Inverse problems for Schrodinger equations with Yang-Mills potentials in domains with obstacles and the Aharonov-Bohm effect

We study the inverse boundary value problems for the Schr\"{o}dinger equations with Yang-Mills potentials in a bounded domain $\Omega_0\subset\R^n$ containing finite number of smooth obstacles $\Omega_j,1\leq j \leq r$. We prove that the Dirichlet-to-Neumann operator on $\partial\Omega_0$ determines the gauge equivalence class of the Yang-Mills potentials. We also prove that the metric tensor can be recovered up to a diffeomorphism that is identity on $\partial\Omega_0$.Comment: 15 page

A new approach to hyperbolic inverse problems

We present a modification of the BC-method in the inverse hyperbolic problems. The main novelty is the study of the restrictions of the solutions to the characteristic surfaces instead of the fixed time hyperplanes. The main result is that the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the self-adjoint hyperbolic operator up to a diffeomorphism and a gauge transformation. In this paper we prove the crucial local step. The global step of the proof will be presented in the forthcoming paper.Comment: We corrected the proof of the main Lemma 2.1 by assuming that potentials A(x),V(x) are real value

Inverse hyperbolic problems and optical black holes

In this paper we give a more geometrical formulation of the main theorem in [E1] on the inverse problem for the second order hyperbolic equation of general form with coefficients independent of the time variable. We apply this theorem to the inverse problem for the equation of the propagation of light in a moving medium (the Gordon equation). Then we study the existence of black and white holes for the general hyperbolic and for the Gordon equation and we discuss the impact of this phenomenon on the inverse problems

Strong wavefront lemma and counting lattice points in sectors

We compute the asymptotics of the number of integral quadratic forms with prescribed orthogonal decompositions and, more generally, the asymptotics of the number of lattice points lying in sectors of affine symmetric spaces. A new key ingredient in this article is the strong wavefront lemma, which shows that the generalized Cartan decomposition associated to a symmetric space is uniformly Lipschitz

Inverse Scattering for Gratings and Wave Guides

We consider the problem of unique identification of dielectric coefficients for gratings and sound speeds for wave guides from scattering data. We prove that the "propagating modes" given for all frequencies uniquely determine these coefficients. The gratings may contain conductors as well as dielectrics and the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page

A linear mixed model approach to gene expression-tumor aneuploidy association studies.

Aneuploidy, defined as abnormal chromosome number or somatic DNA copy number, is a characteristic of many aggressive tumors and is thought to drive tumorigenesis. Gene expression-aneuploidy association studies have previously been conducted to explore cellular mechanisms associated with aneuploidy. However, in an observational setting, gene expression is influenced by many factors that can act as confounders between gene expression and aneuploidy, leading to spurious correlations between the two variables. These factors include known confounders such as sample purity or batch effect, as well as gene co-regulation which induces correlations between the expression of causal genes and non-causal genes. We use a linear mixed-effects model (LMM) to account for confounding effects of tumor purity and gene co-regulation on gene expression-aneuploidy associations. When applied to patient tumor data across diverse tumor types, we observe that the LMM both accounts for the impact of purity on aneuploidy measurements and identifies a new association between histone gene expression and aneuploidy

Formation of hot tear under controlled solidification conditions

Aluminum alloy 7050 is known for its superior mechanical properties, and thus finds its application in aerospace industry. Vertical direct-chill (DC) casting process is typically employed for producing such an alloy. Despite its advantages, AA7050 is considered as a "hard-to-cast" alloy because of its propensity to cold cracking. This type of cracks occurs catastrophically and is difficult to predict. Previous research suggested that such a crack could be initiated by undeveloped hot tears (microscopic hot tear) formed during the DC casting process if they reach a certain critical size. However, validation of such a hypothesis has not been done yet. Therefore, a method to produce a hot tear with a controlled size is needed as part of the verification studies. In the current study, we demonstrate a method that has a potential to control the size of the created hot tear in a small-scale solidification process. We found that by changing two variables, cooling rate and displacement compensation rate, the size of the hot tear during solidification can be modified in a controlled way. An X-ray microtomography characterization technique is utilized to quantify the created hot tear. We suggest that feeding and strain rate during DC casting are more important compared with the exerted force on the sample for the formation of a hot tear. In addition, we show that there are four different domains of hot-tear development in the explored experimental window-compression, microscopic hot tear, macroscopic hot tear, and failure. The samples produced in the current study will be used for subsequent experiments that simulate cold-cracking conditions to confirm the earlier proposed model.This research was carried out within the Materials innovation institute (www.m2i.nl) research framework, project no. M42.5.09340

Distribution of some elements in Veronica scutellata L. from Bolu,Turkey: soil-plant interactions

Veronica scutellata L. occurs in moist and wet habitats, such as ponds, marshes and other wetlands. This study was conducted on this species to examine its mineral element uptake status in terms of interactions between soil and plant. Experimental materials were taken from the Southern coast of Black Sea at coordinates 40º36’N and 31º16’E at an altitude of 1400 m above sea level from Bolu – Turkey; using standard methods and plant (root, stem and leaf parts) and soil mineral element measurements (Al, B, Ca, Cu, Fe, K, Mg, Mn, Na, Ni and Zn) were done. During the study, ICP-OES was employed for the measurement of mineral elements. It was observed that considerable amounts of B, Ca, K, Mg, Mn, Na and Zn are accumulated by the plant