Optimal replenishment time for retailer under partial upstream prepayment and partial downstream overdue payment for quadratic demand

In competitive edge, the proffer of delay payment is of great consequence tool to boost the market demand by exerting influence of more customers. In opposition to, merchandiser may be asked to pay some per cent of purchasing cost before receiving products to reduce the risk of cancellation of order. In this article, optimal replenishment time for merchandiser under partial upstream prepayment and partial downstream overdue payment is presented under quadratic demand with three different models: (1) without deterioration, (2) with constant deterioration and (3) maximum fixed-lifetime deterioration as loss of utility is the real situation of products like fruits, vegetables, juices, etc., and to reduce deterioration of the product, merchandiser spends capital on preservation technology to preserve the item. Quadratic demand is suitable for the products for which demand increases initially and afterward it starts to decrease. The decision policies are analysed for the merchandiser. The objective is to minimize merchandiser’s total cost with respect to decision variables. The models are supported with numerical examples. Sensitivity analysis is carried out to derive insights for decision maker.     

On generalized Toeplitz and little Hankel operators on Bergman spaces

We find a concrete integral formula for the class of generalized Toeplitz operators \(T_a\) in Bergman spaces \(A^p\), \(1<p<\infty \), studied in an earlier work by the authors. The result is extended to little Hankel operators. We give an example of an \(L^2\)-symbol a such that \(T_{|a|} \) fails to be bounded in \(A^2\), although \(T_a : A^2 \rightarrow A^2\) is seen to be bounded by using the generalized definition. We also confirm that the generalized definition coincides with the classical one whenever the latter makes sense.     

Energy Transport in Weakly Anharmonic Chains

We investigate the energy transport in a one-dimensional lattice of oscillators with a harmonic nearest neighbor coupling and a harmonic plus quartic on-site potential. As numerically observed for particular coupling parameters before, and confirmed by our study, such chains satisfy Fourier’s law: a chain of length N coupled to thermal reservoirs at both ends has an average steady state energy current proportional to 1/N. On the theoretical level we employ the Peierls transport equation for phonons and note that beyond a mere exchange of labels it admits nondegenerate phonon collisions. These collisions are responsible for a finite heat conductivity. The predictions of kinetic theory are compared with molecular dynamics simulations. In the range of weak anharmonicity, respectively low temperatures, reasonable agreement is observed.     

Growth of molybdenum disulphide using iodine as transport material

In the present paper an attempt has been made to describe the chemical vapor transport (CVT) technique used for the growth of molybdenum disulphide (MoS₂) single crystals. Iodine (I₂) is used as transporting material for this purpose. The energy dispersive analysis by X-ray (EDAX) confirmed the stoichiometry of the as-grown crystals. The lattice parameters of these crystals were determined from the X-ray diffraction analysis. The grown crystals were examined under the optical zoom microscope for their surface microstructure study.     

Diffusion of vanadium in GaAs

The diffusion of Vanadium has been studied in V-doped GaAs layers (GaAs:V) grown by Metal-Organic Chemical Vapour Deposition (MOCVD) using secondary ion mass spectroscopy (SIMS). The vanadium (V) concentration profiles of sandwiched structures made of alternatively undoped and V doped GaAs layers have shown a concentration independent diffusion coefficient (D_V) for varying V doping levels from 10¹⁸ to 10¹⁹ cm⁻³. Measurements of D_V at 550, 615 and 680 °C indicate that the temperature dependence of D_V can be represented by the Arrhenius equation:  cm² s⁻¹. It is suggested that V diffuses via interstitial sites.     

Pointwise behaviour of semicontinuous supersolutions to a quasilinear parabolic equation

A kind of supersolutions of the so-called p-parabolic equation are studied. These p-superparabolic functions are defined as lower semicontinuous functions obeying the comparison principle. Incidentally, they are precisely the viscosity supersolutions. One of our results guarantees the existence of a spatial Sobolev gradient. For p = 2 we have the supercaloric functions and the ordinary heat equation. Mathematics Subject Classification (2000) 35K55     

Pointwise behaviour of <Emphasis Type="Italic">M</Emphasis><Superscript>1,1</Superscript> Sobolev functions

Our main objective is to study Haj?asz type Sobolev functions with the exponent one on metric measure spaces equipped with a doubling measure. We show that a discrete maximal function is bounded in the Haj?asz space with the exponent one. This implies that every such function has Lebesgue points outside a set of capacity zero. We also show that every Haj?asz function coincides with a Hölder continuous Haj?asz function outside a set of small Hausdorff content. Our proofs are based on Sobolev space estimates for maximal functions.     

Synthesis and Photophysics of Core‐Substituted Naphthalene Diimides: Fluorophores for Single Molecule Applications

The synthesis and photophysics of two new aminopropenyl naphthalene diimide (SANDI) dyes are reported. A general and convenient method for the synthesis of the precursor mono‐, di‐, and tetrabrominated 1,4,5,8‐naphthalene tetracarboxylic dianhydrides is described. The two core‐substituted SANDIs exhibit many of the photophysical properties required for fluorescence labeling applications including high photostability and high fluorescence quantum yields (>0.5) in the visible region of the spectrum. The emission wavelength is sensitive to the number of substituents on the NDI core, and the fluorescence decay times are in the range of ～8–12 ns for both compounds in the solvents investigated. Preliminary fluorescence emission data from single molecules of the compounds embedded in poly(methyl methacrylate) films are also reported and show that single molecules have very low yields of photobleaching, particularly the di‐substituted system. Furthermore, only a small proportion (<10 %) of the single molecules studied display fluorescence intermittencies or “blinks” in their photon trajectory. The compounds appear to be excellent candidates for applications at the single molecule level, for example, as FRET labels.     

Dynamic MR imaging of brain tumors in low field using undersampled projection reconstruction

A new application of the projection reconstruction method was developed, enabling dynamic T(1)-weighted contrast-enhanced magnetic resonance image (MRI) of brain tumors in a low-field imager. Two undersampled projection reconstruction spin echo sequences were implemented in an open low-field (0.23-T) MR imager, one with 64 and another with 42 projections in [0,pi], repetition time 150 ms, echotime 15 ms, and six slices were used in both sequences. The possibility of using these sequences to image dynamic contrast enhancement of brain tumors was studied in laboratory experiments and in two patient cases, one with fibrotic and the other with meningothelial meningioma. The laboratory experiments showed a nearly linear response in signal intensity to the concentration of gadopentetate dimeglumine in purified water up to 1.25 mM. Increasing concentrations up to 5.0 mM did not significantly affect the signal intensity, though starting from 3.0 mM concentration T(2) shortening decreased intensities slightly. The patient cases showed results consistent with an earlier study performed in a high-field imager. The results show that the studied sequences can be used to follow dynamic contrast enhancement in a low-field imager.