Mackie\u27s Arguement for the Infinite Man

Theists and non-theists alike have toiled with the characteristics of the Judeo-Christian God and how they may or may not be contradictory with the existence of evil. Some philosophers, such as J. L. Mackie, have decided that God and evil cannot coexist, mainly because the existence of evil means that any God is unable to keep evil and suffering away from His beloved creation, and such a limited God is no God at all. But Mackie’s argument rests on flawed foundation. Mankind is necessarily finite because even the infinite God cannot do the logically impossible and create the infinite—nothing infinite can be created. Mackie argues that mankind, in its unavoidably limited state, should function with limitless abilities to always choose good over evil. This “solution” requires that finite man can function with infinite capabilities, which is metaphysically impossible. The fact that mankind can potentially always choose the good choice does not mean that he can actualize this desire for good, for this would require an infinite capacity to both know and do good

Asymptotics of the solutions of the stochastic lattice wave equation

We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial data. The limit is understood in the point-wise sense in the former case, and in the weak sense in the latter. On the other hand, the weak limit for square integrable initial data is deterministic

Long time, large scale limit of the Wigner transform for a system of linear oscillators in one dimension

We consider the long time, large scale behavior of the Wigner transform W_\eps(t,x,k) of the wave function corresponding to a discrete wave equation on a 1-d integer lattice, with a weak multiplicative noise. This model has been introduced in Basile, Bernardin, and Olla to describe a system of interacting linear oscillators with a weak noise that conserves locally the kinetic energy and the momentum. The kinetic limit for the Wigner transform has been shown in Basile, Olla, and Spohn. In the present paper we prove that in the unpinned case there exists $\gamma_0>0$ such that for any $\gamma\in(0,\gamma_0]$ the weak limit of W_\eps(t/\eps^{3/2\gamma},x/\eps^{\gamma},k), as \eps\ll1, satisfies a one dimensional fractional heat equation $\partial_t W(t,x)=-\hat c(-\partial_x^2)^{3/4}W(t,x)$ with $\hat c>0$. In the pinned case an analogous result can be claimed for W_\eps(t/\eps^{2\gamma},x/\eps^{\gamma},k) but the limit satisfies then the usual heat equation

Limited Liability for Limited Partners: An Argument for the Abolition of the Control Rule

One of the important features of the limited partnership\u27 that makes investment in this form of business organization attractive is the general immunity afforded to limited partners from liability for the obligations of the partnership. This immunity, however,can be forfeited. Under both the Uniform Limited Partnership Act (ULPA) and the Revised Uniform Limited Partnership Act (RULPA), a limited partner becomes liable for the obligations of the partnership if, in addition to the exercise of the rights and powers of a limited partner, the limited partner takes part in the control of the business.\u27\u27 Not surprisingly, when sophisticated investors are offered limited partnership interests, these investors often request provisions in the certificate of limited partnership or the partnership agreement\u27 providing that the general partners may commit the partnership to certain types of transactions only with the consent of the holders of some specified percentage of the limited partnership interests or that the limited partners be given some voice in the selection of the partnership\u27s managers. Although these requests are understandable, an obvious tension arises between the limited partners\u27 desire to exercise control over important decisions affecting the partnership and the threat of personal liability for taking part, or participating, in the control of the business of the partnership. One of the most vexing problems facing lawyers who represent sophisticated limited partnership investors is advising these investors how much decision-making power they can obtain through negotiation with the general partners without losing immunity from liability for the obligations of the partnership. There has been no dearth of insightful commentary pointing out the uncertainty inherent in the control rule. Most of this commentary has attempted to suggest the appropriate judicial standards for deciding whether the particular conduct of a limited partner in relation to the partnership business should subject the limited partner to personal liability for the obligations of the partnership. Few commentators, however, have had the temerity even to suggest that the control rule be abolished and that limited partners have no personal liability for the obligations of the partnership regardless of the degree to which the limited partners participate in the control of the partnership business. This Article presses that argument. Part II examines the origins and present status of the control rule. This examination ex-poses the uncertain boundaries of a limited partner\u27s potential liability under the rule and the resulting difficulty of advising potential investors in limited partnerships. Part III criticizes the control rule on the grounds that it complicates a potential investor\u27s calculation of the risk of investing in a limited partnership, compromises the negotiating position of limited partners relative to general partners, and is not supported by any valid policy that could not be accommodated by other existing legal principles. Finally, part IV argues that the control rule should be abolished in favor of a rule that generally would free limited partners from personal liability for the obligations of the partnership. Part IV also suggests specific legislation that would effect this change

Understanding the Transition between High School and College Mathematics and Science

Mathematics and science education is gaining increasing recognition as key for the well-being of individuals and society. Accordingly, the transition from high school to college is particularly important to ensure that students are prepared for college mathematics and science. The goal of this study was to understand how high school mathematics and science course-taking related to performance in college. Specifically, the study employed a nonparametric regression method to examine the relationship between high school mathematics and science courses, and academic performance in college mathematics and science courses. The results provide some evidence pertaining to the positive benefits from high school course-taking. Namely, students who completed high school trigonometry and lab-based chemistry tended to earn higher grades in college algebra and general chemistry, respectively. However, there was also evidence that high school coursework in biology and physics did not improve course performance in general biology and college physics beyond standardized test scores. Interestingly, students who completed high school calculus earned better grades in general biology. The implications of the findings are discussed for high school curriculum and alignment in standards between high schools and colleges

Superdiffusion of energy in Hamiltonian systems perturbed by a conservative noise

We review some recent results on the anomalous diffusion of energy in systems of 1D coupled oscillators and we revisit the role of momentum conservation.Comment: Proceedings of the conference PSPDE 2012 https://sites.google.com/site/meetingpspde