Search results for "General Mathematics"

Optimization of Linearized Belief Propagation for Distributed Detection

2020

In this paper, we investigate distributed inference schemes, over binary-valued Markov random fields, which are realized by the belief propagation (BP) algorithm. We first show that a decision variable obtained by the BP algorithm in a network of distributed agents can be approximated by a linear fusion of all the local log-likelihood ratios. The proposed approach clarifies how the BP algorithm works, simplifies the statistical analysis of its behavior, and enables us to develop a performance optimization framework for the BP-based distributed inference systems. Next, we propose a blind learning-adaptation scheme to optimize the system performance when there is no information available a pr…

Quasi *-algebras and generalized inductive limits of C*-algebras

2011

Boundary value problem with integral condition for a Blasius type equation

2016

The steady motion in the boundary layer along a thin flat plate, which is immersed at zero incidence in a uniform stream with constant velocity, can be described in terms of the solution of the differential equation x'''= -xx'', which satisfies the boundary conditions x(0) = x'(0) = 0, x'(∞) = 1. The author investigates the generalized boundary value problem consisting of the nonlinear third-order differential equation x''' = -trx|x|q-1x'' subject to the integral boundary conditions x(0) = x'(0) = 0, x'(∞) = λ∫0ξx(s) ds, where 0 0 is a parameter. Results on the existence and uniqueness of solutions to boundary value problem are established. An illustrative example is provided.

Convergence theorems for the PU-integral

2000

Partial data inverse problems and simultaneous recovery of boundary and coefficients for semilinear elliptic equations

2021

We study various partial data inverse boundary value problems for the semilinear elliptic equation $\Delta u+ a(x,u)=0$ in a domain in $\mathbb R^n$ by using the higher order linearization technique introduced in [LLS 19, FO19]. We show that the Dirichlet-to-Neumann map of the above equation determines the Taylor series of $a(x,z)$ at $z=0$ under general assumptions on $a(x,z)$. The determination of the Taylor series can be done in parallel with the detection of an unknown cavity inside the domain or an unknown part of the boundary of the domain. The method relies on the solution of the linearized partial data Calder\'on problem [FKSU09], and implies the solution of partial data problems fo…

Quantitative Runge Approximation and Inverse Problems

2017

In this short note we provide a quantitative version of the classical Runge approximation property for second order elliptic operators. This relies on quantitative unique continuation results and duality arguments. We show that these estimates are essentially optimal. As a model application we provide a new proof of the result from \cite{F07}, \cite{AK12} on stability for the Calder\'on problem with local data.

A sharp estimate for Neumann eigenvalues of the Laplace-Beltrami operator for domains in a hemisphere

2018

Here, we prove an isoperimetric inequality for the harmonic mean of the first [Formula: see text] non-trivial Neumann eigenvalues of the Laplace–Beltrami operator for domains contained in a hemisphere of [Formula: see text].

D3 Dihedral Logistic Map of Fractional Order

2021

In this paper, the D3 dihedral logistic map of fractional order is introduced. The map presents a dihedral symmetry D3. It is numerically shown that the construction and interpretation of the bifurcation diagram versus the fractional order requires special attention. The system stability is determined and the problem of hidden attractors is analyzed. Furthermore, analytical and numerical results show that the chaotic attractor of integer order, with D3 symmetries, looses its symmetry in the fractional-order variant.

[3 + 2] Cycloadditions in Asymmetric Synthesis of Spirooxindole Hybrids Linked to Triazole and Ferrocene Units: X-ray Crystal Structure and MEDT Stud…

2022

Derivatization of spirooxindole having triazole and ferrocene units was achieved by the [3 + 2] cycloaddition (32CA) reaction approach. Reacting the respective azomethine ylide (AY) intermediate generated in situ with the ethylene derivative produced novel asymmetric cycloadducts with four contiguous asymmetric carbons in an overall high chemical yield with excellent regioselectivity and diastereoselectivity. X-Ray single-crystal structure analyses revealed, with no doubt, the success of the synthesis of the target compounds. The 32CA reaction of AY 5b with ferrocene ethylene 1 has been studied within MEDT. This 32CA reaction proceeds via a two-stage one-step mechanism involving a high asyn…

Shape optimization for Stokes problem with threshold slip boundary conditions

2017

This paper deals with shape optimization of systems governed by the Stokes flow with threshold slip boundary conditions. The stability of solutions to the state problem with respect to a class of domains is studied. For computational purposes the slip term and impermeability condition are handled by a regularization. To get a finite dimensional optimization problem, the optimized part of the boundary is described by B´ezier polynomials. Numerical examples illustrate the computational efficiency. peerReviewed