Several important non-commutative inequalities are proved by using Hansen and Pedersen’s Jensen inequality. This approach is also used to demonstrate a matrix analogue of Maréchal’s generalized perspective construction for convex functions.

In the digital age, SEO optimization plays a crucial role in enhancing visibility and reach of online content. This paper, authored by Jerry Doby, Ph.D., Editor-in-Chief The Hype Magazine, aims to demystify SEO-optimized writing for professionals such as journalists, bloggers, copywriters, other enthusiasts. study delves into step-by-step process optimizing content improve search engine placeme...

Peter Craig, MRC Population Health Sciences Research Network Paul Dieppe, Nuffield Department of Orthopaedic Surgery, University of Oxford Sally Macintyre, MRC Social and Public Health Sciences Unit Susan Michie, Centre for Outcomes Research and Effectiveness, University College London Irwin Nazareth, MRC General Practice Research Framework Mark Petticrew, Department of Public Health and Policy...

Peter Craig, MRC Population Health Sciences Research Network Paul Dieppe, Nuffield Department of Orthopaedic Surgery, University of Oxford Sally Macintyre, MRC Social and Public Health Sciences Unit Susan Michie, Centre for Outcomes Research and Effectiveness, University College London Irwin Nazareth, MRC General Practice Research Framework Mark Petticrew, Department of Public Health and Policy...

Uplifted ultramafic rocks represent an important vector for the transfer of carbon and reducing power from the deep subsurface into the biosphere and potentially support microbial life through serpentinization. This process has a strong influence upon the production of hydrogen and methane, which can be subsequently consumed by microbial communities. The Santa Elena Ophiolite (SEO) on the north...

Mild Cognitive Impairment (MCI) is considered in many as prodromal stage of Alzheimer's disease (AD). Event-related oscillations (ERO) reflect cognitive responses of brain whereas sensory-evoked oscillations (SEO) inform about sensory responses. For this study, we compared visual SEO and ERO responses in MCI to explore brain dynamics (BACKGROUND). Forty-three patients with MCI (mean age=74.0 ye...

A quantum compiling algorithm is an algorithm for decomposing (“compiling”) an arbitrary unitary matrix into a sequence of elementary operations (SEO). Suppose Uin is an NB-bit unstructured unitary matrix (a unitary matrix with no special symmetries) that we wish to compile. For NB > 10, expressing Uin as a SEO requires more than a million CNOTs. This calls for a method for finding a unitary ma...