed from the front panel, where status lights offer an at-a-glance view of switch operation. Front-to-back or back-to-front cooling is consistent with server designs, supporting efficient data center hot- and cold-aisle designs. Serviceability is enhanced with all customer-replaceable units accessible from the front panel.

Energy efficiency: The 10-Gbps switches help data centers operate within their space, power, and cooling parameters while reducing their carbon footprints. The switch power supplies are also capable of maintaining 90 percent efficiency at load conditions of as low as 25 percent utilization. This capability allows the switch to make efficient use of power while still being appropriately sized to support the conditions of a full system load.

Low latency: Cut-through switching enables these switches to support approximately 1 microsecond of port-to-port latency for any packet size with features enabled.

Intelligent Cisco Switched Port Analyzer (SPAN) and Encapsulated SPAN (ERSPAN): SPAN and ERSPAN can be used for troubleshooting and robust monitoring of traffic. The SPAN and ERSPAN capabilities are nondisruptive, with only extra bandwidth capacity used for SPAN and ERSPAN traffic. Enhancements include more efficient allocation of bandwidth to SPAN and ERSPAN traffic so that any fabric bandwidth not used for data traffic can be allocated to SPAN or ERSPAN traffic. The switch can support up to 31 line-rate SPAN and ERSPAN sessions.

Flexible buffer management: The 10-Gbps switches support a 25-MB packet buffer shared by every 3 ports of 40 Gigabit Ethernet or every 12 ports of 10 Gigabit Ethernet. The flexible buffer management capability allows dynamic tuning of the sizes of the shared and dedicated buffers in the event of congestion.

Multicast enhancements: These switches support line-rate Layer 2 and 3 multicast throughput for all frame sizes. They offer optimized multicast replication through the fabric and at the egress point. Support is provided for 32,000 multicast routes and for Internet Group Management Protocol (IGMP) snooping tables in hardware. Multicast enhancements include flow-based hashing for multicast traffic over a port channel and enhanced Bidirectional Protocol-Independent Multicast (Bidir-PIM) support. The switch also supports IP-based forwarding for IGMP snooping.

Inter-Switch Link (ISL): The Cisco Nexus 5672UP-16G switch supports 16-Gbps Fibre Channel ISLs in a Fibre Channel–only environment or, in the case of FCoE, 40-Gbps ISLs. With six such 40-Gbps links available, the ISLs support bandwidth of 240 Gbps. Improved buffer-to-buffer credits (up to 128) on the new switch now provide support for 16-Gbps Fibre Channel ISLs across distances of up to 16 kilometers.

For a complete list of the latest software features supported on the Cisco Nexus 5600 10-Gbps platform, see the product bulletin at https://www.cisco.com/c/en/us/products/collateral/switches/nexus-5000-series-switches/bulletin-c25-735319.html.

The Cisco Nexus 5600 10-Gbps platform supports a number of application scenarios, making it a versatile data center option.

Cisco Fabric Extender Architecture: High-Density Fabric Extender Aggregator

Cisco Fabric Extender Technology (FEX Technology) enables you to build a single, modular fabric that extends from Cisco Nexus switches to Cisco Unified Computing System ™ (Cisco UCS ® ) servers, to adapters (Cisco Adapter FEX), and to virtual machines (Cisco Data Center Virtual Machine FEX [VM-FEX]). FEX Technology is based on the emerging standard IEEE 802.1BR. Designing the network using FEX Technology provides flexibility, reduced cabling infrastructure, and a single point of management, helping customers scale their networks. When the 10-Gbps switches are part of a fabric that includes Cisco Nexus 2200 and 2300 platform fabric extenders, you can use these fabric extenders in single- or dual-connected mode, using enhanced virtual port-channel (vPC+) technology to two upstream 10-Gbps switches. Servers and end hosts can connect to single or dual Cisco Nexus 2200 and 2300 platform fabric extenders using Network Interface Card (NIC) teaming when the parent Cisco Nexus 5600 platform 10-Gbps switch has vPC+ enabled.

