Asymptotic profiles of zero points of solutions to the heat equation

In this paper, we analyze the asymptotic profiles of zero points with respect to the spatial variable of the solutions to the heat equation in one-dimensional space. By giving suitable conditions of the initial data, we prove the existence of a zero point such that the asymptotic behavior is $O(t)$ as $t\to+\infty$ and its coefficient is characterized by a zero point of the bilateral Laplace transform of the initial data. Furthermore, we reveal the second and third-order asymptotic profiles of the zero point

Propagating front solutions in a time-fractional Fisher-KPP equation

In this paper, we treat the Fisher-KPP equation with a Caputo-type time fractional derivative and discuss the propagation speed of the solution. The equation is a mathematical model that describes the processes of sub-diffusion, proliferation, and saturation. First, the behavior of the solution is analyzed by numerical simulations, and it is discussed what kind of solution is appropriate to characterize the propagation of the solution. Based on the insights, we introduce the notion of a traveling wave-like solution, the so-called asymptotic traveling wave solution. Finally, the existence of the asymptotic traveling wave solution is discussed using a monotone iteration method.Comment: The typo is being modified. I hope you will check the latest versio

Beyond: collapsible tools and gestures for computational design

Since the invention of the personal computer, digital media has remained separate from the physical world, blocked by a rigid screen. In this paper, we present Beyond, an interface for 3-D design where users can directly manipulate digital media with physically retractable tools and hand gestures. When pushed onto the screen, these tools physically collapse and project themselves onto the screen, letting users perceive as if they were inserting the tools into the digital space beyond the screen. The aim of Beyond is to make the digital 3-D design process straightforward, and more accessible to general users by extending physical affordances to the digital space beyond the computer screen

Melena due to telangiectasia in migraine

Migraine is a chronic neurological disorder characterized by headaches and extracephalic symptoms. We report a 73-year-old male patient with a history of migraines as well as several other chronic conditions including abdominal pain accompanied by nausea and vomiting, pain and ecchymosis of the limbs, dysmetropsia, syncope, and melena due to telangiectasia of the sigmoid colon. After a thorough evaluation of the migraine condition, we hypothesized that the patient’s melena due to telangiectasia of the sigmoid colon might in fact be a migraine-related phenomenon. In this report, we discuss a possible mechanism for melena due to telangiectasia in migraine patients, as well as “tips” for identifying subtle and/or unreported clinical features of migraine conditions