Diophantine equations with products of consecutive members of binary recurrences

We prove a finiteness result for the number of solutions of a Diophantine equation of the form \(u_n u_{n+1}\cdots u_{n+k}\pm 1 =\pm u_m^2\), where \(\{ u_n\}_{n\ge 1}\) is a binary recurrent sequence whose characteristic equation has roots which are real quadratic units.     

Unexpected formation of higher polythionates in the oxidation of thiosulfate by hypochlorous acid in a slightly acidic medium

It has been clearly shown that not only tetrathionate but also pentathionate or even higher polythionates is formed in the oxidation of thiosulfate by hypochlorous acid in a slightly acidic medium. In thiosulfate excess, the absorbance-time curves registered at 250 nm may go through a maximum followed by a minimum, suggesting the presence of a short-lived absorbing intermediate proposed to be S(2)O(3)OCl(3-). Matrix rank analysis (MRA) studies have revealed that altogether five independent absorbing species are present in the wavelength range 240-400 nm. A kinetic model is suggested to take all of the experimental observations into account.     

Bin covering with a general profit function: approximability results

In the recent paper (Benk? et al. 2010) we introduced a new problem that we call Bin Packing/Covering with Delivery, or BP/CD for short. Mainly we mean under this expression that we look for not only a good, but a “good and fast” packing or covering. In the present paper we investigate the offline case. For the analysis, a novel view on “offline optimum” is introduced, which appears to be relevant concerning all problems where a final solution is ordering-dependent. We prove that if the item sizes are not allowed to be arbitrarily close to zero, then an optimal offline solution can be found in polynomial time. On the other hand, for unrestricted problem instances, no polynomial-time algorithm can achieve an asymptotic approximation ratio better than 6/7 if $P\ne NP$ .     

An efficient solution approach for real-world driver scheduling problems in urban bus transportation

The driver scheduling problem in public transportation is defined in the following way. There is a set of operational tasks, and the goal is to define the sequence of these tasks as shifts in such a way that every task must be assigned to a shift without overlapping. In real-world situations several additional constraints need to be considered, which makes large practical problems challenging to be solved efficiently. In practice it is also an important request with respect to a public transportation scheduling system to offer several versions of quasi-optimal solutions. In this paper we present an efficient driver scheduling solution methodology which is flexible in the above sense.     

Limits of random trees

Local convergence of bounded degree graphs was introduced by Benjamini and Schramm [2]. This result was extended further by Lyons [4] to bounded average degree graphs. In this paper, we study the convergence of a random tree sequence (T _n ), where the probability of a given tree T is proportional to $\prod_{v_{i}\in V(T)}d(v_{i})!$ . We show that this sequence is convergent and describe the limit object, which is a random infinite rooted tree.     

14-Noreudesmanes and a phenylpropane heterodimer from sea buckthorn berry inhibit Herpes simplex type 2 virus replication

Two new 14-noreudesmane sesquiterpenes, one new phenylpropane heterodimer, caulilexin C, and uvaol were isolated from the 70% MeOH extract of the fruit peel of Elaeagnus rhamnoides. The structures of the compounds were elucidated by HRESIMS and advanced NMR methods. The absolute configuration of (R)-6,9-dihydroxy-1-oxo-14-noreudesm-5,7,9-triene was determined by the TDDFT-ECD method. The new compounds, together with structurally similar naphthalenes (musizin, musizin-8-O-glucoside, torachrysone-8-O-glucoside) and 1,4-naphthoquinone (2-methylstipandrone), isolated previously from Rumex aquaticus, were investigated for their antiviral activity against Herpes simplex virus type 2 (HSV-2) using two different methods. Applying the traditional virus yield reduction test, (R)-6,9-dihydroxy-1-oxo-14-noreudesm-5,7,9-triene, 1-[3-methoxy-4-(2-methoxy-4-(1E)-propenyl-phenoxy)-phenyl]-propane-1,2-diol, and musizin caused a 2.00 log₁₀, 3.49 log₁₀, and 2.33 log₁₀ reduction of HSV-2 yield, respectively, at a concentration of 12.5?μM. 2-Hydroxy-1-methoxy-6,9-dioxo-14-noreudesm-1,3,5(10),7-tetraene exhibited an antiviral effect at concentration of 50?μM only. Similar results were obtained when the qPCR method was used to test the antiviral activity of the compounds.     

Chiral separation of lansoprazole and rabeprazole by capillary electrophoresis using dual cyclodextrin systems

Novel capillary electrophoresis methods using CDs as chiral selectors were developed and validated for the chiral separation of lansoprazole and rabeprazole, two proton pump inhibitors. Fourteen different neutral and anionic CDs were screened at pH 4 and 7 in the preliminary analysis. Sulfobutyl‐ether‐β‐CD with a degree of substitution of 6.5 and 10 at neutral pH proved to be the most suitable chiral selector for both compounds. Various dual CD systems were also compared, and the possible mechanisms of enantiomer separation were investigated. A dual selector system containing sulfobutyl‐ether‐β‐CD degree of substitution 6.5 and native γ‐CD proved to be the most adequate system for the separations. Method optimization was carried out using an experimental design approach, performing an initial fractional factorial screening design, followed by a central composite design to establish the optimal analytical conditions. The optimized methods (25 mM phosphate buffer, pH 7, 10 mM sulfobutyl‐ether‐β‐CD/20 mM γ‐CD, +20 kV voltage; 17°C temperature; 50 mbar/3 s injection, detection at 210 nm for lansoprazole; 25 mM phosphate buffer, pH 7, 15 mM sulfobutyl‐ether‐β‐CD/30 mM γ‐CD, +20 kV voltage; 18°C temperature; 50 mbar/3 s injection, detection at 210 nm for rabeprazole) provided baseline separation for lansoprazole (R_s = 2.91) and rabeprazole (R_s = 2.53) enantiomers with favorable migration order (in both cases the S‐enantiomers migrates first). The optimized methods were validated according to current guidelines and proved to be reliable, linear, precise, and accurate for the determination of 0.15% distomer as chiral impurity in dexlansoprazole and dexrabeprazole samples.     

Global stability of a multistrain SIS model with superinfection and patch structure

We study the global stability of a multistrain SIS model with superinfection and patch structure. We establish an iterative procedure to obtain a sequence of threshold parameters. By a repeated application of a result by Takeuchi et al. [Nonlinear Anal Real World Appl. 2006;7:235–247], we show that these parameters completely determine the global dynamics of the system: for any number of patches and strains with different infectivities, any subset of the strains can stably coexist depending on the particular choice of the parameters.