Abstract:
We propose a new remote gaze tracking system as an intelligent TV interface. Our research is novel in the following three ways: first, because a user can sit at various positions in front of a large display, the capture volume of the gaze tracking system should be greater, so the proposed system includes two cameras which can be moved simultaneously by panning and tilting mechanisms, a wide view camera (WVC) for detecting eye position and an auto-focusing narrow view camera (NVC) for capturing enlarged eye images. Second, in order to remove the complicated calibration between the WVC and NVC and to enhance the capture speed of the NVC, these two cameras are combined in a parallel structure. Third, the auto-focusing of the NVC is achieved on the basis of both the user’s facial width in the WVC image and a focus score calculated on the eye image of the NVC. Experimental results showed that the proposed system can be operated with a gaze tracking accuracy of ±0.737°~±0.775° and a speed of 5~10 frames/s.

Abstract:
We study del Pezzo fibrations of degree 1 with terminal singularities. A connection between singularities on del Pezzo surfaces of degree 1 and Kodaira's classification of elliptic singular fibers will be studied in this paper. By this investigation we obtain several results on birational maps of del Pezzo fibrations of degree 1 with terminal singularities.

Abstract:
This paper is an innovative scientific report about the following economic problems.
It considers why the stock price cannot be predicted and the function of the invisible
hand and the law of supply and demand. Incidentally, it is possible to solve these by
other science, for example, the systems’ analysis theory in engineering. Therefore,
economic science is very rational or systematic economic systems are not black boxes.
It cannot be solved with traditional science but with other science, and proved
with simulations. This scientific research has the potential to be sensational for economic
development; therefore, scientists across the world must be informed about its
solution.

Abstract:
This paper provides a clarification of the advanced solution for the mission of complexity in science, which was previously published in 2015; but the new solution is too difficult to scientists; for this, this paper describes the academic reasoning and the relevant scientific background behind solution. Moreover, it shows that the solution can be simulated the complex systems by the computer program MATLAB Simulink or an analog-type simulator under virtual circumstances. Thus, this paper verifies that the new solution has validity and superiority; additionally, it must replace the established older chaos theory with the advanced solution in future, so that this new solution is disadvantageous to many chaos physicists and the famous organization SFI, and others. However, they must suspend their work on complexity, because the complexity is a solvable problem in science.

Abstract:
Let $X$ be a smooth hypersurface of degree $n\geq 3$ in $\mathbb{P}^n$. We prove that the log canonical threshold of $H\in|-K_X|$ is at least $\frac{n-1}{n}$. Under the assumption of the Log minimal model program, we also prove that a hyperplane section $H$ of $X$ is a cone in $\mathbb{P}^{n-1}$ over a smooth hypersurface of degree $n$ in $\mathbb{P}^{n-2}$ if and only if the log canonical threshold of $H$ is $\frac{n-1}{n}$.

Abstract:
We classify all the effective anticanonical divisors on weak del Pezzo surfaces. Through this classification we obtain the smallest number among the log canonical thresholds of effective anticanonical divisors on a given Gorenstein canonical del Pezzo surface.

Abstract:
We study birational transformations into elliptic fibrations and birational automorphisms of quasismooth anticanonically embedded weighted Fano 3-fold hypersurfaces having terminal singularities classified by A.R. Iano-Fletcher, J. Johnson, J. Kollar, and M. Reid.