Some class of analytic functions related to conic domains

For q ∈ (0, 1) let the q-difference operator be defined as follows $$\partial _q f(z) = \frac{{f(qz) - f(z)}} {{z(q - 1)}} (z \in \mathbb{U}),$$ where \(\mathbb{U}\) denotes the open unit disk in a complex plane. Making use of the above operator the extended Ruscheweyh differential operator R _q ^λ f is defined. Applying R _q ^λ f a subfamily of analytic functions is defined. Several interesting properties of a defined family of functions are investigated.     

The market triple

It is a well known fact that at market equilibrium supply equals demand except for instance in North Korea and Europe during the Second World War. The above should be examined from a contemporary perspective (here and now) as well as all the accepted relevant terms, criteria and parameters. Basic terms such as value and market are redefined from this perspective and the organizer element is added. Thus a linear creation of demand and supply is expanded into a two-dimensional structure which provides the definition of a market triple. There are countless markets in the world around us, but only six market triples. Quite unique among the markets is the research market, our proposition for future developments.     

Analysis of lumped models with contact and friction

We consider two mathematical models that describe the vibrations of spring-mass-damper systems with contact and friction. In the first model, both the contact and frictional boundary conditions are described with subdifferentials of nonconvex functions. In the second model, the contact is modeled with a Lipschitz continuous function, and the restitution force is described by a differential equation involving a Volterra integral term. The two models lead to second-order differential inclusions with and without an integral term, in which the unknowns are the positions of the masses. For each model, we prove the existence of a solution by using an abstract result for first-order differential inclusions in finite dimensional spaces. For the second model, in addition, we prove the uniqueness of the solution by using a fixed point argument. Finally, we provide examples of systems with contact and friction conditions for which our results are valid.     

Modeling of diffusive transport of benzoic acid through a liquid membrane

A model of diffusive transport of benzoic acid through a liquid membrane (LM) separating two aqueous solutions, based on diffusion layers and the assumption of a steady state, has been developed and tested using experimental results. It has been found that a model with the apparent partition coefficient dependent on the concentration is able to describe the time dependence of acid concentration in LM with and without a maximum on that dependence. The quality of the model fit with the single apparent diffusion coefficient of benzoic acid is the same as the one which takes into account the diffusion of benzoic acid in different forms (undissociated and dissociated form in aqueous phase, monomer and dimer in organic phase); however, in the second case, the model becomes overparameterized. Assuming that the partition and diffusion coefficients are constant, the diffusion layer model corresponds to the model of reversible consecutive reactions. Analytical solution for such case is given. Apart from the partition equilibrium, also kinetics of partitioning was considered. It was shown that in some basic situations both cases yield identical results.     

Non-homeomorphic density topologies

In [ANISZCZYK, B.-FRANKIEWICZ, R.: Non homeomorphic density topologies, Bull. Polish Acad. Sci. Math. 34 (1986), 211–213] the authors constructed 2^c non-homeomorphic density topologies tied to the concept of measure. In [WROŃSKI, S.: The number of non-homeomorphic I-density topologies. Institute of Mathematics of Polish Academy of Sciences. Preprint 482, December 1990, XXXIV Semester in Banach Center, Theory of Real Functions] an analogous construction has been given for topologies tied to the concept of category. Here we present a generalization containing both the results mentioned above. This generalization based only on the topological ideas is independent of the concept of measure or category. Communicated by L’ubica Holá     

A Unified Approach to Dynamic Contact Problems in Viscoelasticity

In this paper we consider mathematical models describing dynamic viscoelastic contact problems with the Kelvin–Voigt constitutive law and subdifferential boundary conditions. We treat evolution hemivariational inequalities which are weak formulations of contact problems. We establish the existence of solutions to hemivariational inequalities with different types of non-monotone multivalued boundary relations. These results are consequences of an existence theorem for second order evolution inclusions. In a particular case we deliver sufficient conditions under which the solution to a hemivariational inequality is unique. Finally, applications to several unilateral and bilateral problems in contact mechanics are provided.*Research supported in part by the State Committee for Scientific Research of the Republic of Poland (KBN) under Grants no. 2 P03A 003 25 and 4 T07A 027 26.     

Synthesis of unsymmetrical alkyl acetals via addition of primary alcohols to allyl ethers mediated by ruthenium complexes

Abstract  

Ru-catalyzed synthesis of mixed alkyl–alkyl acetals via addition of primary alcohols to allyl ethers has been extended to include long-chain and/or functionalized substrates. The catalytic systems for these reactions were generated from RuCl₂(PPh₃)₃ and [RuCl₂(1,5-COD)]_x and phosphines [PPh₃ or P(p-chlorophenyl)₃] or SbPh₃. Of particular importance is the almost quantitative elimination of transacetalization. The addition proceeds through allyl complexes, not via isomerization of allyl ethers––subsequent addition of ROH to vinyl ethers.     

Multiresidue determination of 160 pesticides in wines employing mixed-mode dispersive-solid phase extraction and gas chromatography-tandem mass spectrometry

A new multiresidue method for the efficient screening, identification and quantification of over 160 pesticides belonging to different chemical classes in red, rose and white wines have been developed. The analysis was based on gas chromatographic-tandem quadrupole mass spectrometric determination (GC-QqQ-MS/MS). An optimization strategy involved the selection of buffering conditions and sorbents for dispersive-solid phase extraction (dispersive-SPE) in order to achieve acceptably high recoveries and reduce co-extractives in the final extracts. As a result, the optimized procedure allowed us to obtain consistent recoveries of the target pesticides including problematic ones such as captan, chlorothalonil, dichlofluanid, folpet and tolylfluanid. The attained recoveries were typically between 80 and 110% (89% on average) with RSD values typically lower than 10% (8% on average) at three spiking levels of 0.01, 0.05 and 0.2 mg kg⁻¹. Linearity was studied in the range between 0.005 and 0.2 mg kg⁻¹ using pesticide standards prepared both in pure solvent and in the presence of matrix, showing coefficients of determination (R²) higher than 0.99 for all the pesticides except for desmedipham, thiabendazole and thiamethoxam in pure solvent. The study of the ratio of the slopes obtained in solvent and in matrix provided information about the matrix effects, which was <10%, 10-20% and >20% for 33, 36 and 31% of the studied pesticides, respectively. To improve accuracy, matrix matched standards were always used for calculation of the quantification results. The expanded uncertainties were estimated by using a “top-down” approach as being 17% on average (coverage factor k = 2, confidence level 95%). Finally, the method was used with success to detect and quantify pesticide residues in commercial wines.     

Multi-degree reduction of tensor product Bézier surfaces with general boundary constraints

We propose an efficient approach to the problem of multi-degree reduction of rectangular Bézier patches, with prescribed boundary control points. We observe that the solution can be given in terms of constrained bivariate dual Bernstein polynomials. The complexity of the method is O(mn₁n₂) with m ? min(m₁, m₂), where (n₁, n₂) and (m₁, m₂) is the degree of the input and output Bézier surface, respectively. If the approximation—with appropriate boundary constraints—is performed for each patch of several smoothly joined rectangular Bézier surfaces, the result is a composite surface of global C^r continuity with a prescribed r ? 0. In the detailed discussion, we restrict ourselves to r ∈ {0, 1}, which is the most important case in practical application. Some illustrative examples are given.