The noncommutative values of quantum observables

We discuss the notion of representing the values of physical quantities by the real numbers, and its limits to describe the nature to be understood in the relation to our appreciation that the quantum theory is a better theory of natural phenomena than its classical analog. Getting from the algebra of physical observables to their values for a fixed state is, at least for classical physics, really a homomorphic map from the algebra into the real number algebra. The limitation of the latter to represent the values of quantum observables with noncommutative algebraic relation is obvious. We introduce and discuss the idea of the noncommutative values of quantum observables and its feasibility, arguing that at least in terms of the representation of such a value as an infinite set of complex numbers, the idea makes reasonable sense theoretically as well as practically.     

Compact ellipse shaped patch with ground slotted broadband monopole patch antenna for head imaging applications

This paper represents an ellipse-shaped patch with a ground slotted broadband patch antenna for microwave head imaging systems. The proposed antenna constructs with a simple ellipse shaped square patch and modified slotted plane. The proposed design is very simple to fabricate and is enclosed in a microwave imaging system. The slotted patch, and the partial ground plane improves the antenna's efficiency, operating frequency range, and gain. The size of the proposed antenna is 70 × 60 × 1.5 mm³ with the electrical dimension being 0.277λ × 0.238λ × 0.006λ at a lower frequency of 1.19 GHz and connected to a 50Ω microstrip feeding line. This antenna is printed onto a low-cost FR-4 substrate whose relative permittivity is 4.4, and whose thickness is 1.5 mm. CST and HFSS software have been used for simulation and thereafter successful completion of the measurements and the fabrication. The comprehensive simulation exhibits that this design provides a bandwidth of 2.37 GHz (1.19 – 3.56 GHz) and 100% of the fractional bandwidths (% BW) with the reflection coefficient of <-10 dB. This antenna on FR-4 can produce an average gain of around 3.63 dBi with 5.95 dBi peak gain at whole operation frequencies. The prototype has a peak radiation efficiency of approximately 97% across the active frequency spectrum with 93% of average. The antenna does have an improved fidelity-factor (> 90 %) with a shorter group-delay. Several design modifications have been performed to get perfect, effective, and suitable results for microwave imaging applications. A 3D-realist Hugo head model is fitted with a single antenna and a 9-antenna array component to verify the performance of both the single antenna, and the configured array antenna. The antenna penetrates the brain human tissues satisfactorily. Across the operational range, the specific absorption rate (SAR) attains a limit of <1 W/kg. The analysis of both numeric and experimental evidence clearly indicates that the suggested antenna is ideal for microwave head-imaging implementations.     

Weak dissipation of electrostatic solitary structures in warm collisional pair-ion plasmas with non-Maxwellian electron population

The localized electrostatic structures with dissipation due to ion-neutral collisions in a symmetric warm pair-ion plasma in the presence of non-Maxwellian population of electrons are studied. The analytical model for ion dynamics is based on fluid equations and the evolution equation is derived by using the reductive perturbation scheme in the form of a damped Korteweg-de Vries equation. The parameter regime relevant to space-based observations and laboratory plasmas is considered and time evolution of the propagating ion-acoustic soliton is discussed. The energetic-particles-driven properties of soliton for various spectral indices, dissipation, ion temperature, and density are illustrated with comparison to the thermal mode for Boltzmann distribution of electrons.     

Investigation of tiny jet locations effect in a sudden expansion duct for high-speed flows control using experimental and optimization methods

Meccanica - The present research focuses on dynamic flow control management using tiny jets with three combinations; the first one located at 90° intervals of the base, the second one located...     

Benzothiazole Pyrazoline: Acid-Switchable Absorption and Fluorescence of Photoinduced Electron Transfer (PET)

Journal of Fluorescence - Acid-responsive fluorescent compounds were prepared by introducing an ortho-hydroxyphenyl to pyrazoline with a benzothiazole backbone. These compounds demonstrated normal...     

Ground States and Phase Transition of the λ Model on the Cayley Tree

We consider the λ model, a generalization of the Potts model, with spin values {1, 2, 3} on the order-two Cayley tree. We describe the model ground states and prove that translation-invariant Gibb measures exist, which means that a phase transition exists. We establish that two-periodic Gibbs measures exist.