We introduce the discrete p-Schrödinger operator L_p,ω and solve the following p-Schrödinger equation: L_p,ωu = −Δ_p,ωu + q|u|^p−2u = f on networks. To show the uniqueness of solutions of the p-Schrödinger equation, we first solve the eigenvalue problem for the p-Schrödinger operator and obtain some properties of the smallest eigenvalue and its corresponding eigenfunction of the p-Schrödinger operator.

In this paper, we investigate the semiclassical strings in AdS₃ × S², in which the string configuration of AdS₃ is classified to three cases depending on the parameters. Each of these has a different anomalous dimension proportional to log S, S^1/3 and S, where S is a angular momentum on AdS₃. Further we generalize the dispersion relations for various string configuration on AdS₃ × S².

This paper proposes a new nondestructive evaluation method for detecting cracks, voids, and other hidden defects inside concrete structures, called "frequency differential electrical impedance scanning (fdEIS)." The primary benefit of fdEIS over the conventional nondestructive methods is that it is possible to determine the thickness of the voids. In fdEIS, we inject a sequence of electrical currents with various frequencies through the tested concrete wall by applying a sinusoidal voltage difference between a surface electrode and a scan probe, which are placed on opposite surfaces of the wall. Through the probe, we measure the derivative d/dw gw of exit currents (Neumann data) with respect to the angular frequency variable w. We find the fundamental concept in fdEIS relating the thickness of the voids to d/dw gw and derive an approximation formula for estimating the thickness of the voids. We demonstrate the performance of our method in numerical simulations.

Ha, T., Choi, Y., Shin, C.S. and Min, D.-J., 2009. Numerical modeling for 3D acoustic wave
equation in the frequency domain. Joumal of Seisnic Exploration, l8t 57-19.
We investigatea frequency-domainfi nite-elementm ethod for three-dimensionaml odeling
of the acousticw ave equation.F requency-domaimn odelingh ass everala dvantageos ver time-domain
modeling,e ven though it requiresh ugec omputationaml emoryc omparedt o time-domainm odeling.
One of these advantages is that multi-shot modeling can be performed more efficiently in the
frequency domain than in the time domain, and another is the ability to work on a
frequency-by-frequencbya sis,w hich makesi t possiblet o distributef requenciesa crossp rocessors.
Consideringt hat frequency-domainm odeling is popular in waveform inversionb ecauseo f source
wavelet estimationa nd multi-shot modeling, 3D frequency-domainfi nite-elementm odelingc an be
effectively used in 3D waveform inversion. We derive a numerical dispersion relationship for the
3D frequency-domainfi nite-elementm ethoda nd then analyzen umericald ispersiono n the basiso f
dispersion curves. From the dispersion analysis, we determine th€ minimum number of grid points
per wavelength. The validity of the 3D finite-element modelirtg algorithm is examined for a
three-layeredm odel and the SEG/EACE salt model.
KEY WORDS:3D modeling, acousticw ave equation,f requency-domainf,i nite-elemem,
numerical dispersion

Tunnel volumes excavated by laboratory groups of the Formosan subterranean termite, Coptotermes formosanus Shiraki (Isoptera: Rhinotermitidae), and the eastern subterranean termite, Reticulitermes flavipes (Kollar) (Isoptera: Rhinotermitidae) were measured by using two-dimensional foraging arenas. Group sizes of 20, 40, 60, 80, 100, and 200 termites were used for the study. Analysis of the images of tunnels taken hourly showed tunnel volume increased and eventually reached equilibrium for both termite species, but Co. formosanus reached the equilibrium faster at lower volume than R. flavipes. Co. formosanus constructed fewer primary tunnels with less branching than R. flavipes and no additional tunneling activity was observed once the tunnel volume reached equilibrium. R. flavipes, however, continued tunnel excavation even after reaching equilibrium, but the equilibrated volume was maintained by filling unused tunnels with sand excavated from newly dug tunnels. For each termite species, the tunnel volume equilibrium was proportional to the group size. The mean individual tunnel volume (mm³ per termite ± SE) of all group sizes computed over the whole experiment was significantly higher for R. flavipes (198.58 ± 1.21) than for Co. formosanus (84.24 ± 0.59). The shape of the growth curves for tunnel volumes indicated the presence of a double feedback system for termite tunneling activity, and we suggest that the positive relationship between nest and population size previously reported for numerous termites species is the result of the self-organized nest-building activity.

The foraging territory of the Formosan subterranean termite, extit{ Coptotermes formosanus} Shiraki, was simulated by using a lattice model in order to understand how the fractal landscape structure affects the foraging territory and interacts with the territory size. Each lattice cell had a value ranging from 0.0 to 1.0, interpreted as a transition probability, extit{P} trans   , which represents the spatially-distributed property of the fractal landscape. The fractal landscape was characterized by a parameter, extit{H}, controlling aggregation of lattice cells with higher values of extit{P} trans   . At the beginning of the simulation, extit{N} (=30, 50, 80 and 100, depending on the condition) termite cells, each representing a founding pair, were randomly distributed within the lattice space. After fourteen simulation years, all territories had reached a steady state in which their shapes did not change over time. In this state, we investigated the size distribution of territories in size descending order. For large-sized territories (rank <  10 -- 20), the size increase with increasing extit{H}, which resulted from the fact that high extit{H }values indicated that fewer but larger, areas of contiguous cells with high values of extit{P} trans   were present. For small-sized territories (rank >  20), extit{H} had little affect on the territory size.

The process through which the Formosan subterranean termite, Coptotermes formosanus Shiraki, establishes territory was simulated using a lattice model in order to understand how such territories are formed from their seeds-founding pairs that fall to the ground every year. The model incorporated, summer–winter cycles, and fourteen years were simulated. Simulated pairs fell to random sites within the lattice space at the beginning of every summer, and their territories grew during the summer season, and shrunk during the winter season. Fourteen years were sufficient for territory size and shape to become stable over time. The simulation revealed that only pairs introduced at t = 0 had established large territories by the end of the simulation (t = 14). Pairs that were introduced later expanded their territory a little at first, but ultimately shrunk back into a single-cell-sized or small-sized territory. This means that stable-state territory size is mostly determined by when that territory was initially established.