DFT based computational study on the excited state intramolecular proton transfer processes in o-hydroxybenzaldehyde

Potential energy (PE) curves for the intramolecular proton transfer in the ground (GSIPT) and excited (ESIPT) states of o-hydroxybenzaldehyde (OHBA) were studied using DFT-B3LYP/6-31G(d) and TD-DFT-B3LYP/6-31G(d) level of theory, respectively. Our calculations suggest the non-viability of ground state intramolecular proton transfer in this compound. Excited states PE calculations support the ESIPT process in OHBA. The contour PE diagram and the variation of oscillator strength along the proton transfer co-ordinate support the dual emission in OHBA. Our calculations also support the experimental observations of Nagaoka et al. [S. Nagaoka, U. Nagashima, N. Ohta, M. Fujita, T. Takemura, J. Phys. Chem. 92 (1988) 166], i.e. normal emission of the title compound comes from S(2) state and the red-shifted proton transfer band appears from the S(1) state. ESIPT process has also been explained in terms of HOMO and LUMO electron density of the enol and keto tautomer of OHBA and from the potential energy surfaces.     

Ultrahigh-resolution full-field optical coherence tomography using spatial coherence gating and quasi-monochromatic illumination

We developed an ultrahigh-resolution full-field optical coherence tomography (FF-OCT) microscope that is based on the spatial, rather than the temporal, coherence gating. The microscope is capable of observing three-dimensional microbiological structures as small as 0.4 μm × 0.4 μm × 1.0 μm (xyz) using quasi-monochromatic light and a liquid crystal retarder. Unlike traditional FF-OCT systems, this microscope can be operated in high resolution for any preferable wavelength with minimized defocusing and dispersion effects. High-resolution images of an onion cell are presented.     

Asymptotic stability for a free boundary problem arising in a tumor model

We consider a tumor model in which all cells are proliferating at a rate μ and their density is proportional to the nutrient concentration. The model consists of a coupled system of an elliptic equation and a parabolic equation, with the tumor boundary as a free boundary. It is known that for an appropriate choice of parameters, there exists a unique spherically symmetric stationary solution with radius RS which is independent of μ. It was recently proved that there is a function μ_∗(RS) such that the spherical stationary solution is linearly stable if μ<μ_∗(RS) and linearly unstable if μ>μ_∗(RS). In this paper we prove that the spherical stationary solution is nonlinearly stable (or, asymptotically stable) if μ<μ_∗(RS).     

Liouville type theorems for fourth order elliptic equations in a half plane

Consider an elliptic equation in the half plane with boundary conditions if and if where are second and third order differential operators. It is proved that if and, for some , if if where for some nonnegative integer , then . Results of this type are also established in case under different conditions on and ; furthermore, in one case has a lower order term which depends nonlocally on . Such Liouville type theorems arise in the study of coating flow; in fact, they play a crucial role in the analysis of the linearized version of this problem. The methods developed in this paper are entirely different for the two cases (i) and (ii) ; both methods can be extended to other linear elliptic boundary value problems in a half plane.

     

Stability of solutions of chemotaxis equations in reinforced random walks

In this paper we consider a nonlinear system of differential equations consisting of one parabolic equation and one ordinary differential equation. The system arises in chemotaxis, a process whereby living organisms respond to chemical substance by moving toward higher, or lower, concentrations of the chemical substance, or by aggregating or dispersing. We prove that stationary solutions of the system are asymptotically stable.     

4-(3-nitrophenyl)-2-pieohne

The preparation of 4-(3-nitrophenyl)-2-pieoline (3) was accomplished in one step by the Zecher-Krohnke ring-closure reaction. Compound 3 is the starling material for 2-lormyl-4-(3-arninophenyl)pyridine thiosemicarbazone (4-APPT), a promising antineoplastie agent.     

Bifurcation from stability to instability for a free boundary problem modeling tumor growth by Stokes equation

We consider a free boundary problem modeling tumor growth in fluid-like tissue. The model equations include a diffusion equation for the nutrient concentration, and the Stokes equation with a source which represents the proliferation of tumor cells. The proliferation rate μ and the cell-to-cell adhesiveness γ which keeps the tumor intact are two parameters which characterize the “aggressiveness” of the tumor. For any positive radius R there exists a unique radially symmetric stationary solution with radius r=R. For a sequence μ/γ=Mn(R) there exist symmetry-breaking bifurcation branches of solutions with free boundary r=R+εYn,0(θ)+O(ε²) (n even ?2) for small |ε|, where Yn,0 is the spherical harmonic of mode (n,0). Furthermore, the smallest Mn(R), say Mn_∗(R), is such that n_∗=n_∗(R)→∞ as R→∞. In this paper we prove that the radially symmetric stationary solution with R=RS is linearly stable if μ/γ<N_∗(RS,γ) and linearly unstable if μ/γ>N_∗(RS,γ), where N_∗(RS,γ)?Mn_∗(RS), and we prove that strict inequality holds if γ is small or if γ is large. The biological implications of these results are discussed at the end of the paper.     

Finite combinations of Baire numbers

Letκ be a regular cardinal. Consider the Bair numbers of the spaces (2^θ)κ for variousθ≥κ. Letl be the number of such different Baire numbers. Models of set theory withl=1 orl=2 are known and it is also known thatl is finite. We show here that ifκ>ω, thenl could be any given finite number.