Logarithmic Properties Research Articles

VCubeChain: A scalable permissioned blockchain

This work presents vCubeChain, a scalable permissioned blockchain based on the vCube virtual topology. vCube is a virtual hierarchical topology that presents several logarithmic properties. vCubeChain employs a leader election algorithm that relies on the failure detection information that vCube provides. The leader employs a vCube-based autonomic reliable broadcast algorithm to disseminate blocks, each consisting of multiple transactions. In case multiple leaders end up concurrently elected due to false suspicions, vCubeChain is proven to recover to a consistent state upon the discovery of contradictory blocks. vCubeChain is described, specified, and correctness and liveness draft proofs are presented. The blockchain was implemented on the Blocksim simulator, and a set of experiments are presented, including comparisons with Bitcoin, Ethereum and Hyperledge Fabric. Results demonstrate the scalability of the solution.

Selection process based on new building construction work using square root vague sets and their aggregated operators

This study discusses novel approaches for solving multi-attribute decision-making problems using logarithmic square root vague sets. Logarithmic square root vague sets can be considered as an extension of vague sets and square root fuzzy sets provides a more profitable method to express the uncertainties in the data to deal with decision making problems. We developed some novel logarithmic square root vague sets, which can overcome the weaknesses of algebraic operations and capture the relationship between various square root vague sets and vague sets. The purpose of this study is to examine several aggregation operators using logarithmic square root vague sets. The weighted logarithmic averaging distance and weighted logarithmic geometric distance operators are distance measure that is based on aggregating model. We discuss the concepts of logarithmic square root vague weighted averaging, logarithmic square root vague weighted geometric, generalized logarithmic square root vague weighted averaging and generalized logarithmic square root vague weighted geometric operators. We communicate that algebraic structures such as associative, distributive, idempotent, bounded, commutativity and monotonicity properties are satisfied by logarithmic square root vague numbers. We discusses some mathematical properties of logarithmic square root vague sets, as well as the Hamming distance and Euclidean distance measures. It measures the similarity of two strings of information by measuring the Hamming distance. An analysis of the proposed operators is presented, along with alternative formulations and families, as well as their main properties. The weighting vector is characterized by multiple classical measures and we propose alternative solutions for dealing with the logarithmic properties of the operators. As a result of studying the weighting vectors of the operators, we present generalizations of them. We examine vague sets with important properties using algebraic operations in more detail. Furthermore, we develop an algorithm to solve multi-attribute decision-making problems using these operators. We provide real-life examples to illustrate how enhanced Euclidean distances, Hamming distances and score values can be applied in real-world situations. To show the superiority and the validity of the proposed aggregation operations, we compared it with the existing method, and concluded from the comparison and sensitivity analysis that our proposed technique is more effective and reliable. Based on the expert assessments, we compared the criteria with the most appropriate options.

Scalable atomic broadcast: A leaderless hierarchical algorithm

Atomic Broadcast is an essential broadcast primitive as it ensures the consistency of distributed replicas. However, it is notoriously non-scalable. In this work, we introduce the Leaderless Hierarchical Atomic Broadcast (LHABcast) algorithm, which has two properties to improve scalability. First, it is a fully decentralized algorithm that does not rely on a sequencer/leader, which is often a significant bottleneck. Processes running LHABcast send messages with local sequence numbers and order messages received from other processes using timestamps inspired on Lamport's logical clocks. A process that receives the required set of timestamps can make a decision about the overall sequence of message delivery. Second, the algorithm is hierarchical: processes are organized on a vCube logical overlay network, which has several logarithmic properties and allows the construction of autonomous spanning trees. vCube also works as a failure detector, assuming crash faults and an asynchronous system model. In this paper, LHABcast is described, specified, and proven to be correct. Both simulation and experimental results are presented. A comparison with an all-to-all strategy shows that the number of messages sent by LHABcast is significantly lower in both fault-free and faulty scenarios. An implementation of LHABcast in Akka.io achieved up to 3.9 times higher throughput in fault-free scenarios than an implementation of the Raft-based Apache Ratis.

Experimental evidence for logarithmic fractal structure of botanical trees.

The area-preserving rule for botanical trees by Leonardo da Vinci is discussed in terms of a very specific fractal structure, a logarithmic fractal. We use a method of the numerical Fourier analysis to distinguish the logarithmic fractal properties of the two-dimensional objects and apply it to study the branching system of real trees through its projection on the two-dimensional space, i.e., using their photographs. For different species of trees (birch and oak) we observe the Q^{-2} decay of the spectral intensity characterizing the branching structure that is associated with the logarithmic fractal structure in two-dimensional space. The experiments dealing with the side view of the tree should complement the area preserving Leonardo's rule with one applying to the product of diameter d and length l of the k branches: d_{i}l_{i}=kd_{i+1}l_{i+1}. If both rules are valid, then the branch's length of the next generation is sqrt[k] times shorter than previous one: l_{i}=sqrt[k]l_{i+1}. Moreover, the volume (mass) of all branches of the next generation is a factor of d_{i}/d_{i+1} smaller than previous one. We conclude that a tree as a three-dimensional object is not a logarithmic fractal, although its projection onto a two-dimensional plane is. Consequently, the life of a tree flows according to the laws of conservation of area in two-dimensional space, as if the tree were a two-dimensional object.