Following are some common deployment options using the Cisco Nexus 2000 Series (including the 2200 and 2300 platforms) and 5600 10-Gbps platform:

● Rack servers with 100 Megabit Ethernet, 1 Gigabit Ethernet, or 10 Gigabit Ethernet NICs the fabric extender can be physically located at the top of the rack, and the 10-Gbps switch can reside in the middle or at the end of the row, or the fabric extender and the 10-Gbps switch can both reside in the middle or at the end of the row

● Rack servers with 10 Megabit Ethernet NICs in full duplex mode connected using the Cisco Nexus 2248TP-E Fabric Extender in conjunction with the Cisco Nexus 5600 platform

● Mixed 1 and 10 Gigabit Ethernet environments in which rack servers are running at either speed in the same rack or in adjacent racks

● 10 Gigabit Ethernet and FCoE deployments using servers with Converged Network Adapters (CNAs) for unified fabric environments

● 10GBASE-T server connectivity with ease of migration from 1 to 10GBASE-T and effective reuse of structured cabling

● 1 and 10 Gigabit Ethernet blade servers with pass-through blades

● Low-latency, high-performance computing environments

In addition to these options, the 10-Gbps switches provide unique value as a high-density fabric extender aggregation platform. For example, the switches can be used in conjunction with the Cisco Nexus 2348UPQ, 2348TQ, 2332TQ, 2248PQ, 2232PP, 2248TP-E, 2232TM-E, 2232TM, 2248TP, and 2224TP Fabric Extenders as a high-density switching system, consolidating 10 Gigabit Ethernet connections in a single management plane. In addition, a variety of blade fabric extender options can be aggregated into the Cisco Nexus 5600 10-Gbps platform switches using 10 Gigabit Ethernet, providing a single point of management for blade server deployments.

Table 1 lists the fabric extenders that are supported by the Cisco Nexus 5600 10-Gbps platform switches. For more information about the products and the minimum software releases supported, see the Cisco Nexus 2200 and 2300 platform data sheets and release notes.

Table 1. Supported Fabric Extenders

32 x 1/10GBASE-T port host interfaces (SFP+) and up to 4 QSFP+ 10/40 Gigabit Ethernet fabric interfaces FCoE support up to 30m with Category 6a or 7 cables

48 x 1/10GBASE-T port host interfaces (SFP+) and up to 6 QSFP+ 10/40 Gigabit Ethernet fabric interfaces FCoE support up to 30m with Category 6a or 7 cables

48 x 1 and 10 Gigabit Ethernet and unified port host interfaces (SFP+) and up to 6 QSFP+ 10/40 Gigabit Ethernet fabric interfaces

24 x 100/1000BASE-T host interfaces and 2 x 10 Gigabit Ethernet fabric interfaces (SFP+)

48 x 100/1000BASE-T host interfaces and 4 x 10 Gigabit Ethernet fabric interfaces (SFP+)

48 x 100/1000BASE-T host interfaces and 4 x 10 Gigabit Ethernet fabric interfaces (SFP+ 32-MB shared buffer)

32 x 1/10 Gigabit Ethernet and FCoE host interfaces (SFP+) and 8 x 10 Gigabit Ethernet and FCoE fabric interfaces (SFP+)

48 x 1/10 Gigabit Ethernet SFP+ host interface and 4 x 40 Gigabit Ethernet (16 x 10 Gigabit Ethernet SFP+) network interfaces

32 x 1/10GBASE-T host interfaces and 8 x 10 Gigabit Ethernet (SFP+) uplink modules

32 x 1/10GBASE-T host interfaces and 8 x 10 Gigabit Ethernet (SFP+) uplink modules (lower power consumption and improved Bit Error Rate [BER])

16 x 1/10GBASE-KR internal host interfaces and 8 x 10 Gigabit Ethernet fabric interfaces (SFP+ network interfaces)

16 x 10GBASE-KR internal host interfaces and 8 x 10 Gigabit Ethernet fabric interfaces (SFP+ network interfaces)

16 x 10GBASE-KR internal host interfaces and 8 x 10 Gigabit Ethernet fabric interfaces (SFP+ network interfaces)

14 x 1/10GBASE-KR internal host interfaces and 8 x 10 Gigabit Ethernet fabric (SFP+ network interfaces)

Large-Scale Fabric (Layers 2 and 3): Leaf and Spine Architecture

Data center designs are evolving, with customers seeking to build large-scale nonblocking fabrics to accommodate different applications, creating patterns of heavy east-west and north-south traffic. The Cisco Nexus 5600 platform 10-Gbps switches are well suited for leaf and spine nodes in a Layer 2 or 3 fabric design. Leaf-and-spine designs using high-density and low-latency switches lead to flatter network architecture, allowing connections that scale from hundreds to more than 10,000 servers with high bidirectional bandwidth and helping ensure low-latency fabric with a low hop count. The spine switches create a nonblocking, low-latency fabric, forwarding packets between leaf switches. The leaf switches provide connectivity to servers. Use of a highly meshed architecture helps ensure the highest possible network availability with little impact on customer traffic in the event of a failure. The 10-Gbps switches can be deployed as Layer 2 or 3 spine or leaf switches, providing a high degree of design flexibility.

