On Darboux transformations for the derivative nonlinear Schr\"odinger equation

We consider Darboux transformations for the derivative nonlinear Schr\"odinger equation. A new theorem for Darboux transformations of operators with no derivative term are presented and proved. The solution is expressed in quasideterminant forms. Additionally, the parabolic and soliton solutions of the derivative nonlinear Schr\"odinger equation are given as explicit examples.Comment: 14 page

Cosmological test of the Yilmaz theory of gravity

We test the Yilmaz theory of gravitation by working out the corresponding Friedmann-type equations generated by assuming the Friedmann-Robertson-Walker cosmological metrics. In the case that space is flat the theory is consistent only with either a completely empty universe or a negative energy vacuum that decays to produce a constant density of matter. In both cases the total energy remains zero at all times, and in the latter case the acceleration of the expansion is always negative. To obtain a more flexible and potentially more realistic cosmology, the equation of state relating the pressure and energy density of the matter creation process must be different from the vacuum, as for example is the case in the steady-state models of Gold, Bondi, Hoyle and others. The theory does not support the cosmological principle for curved space K =/= 0 cosmological metrics

Refutation of C. W. Misner's claims in his article "Yilmaz Cancels Newton''

It is shown that an article by C. W. Misner contains serious errors. In particular, the claim that the Yilmaz theory of gravitation cancels the Newtonian gravitational interaction is based on a false premise. With the correct premise the conclusion of the article regarding the absence of gravitational interactions applies to general relativity and not to the Yilmaz theory.Comment: 12 pages, LaTeX, submitted to Il Nuovo Ciment

Stochastic Semi-Classical Description of Fusion at Near-Barrier Energies

Fusion reactions of heavy ions are investigated by employing a simple stochastic semi-classical model which includes the coupling between relative motion and low frequency collective surface modes of colliding ions similarly to the quantal coupled-channels description. The quantal effect enters into the calculation through the initial zero-point fluctuations of the surface vibrations. Good agreement with the result of coupled-channels calculations as well as data is obtained for the fusion cross sections of nickel isotopes. The internal excitations in non-fusing events as well as the fusion time are investigated.Comment: 8 pages, 8 figures, Published in Phys. Rev.

Clay mineralogy, chemistry, and diagenesis of late devonian K-bentonite occurrences in northwestern Turkey

Thin beds of tephra (K-bentonites) formed by the diagenesis of volcanic ash are exposed within the limestone-dolomitic limestone successions of the Yilanli formation at Zonguldak and Bartin in northwestern Turkey. They were deposited on the Middle Devonian-Lower Carboniferous shallow carbonate platform of the Zonguldak terrane. In this study, K-bentonite samples collected from Gavurpinari and Yilanli Burnu limestone quarries are investigated in order to reveal their mineralogical and geochemical characteristics and diagenetic evolution. Illite is the major clay mineral in the studied K-bentonites. Additionally, kaolinite and mixed-layer illite-smectite are identified in some samples. The nonclay minerals calcite, dolomite, quartz, gypsum, feldspar, pyrite, and zircon are also found. Crystal-chemical characteristics (Kiibler index, d060 values, and polytypes of illites) from two different sampling locations do not show significant variations. Kiibler index values for the Yilanli Burnu and Gavurpinari sampling locations, 0.47-0.93 (average: 0.71 A°29) and 0.69-0.77 (average: 0.72 A°29), respectively, indicate that illites were affected by high-grade diagenetic conditions. The swelling (or smectite) component (~5%), crystallite size (N = 10-20 nm), and polytype (2M1 > 1Md) data of illites support the same conditions. Illite d060 values of 1.491-1.503 A correspond to a range of octahedral Mg+Fe values of 0.27-0.51 atoms per formula, indicating a composition between end-member muscovite and phengite unit. Trace and rare earth element-based chemical classification of the K-bentonite samples revealed that composition of original volcanic ash is basaltic. Illitization took place by fixation of K from volcanic minerals and ash, and diffusion of elements (Mg+Fe) into and out of the beds during diagenesis. Mineralogical-chemical data point out that these K-bentonites evolved in high-grade diagenetic conditions (approximately 100-150 °C) from the products of volcanic eruptions of disputed sources and distances during the Late Devonian time. © 2015 TÜBİTAK

Spinodal Instabilities in Nuclear Matter in a Stochastic Relativistic Mean-Field Approach

Spinodal instabilities and early growth of baryon density fluctuations in symmetric nuclear matter are investigated in the basis of stochastic extension of relativistic mean-field approach in the semi-classical approximation. Calculations are compared with the results of non-relativistic calculations based on Skyrme-type effective interactions under similar conditions. A qualitative difference appears in the unstable response of the system: the system exhibits most unstable behavior at higher baryon densities around $\rho_{b}=0.4 ~\rho_{0}$ in the relativistic approach while most unstable behavior occurs at lower baryon densities around $\rho_{b}=0.2 ~\rho_{0}$ in the non-relativistic calculationsComment: 18 pages, 7 figure