Products of Representations Characterize the Products of Dispersions and the Consistency of Beliefs

A "dispersion" specifies the relative probability between any two elements of a finite domain. It thereby partitions the domain into equivalence classes separated by infinite relative probability. The paper's novelty is to numerically represent not only the order of the equivalence classes, but also the "magnitude" of the gaps between them. The paper's main theorem is that the many products of two dispersions are characterized algebraically by varying the magnitudes of the gaps between each factor's equivalence classes. An immediate corollary is that the many beliefs consistent with two strategies are characterized by varying each player's "steadiness" in avoiding various zero-probability optionsconsistent beliefs, relative probability

Popular Religious Thought in Medieval England as Reflected in the Mystery Play Cycles of York, Toweley, Coventry, and Chester

The particular plays that have been selected to form the basis for this study are especially well suited for this purpose. They are, first of all, plays which enjoyed a long popularity (from the early 1300’s to the late l500\u27s). Consequently their validity as reflections or contemporary religious thinking is strengthened. In the second place, these particular plays were produced and performed, not by professional dramatists and actors, but by the ordinary people of England. And so their claim of being the reflection of the thoughts of the common people is also strengthened. In addition, since these plays are examples of plays from four distinct population areas, and since they represent in the aggregate a total of almost one hundred fifty separate dramatic productions, it is hoped that they will prove to portray a fairly accurate cross section of religious expression

The Concept of ’σδσ’ς in the Book of Acts

The aim of this thesis is to examine the Old Testament and rabbinic literature to see what role, if any, they played in the formation of the ’σδσ’ς concept of Acts. The Septuagint in particular deserves attention since it held such an important position in the Apostolic Church and so largely affected the writers of the New Testament. As H. B. Swete remarks, the New Testament writers not only were familiar with the Septuagint; but were saturated with its thought and vocabulary

2023-3 Dynamic Programming for Pure-Strategy Subgame Perfection in an Arbitrary Game

This paper uses value functions to characterize the pure-strategy subgame-perfect equilibria of an arbitrary, possibly infinite-horizon game. It specifies the game’s extensive form as a pentaform (Streufert 2023p, arXiv:2107.10801v4), which is a set of quintuples formalizing the abstract relationships between nodes, actions, players, and situations (situations generalize information sets). Because a pentaform is a set, this paper can explicitly partition the game form into piece forms, each of which starts at a (Selten) subroot and contains all subsequent nodes except those that follow a subsequent subroot. Then the set of subroots becomes the domain of a value function, and the piece-form partition becomes the framework for a value recursion which generalizes the Bellman equation from dynamic programming. The main results connect the value recursion with the subgame-perfect equilibria of the original game, under the assumptions of upper- and lower-convergence. Finally, a corollary characterizes subgame perfection as the absence of an improving one-piece deviation

The Mystical Union of the Believer with Christ

There is a certain restless dissatisfaction in man as he pursues his daily tasks and endeavors to enjoy his present life to the full. In the case of the believer, there is not this uncertainty and groping. But in the case of the unconverted, there is many a one who substitutes an “unknowab1e Infinity for the true God. Man will strive earnestly to satisfy his craving after the true Reality, but rarely, if ever, will he try to find the truth about God in His Word. Instead of this objective source, man seeks communion with nature and thus hopes to find God there. He seems to feel that there God is present. However, we shall see that this knowledge of God\u27s presence is a limited one, and that man has much to hope for, even though he realizes the presence of God in this way

Dynamic Programming for Pure-Strategy Subgame Perfection in an Arbitrary Game

This paper uses value functions to characterize the pure-strategy subgame-perfect equilibria of an arbitrary, possibly infinite-horizon game. It specifies the game's extensive form as a pentaform (Streufert 2023p, arXiv:2107.10801v4), which is a set of quintuples formalizing the abstract relationships between nodes, actions, players, and situations (situations generalize information sets). Because a pentaform is a set, this paper can explicitly partition the game form into piece forms, each of which starts at a (Selten) subroot and contains all subsequent nodes except those that follow a subsequent subroot. Then the set of subroots becomes the domain of a value function, and the piece-form partition becomes the framework for a value recursion which generalizes the Bellman equation from dynamic programming. The main results connect the value recursion with the subgame-perfect equilibria of the original game, under the assumptions of upper- and lower-convergence. Finally, a corollary characterizes subgame perfection as the absence of an improving one-piece deviation.Comment: 56 pages, 7 figures. Version 3 provides better non-convergent examples in Section 2.

The Doctrine Of The Church and Ministry According to Dr. Walther, in Relation to the Romanizing Tendencies Within The Lutheran Church

When one studies the writings of Dr. Walther in the field of the doctrine of the Church and the Ministry, one cannot fail to notice his peculiar approach to this locus of theology. In employing the word \u27peculiar; we do so advisedly. In a certain sense, he expresses the same doctrine proclaimed by the martyrs of apostolic days. In this respect, Walther is ecumenical, not peculiarly original. On the other hand, placing his theories beside the theories of his contemporaries, we must admit that Walther is an exception to the rule