Discretization of singular functions is an important component in many problems to which level set methods have been applied. We present two methods for constructing consistent approximations to Dirac delta measures concentrated on piecewise smooth curves or surfaces. Both methods are designed to be convenient for level set simulations and are introduced to replace the commonly used but inconsi...

Minimization of the Euclidean distance between output distribution and Dirac delta functions as a performance criterion is known to match the distribution of system output with delta functions. In the analysis of the algorithm developed based on that criterion and recursive gradient estimation, it is revealed in this paper that the minimization process of the cost function has two gradients wit...

let $mathfrak{a}$ be an algebra. a linear mapping $delta:mathfrak{a}tomathfrak{a}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{a}$. given two derivations $delta$ and $delta'$ on a $c^*$-algebra $mathfrak a$, we prove that there exists a derivation $delta$ on $mathfrak a$ such that $deltadelta'=delta^2$ if and only if either $delta'=0$...

At each iteration of a Block Coordinate Descent method one minimizes an approximation the objective function with respect to generally small set variables subject constraints in which these are involved. The unconstrained case and simple were analyzed recent literature. In this paper we address problem block not and, moreover, they defined by global sets equations inequations. A general algorit...

29 computation. On the other hand, for network learning, at least 14-16 bits of precision must be used for the weights to avoid having the training process divert too much from the trajectory of the high precision computation. References [1] D. Hammerstrom. A VLSI architecture for high-performance, low cost, on-chip learning. Figure 10: The average squared dierences between the desired and actu...

Peskin’s Immersed Boundary (IB) method is one of the most popular numerical methods for many years and has been applied to problems in mathematical biology, fluid mechanics, material sciences, and many other areas. Peskin’s IB method is associated with discrete delta functions. It is believed that the IB method is first order accurate in the L∞ norm. But almost none rigorous proof could be foun...

CRDTs are distributed data types that make eventual consistency of a distributed object possible and non ad-hoc. Specifically, state-based CRDTs ensure convergence through disseminating the entire state, that may be large, and merging it to other replicas; whereas operation-based CRDTs disseminate operations (i.e., small states) assuming an exactly-once reliable dissemination layer. We introduc...

A widely used electrostatics model in the biomolecular modeling community, the nonlinear Poisson–Boltzmann equation, along with its finite element approximation, are analyzed in this paper. A regularized Poisson–Boltzmann equation is introduced as an auxiliary problem, making it possible to study the original nonlinear equation with delta distribution sources. A priori error estimates for the f...

poverty is the most serious threat to natural resources and the environment and most of the poor are rural-based who engage in various agricultural activities. land is a critical asset for the rural poor and lacking means to appropriately intensify agriculture which compels the poor to either overuse or misuse this natural resource base to meet basic needs. this study presents empirical relatio...

as special depositional environments which are adjacent to the seas, deltas have provided a field for human habitat establishment. geomorphic features of deltas are in constant transformation due to their dynamic features. constructing dams on rivers can intensify these changes and cause either negative or positive consequences. minab delta in hormozgan province of iran is a round or crescent-s...