Cisco Unified Fabric combines data center and storage networks to deliver a single high-performance, highly available, and scalable network. With the Cisco Nexus 5600 10-Gbps platform switches, Cisco can support end-to-end data center convergence, from the server to storage, by delivering multihop FCoE capability in the data center. The FCoE capability complements the existing FCoE function on the Cisco Nexus 5600 10-Gbps platform. With this broad selection of standards-based FCoE switches, Cisco provides unified fabric support to both the access and core network layers, supporting all storage traffic (FCoE, Small Computer System Interface over IP [iSCSI], and Network-Attached Storage [NAS]) over a simplified infrastructure based on lossless 10 and 40 Gigabit Ethernet.

The Cisco Nexus 5600 10-Gbps platform switches can be deployed as high-density Small Form-Factor (SFF) access-layer switches to consolidate a large number of 10 Gigabit Ethernet servers in deployments that call for only a small number of hops from the server to the upstream network to reduce latency. They have a high density of 10 Gigabit Ethernet ports per rack unit, approximately 1 microsecond of latency port to port for any packet size, integrated line-rate Layer 2 and 3 features, scalability, and integrated data analytics with programmability. They address the needs of High-Performance Computing (HPC) and High-Frequency Trading (HFT) environments, for which InfiniBand solutions lack management visibility and high performance of bulk data transfers across traditional applications.

The capability to function in all these capacities helps protect investments in the data center with a deployment model in which additional features can be enabled as they are needed.

Cisco NX-OS Software Overview

NX-OS is a purpose-built data center operating system designed for performance, resiliency, scalability, manageability, and programmability. NX-OS meets Ethernet and storage networking requirements, providing a robust and comprehensive feature set that can meet the demanding requirements of virtualization and automation in present and future data centers. The enhanced Cisco fabric solution allows the transparent integration of the virtual and physical devices on a unified network. In addition, users can use the comprehensive NX-OS service set to create unique innovations for customized solutions. With its MIBs, native XML interface, and Command-Line Interface (CLI) like that of Cisco IOS ® Software, NX-OS provides drastically simplified management for the devices in which it runs.

Cisco Prime Data Center Network Manager

Cisco Prime ™ Data Center Network Manager (DCNM) provides LAN and SAN management capabilities for the Cisco Nexus and Cisco MDS 9000 Families. DCNM provides a GUI that reduces Operating Expenses (OpEx) compared to traditional CLI methods and allows efficient operation control, monitoring, provisioning, and troubleshooting for your NX-OS devices. The main features include the following:

● Unified fabric visibility and topology display with VMware vSphere integration shows the connectivity from the virtual machine to the VMware ESX host and to the switch and the storage array.

● Event aggregation and filtering helps you quickly find the information you need and identify network problems.

● Deployment wizards and user-modifiable templates help you implement best practices.

● Role-Based Access Control (RBAC) helps secure devices and provide appropriate delegation.

● Integrated domain dashboards, health monitoring, reporting, change tracking, and user auditing provides comprehensive management capabilities.

● Trend monitoring of ports and traffic allow you to optimize your existing resources and anticipate new resource requirements.


Problem: Battery drains quickly

We use our iPhones so much that battery life can be a problem, but in the Apple support forum, some people have been complaining about unusual, rapid battery drain. We found that our iPhone 8 drains quite quickly when playing AR games, but generally the battery life is pretty good. If you’re suffering with an iPhone 8 battery that drains quickly, here’s what to try:

Possible fixes:

  • Take a look at our guide on how to save battery life for a host of handy tips.
  • If those tips don’t work for you, then it’s probably worth trying a factory reset. Make sure you back up first, but after wiping your iPhone, consider setting it up as new — don’t restore your backup — and test to see if the battery problem returns. If it doesn’t, then it’s possible that something in your old settings or an app you had installed was causing the issue.
  • If you do still have battery issues after a factory reset and without restoring your backup, then it could be a hardware fault and you’re going to want to take it into Apple for further testing.

