Application of ultraspherical polynomials to forced oscillations of a third-order non-linear system

In this paper the method of ultraspherical polynomial approximation is applied to study the steady-state response in forced oscillations of a third-order non-linear system. The non-linear function is expanded in ultraspherical polynomials and the expansion is restricted to the linear term. The equation for the response curve is obtained by using the linearized equation and the results are presented graphically. The agreement between the approximate solution and the analog computer solution is satisfactory. The problem of stability is not dealt with in this paper.

A new type of high-order elements based on the mesh-free interpolations

We propose a new type of high-order elements that incorporates the mesh-free Galerkin formulations into the framework of finite element method. Traditional polynomial interpolation is replaced by mesh-free interpolations in the present high-order elements, and the strain smoothing technique is used for integration of the governing equations based on smoothing cells. The properties of high-order elements, which are influenced by the basis function of mesh-free interpolations and boundary nodes, are discussed through numerical examples. It can be found that the basis function has significant influence on the computational accuracy and upper-lower bounds of energy norm, when the strain smoothing technique retains the softening phenomenon. This new type of high-order elements shows good performance when quadratic basis functions are used in the mesh-free interpolations and present elements prove advantageous in adaptive mesh and nodes refinement schemes. Furthermore, it shows less sensitive to the quality of element because it uses the mesh-free interpolations and obeys the Weakened Weak (W2) formulation as introduced in [3, 5].

Fracture Behavior of Multidirectional DCB Specimen: Higher-Order Beam Theories

Mathematical models, for the stress analysis of symmetric multidirectional double cantilever beam (DCB) specimen using classical beam theory, first and higher-order shear deformation beam theories, have been developed to determine the Mode I strain energy release rate (SERR) for symmetric multidirectional composites. The SERR has been calculated using the compliance approach. In the present study, both variationally and nonvariationally derived matching conditions have been applied at the crack tip of DCB specimen. For the unidirectional and cross-ply composite DCB specimens, beam models under both plane stress and plane strain conditions in the width direction are applicable with good performance where as for the multidirectional composite DCB specimen, only the beam model under plane strain condition in the width direction appears to be applicable with moderate performance. Among the shear deformation beam theories considered, the performance of higher-order shear deformation beam theory, having quadratic variation for transverse displacement over the thickness, is superior in determining the SERR for multidirectional DCB specimen.

Order to pay Gershom Seixas for keeping school

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Order to pay Aaron Levy, regarding K. K. Mikve Israel

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Vedestä vai Hengestä? : Uuras Saarnivaaran kasteteologia

Of water or the Spirit? Uuras Saarnivaara s theology of baptism The aim of the study was to investigate PhD and ThD Uuras Saarnivaara s views on baptism as well as their possible changes and the reasons for them. Dr Saarnivaara said himself that he searched for the truth about the relationship between baptism and faith for decades, and had faltered in his views. The method of this research is systematic analysis. A close study of the source material shows that Dr Saarnivaara s views on baptism have most likely changed several times. Therefore, special attention was paid to the time periods defined by when his literary works were published. This resulted in revealing the different perspectives he had on baptism. The fact that Dr Saarnivaara worked on two continents Europe and North America added a challenge to the research process. At the beginning of the research, I described Dr Saarnivaara s phases of life and mapped out his vast literary production as well as presented his theological basis. Saarnivaara s theological view on the means of grace and their interrelation in the church was influenced by the Laestadian movement, which caused him to adopt the view that the Holy Spirit does not dwell in the means of grace, but in the believers. Thus the real presence of Christ in the means of grace is denied. God s word is divided into Biblical revelation and proclamation by believers through the means of grace. Also, the sacraments are overshadowed by the preached word. Because grace is received through the word of the gospel preached publicly or privately by a believer, the preacher s status gains importance at the expense of the actual means of grace. Saarnivaara was intrigued by the content of baptism from the time he was a student until the end of his life. As a young theologian, he would adopt the opinions of his teachers as well as the view of the Evangelical Lutheran Church of Finland, which at the time was dominated by the pietistic movement and the teachings of J. T. Beck. After Saarnivaara had converted to the Laestadian movement, moved to the United States and started his Luther research, he adopted a view on baptism which was to a great extent in accordance with Luther and the Lutheran Symbolical Books. Saarnivaara considered his former views on baptism unbiblical and publicly apologised for them. In the 1950s, after starting his ministry within the Finnish neopietistic movements, Saarnivaara adopted a Laestadian-neopietistic doctrine of baptism. During his Beckian-pietistic era, Saarnivaara based his baptism theology on the event of the disciples of Jesus being baptised by John the Baptist, the revival of Samaria in the Book of Acts and the conversion of Cornelius and his family, all cases where the receiving of the Holy Spirit and the baptism were two separate events in time. In order to defend the theological unity of the Bible, Saarnivaara had to interpret Jesus teachings on baptism in the Gospels and the teachings of the Apostles in the New Testament letters from a viewpoint based on the three events mentioned above. During his Beckian-pietistic era, the abovementioned basic hermeneutic choice caused Saarnivaara to separate baptism by water and baptism by the Holy Spirit in his salvation theology. Simultaneously, the faith of a small child is denied, and rebirth is divided into two parts, the objective and the subjective, the latter being moved from the moment of baptism to a possible spiritual break-through at an age when the person possesses a more mature understanding. During his Laestadian-Lutheran era, Saarnivaara s theology of baptism was biblically consistent and the same for all people regardless of the person s age. Small children receive faith in baptism through the presence of Christ. The task of other people s faith is limited to the act of bringing the child to the baptism so that the child may receive his/her own faith from Christ and be born again as a child of God. The doctrine of baptism during Saarnivaara s Laestadian-neopietistic era represents in many aspects the emphases he presented during his first era, although they were now partly more radical. Baptism offers grace; it is not a means of grace. Justification, rebirth and salvation would take place later on when a person had reached an age with a more mature understanding through the word of God. A small child cannot be born again in baptism because being born again requires personal faith, which is received through hearing and understanding the law and the gospel. Saarnivaara s views on baptism during his first and third era are, unlike during his second era, quite controversial. The question of the salvation of a small child goes unanswered, or it is even denied. The central question during both eras is the demand of conversion and personal faith at a mature age. The background for this demand is in Saarnivaara s anthropology, which accentuates man s relationship to God as an intellectual and mental matter requiring understanding, and which needs no material instruments. The two first theological eras regarding Saarnivaara s doctrine of baptism lasted around ten years. The third era lasted over 40 years until his death.

