Most proofs of the characteristic polynomial of the companion matrix--an important specific case--proceed by induction, and start with a $latex 2\times2$ matrix. It strikes me that an inductive proof has more force (or at least makes more sense) if a larger matrix is used. In this case we will use a "large" (numerical analysts will …
Advice to Graduates: The Importance of an Objective
It's that time of the year again, when some students turn into wage-earners, others just move on to another curriculum, and still others just tank. Once the mediaeval outfits return to the closet while some who just came out of the closet try to push others they don't like into the closet, college faculty are …
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Internal Passports: The Bad Idea of Regional Visas
Some people think otherwise: State and local governments, the authorities best positioned to understand their own needs and capacities, should have a greater say in directing the flow of immigration. To that end, Washington could let states sponsor regional visas. Like H-1B employment visas, regional visas would last three years and could be extended to …
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In South Florida, Taming the People Won't Be Easy
But Palm Beach County sheriff Ric Bradshaw's going to try: Florida House and Senate budget leaders have awarded Palm Beach County Sheriff Ric Bradshaw $1 million for a new violence prevention unit aimed at preventing tragedies like those in Newtown, Conn., and Aurora, Colo., from occurring on his turf. Bradshaw plans to use the extra …
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Christians in the Military: They Really Don't Want Us Anymore
Looks that way: The Pentagon has released a statement confirming that soldiers could be prosecuted for promoting their faith: "Religious proselytization is not permitted within the Department of Defense...Court martials and non-judicial punishments are decided on a case-by-case basis...”. As I noted last year in my piece Go Where the Future Is: That last point …
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Persistent Issues in the Wave Equation for Piling for Both Forward and Inverse Methods
As a slight departure from the usual subjects of this blog, we offer this paper for discussion and consideration: This article is an overview of the current state of both forward and inverse analysis of wave propagation in piling. It begins with a summary of the typical acceptance procedure for the wave equation as applied …
When the Fence Went Away, So Did the American Dream
I recently noted an article about how the American Dream has downsized. The decline of our society as "aspirational" is one of the biggest shifts in attitude that has taken place in my lifetime, and is one I have noted on many occasions. But in the middle of the article, a survey was taken with …
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The Best Way for the Church to Restore the Family–and Itself–is to Be One
Standpoint's Mary Eberstadt hits the nail on the head: Specifically, because the churches need vibrant families — including families that reproduce themselves, as secular people tend not to do — they must also understand that strengthening the natural family is the first order of business in bringing people back to God. As has been amply documented by the British …
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In Facing Terror, Like Business, You're Washed Up When You Start Believing Your Own Lies
That, unfortunately, is where our government is at: In his State of the Union address to the American people earlier this year, Barack Obama declared that he was "confident" of achieving "our objective of defeating the core of al-Qaeda". Although he acknowledged the need to pursue the "remnants" of the terrorist group and its affiliates, …
When the Government Has To Approve Repairs to Your Church
In Palm Beach, where else? In its unanimous approval of the repair project, the board also gave Smith permission to replace wood transom windows above the front doors with bronze windows in a style that would closely match the door pattern. Smith plans to replace the church’s announcement sign with a slightly smaller bronze-framed case …
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