Normal subgroup based power graph of finite groups

Ricerche di Matematica - Let G be a finite group and $$N \unlhd G$$ . The normal subgroup based power graph of G, $$\Gamma _N(G)$$ , is an undirected graph with vertex set $$(G{\setminus }N) \cup...     

New Developments on Operator Reverse AM-GM Inequality for Positive Linear Maps

Acta Mathematica Sinica, English Series - In this research article, we shall give some reverse Arithmetic-Geometric mean inequalities for unital positive linear maps on Hilbert space operators...     

Prediction of flow stress at hot working condition

A mathematical model has been developed to determine flow stress at hot deformation condition. The proposed model is capable of including work softening due to dynamic phase transformations as well as the effect of temperature and strain rate variation on flow stress utilizing the additivity rule for strain. To verify the model, hot compression tests for two grades of steels has been carried out. The comparison between the experimental and theoretical results confirms the validity of the model.     

Delayed feedback control of time-delayed chaotic systems: Analytical approach at Hopf bifurcation

This Letter is concerned with bifurcation and chaos control in scalar delayed differential equations with delay parameter τ. By linear stability analysis, the conditions under which a sequence of Hopf bifurcation occurs at the equilibrium points are obtained. The delayed feedback controller is used to stabilize unstable periodic orbits. To find the controller delay, it is chosen such that the Hopf bifurcation remains unchanged. Also, the controller feedback gain is determined such that the corresponding unstable periodic orbit becomes stable. Numerical simulations are used to verify the analytical results.     

The Phase Transition in Statistical Models Defined on Farey Fractions

We consider several statistical models defined on the Farey fractions. Two of these models may be regarded as spin chains, with long-range interactions, while another arises in the study of multifractals associated with chaotic maps exhibiting intermittency. We prove that these models all have the same free energy. Their thermodynamic behavior is determined by the spectrum of the transfer operator (Ruelle–Perron–Frobenius operator), which is defined using the maps (presentation functions) generating the Farey tree. The spectrum of this operator was completely determined by Prellberg. It follows that these models have a second-order phase transition with a specific heat divergence of the form C [ ln² ]^–1. The spin chain models are also rigorously known to have a discontinuity in the magnetization at the phase transition.     

Magnetocaloric effect and multifunctional properties of Ni–Mn-based Heusler alloys

The studies of magnetocaloric properties, phase transitions, and phenomena related to magnetic heterogeneity in the vicinity of the martensitic transition (MT) in Ni–Mn–In and Ni–Mn–Ga off-stoichiometric Heusler alloys are summarized. The crystal structure, magnetocaloric effect (MCE), and magnetotransport properties were studied for the following alloys: Ni₅₀Mn_50−xIn_x, Ni_50−xCo_xMn₃₅In₁₅, Ni₅₀Mn_35−xCo_xIn₁₅, Ni₅₀Mn₃₅In₁₄Z (Z=Al, Ge), Ni₅₀Mn₃₅In_15−xSi_x, Ni_50−xCo_xMn_25+yGa_25−y, and Ni_50–xCo_xMn_32−yFeyGa₁₈. It was found that the magnetic entropy change, ΔS, associated with the inverse MCE in the vicinity of the temperature of the magneto-structural transition, TM, persists in a range of (125-5) J/(kg K) for a magnetic field change ΔH=5 T. The corresponding temperature varies with composition from 143 to 400 K. The MT in Ni₅₀Mn_50−xIn_x (x=13.5) results in a transition between two paramagnetic states. Associated with the paramagnetic austenite-paramagnetic martensite transition ΔS=24 J/(kg K) was detected for ΔH=5 T at T=350 K. The variation in composition of Ni₂MnGa can drastically change the magnetic state of the martensitic phase below and in the vicinity of TM. The presence of the martensitic phase with magnetic moment much smaller than that in the austenitic phase above TM leads to the large inverse MCE in the Ni₄₂Co₈Mn_32−yFeyGa₁₈ system. The adiabatic change of temperature (ΔT_ad) in the vicinity of TC and TM of Ni₅₀Mn₃₅In₁₅ and Ni₅₀Mn₃₅In₁₄Z (Z=Al, Ge) was found to be ΔT_ad=−2 K and 2 K for ΔH=1.8 T, respectively. It was observed that |ΔT_ad|≈1 K for ΔH=1 T for both types of transitions. The results on resistivity, magnetoresistance, Hall resistivity in some In-based alloys are discussed.     

Magnetic nondestructive technology for detection of tempered martensite embrittlement

A nondestructive eddy current technique is used to evaluate tempered martensite embrittlement in 4340 AISI steels after quench and tempering in the range 240–550 °C. A relation between the responses of the magnetic induction (normalized impedance of the coil) and destructive Charpy impact test results has been established. The study shows that the eddy current method could be used to separate brittle parts due to the microstructure changes.     

Abundant Exact Traveling Wave Solutions of Generalized Bretherton Equation via Improved (G′/G)-Expansion Method

In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves.