Quandles are distributive algebraic structures that were introduced by David Joyce [24] in his Ph.D. dissertation in 1979 and at the same time in separate work by Matveev [34]. Quandles can be used to construct invariants of the knots in the 3-dimensional space and knotted surfaces in 4-dimensional space. Quandles can also be studied on their own right as any non-associative algebraic structures. In this dissertation, we introduce f-quandles which are a generalization of usual quandles. In the first part of this dissertation, we present the definitions of f-quandles together with examples, and properties. Also, we provide a method of producing a new f-quandle from a given f-quandle together with a given homomorphism. Extensions of f-quandles with both dynamical and constant cocycles theory are discussed. In Chapter 4, we provide cohomology theory of f-quandles in Theorem 4.1.1 and briefly discuss the relationship between Knot Theory and f-quandles. In the second part of this dissertation, we provide generalized 2,3, and 4- cocycles for Alexander f-quandles with a few examples. Considering “Hom-algebraic Structures” as our nutrient enriched soil, we planted “quandle” seeds to get f-quandles. Over the last couple of years, this f- quandle plant grew into a tree. We believe this tree will continue to grow into a larger tree that will provide future fruit and contributions.

We present a novel Vertical External Cavity Surface Emitting Laser (VECSEL) cavity design which makes use of multiple interactions with the gain region under different angles of incidence in a single round trip. This design allows for optimization of the net, round-trip Group Delay Dispersion (GDD) by shifting the GDD of the gain via cavity fold angle while still maintaining the high gain of resonant structures. The effectiveness of this scheme is demonstrated with femtosecond-regime pulses from a resonant structure and record pulse energies for the VECSEL gain medium. In addition, we show that the interference pattern of the intracavity mode within the active region, resulting from the double-angle multifold, is advantageous for operating the laser in CW on multiple wavelengths simultaneously. Power, noise, and mode competition characterization is presented.

Francois Javier Garneau was born in Quebec in 1809 and died there in 1866. He has attracted more attention than any other French Canadian historian, although he had first achieved a certain popularity as a nationalist poet. Following the publication of Lord Durham's report, Garneau wrote the Histoire du Canada depuis sa Découverte jusqu'à nos Jours. In doing so he awakened a great interest in the past and has been a principal source of French Canadian nationalistic thought to the present day. As the "historien national" he is always lauded and praised. This was not always the case. Garneau did not follow the pattern of a typical French Canadian boy. He was never educated in a Church school and in fact refused a classical education if he had to become a priest in order to obtain it. Following his formal education he was apprenticed to a Scottish notary who had a library of liberal thought and it was from the liberal thinkers of his day that Garneau formed his philosophy. In 1851 he went to Europe and for two years associated with liberals in England. On his return to Quebec, he worked with the patriote party. He probably began to write his history after Durham's insults to the French Canadian people and published his first edition over three years, 1845, 1846 and 1848. He was as scientific as possible, but was not objective. He wrote interestingly and well and his book was the first of the histories of French Canada to tell the whole story and to carry a theme. His is a history of war and politics and he ignored as much as possible the religious side of the picture. He was a liberal of the type dangerous to the Church at that time, and because he was anti-clerical, the Church opposed him. A second edition in 1852 was changed in style and improved in documentation, but was exactly the same in philosophy. No doubt Church criticism increased. Garneau knew the final results of facing Church antagonism and appears to have written his third edition and then given it to a priest who could remove all material which was doctrinally incorrect before publication in 1859. This third edition is improved again in style and documentation, and is even more nationalistic than the two earlier ones. Because he submitted the third edition to a "competent ecclesiastic" for expurgation, Garneau is lauded, and the third edition is considered to be the one containing his true thoughts. French Canadian historians believe that the act of submission signified conversion. The priest in fact removed much of Garneau's anti-clerical thinking, but could not remove it all without changing the entire work. Evidence remains in the third edition to show that Garneau had not changed his mind. These historians also ignore letters which help to show that Garneau did not change his mind, yet the same letters are used to indicate his qualities as an historian. Without evidence, French Canadian historians insist that Garneau changed his mind on doctrine. They probably feel it necessary to avoid using material suggesting that he had not. Garneau was a nationalistic historian who produced a cult of nationalist writers and prompted an awareness of a glorious past. To keep this awareness alive, French Canadian writers, virtually all Roman Catholic and nationalistic, ignore what is distasteful to them, presumably in order to promote his popularity and their own ends. Nobody seems to have carefully compared the second and third editions, nor to have combined the results of such a comparison with the evidence provided by the printed letters. Garneau's philosophy had been formed by education and experience and it did not change. There is little difference in the two editions except in style, documentation and emphasis; the philosophy, although diluted in the third edition, has not been entirely destroyed. / Arts, Faculty of / History, Department of / Graduate

If an artist were to reproduce on canvas Pisemsky's Muse, from the evidence of the scattered "objective detailed" analyses of his critics, the Muse would definitely be the ugliest thing that any author could choose for his "inspirational" source. The purpose of this study is to illustrate the unfair position accorded Pisemsky in Russian dramaturgy and to assign him a proper place in Russian drama by fresh evaluation of his abilities as the dramatist. The Introduction suggests the possible reasons for which Pisemsky was placed in an oblivion. It also argues that the scepticism, which penetrated some of his works, even if it were somewhat peculiar to him in nature, was definitely aroused by the confusing multi-party Russia of the 1860's and 1870's. Chapter One retraces the more important themes in Russian drama in an attempt to place Pisemsky in the tradition. Chapter Two is a detailed analysis of the lingering critical attitudes toward Pisemsky which claim that his works lacked the revolutionary zeal for improvement of Russia, and that he was not a playwright but an author of pamphlets. In Chapter Three an attempt is made to define the main aspects of Pisemsky's art through his letters and views implicit in his plays. It is also suggested in this Chapter that Pisemsky's plays were revolutionary in their own way, and that they were not directed at the "yawning space", but, to people, directed with harsh rebuke, yet with sincere hope in an eventually brighter future. Chapter Four and the Conclusion are devoted to the analyses of his plays in an effort to show that many of them, in their theme, structure, form and other traditional elements of drama, indeed secure him much better place in Russian dramaturgy than hitherto given him. / Arts, Faculty of / Central Eastern Northern European Studies, Department of / Graduate

This thesis presents Thomas F. Torrance's Trinitarian soteriology, and as such seeks to combine the two most common but often separately treated doctrines in his theological cogitation: Trinity and soteriology. It argues that in a circular manner, Torrance's Trinitarian theology is explicitly soteriological and his soteriology is explicitly Trinitarian. This is because he (1) follows Barth's proposal that God's Being is inseparable from his Act, and vice versa, and (2) consistently employs his comprehensive theological rule that the Trinity is 'the ground and grammar of theology.' As such, this thesis also argues that not only is Torrance's soteriology Trinitarian, but that his soteriology could only be presented, understood and appreciated as Trinitarian. Non-trinitarian or implicitly Trinitarian readings of his soteriology cannot but fail to do justice to Torrance's theological consistency and genius. Furthermore, this thesis argues that Torrance's Trinitarian soteriology is consistent with his scientific and evangelical theology. On the one hand, Torrance's soteriological formulation follows scientific principles because he understands both the arche and telos of human salvation in strict accordance with the Being, Persons and Work of the Triune God. This is referred in the thesis as Torrance's kataphysic soteriology. On the other hand, Torrance's soteriological formulation follows an evangelical procedure grounded in the evangelical content of revelation. Because the content of God's Self-revelation is the Triune God reconciling the world to himself, Torrance understands that the Three Persons are actively involved in the salvific economy in strict accordance with their hypostases as Father, Son and Holy Spirit. The evangelical procedure and sketch that Torrance employs is derived from 2 Corinthians 13:14, 'the grace of the Lord Jesus Christ, the love of God and the fellowship of the Holy Spirit.' For Torrance, the ultimate telos of human salvation is participation in the very Life and Love of the Triune God. This may be referred to as humanity's perichoretic participation in the Communion of Love that God is. Humanity's sharing in the Triune Communion, however, is a mediated participation, encapsulated in the Athanasian aphorism 'from the Father through the Son in the Spirit and in the Spirit through the Son to the Father.' All three Persons of the Triune God fulfil distinct salvific agencies in accordance to their hypostases, but their distinct agencies have a united source and goal: the mediation of reconciliation with the Triune God. It is also argued that our participation in the Triune Communion is a human participation, or that we relate with the Triune God as humanized humans rather than as metamorphosized divine beings.

Research focusing on static scenes with static objects is omitting the time factor from real life examples we are trying to study. Can we say that a lifeguard looking for a drowning man is using the same brain processes that were observed in the laboratory for static scenes? We can conclude that a static scene is a big simplification of the task itself. The aim of this thesis is to prepare a tool which would allow researching dynamic scenes and thus broadening the possibilities of visual detection tasks at hand. Along the tool we also present a couple of simplified examples with which we would like to demonstrate the utilization of the tool. All concluding with a final experiment in which we will try to detect masked patterns in a noisy environment. 1

As the technology is advances the reduced size of hardware gives rise to an additive 1/f baseband noise. This additive 1/f noise is a system noise generated due to miniaturization of hardware and affects the lower frequencies. Though 1/f noise does not show much effect in wide band channels because of its nature to affect only certain frequencies, 1/f noise becomes a prominent in OFDM communication systems where narrow band channels are used. in this thesis, I study the effects of 1/f noise on the OFDM systems and implement algorithms for estimation and suppression of the noise using Kalman filter. Suppression of the noise is achieved by subtracting the estimated noise from the received noise. I show that the performance of the system is considerably improved by applying the 1/f noise suppression.

"Undertaken from the point of view of the librarian, this appraisal of F. Scott Fitzgerald, one of the controversial figures of the 1920's and 1930's, presents information about his life and work, indicates his acceptance as revealed through reviewers' reactions, and assesses his position as a serious writer. The paper deals only with the following books which have appeared in hard covers: This Side of Paradise, Flappers and Philosophers, The Beautiful and Damned, The Vegetable, The Great Gatsby, All the Sad Young Men, Tender is the Night, Taps at Reveille, The Last Tycoon, The Portable F. Scott Fitzgerald, The Crack-Up, Stores, and Afternoon of an Author. The reviews' reactions were secured from reviews located through Book Review Digest"--Introduction. / Carbon copy of typescript. / "June, 1959." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Sarah Rebecca Reed, Professor Directing Paper. / Includes bibliographical references (leaves 77-87).

This video offers some quick questions/points that might be considered when writing about Fitzgerald's short story. / https://dc.etsu.edu/lit-outlines-complete-oer/1007/thumbnail.jpg

We define two related invariants for a d-dimensional local ring (R,m,k) called syzygy and differential symmetric signature by looking at the maximal free splitting of reflexive symmetric powers of two modules: the top dimensional syzygy module of the residue field and the module of Kähler differentials of R over k. We compute these invariants for two-dimensional ADE singularities obtaining 1/|G|, where |G| is the order of the acting group, and for cones over elliptic curves obtaining 0 for the differential symmetric signature. These values coincide with the F-signature of such rings in positive characteristic.