Studying spread of epidemics and diseases are world wide problems especially during the current time where the whole world is suffering from COVID-19 pandemic. Antimicrobial resistance (AMR) and waning vaccination are classified as world wide problems. Both depend on the exposure time to antibiotic and vaccination. Here, a simple model for competition between drug resistant and drug sensitive bacteria is given. Conditions for local stability are investigated which agree with observation. Existence of positive solution in the AMR complex networks is proved. Dynamics of the identical AMR models are explored with different topologies of complex networks such as global, star, line and unidirectional line networks coupled through their susceptible states. Chaotic attractors are shown to be existed as the AMR models are located on all the indicted topologies of complex networks. Thus, it is found that the dynamics of the AMR model become more complicated as it is located on either integer-order or fractional-order complex networks. Furthermore, a discretized version of the fractional AMR model is presented. Complex dynamics such as existence of Neimark–Sacker, flip bifurcations, coexistence of multi attractors, homoclinic connections and multi closed invariant curves are investigated. Basin sets of attraction are also computed. Finally, the discretized system is located on complex networks with different topologies which also show rich variety of complex dynamics. Also, 0-1 test is used to verify the existence of unpredictable dynamics. So, studying the dynamics of AMR models on complex networks is very helpful to understand the mechanism of spread of diseases.

AbstractThe novel coronavirus, also known as COVID-19, has infected at least 1 million persons worldwide. It has also accounted for a number of deaths. No doubt, it has dealt a drastic blow to businesses and the global economy, leaving behind a huge crisis. Thus, the present study discusses management strategies to counter the short and long-term effects of the COVID-19 pandemic on businesses.IntroductionThe novel coronavirus pneumonia is an acute respiratory disease. In December 2019, this disease emerged in Wuhan, China. The Chinese government called it SARS-CoV-2 which was subsequently named COVID-19 by the World Health Organization (WHO) [1]. In January 2020, WHO confirmed it as a sustained human to human disease [2]. The World Health Organization has declared Covid-19 a full-blown pandemic, which means it's a crisis-level disease outbreak in multiple countries. This disease is extremely rare and its unexpected occurrence has major consequences for just about everybody. Covid-19 is similar to past zoonotic coronaviruses, including SARS. It's less lethal than SARS, but spreads more easily. The death rate is under 2 percent, and for people under the age of 60 under 1 percent.In a bid to control its spread, this disease has led to flight cancellations, border closure, postponement of business meetings and so on. In fact, the impact of this pandemic will take years to be fully quantified. Social distancing -- basically keeping people away from each other (as well as avoiding human physical contact and washing hands) has been one of the mostly talked about method of preventing a full-scale outbreak. However, this has led to severe consequences to businesses and even job losses. This is because business is usually conducted by bringing people together, not keeping them apart. People come to work, have meetings, travel to meet with clients, attend trade conferences and purposefully interact with each other to forward the interests of the organization. Thus, this brings to concern how to keep business alive while keeping people apart. No doubt, the COVID-19 pandemic has led to huge economic and business crisis. For instance, oil prices crashed to an 18-year low of $20.09 a barrel, thereby sending a devastating blow to energy demand. In view of the imminent crisis to businesses, it is imperative that efficient management strategies are adapted to this unusual and unpleasant situation. Thus, the present study highlights these key approaches.Immediate stepsTo prevent further escalation of the situation, the following first steps should be observed. They are as follows:·         Appoint a crisis response team that meets daily.·         Monitor government, medical, industry and local sources for updates for the team.·         Implement a communications plan to transparently inform all employees.·         Develop and implement a comprehensive crisis response.·         Develop or update, then communicate and enforce, a remote-work policy.Long-term actionsScenario planning·         Organizations must act with imperative when developing and implementing enhanced risk management practices, focusing on the opportunities scenario planning offers in creating pre-emptive action plans.·         Scenarios enable organizations to see the bigger picture and make effective trade-off decisions on issues like: how much stock to hold – and where, or how to balance the cost of inventory versus the cost of failing to satisfy customers. Simulations can be run swiftly to identify “sweet spots” between apparently conflicting objectives, based on real-time inventory data, customer demand, and supplier capability. Increasingly enabled by AI and automation, these scenarios can help prescribe rather than just predict.·         By analyzing past events and hypothesizing future threats, organizations are able to identify strategic and concentrated supplies that are at risk in major crises, and most importantly, recognize when current internal risk capacities prove insufficient.Supplier risk management·         Real-time supplier data such as system performance category alerts and geopolitical events helps manage performance and issue resolution.·         When alerted, proactive measures should be taken by organizations to uncover additional exposure levels by reaching out to suppliers (from tier 1, tier 2 and below) outside of affected regions to identify upstream supply dependencies within their supply chains.·         Further, organizations could benefit from balancing supply and demand and working with internal stakeholders as well as critical suppliers to contractually agree on logistic-based costs and necessary buffer stock, so as to reduce sudden price increases in the face of a crisis.Technology upgrades·         In line with the technology-enabled business climate we currently operate in, organizations should rethink the way their employees collaborate with each other and customers - within the office, regionally and globally.·         By investing in internal technology, organizations can teach employees how to effectively leverage powered execution tools such as cloud-office technology and zero-touch models. This will help ensure that not only in times of crisis are teams better equipped to work remotely, but as the business environment continues to shift, employees are able to adapt alongside it and continue serving customers.ConclusionIn conclusion, as the novel coronavirus continues to take its toll on businesses as well as the global economy, hope is not lost for business to bounce back strongly. However, this can only be achieved by ensuring that effective short and long-term management strategies are implemented and followed to the letter.References1.            Chan JF-W, Yuan S, Kok K-H, To KK-W, Chu H, Yang J, et al. A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: a study of a family cluster. Lancet. 2020;395(10223):514-23.2.            Organization WH. Coronavirus disease 2019 (COVID-19) situation report–34. Geneva, Switzerland: World Health Organization; 2020.

