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...

Quaternion measurable processes are introduced and the Dirac equation is derived from the Langevin equation associated with a two-valued process.

We discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module. Let A be a Banach algebra and X a Banach A-module, f : X → X and g : A → A. The mappings Δ1 f,g , Δ2 f,g , Δ3 f,g , and Δ4 f,g are defined and it is proved that if ‖Δ1 f,g x, y, z,w ‖ resp., ‖Δ3 f,g x, y, z,w, α, β ‖ is dominated by φ x, y, z,w , then f is a generalized re...

The purpose of this brief paper is to present a new derivation of Biot’s theory of linear poroelasticity [1, 2, 3] in a modern thermodynamically-consistent fashion, and show that it may be deduced as a special case of a more general theory of chemoelasticity.

in this research, a new technetium-99m generator has been developed with addition of cerium oxide to alumina column.  the adsorption behaviors of 99mo in the form of molybdate and 99mtc in the form of pertechnetate on ceo2/al2o3 was investigated and showed that the adsorption capacity of molybdate on this generator is higher than usual generator using al2o3. ceric ions were selected as an addit...

The energy equation for turbulent flow of fiber suspensions was derived in terms of second order correlation tensors. Fiber motion of turbulent energy including the correlation between pressure fluctuations and velocity fluctuations was discussed at two points of flow field, at which the correlation tensors were the functions of space coordinates, distance between two points, and time.

background: hot lab is a specially designed room in a nuclear medicine hospital where the radiopharmaceuticals are delivered, stored and prepared for dispensing. 99mo/99mtc-generator is the major source in the hot lab used for various medical imaging. it is important to maintain a standard for hot lab procedures to optimize the patient care and minimize radiation exposure to all nuclear medicin...

let $mathfrak{a}$ be an algebra. a linear mapping $delta:mathfrak{a}tomathfrak{a}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{a}$. given two derivations $delta$ and $delta'$ on a $c^*$-algebra $mathfrak a$, we prove that there exists a derivation $delta$ on $mathfrak a$ such that $deltadelta'=delta^2$ if and only if either $delta'=0$...