We discuss the proof of and systematic application of Case’s sum rules for Jacobi matrices. Of special interest is a linear combination of two of his sum rules which has strictly positive terms. Among our results are a complete classiﬁcation of the spectral measures of all Jacobi matrices J for which J − J0 is Hilbert-Schmidt, and a proof of Nevai’s conjecture that the Szeg˝ condition o holds if J − J0 is trace class.
Given a connected, undirected graph, a spanning tree of that graph is a subgraph that is a tree and connects all the vertices together. A single graph can have many different spanning trees. We can also assign a weight to each edge, which is a number representing how unfavorable it is, and use this to assign a weight to a spanning tree by computing the sum of the weights of the edges in that spanning tree.
Governments The U.S. Treasury and state and local governments raise large sums in the money market.
The Treasury raises funds in the money market by selling short-term obligations of the U.S. government
called Treasury bills. Bills have the largest volume outstanding and the most active secondary market of any
money market instrument. Because bills are generally considered to be free of default risk, while other
money market instruments have some default risk, bills typically have the lowest interest rate at a given
Even after I got through tampering with it, it was still a tiny thing, a barely tarnished gem. Seven rules of usage, eleven principles of composition, a few matters of form, and a list of words and expressions commonly misused — that was the sum and substance of Professor Strunk's work.
is irrelevant: AC . It may appear tempting to create a product term consisting of the three boxes on the bottom edge of the K-map. This is not valid because it does not result in all boxes sharing a common product relationship, and therefore violates the power-of-two rule mentioned previously. Upon completing the K-map, all product terms are summed to yield a ﬁnal and simpliﬁed Boolean equation that relates the input variables and the output: Y = B + AC . Functions of four variables are just as easy to solve using a K-map. Beyond four variables, it is...
in a word
- briefly, to sum up In a word, the problem with the car is that it needs a new motor.
in a world of one`s own
- in deep thought or concentration, not caring about other people He is always in a world of his own and doesn`t notice what other people say or think.
- the temporary suspension of an activity or a ruling The final estate settlement was in abeyance while the lawyers looked at the will in more detail.
in accordance with (something)
- in agreement with (something) In accordance with the wishes of my grandfather we did not...
In the European Union, the existing insurance and reinsurance directives do not contain any
provisions that place reliance on credit rating agencies. There is no explicit credit risk charge
for the solvency margin in the Solvency I framework. The solvency margin in the Solvency I
framework is not the sum of different capital charges related to different risks, but a single
capital charge calibrated to reflect all the risks an insurance company faces.
These results have been used to unravel the mysteries of the collective behavior of living systems in nature
such as the flocking of birds, schooling of fish, marching of ants and swarming of bees for strategic purposes.
While the individual “agents” in these groups possess only local strategic rules and capacity, their collective
behavior is characterized by an overlaying order, self-organization, and a collective intelligence that is greater
than the sum of the parts.
"Calculus and its applications: 1.5" - Objective: differentiate using the power rule or the sum-difference rule, differentiate a constant or a constant times a function, determine points at which a tangent line has a specified slope.