Foundational ways of thinking for understanding the idea of logarithm

This study explored two undergraduate precalculus students’ understandings of the idea of logarithm as they completed conceptually oriented exploratory lessons on exponential and logarithmic functions. The students participated in consecutive, individual teaching experiments that focused on Sparky – an animated mystical saguaro that doubled in height every week. The exponential lesson focused on developing students’ conceptions of growth factors and tupling (e.g., doubling) periods as a foundational understanding for conceptualizing logarithms and logarithmic properties meaningfully. This paper characterizes conceptions that are productive for students to acquire in introductory lessons on exponential and logarithmic growth, and discusses two understandings that were revealed to be foundational for students’ development of productive meanings for exponents, logarithms and logarithmic properties.

Directionality of the Equals Sign: A Case Study Using Logarithmic Properties

Mathematics educators view the equals sign as a bidirectional relation symbol, but the authors have observed that students might not have such flexibility in their understanding of the equals sign. The authors have observed that students have a hard time viewing mathematical properties (for example, ) with bidirectional flexibility, and subsequently wondered if the “direction” that students are presented mathematical properties has an impact on their ability to use the properties successfully. The authors studied this phenomenon in 11 undergraduate, introductory-level mathematics courses (College Algebra and Precalculus) by presenting logarithmic properties in different “directions” and seeing what effect that had on students’ ability to apply the logarithmic properties successfully. Our results indicate that, despite careful classroom discussion of the meaning of the properties and sustained problem solving activities, the “direction” that the properties are presented to the students does have an effect on their ability to use the properties successfully.

Pemahaman Konsep Logaritma Siswa SMA Ditinjau dari Kemampuan Matematika

This Understanding the concept is the ability of students to understand a mathematical meaning both in theory and its application in solving problems based on the formation of their own knowledge, not just memorizing. The purpose of this study was to analyze the understanding of students' concepts in the material logarithm class x in terms of mathematical abilities. This research is descriptive qualitative research conducted at SMK N 5 Semarang, with research subjects in class X TP 1. To be able to know the understanding of concepts in students it is done by giving a test that includes seven indicators of mathematical abilities namely understanding, solving problems, connections, communication, reasoning, critical thinking, and creative thinking. The stages carried out consisted of three phases, namely: giving a test of mathematical ability, giving a concept understanding test, and interviewing. From the results of the study using triangulation methods, namely by comparing the results of tests of mathematical understanding in writing with the interview test. The results of qualitative analysis show that: (1) students with TKA mathematical abilities can understand the concept by defining logarithms using writing and symbols, can mention and apply logarithmic properties, can transform logarization forms into exponent forms, can compare examples and not logarithmic examples. (2) students with mathematical skills TKC mathematical abilities can understand the concept by defining logarithms with writing and symbols, changing the shape of logarithms to exponent forms, can only apply logarithmic properties to addition and subtraction, can only compare examples and not just 2. logarithms. (4) students with TKE mathematical abilities can understand the concept by defining logarithms using symbols, can only apply the logarithmic properties of addition and subtraction but cannot specify the properties, can only mention examples and not examples of logarithms 1.

An M-QAM Signal Modulation Recognition Algorithm in AWGN Channel

Computing the distinct features from input data, before the classification, is a part of complexity to the methods of automatic modulation classification (AMC) which deals with modulation classification and is a pattern recognition problem. However, the algorithms that focus on multilevel quadrature amplitude modulation (M-QAM) which underneath different channel scenarios is well detailed. A search of the literature revealed that few studies were performed on the classification of high-order M-QAM modulation schemes such as 128-QAM, 256-QAM, 512-QAM, and 1024-QAM. This work focuses on the investigation of the powerful capability of the natural logarithmic properties and the possibility of extracting higher order cumulant’s (HOC) features from input data received raw. The HOC signals were extracted under the additive white Gaussian noise (AWGN) channel with four effective parameters which were defined to distinguish the types of modulation from the set: 4-QAM∼1024-QAM. This approach makes the classifier more intelligent and improves the success rate of classification. The simulation results manifest that a very good classification rate is achieved at a low SNR of 5 dB, which was performed under conditions of statistical noisy channel models. This shows the potential of the logarithmic classifier model for the application of M-QAM signal classification. furthermore, most results were promising and showed that the logarithmic classifier works well under both AWGN and different fading channels, as well as it can achieve a reliable recognition rate even at a lower signal-to-noise ratio (less than zero). It can be considered as an integrated automatic modulation classification (AMC) system in order to identify the higher order of M-QAM signals that has a unique logarithmic classifier to represent higher versatility. Hence, it has a superior performance in all previous works in automatic modulation identification systems.

