JENSEN–MERCER INEQUALITY AND RELATED RESULTS IN THE FRACTAL SENSE WITH APPLICATIONS

The most notable inequality pertaining convex functions is Jensen’s inequality which has tremendous applications in several fields. Mercer introduced an important variant of Jensen’s inequality called as Jensen–Mercer’s inequality. Fractal sets are useful tools for describing the accuracy of inequalities in convex functions. The purpose of this paper is to establish a generalized Jensen–Mercer inequality for a generalized convex function on a real linear fractal set [Formula: see text] ([Formula: see text]. Further, we also demonstrate some generalized Jensen–Mercer-type inequalities by employing local fractional calculus. Lastly, some applications related to Jensen–Mercer inequality and [Formula: see text]-type special means are given. The present approach is efficient, reliable, and may motivate further research in this area.

A Comprehensive Review of COVID-19 Virology, Vaccines, Variants, and Therapeutics

SummarySevere acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the causative pathogen of the coronavirus disease 2019 (COVID-19), has caused more than 179 million infections and 3.8 million deaths worldwide. Throughout the past year, multiple vaccines have already been developed and used, while some others are in the process of being developed. However, the emergence of new mutant strains of SARS-CoV-2 that have demonstrated immune-evading characteristics and an increase in infective capabilities leads to potential ineffectiveness of the vaccines against these variants. The purpose of this review article is to highlight the current understanding of the immunological mechanisms of the virus and vaccines, as well as to investigate some key variants and mutations of the virus driving the current pandemic and their impacts on current management guidelines. We also discussed new technologies being developed for the prevention, treatment, and detection of SARS-CoV-2. In this paper, we thoroughly reviewed and provided crucial information on SARS-CoV-2 virology, vaccines and drugs being used and developed for its prevention and treatment, as well as important variant strains. Our review paper will be beneficial to health care professionals and researchers so they can have a better understanding of the basic sciences, prevention, and clinical treatment of COVID-19 during the pandemic. This paper consists of the most updated information that has been available as of June 21, 2021.

Discrete Fréchet Distance under Translation

The discrete Fréchet distance is a popular measure for comparing polygonal curves. An important variant is the discrete Fréchet distance under translation, which enables detection of similar movement patterns in different spatial domains. For polygonal curves of length n in the plane, the fastest known algorithm runs in time Õ( n 5 ) [12]. This is achieved by constructing an arrangement of disks of size Õ( n 4 ), and then traversing its faces while updating reachability in a directed grid graph of size N := Õ( n 5 ), which can be done in time Õ(√ N ) per update [27]. The contribution of this article is two-fold. First, although it is an open problem to solve dynamic reachability in directed grid graphs faster than Õ(√ N ), we improve this part of the algorithm: We observe that an offline variant of dynamic s - t -reachability in directed grid graphs suffices, and we solve this variant in amortized time Õ( N 1/3 ) per update, resulting in an improved running time of Õ( N 4.66 ) for the discrete Fréchet distance under translation. Second, we provide evidence that constructing the arrangement of size Õ( N 4 ) is necessary in the worst case by proving a conditional lower bound of n 4 - o(1) on the running time for the discrete Fréchet distance under translation, assuming the Strong Exponential Time Hypothesis.

(n − 2)-Fault-Tolerant Edge-Pancyclicity of Crossed Cubes CQn

As one of the most fundamental networks for parallel and distributed computation, cycle is suitable for developing simple algorithms with low communication cost. A graph [Formula: see text] is called [Formula: see text]-fault-tolerant edge-pancyclic if after deleting any faulty set [Formula: see text] of [Formula: see text] vertices and/or edges from [Formula: see text], every correct edge in the resulting graph lies in a cycle of every length from [Formula: see text] to [Formula: see text], inclusively, where [Formula: see text] is the girth of [Formula: see text], the length of a shortest cycle in [Formula: see text]. The [Formula: see text]-dimensional crossed cube [Formula: see text] is an important variant of the hypercube [Formula: see text], which possesses some properties superior to the hypercube. This paper investigates the fault-tolerant edge-pancyclicity of [Formula: see text], and shows that if [Formula: see text] contains at most [Formula: see text] faulty vertices and/or edges then, for any fault-free edge [Formula: see text] and every length [Formula: see text] from [Formula: see text] to [Formula: see text] except [Formula: see text], there is a fault-free cycle of length [Formula: see text] containing the edge [Formula: see text]. The result is optimal in some senses.