Gross primary production (GPP) is a key component of the forest carbon cycle. However, our knowledge of GPP at the stand scale remains uncertain because estimates derived from eddy covariance (EC) and EC itself rely on semi-empirical modeling and the assumptions of the EC technique are sometimes not fully met. We propose using the sap flux/isotope method as an alternative way to estimate canopy GPP, termed GPPiso/SF, at the stand scale and at daily resolution. It is based on canopy conductance inferred from sap flux and intrinsic water-use efficiency estimated from the stable carbon isotope composition of phloem contents. The GPPiso/SF estimate was further corrected for seasonal variations in photosynthetic capacity and mesophyll conductance. We compared our estimate of GPPiso/SF to the GPP derived from PRELES, a model parameterised with EC data. The comparisons were performed in a highly instrumented, boreal Scots pine forest in northern Sweden, including a nitrogen fertilised and a reference plot. The resulting annual and daily GPPiso/SF estimates agreed well with PRELES, in the fertilised plot and the reference plot. We discuss the GPPiso/SF method as an alternative which can be widely applied without terrain restrictions, where the assumptions of EC are not met.

Purpose:There have been concerted efforts towards cataloging rare and deleterious variants in different world population using high throughput genotyping and sequencing based methods. The Indian populations are underrepresented or its information w.r.t. clinically relevant variants are sparse in public datasets. The aim of this study was to estimate the burden of monogenic disease causing variants in Indian populations. Towards this, we have assessed the frequency profile of monogenic phenotype associated ClinVar variants. Methods: The study utilized genotype dataset (global-screening-array, Illumina) from 2795 individuals (multiple in-house genomics cohorts) representing diverse ethnic and geographically distinct Indian populations. Results: Of the analyzed variants from GSA, ~12% were found to be informative and were either not known earlier or underrepresented in public databases in terms of their frequencies. These variants were linked to disorders, viz. Inborn-errors of Metabolism, Monogenic-diabetes, hereditary cancers and various other hereditary conditions. We have also shown that our study cohort is genetically better representatives of Indian populations than its representation in1000 genome project (South-Asians). Conclusion: We have created a database, ClinIndb [(http://clinindb.igib.res.in) and (https://databases.lovd.nl/shared/variants?search_owned_by_=%3D%22Mohamed%20Faruq%22)], to help clinicians and researchers in diagnosis, counseling and development of appropriate genetic screening tools relevant to the Indian populations and Indians living abroad.

