Correlation Functions in Two-Dimensional Dilaton Gravity

The Liouville approach is applied to the quantum treatment of the dilaton gravity in two dimensions. The physical states are obtained from the BRST cohomology and correlation functions are computed up to three-point functions. For the $N=0$ case (i.e., without matter), the cosmological term operator is found to have the discrete momentum that plays a special role in the $c=1$ Liouville gravity. The correlation functions for arbitrary numbers of operators are found in the $N=0$ case, and are nonvanishing only for specific ``chirality'' configurations.Comment: 14 pages, TIT/HEP-204, STUPP-92-13

Large-time Behavior of Solutions to the Inflow Problem of Full Compressible Navier-Stokes Equations

Large-time behavior of solutions to the inflow problem of full compressible Navier-Stokes equations is investigated on the half line $R^+ =(0,+\infty)$. The wave structure which contains four waves: the transonic(or degenerate) boundary layer solution, 1-rarefaction wave, viscous 2-contact wave and 3-rarefaction wave to the inflow problem is described and the asymptotic stability of the superposition of the above four wave patterns to the inflow problem of full compressible Navier-Stokes equations is proven under some smallness conditions. The proof is given by the elementary energy analysis based on the underlying wave structure. The main points in the proof are the degeneracies of the transonic boundary layer solution and the wave interactions in the superposition wave.Comment: 27 page

Right and Left Modules over the Frobenius Skew Polynomial Ring in the F-Finite Case

The main purposes of this paper are to establish and exploit the result that, over a complete (Noetherian) local ring $R$ of prime characteristic for which the Frobenius homomorphism $f$ is finite, the appropriate restrictions of the Matlis-duality functor provide an equivalence between the category of left modules over the Frobenius skew polynomial ring $R[x,f]$ that are Artinian as $R$-modules and the category of right $R[x,f]$-modules that are Noetherian as $R$-modules.Comment: 16 pages, to appear in the Mathematical Proceedings of the Cambridge Philosophical Society. This revised version includes two additionl references and points out that some of the results have been obtained independently by M. Blickle and G. Boeckl

Kondo effect in CeXc_{c} (Xc_{c}=S, Se, Te) studied by electrical resistivity under high pressure

We have measured the electrical resistivity of cerium monochalcogenices, CeS, CeSe, and CeTe, under high pressures up to 8 GPa. Pressure dependences of the antiferromagnetic ordering temperature $T_{N}$, crystal field splitting, and the $\ln T$ anomaly of the Kondo effect have been studied to cover the whole region from the magnetic ordering regime at low pressure to the Fermi liquid regime at high pressure. $T_{N}$ initially increases with increasing pressure, and starts to decrease at high pressure as expected from the Doniach's diagram. Simultaneously, the $\ln T$ behavior in the resistivity is enhanced, indicating the enhancement of the Kondo effect by pressure. It is also characteristic in CeX$_{c}$ that the crystal field splitting rapidly decreases at a common rate of $-12.2$ K/GPa. This leads to the increase in the degeneracy of the $f$ state and further enhancement of the Kondo effect. It is shown that the pressure dependent degeneracy of the $f$ state is a key factor to understand the pressure dependence of $T_{N}$, Kondo effect, magnetoresistance, and the peak structure in the temperature dependence of resistivity.Comment: 9 pages, 5 figures, accepted for publication in J. Phys. Soc. Jp

Do a science experiment for future scientists

[EN] It has been realized that various chemical reactions are accelerated under irradiation of MW. Such Microwave chemistry is known as time-saving, clear and eco-friendly. MW ovens are world-wide domestic tools for cooking which can serve meals quickly. Regardless of its convenience, few understand the essential mechanism of MW ovens. For better understanding of MW chemistry, authors think it is necessary for to introduce elementary knowledge by holding a 1-day program of experiments by using microwave (MW) ovens.“Science with microwave oven”, 1-day program which we developed and named “Hirameki Tokimeki Science” was supported by Japan Society for the promotion of Science, has been performed over four years.More than 100 students of elementary and junior-high school have joined the program.Here we report the program, response from students.Program of experiments: “1: Dyeing handkerchief with onion peer (*1), 2: Cooking of pizza quickly yeast-leavened, 3: Preparation of shining slime with fluorescein dye synthesized in nonsolvent reaction. 4. Plasma in MW oven (*2), etc.”Students realized how MW accelerated chemical reactions and that dyeing under MW was faster and more fixed compared with the conventional methods. Besides, they could enjoy lunch with pizza and dealing with the slime, both they made. They had a good time with a bit of scientific knowledge. Through 1-day program, we can make science more familiar with students, and it will cause young students to become more interested in science, lead them to future research workers.In addition to the “Hirameki Tokimeki (Inspiration and Spark) Program, we have doneVolunteer activities at Ishinomaki, one of the most damaged cities at the Higashi Nihon Big Earthquake, in 2011.“Science with microwave oven” program surely gives students mysterious interest anddream for Science. That is “Inspire and Spark!” (*1) (*2)Kanematsu, Y.; Matsumura, T. (2019). Do a science experiment for future scientists. En AMPERE 2019. 17th International Conference on Microwave and High Frequency Heating. Editorial Universitat Politècnica de València. 334-339. https://doi.org/10.4995/AMPERE2019.2019.9895OCS33433

Deformation of Schild String

We attempt to construct new superstring actions with a $D$-plet of Majorana fermions $\psi^{\cal B}_A$, where ${\cal B}$ is the $D$ dimensional space-time index and $A$ is the two dimensional spinor index, by deforming the Schild action. As a result, we propose three kinds of actions: the first is invariant under N=1 (the world-sheet) supersymmetry transformation and the area-preserving diffeomorphism. The second contains the Yukawa type interaction. The last possesses some non-locality because of bilinear terms of $\psi^{\cal B}_A$. The reasons why completing a Schild type superstring action with $\psi^{\cal B}_A$ is difficult are finally discussed.Comment: 12 pages, Latex, both title and abstract are changed, discussion of some relations among our results, Nambu-Goto string and super Yang-Mills theories, added. Results unchange