Integer Decomposition Property of Free Sums of Convex Polytopes

Let \({\mathcal{P} \subset \mathbb{R}^{d}}\) and \({\mathcal{Q} \subset \mathbb{R}^{e}}\) be integral convex polytopes of dimension d and e which contain the origin of \({\mathbb{R}^{d}}\) and \({\mathbb{R}^{e}}\), respectively. We say that an integral convex polytope \({\mathcal{P}\subset \mathbb{R}^{d}}\) possesses the integer decomposition property if, for each \({n\geq1}\) and for each \({\gamma \in n\mathcal{P}\cap\mathbb{Z}^{d}}\), there exist \({\gamma^{(1)}, . . . , \gamma^{(n)}}\) belonging to \({\mathcal{P}\cap\mathbb{Z}^{d}}\) such that \({\gamma = \gamma^{(1)} +. . .+\gamma^{(n)}}\). In the present paper, under some assumptions, the necessary and sufficient condition for the free sum of \({\mathcal{P}}\) and \({\mathcal{Q}}\) to possess the integer decomposition property will be presented.     

Generalized Aluthge transformation on -hyponormal operators

We shall introduce a generalized Aluthge transformation on -
hyponormal operators and also, by using the Furuta inequality, we shall give several properties on this generalized Aluthge transformation as further extensions of some results of Aluthge.

     

Analysis of transient queues with semidefinite optimization

We derive upper bounds on the tail distribution of the transient waiting time in the GI/GI/1 queue, given a truncated sequence of the moments of the service time and that of the interarrival time. Our upper bound is given as the objective value of the optimal solution to a semidefinite program (SDP) and can be calculated numerically by solving the SDP. We also derive the upper bounds in closed form for the case when only the first two moments of the service time and those of the interarrival time are given. The upper bounds in closed form are constructed by formulating the dual problem associated with the SDP. Specifically, we obtain the objective value of a feasible solution of the dual problem in closed from, which turns out to be the upper bound that we derive. In addition, we study bounds on the maximum waiting time in the first busy period.     

A note on the reducibility of automorphisms of the Klein curve and the -invariant of mapping tori

We give a characterization for the reducibility of automorphisms of the genus 3 Klein curve in terms of the -invariant of finite order mapping tori.

     

Circular autocorrelation of stationary circular Markov processes

The stationary Markov process is considered and its circular autocorrelation function is investigated. More specifically, the transition density of the stationary Markov circular process is defined by two circular distributions, and we elucidate the structure of the circular autocorrelation when one of these distributions is uniform and the other is arbitrary. The asymptotic properties of the natural estimator of the circular autocorrelation function are derived. Furthermore, we consider the bivariate process of trigonometric functions and provide the explicit form of its spectral density matrix. The validity of the model was assessed by applying it to a series of wind direction data.     

Synthetic studies toward swinhoeisterol A,a novel steroid with an unusual carbon skeleton

Swinhoeisterol A is a novel steroid with unusual 6/6/5/7 tetracyclic skeleton. The model compound with BCD rings is constructed by Friedel–Crafts acylation and an oxidative dearomatization as key steps.     

Identification of conjugation positions of urinary glucuronidated vitamin D3 metabolites by LC/ESI–MS/MS after conversion to MS/MS‐fragmentable derivatives

A liquid chromatography/electrospray ionization–tandem mass spectrometry‐based method was developed for the identification of the conjugation positions of the monoglucuronides of 25‐hydroxyvitamin D₃ [25(OH)D₃] and 24,25‐dihydroxyvitamin D₃ [24,25(OH)₂D₃] in human urine. The method employed derivatization with 4‐(4‐dimethylaminophenyl)‐1,2,4‐triazoline‐3,5‐dione to convert the glucuronides into fragmentable derivatives, which provided useful product ions for identifying the conjugation positions during the MS/MS. The derivatization also enhanced the assay sensitivity and specificity for urine sample analysis. The positional isomeric monoglucuronides, 25(OH)D₃‐3‐ and ‐25‐glucuronides, or 24,25(OH)₂D₃‐3‐, ‐24‐ and ‐25‐glucuronides, were completely separated from each other under the optimized LC conditions. Using this method, the conjugation positions were successfully determined to be the C3 and C24 positions for the glucuronidated 25(OH)D₃ and 24,25(OH)₂D₃, respectively. The 3‐glucuronide was not present for 24,25(OH)₂D₃, unlike 25(OH)D₃, thus we found that selective glucuronidation occurs at the C24‐hydroxy group for 24,25(OH)₂D₃.     