Holoprosencephaly (HPE) is the most common congenital anomaly affecting the forebrain and face in humans and occurs as frequently as 1:250 conceptions or 1:10,000 livebirths. Sonic hedgehog (SHH) is one of the best characterized HPE genes that plays crucial roles in numerous developmental processes including midline neural patterning and craniofacial development. The Frizzled class G-Protein Coupled Receptor (GPCR) SMOOTHENED (SMO), whose signalling activity is tightly regulated, is the sole obligate transducer of hedgehog-related signals. However, except for previous reports of somatic oncogenic driver mutations in human cancers (or mosaic tumors in rare syndromes), any potential disease-related role of SMO genetic variation in humans is largely unknown. To our knowledge, ours is the first report of a human hypomorphic variant revealed by functional testing of seven distinct non-synonymous SMO variants derived from HPE molecular and clinical data. Here we describe several zebrafish bioassays developed and guided by a systems biology analysis. This analysis strategy, and detection of hypomorphic variation in human SMO, demonstrates the necessity of integrating the genomic variant findings in HPE probands with other components of the hedgehog gene regulatory network (GRN) in overall medical interpretations.

Conservation agriculture (CA) systems represent a set of three soil management principles that include minimal soil disturbance, permanent soil cover and crop rotations whereas the CA-based systems in this study add the bed and furrow tillage structures as integral elements of CA. This study aimed at investigating the long-term (2005-2013) influence of CA-based systems on soil health and crop productivity in northern Ethiopia. The treatments include two types of CA-based systems (permanent raised bed PRB and contour furrowing CF) and conventional tillage (CT). The experimental layout was arranged in a randomized complete block design. Soil samples were collected at 0-10 cm soil depth to assess soil health. Wheat root samples were used to measure arbuscular mycorrhizal fungi (AMF) colonization percentage using grid line intersect method. Piecewise structural equation modeling (PSEM) was used to understand linkages between management practices, soil health and crop productivity. Higher soil microbial biomass carbon (SMBC), AMF spore abundance and root colonization were recorded in PRB followed by CF as compared to CT (P < 0.05). Carbon sequestration rate, nutrient availability, plant available water capacity and air capacity were significantly higher in PRB and CF compared to CT. Outputs of the PSEM highlighted two pathways in which CA-based systems contributed to improved productivity: (1) via higher density of bacteria and improved hydraulic conductivity, and (2) via higher density of fungi and increase soil organic carbon content in the topsoil. The study concludes that CA-based systems have the potential to improve crop productivity through improved soil health.

In the life cycle of Pyropia yezoensis, sporangial filaments connect conchocelis and thallus, but the mechanisms of maturation and conchospore release of sporangial filaments are poorly understood. We found that the morphological change from vegetative growth form (hollow cells) to reproductive form (bipartite cells), and the release of conchospores from bipartite cells were all closely correlated with culture density and light intensity. Bipartite cells formed at low density (50–1,000 fragments/mL) and when stimulated by high light levels (40–100 µmol photons m−2 s−1), but conchospore release was inhibited at such light intensities. At high densities (5,000–10,000 fragments/mL), sporangial filaments retained the hollow cell morphology and rarely formed bipartite cells. Ultrastructural observation showed that the degradation of autophagosome-like structures in vacuoles caused the typical hollow form. Transcriptome analysis indicated that adaptive responses to environmental changes, mainly autophagy, endocytosis and phosphatidylinositol metabolism, caused the morphological transformation of free-living sporangial filaments. Meanwhile, the extensive promotion of energy accumulation under high light levels promoted vegetative growth of sporangial filaments, and thus inhibited conchospore release from bipartite cells. These results provide a theoretical basis for maturation of sporangial filaments and release of conchospores in P. yezoensis and other related species.

