In a transferable utility context, Choo and Siow (2006) introduced a competitive model of the marriage market with gumbel distributed stochastic part, and derived its equilibrium output, a marriage match- ing function. The marriage matching function defines the gains generated by a marriage between agents of prescribed types in terms of the observed frequency of such marriages within the population, relative to the number of unmarried individuals of the same types. Left open in their work is the issue of existence and uniqueness of equilibrium. We resolve this question in the affirmative, assuming the norm of the gains matrix (viewed as an operator) to be less than two. Our method adapts a strategy called the continuity method,more commonly used to solve elliptic partial differen- tial equations, to the new setting of isolating positive roots of polynomial systems. Finally, the data estimated in [4] falls within the scope of our results.

In a transferable utility context, Choo and Siow (2006) introduced a competitive model of the marriage market with gumbel distributed stochastic part, and derived its equilibrium output, a marriage match- ing function. The marriage matching function defines the gains generated by a marriage between agents of prescribed types in terms of the observed frequency of such marriages within the population, relative to the number of unmarried individuals of the same types. Left open in their work is the issue of existence and uniqueness of equilibrium. We resolve this question in the affirmative, assuming the norm of the gains matrix (viewed as an operator) to be less than two. Our method adapts a strategy called the continuity method,more commonly used to solve elliptic partial differen- tial equations, to the new setting of isolating positive roots of polynomial systems. Finally, the data estimated in [4] falls within the scope of our results.

Multistability is a fundamental attribute of the dynamics of neuronal systems under normal and pathological conditions. The mechanism of bistability of bursting and silence is not well understood and to our knowledge has not been experimentally recorded in single neurons. We considered four models. Two of them described the dynamics of a leech heart interneuron: the canonical model and a low-dimensional model. The other two models described mammalian pacemakers from the respiratory center. We investigated the low-dimensional model and identified six different types of multistability of dynamical regimes. We described six generic mechanisms underlying the co-existence of oscillatory and silent regimes. The mechanisms are based either on a saddle equilibrium or a saddle periodic orbit. The stable manifold of the saddle equilibrium or the saddle orbit sets the threshold between the regimes. In the two models of the leech interneuron the range of the controlling parameters supporting the co-existence of bursting and silence is limited by the Andronov-Hopf and homoclinic bifurcations (Malashchenko, Master Thesis 2007). The bistability was found in a narrow range of the leak currents' parameters. Here, we introduced a propensity index to bistability as the width of the range on a bifurcation diagram; we investigated how the propensity index was affected by modifications of the ionic currents, and found that conductances of only two currents substantially affected the index. The increase of the conductance of the hyperpolarization-activated current, Ih, and the reduction of the fast Ca2+ current, ICaF, notably increased the propensity index. These findings define modulatory conditions under which we suggest the bistability of bursting and silence could be experimentally revealed in leech heart interneurons. We hypothesize that this mechanism could be commonly found in a large variety of neuronal models. We applied our techniques to models of vertebrate neurons controlling respiratory rhythm, which represent two types of inspiratory pacemakers of the Pre-Bӧtzinger Complex. We showed that both types of neurons could exhibit bistability of bursting and silence in accordance with the mechanism which we described.

Recognizing that Christians cannot adequately understand the mysteries of faith from a single vantage point, Catholic theologians have been keen on emphasizing the multidimensional nature of theological understanding since Vatican II. The advantage of such a method has helped believers to understand the rich, in-depth quality of Catholic faith.<br>One of the fields of theology which has not been discussed in the models approach, however, is apologetics&hibar;which includes as one of its aspects the art and science of defending the doctrines and practices of the Catholic Church. When all of the relevant passages in the documents of Vatican II are taken into consideration, a unique apologetical approach emerges that incorporates key advances as they emerged historically from the Church's apologists. Each of the individual apologetic systems from the past will be shown to have its own particular strengths and weaknesses. By way of contrast, I will argue that the best way to "make a defense for" the Gospel in a postconciliar church is to advance the integrated model of the Council. This integrated model of Catholic defense is called combinationalism. The interests and views of the apologists are proven to be complementary rather than competing.<br>This integrated model helps apologists and evangelists to recognize that although one approach might be needed in a certain context, it would be an egregious mistake to take that one system and use it as the exclusive means to reach persons situated within different circumstances and cultural contexts. This essay will not only exploit the different apologetic models in the post-Vatican II period, it will also serve as a serious work of apologetics in its own right by focusing on certain challenges as test cases to highlight the pertinence and livelihood of each model. / McAnulty College and Graduate School of Liberal Arts; / Theology / PhD; / Dissertation;