Part of order of service and Hebrew prayer, recommended during the revolution

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Theological Exegesis in the Canonical Context : Brevard S. Childs' Methodology of Biblical Theology

Modern Christian theology has been at pain with the schism between the Bible and theology, and between biblical studies and systematic theology. Brevard Springs Childs is one of biblical scholars who attempt to dismiss this “iron curtain” separating the two disciplines. The present thesis aims at analyzing Childs’ concept of theological exegesis in the canonical context. In the present study I employ the method of systematic analysis. The thesis consists of seven chapters. Introduction is the first chapter. The second chapter attempts to find out the most important elements which exercise influence on Childs’ methodology of biblical theology by sketching his academic development during his career. The third chapter attempts to deal with the crucial question why and how the concept of the canon is so important for Childs’ methodology of biblical theology. In chapter four I analyze why and how Childs is dissatisfied with historical-critical scholarship and I point out the differences and similarities between his canonical approach and historical criticism. The fifth chapter attempts at discussing Childs’ central concepts of theological exegesis by investigating whether a Christocentric approach is an appropriate way of creating a unified biblical theology. In the sixth chapter I present a critical evaluation and methodological reflection of Childs’ theological exegesis in the canonical context. The final chapter sums up the key points of Childs’ methodology of biblical theology. The basic results of this thesis are as follows: First, the fundamental elements of Childs’ theological thinking are rooted in Reformed theological tradition and in modern theological neo-orthodoxy and in its most prominent theologian, Karl Barth. The American Biblical Theological Movement and the controversy between Protestant liberalism and conservatism in the modern American context cultivate his theological sensitivity and position. Second, Childs attempts to dismiss negative influences of the historical-critical method by establishing canon-based theological exegesis leading into confessional biblical theology. Childs employs terminology such as canonical intentionality, the wholeness of the canon, the canon as the most appropriate context for doing a biblical theology, and the continuity of the two Testaments, in order to put into effect his canonical program. Childs demonstrates forcefully the inadequacies of the historical-critical method in creating biblical theology in biblical hermeneutics, doctrinal theology, and pastoral practice. His canonical approach endeavors to establish and create post-critical Christian biblical theology, and works within the traditional framework of faith seeking understanding. Third, Childs’ biblical theology has a double task: descriptive and constructive, the former connects biblical theology with exegesis, the later with dogmatic theology. He attempts to use a comprehensive model, which combines a thematic investigation of the essential theological contents of the Bible with a systematic analysis of the contents of the Christian faith. Childs also attempts to unite Old Testament theology and New Testament theology into one unified biblical theology. Fourth, some problematic points of Childs’ thinking need to be mentioned. For instance, his emphasis on the final form of the text of the biblical canon is highly controversial, yet Childs firmly believes in it, he even regards it as the corner stone of his biblical theology. The relationship between the canon and the doctrine of biblical inspiration is weak. He does not clearly define whether Scripture is God’s word or whether it only “witnesses” to it. Childs’ concepts of “the word of God” and “divine revelation” remain unclear, and their ontological status is ambiguous. Childs’ theological exegesis in the canonical context is a new attempt in the modern history of Christian theology. It expresses his sincere effort to create a path for doing biblical theology. Certainly, it was just a modest beginning of a long process.

