We solve a long-standing open problem concerning a discrete mathematical model, which has various applications in computer science and several other fields, including frequency assignment and many other problems on resource allocation. A mixed hypergraph H is a triple (X, C,D), where X is the set of vertices, and C and D are two set systems over X , the families of so-called C-edges and D-edges...

The mixed-order eigenvalue problem −δ∆u + ∆u + λu = 0 with δ > 0, modeling small amplitude vibrations of a thin plate, is analyzed in a bounded 2-D domain Ω that contains a single small hole of radius ε centered at some x0 ∈ Ω. Clamped conditions are imposed on the boundary of Ω and on the boundary of the small hole. In the limit ε → 0, and for δ = O(1), the limiting problem for u must satisfy ...

Partial dynamical symmetry describes a situation in which some eigenstates have a symmetry which the quantum Hamiltonian does not share. This property is shown to have a classical analogue in which some tori in phase space are associated with a symmetry which the classical Hamiltonian does not share. A local analysis in the vicinity of these special tori reveals a neighbourhood of phase space f...

Partial dynamical symmetry describes a situation in which some eigenstates have a symmetry which the quantum Hamiltonian does not share. This property is shown to have a classical analogue in which some tori in phase space are associated with a symmetry which the classical Hamiltonian does not share. A local analysis in the vicinity of these special tori reveals a neighbourhood of phase space f...

Ultrasensitive prostate-specific antigen (u-PSA) remains controversial for follow-up after radical prostatectomy (RP). The aim of this study was to model PSA doubling times (PSADT) for predicting biochemical recurrence (BCR) and to capture possible discrepancies between u-PSA and traditional PSA (t-PSA) by utilizing advanced statistical modeling. 555 RP patients without neoadjuvant/adjuvant and...

In this paper we develop the monotone method in the presence of lower and upper solutions for the problem u(t) = f(t, u(t));u(a) − u(b) = λi ∈ R; i = 0, ..., n− 1. Where f is a Carathéodory function. We obtain sufficient conditions in f to guarantee the existence and approximation of solutions between a lower solution α and an upper solution β for n ≥ 3 either α ≤ β or α ≥ β. For this, we study...

We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen's expanded mixed element method. We study the new expanded mixed element method for convection-dominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed proje...

Several recent papers propose competing theoretical explanations for the empirical observation of an inverted U-shape relationship between enviromental degradation and per-capita income. We proprose the following test of the theory: calibrate a theoretical model to an already developed economy using information unrelated to the pollution-income curve. Then simulate the model starting from a les...

LTE in unlicensed spectrum (LTE-U) is a promising approach to overcome the wireless spectrum scarcity. However, to reap the benefits of LTE-U, a fair coexistence mechanism with other incumbent WiFi deployments is required. In this paper, a novel deep learning approach is proposed for modeling the resource allocation problem of LTE-U small base stations (SBSs). The proposed approach enables mult...