Cooperative game analysis of retail space-exchange problems

We analyze retail space-exchange problems where two or more retailers exchange their excess retail spaces to improve the utilization of their space resource. We first investigate the two-retailer space exchange problem. In order to entice both retailers with different bargaining powers to exchange their spaces, we use the generalized Nash bargaining scheme to allocate the total profit surplus between the two retailers. Next, we consider the space-exchange problem involving three or more retailers, and construct a cooperative game in characteristic function form. We show that the game is essential and superadditive, and also prove that the core is non-empty. Moreover, in order to find a unique allocation scheme that ensures the stability of the grand coalition, we propose a new approach to compute a weighted Shapley value that satisfies the core conditions and also reflects retailers’ bargaining powers. Our analysis indicates that the space exchange by more retailers can result in a higher system-wide profit surplus and thus a higher allocation to each retailer under a fair scheme.     

A modular design of ruthenium(II) catalysts with chiral C2-symmetric phosphinite ligands for effective asymmetric transfer hydrogenation of aromatic ketones

Hydrogen-transfer reduction processes are attracting increasing interest from synthetic chemists in view of their operational simplicity. The new chiral C₂-symmetric ligands N,N′-bis-[(1S)-1-sec-butyl-2-O-(diphenylphosphinite)ethyl]ethanediamide, 1 and N,N′-bis-[(1S)-1-phenyl-2-O-(diphenylphosphinite)ethyl]ethanediamide, 2 and the corresponding ruthenium complexes 3 and 4 have been prepared and their structures have been elucidated by a combination of multi-nuclear NMR spectroscopy, IR spectroscopy, and elemental analysis. ¹H–³¹P NMR, DEPT, ¹H–¹³C HETCOR, or ¹H–¹H COSY correlation experiments were used to confirm the spectral assignments. The catalytic activity of complexes 3 and 4 in transfer hydrogenation of acetophenone derivatives by iso-PrOH has also been studied. Under optimized conditions, these chiral ruthenium complexes serve as catalyst precursors for the asymmetric transfer hydrogenation of acetophenone derivatives in iso-PrOH and act as excellent catalysts, giving the corresponding chiral alcohols in 99% yield and up to 75% ee. This transfer hydrogenation is characterized by low reversibility under these conditions.     

Synthesis and characterization of a new soluble metal-free and metallophthalocyanines bearing biphenyl-4-yl methoxy groups

The synthesis and characterization of peripherally tetra-biphenyl-4-yl-methoxy substituted metal-free (4), Ni(II) (5), Cu(II) (6), Zn(II) (7), Co(II) (8) and Pb(II) (9) phthalocyanine derivatives are reported. These new phthalocyanine derivatives show the enhanced solubility in organic solvents and they have been characterized by a combination of IR, ¹H NMR, ¹³C NMR, UV–vis, mass spectral data, elemental analysis and thermal analysis methods (TG/DTA). The photophysical (fluorescence quantum yield and lifetime) and photochemical (singlet oxygen generation and photodegradation quantum yield) properties of tetra-biphenyl-4-yl-methoxy substituted zinc (II) phthalocyanine derivative (7) are also investigated. The fluorescence of this phthalocyanine derivative (7) is effectively quenched by addition of 1,4-benzoquinone (BQ).     

Developing prospective teachers’ covariational reasoning through a model development sequence

Forming part of a wider research study, the current study investigated prospective middle school mathematics teachers’ ways of covariational reasoning on tasks involving simultaneously changing quantities. As the introductory theme of a larger unit on derivative, a model development sequence on covariational reasoning was designed and experimented with 20 participants in a mathematical modeling course offered to prospective teachers. The participants’ developing abilities of covariational reasoning were documented under three categories: (i) identifying the variables, (ii) ways of coordinating the variables, and (iii) ways of quantifying the rate of change. The results revealed significant improvement in the prospective teachers’ ways of identifying and coordinating the variables, and in quantifying the rate of change. Moreover, the results indicated that preference for a particular way of thinking in identifying and coordinating the variables determined the prospective teachers’ way of quantifying the rate of change and thereby their level of covariational reasoning.     

