1Introduction Non-convex optimization is an active area of research in optimization with one of the goals being to establish complexity guarantees for finding approximate stationary points, see the review [40]
As characteristic functions are bounded by 1, the infinite sums in (1) converge for |t|< 1. However, convergence is not really necessary to interpret this formula, since both sides can be considered as formal power series in indeterminate t, with equality meaning that coefficients of powers ...
for the Euler-Maruyama Type Approximate Solutions of Stochastic Differential EquationsFourth and Fifth Order Efficiency: Fisher InformationDirichlet Spaces of Random Processes and Generalizations of It's FormulaOn Stable-Like ProcessesAn Asymmetric Exclusion Process Related to Vortex Flow in Viscous Planer ...
35] on the degree of determinants, we consider the maximum degrees of subdeterminants for aiming to capture cardinality-(un)constrained maximization. We first deal with linear symbolic rational matrices, whereis a matrix over the rational function field. Letℓdenote the maximum degree of ...
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Furthermore, in order to compare the savings obtained by the integrated approach compared to the sequential approach, formula (36) proposed by Kuhn and Liske [52] was considered. Table 4 offers the savings that correspond to all the different considered costs in both absolute numbers and ...
power of inputs to induce spikes in the LIF model increases as the input time course is made less uniform. Our results represent an extension of this idea, providing information about specific time courses that are optimal, not just for the generation of a single spike but for maximizing ...
. we will require the following variational formula for the capacity proved in [ 38 , lemma 2.3]. recall that the green’s function on \({{\,\mathrm{{\mathbb {z}}}\,}}^4\) is defined by $$\begin{aligned} g(x,y) = \frac{1}{\deg y}{\textbf{e}}_x\sum _{n\ge 0}\...
Formula (1) indicates that the brake torque is proportional to the speed of brake disk when the current is kept constant. But the proportional relationship is broken as the disk speed increases. Figure 3 shows the torque versus rotor speed relationship tested on the testing bench. When the ele...
(2020). In a compact square area with homogeneous grids of streets, assuming that no detour is allowed for any ridepooling trip, Daganzo and Ouyang (2019) mathematically depicted the origin- and destination-catchment area of each passenger-OD pair, and proposed a closed-form formula for the ...