SUPER TOUGH GELS WITH A DOUBLE NETWORK STRUCTURE

 Living tissues work with fantastic functions in soft and wet gel-like state. Thus, hydrogels have attracted much attention as excellent soft & wet materials, suitable for making artificial organs for medical treatments.However, conventional hydrogels are mechanically too weak for practical uses. We have created double network (DN) hydrogels with extremely high mechanical strength in order to overcome this problem. DN gels are interpenetrating network (IPN) hydrogels consisting of rigid polyelectrolyte and soft neutral polymer. Their excellent mechanical properties cannot be explained by the standard fracture theories. In this paper, we discuss about the toughening mechanism of DN gels in accordance with their characteristic behavior, such as large hysteresis and necking phenomenon. We also describe the results on tissue engineering application of DN gels.     

Laser Spectroscopic Study of Cold Gas‐Phase Host‐Guest Complexes of Crown Ethers

The structure, molecular recognition, and inclusion effect on the photophysics of guest species are investigated for neutral and ionic cold host‐guest complexes of crown ethers (CEs) in the gas phase. Here, the cold neutral host‐guest complexes are produced by a supersonic expansion technique and the cold ionic complexes are generated by the combination of electrospray ionization (ESI) and a cryogenically cooled ion trap. The host species are 3n‐crown‐n (3nCn; n = 4, 5, 6, 8) and (di)benzo‐3n‐crown‐n ((D)B3nCn; n = 4, 5, 6, 8). For neutral guests, we have chosen water and aromatic molecules, such as phenol and benzenediols, and as ionic species we have chosen alkali‐metal ions (M⁺). The electronic spectra and isomer‐specific vibrational spectra for the complexes are observed with various laser spectroscopic methods: laser‐induced fluorescence (LIF); ultraviolet‐ultraviolet hole‐burning (UV‐UV HB); and IR‐UV double resonance (IR‐UV DR) spectroscopy. The obtained spectra are analyzed with the aid of quantum chemical calculations. We will discuss how the host and guest species change their flexible structures for forming best‐fit stable complexes (induced fitting) and what kinds of interactions are operating for the stabilization of the complexes. For the alkali metal ion?CE complexes, we investigate the solvation effect by attaching water molecules. In addition to the ground‐state stabilization problem, we will show that the complexation leads to a drastic effect on the excited‐state electronic structure and dynamics of the guest species, which we call a “cage‐like effect”.     

A pyrazine-bridged linear pentanuclear copper(II) complex and related tri- and dinuclear complexes showing various coordination structures and magnetic couplings

Sterically bulky pyrazines have been successfully utilized for the preparation of discrete oligo-nuclear TBP (trigonal bipyramidal), SqP (square pyramidal), and Oh (octahedral) copper(II) complexes. We have synthesized a unique linear pentanuclear complex [{Cu(hfac)₂}₅(μ-2-butyl-3-methylpyrazine)₄]. The two terminal copper(II) ions have a SqP structure while the three inner ions have an Oh one. The solvent molecule was incorporated in the clearance of the lattice. From another reaction under harsh conditions, we separated [{Cu(hfac)₂}₃(μ-2-butyl-3-methylpyrazine)₂], which can be regarded as the central moiety of the pentanuclear one. We also prepared a dinuclear complex [{Cu(hfac)₂}₂(μ-tetramethylpyrazine)], in which the pyrazine nitrogen atoms were located at TBP equatorial positions. Single-crystal EPR measurements supported its compressed TBP structure. The exchange coupling was antiferromagnetic with J_TBP–TBP/k_B = −3.6 K. The linear trinuclear [{Cu(hfac)₂}₃(μ-2,3,5-trimethylpyrazine)₂], having two TBP Cu ions with an intervening Oh Cu ion, showed very weak antiferromagnetic coupling. DFT calculations on these compounds indicated that the σ-type orbital overlap between the Cu and N atoms is essential for superexchange interactions.