One Word, One Body, One Voice : Studies in Apophatic Theology and Christocentric Anthropology in Gregory of Nyssa

The thesis consists of five international congress papers and a summary with an introduction. The overarching aim of the studies and the summary is to examine the inner coherency of the theological and anthropological thinking of Gregory of Nyssa (331-395). To the issue is applied an "apophatic approach" with a "Christological focus". It is suggested that the coherency is to be found from the Christological concept of unity between "true God" and "true man" in the one person of Jesus Christ. Gregory is among the first to make a full recognition of two natures of Christ, and to use this recognition systematically in his writings. The aim of the studies is pursued by the method of "identification", a combination of the modern critical "problematic method" and Gregory's own aphairetic method of "following" (akolouthia). The preoccupation with issues relating to the so-called Hellenization of Christianity in the patristic era was strong in the twentieth-century Gregory scholarship. The most discussed questions have been the Greek influence in his thought and his philosophical sources. In the five articles of the thesis it is examined how Gregory's thinking stands in its own right. The manifestly apophatic character of his theological thinking is made a part of the method of examining his thought according to the principles of his own method of following. The basic issue concerning the relation of theology and anthropology is discussed in the contexts of his central Trinitarian, anhtropological, Christological and eschatological sources. In the summary the Christocentric integration of Gregory's thinking is discussed also in relation to the issue of the alledged Hellenization. The main conclusion of the thesis concerns the concept of theology in Gregory. It is not indebted to the classical concept of theology as metaphysics or human speculation of God. Instead, it is founded to the traditional Judeo-Christian idea of God who speaks with his people face to face. In Gregory, theologia connotes the oikonomia of God's self-revelation. It may be regarded as the state of constant expression of love between the Creator and his created image. In theology, the human person becomes an image of the Word by which the Father expresses his love to "man" whom he loves as his own Son. Eventually the whole humankind, as one, gives the divine Word a physical - audible and sensible - Body. Humankind then becomes what theology is. The whole humanity expresses divine love by manifesting Christ in words and deeds, singing in one voice to the glory of the Father, the Son and the Holy Spirit.

Ihanne ja todellisuus : Jäsenyyteen sitoutuminen Suomen evankelis-luterilaisessa kirkossa 1960-luvulta 2000-luvulle

The subject of the study is the ideal and reality of commitment to membership in the Evangelical Lutheran Church of Finland from the 1960s to the 2000s. The research task is to ascertain what manner of commitment the Evangelical Lutheran Church of Finland expects from its members (the ideal) and how in reality membership of the Church is realized (empiria). The research object is also to study the extent to which the ideal of commitment evinced by the Church and the actual relation of commitment to the Church changed during the research period. Additionally, those factors were analysed which influence the relation between the ideal and reality of commitment. In the analysis of the ideal of commitment the research data are official documents of the Evangelical Lutheran Church of Finland. They include confessions of the Church, Catechisms, Christian doctrine, joint strategies and plans of the Church, likewise the Church Act and Church Order. The reality of commitment is explored on the basis of Church membership, participation in parish activity and the private practice of religion, likewise attitude to Christian faith. The empirical data of the study comprise Church statistics, material from Statistics Finland and relevant surveys implemented during the research period. The ideal of commitment alongside membership includes knowing the basic tenets of Christian faith and family life based on prayer and participation in liturgical cycles. A member of the Church is expected to take care of his/her faith by living in participation of the Word and sacrament, bearing responsibility for the parish and faithfully discharging his/her worldly obligations. There have been no major changes in the ideal of commitment during the research period. On the contrary, the reality of commitment has changed. Although the majority of Finns are still members of the Church, there has been a constant decline in their share of the population. The same can be stated with respect to parish life. This has its own strengths, among them Church rites, parish activity around feast days and also work with children and confirmation training. However, the general trend is towards a decline in participation. There has also been a decrease in commitment to belief in God as taught by the Church. On the other hand, private religious observance has not changed at all. From the perspective of commitment the Evangelical Lutheran Church of Finland exists in a state of tension between the theological ideal and sociological empiria. Matters exerting a particular influence over the relation between ideal and reality are communality and varying conceptions of the Church, likewise contextuality and the related private Christianity. Societal change poses a challenge to traditional Church communality. A decline in communality has in turn led to a decline in belonging to the Church. Weakening awareness of membership has undermined the handing down of the tradition among younger generations. Modernization has influence the identity of the Church and brought the Church to an internal divergence. This way it has been able to retain its structure as a folk church but at the same time it has lost its opportunities for the formation of a clear identity. The Church has adjusted to societal change by outward-directed activities (performance) alongside the purely religious message (function). The tension between an unchanged message and a changed operating environment has increased. The challenge of contextuality has led the Church to review parish life, the nature of teaching and activity and the language used by the Church, likewise the cultural modus. Increasingly privatized Christianity challenges above all the theology and teaching of the Church, but also the life of worship and relation to cultural life.

