Rounding Procedures for the Discrete Version of the Capacitated Economic Order Quantity Problem

The capacitated Economic Order Quantity problem (capacitated EOQ) is a well-known problem where products have to be shipped between two points with a vehicle of given capacity. Each shipment has a fixed cost, independent of the shipped quantity, and an inventory cost is generated in the two points. The problem consists in finding the optimal time between consecutive shipments, which minimizes the total cost. The problem is a capacitated variant of the EOQ problem and has a closed form solution. Since such solution is often irrational, it is often rounded to an integer value. In this paper we investigate the errors which are generated by rounding procedures to integer and powers-of-two values. We show that, although in the worst case a tight general relative error of 2 is generated by all the considered rounding procedures, the procedure which rounds to the best between the lower and upper values (integer or powers-of-two) has a performance of $\frac{1}{2}$ ( $\sqrt 2 + 1/\sqrt 2 $ )≈1.06 on classes of instances of high practical relevance.     

On the solutions of the congruence

In this note, we show that if is a positive integer satisfying the congruence , then .

     

Nickel(II)-catalyzed highly enantioselective hydrophosphination of methacrylonitrile

The dicationic Ni(II) complex [Ni(Pigiphos)(THF)](ClO4)2, [1](ClO4)2 ((R)-(S)-Pigiphos = bis-{(R)-1-[(S)-2-(diphenylphosphino)ferrocenyl]ethyl}cyclohexylphosphine), catalyzes the addition of bulky aliphatic secondary phosphines to methaacrylonitrile. This hydrophosphination reaction reaches TON = 900 and enantioselectivities up to 94%. A catalytic cycle involving 1,4-conjugate addition of R2PH to methacrylonitrile is supported by the isolation and characterization of a catalytically active N-coordinated, methacrylonitrile Ni complex.     

Organocatalyzed solvent-free aza-Henry reaction: a breakthrough in the one-pot synthesis of 1,2-diamines

A nitrogen-containing superbase such as TMG was found to be an effective catalyst for the reaction between N-diphenylphosphinoyl imines and nitroalkanes. Exploiting a protocol that avoids the use of any solvent also during workup procedure, we synthesized a series of beta-nitroamines in excellent yields and high diastereomeric ratios. These results, combined with the capability of the indium in conjunction with Zn as the stoichiometric reducing agent to perform in aqueous medium reduction of the nitro group under mild reaction conditions, led us to devise a three-step, one-pot synthesis of a range of 1,2-diamines, making use of environmentally friendly procedures in the various steps.     

The impact of the actual geometrical structure of a thermoelectric material on its electronic transport properties: the case of doped skutterudite systems

By doping CoSb(3) with Sn, Ba, and La, several structural outcomes are possible. The effect these different structures have on the electronic transport properties of the resulting materials is evaluated by means of an ab initio electronic structure approach and by using the semiclassical Boltzmann theory to derive the electronic transport properties from the band structure. It is shown that the calculated Seebeck coefficient is a very useful indicator of both the actual content of the dopant element and of where it mainly locates into the CoSb(3) structure. The use of such an indicator, along with geometrical considerations, demonstrates that the Sn atom occupies both the interstitial and the pnicogen ring positions with relative occupancies and ensuing thermoelectric properties, which heavily depend on the synthesis' conditions. The same indicator also suggests that the La atom, which occupies only interstitial positions, has a far lower maximal solubility in CoSb(3) than that claimed experimentally.     

A new HPLC method for serum neopterin measurement and relationships with plasma thiols levels in healthy subjects

Neopterin, a pyrazinopyrimidine compound, serves as a marker of cellular immune system activation, and it can be used as a prognostic predictor for certain types of diseases. We propose a new simple HPLC method to measure serum neopterin with highly sensitive fluorimetric detection. After TCA serum protein precipitation, the supernatant was diluted five times, injected into a C18 reversed-phase column and eluted at a flow rate of 1.5 mL/min by an isocratic water-acetonitrile (99:1) mobile phase. The natural fluorescence of the molecule was detected at excitation wavelength 353 nm and emission 438 nm. In these conditions the neopterin retention time was about 4 min. Our proposed method was compared with a validated chromatographic separation, and the obtained data of the serum neopterin from 35 healthy volunteers were analysed by Passing-Bablok regression and Bland-Altman test. Neopterin measurement in healthy subjects was also employed to investigate on its potential relationships with plasma thiols levels.     

Sharp regularity for functionals with (p,q) growth

We prove regularity theorems for minimizers of integral functionals of the Calculus of Variations

     

Review: Hamiltonian Linearization of the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge: A Radiation Gauge for Background-Independent Gravitational Waves in a Post-Minkowskian Einstein Spacetime

In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy , we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of non-harmonic 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO) . We define a Hamiltonian linearization of the theory, i.e. gravitational waves, without introducing any background 4-metric, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in . We solve all the constraints of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's , which replace the two polarizations of the TT harmonic gauge, and that linearized Einstein's equations are satisfied. Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation.     

Spin-liquid versus dimerized ground states in a frustrated Heisenberg antiferromagnet

We present a density matrix renormalization group study of the ground-state properties of spin-1/2 frustrated J1-J3 Heisenberg n(l)-leg ladders (with n(l) up to 8). For strong frustration (J(3)/J(1) approximately 0.5), both even-leg and odd-leg ladders display a finite gap to spin excitations, which we argue remains finite in the two-dimensional limit. In this regime, on odd-leg ladders the ground state is spontaneously dimerized, in agreement with the Lieb-Schultz-Mattis prediction, while on even-leg ladders the dimer correlations decay exponentially. The magnitude of the dimer order parameter decreases as the number of legs increases, consistent with a two-dimensional spin-liquid ground state.