Existence results for non-local elliptic systems with Hardy-Littlewood-Sobolev critical nonlinearities

In this article, we study the following nonlinear doubly nonlocal problem involving the fractional Laplacian in the sense of Hardy-Littlewood-Sobolev inequality \begin{equation*} \left\{\begin{aligned} (-\Delta)^s u & = au+bv+\frac{2p}{p+q}\int_{\Omega}\frac{|v(y)|^q}{|x-y|^\mu}dy|u|^{p-2}u+2\xi_1\int_{\Omega}\frac{|u(y)|^{2^*_\mu}}{|x-y|^\mu}dy|u|^{2^*_\mu-2}u,&& \text{in } \Omega;\\ (-\Delta)^s v & = bu+cv+\frac{2q}{p+q}\int_{\Omega}\frac{|u(y)|^p}{|x-y|^\mu}dy|v|^{q-2}v+2\xi_2\int_{\Omega}\frac{|v(y)|^{2^*_\mu}}{|x-y|^\mu}dy|v|^{2^*_\mu-2}v,&& \text{in } \Omega;\\ u &=v=0,\text{ in } \R^N\setminus\Omega, \end{aligned}\right. \end{equation*} where $\Omega$ is a smooth bounded domain in $\R^N$, $N>2s$, $s\in(0,1)$, $\xi_1,\xi_2\geq 0$, $(-\Delta)^s$ is the well known fractional Laplacian, $\mu\in(0,N)$, $1<p,q\leq 2^*_\mu$ where $2^*_\mu=\frac{2N-\mu}{N-2s}$ is the upper critical exponent in the Hardy-Littlewood-Sobolev inequality. Under suitable assumptions on different parameters $p, q, \xi_1,$ and $\xi_2$, we are able to prove some existence and multiplicity results for the above equation by variational methods.Comment: arXiv admin note: text overlap with arXiv:1508.05206 by other author

Experimental investigation of a super performance dew point air cooler

This paper presents an experimental investigation of a super performance dew point air cooler which, by employing a super performance wet material layer, innovative heat and mass exchanger and intermittent water supply scheme, has achieved a significantly higher energy efficiency (i.e. Coefficient of Performance, COP) and a much lower electrical energy use compared to the existing air coolers of the same type. This involves the dedicated system design & construction, fully planned experimental testing under various simulated climatic conditions representing the climate of hot & dry, warm & dry, moderate, warm & humid and standard lab testing condition, testing results analysis and discussion, as well as the parallel comparison against the commercial dew point air cooler. Under the standard test condition, i.e. dry bulb temperature of 37.8 °C and coincident wet bulb temperature of 21.1 °C, the prototype cooler achieved the wet-bulb cooling effectiveness of 114% and dew-point cooling effectiveness of 75%, yielding a significantly high COP value of 52.5 at the optimal working air ratio of 0.364. The testing also indicated that the lower inlet air relative humidity led to a higher cooling efficiency, while the lower cooling output helped increase COP and cooling effectiveness (including the wet-bulb effectiveness and dew-point effectiveness) of the cooler

Total body bone mineral density and various spinal disorders: a Mendelian randomization study

IntroductionObservational studies have yielded inconsistent findings regarding the correlation between bone mineral density (BMD) and various spinal disorders. To explore the relationship between total-body BMD and various spinal disorders further, we conducted a Mendelian randomization analysis to assess this association.MethodsTwo-sample bidirectional Mendelian randomization (MR) analysis was employed to investigate the association between total-body BMD and various spinal disorders. The inverse-variance weighted (IVW) method was used as the primary effect estimate, and additional methods, including weighted median, MR-Egger, simple mode, and weighted mode, were used to assess the reliability of the results. To examine the robustness of the data further, we conducted a sensitivity analysis using alternative bone-density databases, validating the outcome data.ResultsMR revealed a significant positive association between total-body BMD and the prevalence of spondylosis and spinal stenosis. When total-body BMD was considered as the exposure factor, the analysis demonstrated an increased risk of spinal stenosis (IVW odds ratio [OR] 1.23; 95% confidence interval [CI], 1.14–1.32; P &lt; 0.001) and spondylosis (IVW: OR 1.24; 95%CI, 1.16–1.33; P &lt; 0.001). Similarly, when focusing solely on heel BMD as the exposure factor, we found a positive correlation with the development of both spinal stenosis (IVW OR 1.13, 95%CI, 1.05–1.21; P &lt; 0.001) and spondylosis (IVW OR 1.10, 95%CI, 1.03–1.18; P = 0.0048). However, no significant associations were found between total-body BMD and other spinal disorders, including spinal instability, spondylolisthesis/spondylolysis, and scoliosis (P &gt; 0.05).ConclusionThis study verified an association of total-body BMD with spinal stenosis and with spondylosis. Our results imply that when an increasing trend in BMD is detected during patient examinations and if the patient complains of numbness and pain, the potential occurrence of conditions such as spondylosis or spinal stenosis should be investigated and treated appropriately

