Sentence examples for proved continuous from inspiring English sources

By combining the above results with the interpolation theory we proved continuous inclusions between spaces ℓw1(ℓϕ0) and ℓφ(ℓϕ1), where ℓϕ0↪ℓϕ1 and φ is a certain Orlicz function depending on ϕ0 and ϕ1.

A comparison to other proven continuous monitors resulted in good agreement at low relative humidities.

However, downstream of the reaction phase is rarely considered for further intensification, despite the plethora of proven continuous downstreamtechnologies.Thus,inthisworkweconsidertheentireprimary manufacturing stage, from reaction to crystallisation, with the intent of introducing intensification where needed, be it via a continuous option or innovation.

Microreactor and microseparator engineering appears particularly advantageous in this high-value and low-capacity context, both at a pilot-plant and a full-production scale, and it can be combined with a plethora of proven continuous downstream technologies, facilitating the reduction of total organic waste emission and environmental footprint.

Despite the presence of an active infection with a proven continuous residual CFU and cellular immune response, the animals appeared to be in good health, as shown by the welfare checklist conducted as part of the daily clinical monitoring, and continued to gain weight until the end of the experiment.

Preliminary exploration of these structures indicated that features of these structures would largely prove continuous, thus a thorough study of them was deemed implausible in the time-frame allocated to the study.

A 0.2 m3 photobioreactor designed using the proposed approach was proved in continuous outdoor culture of the microalga Phaeodactylum tricornutum.

(1.1)–(1.2) under Lipschitz condition and proved the continuous dependence of mild solution on the initial value and the fractional order.

Many studies have proved that continuous intravenous perfusion of drugs is associated with longer mechanical ventilation [2, 3].

By this new technology, it has been proved that continuous heating and energy savings could be achieved without adopting expensive technologies.

The following is yet another version of Theorem 3.5 which remains a slightly sharpened form of Theorem 1.1 (proved for continuous mapping f).