Synthesis of the DFGH ring system of Type B Physalins: Highly Oxygenated,Cage‐Shaped Molecules

Let the dominos fall : Synthesis of the complex DFGH ring system of the title compounds has been accomplished. The approach features simple treatment of the key intermediate with a Brønsted base to afford the tetracyclic cage‐shaped target in one pot through a four‐step domino transformation (see scheme; Mc= monochloromesylate, MOM=methoxymethyl).

     

Signal processing to evaluate parameters affecting SPE for multi‐residue analysis of personal care products

This paper discusses the development of a comprehensive method for the simultaneous analysis of personal care products (PCPs) based on SPE and GC‐MS. The method was developed on 29 target compounds to represent PCPs belonging to different chemical classes: surfactants in detergents (alkyl benzenes), fragrances in cosmetics (nitro and polycyclic musks), antioxidants and preservatives (phenols), plasticizers (phthalates) displaying a wide range of volatility, polarity, water solubility. In addition to the conventional C₁₈ stationary phase, a surface modified styrene divinylbenzene polymeric phase (Strata^TM X SPE cartridge) has been investigated as suitable for the simultaneous extraction of several PCPs with polar and non‐polar characteristics. For both sorbents different solvent compositions and eluting conditions were tested and compared in order to achieve high extraction efficiency for as many sample components as possible. Comparison of the behavior of the two cartridges reveals that, overall, Strata‐X provides better efficiency with extraction recovery higher than 70% for most of the PCPs investigated. The best results were obtained under the following operative conditions: an evaporation temperature of 40°C, elution on Strata‐X cartridge using a volume of 15 mL of ethyl acetate (EA) as solvent and operating with slow flow rate (–10 KPa). In addition to the conventional method based on peak integration, a chemometric approach based on the computation of the experimental autocovariance function (EACVF_tot) was applied to the complex GC‐MS signal: the percentage recovery and information on peak abundance distribution can be evaluated for each procedure step. The PC‐based signal processing proved very helpful in assisting the development of the analytical procedure, since it saves labor and time and increases result reliability in handling GC complex signals.     

Interpolation problems on the spectrum of <Emphasis Type="Italic">H</Emphasis><Superscript>∞</Superscript>

We characterize those sequences (x _n ) in the spectrum of H ^∞ whose Nevanlinna–Pick interpolation problems admit thin Blaschke products as solutions. We also study under which conditions there is a Blaschke product B with prescribed zero-set distribution and solving problems of the form B(x) = f _n (x) for every x ∈ P(x _n ), where P(x _n ) is the Gleason part associated with the point x _n and where (f _n ) is an arbitrary sequence of functions in the unit ball of H ^∞. As a corollary we get a new characterization of Carleson–Newman Blaschke products in terms of bounded universal functions, a result first proved by Gallardo and Gorkin.      

Quotients of subdirect products of groups

We find the sharp bound for the nilpotency class of the quotients of subdirect products of groups.     

On inverses of GCD matrices associated with multiplicative functions and a proof of the Hong-Loewy conjecture

Let C={1,2,…,m} and f be a multiplicative function such that (f∗μ)(k)>0 for every positive integer k and the Euler product converges. Let (C_f)=(f(i,j)) be the m×m matrix defined on the set C having f evaluated at the greatest common divisor (i,j) of i and j as its ij-entry. In the present paper, we first obtain the least upper bounds for the ij-entry and the absolute row sum of any row of (C_f)^-1, the inverse of (C_f), in terms of ζ_f. Specializing these bounds for the arithmetical functions f=N^ε,J_ε and σ_ε we examine the asymptotic behavior the smallest eigenvalue of each of matrices (C_N^ε),(C_Jε) and (C_σε) depending on ε when m tends to infinity. We conclude our paper with a proof of a conjecture posed by Hong and Loewy [S. Hong, R. Loewy, Asymptotic behavior of eigenvalues of greatest common divisor matrices, Glasg. Math. J. 46 (2004) 551-569].     

Optimal purchasing cycle length of a deteriorating product for intermediary firms

In a supply chain logistics system, the function of an intermediary firm is to purchase products and to sell those purchased products to the public or to other firms. This article investigates how an intermediary firm can optimally determine the purchasing cycle length of a deteriorating product. By incorporating the special structure of the intermediary firm’s environments and the deteriorating nature of the product, the inventory problem encountered by the intermediary firm is mathematically formulated. The optimal purchasing cycle length is derived such that the total profit is maximized. Several interesting properties of the optimal policy are investigated and an efficient iterative algorithm is provided to search for the optimal policy. Also, the convergence of the iterative algorithm developed in this paper is proved. Finally, a numerical example is provided to illustrate the features of the proposed problem and the iterative search algorithm.     

A construction of fully diverse unitary space-time codes

Fully diverse unitary space-time codes are useful in multiantenna communications, especially in multiantenna differential modulation. Recently, two constructions of parametric fully diverse unitary space-time codes for three antennas system have been introduced. We propose a new construction method based on the constructions. In the present paper, fully diverse codes for systems of odd prime number antennas are obtained from this construction. Space-time codes from present construction are found to have bet...     

On <Emphasis Type="Italic">U</Emphasis>-orthodox semigroups

As a generalization of an orthodox semigroup in the class of regular semigroups, a type W semigroup was first investigated by El-Qallali and Fountain. As an analogy of the type W semigroups in the class of abundant semigroups, we introduce the U-orthodox semigroups. It is shown that the maximum congruence μ contained in on U-orthodox semigroups can be determined. As a consequence, we show that a U-orthodox semigroup S can be expressed by the spined product of a Hall semigroup W _U and a V-ample semigroup (T,V). This theorem not only generalizes a known result of Hall-Yamada for orthodox semigroups but also generalizes another known result of El-Qallali and Fountain for type W semigroups. This work was supported by National Natural Science Foundation of China (Grant No. 10671151) and Natural Science Foundation of Shaanxi Province (Grant No. SJ08A06), and partially by UGC (HK) (Grant No. 2160123)     

银行项目信贷风险决策分析

利用实物期权的方法对银行项目信贷的期权特性进行了讨论,对项目的收益与风险进行了更为准确的数理分析.为使结论更加准确可靠,并对具体的实例进行了剖析,说明了衍生产品在银行的项目信贷过程中也可以很好地理论指导实践,使银行能够更好地对贷前风险进行有效控制.     

A Compactification of the Space of Expanding Maps on the Circle

We show the space of expanding Blaschke products on S¹ is compactified by a sphere of invariant measures, reminiscent of the sphere of geodesic currents for a hyperbolic surface. More generally, we develop a dynamical compactification for the Teichmüller space of all measure preserving topological covering maps of S¹. Research supported in part by the NSF.