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.     

Existence of energy-minimal diffeomorphisms between doubly connected domains

The paper establishes the existence of homeomorphisms between two planar domains that minimize the Dirichlet energy.     

Electrical resistance measurements under pressure on NbTe2 single crystal

Transition metal dichalcogenides, because of their layered structure, are well suited for extreme pressure lubrication. These materials being semiconducting and of layered structure may undergo structural and electronic transitions under pressure. Here we report the details of the preparation and characterization of single crystals of NbTe₂ and the results of electrical resistance measurements under pressure carried out on it to investigate this possibility. Single crystals were grown by the chemical vapor transport technique, using iodine as a transporting agent. The composition of the grown crystals was confirmed on the basis of Energy Dispersive Analysis by X-ray (EDAX) and remaining structural characterization was also accomplished by X-ray Diffraction (XRD) studies. Electrical resistance was measured employing a Bridgman anvil set up to 10?GPa and diamond anvil cell (DAC) assembly up to 25?GPa. A technique slightly modified from that described in the literature for carrying out electrical resistivity measurements in the diamond anvil cell (DAC) under pressure has been standardized.     

Homeomorphisms of Bounded Variation

We show that the inverse of a planar homeomorphism of bounded variation is also of bounded variation. In higher dimensions we show that f ⁻¹ is of bounded variation provided that f ϵ W ^1,1(Ω; R ⁿ ) is a homeomorphism with |Df| in the Lorentz space L ^n-1,1(Ω). Dedicated to Tadeusz Iwaniec on his 60th birthday     

Atmospheric-pressure metal–organic vapor-phase epitaxy of GaAsBi alloys on high-index GaAs substrates

We investigated the growth characteristics and properties of GaAsBi layers grown by atmospheric-pressure metal–organic vapor-phase epitaxy on different GaAs substrate orientations. The surface morphology of GaAsBi alloys was investigated by means of scanning electron microscopy. The structural and optical properties of the alloys were examined using high-resolution X-ray diffraction (HRXRD) and photoreflectance spectroscopy, respectively. HRXRD results show that the GaAsBi growth rate was significantly lower on (1 1 5)A than on (0 0 1), (1 1 1)A and (1 1 4)A GaAs. The highest Bi content was obtained for GaAsBi layers grown on (1 1 5)A GaAs substrates.     

Rhodium(II)‐Catalyzed Nondirected Oxidative Alkenylation of Arenes: Arene Loading at One Equivalent

A bimetallic Rh^II catalyst promoted the C? H alkenylation of simple arenes at 1.0 equivalent without the use of a directing group. A phosphine ligand as well as cooperative reoxidation of Rh^II with Cu(TFA)₂ and V₂O₅ proved essential in providing monoalkenylated products in good yields and selectivities, especially with di‐ and trisubstituted arenes.     

On the phonon frequencies of copper in off symmetry directions

A previously proposed five parameter phenomenological screened shell model for the lattice dynamics of cubic metals is applied to compute the phonon frequencies of copper in the off-symmetry directions. The theoretical results are compared with the experimental findings for the first time. It has been pointed out that a model which gives excellent results in the symmetry directions may not necessarily reproduce similar results in the off-symmetry directions.     

Strong Exchange Coupling in a Trimetallic Radical‐Bridged Cobalt(II)‐Hexaazatrinaphthylene Complex

Reducing hexaazatrinaphthylene (HAN) with potassium in the presence of 18‐c‐6 produces [{K(18‐c‐6)}HAN], which contains the S=1/2 radical [HAN]^.?. The [HAN]^.? radical can be transferred to the cobalt(II) amide [Co{N(SiMe₃)₂}₂], forming [K(18‐c‐6)][(HAN){Co(N′′)₂}₃]; magnetic measurements on this compound reveal an S=4 spin system with strong cobalt–ligand antiferromagnetic exchange and J≈?290 cm^?1 (?2 J formalism). In contrast, the Co^II centres in the unreduced analogue [(HAN){Co(N′′)₂}₃] are weakly coupled (J≈?4.4 cm^?1). The finding that [HAN]^.? can be synthesized as a stable salt and transferred to cobalt introduces potential new routes to magnetic materials based on strongly coupled, triangular HAN building blocks.     

Constructibility Classes for Triangle Location Problems

Straightedge-and-compass construction problems are well known for different reasons. One of them is the difficulty to prove that a problem is not constructible: it took about two millennia to prove that it is not possible in general to cut an angle into three equal parts by using only straightedge and compass. Today, such proofs rely on algebraic tools difficult to apprehend by high school student. On the other hand, the technique of problem reduction is often used in theory of computation to prove other kinds of impossibility. In this paper, we adapt the notion of reduction to geometric constructions in order to have geometric proofs for unconstructibility based on a set of problems known to be unconstructible. Geometric reductions can also be used with constructible problems: in this case, besides having constructibility, the reduction also yields a construction. To make the things concrete, we focus this study to a corpus of triangle location problems proposed by William Wernick in the eighties.