A stochastic production planning model with a dynamic chance constraint

This paper deals with the optimal production planning for a single product over a finite horizon. The holding and production costs are assumed quadratic as in Holt, Modigliani, Muth and Simon (HMMS) [7] model. The cumulative demand is compound Poisson and a chance constraint is included to guarantee that the inventory level is positive with a probability of at least α at each time point. The resulting stochastic optimization problem is transformed into a deterministic optimal control problem with control variable and of the optimal solution is presented. The form of state variable inequality constraints. A discussion the optimal control (production rate) is obtained as follows: if there exists a time t₁ such that t₁?[O, T]where T is the end of the planning period, then (i) produce nothing until t₁ and (ii) produce at a rate equal to the expected demand plus a ‘correction factor’ between t₁ and T. If t₁ is found to be greater than T, then the optimal decision is to produce nothing and always meet the demand from the inventory.     

On the existence of $$\kappa $$-existentially closed groups

Using explicit constructions of the Weierstrass mock modular form and Eisenstein series coefficients, we obtain closed formulas for the generating functions of values of shifted convolution L-functions associated to certain elliptic curves. These identities provide a surprising relation between weight 2 newforms and shifted convolution L-values when the underlying elliptic curve has modular degree 1 with conductor N such that \(\text {genus}(X_0(N)) = 1\).     

Measurement and optimization of responsiveness in supply chain networks with queueing structures

In this paper we consider supply chains with multiple stages of serial or network structure. The supply chains are endogenous in the sense that they involve queues because each order’s lead-time is dependent on the orders already in the system. We define supply chain responsiveness as the probability of fulfilling customer orders within a promised lead-time and study the problems of measuring and optimizing supply chain responsiveness using queueing network models. We first consider a single-server multi-stage serial supply chain and find a closed form expression for the fulfilment time distribution. For the multi-server multi-stage problem, the closed form evaluation of the fulfilment time distribution becomes intractable due to the dependency of the lead-times in different stages. We circumvent this difficulty by proposing a novel FCFS discipline which enables a closed-form analysis. For the multi-server multi-stage Jackson-type supply chain network, to enable analysis, we convert the system into an equivalent single server single stage system with state-dependent rates. For each case, we present detailed numerical examples for both measurement and the optimization of supply chain responsiveness.     

Radioactivity concentrations in topsoil samples from the Thrace region of Turkey and assessment of radiological hazard

The activity concentrations of gamma emitting radionuclides were measured in surface soil samples from the Thrace region. ²³²Th, ²³⁸U, ²²⁶Ra, ⁴⁰K and ¹³⁷Cs activities and physico-chemical parameters of the soil samples were determined in samples collected from 73 sampling stations. Radionuclide concentrations measured were compared with those found in the samples from other locations of Turkey and from different countries. The average activity concentrations of ²³²Th, ²³⁸U, ²²⁶Ra, ⁴⁰K and ¹³⁷Cs were found to be 24.71 ± 8.79, 22.30 ± 7.93, 32.09±12.44, 509.00±160.05, 32.74±29.24 Bq kg^?1, respectively. The mean value of the annual effective dose equivalent from the outdoor terrestrial gamma radiation was calculated as 57.2 μ Sv.     

Nonlinear modeling and control of slosh in liquid container transfer via a PPR robot

This paper studies the point-to-point liquid container transfer control problem for a PPR robot. The robot manipulator is represented as three rigid links, and the liquid slosh dynamics are included using a multi-mass-spring model. It is assumed that two forces and a torque applied to the prismatic joints and the revolute joint, respectively, are available as control inputs. The objective is to control the robot end-effector movement while suppressing the sloshing modes. A nonlinear mathematical model that reflects all of these assumptions is first introduced. Then, Lyapunov-based feedback controllers are designed to achieve the control objective. Two cases are considered: partial-state feedback that does not use slosh state information and full-state feedback that uses both robot state and slosh state measurements or estimations. Computer simulations are included to illustrate the effectiveness of the proposed control laws.     

Collective firing regularity of a scale-free Hodgkin–Huxley neuronal network in response to a subthreshold signal

We consider a scale-free network of stochastic HH neurons driven by a subthreshold periodic stimulus and investigate how the collective spiking regularity or the collective temporal coherence changes with the stimulus frequency, the intrinsic noise (or the cell size), the network average degree and the coupling strength. We show that the best temporal coherence is obtained for a certain level of the intrinsic noise when the frequencies of the external stimulus and the subthreshold oscillations of the network elements match. We also find that the collective regularity exhibits a resonance-like behavior depending on both the coupling strength and the network average degree at the optimal values of the stimulus frequency and the cell size, indicating that the best temporal coherence also requires an optimal coupling strength and an optimal average degree of the connectivity.