'Power' to return with final five episodes in January

Nov. 4 (UPI) -- Starz announced on Monday the final five episodes of Power will premiere on Jan. 5 at 8 p.m. EDT.

The episodes will close out the crime drama's sixth and final season. A spinoff series titled Power Book II: Ghost featuring Mary J. Blige, is in the works.

The mid-season finale feature series lead James 'Ghost' St. Patrick (Omari Hardwick) being shot and possibly killed by an unknown assailant.

Starz released a teaser trailer for the final five episodes featuring the seven possible shooters which include Tommy Egan (Joseph Sikora).

Power, from creator and showrunner Courtney A. Kemp and executive producer Curtis '50 Cent' Jackson, premiered on Starz in 2014. Naturi Naughton, Lela Loren and Shane Johnson also star.


8 Shows Like Good Witch You Should Watch If You Like Good Witch

Good Witch is back! After what seemed like forever, Hallmark's Good Witch Season 7 finally premiered on May 16, delivering a comforting return to the town of Middleton to catch up with Cassie (Catherine Bell) and Grace (Bailee Madison). But if you've already watched the premiere a million times and are tired of waiting for a new episode of Good Witch, you can always entertain yourself with more shows about witches, quirky small towns, and powerful women.

All of the little elements that make Good Witch such a fun series can be found in other shows, so if you're looking for something similar to watch next, we've got you covered! From magical teens to small-town drama, here are a few series like Good Witch that you should watch next!

Looking for more recommendations of what to watch next? We have a ton of them! And if you're looking for more hand-picked recommendations based on shows you love, we have those too.

The Good Witch (TV Movies)

The first and most obvious choice as a substitute is to watch any of Hallmark's The Good Witch TV movies that the series spun off from. It may seem crazy, but there are actually fans out there that didn't watch these movies before watching the TV show. If you're one of them, hop on these prequels ASAP and then do a series rewatch. You'll thank us later. They're full of storylines that have gotten shoutouts on the series, including Cassie's love story with her first husband, who left her a widow in the pilot. [Watch on Amazon Prime with Hallmark Movies Now]

Legacies

If you're looking for a series that has all the small-town drama of Good Witch with a little more magic and monsters on the side, Legacies is the show for you. Set in a small town with a secret magical school for youngsters, Legacies focuses on a group of teen witches, vampires, werewolves, and other supernatural creatures as they try to defend their home from weekly incursions of monsters. Be warned though, Legacies is a spin-off of The Originals, which is itself a spin-off of The Vampire Diaries, so binge-watching this show might tempt you to binge the other two, and that might occupy the rest of your year. [Watch on Netflix, The CW]

Gilmore Girls

Lauren Graham and Alexis Bledel, Gilmore Girls: A Year in the Life

This one might seem like an odd addition to the list, but there's just no denying the similarities between Gilmore Girls and Good Witch. They both follow a single mother raising her daughter in an eccentric American town with enough hijinks to create years of good TV. From the nosy mayor to the "new kid in town" romantic subplots, these two series surprisingly have more in common than not. The only real difference is that Lorelai (Lauren Graham) and Rory's (Alexis Bledel) "powers" are the ability to drink endless amounts of coffee and talk double-time. [Watch on Netflix]

Witches of East End

We can't imagine a world in which any fans of Good Witch have not also watched every season of Witches of East End, but if that's the case, you're in for a treat. This series might be less wholesome than you're looking for -- the benefits of being on Lifetime instead of Hallmark -- but it has that uncanny ability to melt your heart. The witches in the series also come complete with past lives and eternal youth in some cases, so there are so seriously cool flashbacks to keep things interesting when you're not focused on the steamy romances. [Watch on Hulu, IMDb TV (free with ads)]

The Secret Circle

If you loved Cassie's teenage daughter Grace's storylines in Good Witch, we suggest a short and sweet binge of The CW's The Secret Circle. Though it ventures a little further into the dark side of magic, The Secret Circle indulges in all the juicy teen drama of young witches discovering and learning to use their powers while trying to keep a lot of odd behavior secret. There's also a great mystery at the heart of the show, so even though it got canceled after only one season, it's still worth a look! [Watch on CW Seed]

