Elementary Techniques Research Articles

Proper extensions of the 2-sphere’s conformal group present entropy and are 4-transitive

AbstractIn this paper, we prove using elementary techniques that any group of diffeomorphisms acting on the 2-sphere and properly extending the conformal group of Möbius transformations must be at least 4-transitive or, more precisely, arc 4-transitive. As an important consequence, we derive that any such group must always contain an element of positive topological entropy. We also provide a self-contained characterization, in terms of transitivity, of the Möbius transformations within the full group of sphere diffeomorphisms.

Tracer or toxicant: Does stable isotope labeling affect central processes in aquatic food webs?

Stable isotope analysis (SIA) is an elementary technique in food web ecology, but its insights become increasingly ambiguous in complex systems. One approach to elevate the utility of SIA in such systems is the use of heavy isotope tracers (i.e., labeling). However, the fundamental assumption that the addition of such tracers does not affect in situ conditions has been challenged. This study tests if labeling is suitable for autotrophy-based and detritus-based aquatic food webs. For the former, the survival and reproduction of Daphnia magna fed with phytoplankton cultured at different levels of 15N addition were assessed. For the latter, the microbial decomposition of leaf litter was assessed at the same tracer levels. While no significant differences were observed, effect patterns were comparable to a previous study, supporting the isotopic redundancy hypothesis that postulates discrete quantum mechanical states at which the reaction speeds of metabolic processes are altered. Although physiology (reproduction) and activity (microbial decomposition) might not be altered to an ecologically significant level, labeling with heavy stable isotopes could potentially affect isotopic fractionation in biochemical processes and bias conclusions drawn from resulting SI ratios.

Развитие личности младшего школьника — приоритетная цель современного начального образования (часть 3)

The article deals with the problem of the development of the personality of a younger schoolchild as a member of Russian society, a citizen of the Russian Federation, as well as a subject of a new for him, socially important educational and cognitive activity. The content of the process of education in elementary school, its methods, techniques and forms of organization are characterized. Examples of the integration of educational and upbringing tasks in the classroom and in extracurricular activities of schoolchildren are given.

A note on the rate of convergence in the Boolean central limit theorem

Several results giving upper bounds for the speed of convergence in non-commutative central limit theorems are known. A natural question is whether there also exist lower bounds, or whether there exist classes of probability measures where the speed of convergence is faster. In this paper, we answer this for the Boolean central limit theorem in the bounded support case and using the Lévy distance. We show that for a probability measure [Formula: see text] of bounded support and nonzero third moment the rate of convergence is at least [Formula: see text], and when we have zero third moment, then the rate of convergence is [Formula: see text]. To achieve this, we improve a previous result concerning the position and weights of two atoms that eventually appear in the converging measure. The proofs only require elementary techniques of complex analysis.

An Interference-Aware Resource-Allocation Scheme for Non-Cooperative Multi-Cell Environment

Inter-cell interference cancellation has been investigated for several decades and has become an elementary technique for modern wireless networks. However, the existing interference cancellation mechanism rarely considers the historical channel variations and interference characteristics. In this paper, we propose an interference-aware prediction-based resource-allocation strategy to deal with multi-cell interference, where the historical noisy channel state and the acknowledgment feedback are fully utilized. Together with the predicted interference patterns, our proposed joint sub-channel allocation and rate selection mechanism can achieve better average throughput performance. Through the numerical as well as the prototyping results, we show that our proposed scheme is able to provide more than 9.7% and 8% average throughput improvement compared with many existing baselines.

Consecutive integers in the form $ a^x+y^b $

<abstract><p>Let $ a, b $ and $ k $ be integers greater than $ 1 $. For a tuple of $ k $ consecutive integers sorted in ascending order, denoted by $ T_k $, call $ T_k $ a nice $ k $-tuple if each integer of $ T_k $ is a sum of two powers of the form $ a^x+y^b $ and a perfect $ k $-tuple if each integer of $ T_k $ is a sum of two perfect powers of the form $ a^x+y^b $, respectively. Let $ N_k(a, b) $ be the number of nice $ k $-tuples and $ \widetilde{N}_k(a, b) $ be the number of perfect $ k $-tuples. For a given $ (a, b) $, it is quite interesting to find out $ N_k(a, b) $ and $ \widetilde{N}_k(a, b) $. In 2020, Lin and Cheng obtained the formula for $ N_k(2, 2) $. The main goal of this paper is to establish the formulas for $ N_k(a, b) $ and $ \widetilde{N}_k(a, b) $. Actually, by using the method of modulo coverage together with some elementary techniques, the formulas for $ \widetilde{N}_k(2, 2) $, $ \widetilde{N}_k(3, 2) $ and $ N_k(3, 2) $ are derived.</p></abstract>

