Flow regimes and pressure drop of a composite tridimensional rotational flow sieve tray under concurrent gas--liquid flow

A new type of composite tridimensional rotational flow sieve tray is proposed. The flow pattern and operation domain of the tray were defined and divided by the image shooting method, combined with the standard deviation of the pressure difference sequence. There are membrane–drip column and foam–embolic flow in the TRST area of the internal packing–type tray, while bubbly and milk froth-ribbon flow are present in the packing area of the external packing-type tray. This study focused on the influence of the tray structure parameters on the pressure drop. Under the experimental operating conditions, the dry pressure drop was within 160 Pa, while the wet pressure drop was within 900 Pa. Under the same structural parameters, the internal packing–type pressure drop of the tray was higher than that of the external packing-type tray. A mathematical model of the pressure drop between dry and wet trays was established.

NEW GENERALIZED CIESARO SPACE WITH SOME TOPOLOGICAL PROPERTIES

The sequence space introduced by M. Et and have studied its various properties. The aim of the present paper is to introduce the new pranormed generalized difference sequence space. and , We give some topological properties and inclusion relations on these spaces. 2010 AMS Mathematical Subject Classification: 46A45; 40C05.

Kannan nonexpansive maps on generalized Cesàro backward difference sequence space of non-absolute type with applications to summable equations

In this article, we investigate the notion of the pre-quasi norm on a generalized Cesàro backward difference sequence space of non-absolute type $(\Xi (\Delta,r) )_{\psi }$ ( Ξ ( Δ , r ) ) ψ under definite function ψ. We introduce the sufficient set-up on it to form a pre-quasi Banach and a closed special space of sequences (sss), the actuality of a fixed point of a Kannan pre-quasi norm contraction mapping on $(\Xi (\Delta,r) )_{\psi }$ ( Ξ ( Δ , r ) ) ψ , it supports the property (R) and has the pre-quasi normal structure property. The existence of a fixed point of the Kannan pre-quasi norm nonexpansive mapping on $(\Xi (\Delta,r) )_{\psi }$ ( Ξ ( Δ , r ) ) ψ and the Kannan pre-quasi norm contraction mapping in the pre-quasi Banach operator ideal constructed by $(\Xi (\Delta,r) )_{\psi }$ ( Ξ ( Δ , r ) ) ψ and s-numbers has been determined. Finally, we support our results by some applications to the existence of solutions of summable equations and illustrative examples.

On the paranormed Nörlund difference sequence space of fractional order and geometric properties

In this article we introduce paranormed Nörlund difference sequence space of fractional order α, Nt (p, Δ(α)) defined by the composition of fractional difference operator Δ(α), defined by ( Δ ( α ) x ) k = ∑ i = 0 ∞ ( − 1 ) i Γ ( α + 1 ) i ! Γ ( α − i + 1 ) x k − i , $\begin{array}{} \displaystyle (\Delta^{(\alpha)}x)_k=\sum_{i=0}^{\infty}(-1)^i\frac{\Gamma(\alpha+1)}{i!\Gamma(\alpha-i+1)}x_{k-i}, \end{array}$ and Nörlund matrix Nt . We give some topological properties, obtain the Schauder basis and determine the α−, β− and γ-duals of the new space. We characterize certain matrix classes related to this new space. Finally we investigate certain geometric properties of the space Nt (p, Δ(α)).