Let G = (V,E) be a connected graph and let k be a positive integer with k ≤ rad(G). A subset D ⊆ V is called a distance k-dominating set of G if for every v ∈ V − D, there exists a vertex u ∈ D such that d(u, v) ≤ k. In this paper we study the fractional version of distance k-domination and related parameters.

LetGn,k(K) be the Grassmannian manifold of k-dimensional K-subspaces in K where K = R,C,H is the field of real, complex or quaternionic numbers. For 1 ≤ k ≤ k ≤ n − 1 we define the Radon transform (Rf)(η), η ∈ Gn,k′(K), for functions f(ξ) on Gn,k(K) as an integration over all ξ ⊂ η. When k+ k ≤ n we give an inversion formula in terms of the G̊arding-Gindikin fractional integration and the Cayley...

We determine the exact minimum l-degree threshold for perfect matchings in k-uniform hypergraphs when the corresponding threshold for perfect fractional matchings is significantly less than 1 2 ( n k−l ) . This extends our previous results [18, 19] that determine the minimum l-degree thresholds for perfect matchings in k-uniform hypergraphs for all l ≥ k/2 and provides two new (exact) threshold...

We use a variety of combinatorial techniques to prove several theorems concerning fractional dimension of partially ordered sets. In particular, we settle a conjecture of Brightwell and Scheinerman by showing that the fractional dimension of a poset is never more than the maximum degree plus one. Furthermore, when the maximum degree k is at least two, we show that equality holds if and only if ...

Regression predictors are usually entered into a model without transformation. However, it is not unusual for regression relationships to be distinctly nonlinear. Fractional polynomials account for nonlinearity through real-valued power transformations of primary predictors. Adaptive methods have been developed for searching through alternative fractional polynomials based on one or more primar...

Linear canonical transform is an integral transform with four parameters and has been proved to be powerful tool for optics, radar system analysis, filter design etc. Fractional Fourier transform and Fresnel transform can be seen as a special case of linear canonical transform with real parameters. Further generalization of linear canonical transform with complex parameters is also developed an...

Fractional (hyper-)graph theory is concerned with the specific problems that arise when fractional analogues of otherwise integer-valued invariants are considered. The focus this paper on edge covers hypergraphs. Our main technical result generalizes and unifies previous conditions under which size support bounded independently hypergraph itself. This allows us to extend tractability results fo...

Abstract—The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the correspondi...

In recent years, the eeect of the curse of high dimensionality has been studied in great detail on several problems such as clustering, nearest neighbor search, and indexing. In high dimensional space the data becomes sparse, and traditional indexing and algorithmic techniques fail from a eeciency and/or eeectiveness perspective. Recent research results show that in high dimensional space, the ...

An increase in Na+/glucose cotransport upstream to the macula densa might contribute to the increase in single nephron GFR (SNGFR) in early diabetes mellitus by lowering the signal of the tubuloglomerular feedback, i.e., the luminal Na+, Cl-, and K+ concentration sensed by the macula densa. To examine this issue, micropuncture experiments were performed in nephrons with superficial glomeruli of...