We present a theoretical framework, which successfully combines two different fields of photonics: i) the laser rate equations and ii) cavity perturbation theory, focusing particularly on micro-cavity lasers with optical anisotropies. Our approach is formally analogous to quantum-mechanical time-dependent in however gain medium permittivity tensor distribution are perturbed instead Hamiltonian....

Growing concerns about the impacts of food systems have led to fierce debate over pros and cons different modes production. In parallel, conservationists debated “land-sparing” versus “land-sharing” as competing rationales for a land use policy that aims halt biodiversity loss. As contribution these debates, we share research conducted in South-East England where contrasting practices managing ...

Currently used one-way wave equations in depth fail at horizontal propagation. One-way wave equations in time do not have that shortcoming; they are omni-directional in space. In these equations, spatial derivatives appear in a pseudo-differential operator—the square root of the Laplacian. With an appropriate definition of this operator, we have proved via ray theory that the solutions of one-w...

In R2, we consider an analytic family of fractional integrals , whose convolution kernel is obtained by taking some transverse derivatives of arclength measure on the parabola (t, t2) multiplied by |t|γ , and doing so in a homogeneous way. We determine the exact range of p, q for which the analytic family maps Lp to Lq . We also resolve a similar issue on the Heisenberg group.

Over the past fifteen years or so, advocates of a relational theory of psychoanalytic process have developed a compelling challenge to the classical approach to clinical work. Their critique of a fixed "standard technique," applicable across the board to all analyzable patients, has been particularly effective. The new approach opens the possibility of tailoring technique to individual analysan...

A combined numerical and analytic approach is presented to obtain a general matrix form of constitutive relations for a bi-anisotropic material which consists of arbitrary inclusions in a host medium. This approach is based on the quasi-static Lorentz-Lorenz theory which relates the constitutive parameters of the material with the electric and magnetic dipole moments of the inclusions which can...

This paper provides an overview of the theory of Bruhat-Tits buildings. Besides, we explain how Bruhat-Tits buildings can be realized inside Berkovich spaces. In this way, Berkovich analytic geometry can be used to compactify buildings. We discuss in detail the example of the special linear group. Moreover, we give an intrinsic description of Bruhat-Tits buildings in the framework of non-Archim...

Analytic reports are special textual documents containing condensed results from a data mining process. Embedded knowledge enables the interpretation of the reports by automated procedures, which opens the way to content-based retrieval. We elaborate the technique for statistical association rules as specific form of discovered knowledge, demonstrate its formal apparatus on examples from the me...

We review the way to analytically continue the Lippmann–Schwinger bras and kets into the complex plane. We will see that a naive analytic continuation leads to nonsensical results in resonance theory, and we will explain how the non-obvious but correct analytical continuation is done. We will see that the physical basis for the non-obvious but correct analytic continuation lies in the invarianc...