Superadditivity, Monotonicity, and Exponential Convexity of the Petrović-Type Functionals

We consider functionals derived from Petrović-type inequalities and establish their superadditivity, subadditivity, and monotonicity properties on the corresponding real n-tuples. By virtue of established results we also define some related functionals and investigate their properties regarding exponential convexity. Finally, the general results are then applied to some particular settings

Combinatorial extensions of Popoviciu\u27s inequality via Abel-Gontscharoff polynomial with applications in information theory

We establish new refinements and improvements of Popoviciu’s inequality for n-convex functions using Abel-Gontscharoff interpolating polynomial along with the aid of new Green functions. We construct new inequalities for n-convex functions and compute new upper bounds for Ostrowski and Grüss type inequalities. As an application of our work in information theory, we give new estimations for Shannon, Relative and Zipf-Mandelbrot entropies using generalized Popoviciu’s inequality

Weighted Popoviciu type inequalities via generalized Montgomery identities

We obtained useful identities via generalized Montgomery identities, by which the inequality of Popoviciu for convex functions is generalized for higher order convex functions. We investigate the bounds for the identities related to the generalization of the Popoviciu inequality using inequalities for the Čebyšev functional. Some results relating to the Grüss and Ostrowski type inequalities are constructed. Further, we also construct new families of exponentially convex functions and Cauchy-type means by looking at linear functionals associated with the obtained inequalities

NON-SYMMETRIC STOLARSKY MEANS

Abstract. In this paper we construct n -exponentially convex functions and exponentially convex functions using the functional defined as the difference of the right parts of the HermiteHadamard inequality, for different classes of functions. Applying these results on some starshaped functions, we derive non-symmetric means of Stolarsky type

Superadditivity, Monotonicity, and Exponential Convexity of the Petrović-Type Functionals

We consider functionals derived from Petrović-type inequalities and establish their superadditivity, subadditivity, and monotonicity properties on the corresponding real n-tuples. By virtue of established results we also define some related functionals and investigate their properties regarding exponential convexity. Finally, the general results are then applied to some particular settings

Some Hermite-Hadamard and midpoint type inequalities in symmetric quantum calculus

The Hermite-Hadamard inequalities are common research topics explored in different dimensions. For any interval $[\mathrm{b_{0}}, \mathrm{b_{1}}]\subset\Re$, we construct the idea of the Hermite-Hadamard inequality, its different kinds, and its generalization in symmetric quantum calculus at $\mathrm{b_{0}}\in[\mathrm{b_{0}}, \mathrm{b_{1}}]\subset\Re$. We also construct parallel results for the Hermite-Hadamard inequality, its different types, and its generalization on other end point $\mathrm{b_{1}}$, and provide some examples as well. Some justification with graphical analysis is provided as well. Finally, with the assistance of these outcomes, we give a midpoint type inequality and some of its approximations for convex functions in symmetric quantum calculus

Pain after upper limb surgery under peripheral nerve block is associated with gut microbiome composition and diversity

peer-reviewedGut microbiota play a role in certain pain states. Hence, these microbiota also influence somatic pain. We aimed to determine if there was an association between gut microbiota (composition and diversity) and postoperative pain. Patients (n = 20) undergoing surgical fixation of distal radius fracture under axillary brachial plexus block were studied. Gut microbiota diversity and abundance were analysed for association with: (i) a verbal pain rating scale of < 4/10 throughout the first 24 h after surgery (ii) a level of pain deemed “acceptable” by the patient during the first 24 h following surgery (iii) a maximum self-reported pain score during the first 24 h postoperatively and (iv) analgesic consumption during the first postoperative week. Analgesic consumption was inversely correlated with the Shannon index of alpha diversity. There were also significant differences, at the genus level (including Lachnospira), with respect to pain being “not acceptable” at 24 h postoperatively. Porphyromonas was more abundant in the group reporting an acceptable pain level at 24 h. An inverse correlation was noted between abundance of Collinsella and maximum self-reported pain score with movement. We have demonstrated for the first time that postoperative pain is associated with gut microbiota composition and diversity. Further work on the relationship between the gut microbiome and somatic pain may offer new therapeutic targets

