(1) If p ≥ 0 and r ≥ 0, then p+ r ≥ 2 ·√p · r. (2) sin is increasing on ]0, 2 [. (3) sin is decreasing on ]2 ,π[. (4) cos is decreasing on ]0, 2 [. (5) cos is decreasing on ]2 ,π[. (6) sin is decreasing on ]π, 2 ·π[. (7) sin is increasing on ] 3 2 ·π,2 ·π[. (8) cos is increasing on ]π, 2 ·π[. (9) cos is increasing on ] 3 2 ·π,2 ·π[. (10) sin(t1) = sin(2 ·π ·n+ t1). (11) cos(t1) = cos(2 ·π ·n+ t1).

Bacteriophage lambda packages the DNA of the related phage 21 poorly [Hohn, B. (1975) J. Mol. Biol. 98, 93--106]. To understand the nature of the packaging defect, the interaction of the cohesive end site (cos) specific for phage 21 (cos phi 21) with phage lambda terminase has been investigated. The ability of lambda terminase to cleave cos phi 21 was studied in vitro; lambda terminase cleaved ...

We estimate the contribution of millisecond pulsars to the diffuse gamma-ray background of the Galaxy, and show that a significant fraction of the Galactic background may originate from them. A small number of the unidentified COS-B point sources may, in fact, be millisecond pulsars. It is argued that several hundred millisecond pulsars may be detectable as point sources by the GRO satellite.

as the price relative which is how much a stock goes up or down in a single day. St denotes the amount of wealth we have at the start of day t and we assume S1 = 1. We denote wt(i) to be the fraction of our wealth that we have in stock i at the beginning of day t which can be viewed as a probability distribution as ∀i, wt(i) ≥ 0 and ∑ iwt(i) = 1. We can then derive the total wealth in stock i a...

The new curve contains all of the information about the original curve’s tangent lines. For example, it crosses the y-axis whenever the original curve has a horizontal tangent line. The straight line y = mx + b, or (x(t), y(t)) = (t,mt + b), has only one tangent line and thus a trivial transformation to a point, (x∗(t), y∗(t)) = (m, b). Some conic sections transform to conic sections. For examp...

This course is about data! Data is everywhere. Everything is computerized now and vast amounts of data can be easily stored. Concomitant with vast amounts of data is the belief that this data will be useful. There are many practical issues regarding data which this course will not cover such as storing data, databases, transferring data, etc. This class will be concerned with how to get the mos...

In other words, if ≤ 1/8 and δ ≤ 1/8, then PAC learning is not possible with fewer than d/2 examples. The outline of the proof is: To prove that there exists a concept c ∈ C and a distribution D, we are going to construct a fixed distribution D, but we do not know the exact target concept c used. Instead, we will choose c at random. If we get an expected probability of error over c, then there ...

Take the case of horse racing as an example, we can think of each expert predicting the probability that each horse will win. Another way to motivate this model is to consider coding theory. Suppose Alice wants to send Bob a file consisting of messages x1, . . . , xt, . . . xT , where xt ∈ X, the set of all possible messages. Alice can wait until she sees all messages, which is an offline appro...