Doubly commuting submodules of the Hardy module over polydiscs

In this note we establish a vector-valued version of Beurling's Theorem (the Lax-Halmos Theorem) for the polydisc. As an application of the main result, we provide necessary and sufficient conditions for the completion problem in $H^\infty(\mathbb{D}^n)$.Comment: 14 pages, revised, to appear in Studia Mathematic

SAR Analysis Using a Dipole Antenna in a Non-layered and Multi-layered Human Head Model

The public complaints about health are on the rise as a result of mobile phone usage. Limits on the radiation strength emitted by these devices have already been recommended by standard bodies such as The Federal Communication Commission (FCC) of the United States and the International Commission on Non-Ionizing Radiation Protection (ICNIRP) to safeguard public from excessive exposure to electromagnetic fields. Some recent research have found that long-duration use of calls on mobile phones increases the incidence of health hazards and has negative consequences. After survey the research on investigation of specific absorption rate (SAR) in the human head is becoming increasingly essential. In proposed work, Investigations were done on how human head model and electromagnetic source interacted. The goal of this work is to demonstrate that the one layer head model is not a good model rather appear to be unreliable to evaluate SAR since genuine human skull tissue is not modelled in the same way. But investigation of SAR in six layers (Brain, CSF, Dura, Bone, Fat and Skin) human head appears better and reliable. Affection to the six layered human head may be dominant when exposed to electromagnetic (EM) fields

The Levy-Lieb embedding of density functional theory and its Quantum Kernel: Illustration for the Hubbard Dimer using near-term quantum algorithms

The constrained-search formulation of Levy and Lieb provides a concrete mapping from N-representable densities to the space of N-particle wavefunctions and explicitly defines the universal functional of density functional theory. We numerically implement the Levy-Lieb procedure for a paradigmatic lattice system, the Hubbard dimer, using a modified variational quantum eigensolver approach. We demonstrate density variational minimization using the resulting hybrid quantum-classical scheme featuring real-time computation of the Levy-Lieb functional along the search trajectory. We further illustrate a fidelity based quantum kernel associated with the density to pure-state embedding implied by the Levy-Lieb procedure and employ the kernel for learning observable functionals of the density. We study the kernel's ability to generalize with high accuracy through numerical experiments on the Hubbard dimer.Comment: 9 pages, 6 figure

Magnetic mirror cavities as THz radiation sources and a means of quantifying radiation friction

We propose a radiation source based on a magnetic mirror cavity. Relativistic electrons are simulated entering the cavity and their trajectories and resulting emission spectra are calculated. The uniformity of the particle orbits is found to result in a frequency comb in terahertz range, the precise energies of which are tuneable by varying the electron's $\gamma$-factor. For very high energy particles radiation friction causes the spectral harmonics to broaden and we suggest this as a possible way to verify competing classical equations of motion.Comment: 8 pages, 10 figure

A Comparative Analysis of Wound Closure Techniques in Uncomplicated Open Inguinal Hernia Surgery: Sutures vs. Skin Staplers

  Objective: This study compared the results of wound closure with skin staplers and traditional sutures in uncomplicated open inguinal hernia surgery. Methods: An 18-month prospective cohort study was carried out in a tertiary care facility. Patients (n = 100) who met the eligibility requirements were randomly assigned to one of two groups: suture (n = 50) or skin stapler (n = 50). We evaluated wound infection rates, wound healing times, postoperative pain levels, and aesthetic results. Chi-squared tests, t-tests, and Mann-Whitney U tests were used in the statistical analysis. Results: Skin staplers demonstrated lower wound infection rates (2% vs. 10%) and faster wound healing (10.5 ± 1.8 days vs. 14.2 ± 2.1 days) compared to sutures. Postoperative pain scores were consistently lower in the skin stapler group at 24 hours (2.4 ± 0.8 vs. 3.7 ± 1.2), 1 week (1.4 ± 0.6 vs. 2.1 ± 0.9), and 4 weeks (0.6 ± 0.3 vs. 0.9 ± 0.4) post-surgery. Skin staplers with a higher percentage of "excellent" results (54% vs. 14%) had better cosmetic results. Conclusion: In uncomplicated open inguinal hernia surgery, skin staplers are superior to conventional sutures in terms of lower wound infection rates, quicker wound healing, decreased postoperative pain, and enhanced cosmetic results. Surgeons’ ought to think about how skin staplers could improve patient satisfaction and outcomes. Inguinal hernia surgery wound closure techniques may be improved with further study and practical practice