CALORIMETRY OF PARTIAL MARTENSITIC TRANSFORMATIONS

Partial thermoelastic martensitic transformations have been studied by calorimetry on CuAlNi single crystals with special methods. The chemical enthalpy change, the elastic energy stored at the interfaces or inside of the martensite and the energy dissipated in acoustic emission were calculated for a partial transformation; the relationship among them was studied based on measured latent heat and transformation temperatures. The influence of specimen shape on the stored elastic energy was evaluated and discussed.

A NONLINEAR LAVRENTIEV-BITSADZE MIXED TYPE EQUATION

In this paper the Tricomi problem for a nonlinear mixed type equation is studied. The coefficients of the mixed type equation are discontinuous on the line, where the equation changes its type. The existence of solution to this problem is proved. The method developed in this paper can be applied to study more difficult problems for nonlinear mixed type equations arising in gas dynamics.

OSCILLATION CRITERIA FOR CERTAIN EVEN ORDER NEUTRAL DIFFERENTIAL EQUATIONS

Using the generalized Riccati technique and the averaging technique, we establish several oscillation criteria for certain even order neutral differential equation. The results obtained in this paper extend and improve some known results in the previous literatures.

Invariant Metrics and Laplacians on Siegel-Jacobi Disk

Let D n be the generalized unit disk of degree n.In this paper,Riemannian metrics on the Siegel-Jacobi disk D n × C (m,n) which are invariant under the natural action of the Jacobi group are found explicitly and the Laplacians of these invariant metrics are computed explicitly.These are expressed in terms of the trace form.

Sampling formulas for 2D quaternionic signals associated with various quaternion Fourier and linear canonical transforms

The main purpose of this paper is to study different types of sampling formulas of quaternionic functions,which are bandlimited under various quaternion Fourier and linear canonical transforms.We show that the quaternionic bandlimited functions can be reconstructed from their samples as well as the samples of their derivatives and Hilbert transforms.In addition,the relationships among different types of sampling formulas under various transforms are discussed.First,if the quaternionic function is bandlimited to a rectangle that is symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are identical.If this rectangle is not symmetric about the origin,then the sampling formulas under various quaternion Fourier transforms are different from each other.Second,using the relationship between the two-sided quaternion Fourier transform and the linear canonical transform,we derive sampling formulas under various quaternion linear canonical transforms.Third,truncation errors of these sampling formulas are estimated.Finally,some simulations are provided to show how the sampling formulas can be used in applications.

Simulation of Inviscid Compressible Flows Using PDE Transform

The solution of systems of hyperbolic conservation laws remains an interesting and challenging task due to the diversity of physical origins and complexity of the physical situations.The present work introduces the use of the partial differential equation(PDE)transform,paired with the Fourier pseudospectral method(FPM),as a new approach for hyperbolic conservation law problems.The PDE transform,based on the scheme of adaptive high order evolution PDEs,has recently been applied to decompose signals,images,surfaces and data to various target functional mode functions such as trend,edge,texture,feature,trait,noise,etc.Like wavelet transform,the PDE transform has controllable time-frequency localization and perfect reconstruction.A fast PDE transform implemented by the fast Fourier Transform(FFT)is introduced to avoid stability constraint of integrating high order PDEs.The parameters of the PDE transform are adaptively computed to optimize the weighted total variation during the time integration of conservation law equations.A variety of standard benchmark problems of hyperbolic conservation laws is employed to systematically validate the performance of the present PDE transform based FPM.The impact of two PDE transform parameters,i.e.,the highest order and the propagation time,is carefully studied to deliver the best effect of suppressing Gibbs’oscillations.The PDE orders of 2-6 are used for hyperbolic conservation laws of low oscillatory solutions,while the PDE orders of 8-12 are often required for problems involving highly oscillatory solutions,such as shock-entropy wave interactions.The present results are compared with those in the literature.It is found that the present approach not only works well for problems that favor low order shock capturing schemes,but also exhibits superb behavior for problems that require the use of high order shock capturing methods.