Dimensionally Dependent Tensor Identities by Double Antisymmetrisation

Some years ago, Lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure, and could all be considered consequences in n-dimensional space of a pair of fundamental identities involving trace-free (p,p)-forms where 2p >= n$. We generalise Lovelock's results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrising over n+1 indices, we establish a very general 'master' identity for all trace-free (k,l)-forms. We then show how various other special identities are direct and simple consequences of this master identity; in particular we give direct application to Maxwell, Lanczos, Ricci, Bel and Bel-Robinson tensors, and also demonstrate how relationships between scalar invariants of the Riemann tensor can be investigated in a systematic manner.Comment: 17 pages, 2 figure

A re-interpretation of the concept of mass and of the relativistic mass-energy relation

For over a century the definitions of mass and derivations of its relation with energy continue to be elaborated, demonstrating that the concept of mass is still not satisfactorily understood. The aim of this study is to show that, starting from the properties of Minkowski spacetime and from the principle of least action, energy expresses the property of inertia of a body. This implies that inertial mass can only be the object of a definition - the so called mass-energy relation - aimed at measuring energy in different units, more suitable to describe the huge amount of it enclosed in what we call the "rest-energy" of a body. Likewise, the concept of gravitational mass becomes unnecessary, being replaceable by energy, thus making the weak equivalence principle intrinsically verified. In dealing with mass, a new unit of measurement is foretold for it, which relies on the de Broglie frequency of atoms, the value of which can today be measured with an accuracy of a few parts in 10^9

Gender differences in self reported long term outcomes following moderate to severe traumatic brain injury

<p>Abstract</p> <p>Background</p> <p>The majority of research on health outcomes after a traumatic brain injury is focused on male participants. Information examining gender differences in health outcomes post traumatic brain injury is limited. The purpose of this study was to investigate gender differences in symptoms reported after a traumatic brain injury and to examine the degree to which these symptoms are problematic in daily functioning.</p> <p>Methods</p> <p>This is a secondary data analysis of a retrospective cohort study of 306 individuals who sustained a moderate to severe traumatic brain injury 8 to 24 years ago. Data were collected using the Problem Checklist (PCL) from the Head Injury Family Interview (HIFI). Using Bonferroni correction, group differences between women and men were explored using Chi-square and Wilcoxon analysis.</p> <p>Results</p> <p>Chi-square analysis by gender revealed that significantly more men reported difficulty setting realistic goals and restlessness whereas significantly more women reported headaches, dizziness and loss of confidence. Wilcoxon analysis by gender revealed that men reported sensitivity to noise and sleep disturbances as significantly more problematic than women, whereas for women, lack of initiative and needing supervision were significantly more problematic in daily functioning.</p> <p>Conclusion</p> <p>This study provides insight into gender differences on outcomes after traumatic brain injury. There are significant differences between problems reported by men compared to women. This insight may facilitate health service planners and clinicians when developing programs for individuals with brain injury.</p

Exploring the Role of Explicit and Implicit Self-Esteem and Self-Compassion in Anxious and Depressive Symptomatology Following Acquired Brain Injury

[EN] Objectives Acquired brain injury (ABI) can lead to the emergence of several disabilities and is commonly associated with high rates of anxiety and depression symptoms. Self-related constructs, such as self-esteem and self-compassion, might play a key role in this distressing symptomatology. Low explicit (i.e., deliberate) self-esteem is associated with anxiety and depression after ABI. However, implicit (i.e., automatic) self-esteem, explicit-implicit self-discrepancies, and self-compassion could also significantly contribute to this symptomatology. The purpose of the present study was to examine whether implicit self-esteem, explicit-implicit self-discrepancy (size and direction), and self-compassion are related to anxious and depressive symptoms after ABI in adults, beyond the contribution of explicit self-esteem. Methods The sample consisted 38 individuals with ABI who were enrolled in a long-term rehabilitation program. All participants completed the measures of explicit self-esteem, implicit self-esteem, self-compassion, anxiety, and depression. Pearson's correlations and hierarchical regression models were calculated. Results Findings showed that both self-compassion and implicit self-esteem negatively accounted for unique variance in anxiety and depression when controlling for explicit self-esteem. Neither the size nor direction of explicit-implicit self-discrepancy was significantly associated with anxious or depressive symptomatology. Conclusions The findings suggest that the consideration of self-compassion and implicit self-esteem, in addition to explicit self-esteem, contributes to understanding anxiety and depression following ABI.Lorena Desdentado is supported by a FPU doctoral scholarship (FPU18/01690) from the Spanish Ministry of Universities. 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