The Kuzmin-Toomre family of discs is used to construct potentialdensity pairs that represent flat ring structures in terms of elementary functions. Systems composed of two concentric flat rings, a central disc surrounded by one ring and a ring with a centre of attraction are also presented. The circular velocity of test particles and the epicyclic frequency of small oscillations about circular ...

Closed forms are derived for the effective actions for free, massive spinless fields in anti-de Sitter spacetimes in arbitrary dimensions. The results have simple expressions in terms of elementary functions (for odd dimensions) or multiple Gamma functions (for even dimensions). We use these to argue against the quantum validity of a recently-proposed duality relating such theories with differi...

A variety of problems in mathematical calculus can be solved by recursively applying a finite number of rules. Often, a generic solving strategy can be extracted and an interactive exercise system that emulates a tutor can be implemented. In this paper we show how software developed by us can be used to realize this interactivity. In particular, an implementation of a generic exercise for compu...

Many texture-segmentation schemes use an elaborate bank of filters to decompose a textured image into a joint spacehpatial-frequency representation. Although these schemes show promise, and although some analytical work work has been done, the relationship between texture differences and the filter configurations required to distinguish them remain largely unknown. This paper examines the issue...

Keywords: Frobenius integrable decompositions Partial differential equations Differential polynomials Bäcklund transformations Ordinary differential equations Nonlinearity a b s t r a c t Frobenius integrable decompositions are presented for a kind of ninth-order partial differential equations of specific polynomial type. Two classes of such partial differential equations possessing Frobenius i...

Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions" (2016). Faculty Publications, Department of Mathematics. 87. Abstract In this article we discuss some of the qualitative properties of fractional difference operators. We especially focus on the connections between the fractional difference operator and the mon...

Over the last few decades, astronomers and cosmologists have accumulated vast amounts of data clearly demonstrating that our current theories of fundamental particles and of gravity are inadequate to explain the observed discrepancy between the dynamics and the distribution of the visible matter in the Universe. The Modified Newtonian Dynamics (MOND) proposal aims at solving the problem by post...

A few recent processors allow very efficient double-precision floating point interval arithmetic for the basic operations. In comparison, the elementary functions available in current interval arithmetic packages suffer two major weaknesses. The first is accuracy, as intervals grow more in an elementary function than what is mathematically possible considering only the number format. The second...

We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution, from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic gravitational potential; and the integration can be completed exactly for particular isotropic seed metrics. A good feature of our approach is that the anisotropic ...

Using a circular contour integral representation for the generalized Marcum-Q function, ( ), we derive a new closed-form formula for the moment generating function (MGF) of the output signal power of a dual-diversity selection combiner (SC) in bivariate (correlated) Nakagamifading with positive integer fading severity index. This result involves only elementary functions and holds for any value...