A Central Limit Theorem for Costs in Bulinskaya’s Inventory Management Problem When Deliveries Face Delays

It is common in inventory theory to consider policies that minimize the expected cost of ordering and holding goods or materials. Nevertheless, the realized cost is a random variable, and, as the Saint Petersburg Paradox reminds us, the expected value does not always capture the full economic reality of a decision problem. Here we take the classic inventory model of Bulinskaya (Theory of Probability & Its Applications, 9, 3, 389–403, 1964), and, by proving an appropriate central limit theorem, we show in a reasonably rich (and practical) sense that the mean-optimal policies are economically appropriate. The motivation and the tools are applicable to a large class of Markov decision problems.     

Local solvability for partial differential equations with multiple characteristics in mixed Gevrey-C ∞ spaces

In this paper, we consider a class of linear partial differential equations with multiple characteristics, whose principal part is elliptic in a set of variables. We assume that the subprincipal symbol has real part different from zero and that its imaginary part does not change sign. We then prove the local solvability of such a class of operators in mixed Gevrey-C ^∞ spaces, in the sense that the linear equation admits a local solution when the datum is Gevrey in some variables and only C ^∞ in the other ones.     

Effect of the exchange of substituent position in an amide amphiphile on the monolayer characteristics

The monolayer characteristics of two very similar amphiphiles, N-tridecyl-beta-hydroxypropionic acid amide (C13H27-NH-CO-C2H4OH; THPA) and N-(beta-hydroxyethyl)tridecanoic acid amide (C13H27-CO-NH-C2H4OH; HETA), the chemical structure of which is only changed by exchanging the position of the two substituents at the acid amide group, are compared. These small changes in the chemical structure give rise to large differences in the phase behavior of the HETA and THPA monolayers, as concluded from the differences in the surface pressure-area (pi-A) isotherms. Since both amphiphiles have the same alkyl chain length, the shift of the fluid/condensed phase transition pressure pi(c) to higher temperatures from THPA to HETA indicates a stronger polar character of the THPA headgroup. Considerable differences between the HETA and THPA monolayers also exist in the domain morphology, although, in both cases, six arms usually grow from a round center. The fractal-shaped HETA domains grow by tip splitting under the formation of numerous doubloons so that branching is considerably limited. This suggests a certain fluidity of the HETA condensed phase. The main differences of the domains result from the higher crystallinity. The starlike THPA domains have dendritic character and can form curved dendrites, which are partially two-dimensional twins due to the formation of dislocations in the two-dimensional lattice structure. In the case of HETA monolayers, the grazing incidence X-ray diffraction studies reveal a hexagonal packing of the alkyl chains oriented perpendicularly to the surface in an LS phase. In the case of THPA monolayers, an oblique lattice is formed. However, at low temperatures, a second phase transition between two condensed phases occurs that is demonstrated by an abrupt transition between two different oblique lattice structures at the surface pressure where a cusp in the pi-A isotherms occurs at T < 10 degrees C.     

Nuclear spin relaxation driven by intermolecular dipolar interactions: the role of solute-solvent pair correlations in the modeling of spectral density functions

Nuclear spin relaxation provides useful information related to the dynamics of molecular systems. When relaxation is driven by intermolecular dipolar interactions, the relevant spectral density functions (SDFs) also have significant contributions, in principle, from distant spins all over the dynamic range typically probed by NMR experiments such as NOESY. In this work, we investigate the intermolecular dipolar spin relaxation as driven by the relative diffusion of solvent and solute molecules taking place under a central force field, and we examine the relevant implications for (preferential) solvation studies. For this purpose, we evaluate the SDFs by employing a numerical approach based on spatial discretization of the time-propagation equation, and we supply an analytical solution for the simplest case of a steplike mean-field potential. Several situations related to different solute-solvent pair correlation functions are examined in terms of static/dynamic effects and relaxation modes, and some conclusions are drawn about the interpretation of NOE measurements. While we confirm previous results concerning the spoiling effect of long-range spins (Halle, B. J. Chem. Phys. 2003, 119, 12372), we also show that SDFs are sufficiently sensitive to pair correlation functions that useful, yet rather complicated, inferences can be made on the nature of the solvation shell.     