MUSiC : a model-unspecific search for new physics in proton-proton collisions at root s=13TeV

Results of the Model Unspecific Search in CMS (MUSiC), using proton-proton collision data recorded at the LHC at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb(-1), are presented. The MUSiC analysis searches for anomalies that could be signatures of physics beyond the standard model. The analysis is based on the comparison of observed data with the standard model prediction, as determined from simulation, in several hundred final states and multiple kinematic distributions. Events containing at least one electron or muon are classified based on their final state topology, and an automated search algorithm surveys the observed data for deviations from the prediction. The sensitivity of the search is validated using multiple methods. No significant deviations from the predictions have been observed. For a wide range of final state topologies, agreement is found between the data and the standard model simulation. This analysis complements dedicated search analyses by significantly expanding the range of final states covered using a model independent approach with the largest data set to date to probe phase space regions beyond the reach of previous general searches.Peer reviewe

Search for new particles in events with energetic jets and large missing transverse momentum in proton-proton collisions at root s=13 TeV

A search is presented for new particles produced at the LHC in proton-proton collisions at root s = 13 TeV, using events with energetic jets and large missing transverse momentum. The analysis is based on a data sample corresponding to an integrated luminosity of 101 fb(-1), collected in 2017-2018 with the CMS detector. Machine learning techniques are used to define separate categories for events with narrow jets from initial-state radiation and events with large-radius jets consistent with a hadronic decay of a W or Z boson. A statistical combination is made with an earlier search based on a data sample of 36 fb(-1), collected in 2016. No significant excess of events is observed with respect to the standard model background expectation determined from control samples in data. The results are interpreted in terms of limits on the branching fraction of an invisible decay of the Higgs boson, as well as constraints on simplified models of dark matter, on first-generation scalar leptoquarks decaying to quarks and neutrinos, and on models with large extra dimensions. Several of the new limits, specifically for spin-1 dark matter mediators, pseudoscalar mediators, colored mediators, and leptoquarks, are the most restrictive to date.Peer reviewe

Measurement of prompt open-charm production cross sections in proton-proton collisions at root s=13 TeV

The production cross sections for prompt open-charm mesons in proton-proton collisions at a center-of-mass energy of 13TeV are reported. The measurement is performed using a data sample collected by the CMS experiment corresponding to an integrated luminosity of 29 nb(-1). The differential production cross sections of the D*(+/-), D-+/-, and D-0 ((D) over bar (0)) mesons are presented in ranges of transverse momentum and pseudorapidity 4 < p(T) < 100 GeV and vertical bar eta vertical bar < 2.1, respectively. The results are compared to several theoretical calculations and to previous measurements.Peer reviewe

Combined searches for the production of supersymmetric top quark partners in proton-proton collisions at root s=13 TeV

A combination of searches for top squark pair production using proton-proton collision data at a center-of-mass energy of 13 TeV at the CERN LHC, corresponding to an integrated luminosity of 137 fb(-1) collected by the CMS experiment, is presented. Signatures with at least 2 jets and large missing transverse momentum are categorized into events with 0, 1, or 2 leptons. New results for regions of parameter space where the kinematical properties of top squark pair production and top quark pair production are very similar are presented. Depending on themodel, the combined result excludes a top squarkmass up to 1325 GeV for amassless neutralino, and a neutralinomass up to 700 GeV for a top squarkmass of 1150 GeV. Top squarks with masses from 145 to 295 GeV, for neutralino masses from 0 to 100 GeV, with a mass difference between the top squark and the neutralino in a window of 30 GeV around the mass of the top quark, are excluded for the first time with CMS data. The results of theses searches are also interpreted in an alternative signal model of dark matter production via a spin-0 mediator in association with a top quark pair. Upper limits are set on the cross section for mediator particle masses of up to 420 GeV

Probing effective field theory operators in the associated production of top quarks with a Z boson in multilepton final states at root s=13 TeV

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Measurement of B-c(2S)(+) and B-c*(2S)(+) cross section ratios in proton-proton collisions at root s=13 TeV

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