This work presents new findings about the spatial arrangement of up to three biominerals in plant trichomes. Many plants develop hard, mineralized structures primarily as a defence against herbivores. Stinging hairs and other trichomes particularly of Loasaceae show the most complex mineralization patterns in any living organism in the form of single-celled structures with the three biominerals calcium phosphate, calcium carbonate, and silica. Scanning electron microscopy with high-resolution EDX element analyses of sample surfaces and sections provides a three-dimensional view of the extreme chemical heterogeneity of cell walls. All three biominerals occur in two different contexts: either as nearly pure mineral structures, e.g., on surfaces and in hooks, or as composite materials with a higher proportion of carbohydrates (cellulose, pectin), especially in the bulk of the cell wall. Raman spectroscopy permits the identification of both organic and inorganic compounds side by side. The chemical composition of cell walls may change abruptly, or gradually across cell walls; the cell lumen may be additionally filled with amorphous minerals. Water-solubility of the different mineral fractions is remarkably divergent. Overall, we here demonstrate that different mineral and organic components permit plants to fine-tune the mechanical properties of cells and tissues.

Knowing which restoration approach provides the best returns on investment for accumulating carbon is essential to foster restoration planning, financing, and implementation. We assessed the recovery of carbon stocks, implementation and land opportunity costs of forests established by natural regeneration and high-diversity native tree plantations. Our study was based on chronosequences (10-60 yr) of 12 naturally regenerating forests, 13 restoration plantations, and 5 reference forests located in Brazil’s Atlantic Forest. Restoration plantations accumulated approximately 50% more above-ground carbon than regenerating forests throughout the chronosequence. When controlling for soil clay content, soil carbon stocks were higher in reference than in restored forests, but they were comparable between plantations and regenerating forests. After 60 years of stand development, recovery of total carbon stocks in both restoration management types reached only half of the average stocks of reference forests. Total cost-effectiveness for carbon accumulation, including both implementation and land opportunity costs, was on average 60% higher for regenerating forests than for plantations (15.1 kgC.US$-1 and 9.4 kgC.US$-1, respectively). Both restoration management types had cost-effectiveness for carbon accumulation markedly lower than the price of carbon credits considered, so some voluntary forest carbon markets are not adequately priced to support restoration derived offsets. Although tree plantations initially had higher rates of carbon storage than regenerating forests, their higher implementation and land opportunity costs make them less cost-effective for carbon farming. Our results further suggest that carbon markets alone have a limited potential to up-scale restoration efforts in Brazil’s Atlantic Forest.

B. terrestris dalmatinus is native and the most widespread Bombus terrestris subspecies which occurs at different altitudes and habitats in the Mediterranean region where commercial B. terrestris colonies have been used for pollination in greenhouses crops for more than two decades. In this study, we sampled B. terrestris from greenhouses (commercial populations, CP1-CP7), within the five km areas surrounding the greenhouses (AK, KM, DM and GB) and more distant native populations (TM, BB and FS) in the Mediterranean region to determine the genetic structure of native and commercial B. terrestris populations and to better understand genetic introgression of commercial greenhouse B. terrestris populations into the native B. t. dalmatinus populations using twenty microsatellite markers and two mitochondrial genes (COI and cyt b). Microsatellite analysis showed adequate levels of genetic diversity in both commercial and native populations. However, populations could not been clearly separated from each other (FST = 0.014-0.045; p>0.05). All populations deviated from Hardy-Weinberg equilibrium due to high inbreeding (mean Fis: 0.234). In the mitochondrial analyses, we found two haplotypes for COI and six haplotypes for cyt b gene. Genotypes belonging to the subspecies B. t. dalmatinus were determined in all populations, while genotypes belonging to the subspecies B. terrestris terrestris were determined in some commercial populations and nearby greenhouses populations. Our results thus indicate that native populations are threatened by gene flow from non native B. t. terrestris subspecies. Our data also suggest that aestivated native FS population should be primarily conserved to avoid extinction.

