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On cumulative residual extropy of coherent and mixed systems
No full textIn system reliability, coherent systems play a central role since without them any system is considered flawed. A system is coherent if all the components are relevant to that system i.e. functioning of every component has an effect in the functioning of the system and the structure of the system is monotone. Monotone structure means that improving any component will not deteriorate the system. A mixed system is a stochastic mixture of coherent systems and any coherent system is a special case of a mixed system. In reliability engineering, one major problem is to compare various coherent and mixed systems so that the better system can be used to increase the overall reliability. Another important problem is to measure the complexity of systems. A highly complex system will naturally have a higher running and maintenance cost associated with it and it is desirable for a reliability engineer to have an understanding regarding the complexity of systems beforehand. In this paper, we address these two problems from an information theoretic approach. Extropy is a measure of information which is the dual of the famous Shannon entropy measure. Recently, a new measure related to extropy, called cumulative residual extropy (CREx), was introduced in the literature by Jahanshahi et al. (Probab Eng Inf Sci 1–21, 2019). This measure is based on the survival function of the underlying random variable and it has some advantages over extropy measure. In this work, we analyze the CREx measure for coherent and mixed systems and develop some comparison results among systems. We also obtain some bounds of CREx of coherent and mixed systems consisting of independent and identically distributed (iid) and dependent and identically distributed (d.i.d.) components. We propose a new divergence measure to calculate the complexity of systems having iid components. Also, we introduced a new discrimination measure to compare various coherent and mixed systems when pairwise comparisons by usual stochastic order is not possible. Finally, we discuss analysis of the CREx measure of coherent systems having heterogeneous components. We also provide applications involving redundancy allocation. Various numerical examples are considered for illustrative purposes
Optimization and characterization of boric acid powder mixed electrical discharge machining of Ti-6Al-4V ELI
No full textThe powder mixed electrical discharge machining (PMEDM) process is used for enhancing machining efficiency and improving the surface characteristics of the workpiece compared to normal EDM. The present study evaluates the effect of boric acid powder mixed in deionized water in PMEDM of Ti-6Al-4V ELI (extra low interstitial). The PMEDM process is assessed by evaluating material removal rate (MRR) and surface roughness (SR) at varying powder concentration (PC), current and pulse duration (Ton). Boric acid PMEDM exhibits advantageous for both MRR and SR, where MRR increases and SR decreases with an increase in PC. To simultaneously achieve higher MRR and lower SR, the grey-fuzzy logic method is employed. Initially, the raw input data is normalized into grey numbers and a single index is obtained through grey relational analysis. Subsequently, triangular membership functions are assigned to the inputs and output. Fuzzy logic rules are then formulated, and grey fuzzy relational grade (GFRG) is calculated for each condition. The optimum condition (GFRG = 0.787) is attained at 15 g/l PC, 9 A current and 106 µs Ton, resulting in a 63% improvement compared to the initial condition. At the optimum condition, MRR increased by 145% and SR decreased by 29% compared to the initial condition. The effect of boric acid in PMEDM can be visualized through the formation of smooth surfaces, exhibiting reduced SR, smaller and shallower craters, and fewer debris and globules. Additionally, the boric acid PMEDM experiments resulted in the formation of a hard TiB phase on Ti-6Al-4V, thus improving its wear resistance
Proterozoic mobile belts-magmatism, metamorphism, geochronology and tectonics in the context of formation of the Greater Indian Landmass
No full textIn this work, we make a review of the published literature on the magmatic, metamorphic, geochronological and tectonic evolutionary history of the Proterozoic mobile belts of western (cf. Aravalli-Delhi Mobile Belt), central (cf. Central Indian Tectonic Zone), eastern (cf. Chotanagpur Gneissic Complex), north-eastern (cf. Shillong-Plateau Gneissic Complex) and eastern (cf. Eastern Ghats Belt) India. We collate the key findings in this review to advocate a model of three-stage orogenesis (at ca. 2.1–1.7 Ga, ca.1.75–1.54 Ga and ca.1.06–0.90 Ga) to produce the final configuration of the Greater Indian Landmass as a miniature Rodinia
Quantum symmetry in multigraphs (part II)
No full textThis paper is a continuation of Ref. 7. In this paper, we give an explicit construction of a non-Bichon type co-action on a multigraph that is, it preserves quantum symmetry of (V,E) in our sense but not always in Bichon\u27s sense.2 This construction itself is motivated from automorphisms of quantum graphs
Ramified covering maps of singular curves and stability of pulled back bundles
No full textLet f:X⟶Y be a generically smooth nonconstant morphism between irreducible projective curves, defined over an algebraically closed field, which is étale on an open subset of Y that contains both the singular locus of Y and the image, in Y, of the singular locus of X. We prove that the following statements are equivalent: The homomorphism of étale fundamental groups (Formula presented.) induced by f is surjective. There is no nontrivial étale covering ϕ:Y′⟶Y admitting a morphism q:X⟶Y′ such that ϕ∘q=f. The fiber product X×YX is connected. dimH0(X,f∗f∗OX)=1. OY⊂f∗OX is the maximal semistable subsheaf. The pullback f∗E of every stable sheaf E on Y is also stable
Registration of CT and MR image in multi-resolution framework using embedded entropy and feature fusion
No full textIn this paper, a new scheme for the registration of brain CT and noisy MR images is proposed in a multi-resolution framework based on the notions of embedded entropy and nonlinear combination of the mutual information (MI) corresponding to Renyi’s and Tsallis entropy. Gabor and Sobel’s features are fused probabilistically and the registration is carried out in fused feature space. The weights for the fusion of the two distributions are obtained using the Bhattacharyya distance as the similarity measure. Registration parameter is obtained at different resolutions by maximising the combined mutual information obtained at different resolutions. The proposed algorithm is tested with the real patient data obtained from Retrospective Image Registration Evaluation (RIRE) database. It is found that the optimum registration parameter obtained at a low resolution of (64 × 64) has high accuracy. The proposed scheme exhibits improved performance as compared to other existing algorithms
