A polynomial path-following interior point algorithm for general linear complementarity problems

Linear Complementarity Problems (LCPs) belong to the class of \mathbbNP{\mathbb{NP}} -complete problems. Therefore we cannot expect a polynomial time solution method for LCPs without requiring some special property of the coefficient matrix. Our aim is to construct interior point algorithms which, according to the duality theorem in EP (Existentially Polynomial-time) form, in polynomial time either give a solution of the original problem or detects the lack of property P_*([(k)\tilde]){\mathcal{P}_*(\tilde\kappa)} , with arbitrary large, but apriori fixed [(k)\tilde]{\tilde\kappa}). In the latter case, the algorithms give a polynomial size certificate depending on parameter [(k)\tilde]{\tilde{\kappa}} , the initial interior point and the input size of the LCP). We give the general idea of an EP-modification of interior point algorithms and adapt this modification to long-step path-following interior point algorithms.     

Synthesis and application of a fluorous Lawesson's reagent: convenient chromatography-free product purification

[reaction: see text] A fluorous analogue of Lawesson's reagent for thionation of carbonyl compounds has been developed and its use demonstrated on a series of amides, esters, and ketones. The separation of the Lawesson's reagent-derived byproducts can be achieved by a simple fluorous solid-phase extraction.     

Absolute convergence of Walsh-Fourier series and related results

We consider the Walsh orthonormal system on the interval [0, 1) in the Paley enumeration and the Walsh-Fourier coefficients $ \hat f $ (n), n ∈ ?, of functions f ∈ L ^p for some 1 < p ≤ 2. Our aim is to find best possible sufficient conditions for the finiteness of the series Σ _n=1 ^∞ a _n | $ \hat f $ (n)| ^r , where {a _n } is a given sequence of nonnegative real numbers satisfying a mild assumption and 0 < r < 2. These sufficient conditions are in terms of (either global or local) dyadic moduli of continuity of f. The sufficient conditions presented in the monograph [2] are special cases of our ones.     

On the feasibility to study inverse proximity effect in a single S/F bilayer by Polarized Neutron Reflectometry

Here we report on a feasibility study aiming to explore the potential of Polarized Neutron Reflectometry (PNR) for detecting the inverse proximity effect in a single superconducting/ferromagnetic bilayer. Experiments, conducted on the V (40 nm)/Fe (1 nm) S/F bilayer, have shown that experimental spin asymmetry measured at T = 0.5T _C is shifted towards higher Q values compared to the curve measured at T = 1.5T _C . Such a shift can be described by the appearance in superconducting vanadium of magnetic sublayer with a thickness of 7 nm and a magnetization of +0.8 kG.     

Vibrational Spectroscopy of Phenols and Phenolic Polymers. Theory,Experiment, and Applications

In the first part of this review, the authors give a survey on the literature of vibrational spectroscopy of phenol, phenol derivatives, and other phenolic componds from the last decade of the last century through today. The classical and modern methods of vibrational spectroscopy are also introduced and a glossary is included to aid comprehension. The second part deals with the literature regarding the importance of vibrational spectroscopy in the investigation and identification of phenolic compounds in natural substances, the application of vibrational spectroscopy in composite and synthetic polymer chemistry, and following of chemical processes and investigating their resulting products. Vibrational spectroscopy is a very good tool for determination of molecular structures and is important in chemical analysis and in the chemical industry.     

Lower bounds on the minimum distance in Hermitian one-point differential codes

Korchmáros and Nagy [Hermitian codes from higher degree places. J Pure Appl Algebra, doi: 10. 1016/j.jpaa.2013.04.002, 2013] computed the Weierstrass gap sequence G(P) of the Hermitian function field Fq2( H ) at any place P of degree 3, and obtained an explicit formula of the Matthews-Michel lower bound on the minimum distance in the associated differential Hermitian code CΩ(D, mP ) where the divisor D is, as usual, the sum of all but one 1-degree Fq2-rational places of Fq2( H ) and m is a positive integer. For plenty of values of m depending on q, this provided improvements on the designed minimum distance of CΩ(D, mP). Further improvements from G(P) were obtained by Korchmáros and Nagy relying on algebraic geometry. Here slightly weaker improvements are obtained from G(P) with the usual function-field method depending on linear series, Riemann-Roch theorem and Weierstrass semigroups. We also survey the known results on this subject.     

