We give an informal exposition of pushforwards and orientations in generalized cohomology theories in the language of spectra. The whole note can be seen as an attempt at convincing the reader that Todd classes in Grothendieck–Hirzebruch–Riemann–Roch type formulas are not Devil’s appearances but rather that things just go in the most natural possible way. 相似文献
The machining process is primarily used to remove material using cutting tools. Any variation in tool state affects the quality of a finished job and causes disturbances. So, a tool monitoring scheme (TMS) for categorization and supervision of failures has become the utmost priority. To respond, traditional TMS followed by the machine learning (ML) analysis is advocated in this paper. Classification in ML is supervised based learning method wherein the ML algorithm learn from the training data input fed to it and then employ this model to categorize the new datasets for precise prediction of a class and observation. In the current study, investigation on the single point cutting tool is carried out while turning a stainless steel (SS) workpeice on the manual lathe trainer. The vibrations developed during this activity are examined for failure-free and various failure states of a tool. The statistical modeling is then incorporated to trace vital signs from vibration signals. The multiple-binary-rule-based model for categorization is designed using the decision tree. Lastly, various tree-based algorithms are used for the categorization of tool conditions. The Random Forest offered the highest classification accuracy, i.e., 92.6%.
A kinetic study of the reactions of potentially bioactive 2-amino-4-arylthiazoles with highly reactive 4,6-dinitrobenzofuroxan (DNBF) is reported herein in acetonitrile solution. The complexation reaction was followed by recording the UV–vis spectra with time at λmax = 482 nm. Electronic effects of substituents influencing the rate of reaction have been studied using structure-reactivity relationships. It is shown that the Hammett plot relative to the reaction of DNBF with 2-amino-4-(4-chlorophenyl)thiazole exhibit positive deviation from the log k1 versus σ correlation, while it showed excellent linear correlation in terms of Yukawa–Tsuno equation. It has be noticed that the nonlinear Hammett plot observed for 2-amino-4-(4-chlorophenyl) thiazole is not attributed to a change in rate-determining step but is due to nature of electronic effect of substituent caused by the resonance of stabilization of substrates. The second-order rate constant (k1) relating to the bond C–C and C-N forming step of the complexation processes of DNBF with 4-substituted-aminothiazoles and 2-amino-5-methyl-4-phenylthiazole, respectively, is fit into the linear relationship log k = sN (N + E), thereby permitting the assessment of the nucleophilicity parameter (N) of the 2-amino-4-arylthiazoles of the range (4.90 < N < 6.85). 2-amino-4-arylthiazoles is subsequently ranked by positioning its reactivity on the general nucleophilicity scale developed recently by Mayr and coworkers (2003) leading an interesting and a direct comparison over a large domain of π-, σ -, and n-nucleophiles. The global electrophilicity/nucleophilicity reactivity indexes of the 2-amino-4-arylthiazoles have been investigated by means of a density functional theory (DFT) method. . 相似文献
Transformation of flow turbulence structure with cavitation occurrence, determination of the flow conditions favorable for nucleation of cavitation bubbles, influence of the statistical structure of turbulence on this process and the inverse effect of cavitation on the flow dynamics are challenging problems in modern fluid mechanics. The paper reports on the results of statistical processing of the velocity fields measured by a PIV technique in cavitating flow over a 2D symmetric hydrofoil for four flow conditions, starting from a cavitation-free regime and finishing by unsteady cloud cavitation. We analyze basic information on the statistical structure of velocity fluctuations in the form of histograms and Q-Q diagrams along with profiles of the mean velocity and turbulent kinetic energy. The research reveals that the flow turbulence pattern and distributions of turbulent fluctuations change significantly with the cavitation development. Under unsteady cloud cavitation conditions, the probability density function of the fluctuating velocity has a two-mode distribution, which indicates switching of two alternating flow conditions in a region above the hydrofoil aft part due to periodic passing of cavitation clouds. Behaviors of the mean and most probable velocities unexpectedly appear to be different with a monotonous increase of the incoming flow velocity. This finding must be caused by modification of the skewness coefficient of the fluctuating velocity. 相似文献
We consider the random‐cluster model (RCM) on with parameters p∈(0,1) and q ≥ 1. This is a generalization of the standard bond percolation (with edges open independently with probability p) which is biased by a factor q raised to the number of connected components. We study the well‐known Fortuin‐Kasteleyn (FK)‐dynamics on this model where the update at an edge depends on the global geometry of the system unlike the Glauber heat‐bath dynamics for spin systems, and prove that for all small enough p (depending on the dimension) and any q>1, the FK‐dynamics exhibits the cutoff phenomenon at with a window size , where λ∞ is the large n limit of the spectral gap of the process. Our proof extends the information percolation framework of Lubetzky and Sly to the RCM and also relies on the arguments of Blanca and Sinclair who proved a sharp mixing time bound for the planar version. A key aspect of our proof is the analysis of the effect of a sequence of dependent (across time) Bernoulli percolations extracted from the graphical construction of the dynamics, on how information propagates. 相似文献
In order to find out whether the geomagnetic storms and large-mega earthquakes are correlated or not, statistical studies based on Superposed Epoch Analysis (SEA), significance analysis, and Z test have been applied to the Dst index data and M ≥ 7.0 global earthquakes during 1957–2020. The results indicate that before M ≥ 7.0 global earthquakes, there are clearly higher probabilities of geomagnetic storms than after them. Geomagnetic storms are more likely to be related with shallow earthquakes rather than deep ones. Further statistical investigations of the results based on cumulative storm hours show consistency with those based on storm days, suggesting that the high probability of geomagnetic storms prior to large-mega earthquakes is significant and robust. Some possible mechanisms such as a reverse piezoelectric effect and/or electroosmotic flow are discussed to explain the statistical correlation. The result might open new perspectives in the complex process of earthquakes and the Lithosphere-Atmosphere-Ionosphere (LAI) coupling. 相似文献
The critical dimension necessary for a flame to propagate in suspensions of fuel particles in oxidiser is studied analytically and numerically. Two types of models are considered: First, a continuum model, wherein the individual particulate sources are not resolved and the heat release is assumed spatially uniform, is solved via conventional finite difference techniques. Second, a discrete source model, wherein the heat diffusion from individual sources is modelled via superposition of the Green's function of each source, is employed to examine the influence of the random, discrete nature of the media. Heat transfer to cold, isothermal walls and to a layer of inert gas surrounding the reactive medium are considered as the loss mechanisms. Both cylindrical and rectangular (slab) geometries of the reactive medium are considered, and the flame speed is measured as a function of the diameter and thickness of the domains, respectively. In the continuum model with inert gas confinement, a universal scaling of critical diameter to critical thickness near 2:1 is found. In the discrete source model, as the time scale of heat release of the sources is made small compared to the interparticle diffusion time, the geometric scaling between cylinders and slabs exhibits values greater than 2:1. The ability of the flame in the discrete regime to propagate in thinner slabs than predicted by continuum scaling is attributed to the flame being able to exploit local fluctuations in concentration across the slab to sustain propagation. As the heat release time of the sources is increased, the discrete source model reverts back to results consistent with the continuum model. Implications of these results for experiments are discussed. 相似文献