Solid–liquid phase equilibria in the systems K2SO4–MSO4–H2O (M = Co,Ni, Cu) from ambient to enhanced temperatures

Reviewing the literature solubility isotherms in the ternary systems K₂SO₄–MSO₄–H₂O (M = Co, Ni, Cu, Zn) revealed a lack at ambient temperatures. The solid–liquid phase equilibria have been determined in the systems K₂SO₄–MSO₄–H₂O (M = Co, Ni, Cu) at T = 313 K. With increasing bivalent metal sulfate concentration, the solubility of potassium sulfate rises until the two-salt point is reached. Reciprocally, the solubility of the bivalent metal sulfate hydrates (CoSO₄·7H₂O, α-NiSO₄·6H₂O, CuSO₄·5H₂O) increases with rising potassium sulfate concentration. In all three systems the double salts of Tutton's type K₂SO₄·MSO₄·6H₂O (M = Co, Ni, Cu) are formed.     

Profit loss in differentiated oligopolies

We provide sharp lower and upper bounds on the ratio of decentralized to centralized profits when multiproduct firms offering differentiated products engage in price competition. The bounds depend on the demand sensitivity matrix but are independent of marginal costs.     

Dynamic pricing and inventory control: robust vs. stochastic uncertainty models—a computational study

In this paper, we consider a variety of models for dealing with demand uncertainty for a joint dynamic pricing and inventory control problem in a make-to-stock manufacturing system. We consider a multi-product capacitated, dynamic setting, where demand depends linearly on the price. Our goal is to address demand uncertainty using various robust and stochastic optimization approaches. For each of these approaches, we first introduce closed-loop formulations (adjustable robust and dynamic programming), where decisions for a given time period are made at the beginning of the time period, and uncertainty unfolds as time evolves. We then describe models in an open-loop setting, where decisions for the entire time horizon must be made at time zero. We conclude that the affine adjustable robust approach performs well (when compared to the other approaches such as dynamic programming, stochastic programming and robust open loop approaches) in terms of realized profits and protection against constraint violation while at the same time it is computationally tractable. Furthermore, we compare the complexity of these models and discuss some insights on a numerical example.     

The role of optimization in some recent advances in data-driven decision-making

Mathematical Programming - In this paper, we present a new framework of bi-level unconstrained minimization for development of accelerated methods in Convex Programming. These methods use...     

Free radical reactions for heterocycle synthesis. Part 6: 2-Bromobenzoic acids as building blocks in the construction of nitrogen heterocycles

A general method to construct a variety of nitrogen heterocycles is introduced. 2-Bromobenzoic acids or acid chlorides are used as the common building blocks to couple with appropriate nitrogen-containing compounds. Sequential aryl radical cyclizations including conjugate additions, spirocyclizations, homolytic and ipso aromatic substitutions, and 1,5-hydrogen atom transfers are employed to prepare tri- and tetracyclic isoindolinones, benzolactams, isoquinolinones, azabenzoisocoumarins, and bridged-azabicyclic compounds.     

Dimensions of irreducible modules for partition algebras and tensor power multiplicities for symmetric and alternating groups

The partition algebra \(\mathsf {P}_k(n)\) and the symmetric group \(\mathsf {S}_n\) are in Schur–Weyl duality on the k-fold tensor power \(\mathsf {M}_n^{\otimes k}\) of the permutation module \(\mathsf {M}_n\) of \(\mathsf {S}_n\), so there is a surjection \(\mathsf {P}_k(n) \rightarrow \mathsf {Z}_k(n) := \mathsf {End}_{\mathsf {S}_n}(\mathsf {M}_n^{\otimes k})\), which is an isomorphism when \(n \ge 2k\). We prove a dimension formula for the irreducible modules of the centralizer algebra \(\mathsf {Z}_k(n)\) in terms of Stirling numbers of the second kind. Via Schur–Weyl duality, these dimensions equal the multiplicities of the irreducible \(\mathsf {S}_n\)-modules in \(\mathsf {M}_n^{\otimes k}\). Our dimension expressions hold for any \(n \ge 1\) and \(k\ge 0\). Our methods are based on an analog of Frobenius reciprocity that we show holds for the centralizer algebras of arbitrary finite groups and their subgroups acting on a finite-dimensional module. This enables us to generalize the above result to various analogs of the partition algebra including the centralizer algebra for the alternating group acting on \(\mathsf {M}_n^{\otimes k}\) and the quasi-partition algebra corresponding to tensor powers of the reflection representation of \(\mathsf {S}_n\).     

