In this paper we introduce a class of partially ordered sets, called differential posets, with many remarkable combinatorial and algebraic properties. (Terminology from lattice theory and the theory of partially ordered sets not explained here may be found in [St6].) The combinatorial properties of differential posets are concerned with the counting of saturated chains Xl < x2 < ... < x k or of...

I recently became sexually active at 21, and my partner is a bit older and has had multiple partners. At this point, we are exclusive, and have used a condom on the few occasions we have had intercourse. I went to the local Planned Parenthood recently, and am now on a birth control pill (I am absolutely sure I don't want or need to be pregnant at this point or ever in my life, personal choice.....

I recently became sexually active at 21, and my partner is a bit older and has had multiple partners. At this point, we are exclusive, and have used a condom on the few occasions we have had intercourse. I went to the local Planned Parenthood recently, and am now on a birth control pill (I am absolutely sure I don't want or need to be pregnant at this point or ever in my life, personal choice.....

I recently became sexually active at 21, and my partner is a bit older and has had multiple partners. At this point, we are exclusive, and have used a condom on the few occasions we have had intercourse. I went to the local Planned Parenthood recently, and am now on a birth control pill (I am absolutely sure I don't want or need to be pregnant at this point or ever in my life, personal choice.....

Proof. Kalai and Lehrer [2] studied a model which can be equivalently described as a single-state SBG (i.e. |S| = 1) with a pure type distribution and product posterior. They showed that, if the player’s assessment of future play is absolutely continuous with respect to the true probabilities of future play (i.e. any event that has true positive probability is assigned positive probability by t...

We are interested in the nature of spectrum one-dimensional Schr\"odinger operator $$ - \frac{d^2}{dx^2}-Fx + \sum_{n \in \mathbb{Z}}g_n \delta(x-n) \qquad\text{in } L^2(\mathbb{R}) with $F>0$ and two different choices coupling constants $\{g_n\}_{n\in \mathbb{Z}}$. In first model $g_n \equiv \lambda$ we prove that if $F\in \pi^2 \mathbb{Q}$ then is $\mathbb{R}$ furthermore absolutely continuou...

Using the description of dominions in the variety of nilpotent groups of class at most two, we give a characterization of which groups are absolutely closed in this variety. We use the general result to derive an easier characterization for some subclasses; e.g. an abelian group G is absolutely closed in N2 if and only if G/pG is cyclic for every prime number p . The main result of this paper i...