We consider the two-dimensional Cahn-Hilliard equation with logarithmic potentials and periodic boundary conditions. employ standard semi-implicit numerical scheme which treats linear fourth-order dissipation term implicitly nonlinear explicitly. Under natural constraints on time step we prove strict phase separation energy stability of scheme. This appears to be first rigorous result for discr...

Logarithmic number system (LNS) is an attractive alternative to realize finite-length impulse response filters because of multiplication in the linear domain being only addition in the logarithmic domain. In the literature, linear coefficients are directly replaced by the logarithmic equivalent. In this paper, an approach to directly optimize the finite word length coefficients in the LNS domai...

ABSTRACT In this paper, we present a temperature compensation method for logarithmic CMOS image sensors. As Bandgap technique, the compensation circuit generates VPTAT1 and VPTAT2 voltages to compensate temperature variation of the sensor output signal voltage (Out-AC-Signal) which we call VCTAT1 and output reference voltage (VRef−ph) which we call VCTAT2. The proposed method is divided into th...

The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical sta...

The paper concerns the pairwise comparison method used to rank a finite, usually small number of alternatives, in the Analytic Hierarchy Process (AHP), which belongs to a certain class of multiple attribute decision making methods. Ranking of alternatives is calculated based on expert judgments expressing relative importance for each pair of alternatives. From mathematical point of view calcula...

We present a novel automated technique for parallelizing quantum circuits via forward and backward translation to measurement-based quantum computing patterns and analyze the trade oo in terms of depth and space complexity. As a result we distinguish a class of polynomial depth circuits that can be parallelized to logarithmic depth while adding only polynomial many auxiliary qubits. In particul...

At future linear e+e− collider experiments in the TeV range, Sudakov double logarithms originating from massive boson exchange can lead to significant corrections to the cross sections of the observable processes. These effects are important for the high precision objectives of the Next Linear Collider. We use the infrared evolution equation, based on a gauge invariant dispersive method, to obt...