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Recently, an expansion as a power series in 1 /d has been presented for the specific entropy of a complete dimer covering of a d-dimensional hypercubic lattice. This paper extends from 3 to 10 the number of terms known in the series. Likewise, an expansion for the entropy, dependent on the dimer density p, of a monomer-dimer system, involving a sum &#931k;ak (d)pk, has been offered recently. We herein extend the number of known expansion coefficients from 6 to 20 for the hypercubic lattices of general dimensionality d and from 6 to 24 for the hypercubic lattices of dimensionalities d < 5. We show that these extensions can lead to accurate numerical estimates of the p-dependent entropy for lattices with dimension d > 2. The computations of this paper have led us to make the following marvelous conjecture: In the case of the hypercubic lattices, all the expansion coefficients ak(d) are positive. This paper results from a simple melding of two disparate research programs: one computing to high orders the Mayer series coefficients of a dimer gas and the other studying, the development of entropy from these coefficients. An effort is made to make this paper self-contained by including a review of the earlier works. [ABSTRACT FROM AUTHOR]

Introduction: Temporomandibular disorders (TMDs) are musculoskeletal disorders characterised by jaw pain and typically temporomandibular joint limitations. Resistance training (RT) has been shown to be effective at reducing pain and improving function for different musculoskeletal conditions (eg, neck pain, low back pain); however, the effectiveness of RT for patients with TMDs remains unclear. This systematic review will evaluate the effectiveness of RT on pain and temporomandibular joint range of motion in people with TMDs., Methods and Analysis: The report of this protocol aligns with the Preferred Reporting Items for Systematic Reviews and Meta-Analysis Protocols. The search strategy will be conducted from 1 March 2024 to 31 March 2024 via the following electronic databases: MEDLINE (OVID interface), EMBASE (OVID interface), SCOPUS, Web of Science, PubMed and Cochrane Central Register of Controlled Trials. Any randomised controlled trials or non-randomised studies of interventions in adults with TMD that examine RT targeting the masticatory muscles, compared to other interventions not including RT, will be included. Primary outcomes will be jaw pain intensity and maximal mouth opening. Secondary outcomes will include measures of neuromuscular performance and pressure pain thresholds. Two independent reviewers will conduct the screening of articles for inclusion, data extraction, risk-of-bias assessment using the revised Cochrane risk-of-bias tool for included studies and will evaluate the overall quality of evidence following the Grading of Recommendations Assessment, Development and Evaluation framework. A meta-analysis will be performed where applicable. Alternately, a narrative synthesis will be performed by adhering to the synthesis without meta-analysis guidelines. Data will be summarised according to the outcome measures or, when this is not possible, according to other pertinent variables such as TMD type (ie, temporomandibular joint disorders, masticatory muscle disorders and mixed disorders)., Ethics and Dissemination: Ethical approval is not necessary, since this study does not involve the collection of primary data. The results will be disseminated through presentations at scientific conferences and publication in a peer-reviewed journal., Prospero Registration Number: CRD42023476269., Competing Interests: Competing interests: None declared., (© Author(s) (or their employer(s)) 2024. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.)