Groups of Order 2048 with Three Generators and Three Relations

It is shown that there are exactly seventy-eight 3-generator 2- groups of order 2^11 with trivial Schur multiplier. We then give 3-generator, 3-relation presentations for forty-eight of them proving that these groups have deficiency zero

Heat and mass transfer in membrane distillation used for desalination with slip flow

A theoretical model for the transport phenomena in an air gap membrane distillation is presented. The model is based on the conservation equations for the mass, momentum, energy and species within the feed water solution as well as on the mass and energy balances on the membrane sides. The slip flow occurs due to the hydrophobic properties of the membrane. The slip boundary condition applied on the feed saline solution-membrane interface is taken into consideration showing its effects on process parameters particularly permeate flow, heat transfer coefficient and thermal efficiency. The theoretical model was validated with available experimental data and was found to be in good agreement especially when the slip condition is introduced. Increasing slip length from zero to 200 μm was found to increase the permeate flux and the thermal efficiency by 33% and 1.7% respectively

Near-Term Quantum Algorithms for Classical Sampling

In the current era of noisy intermediate-scale quantum devices, quantum sampling algorithms have been of great interest as they permit errors in their execution while maintaining their advantage over classical counterparts [26]. However, the sampling problems considered often do not possess immediate practical relevance. This thesis explores two quantum algorithms for applicable classical sampling problems that can be implemented on today’s quantum devices. Specifically, we are considering algorithms to sample from a Boltzmann distribution of a classical Hamiltonian. This sampling task is of significant importance in the fields of statistical physics, machine learning, and optimization. The first such algorithm adiabatically prepares a quantum state which encodes the desired Boltzmann distribution [44]. Projectively measuring this state then produces uncorrelated samples from the desired distribution. The state preparation time scaling of this algorithm can be related to the properties of quantum phase transitions, giving physical insights into the mechanism of speedups found. Numerical investigations of the algorithmic performance on the Ising chain are reproduced, showing a quadratic improvement over a classical Markov chain Monte Carlo (MCMC) method. On the same model, counterdiabatic driving protocols are explored with the limitation of local driving terms. It is shown numerically this restriction of local driving terms leads to unfavourable scaling of the state preparation time. Next, the quantum-enhanced Markov Chain Monte Carlo algorithm is explored [23]. This hybrid algorithm creates a Markov chain over the classical configuration space, where new configurations are proposed through a projectively measured quantum evolution. This algorithm has guaranteed convergence, independent of the quality of the evolution, making it an algorithm suited for near-term implementation. The performance of this algorithm on the Sherrington-Kirkpatrick model is numerically reproduced, showing faster mixing time than classical MCMC in the low-temperature limit. Bottlenecks of this chain are then explored for the Ising chain, giving an analytic bound on performance showing the algorithmic advantage found for small systems numerically persists for larger system sizes. Finally, this algorithm is tested numerically on the maximum independent set problem, which is native to an array of Rydberg atoms and has been experimentally realized on current quantum devices [12]. Our findings did not indicate any advantage of the quantumenhanced MCMC algorithm over classical algorithms for the limited number of numerically accessible system sizes

Finding the Dynamics of an Integrable Quantum Many-Body System via Machine Learning

We study the dynamics of the Gaudin magnet ("central-spin model") using machine-learning methods. This model is of practical importance, e.g., for studying non-Markovian decoherence dynamics of a central spin interacting with a large bath of environmental spins and for studies of nonequilibrium superconductivity. The Gaudin magnet is also integrable, admitting many conserved quantities: For $N$ spins, the model Hamiltonian can be written as the sum of $N$ independent commuting operators. Despite this high degree of symmetry, a general closed-form analytic solution for the dynamics of this many-body problem remains elusive. Machine-learning methods may be well suited to exploiting the high degree of symmetry in integrable problems, even when an explicit analytic solution is not obvious. Motivated in part by this intuition, we use a neural-network representation (restricted Boltzmann machine) for each variational eigenstate of the model Hamiltonian. We then obtain accurate representations of the ground state and of the low-lying excited states of the Gaudin-magnet Hamiltonian through a variational Monte Carlo calculation. From the low-lying eigenstates, we find the non-perturbative dynamic transverse spin susceptibility, describing the linear response of a central spin to a time-varying transverse magnetic field in the presence of a spin bath. Having an efficient description of this susceptibility opens the door to improved characterization and quantum control procedures for qubits interacting with an environment of quantum two-level systems. These systems include electron-spin and hole-spin qubits interacting with environmental nuclear spins via hyperfine interactions or qubits with charge or flux degrees of freedom interacting with coherent charge or paramagnetic impurities.Comment: 13 pages, 9 figure

Commuting automorphisms of some finite groups

Let G be a group. An automorphism α of G is called a commuting automorphism if xxα=xα x for all x G. We denote the set of all commuting automorphisms of G by A(G). Moreover a group G is called an AC-group if the centralizer of every non-central element of G is abelian. In this paper we show that A(G) is a subgroup of the automorphism group of G for all finite AC-groups, p-groups of maximal class, and metacyclic p-groups

Ambientes digitales de literatura infantil. Los nuevos escenarios para la lectura

En tiempos de pandemia, los espacios de lectura para los niños han sido replanteados en cuanto a que los escenarios educativos se movilizaron al hogar; por lo que los espacios, tiempos, recursos y los roles del lector o iniciador a la lectura se invisibilizan en las dinámicas de la familia. Por consiguiente, esta es una indagación sobre la importancia de la lectura para los más pequeños y los posibles nuevos escenarios que sostenga en el tiempo una conexión con los ambientes de la lectura para encontrar nuevas formas, recursos y apoyos a los primeros lectores, sugiriendo así, algunos espacios digitales distritales, nacionales e internacionales comprometidos con la lectura y su acceso a la literatura infantil

Use of medicinal plants by cancer patients at the National Institute of Oncology, Rabat: a cross-sectional survey

Introduction: the use of medicinal plants has increased significantly in recent years. According to the World Health Organization, 80% of the world's population uses medicinal plants to treat themselves. Our study aims to estimate the prevalence of medicinal plant use by cancer patients, list the different plants and identify their adverse effects cited by users and their reported efficacy. Methods: this study was realised among 100 patients via a questionnaire with 14-items. Socio-economic and clinical characteristics have been analysed. The bivariate and multivariate analyses have been used to demonstrate the association between the socio-demographic characteristics of the participants, the duration of the disease and the use of medicinal plants. Results: 45% of participants used medicinal plants. The most commonly reported reason for using medicinal plants was cancer cure (22%). During this study, 32 plants were identified. The Honey was the most commonly used (25%), thyme was also consumed at 15%, fenugreek at 13% and garlic at 7%. According to the multivariate analysis, the residence is predictor of medicinal plant use, urban residents used medicinal plants more than rural patients with an OR: 3,098, IC, 95%: [1,183-8,113] and P = 0,021. Fifty patients reported the moderate efficacy of the use of medicinal plants, and 20% described some side effects such as abdominal pain in 34%. Conclusion: in order to avoid any interaction with oncological drugs and to improve their effectiveness, a great importance must be given to information, education and awareness sessions