Applications of CGO solutions to coupled-physics inverse problems
Ilker Kocyigit Ru-Yu Lai Lingyun Qiu Yang Yang Ting Zhou

This paper surveys inverse problems arising in several coupled-physics imaging modalities for both medical and geophysical purposes. These include Photo-acoustic Tomography (PAT), Thermo-acoustic Tomography (TAT), Electro-Seismic Conversion, Transient Elastrography (TE) and Acousto-Electric Tomography (AET). These inverse problems typically consists of multiple inverse steps, each of which corresponds to one of the wave propagations involved. The review focuses on those steps known as the inverse problems with internal data, in which the complex geometrical optics (CGO) solutions to the underlying equations turn out to be useful in showing the uniqueness and stability in determining the desired information.

keywords: Coupled-physics imaging modalities internal data CGO solutions uniqueness stability
Multiwave tomography with reflectors: Landweber's iteration
Plamen Stefanov Yang Yang

We use the Landweber method for numerical simulations for the multiwave tomography problem with a reflecting boundary and compare it with the averaged time reversal method. We also analyze the rate of convergence and the dependence on the step size for the Landweber iterations on a Hilbert space.

keywords: Thermoacoustic tomography microlocal analysis Landweber iterations medical imaging
Even periodic and odd periodic complementary sequence pairs from generalized Boolean functions
Yang Yang Xiaohu Tang Guang Gong
A pair of two sequences is called the even periodic (odd periodic) complementary sequence pair if the sum of their even periodic (odd periodic) correlation function is a delta function. The well-known Golay aperiodic complementary sequence pair (Golay pair) is a special case of even periodic (odd periodic) complementary sequence pair. In this paper, we presented several classes of even periodic and odd periodic complementary pairs based on the generalized Boolean functions, but which do not form Gloay pairs. The proposed sequences could be used to design signal sets, which have been applied in direct sequence code division multiple (DS-CDMA) cellular communication systems.
keywords: Even periodic complementary sequence pair Golay complementary pair odd periodic complementary sequence pair Golay sequences generalized Boolean function.
Positive solutions of nonhomogeneous fractional Laplacian problem with critical exponent
Xudong Shang Jihui Zhang Yang Yang
In this paper, we study the following problem \begin{eqnarray} (-\Delta)^{\frac{\alpha}{2}}u = K(x)|u|^{2_{\alpha}^{*}-2}u + f(x) \quad in \ \Omega,\\ u=0 \quad on \ \partial \Omega, \end{eqnarray} where $\Omega\subset R^N$ is a smooth bounded domain, $0< \alpha < 2$, $N>\alpha$, $ 2_{\alpha}^{*}= \frac{2N}{N-\alpha}$, $f\in H^{-\frac{\alpha}{2}}(\Omega)$ and $K(x)\in L^\infty(\Omega)$. Under appropriate assumptions on $K$ and $f$, we prove that this problem has at least two positive solutions. When $\alpha = 1$, we also establish a nonexistence result for a positive solution in a class of linear positive-type domains are more general than star-shaped ones.
keywords: Positive solutions fractional Laplacian critical exponent.
Global compactness results for nonlocal problems
Lorenzo Brasco Marco Squassina Yang Yang

We obtain a Struwe type global compactness result for a class of nonlinear nonlocal problems involving the fractional $p-$Laplacian operator and nonlinearities at critical growth.

keywords: Fractional $p$-Laplacian variational methods global compactness
New almost perfect, odd perfect, and perfect sequences from difference balanced functions with d-form property
Yang Yang Xiaohu Tang Guang Gong

By using shift sequences defined by difference balanced functions with d-form property, and column sequences defined by a mutually orthogonal almost perfect sequences pair, new almost perfect, odd perfect, and perfect sequences are obtained via interleaving method. Furthermore, the proposed perfect QAM+ sequences positively answer to the problem of the existence of perfect QAM+ sequences proposed by Boztaş and Udaya.

keywords: Almost perfect sequences perfect sequences odd perfect sequences QAM+ sequences difference balanced function d-form.
Asymptotics for ruin probabilities in Lévy-driven risk models with heavy-tailed claims
Yang Yang Kam C. Yuen Jun-Feng Liu

Consider a bivariate Lévy-driven risk model in which the loss process of an insurance company and the investment return process are two independent Lévy processes. Under the assumptions that the loss process has a Lévy measure of consistent variation and the return process fulfills a certain condition, we investigate the asymptotic behavior of the finite-time ruin probability. Further, we derive two asymptotic formulas for the finite-time and infinite-time ruin probabilities in a single Lévy-driven risk model, in which the loss process is still a Lévy process, whereas the investment return process reduces to a deterministic linear function. In such a special model, we relax the loss process with jumps whose common distribution is long tailed and of dominated variation.

keywords: Lévy-driven risk model finite-time and infinite-time ruin probabilities consistent variation dominated variation long tail asymptotics
On a perturbed compound Poisson model with varying premium rates
Zhimin Zhang Yang Yang Chaolin Liu

In this paper, we consider a perturbed compound Poisson model with varying premium rates. The surplus process is observed at a sequence of review times. The effective premium rate is adjusted according to the surplus increment between the inter-review times. We study the Gerber-Shiu functions by Laplace transform method. When the claim size density is a combination of exponentials, the explicit expressions for the Laplace transforms of ruin time are derived.

keywords: Varying premium rates Gerber-Shiu function Laplace transform ruin
On $\omega$-cyclic-conjugated-perfect quaternary GDJ sequences
Yang Yang Guang Gong Xiaohu Tang
A sequence is called perfect if its autocorrelation function is a delta function. In this paper, we give a new definition of autocorrelation function: $\omega$-cyclic-conjugated autocorrelation. As a result, we present several classes of $\omega$-cyclic-conjugated-perfect quaternary Golay sequences, where $\omega=\pm 1$. We also considered such perfect property for $4^q$-QAM Golay sequences, $q\ge 2$ being an integer.
keywords: quaternary sequences quadrature amplitude modulation (QAM) Golay sequence $\omega$-cyclic-conjugated autocorrelation. $\omega$-cyclic autocorrelation Golay-Davis-Jedweb (GDJ) sequences

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