Exact solutions of Kolmogorov-Petrovskii-Piskunov equation using the modified simple equation method

The modified simple equation method is employed to find the exact solutions of the nonlinear Kolmogorov-Petrovskii-Piskunov （KPP） equation. When certain parameters of the equations are chosen to be special values, the solitary wave solutions are derived from the exact solutions. It is shown that the modified simple equation method provides an effective and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.     

Corrected Entropy of BTZ Black Holes

In this paper, corrected entropy of a class of BTZ black holes, include charge and rotation, studied. We obtain corrected Bekenstein-Hawking entropy and find that effect of charge viewed at order A ^?2, and effect of rotation viewed at order A ^?6, therefore Q and J don’t have contribution in corrected entropy lower than the second order. We also write the first law of black hole thermodynamics for the case of charged rotating BTZ black hole.     

Analysis of multi-level queueing systems with servers breakdown by using recursive solution technique

In this paper we construct a multi-level queueing model that alternates between three modes of an operation system. The service times have followed an Erlang type K   distribution with parameter μ$\mu$. Customers arrive in batches according to a time-homogeneous compound Poisson process with mean rate λ$\lambda$ for the batches. Our aim is to give a recursive scheme for the solution of the steady state equations. Next we derive some important measures of performance which may affect the efficiency of the system under consideration such as the expected waiting time per customer, the expected number of customers who arrive to a full system. The expected number of customers will also be calculated. Finally, we can also calculate the efficiency measures of the system by using the recursive results through an example.     

An analytic framework to develop policies for testing, prevention, and treatment of two-stage contagious diseases

In this paper we consider healthcare policy issues for trading off resources in testing, prevention, and cure of two-stage contagious diseases. An individual that has contracted the two-stage contagious disease will initially show no symptoms of the disease but is capable of spreading it. If the initial stages are not detected which could lead to complications eventually, then symptoms start appearing in the latter stage when it would be necessary to perform expensive treatment. Under a constrained budget situation, policymakers are faced with the decision of how to allocate budget for prevention (via vaccinations), subsidizing treatment, and examination to detect the presence of initial stages of the contagious disease. These decisions need to be performed in each period of a given time horizon. To aid this decision-making exercise, we formulate a stochastic dynamic optimal control problem with feedback which can be modeled as a Markov decision process (MDP). However, solving the MDP is computationally intractable due to the large state space as the embedded stochastic network cannot be decomposed. Hence we propose an asymptotically optimal solution based on a fluid model of the dynamics in the stochastic network. We heuristically fine-tune the asymptotically optimal solution for the non-asymptotic case, and test it extensively for several numerical cases. In particular we investigate the effect of budget, length of planning horizon, type of disease, population size, and ratio of costs on the policy for budget allocation.     

Efficient and Ecofriendly Route for the Solvent-Free Synthesis of 4-Alkoxy-5H-chromen[2,3-d]pyrimidines Using Phosphonic Acid Functionalized KIT-6 Confined Ionic Liquid as Recoverable Catalyst

Phosphonic acid functionalized KIT-6 confined ionic liquid (IL, 1-butyl-3-methylimidazolium tetrafluoroborate [BMIm][BF₄]) catalyzed the one-pot condensation reaction of iminochromenes and salicylaldehydes with different primary alcohols to achieve the corresponding 4-alkoxy-5H-chromen[2,3-d]pyrimidines under solvent-free conditions and in good yields. This efficient nanocatalyst can be recovered for at least five reaction runs without significant loss of either activity or confined IL.     

KAl(SO4)2 · 12H2O as a Recyclable Lewis Acid Catalyst for Synthesis of Spirooxindoles in Aqueous Media

A simple and efficient procedure for the synthesis of spirooxindole has been described that employs a three-component condensation reaction in one pot using isatin, active methylene reagent, and 1,3-dicarbonyl compounds in an aqueous medium.     

