Hilbert functions of Gorenstein monomial curves

It is a conjecture due to M. E. Rossi that the Hilbert function of a one-dimensional Gorenstein local ring is non-decreasing. In this article, we show that the Hilbert function is non-decreasing for local Gorenstein rings with embedding dimension four associated to monomial curves, under some arithmetic assumptions on the generators of their defining ideals in the non-complete intersection case. In order to obtain this result, we determine the generators of their tangent cones explicitly by using standard basis computations under these arithmetic assumptions and show that the tangent cones are Cohen-Macaulay. In the complete intersection case, by characterizing certain families of complete intersection numerical semigroups, we give an inductive method to obtain large families of complete intersection local rings with arbitrary embedding dimension having non-decreasing Hilbert functions.

     

Dynamic programming for stochastic target problems and geometric flows

Given a controlled stochastic process, the reachability set is the collection of all initial data from which the state process can be driven into a target set at a specified time. Differential properties of these sets are studied by the dynamic programming principle which is proved by the Jankov-von Neumann measurable selection theorem. This principle implies that the reachability sets satisfy a geometric partial differential equation, which is the analogue of the Hamilton-Jacobi-Bellman equation for this problem. By appropriately choosing the controlled process, this connection provides a stochastic representation for mean curvature type geometric flows. Another application is the super-replication problem in financial mathematics. Several applications in this direction are also discussed. Received October 24, 2000 / final version received July 24, 2001?Published online November 27, 2001     

Spectroscopic determination of acid dissociation constants of N-substituted-6-acylbenzothiazolone derivatives

The acid dissociation constants of twelve novel drug precursor N-substituted-6-acylbenzothiazolone derivatives were determined by using the UV-vis spectroscopic technique. The protonation and deprotonation behaviors of the investigated molecules were researched from the super basic to super acid regions (i.e., 8 mol·L(-1) KOH to 98% H(2)SO(4)) including the pH region. It is observed that all of the molecules are protonated in the super acidic region. The calculated relative stability values of possible tautomer structures indicate that the keto form of investigated molecules is favored over the enol form. It was predicted that protonation occurs at the amide (oxo) group found in the keto form.     

Molecular structure, harmonic and anharmonic frequency calculations of 2,4-dichloropyrimidine and 4,6-dichloropyrimidine by HF and density functional methods

Quantum chemical calculations of energies, geometrical structural parameters, harmonic and anharmonic frequencies of 2,4-DCP and 4,6-DCP were carried out by HF and density functional theory methods with 6-311++G(d,p) as basis set. The assignment of each normal mode has been made using the observed and calculated frequencies, their IR and Raman intensities. A detailed interpretation of the FT-IR and FT-Raman spectra of 2,4-DCP and 4,6-DCP was reported on the basis of the calculated potential energy distribution (PED). A comparison of theoretically calculated vibrational frequencies at B3LYP/6-311++G(d,p) with FT-IR and FT-Raman experimental data shows good agreement between them. Natural atomic charges of 2,4-DCP and 4,6-DCP were calculated and compared with pyrimidine molecule.     

Annular, cosh and cos Gaussian beams in strong turbulence

For the strong atmospheric turbulence regime, the asymptotic on-axis scintillation behavior of annular, cosh and cos Gaussian beams is theoretically derived and illustrated with numerical examples. It is observed from the plots that annular Gaussian beams exhibit more scintillations than a Gaussian beam, regardless of the amplitude coefficient and source size settings. For small source sizes, cosh Gaussian beams seem to have an advantage over Gaussian beams in terms of reduced scintillation, but for large source sizes a switchover occurs where cos Gaussian beams assume the advantage. Analysis of the effect of inner scale value shows that scintillations increases for all beams as the inner scale increases.     

On the exact distribution and mean value function of a geometric process with exponential interarrival times

The geometric process is considered when the distribution of the first interarrival time is assumed to be exponential. An analytical expression for the one dimensional probability distribution of this process is obtained as a solution to a system of recursive differential equations. A power series expansion is derived for the geometric renewal function by using an integral equation and evaluated in a computational perspective. Further, an extension is provided for the power series expansion of the geometric renewal function in the case of the Weibull distribution.     

Evaluation of high hydrostatic pressure effects on bovine red blood cells and platelets

The objective of this study was to investigate the effects of high hydrostatic pressure (HHP) on the stability of red blood cells (RBCs) and platelets. Bovine blood cells (n=5) were treated with the pressure of 55, 110, 154 and 220 MPa at 25 °C for 5 min. Light microscopy, atomic force microscopy and flow cytometry studies revealed that RBCs were morphologically stable up until the 220 MPa pressure treatments, at which surface modifications were observed. The platelets were found to be less stable than RBCs. HHP application did not cause any significant change in the signal intensity, band area and frequency values of the infrared bands with the exception that a significant variation was observed in the area of the cholesterol band. No statistically significant variations were observed in the secondary structure elements due to HHP treatment according to the artificial neural network study based on the FTIR data.     

Merton problem in a discrete market with frictions

We study the classical optimal investment and consumption problem of Merton in a discrete time model with frictions. Market friction causes the investor to lose wealth due to trading. This loss is modeled through a nonlinear penalty function of the portfolio adjustment. The classical transaction cost and the liquidity models are included in this abstract formulation. The investor maximizes her utility derived from consumption and the final portfolio position. The utility is modeled as the expected value of the discounted sum of the utilities from each step. At the final time, the stock positions are liquidated and a utility is obtained from the resulting cash value. The controls are the investment and the consumption decisions at each time. The utility function is maximized over all controls that keep the after liquidation value of the portfolio non-negative. A dynamic programming principle is proved and the value function is characterized as its unique solution with appropriate initial data. Optimal investment and consumption strategies are constructed as well.     

Radiation transfer in photobiological carbon dioxide fixation and fuel production by microalgae

Solar radiation is the energy source driving the metabolic activity of microorganisms able to photobiologically fixate carbon dioxide and convert solar energy into biofuels. Thus, careful radiation transfer analysis must be conducted in order to design and operate efficient photobioreactors. This review paper first introduces light harvesting mechanisms used by microorganisms as well as photosynthesis and photobiological fuel production. It then provides a thorough and critical review of both experimental and modeling efforts focusing on radiation transfer in microalgae suspension. Experimental methods to determine the radiation characteristics of microalgae are presented. Methods for solving the radiation transfer equation in photobioreactors with or without bubbles are also discussed. Sample measurements and numerical solutions are provided. Finally, novel strategies for achieving optimum light delivery and maximizing sunlight utilization in photobioreactors are discussed including genetic engineering of microorganisms with truncated chlorophyll antenna.     

The electronic structure,solvatochromism, and electric dipole moments of new Schiff base derivatives using absorbance and fluorescence spectra

Structural Chemistry - The electronic structure and electronic transitions of four new mono Schiff base derivatives are interpreted by using absorption and fluorescence spectra including 28...