scholarly journals On the Solution of Generalized Banach Space Valued Equations

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 132
Author(s):  
Ramandeep Behl ◽  
Ioannis K. Argyros
Keyword(s):  
Banach Space ◽  
Solution Technique ◽  
Precise Knowledge

We develop a class of Steffensen-like schemes for approximating solution of Banach space valued equations. The sequences generated by these schemes are, converging to the solution under certain hypotheses that are weaker than in earlier studies. Hence, extending the region of applicability of these schemes without additional hypotheses. Benefits include: more choices for initial points; the computation of fewer iterates to reach a certain accuracy in the error distances, and a more precise knowledge of the solution. Technique is applicable on other schemes our due to its generality.

Residual Gas Reaction in the Electron Microscope: II The Design of a Gas-Control Chamber for Quantitative Observations

1969 ◽  
Vol 27 ◽  
pp. 82-83
Author(s):  
Chester J. Calbick ◽  
Richard E. Hartman
Keyword(s):  
Electron Beam ◽  
Electron Microscope ◽  
Local Environment ◽  
Chamber Pressure ◽  
Objective Lens ◽  
Ion Pump ◽  
Quantitative Studies ◽  
Precise Knowledge ◽  
Differential Pumping ◽  
And Control

Quantitative studies of the phenomenon associated with reactions induced by the electron beam between specimens and gases present in the electron microscope require precise knowledge and control of the local environment experienced by the portion of the specimen in the electron beam. Because of outgassing phenomena, the environment at the irradiated portion of the specimen is very different from that in any place where gas pressures and compositions can be measured. We have found that differential pumping of the specimen chamber by a 4" Orb-Ion pump, following roughing by a zeolite sorption pump, can produce a specimen-chamber pressure 100- to 1000-fold less than that in the region below the objective lens.

New approaches for the determination of dextran in the sugar production process

2018 ◽  
pp. 138-146 ◽  
Author(s):  
Karin Abraham ◽  
Eckhard Flöter
Keyword(s):  
Molecular Mass ◽  
Mass Distribution ◽  
Molecular Mass Distribution ◽  
Molecular Size ◽  
Mass Variation ◽  
Negative Effects ◽  
New Approaches ◽  
Precise Knowledge ◽  
Enzyme Application

The presence of polysaccharides in cane and beet raw juices causes several negative effects during the sugar manufacture. These are usually mitigated by enzymatic decomposition of dextrans. Such effects not only depend on the content, but also on the molecular mass distribution. This means that the different dextran fractions specifically affect the process. An accurate process control hence requires the most precise knowledge about the existing content and the molecular mass distribution present. A detailed understanding of the specific processing problems and also a targeted enzyme application hence requires the determination of a total dextran content and also its characterization including the differentiation between the different dextran fractions. An accurate analytical tool which equally satisfies industrial applicability is still lacking. To improve on this situation, two new approaches for the determination of dextran were developed and benchmarked against the commonly used and established Haze Method, which is rather inaccurate and also sensitive to molecular mass variation. The two new approaches are both based on polarimetry. These two methods indicate to be superior over the Haze Method with respect two molecular mass variation and hence enable the determination of a broader molecular size range including also low molecular mass dextrans.

On the domain of Riesz mean in the space Ls

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 925-940 ◽  
Author(s):  
Medine Yeşilkayagil ◽  
Feyzi Başar
Keyword(s):  
Banach Space ◽  
Sequence Space ◽  
Double Sequence ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Double Sequences ◽  
Riesz Mean ◽  
Double Sequence Space ◽  
Necessary And Sufficient ◽  
Barrelled Space

Let 0 < s < ?. In this study, we introduce the double sequence space Rqt(Ls) as the domain of four dimensional Riesz mean Rqt in the space Ls of absolutely s-summable double sequences. Furthermore, we show that Rqt(Ls) is a Banach space and a barrelled space for 1 ? s < 1 and is not a barrelled space for 0 < s < 1. We determine the ?- and ?(?)-duals of the space Ls for 0 < s ? 1 and ?(bp)-dual of the space Rqt(Ls) for 1 < s < 1, where ? ? {p, bp, r}. Finally, we characterize the classes (Ls:Mu), (Ls:Cbp), (Rqt(Ls) : Mu) and (Rqt(Ls):Cbp) of four dimensional matrices in the cases both 0 < s < 1 and 1 ? s < 1 together with corollaries some of them give the necessary and sufficient conditions on a four dimensional matrix in order to transform a Riesz double sequence space into another Riesz double sequence space.

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