Enhancement of two-photon absorption cross-section and singlet-oxygen generation in porphyrins upon beta-functionalization with donor-acceptor substituents

The microwave-enhanced synthesis, comparative singlet oxygen sensitization efficiency, and nonlinear optical characterization of a new beta-functionalized porphyrin and its copper complex are described. We show that the introduction of a donor-acceptor push-pull conjugated fragment in the beta position strongly perturbs the porphyrin electronic structure leading to a remarkable one- and two-photon NIR absorption enhancement.     

Modeling elongational viscosity of blends of linear and long-chain branched polypropylenes

To enhance the melt strength of a conventional linear polypropylene (L-PP), blends with a long-chain branched polypropylene (LCB-PP) were produced by adding 2, 5, 10, 25, 50, and 75 wt% of LCB-PP to L-PP and mixing in a twin screw extruder. It was found that, already, an addition of 10% or less of LCB-PP to L-PP leads to significant strain hardening. Elongational viscosity data of L-PP and LCB-PP and those of their blends were analyzed by the use of the molecular stress function (MSF) theory. While L-PP is characterized by the MSF parameter, β=1 (typical for linear melts), and shows very little chain stretch (), melt elongational behavior of LCB-PP is characterized by the MSF parameters, β=2 (typical of LCB melts), and (which corresponds to a maximum stretch of molecular chains by a factor of 15). By extruding LCB-PP, a refining effect is observed similar to the refining effects seen in low density polyethylene (LDPE), which reduces the steady-state elongational viscosity and reduces to 121. A second-order mixing rule for the fractional relaxation moduli, g _i , was found to show good agreement with the linear-viscoelastic data of the blends. To simulate the elongational viscosities of the L-PP/LCB-PP blends, a similar second-order mixing rule was used for the MSF parameter, β, while a first-order mixing rule was found to be appropriate for . This allows for a quantitative prediction of the time-dependent elongational viscosities of all L-PP/LCB-PP blends on the basis of the linear and nonlinear parameters of the mixing components L-PP and LCB-PP only. Comparison between the steady-state elongational viscosities as obtained from creep experiments shows good agreement with predictions.     

Subdiffusion and long-time anticorrelations in a stochastic single file

The subdiffusion of a stochastic single file is interpreted as a jumping process. Contrary to the current continuous time random walk models, its statistics is characterized by finite averages of the jumping times and square displacements. Subdiffusion is then related to a persistent anticorrelation of the jump sequences. In continuous time representation, this corresponds to negative power-law velocity autocorrelations, attributable to the restricted geometry of the file diffusion.     

Is cosmology compatible with sterile neutrinos?

By combining data from cosmic microwave background experiments (including the recent WMAP third year results), large scale structure, and Lyman-alpha forest observations, we constrain the hypothesis of a fourth, sterile, massive neutrino. For the 3 massless+1 massive neutrino case, we bound the mass of the sterile neutrino to ms<0.26 eV (0.44 eV) at 95% (99.9%) C.L., which excludes at high significance the sterile neutrino hypothesis as an explanation of the LSND anomaly. We generalize the analysis to account for active neutrino masses and the possibility that the sterile abundance is not thermal. In the latter case, the contraints in the plane are nontrivial. For a mass of >1 or <0.05 eV, the cosmological energy density in sterile neutrinos is always constrained to be omeganu<0.003 at 95% C.L., but for a mass of approximately 0.25 eV, omeganu can be as large as 0.01.     

Experimental test of two-way quantum key distribution in the presence of controlled noise

We describe the experimental test of a quantum key distribution performed with a two-way protocol without using entanglement. An individual incoherent eavesdropping is simulated and induces a variable amount of noise on the communication channel. This allows a direct verification of the agreement between theory and practice.     

Double transverse-spin asymmetries in Drell–Yan processes with antiprotons

We present next-to-leading order predictions for double transverse-spin asymmetries in Drell–Yan dilepton production initiated by proton–antiproton scattering. The kinematic region of the proposed PAX experiment at GSI: 30?s?200 GeV²$30?s?200{\text{GeV}}^2$ and 2?M?7 GeV$2?M?7\text{GeV}$ is examined. The Drell–Yan asymmetries turn out to be large, in the range 20–40%. Measuring these asymmetries would provide the cleanest determination of the quark transversity distributions.