Comparison of the Airtraq® and Truview® laryngoscopes to the Macintosh laryngoscope for use by Advanced Paramedics in easy and simulated difficult intubation in manikins

<p>Abstract</p> <p>Background</p> <p>Paramedics are frequently required to perform tracheal intubation, a potentially life-saving manoeuvre in severely ill patients, in the prehospital setting. However, direct laryngoscopy is often more difficult in this environment, and failed tracheal intubation constitutes an important cause of morbidity. Novel indirect laryngoscopes, such as the Airtraq^®and Truview^®laryngoscopes may reduce this risk.</p> <p>Methods</p> <p>We compared the efficacy of these devices to the Macintosh laryngoscope when used by 21 Paramedics proficient in direct laryngoscopy, in a randomized, controlled, manikin study. Following brief didactic instruction with the Airtraq^®and Truview^®laryngoscopes, each participant took turns performing laryngoscopy and intubation with each device, in an easy intubation scenario and following placement of a hard cervical collar, in a SimMan^®manikin.</p> <p>Results</p> <p>The Airtraq^®reduced the number of optimization manoeuvres and reduced the potential for dental trauma when compared to the Macintosh, in both the normal and simulated difficult intubation scenarios. In contrast, the Truview^®increased the duration of intubation attempts, and required a greater number of optimization manoeuvres, compared to both the Macintosh and Airtraq^®devices.</p> <p>Conclusion</p> <p>The Airtraq^®laryngoscope performed more favourably than the Macintosh and Truview^®devices when used by Paramedics in this manikin study. Further studies are required to extend these findings to the clinical setting.</p

Comparison of the Airtraq® and Truview® laryngoscopes to the Macintosh laryngoscope for use by Advanced Paramedics in easy and simulated difficult intubation in manikins

<p>Abstract</p> <p>Background</p> <p>Paramedics are frequently required to perform tracheal intubation, a potentially life-saving manoeuvre in severely ill patients, in the prehospital setting. However, direct laryngoscopy is often more difficult in this environment, and failed tracheal intubation constitutes an important cause of morbidity. Novel indirect laryngoscopes, such as the Airtraq^®and Truview^®laryngoscopes may reduce this risk.</p> <p>Methods</p> <p>We compared the efficacy of these devices to the Macintosh laryngoscope when used by 21 Paramedics proficient in direct laryngoscopy, in a randomized, controlled, manikin study. Following brief didactic instruction with the Airtraq^®and Truview^®laryngoscopes, each participant took turns performing laryngoscopy and intubation with each device, in an easy intubation scenario and following placement of a hard cervical collar, in a SimMan^®manikin.</p> <p>Results</p> <p>The Airtraq^®reduced the number of optimization manoeuvres and reduced the potential for dental trauma when compared to the Macintosh, in both the normal and simulated difficult intubation scenarios. In contrast, the Truview^®increased the duration of intubation attempts, and required a greater number of optimization manoeuvres, compared to both the Macintosh and Airtraq^®devices.</p> <p>Conclusion</p> <p>The Airtraq^®laryngoscope performed more favourably than the Macintosh and Truview^®devices when used by Paramedics in this manikin study. Further studies are required to extend these findings to the clinical setting.</p

Hermite–Hadamard type inequalities for multiplicatively harmonic convex functions

Abstract In this work, the notion of a multiplicative harmonic convex function is examined, and Hermite–Hadamard inequalities for this class of functions are established. Many inequalities of Hermite–Hadamard type are also taken into account for the product and quotient of multiplicative harmonic convex functions. In addition, new multiplicative integral-based inequalities are found for the quotient and product of multiplicative harmonic convex and harmonic convex functions. In addition, we provide certain upper limits for such classes of functions. The obtained results have been verified by providing examples with included graphs. The findings of this study may encourage more research in several scientific areas