Highly Proton-Conductive Zinc Metal-Organic Framework Based On Nickel(II) Porphyrinylphosphonate

The design of new solid-state proton-conducting materials is a great challenge for chemistry and materials science. Herein, a new anionic porphyrinylphosphonate-based MOF ( IPCE-1Ni ), which involves dimethylammonium (DMA) cations for charge compensation, is reported. As a result of its unique structure, IPCE-1Ni exhibits one of the highest value of the proton conductivity among reported proton-conducting MOF materials based on porphyrins (1.55×10⁻³ S cm⁻¹ at 75 °C and 80 % relative humidity).     

One-pot five-component high diastereoselective synthesis of polysubstituted 2-piperidinones from aromatic aldehydes,nitriles, dialkyl malonates and ammonium acetate

Molecular Diversity - A novel five-component diastereoselective synthesis of polysubstituted 2-piperidinones is reported. The Knoevenagel condensation–Michael addition–Mannich cascade...     

Condensation of all-cis-tetraphenylcyclotetrasiloxanetetraol in ammonia: new method for preparation of ladder-like polyphenylsilsesquioxanes

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Purcell Effect and Nonlinear Behavior of the Emission in a Periodic Structure Composed of InAs Monolayers Embedded in a GaAs Matrix

Enhancement of spontaneous emission in a resonant Bragg quantum well (QW) structure with 60 periods of triple InAs monolayers embedded in a GaAs matrix is studied experimentally and theoretically. From measurements of the time‐resolved photoluminescence, besides the QW exciton at 1.47 eV, a specific super‐radiant (SR) emission demonstrating nonlinear properties is found. The SR mode shows a near‐quadratic dependence of intensity on excitation power, while its energy position follows the Bragg condition. It is revealed that the SR mode shows a peculiar non‐monotonic dependence of intensity on direction, with a maximum observed at approximately 40°. The enhancement in the SR emission at a specific direction is correlated well with suggested theoretical consideration of the modal Purcell factor for periodic quantum well structures.     

An invariant of tangle cobordisms

We construct a new invariant of tangle cobordisms. The invariant of a tangle is a complex of bimodules over certain rings, well-defined up to chain homotopy equivalence. The invariant of a tangle cobordism is a homomorphism between complexes of bimodules assigned to boundaries of the cobordism.

     

Solving Problems with Min-Type Functions by Disjunctive Programming

We consider applications of disjunctive programming to global optimization and problems with equilibrium constraints. We propose a modification of the algorithm of F. Beaumont for disjunctive programming problems and show its numerical efficiency.     

Damped waves in a cylinder shadow

The sound field in the region of a deep shadow behind an impedance cylinder is analyzed for the case of plane wave diffraction by the cylinder surface. The main part of the field is represented by a cylindrical wave that has a complex index determined from the boundary conditions and decays with the angular coordinate. An expression for the amplitude of this wave is determined by extracting it from the total field formed in the shadow region. It is demonstrated that this wave approximates more closely the total field behind the cylinder, as compared to the least damped wave in the field representation obtained on the basis of the Watson transform. A way to improve the sound barriers is indicated.     

Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type

We establish the existence and stability of multidimensional transonic shocks for the Euler equations for steady potential compressible fluids. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for the velocity, can be written as a second-order, nonlinear equation of mixed elliptic-hyperbolic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the location of the transonic shock which divides the two regions of smooth flow, and the equation is hyperbolic in the upstream region where the smooth perturbed flow is supersonic. We develop a nonlinear approach to deal with such a free boundary problem in order to solve the transonic shock problem. Our results indicate that there exists a unique solution of the free boundary problem such that the equation is always elliptic in the downstream region and the free boundary is smooth, provided that the hyperbolic phase is close to a uniform flow. We prove that the free boundary is stable under the steady perturbation of the hyperbolic phase. We also establish the existence and stability of multidimensional transonic shocks near spherical or circular transonic shocks.