Subnormal n-th roots of matricially and spherically quasinormal pairs

In a recent paper, Curto et al. [4] asked the following question: ?Let T be a subnormal operator, and assume that T2 is quasinormal. Does it follow that T is quasinormal??. Pietrzycki and Stochel have answered this question in the affirmative [18] and proved an even stronger result. Namely, the authors have showed that the subnormal n-th roots of a quasinormal operator must be quasinormal. In the present paper, using an elementary technique, we present a much simpler proof of this result and generalize some other results from [4]. We also show that we can relax a condition in the definition of matricially quasinormal n-tuples and we give a correction for one of the results from [4]. Finally, we give sufficient conditions for the equivalence of matricial and spherical quasinormality of T(n,n) := (Tn 1, Tn 2 ) and matricial and spherical quasinormality of T = (T1, T2), respectively.

Group-valued invariant of knots in the full torus

Knot concordance plays a crucial role in the low-dimensional topology. We propose a very elementary techniques which allows one to construct a lot of sliceness obstructions for knots in the full torus. Our approach deals with group theoretical techniques; it is completely combinatorial, and the groups are very easy to deal with.

Elementary proof for the existence of periodic points with real and simple spectrum for diffeomorphisms in any dimension

Using only elementary techniques we prove that for any $ C^r $ diffeomorphism, $ f $, of a compact manifold of dimension $ d>2 $, $ 1\leq r\leq \infty $, admitting a transverse homoclinic intersection, we can find a $ C^1 $-open neighborhood of $ f $ containing a $ C^1 $-open and $ C^r $-dense set of $ C^r $ diffeomorphisms which have a periodic point with real and simple spectrum. We use this fact to prove that $ C^r $-generically among $ C^r $ diffeomorphisms with horseshoes, we have density of periodic points with real and simple spectrum inside the horseshoe. As a corollary, we obtain that generically in the $ C^1 $-topology the unique obstruction to the existence of periodic points with real and simple spectrum are the Morse-Smale diffeomorphisms with all the periodic points admitting non-real eigenvalues.

Complete hierarchy of linear systems for certifying quantum entanglement of subspaces

We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms known methods already at the first level, and it is complete in the sense that every entangled subspace is shown to be so at some finite level of the hierarchy. It straightforwardly generalizes to the case of higher Schmidt rank, as well as the multipartite cases of completely and genuinely entangled subspaces. These hierarchies work extremely well in practice even in very large quantum systems, as they can be implemented via elementary linear algebra techniques rather than the semidefinite programming techniques that are required by previously known hierarchies.

Развитие личности младшего школьника – приоритетная цель современного начального образования (часть 2)

The article deals with the problem of the development of the personality of a younger schoolchild as a member of Russian society, a citizen of the Russian Federation, as well as a subject of a new for him, socially important educational and cognitive activity. The content of the process of education in elementary school, its methods, techniques and forms of organization are characterized. Examples of the integration of educational and upbringing tasks in the classroom and in extracurricular activities of schoolchildren are given.

Commutator method for averaging lemmas

We introduce a commutator method with multipliers to prove averaging lemmas, the regularizing effect for the velocity average of solutions for kinetic equations. This method requires only elementary techniques in Fourier analysis and shows a new range of assumptions that are sufficient for the velocity average to be in $L^2([0,T],H^{1/2}_x).$ This result not only shows an interesting connection between averaging lemmas and local smoothing property of dispersive equations, but also provide a direct proof for the regularizing effect for the measure-valued solutions of scalar conservation laws in space dimension one.

Interpolation over ℤ and torsion in class groups

We prove an interpolation result for homogeneous polynomials over the integers, or more generally for PIDs with finite residue fields. Previous proofs of this result use the well-known but nontrivial fact that class groups of rings of integers are torsion. We provide an independent proof using elementary techniques.

Perturbation theory without power series: Iterative construction of non-analytic operator spectra

It is well known that quantum-mechanical perturbation theory often gives rise to divergent series that require proper resummation. Here I discuss simple ways in which these divergences can be avoided in the first place. Using the elementary technique of relaxed fixed-point iteration, I obtain convergent expressions for various challenging ground-states wave functions, including quartic, sextic and octic anharmonic oscillators, the hydrogenic Zeeman problem, and the Herbst-Simon Hamiltonian (with finite energy but vanishing Rayleigh-Schrödinger coefficients), all at arbitarily strong coupling. These results challenge the notion that non-analytic functions of coupling constants are intrinsically “non-perturbative”. A possible application to exact diagonalization is briefly discussed.

