Current practices in elementary school science with reference to courses of study published from 1940 to 1952, and the extent of activities undertaken for the improvement of instruction.

Thesis (Ed.D.)--Boston University

Optimal Stopping Rules and Maximal Inequalities for Bessel Processes

We consider, for Bessel processes X ∈ Besα with arbitrary order (dimension) α ∈ R, the problem of the optimal stopping (1.4) for which the gain is determined by the value of the maximum of the process X and the cost which is proportional to the duration of the observation time. We give a description of the optimal stopping rule structure (Theorem 1) and the price (Theorem 2). These results are used for the proof of maximal inequalities of the type E max Xrr≤r ≤ γ(α) is a constant depending on the dimension (order) α. It is shown that γ(α) ∼ √α at α → ∞

A review of the research in testing in secondary chemistry and physics from 1938-1948 including 14 reviews of standardized tests.

Thesis (M.A.)--Boston University N.B.: Pages 16,17 missing from the originals

Fairly Allocating Contiguous Blocks of Indivisible Items

In this paper, we study the classic problem of fairly allocating indivisible items with the extra feature that the items lie on a line. Our goal is to find a fair allocation that is contiguous, meaning that the bundle of each agent forms a contiguous block on the line. While allocations satisfying the classical fairness notions of proportionality, envy-freeness, and equitability are not guaranteed to exist even without the contiguity requirement, we show the existence of contiguous allocations satisfying approximate versions of these notions that do not degrade as the number of agents or items increases. We also study the efficiency loss of contiguous allocations due to fairness constraints.Comment: Appears in the 10th International Symposium on Algorithmic Game Theory (SAGT), 201

Skew-Product Decomposition of Planar Brownian Motion and Complementability

International audienceLet $Z$ be a complex Brownian motion starting at 0 and $W$ the complex Brownian motion defined by $W_ t = \int_0^\cdot \frac{Z_s}{|Z_s|} dZ_s$. The natural filtration $\mathcal{F}_W$ of $W$ is the filtration generated by $Z$ up to an arbitrary rotation. We show that given any two different matrices $Q_1$ and $Q_2$ in $O_2(\mathbb{R})$, there exists an $\mathcal{F}_Z$-previsible process $H$ taking values in $\{Q_1,Q_2\}$ such that the Brownian motion $\int_0^\cdot H \cdot dW$ generates the whole filtration $\mathcal{F}_Z$. As a consequence, for all $a$ and $b$ in $\mathbb{R}$ such that $a^2 + b^2 = 1$, the Brownian motion $a \mathrm{Re}(W) + b \mathrm{Im}(W)$ is complementable in $\mathcal{F}_Z$

Countably Additive Gambling and Optimal Stopping

1 online resource (PDF, 30 pages

On the Adequacy of Stationary Plans for Gambling Problems

1 online resource (PDF, 31 pages