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The phrase "hereby we demonstrate" is correct and usable in written English.
It is typically used in formal contexts, such as legal documents or academic papers, to indicate that the speaker is presenting evidence or proof of a claim. Example: "In this report, hereby we demonstrate the effectiveness of our new methodology through a series of experiments."
Exact(2)
Hereby, we demonstrate the application of vertically arranged multilayered-graphene, namely carbon nanowalls (CNW), as a potential high power anode to be used in Li-ion secondary batteries.
Hereby we demonstrate the greatest level of osteoblastic activity induced in cells grown on PCL/HAp surfaces comprising periodically arranged topographic features, as opposed to the control polystyrene, flat PCL/HAp films or PCL/HAp films with identical but randomized surface features.
Similar(57)
Hereby, we demonstrated the toxicity of 16-96 nm ranged biosynthesized CuNPs and ZnONPs in male wistar rats through intraperitoneal (i/p) and intravenous (i/v) injectionsat the desired on 14th and 28th day of observation.
Hereby, we present a recently experienced case.
We demonstrate the capabilities of our method on Germany's largest transport networks and hereby present numerical results on the largest instances that were ever reported in the literature for this problem class.
We hereby demonstrate for the first time that the structurally complex antiretroviral drug enfuvirtide (Enf), which normally is unable to penetrate the cerebrospinal fluid, is allowed to cross the blood brain barrier (BBB) in mice by conjugation with a nanoconstruct.
We hereby demonstrate that a facile SS modification results in up to 45.367 mA cm−3 current production at room temperature – the highest volumetric current density reported to date for BES bioanodes but that this benefit comes at a high risk of corrosion, which compromises the applicability of SS-based Microbial Fuel Cells.
We hereby demonstrate that immunization with HIVBr18, a DNA plasmid encoding a string of conserved multiple HLA class II-binding HIV-1 CD4+ T cell epitopes, can induce IFN-γ secretion, CD4+ and even some CD8+ T cell proliferation against multiple epitopes.
In summary, we hereby demonstrate an additional mechanism relating telomerase inhibition and reduced cell proliferation, not necessarily mediated via the known tyrosine kinase targets of IM.
Noticing that connecting chemical groups to carbon can provide large pseudo-capacitance, we hereby demonstrated that the position of the chemical groups also plays an important role in the pseudo-capacitance.
We hereby demonstrated that immunization with HIVBr18, a DNA plasmid encoding a string of conserved multiple HLA class II-binding HIV-1 CD4+ T cell epitopes, can induce broad, polyfunctional, long-lived CD4+ and CD8+ T cell responses.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com