Review on the correlation between chronic obstructive pulmonary disease and eosinophil in peripheral blood

Chronic obstructive pulmonary disease (COPD) is an irreversible disease characterized by the limitation of continuous airflow. Eosinophil (EOS) in peripheral blood plays a key role in the acute exacerbation of COPD. Eosinophil-increased COPD has become an important variant of COPD and the focus of individualized treatment of COPD. Numerous studies have shown that an increased eosinophil count or an increased percentage in the peripheral blood closely correlates to the acute exacerbation and prognosis of COPD. Therefore, this study intends to review the progress of domestic and foreign research on the correlation between COPD and EOS.

On the Transit-Based Evacuation Strategies in an Integrated Network Topology

Evacuation planning problem deals with sending the maximum number of evacuees from the danger zone to the safe zone in minimum time as eciently as possible. The dynamic network flow models for various evacuation network topology have been found suitable for the solution of such a problem. Bus based evacuation planning problem (BEPP), as an important variant of the vehicle routing problem (VRP), is one of the emerging evacuation planning problems. In this work, an organized overview of this problem with a focus on their solution status is compactly presented. Arrival patterns of the evacuees including their transshipments at different pickup locations and their assignments are presented. Finally, a BEPP model and a solution for a special network are also proposed.

Open Bioeconomy—A Bibliometric Study on the Accessibility of Articles in the Field of Bioeconomy

Open access (OA) to scientific information is one of the major challenges and objectives of actual public research policy. The purpose of this paper is to assess the degree of openness of scientific articles on bioeconomy, as one of the emergent research fields at the crossroads of several disciplines and with high societal and industrial impact. Based on a Web of Science (WoS) corpus of 2489 articles published between 2015 and 2019, we calculated bibliometric indicators, explored the openness of each article and assessed the share of journals, countries and research areas of these articles. The results show a sharp increase and diversification of articles in the field of bioeconomy, with a beginning long tail distribution. 45.6% of the articles are freely available and the share of OA articles is steadily increasing, from 31% in 2015 to 52% in 2019. Gold is the most important variant of OA. Open access is low in the applied research areas of chemical, agricultural and environmental engineering but higher in the domains of energy and fuels, forestry and green and sustainable science and technology. The UK and the Netherlands have the highest rates of OA articles, followed by Spain and Germany. The funding rate of OA articles is higher than of non-OA articles. This is the first bibliometric study on open access to articles on bioeconomy. The results can be useful for the further development of OA editorial and funding criteria in the field of bioeconomy.

Paediatric Extensive Cervical Plexiform Neurofibroma Mimicking a Parotid Lesion

Neurofibromatosis Type 1 (NF1), also known as von Recklinghausen’s disease is a multisystem genetic disorder that occurs with an incidence of 1 in 4000 live births. Plexiform nmeurofibroma (PN) is a rare important variant of NF1, seen in 5 to 15% of cases. We report a 7-year-old boy, without family history of neurofibromatosis presented with left neck swelling associated with multiple café au lait spots for one-year duration. Computed tomography of head and neck revealed an extensive soft tissue lesion involving the left parapharyngeal, carotid space and parotid space encasing the left internal and common carotid artery until its origin at the arch of aorta with erosion of the basiocciput. He underwent transcervical excision of the lesion, which was confirmed histopathologically as PN.

Semiotic Approach to the Truth of the Reliability Results of Socio-Economic Research

The semiotic approach is still unreasonably rarely used in research in the field of Economics; more precisely, even the actual inclusion of its or its elements in the development of materials of any research is still not accompanied by awareness of this and an indication of their semiotic nature. The article analyzes the results of our long-term experience of semiotic analysis and control of dozens of heterogeneous (mainly conducted with our active participation) socio-economic and other studies. The analysis begins with a theoretical consideration of the process of achieving not only the reliability, but also the truth of the results of research (on the basis of philosophical theories of truth). The semiotic control of the correctness of the epistemological, socio-economic and mathematical propositions used is illustrated by the material of various studies. They were analyzed and implemented using the proposed semiotic methodology to ensure the reliability of indicators. It has no analogues known to us so far and includes a general semiotic methodology and its important variant – a comparative methodology for determining the indicators of state statistics. This allowed us to solve some problems of general economic nature (starting with the most important language the correctness of the use of formally rigorous mathematical apparatus in research in the natural), and a number of serious problems to determine the practical effectiveness (or inefficiency) of the parameters of social policy.