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By the time of 2011, Taiwan Futures Exchange has issued 8 kinds of stock index futures. By taking a closer look at the transaction of the index futures, we found out that, in terms of trading volume, there is a significant difference among each others. Based on the observation, our research focuses on studying the existence value of the index futures in terms of hedging and speculating functions. The definition of futures¡¦ existence value is that the investors can use the futures to achieve the objectives of hedging and speculating in financial market. The research objects are TX, TE, TF, MTX, XIF, and GTF. The method to measure the hedging function is based on Portfolio and Hedging Theory of Johnson (1959). We estimate the hedging ratio with different data periods to calculate the hedging effectiveness. The method to measure the speculating function is based on the theory of Rutledge (1979) et al. We calculate the speculating trading volume to study the relationship with the basis by using OLS model. The empirical result shows that, in the hedging function, all of the index futures¡¦ hedging ratios are almost less than 1, and all have high hedging effectiveness. There is no significant influence on hedging effectiveness with different data periods and issuing time. In the speculating function, TX, MTX, and GTF will make speculating activities increase when the basis get bigger but TE, TF, and XIF will not. To sum up, TX, MTX, and GTF have higher existence value than TE, TF, and XIF. At last, based on the observation from this study, we propose several policy suggestions for enhancing the existence value of the index futures in financial market.

Edward Albee is influenced by the Absurd Drama of Samuel Beckett whose works involve existential concerns. Albee follows Beckett&rsquo / s traces in the dramatization of uncertainty, alienation and the question of freedom. Albee&rsquo / s characters do not have fixed identities, and they suffer from their identity problems. The notion of Other enhances this uncertainty. The ambiguity of existence, whether they really are or not, presents another problem for these characters. Their lives are based on illusions, and the line between the reality and fantasy is absent. Alienation of the human being from the self and the others is another existential theme that Albee deals with. Alienation is partly caused by lack of communication, and as a result, the isolated self is entrapped in his own condition. Freedom becomes a confusing question in his works as it makes the characters anxious while choosing one option among various others on his own, and as it renders the characters responsible for their free choices. So, the characters tend to be passive agents in life, which is in fact another choice. Albee extends Beckett&rsquo / s absurdist ideas and adopts the Absurd Drama to highlight his social concerns as he is also a social critic. The targets of his criticism are materialism, loss of values and broken human relationships. The playwright challenges the audience for a reform on these points.

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As a violinist, teacher, and thinker, I am concerned to articulate the relevance of music to the lives of my audience, my students and myself. But my concern is not merely to describe the meanings that people experience when they engage music. Rather, I am interested in constituting the musical relevance that each of us must actualize as we work to make our lives vital and meaningful. Accordingly, in my study I articulate in philosophical, yet practical, terms, a particular attitude of musical engagement that I call meeting. Grounded in Martin Buber’s idea of human existence as I-Thou, my conception of meeting has a specific character. Each side of the meeting must meet itself in its work to constitute the adequacy of its engagement with the other as it must meet with the other in its work to constitute the adequacy of its engagement with itself. It follows that the essence of human meeting is not merely the “reality” – physical, cultural, intellectual – of people who come together. Rather, the essence is their self-critical thought that is created as they share their lives with each other. The focus, then, is not the meeting’s outcome but rather the meeting itself insofar as it constitutes mutual understanding, communication and love. Thus, at the heart of my study, I constitute music in the same way, not as a physical or cultural “reality,” but rather as the meeting between music and musical participant that demands that each – music and participant – attend to self and other. The idea that music’s whole being is meeting has profound implications for how we conceive of music education. Accordingly, the ultimate purpose of my study is to bring my ideas of musical meeting to bear upon how we teach and learn music in the classroom.

In recent decades, significant interest, based on physics and engineering applications, has developed on so-called anomalous diffusion processes that possess different spread functions with classical ones. The resulting differential equation whose fundamental solution matches this decay process is best modeled by an equation containing a fractional order derivative. This dissertation mainly focuses on some inverse problems for fractional diffusion equations. After some background introductions and preliminaries in Section 1 and 2, in the third section we consider our first inverse boundary problem. This is where an unknown boundary condition is to be determined from overposed data in a time- fractional diffusion equation. Based upon the fundamental solution in free space, we derive a representation for the unknown parameters as the solution of a nonlinear Volterra integral equation of second kind with a weakly singular kernel. We are able to make physically reasonable assumptions on our constraining functions (initial and given boundary values) to be able to prove a uniqueness and reconstruction result. This is achieved by an iterative process and is an immediate result of applying a certain fixed point theorem. Numerical examples are presented to illustrate the validity and effectiveness of the proposed method. In the fourth section a reaction-diffusion problem with an unknown nonlinear source function, which has to be determined from overposed data, is considered. A uniqueness result is proved and a numerical algorithm including convergence analysis under some physically reasonable assumptions is presented in the one-dimensional case. To show effectiveness of the proposed method, some results of numerical simulations are presented. In Section 5, we also attempted to reconstruct a nonlinear source in a heat equation from a number of known input sources. This represents a new research even for the case of classical diffusion and would be the first step in a solution method for the fractional diffusion case. While analytic work is still in progress on this problem, Newton and Quasi-Newton method are applied to show the feasibility of numerical reconstructions. In conclusion, the fractional diffusion equations have some different properties with the classical ones but there are some similarities between them. The classical tools like integral equations and fixed point theory still hold under slightly different assumptions. Inverse problems for fractional diffusion equations have applications in many engineering and physics areas such as material design, porous media. They are trickier than classical ones but there are also some advantages due to the mildly ill-conditioned singularity caused by the new kernel functions.