In this paper, we study some limit properties and inequalities involving the degenerate exponential function. Utilizing analytical methods, we also obtain some monotonic properties involving the ...function.
We prove a dichotomy for o‐minimal fields R$\mathcal {R}$, expanded by a T$T$‐convex valuation ring (where T$T$ is the theory of R$\mathcal {R}$) and a compatible monomial group. We show that if T$T$ ...is power bounded, then this expansion of R$\mathcal {R}$ is model complete (assuming that T$T$ is), it has a distal theory, and the definable sets are geometrically tame. On the other hand, if R$\mathcal {R}$ defines an exponential function, then the natural numbers are externally definable in our expansion, precluding any sort of model‐theoretic tameness.
This paper retrieves new periodic solitary wave solutions for the (3+1)-dimensional extended Jimbo–Miwa equations, based on the Hirota bilinear method, by utilizing Maple software. As a result, the ...Hirota bilinear method is successfully employed and acquired several classes of solitary wave solutions in terms of a new combination of exponential function, trigonometric function and hyperbolic functions. All solutions have been verified back into its corresponding equation by Maple. We depicted the physical explanation of the extracted solutions with the free choice of the different parameters by plotting some 3D and 2D illustrations. Finally, it has been illustrated that the executed method is robust and more efficient than other methods and the obtained solutions are trustworthy in the applied sciences.
Abstract
With the spread of lubricating oils, the usage of viscosity becomes more and more significant in various industries. This essay is used to determine the relationship between viscosity and ...the change of concentration and temperature to avoid problems during production process. This research uses the high-degree function and exponential function to simulate the change trend of viscosity due to the two variables. Through research, the author discovered the exponential relationship between the temperature as well as concentration and viscosity of lubricating oils and other complex fluids. Based on the results of this research, the enterprise can also avoid excessive wear of the machine and high waste in the production process.
A single-photon source is an enabling technology in device-independent quantum communication
, quantum simulation
, and linear optics-based
and measurement-based quantum computing
. These ...applications employ many photons and place stringent requirements on the efficiency of single-photon creation. The scaling on efficiency is typically an exponential function of the number of photons. Schemes taking full advantage of quantum superpositions also depend sensitively on the coherence of the photons, that is, their indistinguishability
. Here, we report a single-photon source with a high end-to-end efficiency. We employ gated quantum dots in an open, tunable microcavity
. The gating provides control of the charge and electrical tuning of the emission frequency; the high-quality material ensures low noise; and the tunability of the microcavity compensates for the lack of control in quantum dot position and emission frequency. Transmission through the top mirror is the dominant escape route for photons from the microcavity, and this output is well matched to a single-mode fibre. With this design, we can create a single photon at the output of the final optical fibre on-demand with a probability of up to 57% and with an average two-photon interference visibility of 97.5%. Coherence persists in trains of thousands of photons with single-photon creation at a repetition rate of 1 GHz.
In the current article, we consider certain subfamilies S e ∗ and C e of univalent functions associated with exponential functions which are symmetric along real axis in the region of open unit disk. ...For these classes our aim is to find the bounds of Hankel determinant of order three. Further, the estimate of third Hankel determinant for the family S e ∗ in this work improve the bounds which was investigated recently. Moreover, the same bounds have been investigated for 2-fold symmetric and 3-fold symmetric functions.
This paper focuses on the generalized Calogero–Bogoyavlenskii–Schiff equation to extract new complex solutions by using two analytical methods, namely, Bernoulli sub-equation function method, ...Modified exponential function method. For better understanding of physical meanings of solutions, simulations are reported by using a computational package program. Moreover, strain conditions for validity of complex solutions are also archived. Finally, a conclusion part completes the paper by mentioning the novelties of paper.
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