We introduce a realistic frequency-dependent channel model for ultra-wideband (UWB) communication systems and develop a generalized broadband Capon spatial spectrum estimator for localization of multiple incoherently distributed scattering clusters. The proposed estimator is able to address the three crucial features of practical UWB impulse propagation: presence of local scattering for multipl...

We consider the existence of pairs of probability ensembles which may be efficiently distinguished from each other given k samples but cannot be efficiently distinguished given k0 < k samples. It is well known that in any such pair of ensembles it cannot be that both are efficiently computable (and that such phenomena cannot exist for nonuniform classes of distinguishers, say, polynomial-size c...

We calculate the exceptional points of eigenvalues several parameter-dependent Hamiltonian operators mathematical and physical interest. show that calculation is greatly facilitated by application discriminant to secular determinant. In this way, problem reduces finding roots a polynomial function just one variable, parameter in operator. As illustrative examples, we consider particle one-dimen...

The Sch\"{o}nberg-Chandrasekhar limit in post main sequence evolution for stars of masses the range $1.4\lesssim M/M_{\odot}\lesssim 6$ gives maximum pressure that stellar core can withstand, once central hydrogen is exhausted. It usually expressed as a quadratic function $1/\alpha$, with $\alpha$ being ratio mean molecular weight to envelope. Here, we revisit this scenarios where balance equat...

&lrm;In this article&lrm;, &lrm;we develop two nonparametric smoothing estimators for parameter of a time-variant parametric model&lrm;. &lrm;This parameter can be from any parametric family or from any parametric or semi-parametric regression model&lrm;. &lrm;Estimation is based on a two-step procedure&lrm;, &lrm;in which we first get the raw estimate of the parameter at a set of disjoint time...

Abstract We develop a theory of two-parameter quantum polynomial functors. Similar to how (strict) functors give new interpretation representations the general linear groups GL n , (polynomial) symmetric pair ( $$ {U}_{Q,q}^B U Q , q ...

Preprocessing (data reduction or kernelization) to reduce instance size is one of the most commonly deployed heuristics in the implementation practice to tackle computationally hard problems. However, a systematic theoretical study of them remained elusive so far. One of the reasons for this is that if an input to an NP -hard problem can be processed in polynomial time to an equivalent one of s...

This is an overview of our recent works on the global bifurcation analysis multi-parameter polynomial dynamical systems. In particular, using bifurcation-geometric approach, we study dynamics and solve problem maximum number distribution limit cycles in a Euler–Lagrange–Liénard-type mechanical system. We also consider rational endocrine system by carrying out reduced planar quartic Topp system,...