increasing function
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2022 ◽  
Vol 6 (1) ◽  
pp. 42
Author(s):  
Soubhagya Kumar Sahoo ◽  
Muhammad Tariq ◽  
Hijaz Ahmad ◽  
Bibhakar Kodamasingh ◽  
Asif Ali Shaikh ◽  
...  

The comprehension of inequalities in convexity is very important for fractional calculus and its effectiveness in many applied sciences. In this article, we handle a novel investigation that depends on the Hermite–Hadamard-type inequalities concerning a monotonic increasing function. The proposed methodology deals with a new class of convexity and related integral and fractional inequalities. There exists a solid connection between fractional operators and convexity because of its fascinating nature in the numerical sciences. Some special cases have also been discussed, and several already-known inequalities have been recaptured to behave well. Some applications related to special means, q-digamma, modified Bessel functions, and matrices are discussed as well. The aftereffects of the plan show that the methodology can be applied directly and is computationally easy to understand and exact. We believe our findings generalise some well-known results in the literature on s-convexity.


2022 ◽  
Vol 258 ◽  
pp. 10004
Author(s):  
Adrita Chakraborty

We study two important properties of 2+1D QCD, namely confinement and Pseudoscalar glueball spectrum, using holographic approach. The confined state of the bounded quark-antiquark pair occurs in the self-coupling dominated nonperturbative regime, where the free gluons form the bound states, known as glueballs. The gauge theory corresponding to low energy decoupled geometry of isotropic non-supersymmetric D2 brane, which is again similar to the 2+1D YM theory, has been taken into account but in this case the coupling constant is found to vary with the energy scale. At BPS limit, this theory reduces to supersymmetric YM theory. We have considered NG action of a test string and calculate the potential of such confined state located on the boundary. The QCD flux tube tension for large quark-antiquark separation is observed to be a monotonically increasing function of running coupling. The mass spectrum of Pseudoscalar glueball is evaluated numerically from the fluctuations of the axion in the gravity theory using WKB approximation. This produces the mass to be related to the string tension and the levels of the first three energy states. The various results that we obtained quite match with those previously studied through the lattice approach.


Author(s):  
Wojciech Olszewski

The result that says the sequence of iterations [Formula: see text] converges if [Formula: see text] is an increasing function has numerous applications in elementary economic analysis. I generalize this simple result to some mappings [Formula: see text]. The applications of the new result include the convergence of the best-response dynamics in the general version of the Crawford and Sobel model and in some versions of the Hotelling and Tiebout models.


2021 ◽  
Vol 10 (4) ◽  
Author(s):  
Chloe Partlow ◽  
Patricia Talarczyk

This study investigated the relationship between absurd humor in meme stills and the perceived humor among Generation Z students. Students of a high school in Northeast Ohio were given one of two seemingly identical surveys, each with a selection of six memes and individual Likert scales corresponding to the presented memes. A rubric was created with guidelines for visual components that was used to assign the presented memes an absurdity score with categories of “minimal absurdism,” “semi-absurd,” and “absurd.” Participants (n=298)  were asked to rank the memes on the Likert scale ranging from a value of 1—not at all funny to a maximum value of 5—extremely funny. Following a chi-squared test, we can be over 99% confident that there is a present relationship between absurdist humor content in meme stills and how humorous they are rated by Generation Z students. These findings can be applied to the usage of memes in marketing, an ever-increasing function of meme humor, to make advertisements and communication more effective.


2021 ◽  
Vol 26 (6) ◽  
pp. 1123-1143
Author(s):  
A. Mahdy ◽  
S.E. Ahmed ◽  
M.A. Mansour

This contribution gives a numerical investigation of buoyancy-driven flow of natural convection heat transfer and entropy generation of non-Newtonian hybrid nanofluid (Al2O3-Cu) within an enclosure square porous cavity. Hybrid nanofluids represent a novel type of enhanced active fluids. During the current theoretical investigation, an actual available empirical data for both thermal conductivity and dynamic viscosity of hybrid nanofluids are applied directly. Numerical simulation have been implemented for solid nanoparticles, the volumetric concentration of which varies from 0.0% (i.e., pure fluid) to 0.1% of hybrid nanofluids. Heat and sink sources are situated on a part of the left and right sides of the cavity with length B, while the upper and bottom horizontal sides are kept adiabatic. The stated partial differential equations describing the flow are mutated to a dimensionless formulas, then solved numerically via the help of an implicit finite difference approach. The acquired computations are given in terms of streamlines, isotherms, isomicrorotations, isoconcentraions, local Began number, total entropy, local and mean Nusselt numbers. The data illustrates that variations of ratio of the average Nusselt number to the averageNusselt of pure fluid Num+ is a decreasing function of Ha and φ, while e+ is an increasing function of Ha and φ parameters of hybrid nanofluid.


