We consider a class of generalized binomials emerging in fractional calculus. After establishing some general properties, we focus on particular yet relevant case, for which provide several ready-for-use combinatorial identities, including an adapted version the Pascal's rule. then investigate associated generating functions, establish recursive, and integral formulation. From this, derive asym...

This paper is the continuation of a previous work (Fasano 2004), dedicated to a MIP formulation for non-standard three-dimensional packing issues, with additional conditions. The Single Bin Packing problem (Basic Problem) is considered and its MIP formulation shortly surveyed, together with some possible extensions, including balancing, tetris-like items and non-standard domains. A MIP-based he...

This article presents a sparse, low-memory footprint optimization algorithm for the implementation of model predictive control (MPC) tracking formulation in embedded systems. MPC has several advantages over standard formulations, such as an increased domain attraction and guaranteed recursive feasibility even event sudden reference change. However, this comes at expense addition small amount de...

we study the limiting distribution of the degree of a given node in a scaled attachment random recursive tree, a generalized random recursive tree, which is introduced by devroye et. al (2011). in a scaled attachment random recursive tree, every node $i$ is attached to the node labeled $lfloor ix_i floor$ where $x_0$, $ldots$ , $x_n$ is a sequence of i.i.d. random variables, with support in [0,...

a recursive-circulant $g(n; d)$ is defined to be acirculant graph with $n$ vertices and jumps of powers of $d$.$g(n; d)$ is vertex-transitive, and has some strong hamiltonianproperties. $g(n; d)$ has a recursive structure when $n = cd^m$,$1 leq c < d $ [10]. in this paper, we will find the automorphismgroup of some classes of recursive-circulant graphs. in particular, wewill find that the autom...

This paper examines an extension of QR-RLS lattice filtering to the case of multiple input signals. The proposed adaptation algorithm is based on a compact square-root array formulation that is amenable to hardware implementation due to its scalar-only nature, parallelizability and numerical robustness. A technique that provides increased design flexibility by allowing unequal filter lengths to...

Once we have studied effectively computable operations on numbers it is natural to ask whether there is a comparable notion for operations on functions. The essential difference between functions and numbers as basic objects is that functions are usually infinite rather than finite. With this in mind, in §1 of this chapter we discuss the features we might reasonably expect of an effective opera...

This paper considers the optimal linear estimates recursion problem for discrete-time linear systems in its more general formulation. The system is allowed to be in descriptor form, rectangular, time-variant, and with the dynamical and measurement noises correlated. We propose a new expression for the filter recursive equations which presents an interesting simple and symmetric structure. Conve...

A communication model for the Hypothesis Boosting (HB) problem is proposed. Under this model, AdaBoost algorithm can be viewed as a threshold decoding approach for a repetition code. Generalization of such decoding view under theory of theory of Recursive Error Correcting Codes allows the formulation of a generalized class of low-complexity learning algorithms applicable in high dimensional cla...