Method to reduce the signal‐to‐noise ratio required for modulation recognition based on logarithmic properties

Here, the authors present a novel, simple, and effective way of improving additive white Gaussian noise resistance and reducing the signal-to-noise ratio (SNR) required for modulation recognition. Working on the theoretical basis that the ratio of two logarithmic functions with the same variable is a constant, the authors selected QPSK, 16QAM, and 64QAM for investigation. For each of these, the authors constructed distribution curves of higher-order cumulants, using SNR as the variable, and examined how they might work as logarithmic curves. First, their logarithmic similarities were measured. Then their former features were divided by logarithmic functions to construct new features whose distribution curves were more parallel to the threshold line. Finally, an algorithm for classifying the selected modulation formats was designed whose computational complexity was then compared with that of adaptive-threshold classification algorithm, and the recognition rate was assessed statistically. For the purposes of validation, the algorithm was tested experimentally using actual signals. The experiment confirmed that the new logarithmic features with fixed thresholds were able to maintain an efficient recognition rate of 80% when SNR was reduced from 11 to 6 dB, and suffered less computational complexity than traditional cumulants with adaptive thresholds which were achieved by support vector machine.

Adaptabilidade de Objetos de Aprendizagem usando Calibragem e Sequenciamento Adaptativo de Exercícios

The work approaches theoretical and implementation issues of a framework for creating and executing Learning Objects (LOs) where problem-solving tasks are ordered according to the matching of two parameters, both calculated automatically: (1) student skill level and (2) problem solution difficulty. They are formally defined as algebraic expressions. The definition of skill level is achieved through a rating-based measure that resembles the ones of game mastery scales, while the solution difficulty is based on mistakes and successes of learners to deal with the problem. An empirical study based on existing students data demonstrated the suitability of the formulas. Besides, the motivational aspects of learning are considered in depth. In this sense, it is important to propose activities according to the student’s level of expertise, which is achieved through presenting students with exercises that are compatible with the difficulty degree of their cognitive skills. Also, the results of an experiment conducted with four highschool classes using the framework for the domain of logarithmic properties are presented.

Adaptabilidade de Objetos de Aprendizagem usando Calibragem e Sequenciamento Adaptativo de Exercícios

The work approaches theoretical and implementation issues of a framework for creating and executing Learning Objects (LOs) where problem-solving tasks are ordered according to the matching of two parameters, both calculated automatically: (1) student skill level and (2) problem solution difficulty. They are formally defined as algebraic expressions. The definition of skill level is achieved through a rating-based measure that resembles the ones of game mastery scales, while the solution difficulty is based on mistakes and successes of learners to deal with the problem. An empirical study based on existing students data demonstrated the suitability of the formulas. Besides, the motivational aspects of learning are considered in depth. In this sense, it is important to propose activities according to the student’s level of expertise, which is achieved through presenting students with exercises that are compatible with the difficulty degree of their cognitive skills. Also, the results of an experiment conducted with four highschool classes using the framework for the domain of logarithmic properties are presented.

An autonomic hierarchical reliable broadcast protocol for asynchronous distributed systems with failure detection

Reliable broadcast is a fundamental building block in fault-tolerant distributed systems. It consists of a basic primitive that provides agreement among processes of the system on the delivery of each broadcast message, i.e., either none or all correct processes deliver the message, despite failures of processes. In this work, we propose a reliable broadcast solution on top of VCube, assuming that the system is asynchronous. VCube is an autonomic monitoring layer that organizes processes on a hypercube-like overlay which provides several logarithmic properties even in the presence of processes failures. We consider that processes can fail by crashing, do not recover, and faults are eventually detected by all correct processes. The protocol tolerates false suspicions by sending additional messages to suspected processes but logarithmic properties of the algorithm are still kept. Experimental results show the efficiency of the proposed solution compared to an one-to-all strategy.

A distributed virtual hypercube algorithm for maintaining scalable and dynamic network overlays

SummaryNetwork overlays support the execution of distributed applications, hiding lower level protocols and the physical topology. This work presents DiVHA: a distributed virtual hypercube algorithm that allows the construction and maintenance of a self‐healing overlay network based on a virtual hypercube. DiVHA keeps logarithmic properties even when the number of nodes is not a power of two, presenting a scalable alternative to connect distributed resources. DiVHA assumes a dynamic fault situation, in which nodes fail and recover continuously, leaving and joining the system. The algorithm is formally specified, and the latency for detecting changes and the subsequent reconstruction of the topology is proved to be bounded. An actual overlay network based on DiVHA called HyperBone was implemented and deployed in the PlanetLab. HyperBone offers services such as monitoring and routing, allowing the execution Grid applications across the Internet. HyperBone also includes a procedure for detecting groups of stable nodes, which allowed the execution of parallel applications on a virtual hypercube built on top of PlanetLab. Copyright © 2014 John Wiley & Sons, Ltd.

