Optimal switching for systems governed by nonlinear evolution equations

Optimal switching for a nonlinear evolution equation is considered. A type of approximating problems with value functions {u_u0<u<u₀} is studied. We prove that each u_u is the unique viscositY solution of corresponding Hami1ton-Jacoby system, u_u convergesto the value function u of the original problem as µ goes to 0, and an optimal control is determined.     

Singular fractional differential equations

Fractional differential equations have received increasing attention during recent years since the behavior of many physical systems can be properly described using the fractional order system theory. By fractional analog for Duhamel principle we give the existence-uniqueness result for linear and nonlinear time fractional evolution equations with singularities in corresponding norm in extended Colombeau algebra of generalized functions. In order to find the explicit solutions we use integral representation of the solution obtained via Laplace and Fourier transforms in succession and their inverses. We deal with some nonlinear models with singularities appearing in viscoelasticity and in anomalous processes, extending the results in viscoelasticity, continuum random walk, seismology, continuum mechanics and many other branches of life and science. The main task is finding existence-uniqueness results like in the case of evolution equations with entire derivatives. By examining the fractional evolution equations it turns out that they lead to till now known results from the evolution equations with entire derivatives in limiting case. They give more, behavior of the solution when order of derivatives are inside the intervals of entire points. In this way we can follow the influence of the operators generated by entire derivative in many fractional time evolution PDEs especially with singular initial data, and non-Lipschitz's nonlinear term. Apart from evolution equations we prove also an existence-uniqueness result for an initial value problem with singularities for linear and nonlinear fractional elliptic equation of Helmholtz type and fractional order α, where 1 < Re(α) ≤ 2, with respect to the one variable from R ₊. As a framework, we employ also Colombeau algebra of generalized functions containing fractional derivatives and operations among them in order to deal with the fractional equations with singularities. We apply the same techniques to the fractional Laplace and Poisson equation linear and nonlinear ones. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of vibration effects on the comfort of intercity bus users by oscillatory model with ten degrees of freedom

The paper analyzes the effects of vibrations on the comfort of intercity bus IK-301 users. Evaluation of vibration effects was carried out according to the criteria set out in the 1997 ISO 2631-1 standard for comfort in public means of transport. Comfort is determined for the space of a driver, passenger in the middle part of the bus and passenger in the rear overhang. Also, the allowable exposure time to vibrations in drivers for the reduced comfort criterion was determined according to the 1978 ISO 2631-1 standard. The bus spatial oscillatory model with ten degrees of freedom was developed for the needs of the analysis. Bus excitation was generated applying the Power Spectral Density of the asphalt-concrete road roughness, as described by the H. Braun model. The allowable vibration exposure time for the driver’s body decreases as the spring stiffness of the driver’s seat suspension system increases. Simulation was performed using the MATLAB software.     

Essential oil composition of Erica spiculifolia Salisb - first report

The essential oil isolated from Erica spiculifolia Salisb. by hydrodistillation was analysed by GC-MS. One hundred compounds representing 92.6% of total oil were identified. Among the detected compounds 38 were monoterpenoids (46.2%), 30 were sesquiterpenoids (31.7%), 2 diterpene (0.4%) and 30 compounds (14.3%) were with various non-terpenoid structures. Oxygenated monoerpenes were by far the main class (45.3%) with α-terpineol (7.5%) endo-borneol (7.2%), pinocarveol (5.9%) and thymol (3.7%) as the major compounds. The predominant components of sesquiterpenes were caryophyllene oxide (5.0%), caryophyllene (4.2%), τ –murrolol (3.5%), spathulenol (2.9) and α-cadinol (2.3%).     

Controlling the moving boundary of the parabolic obstacle problem

We consider the controlled parabolic obstacle problem with the controlu appearing through the Neumann condition y/v=u on the boundary of an open domain ofR ^N . Given a smooth open subsetQ ⁰ of ×(0,T) we prove that the problemQ ⁰ {(x, t) Q, y ^u (x, t)=0} is approximately solvable. Numerical tests are given.This work was done while Viorel Barbu was the Otto Szasz Visiting Professor at the University of Cincinnati.     

N,Se-Acetals: Preparation and use in diastereoselective radical reactions

A new facile synthesis of N,S- and N,Se-acetals starting from aldehydes and primary amines is presented (Schemes 3–5). These acetals are used as precursors for stereoselective radical deuteration and allylation reactions (Schemes 6 and 7, Tables 1 and 2). The stereochemical outcome of the reactions depends on the radical trap and the substituents at the N-atom. Deuterations give always anti products with moderate to high selectivities. The allylation reactions give either syn or anti products with low to moderate selectivities. The observed stereoselectivities can be explained with a model based on minimization of A^1,3 strain and are controlled by steric and stereoelectronic effects.     

Stereoselective Reactions of Phthalimido-Substituted Radicals Derived from (±)-Threonine: A comparison with reactions of N-phthaloyliminium ions

Stereoselective reactions of phthalimido-substituted radicals derived from (±)-threonine with different radical traps are reported (Scheme 3, Table 1). A strong influence of the nature of the radical trap on the stereoselectivity was noticed. Small nucleophilic radical traps gave preferentially the syn products. The observed selectivities are explained with the A^1,3 strain model and depend on steric and electronic effects (Fig. 2). Reactions with electrophilic radical traps such as diphenyl diselenide gave the anti diastereoisomers with moderate stereocontrol, presumably due to stereoelectronic effects. The same stereochemical outcome, i.e., preferential formation of the anti products, was observed for the reactions of the related N-phthaloyliminium ion (Scheme 5, Table 2). The stereochemistry of the ionic reaction is rationalized by a Felkin-Anh model (Fig. 3).     

Suspicion Distillation Gradient Descent Bit-Flipping Algorithm

We propose a novel variant of the gradient descent bit-flipping (GDBF) algorithm for decoding low-density parity-check (LDPC) codes over the binary symmetric channel. The new bit-flipping rule is based on the reliability information passed from neighboring nodes in the corresponding Tanner graph. The name SuspicionDistillation reflects the main feature of the algorithm—that in every iteration, we assign a level of suspicion to each variable node about its current bit value. The level of suspicion of a variable node is used to decide whether the corresponding bit will be flipped. In addition, in each iteration, we determine the number of satisfied and unsatisfied checks that connect a suspicious node with other suspicious variable nodes. In this way, in the course of iteration, we “distill” such suspicious bits and flip them. The deterministic nature of the proposed algorithm results in a low-complexity implementation, as the bit-flipping rule can be obtained by modifying the original GDBF rule by using basic logic gates, and the modification is not applied in all decoding iterations. Furthermore, we present a more general framework based on deterministic re-initialization of the decoder input. The performance of the resulting algorithm is analyzed for the codes with various code lengths, and significant performance improvements are observed compared to the state-of-the-art hard-decision-decoding algorithms.