Reading a book is also kind of better solution when you have no enough money or time to get your own adventure. This is one of the reasons we show the program derivation the development of programs from specifications as your friend in spending the time. For more representative collections, this book not only offers it's strategically book resource. It can be a good friend, really good friend w...

The aim of this paper is to introduce the notion of derivations of subtraction algebras. We define a derivation of a subtraction algebra X as a function d on X satisfying d(x − y) = (d(x) − y) ∧ (x − d(y)) for all x, y ∈ X. Then it is characterized as a function d satisfying d(x− y) = d(x)− y for all x, y ∈ X. Also we define a simple derivation as a function da on X satisfying da(x) = x−a for a...

A bstract We examine strong/weak dualities in two dimensional conformal field theories by generalizing the Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality between Witten’s cigar model described $$ \mathfrak{sl}(2)/\mathfrak{u}(1) sl 2 / u <m...

The dependence of the reflectance at the surface on the vertical structure of optical parameters is derived from first principles. It is shown that the depth dependence is a function of the derivative of the round trip attenuation of the downwelling and backscattered light. Previously the depth dependence was usually modeled as being dependent on the round trip attenuation. Using the new relati...

The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the conformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime, reconstructing the local data in the bulk from the entanglement on the boundary. W...

We give a derivation of the DeAngelis-Beddington functional response in terms of mechanisms at the individual level, and for the first time involving prey refuges instead of the usual interference between predators.

The time-dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schrödinger equation with a short-scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short-scale correlation structure in the condensate.

Final size relations are known for many epidemic models. The derivations are often tedious and difficult, involving indirect methods to solve a system of integro-differential equations. Often when the details of the disease or population change, the final size relation does not. An alternate approach to deriving final sizes has been suggested. This approach directly considers the underlying sto...