Matrix multiplication operators on Banach function spaces

In this paper, we study the matrix multiplication operators on Banach function spaces and discuss their applications in semigroups for solving the abstract Cauchy problem.     

Solutions of SPDE’s Associated with a Stochastic Flow

Potential Analysis - We consider the following stochastic partial differential equation, $$begin{array}{@{}rcl@{}} &&dY_{t} = L^{ast} Y_{t} dt + A^{ast} Y_{t} cdot dB_{t}...     

A weak immersion relation on graphs and its applications

Weak immersion is a generalization of the immersion relation defined by Nash-Williams. A graph H is said to be weakly immersed in a graph G if H can be obtained from G by a sequence of these three operations: taking a subgraph, splitting a vertex, and lifting a pair of adjacent edges. The weak immersion relation has the useful property that finite graphs are well-quasi-ordered by it, which also holds for graphs with some vertices designated as terminals. As a result, any family of finite graphs that is closed under weak immersion can be characterized by a finite number of minimal forbidden graphs called obstructions. Weak immersion offers two advantages over immersion for practical applications. First, although closure under weak immersion implies closure under immersion, families can have significantly fewer obstructions under weak immersion. Hence weak immersion can provide simpler characterizations for closed families. Examples include graphs of bounded cutwidth and graphs of bounded multiway cutsize. The difference in the number of obstructions is at least exponential in the cutwidth and in the square-root of the multiway cutsize. Second, for every fixed graph H, there is a polynomial-time algorithm to decide whether H is weakly immersed in an input graph G. Consequently, there is a polynomial-time membership test for any family that is closed under weak immersion. In principle, testing for weak immersion is as fast as testing for immersion. Thus the simpler characterization provided by weak immersion may lead to faster membership algorithms.     

An approximate analytical solution of one-dimensional phase change problems in a finite domain

In this paper, we present an approximate analytical solution for solving one dimensional two phase Stefan problem. The finite sine transform technique is used to convert the non dimensional form from a space domain to a wave number domain. Inverse finite sine transform is used to obtain the desired solution. The location of moving interface during freezing process in a finite domain is studied and the result thus obtained are discussed graphically. The whole analysis is presented in a non dimensional form.     

Post-buckling of cantilever columns having variable cross-section under a combined load

Post-buckling of a cantilever column is examined under a combined load consisting of a tip-concentrated load and a distributed axial load, through dynamic formulation. The formulation of the problem is based on the moment–curvature relationship. The two-point boundary value problem described by the governing equations is dependent on the frequency parameter and the two load parameters. The buckling loads are those loads at which the eigencurve, namely, the load versus frequency curve of the column meets the load axis. A simple and reliable iterative procedure to convert the two-point boundary value problem into an initial value problem is followed and solved the non-linear differential equations utilizing a fourth-order Runge–Kutta integration scheme. To demonstrate the potentiality of the adopted numerical scheme, linear vibration frequencies of truncated, tapered cantilever wedges and cones are determined and compared with the published analytical and test results. Buckling and post-buckling loads of a simply supported stepped column are obtained and compared with the published test results. The loads and deflections of non-uniform cantilever columns are obtained for various slopes at the tip. The interaction of load parameters for a free–free truncated conical column has also been examined. The numerical results indicate that the path represented by the two load parameters turns out to be nearly a straight line.     

An intrinsic approach to Lichnerowicz conjecture

In this paper we give a proof of Lichnerowicz conjecture for compact simply connected manifolds which is intrinsic in the sense that it avoids thenice embeddings into eigenspaces of the Laplacian. Even if one wants to use these embeddings, this paper gives a more streamlined proof. As a byproduct, we get a simple criterion for a polynomial to be a Jacobi polynomial.     

Emeritus Professor Shan-Fu Shen,Cornell University

A numerical analysis of blood flow in a rigid artery has been performed to observe the variations in flow pattern and haemodynamic parameters under the influence of multiple (double) stenoses. The interspacing distance, degree of stenotic severity and Reynolds number of flow have been varied. It is found that two stenoses interact when the interspacing distance is lower than a critical value that corresponds to the redevelopment length of fully developed flow after the proximal stenosis. In the case of non-interacting stenoses the haemodynamic parameters, like the peak centreline velocity (representing the peak systolic velocity ratio in medical term), the maximum wall shear stress, region of low shear stress and the irrecoverable pressure drop at the stenosis site, repeat themselves at each individual stenosis. However, when the stenoses interact hydrodynamically because of their proximity, the parameters behave differently, which can lead to a different haemodynamic profile in the arteries and pose difficulties in their pathological interpretation. This work evaluates the influence of double stenoses on the variations in the key haemodynamic features under different degree of stenoses and interspacing distance between the stenoses.     

Inverse analysis of an internal reforming solid oxide fuel cell system using simplex search method

An inverse problem is solved for estimating fuel cell operating parameters such as current density, pressure and fuel flow rate (FFR) separately and then simultaneously two parameters in an internal reforming solid oxide fuel cell (IRSOFC). Initially, a mathematical model for the forward problem is developed to simulate the IRSOFC steady state operation and its performance in terms of power output and then an inverse problem is solved for recovering the above parameters using a simplex search minimization algorithm. The objective function (IRSOFC power) and the estimation accuracy are studied for the effects of initial guess values of the operating parameters and the number of iterations required for retrieval of these parameters. The objective function is represented by the sum of square of the error between a given IRSOFC power and the power evaluated based on some arbitrary guessed values of the unknowns which is then regularized in an iterative manner for solution of the inverse fuel cell problem. The study reveals that a multiple combinations of parameters (current density, operating pressure and FFR) exist which provides guidelines for selecting feasible combinations of these parameters required for meeting a given power requirement. The results show relatively good agreement between the inverse and exact solutions.     

Estimating Precision in Functional Images

Abstract

Functional imaging of biologic parameters like in vivo tissue metabolism is made possible by Positron Emission Tomography (PET). Many techniques have been suggested for extracting such images from dynamic time-course sequences of reconstructed PET scans. Quantitating the precision of these estimates is important for drawing inferences on the biologic parameters. Analytic variance formulas are not immediate owing to the nonlinear methods used in extraction. The usual resampling approach is infeasible because each image reconstruction in PET is a computationally demanding solution to a high-dimensional linear inverse problem. We suggest an alternative simulation approach that approximates the distribution of reconstructed PET scans and performs a parametric bootstrap in the imaging domain. Results on a simplified model chosen to match the characteristics of PET reconstruction are very encouraging. Mixture analysis is used to estimate functional images; however, the suggested approach is general enough to extend to other techniques or imaging methods.