Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence

In this paper we use the Euler-Seidel method for deriving new identities for hyperharmonic and r-Stirling numbers. The exponential generating function is determined for hyperharmonic numbers, which result is a generalization of Gosper’s identity. A classification of second order recurrence sequences is also given with the help of this method.      

Optimal static pricing for a service facility with holding costs

We study a service facility modelled as a single-server queueing system with Poisson arrivals and limited or unlimited buffer size. In systems with unlimited buffer size, the service times have general distributions, whereas in finite buffered systems service times are exponentially distributed. Arriving customers enter if there is room in the facility and if they are willing to pay the posted price. The same price is charged to all customers at all times (static pricing). The service provider is charged a holding cost proportional to the time that the customers spend in the system. We demonstrate that there is a unique optimal price that maximizes the long-run average profit per unit time. We also investigate how optimal prices vary as system parameters change. Finally, we consider buffer size as an additional decision variable and show that there is an optimal buffer size level that maximizes profit.     

Computation of ionization and various excited state energies ofhelium and helium‐like quantum dots

In the effective mass approximation, we calculated the wave functions and some energy states of helium and helium‐like quantum dots (QDs) with impurity charges Z = 0, 1, 2, 3, and 4. In addition, we carried out the ionization energies of these QDs as a function of dot radius, and we investigated the influence of impurity on the ionization energy. We utilized the method that is a combination of quantum genetic algorithm (QGA) and Hartree‐Fock Roothaan (HFR). The results are in a good agreement with literature results. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

PEG crosslinked poly(vinylbenzene boronic acid) polymer electrolytes for Li-ion batteries

Poly(4-vinylbenzeneboronic acid), PVBBA was synthesized via free-radical polymerization of 4-vinylbenzeneboronic acid (4-VBBA) and followed by crosslinking with polyethylene glycol (PEG) with different molecular weights to produce boron containing crosslinked polymers. Prior to crosslinking, the materials were doped with CF₃SO₃Li at several stoichiometric ratios to get PVBBAPEGX-Y where X is the molecular weight of PEG and Y is the EO/Li ratio. The materials were characterized by using Fourier transform infrared spectroscopy (FT-IR), thermogravimetric analysis (TGA) and differential scanning calorimeter (DSC). The ionic conductivity of these novel crosslinked electrolytes was studied by dielectric-impedance spectroscopy. Li-ion conductivity of these polymer electrolytes depends on the length of the side units as well as the doping ratio. PVBBAPEG200-10 illustrated a satisfactory ionic conductivity of 3.1 × 10^?5 S/cm at 20 °C and 1.8 × 10^?3 S/cm at 100 °C.     

Chemical vapor deposition of graphene on silver foil as a tarnish‐resistant coating

Here, we demonstrate the synthesis of graphene on Ag foil by an atmospheric‐pressure (AP) chemical vapor deposition (CVD) process as tarnish‐resistant coating. Synthesis of a continuous graphene film on Ag foil is achieved using the solid camphor as carbon precursor in a gas mixture of Ar and H₂. Tarnishing of the Ag surface through sulfidation is investigated with and without coating of the graphene film. It is observed that the bare Ag surface immediately reacts with sulfur vapor to turn black, whereas graphene coating passivates the Ag surface robustly and thereby restrains the sulfur reaction to preserve from tarnishing. Our findings show that a large‐area graphene film can be effectively grown on Ag surface by a CVD process as a tarnish and corrosion resistance barrier.

     

Optimal assignment of servers to tasks when collaboration is inefficient

Consider a Markovian system of two stations in tandem with finite intermediate buffer and two servers. The servers are heterogeneous, flexible, and more efficient when they work on their own than when they collaborate. We determine how the servers should be assigned dynamically to the stations with the goal of maximizing the system throughput. We show that the optimal policy depends on whether or not one server is dominant (i.e., faster at both stations) and on the magnitude of the efficiency loss of collaborating servers. In particular, if one server is dominant then he must divide his time between the two stations, and we identify the threshold policy the dominant server should use; otherwise each server should focus on the station where he is the faster server. In all cases, servers only collaborate to avoid idleness when the first station is blocked or the second station is starved, and we determine when collaboration is preferable to idleness as a function of the efficiency loss of collaborating servers.     

The Fields of Real and Complex Numbers with a Small Multiplicative Group

We consider the model theory of the real and complex fieldswith a multiplicative group having the Mann property. Amongthese groups are the finitely generated multiplicative groupsin these fields. As a by-product we obtain some results on groupswith the Mann property in rings of Witt vectors and in fieldsof positive characteristic.k 2000 Mathematics Subject Classification03C10, 03C35, 03C60, 03C64, 03C98, 13K05.     

Calculation of linear and nonlinear optical absorption coefficients of a spherical quantum dot with parabolic potential

In the effective mass approximation, we calculated the binding energy and wave function for the 1s-, 1p-, 1d- and 1f-states of a spherical quantum dot (QD) with parabolic potential by using a combination of quantum genetic algorithm (QGA) and Hartree-Fock-Roothaan (HFR) method. In addition, we also investigated the linear and the third-order nonlinear optical absorption coefficients as a function of the incident photon energy for the 1s-1p, 1p-1d and 1d-1f transitions. Our results are shown that the existence of impurity has great influence on optical absorption coefficients. Moreover, the optical absorption coefficients are strongly affected by the incident optical intensity, relaxation time, parabolic potential and dot radius.     

Low-threshold lasing eigenmodes of an infinite periodic chain of quantum wires

We study the lasing eigenvalue problems for a periodic open optical resonator made of an infinite grating of circular dielectric cylinders standing in free space, in the E- and H-polarization modes. If possessing a "negative-absorption" refractive index, such cylinders model a chain of quantum wires made of the gain material under pumping. The initial-guess values for the lasing frequencies are provided by the plane-wave scattering problems. We demonstrate a new effect: the existence of specific grating eigenmodes that have a low threshold of lasing even if the wires are optically very thin.     

Two photon absorption characteristics of bulk GaTe crystal

We have investigated the structural and optical properties of bulk GaTe crystal grown by vertical Bridgman method. Two photon absorption (TPA) properties of GaTe crystal have been investigated by the open aperture Z-scan technique under 1064 nm wavelength with 4 ns or 65 ps pulse durations. The TPA coefficients are greater in ns regime than that of ps regime. Upon increasing intensity of incident light from 5.02×10⁷ W/cm² to 1.07×10⁸ W/cm², the TPA coefficients increased from 3.47×10^?6 cm/W to 8.53×10^?6 cm/W for nanosecond excitation. Similarly, when intensity of incident light was increased from 6.81×10⁸ W/cm² to 9.94×10⁸ W/cm² the TPA coefficients increased from 3.53×10^?7 cm/W to 6.83×10^?7 cm/W for picosecond excitation. Measured TPA coefficient of GaTe crystal is larger than that of GaSe and GaS layered crystals.