Revisiting Dynamic Scheduling of Control Tasks: A Performance-Aware Fine-Grained Approach
No full textModern cyber-physical systems (CPSs) employ an increasingly large number of software control loops to enhance their autonomous capabilities. Such large task sets and their dependencies may lead to deadline misses caused by platform-level timing uncertainties, resource contention, etc. To ensure the schedulability of the task set in the embedded platform in the presence of these uncertainties, there exist co-design techniques that assign task periodicities such that control costs are minimized. Another line of work exists that addresses the same platform schedulability issue by skipping a bounded number of control executions within a fixed number of control instances. Considering that control tasks are designed to perform robustly against delayed actuation (due to deadline misses, network packet drops etc.) a bounded number of control skips can be applied while ensuring certain performance margin. Our work combines these two control scheduling co-design disciplines and develops a strategy to adaptively employ control skips or update periodicities of the control tasks depending on their current performance requirements. For this we leverage a novel theory of automata-based control skip sequence generation while ensuring periodicity, safety and stability constraints. We demonstrate the effectiveness of this dynamic resource sharing approach in an automotive Hardware-in-loop setup with realistic control task set implementations
Robust Statistical Modeling of Monthly Rainfall: The Minimum Density Power Divergence Approach
No full textStatistical modeling of monthly, seasonal, or annual rainfall data is an important research area in meteorology. These models play a crucial role in rainfed agriculture, where a proper assessment of the future availability of rainwater is necessary. The rainfall amount during a rainy month or a whole rainy season can take any positive value and some simple (one or two-parameter) probability models supported over the positive real line that are generally used for rainfall modeling are exponential, gamma, Weibull, lognormal, Pearson Type-V/VI, log-logistic, etc., where the unknown model parameters are routinely estimated using the maximum likelihood estimator (MLE). However, the presence of outliers or extreme observations is a common issue in rainfall data and the MLEs being highly sensitive to them often leads to spurious inference. Here, we discuss a robust parameter estimation approach based on the minimum density power divergence estimator (MDPDE). We fit the above four parametric models to the detrended areally-weighted monthly rainfall data from the 36 meteorological subdivisions of India for the years 1951-2014 and compare the fits based on MLE and the proposed ‘optimum’ MDPDE; the superior performance of MDPDE is showcased for several cases. For all month-subdivision combinations, we discuss the best-fit models and median rainfall amounts
Role Reversals in a Tri-Trophic Prey–Predator Interaction System: A Model-Based Study Using Deterministic and Stochastic Approaches
No full textIt is frequently observed that adult members of prey species sometimes use their predation mechanism on juvenile members of predator species. Ecological literature describes this phenomenon as prey–predator role reversal dynamics.Numerous authors have observed and described the biological development behind this feeding behaviour. However, the dynamics of this role reversal have hardly been illustrated in the literature in a precise way. In this regard, we formulated an ecological model using the standard prey–predator interactions, allowing for a reverse feeding mechanism. The mathematical model consisted of a three-species food-web structure comprising the common prey, intermediate predator, and top predator. Note that a role-reversal mechanism was observed between the intermediate and top predators based on the scarcity of the prey population. However, we observed the most critical parameters had a significant effect on this reverse feeding behaviour. The bifurcation analysis is the primary criterion for this identification. The proposed deterministic model is then extended to its stochastic analogue by allowing for environmental influences on the tri-trophic food web structure. The conditional moment approach is applied to obtain the equilibrium distribution of populations and their conditional moments in the system. The stochastic setup analysis also supports the stability of this food chain structure, with some restricted conditions. Finally, to facilitate the interpretation of our mathematical results, we investigated it using numerical simulations
Second-order trace formulas
No full textKoplienko [Sib. Mat. Zh. 25 (1984), 62–71; English transl. in Siberian Math. J. 25 (1984), 735–743] found a trace formula for perturbations of self-adjoint operators by operators of Hilbert–Schmidt class (Formula presented.). Later, Neidhardt introduced a similar formula in the case of pairs of unitaries (Formula presented.) via multiplicative path in [Math. Nachr. 138 (1988), 7–25]. In 2012, Potapov and Sukochev [Comm. Math. Phys. 309 (2012), no. 3, 693–702] obtained a trace formula like the Koplienko trace formula for pairs of contractions by answering an open question posed by Gesztesy, Pushnitski, and Simon [Zh. Mat. Fiz. Anal. Geom. 4 (2008), no. 1, 63–107, 202; Open Question 11.2]. In this paper, we supply a new proof of the Koplienko trace formula in the case of pairs of contractions (Formula presented.), where the initial operator (Formula presented.) is normal, via linear path by reducing the problem to a finite-dimensional one as in the proof of Krein\u27s trace formula by Voiculescu [Oper. Theory Adv. Appl. 24 (1987) 329–332] and Sinha and Mohapatra [Proc. Indian Acad. Sci. Math. Sci. 104 (1994), no. 4, 819–853] and [Integral Equations Operator Theory 24 (1996), no. 3, 285–297]. Consequently, we obtain the Koplienko trace formula for a class of pairs of contractions using the Schäffer matrix unitary dilation. Moreover, we also obtain the Koplienko trace formula for a pair of self-adjoint operators and maximal dissipative operators using the Cayley transform. At the end, we extend the Koplienko–Neidhardt trace formula for a class of pairs of contractions (Formula presented.) via multiplicative path using the finite-dimensional approximation method