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...

From the literature the analytical calculation of local power and astigmatism of a wavefront after refraction and propagation is well known; it is, e.g., performed by the Coddington equation for refraction and the classical vertex correction formula for propagation. Recently the authors succeeded in extending the Coddington equation to higher order aberrations (HOA). However, equivalent analyti...

We propose a new upscaling scheme for the passage from atomistic to continuum mechanical models for crystalline solids. It is based on a Taylor expansion of the deformation function and allows us to capture the microscopic properties and the discreteness effects of the underlying atomistic system up to an arbitrary order. The resulting continuum mechanical model involves higher order terms and ...

In this work we present a unifying approach of boundary layer approximations for newtonian flows in domains with periodic rugous boundaries. We simplify the problem considering the laplace operator. We construct high order approximations and justify rigorously rates of convergence w.r.t. ǫ, the thickness of the ruogosity. We show a negative result for averaged second-order like wall-laws. To ci...

The technique of higher derivative regularization is applied to the Super-WeylKähler anomaly in supergravity coupled with chiral matters and gauge multiplet. Our method makes it possible to derive directly and diagrammatically the formulae for the gaugino mass (in the Abelian case). Our procedure is applied to derivation of not only the mass formulae known in the anomaly mediation scenario, but...

We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding solitary waves. The first order equation is shown to be equivalent to the Korteweg−de Vries (KdV) equation, while the second order equation is solved numeric...

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...