Background: The respiratory system changes with age and understanding these changes may help detect and prevent respiratory dysfunctions in the elderly. In addition, although the influence of smoking on lung function is well known, its influence on lung function and mechanics of elderly are unknown. Impulse oscillometry system (IOS) is a technique for measurements of lung mechanics, which don’t need patient effort and a minimal collaboration, beyond to reflect more precisely airway resistance/obstruction and lung tissue elastance than spirometric measurements. Aims: Thus, the present study aimed to investigate whether IOS could be or not be sensible enough to differentiate the effects of smoking in the pulmonary response of non-smokers from smokers’ elderlies. Methods: The present study compared 30 elderlies never smokers (70,96 ± 6,61) with 30 elderlies’ current smokers (69,96 ± 5,94 years old and 35,33 ± 24,93/packs/year tobacco load), without asthma or any other pulmonary disease in terms of lung function and mechanics. Results: The following differences between elderly never smokers versus smokers for spirometric values were found (FVC p<0.02; FEV1 p<0.04; FEV1/FVC p<0.04; PEF p<0.01; MEF25% p<0.02; MEF50% p<0.02; MEF75% p<0.01, IVC p<0.01) and for oscilometric values (Z5hz p<0.03; R5Hz 0.01; R20Hz p<0.04; X5Hz p<0.02), while RFres and R5Hz-R20Hz did not present differences (p>0.05). Conclusions: Impulse oscilometry can detect small airway resistance/obstruction to better differentiate the functional pulmonary alterations among never smokers from smokers’ elderlies.

European bat lyssavirus 1 (EBLV-1) is widespread and frequent in European bats, particularly of the genus Eptesicus. However, other species can be seropositive, suggesting a complex ecology still mostly unknown. In Italy, EBLV-1 antibodies are described since 2012 in South Tyrolean Myotis myotis. This study provide phylogenetic evidence for either the current or the recent movement of M. myotis from continental Europe to South Tyrol across the Alpine valleys, which might allow for the introduction of LYSVs. Serological analyses confirmed antibodies against EBLV-1 in this bat across the entire region, showing marked seasonal pattern and a sharp peak of positivity in late summer. No statistical difference was detected between the maternity colonies investigated in either the likelihood for infection or the antibody titres. Indeed, South Tyrolean populations of M. myotis showed no significant genetic differentiation using nuclear and mitochondrial markers, supporting the existence of a regional meta-population and a low philopatric behaviour. This structure, never described for M. myotis elsewhere, well explains the spread and maintenance of LYSVs trough the movement of female bats between colonies. Since no virus was detected in the study, we cannot exclude that our serological data don’t derive from a cross-reaction with an unknown LYSV. However, because all LYSVs can cause clinical rabies in humans, this study has a strong impact on public health regardless of the viral species actually circulating. In addition, the unravelling of the peculiar genetic structure of South Tyrolean M. myotis is crucial to inform conservation strategies for this endangered species.