Structure of bis(2-pyridine-N-oxide) diselenide and its formation from tetraphenylantimony(V)selenopyridine-N-oxide

The structure of bis(2-pyridine-N-oxide) diselenide was determined by single crystal X-ray diffraction. The compound crystallized in the triclinic system and the structure was solved in the space group . The lattice constants were determined to bea=7.174(2),b=7.176(2),c=11.070(2) , =87.67(2)°, =73.68(2)°, and =89.57(2)°;Z=2,D _x=1.906 Mg m^–3. The final least squares refinement based on 1942 independent observed reflections yieldedR=0.033,wR=0.044. The Se–Se bond length is 2.326(1) and each Se is coordinated to the O atom of the corresponding N-oxide moiety at a distance of about 2.6 .     

Electronic interplay on illuminated aqueous carbon nanohorn-porphyrin ensembles

Tetracationic water-soluble porphyrin (H(2)P(4+)) has been immobilized by pi-pi stacking interactions onto the skeleton of carbon nanohorns (CNH), without disrupting their pi-electronic network. The stable aqueous solution of the CNH-H(2)P(4+) nanoensemble was examined by both electron microscopy and spectroscopic techniques. The efficient fluorescence quenching of the H(2)P(4+) moiety in the CNH-H(2)P(4+) nanoensemble was probed by steady-state as well as time-resolved fluorescence emission spectroscopy, suggesting charge separation from the photoexcited H(2)P(4+) to CNH. In the presence of methyl viologen dication (MV(2+)) and a hole trap, accumulation of the reduced species of methyl viologen was observed by the photoillumination of CNH-H(2)P(4+), suggesting that the electron migration from the initially formed charge-separated state takes place. Transient absorption spectroscopy gave further insights on the transient species such as the charge-separated state (CNH(*-))-(H(2)P(4+))(*+), which was consumed in the presence of MV(2+) and hole shifter, leaving the reduced methyl viologen.     

Dimensionality control of coupled scattering equations using partitioning techniques

A method of variable reduction of the dimensionality of the coupled equations for inelastic scattering is presented, based upon a projection operator P with a restricted range of orbital angular momentum states. For rotational states in the range O?j ?j^* and total angular momentum large, the coupled equations have dimensionality (j^* + 1) ? N ?(j^* + 1)², where the value of N is controlled by the choice of P. This is in contrast to conventional partitioning techniques which utilize further restrictions on the important molecular rotational states. The equations for the P subspace and its complementary Q subspace are decoupled by an approximation on the equation of motion of Qψ_scat. Information about scattering into the Q subspace is retained, within this degree of approximation, and is reintroduced at the end of the computation with little additional labor. The theory is developed in terms of atom-rigid-rotor scattering, although addition of vibrational modes would not in any way interfere with the basic techniques used.     

Structural anisotropy in unstretched and uniaxially stretched poly(p‐phenylene vinylene)

Poly(p‐phenylene vinylene) or PPV is gaining increasing importance because of its superior electroluminescent efficiency and electrical conductivity. The most widely followed synthetic route for PPV involves synthesis of a precursor polymer using a sulfonium monomer salt. Previous studies have proven that the monomer salt which contains cyclic sulfonium groups yields better quality PPV than when the monomer containing dialkyl sulfonium groups is used. The structure of PPV synthesized using cyclic sulfonium precursor has not been as widely reported as that synthesized using dialkyl sulfonium monomer. In the current work, the structure of PPV, synthesized using a cyclic viz. tetrahydrothiophenium monomer salt, has been studied in detail using the wide angle X‐ray diffraction (WAXD) technique. The study reveals that even in the cast (unstretched) form, PPV shows considerable biaxial orientation in the plane of the film. This preferred orientation is found to occur during the casting process and is independent of the solvent used and casting substrate. On stretching these films to a final draw ratio of 7 : 1, this biaxial orientation is transformed into uniaxial orientation with nematic ordering of PPV chains along the stretch direction and PPV chains assuming three preferred orientations in the plane of the film. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 605–614, 1999