Minimal infeasible constraint sets in convex integer programs

In this paper we investigate certain aspects of infeasibility in convex integer programs, where the constraint functions are defined either as a composition of a convex increasing function with a convex integer valued function of n variables or the sum of similar functions. In particular we are concerned with the problem of an upper bound for the minimal cardinality of the irreducible infeasible subset of constraints defining the model. We prove that for the considered class of functions, every infeasible system of inequality constraints in the convex integer program contains an inconsistent subsystem of cardinality not greater than 2 ⁿ , this way generalizing the well known theorem of Scarf and Bell for linear systems. The latter result allows us to demonstrate that if the considered convex integer problem is bounded below, then there exists a subset of at most 2 ⁿ −1 constraints in the system, such that the minimum of the objective function subject to the inequalities in the reduced subsystem, equals to the minimum of the objective function over the entire system of constraints.     

Weak convergence of almost orbits of asymptotically nonexpansive commutative semigroups

We give three equivalent conditions for weak convergence of almost orbits of an asymptotically nonexpansive commutative semigroup acting on a nonempty bounded closed convex subset of a uniformly convex Banach space whose dual has the Kadec property.     

Leggett-Williams norm-type theorems for coincidences

We study the existence of positive solutions to the operator equation Lx = Nx, where L is a linear Fredholm mapping of index zero and N is a nonlinear operator. Using the properties of cones in Banach spaces and Leray-Schauder degree for completely continuous operators, k-set contractions and condensing mappings, we obtain some refinements of the results established in [3] and [14]. Received: 9 July 2005; revised: 12 January 2006     

Feasibility in reverse convex mixed-integer programming

In this paper we address the problem of the infeasibility of systems defined by reverse convex inequality constraints, where some or all of the variables are integer. In particular, we provide a polynomial algorithm that identifies a set of all constraints critical to feasibility (CF), that is constraints that may affect a feasibility status of the system after some perturbation of the right-hand sides. Furthermore, we will investigate properties of the irreducible infeasible sets and infeasibility sets, showing in particular that every irreducible infeasible set as well as infeasibility sets in the considered system, are subsets of the set CF of constraints critical to feasibility.     

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.     

Composition of oxygen precipitates in Czochralski silicon wafers investigated by STEM with EDX/EELS and FTIR spectroscopy

In this work, we investigated the stoichiometry of oxygen precipitates in Czochralski silicon wafers. The thickness dependence of the Cliff–Lorimer sensitivity factor for the silicon/oxygen system was determined and applied for the investigation of the stoichiometry of oxygen precipitates by EDX. The results show that both plate‐like oxygen precipitates and a transitional form between plate‐like and octahedral precipi‐ tates consist of SiO₂. This was confirmed by EELS low loss spectra where the typical spectrum for amorphous SiO₂ was observed. Moreover, the absorption band of plate‐like precipitates at 1227 cm^–1 was found in the low temperature FTIR spectrum. It was demonstrated that this band can only be simulated by the dielectric constants of amorphous SiO₂. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Enthalpimetric and Colorimetric Determinations of the Inhibition Constant for the Inhibition of Urease by Boric Acid

Continuous enthalpimetric and fixed-time-point colorimetric analytical studies of jack bean urease-catalyzed hydrolysis of urea uninhibited and inhibited by boric acid were performed. The effect of boric acid on urease activity was studied in 100 mM phosphate buffer of pH 7 (H₃PO₄+NaOH, 2 mM EDTA) at 25°C. The inhibition constant of boric acid was obtained with use of differential and integration methods. It was found that boric acid is a simple competitive inhibitor of urease. The methods produced comparable values of the inhibition constant K_i: the former 0.19 mM and the latter 0.18 mM. This revised version was published online in July 2006 with corrections to the Cover Date.     