REACTIONS OF PHENYL ISOTHIOCYANATE AND SULFUR WITH DIMERIC ADDUCTS: NOVEL SYNTHESIS OF THIAZOLES,THIAZOLO-[4,5-d]PYRIMIDINE AND THIAZOLO[4,5-d]-PYRIDINE DERIVATIVES

Abstract

Dimeric adducts 1–3 react with phenyl isothiocyanate and sulfur to afford the thiazole derivatives 4, 12 and 14. The latter products react with different chemical reagents to afford new thiazoles and their fused derivatives which show high fungicidal and bactericidal activities.     

Design and synthesis of novel antimicrobial acyclic and heterocyclic dyes and their precursors for dyeing and/or textile finishing based on 2-N-acylamino-4,5,6,7-tetrahydro-benzo[b]thiophene systems

A series of novel polyfunctionalized acyclic and heterocyclic dye precursors and their respective azo (hydrazone) counterpart dyes and dye precursors based on conjugate enaminones and/or enaminonitrile moieties were synthesized. The dyes and their precursors are based on 2-cyano-N-(3-cyano-4,5,6,7-tetrahydrobenzo[b]thiophen-2-yl)-acetamide, 2-ethoxycarbonyl-N-(3-cyano-4,5,6,7-tetrahydrobenzo[b]thiophen-2-yl)-acetamide or 2-phenylcarbamoyl-N-(3-cyano-4,5,6,7-tetrahydrobenzo[b]thiophen-2-yl)-acetamide systems as precursors. The latter compounds were used to synthesize polyfunctional thiophene-, thiazole-, pyrazole, pyridine-, pyrimidine-, oxazine-, as well as acyclic moieties. The dyes and dye precursors were characterized by elemental analysis and spectral methods. All dyes and their precursors were screened in vitro and evaluated for both their antibacterial and antifungal activities. MIC data of the novel dye systems and their respective precursors showed significant antimicrobial activity against most tested organisms. Some compounds exhibited comparable or even higher efficiency than selected standards. Dyes were applied at 5% depth for disperse dyeing of nylon, acetate and polyester fabrics. Their spectral characteristics and fastness properties were measured and evaluated.     

Photosynthetic light-harvesting is tuned by the heterogeneous polarizable environment of the protein

In photosynthesis, special antenna proteins that contain multiple light-absorbing molecules (chromophores) are able to capture sunlight and transfer the excitation energy to reaction centers with almost 100% quantum efficiencies. The critical role of the protein scaffold in holding the appropriate arrangement of the chromophores is well established and can be intuitively understood given the need to keep optimal dipole-dipole interactions between the energy-transferring chromophores, as described by Fo?rster theory more than 60 years ago. However, the question whether the protein structure can also play an active role by tuning such dipole-dipole interactions has not been answered so far, its effect being rather crudely described by simple screening factors related to the refractive index properties of the system. Here, we present a combined quantum chemical/molecular mechanical approach to compute electronic couplings that accounts for the heterogeneous dielectric nature of the protein-solvent environment in atomic detail. We apply the method to study the effect of dielectric heterogeneity in the energy migration properties of the PE545 principal light-harvesting antenna of the cryptomonad Rhodomonas CS24. We find that dielectric heterogeneity can profoundly tune by a factor up to ～4 the energy migration rates between chromophore sites compared to the average continuum dielectric view that has historically been assumed. Our results indicate that engineering of the local dielectric environment can potentially be used to optimize artificial light-harvesting antenna systems.     

Click approaches to functional water-sensitive organotriethoxysilanes

The derivatization of functional organic fragments with triethoxysilyl groups to afford hydrolyzable organosilanes with targeted properties using the copper-catalyzed alkyne azide cycloaddition reaction under strictly anhydrous conditions is described according to two approaches, starting from five silylated substrates. This high yield, fast, and selective method is applicable to a wide range of substrates and is expected to lead to important achievements in the field of functional hybrid silica.