We present a closed-form expression for the irradiance at a point on a surface due to an arbitrary polygonal Lambertian luminaire with linearly-varying radiant exitance. The solution consists of elementary functions and a single wellbehaved special function that can be either approximated directly or computed exactly in terms of classical special functions such as Clausen’s integral or the clos...

relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $m$, called {em $tau$-rank of} $m$, which coincides with the reduced rank of $m$ whenever $tau$ is the goldie torsion theory. it is shown that the $tau$-rank of $m$ is measured by the length of certain decompositions of the $tau$-injective hull of $m$. moreover, some relations between the $tau$-rank of $m$ and c...

We present a first-principles implementation of the stochastic path-integral approach proposed by Liu et al. [H. Liu, Y. Yuan, D. X.-Z. Li, and J. Shi, Phys. Rev. Research 2, 013340 (2020)] for estimating superconducting transition temperature ($T_c$) liquid. The is based on all-electron projector-augmented-wave (PAW) method. generalize al.'s formalism to accommodate pseudo-description electron...

the present paper investigates the potential application of graphene sheets with attached nanoparticles as resonant sensors by introducing a nonlocal shear deformation plate model. to take into account an elastic connection between the nanoplate and the attached nanoparticle, the nanoparticle is considered as a mass-spring system. then, a combination of pseudo-spectral and integral quadrature m...

This paper introduces a new method for approximating the Biot-Savart integral for elliptical Gaussian functions using high-order interpolation and compares it to an existing method based on small aspect ratio asymptotics. The new evaluation technique uses polynomials to approximate the kernel corresponding to the integral representation of the streamfunction. We determine the polynomial coeffic...

The standard method of modelling axisymmetric stellar systems begins from the assumption that mass follows light. The gravitational potential is then derived from the luminosity distribution, and the unique two-integral distribution function f (E, L 2 z) that generates the stellar density in this potential is found. It is shown that the gravitational potential can instead be generated directly ...

This paper presents an extension of the comprehensive (overall) concordance index of ELECTRE methods, which takes the interaction between criteria into account. In real-world decisionmaking situations, it is reasonable to consider the interaction between a small number of criterion pairs. Three types of interaction have been considered: mutual strengthening, mutual weakening, and antagonistic. ...

A pseudo-Anosov surface automorphism φ has associated to it an algebraic unit λφ called the dilatation of φ. It is known that in many cases λφ appears as the spectral radius of a Perron–Frobenius matrix preserving a symplectic form L. We investigate what algebraic units could potentially appear as dilatations by first showing that every algebraic unit λ appears as an eigenvalue for some integra...