Bayesian methods of matrix factorization (MF) have been actively explored recently as promising alternatives to classical singular value decomposition. In this paper, we show that, despite the fact that the optimization problem is non-convex, the global optimal solution of variational Bayesian (VB) MF can be computed analytically by solving a quartic equation. This is highly advantageous over a...

By application of the duality transformation, which implies interchange of active and passive electric parts of the Riemann curvature (equivalent to interchange of Ricci and Einstein tensors) it is shown that the global monopole solution in the Kaluza-Klein spacetime is dual to the corresponding vacuum solution. Further we also obtain solution dual to flat space which would in general describe ...

In [] Rammaha and Sakuntasathien studied the global well posedness of the solution of problem (.). Agre and Rammaha [] studied the global existence and the blow up of the solution of problem (.) for k = l = θ = = , and also Alves et al. [] investigated the existence, uniform decay rates and blow up of the solution to systems. After that, the blow up result was improved by Houari []. Al...

The existence and uniqueness of the global strong solution with small initial data to the three-dimensional density-dependent incompressible viscoelastic fluids is established. The local existence and uniqueness of the global strong solution with small initial data to the three-dimensional compressible viscoelastic fluids is also obtained. A new method is developed to estimate the solution with...

Abstract. In a paper published in 1955, E.M. Wright proved that all solutions of the delay differential equation z(t) = −αz(t − 1)(1 + z(t)) converge to zero for α ∈ [0, 1.5], and conjectured that this is even true for α ∈ [0, π/2]. The present paper provides a computer-assisted proof that for α ∈ [1.5, 1.5705], this delay differential equation has no periodic solution with an amplitude larger ...

The ‘surplus’ of oceanic water generated by climate change offers an unprecedented opportunity to tackle a number of global issues through a very pragmatic process: shifting the excess water from the oceans onto the land. Here we propose that sea-level rise could be mitigated through the desalination of very large amounts of seawater in massive desalination plants. To efficiently mitigate sea-l...

We present a rigorous geometric analysis of the computation of the global position of an airborne video camera using aerial images of known landmarks. This has also been known as the perspective-n-point (PnP) problem. Based on the analysis, a robust Hough transform-like method, facilitated by a class of CORDIC-structured computations, to nd the solution for the problem, is shown feasible within...

We study the domain of existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions. The Riemann problem is the expansion of a quadrant of gas of constant state into the other three vacuum quadrants. The global existence of a smooth solution was established in Dai and Zhang [Arch. Rational Mech. Anal., 155(2000), 277-298] up to the free boundary of vac...

Global trade and supply chains are expanding due to the robust growth of markets across international boundaries. This has driven the establishment of manufacturing sites in distant locations supported by a global supplier base. Trade volumes have increased by 13.5% in 2010 and with it security requirements in managing global trade have increased accordingly. With such growth and security deman...

In this paper, compared with the previous results, a new global existence for strong solutions to the equation is acquired provided that the potential (1−∂2 x)u0 changes sign on R, which improves considerably the previous result. Mathematics Subject Classification: 35G25, 35L05, 35Q35