Analysis of the Application of the Group Investigation Learning Model and Its Influence on Students' Critical Thinking Ability in Elementary Chemical Materials in Class XII MIA SMAN 5 Jambi City

Purpose of research: research on the application of the study model of the group investigation on chemical materials and its impact on the students' critical thinking ability are aimed at seeing how the model is performing on the critical thinking ability of the xii class student at sman 5 city jambi.Methodology: the study is a korelational descriptive study with mixed method mixed method mixed nowadays embedded. Samples were determined by an elementary sampling technique with an expert consideration. Research instruments form an observation sheet for the performance of the model group investigation and student critical thinking ability. The data analysis is performed to see how the gi model's performance of critical thinking capabilities is done with Pearson's bivariate and t-testing.
 Major findings: gi model performance is categorized well, reviewed by teachers and students at an average of 78.55% and 74.5%. The results of the similarity of the two average data of model accessibility by teachers and students gained thitung = 0.5015 and ttabel = 4.3. Research results prove that the performance of the study model of the group investigation is going well and there is an influence between the performance of the study model group investigation with the students' critical thinking ability on an xii chemical element at the five cities jambi.Research update: this study strengthens a significant impact between gi models on students' critical thinking ability, especially at chemistry lessons.

Развитие личности младшего школьника – приоритетная цель современного начального образования

The article deals with the problem of the development of the personality of a younger schoolchild as a member of Russian society, a citizen of the Russian Federation, as well as a subject of a new for him, socially important educational and cognitive activity. The content of the process of education in elementary school, its methods, techniques and forms of organization are characterized. Examples of the integration of educational and upbringing tasks in the classroom and in extracurricular activities of schoolchildren are given.

Facilely Achieved Self-Biased Black Silicon Heterojunction Photodiode with Broadband Quantum Efficiency Approaching 100.

Photodiodes are fundamental components in modern optoelectronics. Heterojunction photodiodes, simply configured by two different contact materials, have been a hot research topic for many years. Currently reported self-biased heterojunction photodiodes routinely have external quantum efficiency (EQE) significantly below 100% due to optical and electrical losses. Herein, an approach that virtually overcomes this 100% EQE challenge via low-aspect-ratio nanostructures and drift-dominated photocarrier transport in a heterojunction photodiode is proposed. Broadband near-ideal EQE is achieved in nanocrystal indium tin oxide/black silicon (nc-ITO/b-Si) Schottky photodiodes. The b-Si comprises nanostalagmites which balance the antireflection effect and surface morphology. The built-in electric field is explored to match the optical generation profile, realizing enhanced photocarrier transport over a broadband of photogeneration. The devices exhibit unprecedented EQE among the reported leading-edge heterojunction photodiodes: average EQE surpasses ≈98% for wavelengths of 570-925nm, while overall EQE is greater than ≈95% from 500 to 960nm. Further, only elementary fabrication techniques are explored to achieve these excellent device properties. A heart rate sensor driven by nanowatt faint light is demonstrated, indicating the enormous potential of this near-ideal b-Si photodiode for low power consuming applications.

Diagnostics of the level of formation of structural components of productive experience in younger children school age

The purpose of this study was to identify the initial level of formation of structural components (motivational, cognitive, activity, reflexive) of productive experience in primary school children. The meaningful productive experience of primary school children is expressed in a value attitude to productive activities, in showing interest in various types of productive activities, knowledge of the types of materials, their properties and features of their practical application, the ability to qualitatively perform elementary operations and techniques for making simple products, the manifestation of creative activity, the ability to evaluate the result and personal contribution to the the task. In the course of the study, groups of younger schoolchildren with high, medium and low levels of formation of structural components of productive experience were identified. The results of the study indicate that a fairly large group consists of younger schoolchildren who have low indicators of the cognitive component, a weak degree of interest in productive activities, lack of independence in performing the proposed tasks; instability of volitional aspirations; showing significant difficulties in the orientation of the task, in choosing the goal of the upcoming activity, not able to plan the sequence of their actions.

Explainable Planner Selection for Classical Planning

Since no classical planner consistently outperforms all others, it is important to select a planner that works well for a given classical planning task. The two strongest approaches for planner selection use image and graph convolutional neural networks. They have the drawback that the learned models are complicated and uninterpretable. To obtain explainable models, we identify a small set of simple task features and show that elementary and interpretable machine learning techniques can use these features to solve roughly as many tasks as the complex approaches based on neural networks.

Domination in Kn\"odel Graphs

Given a graph and an integer $k$, it is an NP-complete problem to decide whether there is a dominating set of size at most $k$. In this paper we study this problem for the Kn\"odel Graph on $n$ vertices using elementary number theory techniques. In particular, we show an explicit upper bound for the domination number of the Kn\"odel Graph on $n$ vertices any time that we can find a prime number $p$ dividing $n$ for which $2$ is a primitive root.