Since the 1990s, Internet communications technologies have influenced human activity. Over the last 15 years, a phenomenon called virality—i.e., when content circulates via Internet among an increasingly broad audience at an exponentially rapid rate—has been especially impactful. Only some information achieves virality, so the phenomenon invites reflection. Yet, scholars have failed to adequate...

WZW models are abstract conformal field theories with an infinite dimensional symmetry which accounts for their integrability, and at the same time have a sigma model description of closed string propagation on Lie group manifolds which endows the models with an intuitive geometric meaning. We exploit this dual algebraic and geometric property of WZW models to provide an explicit example of new...

In this paper we develop a theory of linear differential systems analogous to the classical one for ODEs, including the obtaining of fundamental matrices, the development of a variation of parameters formula and the expression of the Green’s functions. We also derive interesting results in the case of differential equations with reflection and generalize the Hyperbolic Phasor Addition Formula t...

We present an analytical method for solution of one-dimensional optical systems, based on the differential transfer matrices. This approach can be used for exact calculation of various functions including reflection and transmission coefficients, band structures, and bound states. We show the consistency of the WKB method with our approach and discuss improvements for even symmetry and infinite...

We calculate the complex refractive index of inhomogeneous thin films using the transfer matrix method and reflection/transmission measurements. To this end we have developed a model for both the 3D distribution of inhomogeneities inside thin films and for light propagation through the inhomogeneities. The model involves splitting the light into contributions from the homogeneous section of the...

In this paper we give general recommendations for successful application of the Douglas–Rachford reflection method to convex and non-convex real matrix-completion problems. These guidelines are demonstrated by various illustrative examples.

By solving the right reflection equation proposed in reference[16] to describe the Z = 0 giant graviton branes, we obtain a boundary matrix with two free parameters for the AdS/CFT SU(1|1) spin chain.

We develop a model for the reflection and transmission of plane waves by an isotropic layer sandwiched between two uniaxial crystals of arbitrary orientation. In the laboratory frame, reflection and transmission coefficients corresponding to the principal polarization directions in each crystal are given explicitly in terms of the [Formula: see text] axis and propagation directions. The solutio...

We generalize derived equivalences for triangular matrix rings induced by a certain type of classical tilting module introduced by Auslander, Platzeck and Reiten to generalize reflection functors in the representation theory of quivers due to Bernstein, Gelfand and Ponomarev.

We examine the reflection matrix acting on the SO(N) vector multiplet and fuse it to obtain that acting on the rank two particle multiplet, and give its decomposition.