Shock Waves ◽  
2021 ◽  
Author(s):  
C. J. Aouad ◽  
W. Chemissany ◽  
P. Mazzali ◽  
Y. Temsah ◽  
A. Jahami

AbstractThe evolution of the fireball resulting from the August 2020 Beirut explosion is traced using amateur videos taken during the first 400 ms after the detonation. Thirty-nine frames separated by 16.66–33.33 ms are extracted from six different videos located precisely on the map. Time evolution of the shock wave radius is traced by the fireball at consecutive time moments until about $$ t \approx 170$$ t ≈ 170  ms and a distance $$ d \approx 128$$ d ≈ 128  m. Pixel scales for the videos are calibrated by de-projecting the existing grain silos building, for which accurate as-built drawings are available, using the length, the width, and the height and by defining the line-of-sight incident angles. In the distance range $$ d \approx $$ d ≈ 60–128 m from the explosion center, the evolution of the fireball follows the Sedov–Taylor model with spherical geometry and an almost instantaneous energy release. This model is used to derive the energy available to drive the shock front at early times. Additionally, a drag model is fitted to the fireball evolution until its stopping at a time $$ t \approx 500$$ t ≈ 500  ms at a distance $$d \approx 145\pm 5$$ d ≈ 145 ± 5  m. Using the derived TNT equivalent yield, the scaled stopping distance reached by the fireball and the shock wave-fireball detachment epoch within which the fireball is used to measure the shock wave are in excellent agreement with other experimental data. A total TNT equivalence of $$ 200\pm 80\,\mathrm{t}$$ 200 ± 80 t at a distance $$ d \approx 130$$ d ≈ 130  m is found. Finally, the dimensions of the crater size taken from a hydrographic survey conducted 6 days after the explosion are scaled with the known correlation equations yielding a close range of results. A recent published article by Dewey (Shock Waves 31:95–99, 2021) shows that the Beirut explosion TNT equivalence is an increasing function of distance. The results of the current paper are quantitatively in excellent agreement with this finding. These results present an argument that the actual mass of ammonium nitrate that contributed to the detonation is much less than the quantity that was officially claimed available.


Author(s):  
Tejas Bodas ◽  
Ayalvadi Ganesh ◽  
D. Manjunath

AbstractCongestion externalities are a well-known phenomenon in transportation and communication networks, healthcare etc. Optimization by self-interested agents in such settings typically results in equilibria which are sub-optimal for social welfare. Pigouvian taxes or tolls, which impose a user charge equal to the negative externality caused by the marginal user to other users, are a mechanism for combating this problem. In this paper, we study a non-atomic congestion game in which heterogeneous agents choose amongst a finite set of heterogeneous servers. The delay at a server is an increasing function of its load. Agents differ in their sensitivity to delay. We show that, while selfish optimisation by agents is sub-optimal for social welfare, imposing admission charges at the servers equal to the Pigouvian tax causes the user equilibrium to maximize social welfare. In addition, we characterize the structure of welfare optimal and of equilibrium allocations.


Materials ◽  
2021 ◽  
Vol 14 (17) ◽  
pp. 5081
Author(s):  
Bożena Łosiewicz ◽  
Patrycja Osak ◽  
Joanna Maszybrocka ◽  
Julian Kubisztal ◽  
Sylwia Bogunia ◽  
...  

Calcium phosphate (CaP) coatings are able to improve the osseointegration process due to their chemical composition similar to that of bone tissues. Among the methods of producing CaP coatings, the electrochemically assisted deposition (ECAD) is particularly important due to high repeatability and the possibility of deposition at room temperature and neutral pH, which allows for the co-deposition of inorganic and organic components. In this work, the ECAD of CaP coatings from an acetate bath with a Ca:P ratio of 1.67, was developed. The effect of the ECAD conditions on CaP coatings deposited on commercially pure titanium grade 4 (CpTi G4) subjected to sandblasting and autoclaving was presented. The physicochemical characteristics of the ECAD-derived coatings was carried out using SEM, EDS, FTIR, 2D roughness profiles, and amplitude sensitive eddy current method. It was showed that amorphous calcium phosphate (ACP) coatings can be obtained at a potential −1.5 to −10 V for 10 to 60 min at 20 to 70 °C. The thickness and surface roughness of the ACP coatings were an increasing function of potential, time, and temperature. The obtained ACP coatings are a precursor in the process of apatite formation in a simulated body fluid. The optimal ACP coating for use in dentistry was deposited at a potential of −3 V for 30 min at 20 °C.


2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Sh. Rezapour ◽  
M. Q. Iqbal ◽  
A. Hussain ◽  
A. Zada ◽  
S. Etemad

The main concentration of the present research is to explore several theoretical criteria for proving the existence results for the suggested boundary problem. In fact, for the first time, we formulate a new hybrid fractional differential inclusion in the φ -Caputo settings depending on an increasing function φ subject to separated mixed φ -hybrid-integro-derivative boundary conditions. In addition to this, we discuss a special case of the proposed φ -inclusion problem in the non- φ -hybrid structure with the help of the endpoint notion. To confirm the consistency of our findings, two specific numerical examples are provided which simulate both φ -hybrid and non- φ -hybrid cases.


2021 ◽  
Vol 263 (5) ◽  
pp. 1261-1266
Author(s):  
Modeste Assemien ◽  
Alain Le Bot

This paper presents an experiment to measure the vibration level generated when a light solid slides over a dry and rough surface. The experimental set-up is based on linear constant motion with speed range from 1 to 1000 mm/sec. The aim is to study the evolution of the vibration level as a function of the sliding speed and the friction area. Measurements show that the vibration level is a logarithmic increasing function of the sliding speed with a transient velocity. It is also observed that two regimes exist for the evolution of vibration level versus apparent contact area. On the one hand the vibration level is proportional to the friction area, but on the other hand this level is constant.


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