We give a unified treatment of decay of correlations for nonuniformly expanding systems with a good inducing scheme. In addition to being more elementary than previous treatments, our results hold for general integrable return time functions under fairly mild conditions on the inducing scheme.

Let M be a compact invariant set contained in a boundary hyperplane of the positive orthant of R for a discrete or continuous time dynamical system defined on the positive orthant. Using elementary arguments, we show that M is uniformly weakly repelling in directions normal to the boundary in which M resides provided all normal Lyapunov exponents are positive. This result is useful in establish...

Correspondence: [email protected] Department of Elementary Education, Heze University, Heze 274000, Shandong, People’s Republic of China Abstract By obtaining intervals of the parameter l, this article investigates the existence of a positive solution for a class of nonlinear boundary value problems of second-order differential equations with integral boundary conditions in abstract spaces. ...

Stability and Extremal Theorems for Plane Curves with Bounded Curvature Ralph Howard and Andrejs Treibergs In this note we dis uss some elementary theorems about the relation between area and length of losed embedded plane urves with bounded urvature. Our main result (see Theorem 4.1) solves the extremal problem of whi h domain has largest boundary length among embedded disks in the plane whose...

We consider an economic model with a deterministic money market account and a finite set of basic economic risks. The real-world prices of the risks are represented by continuous time stochastic processes satisfying a stochastic differential equation of diffusion type. For the simple class of log-normally distributed instantaneous rates of return, we construct an explicit state-price deflator. ...

In this manuscript we present a detailed investigation of the form factors of boundary fields of the sinh-Gordon model with a particular type of Dirichlet boundary condition, corresponding to zero value of the sinh-Gordon field at the boundary, at the self-dual point. We follow for this the boundary form factor program recently proposed by Z. Bajnok, L. Palla and G. Takacs [1], extending the an...

The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge from considerations on the domain of the quantum Hamiltonian, this domain being often specified by boundary conditions in elementary quantum physics. Several ex...

Instead of traditional mathematical notation, we can describe formal mathematical systems in visual form. While traditional notation uses a linear sequence of symbols, visual mathematics uses boundary notation, which is comprised of objects and boundaries to enclose objects. Boundary notation is abstract, decoupling the underlying mathematics of a system from its visual representation. Once a s...

This paper studies the expected return of a stock investment with a stop-loss strategy. The probability density function for the investment value is formulated as the solution for a boundary value problem of a partial differential equation. Then, the expected value is manipulated as a function of the stop-loss probability. Two examples are solved by an analytic method. Finally, we design a boun...