Mixture estimation with state-space components and Markov model of switching

The paper proposes a recursive algorithm for estimation of mixtures with state-space components and a dynamic model of switching. Bayesian methodology is adopted. The main features of the presented approach are: (i) recursiveness that enables a real-time performance of the algorithm; (ii) one-pass elaboration of the data sample; (iii) dynamic nature of the model of switching active components; (iv) orientation at explicit solutions with exploitation of numerical procedures only in those parts which cannot be computed analytically; (v) systematic approach to the Bayesian mixture estimation theory.     

On the regular convergence of multiple series of numbers and multiple integrals of locally integrable functions over ℝ̄ + m

We investigate the regular convergence of the m-multiple series (*) $$\sum\limits_{j_1 = 0}^\infty {\sum\limits_{j_2 = 0}^\infty \cdots \sum\limits_{j_m = 0}^\infty {c_{j_1 ,j_2 } , \ldots j_m } }$$ of complex numbers, where m ≥ 2 is a fixed integer. We prove Fubini’s theorem in the discrete setting as follows. If the multiple series (*) converges regularly, then its sum in Pringsheim’s sense can also be computed by successive summation. We introduce and investigate the regular convergence of the m-multiple integral (**) $$\int_0^\infty {\int_0^\infty { \cdots \int_0^\infty {f\left( {t_1 ,t_2 , \ldots ,t_m } \right)dt_1 } } } dt_2 \cdots dt_m ,$$ where f : ?? ₊ ^m → ? is a locally integrable function in Lebesgue’s sense over the closed nonnegative octant ?? ₊ ^m := [0,∞) ^m . Our main result is a generalized version of Fubini’s theorem on successive integration formulated in Theorem 4.1 as follows. If f ∈ L _loc ¹ (?? ₊ ^m ), the multiple integral (**) converges regularly, and m = p + q, where p and q are positive integers, then the finite limit $$\mathop {\lim }\limits_{v_{_{p + 1} } , \cdots ,v_m \to \infty } \int_{u_1 }^{v_1 } {\int_{u_2 }^{v_2 } { \cdots \int_0^{v_{p + 1} } { \cdots \int_0^{v_m } {f\left( {t_1 ,t_2 , \ldots t_m } \right)dt_1 dt_2 } \cdots dt_m = :J\left( {u_1 ,v_1 ;u_2 v_2 ; \ldots ;u_p ,v_p } \right)} , 0 \leqslant u_k \leqslant v_k < \infty } ,k = 1,2, \ldots p,}$$ exists uniformly in each of its variables, and the finite limit $$\mathop {\lim }\limits_{v_1 ,v_2 \cdots ,v_p \to \infty } J\left( {0,v_1 ;0,v_2 ; \ldots ;0,v_p } \right) = I$$ also exists, where I is the limit of the multiple integral (**) in Pringsheim’s sense. The main results of this paper were announced without proofs in the Comptes Rendus Sci. Paris (see [8] in the References).     

Electron impact ionization of diatomic molecules

Cross sections for the ionization of N₂, CO and O₂ diatomic molecules by electron impact are calculated. The applied distorted wave model is based on our previous studies for positron impact, the molecular orbitals being described by Gaussian wavefunctions. Our study emphasizes the importance of electron exchange and of using correct distorted waves for the ejected electron.     

Experimental studies of flow boiling heat transfer by using nanofluids

Journal of Thermal Analysis and Calorimetry - Flow boiling heat transfer widely utilized in numerous industrial applications such as boiler tubes, evaporators and cooling of reactors in a nuclear...