Eru Ilúvatar : Jumala J.R.R. Tolkienin legendariumissa

The purpose of my research is to inquire into the essence and activity of God in the legendarium of the English philologist and writer J.R.R. Tolkien (1892-1973). The legendarium, composed of Tolkien’s writings related to Middle-earth, was begun when he created two Elvish languages, Quenya based on Finnish, Sindarin based on Welsh. Tolkien developed his mythology inspired by Germanic myths and The Kalevala. It is a fictional ancient history set in our world. The legendarium is monotheistic: God is called Eru ‘The One’ and Ilúvatar ‘Father of All’. Eru is the same as the Christian God, for Tolkien wanted to keep his tales consistent with his faith. He said his works were Christian by nature, with the religious element absorbed into the story and the symbolism. In The Silmarillion, set in the primeval ages of Middle-earth, the theological aspects are more conspicuous, while in The Lord of the Rings, which brings the stories to an end, they are mostly limited to symbolic references. The legendarium is unified by its realistic outlook on creaturely abilities and hope expressing itself as humbly defiant resistance. ”The possibility of complexity or of distinctions in the nature of Eru” is a part of the legendarium. Eru Ilúvatar is Trinitarian, as per Tolkien’s faith. Without contextual qualifiers, Eru seems to refer to God the Father, like God in the Bible. Being the creator who dwells outside the world is attributed to Him. The Holy Spirit is the only Person of the Trinity bestown with names: the Flame Imperishable and the Secret Fire. When Eru creates the material world with His word, He sends the Flame Imperishable to burn at the heart of the world. The Secret Fire signifies the Creative Power that belongs to God alone, and is a part of Him. The Son, the Word, is not directly mentioned, but according to one writing Eru must step inside the world in order to save it from corruption, yet remain outside it at the same time. The inner structure of the legendarium refers to the need for a future salvation. The creative word of Eru, “Eä! Let these things Be!”, probably has a connection with the Logos in Christianity. Thus we can find three “distinctions” in Eru: a Creator who dwells outside the world, a Sustainer who dwells inside it and a Redeemer who shall step inside it. Some studies of Tolkien have claimed that Eru is distant and remote. This seems to hold water only partially. Ilúvatar, the Father of All, has a special relation with the Eruhíni, His Children, the immortal Elves and the mortal Men. He communicates with them directly only through the Valar, who resemble archangels. Nevertheless, only the Children of Eru can fight against evil, because their tragic fortunes turn evil into good. Even though religious activities are scarce among them, the fundamental faith and ultimate hope of the “Free Peoples” is directed towards Eru. He is present in the drama of history as the “Author of the Story”, who at times also interferes with its course through catastrophes and eucatastrophes, ‘good catastrophes’. Eru brings about a catastrophe when evil would otherwise bring good to an end, and He brings about a eucatasrophe when creaturely strength is not sufficent for victory. Victory over corruption is especially connected with mortal Men, of whom the most (or least) insignificant people are the Hobbits. However, because of the “primeval disaster” (that is, fall) of Mankind, ultimate salvation can only remain open, a hope for the far future.

Random vibration of a second order non-linear elastic system

A method is presented for obtaining, approximately, the response covariance and probability distribution of a non-linear oscillator under a Gaussian excitation. The method has similarities with the hierarchy closure and the equivalent linearization approaches, but is different. A Gaussianization technique is used to arrive at the output autocorrelation and the input-output cross-correlation. This along with an energy equivalence criterion is used to estimate the response distribution function. The method is applicable in both the transient and steady state response analysis under either stationary or non-stationary excitations. Good comparison has been observed between the predicted and the exact steady state probability distribution of a Duffing oscillator under a white noise input.

Ultraspherical polynomials approach to the study of third-order non-linear systems

In this study, the Krylov-Bogoliubov-Mitropolskii-Popov asymptotic method is used to determine the transient response of third-order non-linear systems. Instead of averaging the non-linear functions over a cycle, they are expanded in ultraspherical polynomials and the constant term is retained. The resulting equations are solved to obtain the approximate solution. A numerical example is considered and the approximate solution is compared with the digital solution. The results show that there is good agreement between the two values.