Libraries -- Marketing.

Nancy Heckman

Source: Statist. Surv., Volume 6, 113--141.

Abstract:
The popular cubic smoothing spline estimate of a regression function arises as the minimizer of the penalized sum of squares $sum_{j}(Y_{j}-mu(t_{j}))^{2}+lambda int_{a}^{b}[mu''(t)]^{2},dt$, where the data are $t_{j},Y_{j}$, $j=1,ldots,n$. The minimization is taken over an infinite-dimensional function space, the space of all functions with square integrable second derivatives. But the calculations can be carried out in a finite-dimensional space. The reduction from minimizing over an infinite dimensional space to minimizing over a finite dimensional space occurs for more general objective functions: the data may be related to the function $mu$ in another way, the sum of squares may be replaced by a more suitable expression, or the penalty, $int_{a}^{b}[mu''(t)]^{2},dt$, might take a different form. This paper reviews the Reproducing Kernel Hilbert Space structure that provides a finite-dimensional solution for a general minimization problem. Particular attention is paid to the construction and study of the Reproducing Kernel Hilbert Space corresponding to a penalty based on a linear differential operator. In this case, one can often calculate the minimizer explicitly, using Green’s functions.

It’s always interesting to know about some cool tricks that you can use when it comes to modelling within SOLIDWORKS. Well, within this blog we just happen to have one of those tricks for you. They always say a magician never

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This recipe is a great base for all your chicken salad ideas. Easily add grapes for a refreshing twist. Chopped pecans for the girls. It's all in the dressing. We all have a different preference on how much mayonnaise we like. Please change to your likings. The best part is you can use leftover chicken or do what I do...Costco has the white meat rotisserie chicken in a bag just waiting for you.  -- posted by shadowgirl...

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In the lead-up to the Truth Matters conference in October, we will be focusing our attention on the sufficiency, authority, and clarity of Scripture. Of our previous blog series, none better embodies that emphasis than Frequently Abused Verses. The following entry from that series originally appeared on September 21, 2015. -ed.

Few things are more destructive than misinterpreting God’s Word. A wrong interpretation can lead to physical harm (e.g., handling snakes based on Mark 16:18) or spiritual harm (e.g., consternation over one’s salvation in the absence of speaking in tongues).

Aside from misunderstanding the text as it is written, misinterpretation often happens when we ignore, or are ignorant of, the historical background of the text. We can easily forget that the divine words we read in each biblical account rise out of the milieu of each human author’s cultural context. And when we do, we run the risk of wrongly assuming why the authors wrote certain things, and what they meant, and how it applies to us. On the other hand, Scripture becomes so much clearer and more profound when understood in its original context.

Christ’s warning to the lukewarm Laodicean church takes on a new flavor when we understand how the city of Laodicea sat on an aqueduct of putrid water that was neither hot nor cold (Revelation 3:14–16). Exhortations to the suffering Philippians carry a greater force once we realize that Paul wrote them from his prison cell (Philippians 1:28–30). And Christ’s confrontations with the Pharisees are all the more condemning when we understand the blasphemy and hypocrisy of their works-righteousness (cf. Luke 20; John 8:12–59).

The modern trend of Christian contextualization is antithetical to a historical interpretation. Rather than taking the audience back to the original setting of the text at hand, many of today’s preachers labor to sever the biblical text from its historical moorings and transport it into a contemporary setting. Hence the explosion of sermons based on pop culture, racy subject matter, and social justice. Even the WWJD (What Would Jesus Do) juggernaut is symptomatic of this problem, by speculating about what Jesus might do, rather than examining what He did do.

Moreover, such an approach relegates the biblical text to the role of supporting cast in the preacher’s consumer-driven production. And when Scripture no longer holds primacy, the ability to play fast and loose with the biblical text grows. Nowhere is that trend more evident than in churches where growth is measured numerically rather than spiritually. By widening the narrow gate, seeker-sensitive churches have filled vast auditoriums with people who do not understand the cost of faith and repentance. Instead of being sensitive to the only true Seeker, they have pandered to the preferences of unbelievers.

Recently we discussed the dangers of a man-centered theology of salvation. Seeker-sensitive pastors routinely provide a path of least biblical resistance for the unbeliever to gain entry into God’s kingdom. And for many, Romans 10:9 is the shortcut they’ve been looking for: “If you confess with your mouth Jesus as Lord, and believe in your heart that God raised Him from the dead, you will be saved.”   