Fluid catalytic cracking unit, which batch operations are operated in a multirate mode, is a typical continuous process with batch operations. The integration optimization of this problem can be formulated as a hybrid dynamic optimization in terms of parameters and continuous variables. To obtain a high-quality solution, adaptive direct methods are usually required to solve the problem iteratively. However, this paper proposes a novel scheme, which obtains an equivalent or better precision solution with relatively coarse discretization. In detail, by designating the batch operations as complicating variables, an optimal solution and sensitivity information about batch operations are obtained by a nonconvex sensitivity-based general Benders decomposition algorithm. Then the optimal continuous operations are implemented as extra closed-loop controllers by tracking the necessary conditions of optimality, while the optimal batch operations are improved by a line method. The simulation results also analyze the economic effect of different batch operations.

Spherical agglomeration (SA) is a process intensification (PI) strategy, which can reduce the number of unit operations in pharmaceutical manufacturing. SA merges drug substance crystallization with drug product wet granulation, reducing capital and operating costs. However, SA is a highly nonlinear process, thus for its efficient operation model-based design and control strategies are beneficial. These require the development of a high-fidelity process model with appropriately estimated parameters. There are two major problems associated with the development of a high-fidelity process models – (i) selection of the appropriate model corresponding to the underlying process mechanisms, and (ii) accurate estimation of the parameters. This work focuses on the identification of the best fitting model that correlates with experimental observations using cross-validation experiments. Further, an Iterative Model Based Experimental Design (IMED) strategy is developed, which uses D-optimal experimental design criterion to minimize the number of experiments necessary to obtain accurate parameter estimates.

we have assembled the 2D MXene flakes and acid activated carbon (AAC) into a 3D sandwich architecture expected to avoid the serious restacking problem of 2D MXene flakes and develop MXene-based functional materials. When used for energy storage, 2D MXene, as a flexible, conductive and electrochemically active binder, furnishes a new perspective and possibility to assemble flexible and conductive electrodes without any current collector, binders or conductive additives. The flexible MXene/AAC 2:1 electrode delivers the specific capacitance of 378 F g-1 at 0.5 A g-1 and a capacitance retention of 88.9% at 30 A g-1. Impressively, asymmetrical supercapacitors have been assembled with MXene/AAC hybrids as positive electrode and delivers exceptional electrochemical properties. The MXene/AAC 2:1//AAC achieves 177 F g-1 at 0.5 A g-1, 97.4% retention after 10000 circles of GCD measurements at 5 A g-1. Moreover, the 3D sandwich architecture of MXene/AAC hybrids with great specific surface exhibits noteworthy absorption

The bending of the surfaces of the binormals by deformation of the directing curve, which is the slope line, is considered. Such deformation changes the curvature of the curve, but it remains a slope line. The rectilinear generators of the surfaces at deformation of the curve coincide with the unit binormal of the accompanying trihedral at all its points. Parametric equations of continuous bending of these surfaces have been made by changing the angle of inclination of the directional slope line. The initial slope curve is given by the angle of its rise and the conformity of change of curvature as a function of arc length. The partial case where the curvature of the initial curve is constant is considered. In this case, it is shown that helicoids, including the screw conoid, are the set of surface bends. Specific examples are considered. According to the obtained equations, the surfaces that are the bending of the initial are constructed.

This paper suggests a simple analytical method for Volterra-Fredholm integral equations, the solution process is similar to that by variational-based analytical method, e.g., Ritz method. The examples show the method is straightforward and effective.

The COVID-19 pandemic has placed an extraordinary demand on the United States healthcare system. Many institutions have cancelled elective and non-urgent procedures to conserve resources and limit exposure. While operational definitions of elective and urgent categories exist, there is a degree of surgeon judgment in designation. In the present commentary, we provide a framework for prioritizing head and neck surgery during the pandemic. Unique considerations for the head and neck patient are examined including risk to the oncology patient, outcomes following delay in head and neck cancer therapy, and risk of transmission during otolaryngologic surgery. Our case prioritization criteria consist of four categories: urgent – proceed with surgery, less urgent – consider postpone > 30 days, less urgent – consider postpone 30–90 days, and case-by-case basis. Finally, we discuss our preoperative clinical pathway for transmission mitigation including defining low-risk and high-risk surgery for transmission and role of preoperative COVID-19 testing.

