Convergence of monotone iterations to initial value problems of functional differential equations

The method of quasilinearization is a well-known technique for obtaining approximate solutions of nonlinear differential equations. We use this technique to initial value problems of functional differential equations showing that corresponding linear iterations converge to the unique solution of our problem and this convergence is superlinear     

A combinatorial theory of minimal social situations

A minimal social situation is a game‐like situation in which there are two actors, each of them has two possible actions, and both evaluate the outcomes of their joint actions in terms of two categories (say, ‘success’ and ‘failure'). By fixing actors and actions and varying ‘payoffs’ the set of 256 ‘configurations’ is obtained. This set decomposes into 43 ‘structural forms’, or equivalence classes with respect to the relation of isomorphism defined on it. This main theorem and other results concerning related configurations (minimal decision situations) are derived in this paper by means of certain tools of group theory. Some extensions to larger structures are proved in the Appendix. In the introductory section after a brief explanation of the meaning given to the terms ‘structure’ and ‘isomorphism’ in mathematics (Bourbaki) it is shown how these terms can be used to formalize the concept of ‘social form’.     

Gradient Estimates of q-Harmonic Functions of Fractional Schrödinger Operator

We study gradient estimates of q-harmonic functions u of the fractional Schrödinger operator Δ ^α/2?+?q, α?∈?(0, 1] in bounded domains D???? ^d . For nonnegative u we show that if q is Hölder continuous of order η?>?1???α then $\nabla u(x)$ exists for any x?∈?D and $|\nabla u(x)| \le c u(x)/ ({\rm dist}(x,\partial D) \wedge 1)$ . The exponent 1???α is critical i.e. when q is only 1???α Hölder continuous $\nabla u(x)$ may not exist. The above gradient estimates are well known for α?∈?(1, 2] under the assumption that q belongs to the Kato class $\mathcal{J}^{\alpha - 1}$ . The case α?∈?(0, 1] is different. To obtain results for α?∈?(0, 1] we use probabilistic methods. As a corollary, we obtain for α?∈?(0, 1) that a weak solution of Δ ^α/2 u?+?q u?=?0 is in fact a strong solution.     

Properties of biomass vs. coal fly ashes deposited in electrostatic precipitator

This paper presents comparative experimental studies of the morphology and elemental composition of fly ash particles from coal- and biomass-fired boilers, deposited in each stage of 3-stage electrostatic precipitators (ESPs). It was shown that fly ash morphology, its physical properties, and the percentage of elements in the fly ash taken from each stage of ESP depend on the kind of fuel. The biomass fly ash contains many irregular large particles, which are pieces of unburned wood. Bulk density of biomass fly ash is on average lower than that of coal fly ash, and drastically decreases in the second and third stages of ESP. The resistivity, measured at electric field of 4 kV/cm, of fly ash from biomass-fired boilers is much lower than that from coal, and can be below 10² Ω m, whereas from coal, except the first stage, varies in the range from 10⁷ to 10¹⁰ Ω m. The low resistivity of coal fly ash in the first stage of ESP results from high carbon content, and of biomass is probably an effect of additional high percentage of potassium, calcium and sodium sulfates. The percentage of Si, Al, Na, Fe, and Ti in fly ash from coal-fired boilers is much higher than from biomass, and in the opposite, the percentage of Mg, K, Ca, Mn, Mo, S, Cl, and P in biomass ash exceeds that in coal fly ash. Potential detrimental effects of biomass combustion products (salts, acids, tar) leaving the boiler on the construction elements of the electrostatic precipitator, including electrodes and HV insulators have been discussed in this paper. It was concluded that the long-term effects of biomass co-firing on the electrostatic precipitator performance, including the collection efficiency, have not been sufficiently studied in the literature and these issues require further detailed investigations.     

Stereocontrolled Synthesis of Chiral Heteroaromatic Propellers with Small Optical Bandgaps

Chiral heteroaromatic propellers based on radially π‐extended hexapyrrolohexaazacoronenes were obtained in a concise synthesis from suitably functionalized donor–acceptor monopyrroles. To overcome steric hindrance, a new cyclodehydrogenation method was developed, and it uses bromine electrophiles as oxidative coupling agents instead of the commonly employed high‐potential oxidants. The new reaction offers high yields of propeller‐shaped targets, even for electron‐deficient precursors, and shows electrophile‐dependent stereoselectivity, with N‐bromosuccinimide and dibromine yielding, respectively D₆‐ and C₂‐symmetric products. The propeller azacoronenes are chiral and can be separated into configurationally stable enantiomers. In addition to providing steric bulk, peripheral functionalization considerably affects the electronic properties of the propellers, which exhibit reduced optical and electrochemical band gaps, and a more clearly defined electroreduction behavior.     

Fractal threshold behavior in vacuum gravitational collapse

We present the numerical evidence for fractal threshold behavior in the five dimensional vacuum Einstein equations satisfying the cohomogeneity-two triaxial Bianchi type-IX ansatz. In other words, we show that a flip of the wings of a butterfly may influence the process of the black hole formation.     

A new approximation approach to optimality and duality for a class of nonconvex differentiable vector optimization problems

Computational Management Science - In this paper, a new approximation method for a characterization of (weak) Pareto solutions in some class of nonconvex differentiable multiobjective programming...     

Diffusion Model of a Non-Integer Order PIγ Controller with TCP/UDP Streams

In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented. In order to control traffic congestion, an environment of IP routers applying AQM (Active Queue Management) algorithms has been introduced. Furthermore, the impact of the fractional controller PIγ and its parameters on the transport protocols is investigated. The controller has been elaborated in accordance with the control theory. The TCP and UDP flows are transmitted simultaneously and are mutually independent. Only the TCP is controlled by the AQM algorithm. Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.     

Optimality conditions and Mond–Weir duality for a class of differentiable semi-infinite multiobjective programming problems with vanishing constraints

4OR - In this paper, the class of differentiable semi-infinite multiobjective programming problems with vanishing constraints is considered. Both Karush–Kuhn–Tucker necessary optimality...