Assembly of a Benzo-Fused Bridged Ketone Scaffold from 1,5,10-Enediynes through One-Pot Ruthenium-Catalyzed Cyclization/Iodine-Mediated Oxidative Ring Expansion

In the presence of a cationic Ru catalyst, 1,6-diynes bearing a terminal styryl moiety underwent [2+2+2] cyclization to produce dehydrobiphenylenes fused with a five-membered ring. Although the cycloadducts were unstable toward purification, their one-pot iodine-mediated ring expansion successfully afforded unprecedented bridged ketone products containing a benzo-fused bicyclo[3.2.1] framework.     

The second-generation synthesis of BICMAP analogues

We previously reported the synthesis of BICMAP (1a) via 6-diphenylphosphino-2,3-dihydrobenzofuran as a key intermediate. However, we did not successfully synthesize BICMAP analogues via a similar synthetic route. Herein we report the second-generation synthesis of BICMAP and its derivatives via diethylphosphonate as a key intermediate.     

Chemical Stimulus‐responsive Folding and Unfolding of a Dendrimeric Assembly

A dendrimeric trimer undergoes folding and unfolding in response to a chemical stimulus. The trimer of interest contains a central dendrimer with a butadiyne‐linked zinc porphyrin dimer ((ZnP)₂) core, in addition to two terminal dendrimers with zinc porphyrin (ZnP) cores. The obtained absorption spectra indicate that the unfolded form is the exclusive conformer in chloroform, while the addition of 1,4‐diazabicyclo[2.2.2]octane (DABCO) in chloroform leads to transformation from the unfolded to the folded structure containing two DABCO units per trimer; the folded structure originates from the cross‐linking of (ZnP)₂ and ZnP with DABCO. Moreover, the addition of excess DABCO promotes the generation of the unfolded structure containing four DABCO units.     

An intramolecular diels-alder approach to quassinoids—a stereoselective construction of a-aromatic klaineanone

Thermolysis of a benzocyclobutene derivative ($\text{20}$) prepared from norcamphor produced stereoselectively a tetracyclic compound ($\text{2}$), which was converted to a lactone ($\text{21}$) having correct stereochemistry at C₇, C₈, C₉, C₁₁, C₁₃, and C₁₄ positions of (±)-klaineanone.     

Simple methods for the syntheses of (E)-4- and (E)-5-alkenoic acids by the SN2′ type reactions of γ-vinyl-γ-butyrolactone and δ-vinyl-δ-valerolactone with organocopper reagents

γ-Vinyl-γ-butyrolactone and δ-vinylδ-valerolactone react regio- and stereoselectivity with Grignard reagents in the presence of a copper(I) catalyst or with diorganocuprates to afford (E)-4- and (E)-5-alkenoic acids, respectively, in high yields. Synthetic utility of the former reaction is demonstrated in the simple synthesis of (4E,7Z)-4,7-tridecadienyl acetate.     

Stackelberg solutions for fuzzy random two-level linear programming through level sets and fractile criterion optimization

This paper considers Stackelberg solutions for two-level linear programming problems under fuzzy random environments. To deal with the formulated fuzzy random two-level linear programming problem, an α-stochastic two-level linear programming problem is defined through the introduction of α-level sets of fuzzy random variables. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced and the α-stochastic two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through fractile criterion optimization in stochastic programming, the transformed stochastic two-level programming problem can be reduced to a deterministic two-level programming problem. An extended concept of Stackelberg solution is introduced and a numerical example is provided to illustrate the proposed method.     

A family of quantum projective spaces and related -hypergeometric orthogonal polynomials

A one-parameter family of two-sided coideals in is defined and the corresponding algebras of infinitesimally right invariant functions on the quantum unitary group are studied. The Plancherel decomposition of these algebras with respect to the natural transitive -action is shown to be the same as in the case of a complex projective space. By computing the radial part of a suitable Casimir operator, we identify the zonal spherical functions (i.e. infinitesimally bi-invariant matrix coefficients of finite-dimensional irreducible representations) as Askey-Wilson polynomials containing two continuous and one discrete parameter. In certain limit cases, the zonal spherical functions are expressed as big and little -Jacobi polynomials depending on one discrete parameter.

     

A multi-objective lead time control problem in multi-stage assembly systems using genetic algorithms

In this paper, we develop a multi-objective model to optimally control the lead time of a multi-stage assembly system, using genetic algorithms. The multi-stage assembly system is modelled as an open queueing network. It is assumed that the product order arrives according to a Poisson process. In each service station, there is either one or infinite number of servers (machines) with exponentially distributed processing time, in which the service rate (capacity) is controllable. The optimal service control is decided at the beginning of the time horizon. The transport times between the service stations are independent random variables with generalized Erlang distributions. The problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. The objective functions are the total operating costs of the system per period (to be minimized), the average lead time (min), the variance of the lead time (min) and the probability that the manufacturing lead time does not exceed a certain threshold (max). Finally, we apply a genetic algorithm with double strings using continuous relaxation based on reference solution updating (GADSCRRSU) to solve this multi-objective problem, using goal attainment formulation. The results are also compared against the results of a discrete-time approximation technique to show the efficiency of the proposed genetic algorithm approach.     

Discrete Dynamical Systems with W(A (1) m−1 × A (1) n−1) Symmetry

We give a birational realization of affine Weyl group of type A ⁽¹⁾ _m–1 × A ⁽¹⁾ _n–1. We apply this representation to construct some discrete integrable systems and discrete Painlevé equations. Our construction has a combinatorial counterpart through the ultra-discretization procedure.