Preparation and properties of yttrium,lanthanum, and lanthanidem-nitrobenzoates

The conditions of the formation of rare earth elementm-nitrobenzoates were studied and their quantitative composition and solubilities in water and benzene at 298 K were determined (their solubilities are in the orders of 10^–3 mol dm^–3 and 10^–4 mol dm^–3, respectively). From the values of solubilities in water the solubility products were established (they are in the orders of 10^–10 mol⁴ dm^–12).The IR and X-ray spectra for the prepared complexes and the dehydrated rare earthm-nitrobenzoates were recorded. All obtained complexes were found to be crystalline compounds. The conditions of thermal decomposition for complexes were also studied. It was found that on heating above 573 K the complexes decompose explosively and undergo a melting process at the same time. Therefore the thermal decomposition was carried out in the temperature range 273–573 K. The obtained results show that during dehydration process no transformation of the nitro group to nitrito occurs.

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Darstellung und Eigenschaften von Y, La und Lanthaniden-meta-Nitrobenzoaten

Zusammenfassung Die Bedingungen zur Darstellung von Y-, La- und Lanthanidenmeta-Nitrobenzoaten wurden untersucht. Ihre quantitative Zusammensetzung und ihre Wasserlöslichkeit bei 298K wurden bestimmt (die Löslichkeit ist in der Größenordnung 10^–3 mol dm^–3). Die Infrarot- und Röntgenspektren der erhaltenen Komplexe sowie derm-Nitrobenzoate der seltenen Erden nach der Dehydratisierung wurden gemessen und dabei festgestellt, daß es sich stets um kristalline Verbindungen handelt. Das thermische Verhalten der erhaltenen Komplexe wurde festgestellt: Sie zerfallen über 573 K explosiv und schmelzen zugleich. Der thermische Zerfall der erhaltenenm-Nitrobenzoate der seltenen Erden wurde im Temperaturbereich von 273–573 K untersucht. Es wurde festgestellt, daß die Y-, La- und Lanthaniden-m-Nitrobenzoate bei Temperaturzunahme oder im Dehydratisierungsprozeß keiner Umgruppierung in entsprechende Nitritoverbindungen unterliegen.

     

Preparation and properties of yttrium,lanthanum, and lanthanide 3,5-dinitrobenzoates

Summary The condition of the formation of rare earth 3,5-dinitrobenzoates were studied and their quantitative composition and solubilities in water at 298 K determined (their solubilities are of the order of 10^–4 mol dm^–3). From the values of solubilities in water the solubility products were established (in the order of 10^–12 mol⁴ dm^–12). The IR and X-ray spectra for the hydrated and dehydrated complexes were recorded and studied. All complexes are crystalline compounds. The condition of thermal decomposition of the complexes was also investigated. On heating above 573 K the 3,5-dinitrobenzoates decompose explosively and undergo a melting process at the same time. Accordingly, the thermal decomposition for the complexes was studied in the temperature range 273–573 K. The thermal stability data reveal them to dehydrate in two steps. From the obtained results it appears that during the dehydration process no izomerization of the nitro group to the nitrito group occurs.

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Herstellung und Eigneschaften von Y-, La- und Lanthaniden-3,5-Dinitrobenzoaten

Zusammenfassung Die Bedingungen zur Darstellung von Y-, La- und Lanthaniden-3,5-Dinitrobenzoaten wurden untersucht. Ihre quantitative Zusammensetzung und ihre Wasserlöslichkeit bei 298 K wurden bestimmt (die Löslichkeit ist in der Größenordnung 10^–4 mol dm^–3). Die Infrarot- und Röntgenspektren der erhaltenen Komplexe sowie der 3,5-Dinitrobenzoate der seltenen Erden nach der Dehydratisierung wurden gemessen. Es wurde festgestellt, daß es sich stets um kristalline Verbindungen handelt. Das thermische Verhalten der erhaltenen Komplexe wurde untersucht: sie zerfallen über 573 K explosiv und schmelzen zugleich. Der thermische Zerfall der erhaltenen 3,5-Dinitrobenzoate der seltenen Erden wurde im Temperaturbereich von 273–523 K untersucht. Es wurde festgestellt, daß die Y-, La-, und Lanthaniden — 3,5-Dinitrobenzoate bei Temperaturerhöhung oder im Dehydratisierungsprozeß keine Umgruppierung in die entsprechenden Nitritoverbindungen erleiden.