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 paper, we study the classification of finite-dimensional real solvable Lie algebras whose derived are codimension 1 or 2. We present an effective method to classify (n+1)-dimensional having 1-codimensional provided that a full n-dimensional nilpotent is given. addition, problem classifying (n+2)-dimensional 2-codimensional proved be wild. case, subclass considered which extended from th...

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.

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 $delta'=0$...

The scattering of elastic waves in a medium with damage from microcracking is discussed. The influence of damage from penny-shaped microcracks within a homogeneous medium is considered. The microcracks are assumed to be randomly oriented and uniformly distributed. Explicit expressions are derived for the attenuation of longitudinal and shear elastic waves in terms of the damage parameter and th...