N‐(4‐Methoxy­benzyl­idene)‐N′‐(2‐pyridyl)­hydrazine

Molecules of the title compound (alternative name p‐methoxybenzaldehyde 2‐pyridyl­hydrazone), C₁₃H₁₃N₃O, adopt an E configuration about the azomethine C=N double bond. Molecules are almost planar, the dihedral angle between the pyridine and methoxy­phenyl rings being only 6.19 (12)°. Pairwise N—H⃛N hydrogen bonds [R(8) in graph‐set notation] link centrosymmetrically related mol­ecules into discrete pairs.     

Synthesis, spectroscopic and electrochemical studies on bis-[1,3-substituted (Cl, Br) phenyl-5-phenyl formazanato]nickel(II) complexes

In this study, new 1:2 Ni complexes of 1,3-substituted phenyl-5-phenylformazans were synthesized with -Cl, -Br substituents in the o-, m-, p-positions of the 1-phenyl ring and -NO(2) group in the m-position of the 3-phenyl ring. Their structures were elucidated and spectral behaviors were investigated with the use of elemental analysis, GC-Mass, (1)H NMR, (13)C NMR, FTIR, UV-vis spectra. Furthermore electrochemical properties such as number of electrons transferred (n), diffusion coefficients (D) and possible reaction mechanism of the compounds were determined with the use of cyclic voltammetry, ultramicrodisc electrode and chronoamperometry. The relation between their absorption properties and electrochemical properties was examined. A linear correlation was obtained between Hammett substituent coefficients with lambda(max) values.     

A General Approach for the Exact Solution of the Schrödinger Equation

The Schrödinger equation is solved exactly for some well known potentials. Solutions are obtained reducing the Schrödinger equation into a second order differential equation by using an appropriate coordinate transformation. The Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions.     

Di­aqua­bis­(pyridine‐2‐carbox­amide‐κ2N1,O2)­nickel(II) disaccharinate tetrahydrate

In the crystal structure of the title compound, [Ni(C₆H₆N₂O)₂(H₂O)₂](C₇H₄NO₃S)₂·4H₂O or [Ni(pia)₂(H₂O)₂](sac)₂·4H₂O (pia is picolin­amide or pyridine‐2‐carbox­amide, and sac is the saccharinate anion), the Ni²⁺ cation, located on a centre of symmetry, is coordinated by two symmetry‐related aqua ligands together with a pair of symmetry‐related bidentate pia mol­ecules and exhibits a distorted octahedral environment. The unique unligated sac anion in the asymmetric unit resides on a general position and has a single negative charge. The coordinated water mol­ecules link the sac ions to the metal complex via O—H⋯O hydrogen bonds. In addition, the sac ions are linked to the metal complex via intermolecular π–π interactions between the benzene ring of the sac ion and the pyridine ring of a pia ligand. Each uncoordinated water mol­ecule is hydrogen bonded to sac moieties through O—H⋯O and O—H⋯N hydrogen bonds.     

[N‐(2‐Hydroxy­ethyl)ethyl­enediamine‐κ3N,N′,O]‐cis‐bis(isothio­cyanato‐κN)copper(II)

In the novel transition metal isothio­cyanate complex of N‐(2‐hydroxy­ethyl)ethyl­enediamine (hydet‐en) with copper, [Cu(NCS)₂(C₄H₁₂N₂O)], the Cu atom lies in a distorted square‐pyramidal environment, coordinated by four N atoms in the basal plane and an apical O atom. The hydet‐en ligand is N,N,O‐tridentate, in contrast to the disposition in previously studied complexes, while the isothio­cyanate ions act as N‐atom donor ligands. The monomeric units are linked to one another by hydrogen bonds.     

Control of systems with flexible multi-server pools: a shadow routing approach

A general model with multiple input flows (classes) and several flexible multi-server pools is considered. We propose a robust, generic scheme for routing new arrivals, which optimally balances server pools’ loads, without the knowledge of the flow input rates and without solving any optimization problem. The scheme is based on Shadow routing in a virtual queueing system. We study the behavior of our scheme in the Halfin–Whitt (or, QED) asymptotic regime, when server pool sizes and the input rates are scaled up simultaneously by a factor r growing to infinity, while keeping the system load within \(O(\sqrt{r}\,)\) of its capacity.The main results are as follows. (i) We show that, in general, a system in a stationary regime has at least \(O(\sqrt{r}\,)\) average queue lengths, even if the so called null-controllability (Atar et al., Ann. Appl. Probab. 16, 1764–1804, 2006) on a finite time interval is possible; strategies achieving this \(O(\sqrt{r}\,)\) growth rate we call order-optimal. (ii) We show that some natural algorithms, such as MaxWeight, that guarantee stability, are not order-optimal. (iii) Under the complete resource pooling condition, we prove the diffusion limit of the arrival processes into server pools, under the Shadow routing. (We conjecture that result (iii) leads to order-optimality of the Shadow routing algorithm; a formal proof of this fact is an important subject of future work.) Simulation results demonstrate good performance and robustness of our scheme.     

Controlling the Structure and Length of Self‐Synthesizing Supramolecular Polymers through Nucleated Growth and Disassembly

Directing self‐assembly processes out‐of‐equilibrium to yield kinetically trapped materials with well‐defined dimensions remains a considerable challenge. Kinetically controlled assembly of self‐synthesizing peptide‐functionalized macrocycles through a nucleation–growth mechanism is reported. Spontaneous fiber formation in this system is effectively shut down as most of the material is diverted into metastable non‐assembling trimeric and tetrameric macrocycles. However, upon adding seeds to this mixture, well‐defined fibers with controllable lengths and narrow polydispersities are obtained. This seeded growth strategy also allows access to supramolecular triblock copolymers. The resulting noncovalent assemblies can be further stabilized through covalent capture. Taken together, these results show that self‐synthesizing materials, through their interplay between dynamic covalent bonds and noncovalent interactions, are uniquely suited for out‐of‐equilibrium self‐assembly.     

Optimal control of parallel server systems with many servers in heavy traffic

We consider a parallel server system that consists of several customer classes and server pools in parallel. We propose a simple robust control policy to minimize the total linear holding and reneging costs. We show that this policy is asymptotically optimal under the many-server heavy traffic regime for parallel server systems when the service times are only server pool dependent and exponentially distributed. J.G. Dai’s research supported in part by National Science Foundation grants CMMI-0727400 and CNS-0718701, and by an IBM Faculty Award.     

The HN method for half-space Albedo and constant source problems for isotropic and anisotropic scattering kernels

The H_N method, which is developed recently, is used to solve the half-space albedo and the half-space constant source problems for both isotropic and extremely anisotropic scattering kernels. It has been shown that the method solves the problems in a concise manner and leads to fast converging numerical results as shown in tables.