The 2019 novel coronavirus disease (COVID-19) has presented the world and physicians with a unique public health challenge. In light of its high transmissibility and large burden on the healthcare system, many hospitals and practices have opted to cancel elective surgeries in order to mobilize resources, ration personal protective equipment and guard patients from the virus. Head and neck cancer physicians are particularly affected by these changes given their scope of practice, complex patient population, and interventional focus. In this viewpoint, we discuss some of the many challenges faced by head and neck surgeons in this climate. Additionally, we outline the utility of telemedicine as a potential strategy for allowing physicians to maintain an effective continuum of care.

In December 2019, the world started to face a new pandemic situation, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Although COVID-19 clinical manifestations are mainly respiratory, major cardiac complications are being reported. Cardiac manifestations etiology seems to be multifactorial, comprising direct viral myocardial damage, hypoxia, hypotension, enhanced inflammatory status, ACE2-receptors downregulation, drug toxicity, endogenous catecholamine adrenergic status, among others. Studies evaluating COVID-19 patients presenting cardiac injury markers show that it is associated with poorer outcomes, and arrhythmic events are not uncommon. Besides, drugs currently used to treat the COVID-19 are known to prolong the QT interval and can have a proarrhythmic propensity. This review focus on COVID-19 cardiac and arrhythmic manifestations and, in parallel, makes an appraisal of other virus epidemics as SARS-CoV, MERS-CoV, and H1N1 influenza.

In this paper, we investigate the surface-dependent growth model in Euclidean 3-space. The surface-dependent model is developed to model the kinematics of surface growth for objects that can be generated by the curves on the surface, such as parasites and plants. This paper includes two main purposes for this model. The first one is to parametrize this model by using the quaternions and homothetic motions.Furthermore, we express the matrix representations of the surface-dependent growth model. The second one is to construct the surface-dependent growth model by using the growth velocity components related to the Darboux frame at each point of the generating curve. Moreover, to support the theory studied in the paper various illustrated examples are presented.

The existing literature discusses different strategies to solve a scalar ordinary differential equation using Lie point symmetries. We focus on three of these strategies in order to frame methods for finding solutions of non-linear systems of ordinary differential equations. These include Lie's integration theorem, method of successive reduction of order and the method of using the invariants of the admitted symmetry generators. Illustrative examples and those taken from mechanics are presented to highlight the use of these methods.

An advanced class of convexity has been introduced in this article, named as co-ordinated σ-convexity. This variant holds some other types of two variable convex functions on co-ordinates as it’s special cases. We also constituted integral inequalities enmeshed with the Hermite-Hadamard type for co-ordinated σ-convex functions, as an application.

Heated curved panels flutter in supersonic air flow will affect fatigue life and flight performance of aircrafts, thus the research on heated curved panels flutter was an important problem in flight design. A nonlinear aero-elastic partial differential equation for two-dimensional heated curved panels in supersonic flow was established based on the von-Karman nonlinear strain-displacement relation and aerodynamic force model of supersonic flow, which was described by improved piston theory. The aero-elastic partial differential equation was derived to a four-dimensional ordinary differential equation system by using second order Galerkin discretization method. The algebraic criterion of the Hopf bifurcation was utilized in the equation system to derive the Hopf bifurcation point of the system (also the flutter critical value).Therefore, analytical expressions of flutter critical dynamic pressure and vibration frequency were theoretically derived. Then, a numerical experiment was established, and the agreement of numerical result and theoretical value was validated. The result showed that flutter dynamic pressure decreased and then increased with initial curvature rising. For small curvature panel, flutter dynamic pressure also first decreased and then increased with temperature rising, while for large curvature panel flutter dynamic pressure always increased with temperature rising. The established equation system and analytical expression of Hopf bifurcation point can provide some guidance for heated curved panel in supersonic air flow.