Sweet Magnolias

Netflix's Sweet Magnolias may not have the supernatural element you love from Good Witch, but it's got all the same quaint, character-driven story arcs you'll know and love. A single mom in a small town finding unexpected love while gossipy townies get in the way at every turn? Yep, sure sounds like a great Good Witch alternative to us! And just like Good Witch, Sweet Magnolias makes the excellent point that your first epic love doesn't always have to be your last. [Watch on Netflix] [More shows like Sweet Magnolias]

When Calls the Heart

If you're looking for a show that's got major "kick back with a glass of wine and just forget about the world for a while" vibes, Hallmark's When Calls the Heart is your ticket. Set in frontier times, this series has all the good hallmarks (see what we did there?) of a feel-good story full of happiness and heartbreak. If you're looking for a slow-burn love story that just a wholesome as Cassie and Sam's, this should definitely be your next binge. And with seven seasons under its belt, this one will definitely keep you glued to your TV for a while. [Watch on Amazon Prime (for purchase)]

Charmed

Sarah Jeffery, Madeleine Mantock and Melonie Diaz, Charmed

If you're in the mood to double down on magical shenanigans and girl power, the CW's Charmed reboot has a modern take on a family of witches balancing their personal lives with their magical ones. Rather than a mother/daughter duo, Charmed tells the story of three sister witches whose problems range from rushing college sororities to fighting the Source of All Evil. Talk about women who can multi-task! This show also has a fun vibe that hooks you in and really lets you invest in the character's personal lives, just like Good Witch! [Watch on Netflix, The CW]


Powering a series circuit:

The loop concept is no problem by now and you definitely could figure how how to wire it, but how about powering a series circuit.

The second bullet point above states, “The total voltage of the circuit is the sum of the voltages across each LED”. This means you have to supply, at minimum, the sum of the forward voltages of each LED. Lets take a look at this by using the above circuit again as an example and lets assume the LED is a Cree XP-L driven at 1050mA with a forward voltage of 2.95V. The sum of three of these LED forward voltages is equal to 8.85Vdc. So theoretically, 8.85V is the minimum required input voltage to drive this circuit.

In the beginning, we mentioned using a constant current LED driver because these power modules can vary their output voltages to match the series circuit. As LEDs heat up their forward voltages change, so it’s important to use a driver that can vary its output voltage, but keep the same output current. For a deeper understanding of LED drivers take a look here. But, in general it’s important to make sure that your input voltage into the driver can deliver an output voltage equal to or greater than the 8.85V we figured above. Some drivers require inputting slightly more to account for powering the internal circuitry of the driver (the BuckBlock Driver needs a 2V overhead), while others have boosting (FlexBlock) features that allow you to input less.

Hopefully you are able to find a driver that can accomplish your LED circuit with the diodes in-series, however there are circumstances that might make it impossible. Sometimes the input voltage might not be enough to power multiple LEDs in-series, or maybe there are too many LEDs to have in-series or you just want to limit the cost of LED drivers. Whatever the reason, here is how to understand and configure a parallel LED circuit.


What are the 'Power' spin-off shows and when do they premiere?

The second series in the franchise is titled Power Book II: Ghost and will debut in a few months. The storyline picks up just days after the events of Power’s final episode, and follows several familiar faces, including Tariq St. Patrick (Michael Rainey Jr.), Tasha St. Patrick (Naturi Naughton), Cooper Saxe (Shane Johnson), and Tameika Robinson (Quincy Tyler Bernstine).

As fans learned in the OG drama’s last few moments (SPOILER ALERT!), Tariq is the one who killed his father, Ghost, but his mother Tasha is currently behind bars for the murder. 

Power Book II will focus on Tariq’s new life as a freshman in college "in which his desire to shed his father’s legacy comes up against the mounting pressure to save his family." Method Man and Mary J. Blige also join the show in mystery roles. 

As for the other three spin-offs, their casts are either shrouded in secrecy or have yet to be set, though we do know that each show revolves around a character already established in the world of Power.

Power Book III: Raising Kanan is the first prequel in the franchise, and will explore the early years of Kanan Stark (50 Cent) — aka the �s. It&aposs currently unclear in what capacity the rapper will appear on the series, but we don’t doubt that he’ll be on screen at some point.


Watch the video: Find a power series representation for fx = x9+x2. Determine interval of convergence (November 2021).