Paul could never have imagined his glorious, hope-filled promise would be exploited 2,000 years later as a two-step altar call formula—simply confess and believe. It has become a comfortable, spiritual Fast Pass for people who have no interest in submitting to the lordship of Christ.

Joseph Prince, a mega-church pastor, best-selling author, and TBN regular, offers this cheap invitation to those who visit his website:

The Bible tells us how to be saved and have eternal life: Believe in our hearts that Jesus died for our sins and was raised from the grave, and confess with our mouths that He is our Lord and Savior. . . . To be saved and to receive all that Jesus has done for you, you can make Him your Lord and Savior today by praying this prayer: “Lord Jesus, thank You for loving me and dying for me on the cross. Your precious blood washes me clean of every sin. You are my Lord and my Savior, now and forever. I believe that You rose from the dead and that You are alive today. Because of Your finished work, I am now a beloved child of God and heaven is my home. Thank You for giving me eternal life, and filling my heart with Your peace and joy. Amen” (emphasis added). ^[1] http://support.josephprince.org/index.php?/Knowledgebase/Article/View/124/22/a-is-jesus-christ-the-only-way-to-heaven-what-must-i-do-to-be-saved-and-have-eternal-life

Unfortunately, Joseph Prince’s textploitation is nothing unusual in the current evangelical climate. Regardless, reading the rest of Romans would be far more beneficial than tuning into Prince’s next broadcast. Paul made it clear elsewhere that our confession and faith are proven false if there is no fruit of repentance in our lives (Romans 6:1–18).

So with that in mind, what do we make of Paul’s simple confession of faith? Is it really all that’s required for salvation? This is why the original context is vital.

Paul wrote his theological magnum opus to Christians whose lives were under constant threat from the Roman government. The god-complex carried by deluded emperors developed into a cult of Caesar among the residents of Rome. Citizens needed to express their primary allegiance to their self-deified ruler by confessing “Caesar is lord.” Failure to do so was usually met with a grizzly death.

Paul’s readers needed to be encouraged to remain steadfast in their faithfulness to Christ under the threat of execution. The promise of salvation through confession and belief was never intended to provide a ticket to heaven by jumping through two easy hoops. It was the promise of eternal life to Christians who could very well lose their physical life because they confessed Jesus—not Caesar—as Lord.

The greatest tragedy of Prince’s mishandling of Romans 10:9 is that he has taken a profession of faith that cost many Christians their lives and turned it into a profession of faith that avoids any personal cost whatsoever. It may create more converts, but what exactly are they converting to?

John MacArthur warns strongly against treating Romans 10:9 as a minimum requirement for salvation. He points out that words like “Lord” and “believe” are loaded with implicit meaning that far exceeds a path of least resistance into God’s kingdom:

Many people acknowledge that Jesus is both the Son of God and Lord of the universe. But Paul is speaking of the deep, personal, abiding conviction that, without any reservation or qualification, will confess . . . Jesus as Lord, that is, will confess that Jesus is the believer’s own sovereign, ruling Lord, in whom alone he trusts for salvation and to whom he submits.

James teaches that even demons acknowledge truth about God. In a purely factual sense, they are completely orthodox in their theology. “You believe that God is one,” he writes. “You do well; the demons also believe, and shudder” (James 2:19). In other words, demons are monotheists. Satan and his fallen angels are also confirmed creationists, having watched God form the heavens and the earth simply by speaking them into existence. . . .

James’s point is that men can hold such demon belief, belief that is theologically correct but that does not include reception of Jesus as Lord. People may be well aware of their sin, be under deep conviction about it, and even have a great emotional sense of guilt from which they long to be delivered. But they do not repent and forsake the sin that causes the guilt, nor do they trust in the Savior who can forgive and remove the sin. Speaking about such people, the writer of Hebrews gives one of the most sobering warnings to be found in Scripture: “For in the case of those who have once been enlightened and have tasted of the heavenly gift and have been made partakers of the Holy Spirit, and have tasted the good word of God and the powers of the age to come, and then have fallen away, it is impossible to renew them again to repentance, since they again crucify to themselves the Son of God, and put Him to open shame” (Hebrews 6:4–6). ^[2] John MacArthur, The MacArthur New Testament Commentary: Romans 9–16 (Chicago: Moody Press, 1994) 73.

In other words, a person can verbally confess Christ’s lordship and affirm His resurrection, and still go to hell. Confession and belief are not hoops to be jumped through. They are the affirming signs of genuine repentance from sin, true saving faith in the resurrected Savior, and authentic obedience to His commands.

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