A ppb-level formaldehyde gas sensor based on CuO nanocubes prepared using a polyol process

We fabricated and characterized a highly formaldehyde-sensitive gas sensor based on CuO nanocubes. Cu2O nanocubes were synthesized through a wet, facile, and mass-producible polyol process, and oxidized CuO nanocubes were prepared using thermal oxidation under air conditions. The synthesized nanocubes were monodisperse, and the average edge size was about 90nm and average pore size about 52nm. We determined the operating temperature of the gas sensors to be 300°C, considering the proper sensitivity and a rapid response. At this operating temperature, the CuO nanocube gas sensors showed a high HCHO gas response, that is, logarithmic properties in an HCHO gas concentration range of 0.05–3 parts per million (ppm). The gas sensors demonstrated excellent reproducibility (coefficient of variation of 1.17% with 800 parts per million (ppb) at 300°C) and a very low limit of detection of 6 ppb at 250°C. Furthermore, among the tested gases that commonly exist in the indoor ambient air, like C6H6, NO2, CO, CO2, NH3, and HCHO, the CuO nanocube gas sensors showed the most strong response to HCHO gas at 300°C. This investigation therefore indicates that an HCHO gas sensor using CuO nanocubes can be a simple and useful platform for sensing very hazardous indoor formaldehyde gas at several levels of ppb.

Objective function and logarithmic barrier function properties in convex programming: level sets, solution attainment and strict convexity*

We give several results, some new and some old, but apparently overlooked, that provide useful characterizations of barrier functions and their relationship to problem function properties. In particular, we show that level sets of a barrier function are bounded if and only if feasible level sets of the objective function are bounded and we obtain conditions that imply solution existence, strict convexity or a positive definite Hessian of a barrier function. Attention is focused on convex programs and the logarithmic barrier function. Such results suggest that it would seem possible to extend many recent complexity results by relaxing feasible set compactness to the feasible objective function level set boundedness assumption.

Magnetic Field Structure near the Plasma Boundary in Helical Systems and Divertor Tokamaks

The magnetic field structure of the scrape-off layer (SOL) region in both helical systems and divertor tokamaks is studied numerically by using model fields. The connection length of the field line to the wall, L, is calculated. In helical systems, L has logarithmic properties in the SOL region. The effect of axisymmetric fields on the field structure is determined. In divertor tokamaks, L also has logarithmic properties near the separatrix. Even when the perturbations which resonate to rational surfaces near the plasma boundary are added, the logarithmic properties are not changed. The connection length of torsatron/helical-heliotron systems is compared with that of divertor tokamaks.

The logarithmic properties of active and passive mandibular growth

The growth of the human mandible in a series of orthodontically normal children was examined by methods designed to demonstrate both the vectors of active and passive growth and the logarithmic attributes of such growth. Both methods are described and illustrated. The individual differences in the vectorial properties of active and passive growth during relatively short periods of time suggest that is is hazardous to predict such growth increments within clinically useful tolerances. Further, all mandibular growth is shown to be logarithmic. As such, mandibular growth shares three logarithmic attributes: Its growth is allometric (expressed by the relative growth equation); growth of all human mandibles is capable of graphic presentation as a unitary logarithmic spiral; and its growth is gnomonic, that is, it changes its size while retaining the same shape. A synthesis of mandibular growth is presented in terms of the interrelationship between active and passive growth processes and their logarithmic attributes.

Comments on Amusia and Starodubsky's paper on logarithmic properties of a Fermi liquid

Amusia and Starodubsky's paper on the logarithmic temperature dependence of the spin susceptibility of a Fermi liquid and on the interpretation of experiments is critically discussed.

Some Logarithmic Properties of Photomultipliers

The logarithmic properties of a photomultiplier are investigated. There is a logarithmic relationship between the voltage and gain of a group of three dynodes of a photomultiplier. An exponential current generator for the calibration of logarithmic amplifiers based on these principles is described. The dynamic range of the generator is about 4 decades with an output current of 250 mA. The exponent is constant within a few percent over the entire range. The calibration of a fast logarithmic amplifier is shown. The generator can also be used to simulate the wave shape of fast scintillators with exponents as fast as a few nanoseconds.

On a Property of Logarithmic Spirals

Logarithmic spirals, analyzing curve on surface of cylinder, existence and conditions of ellipticity conditions, determining curve transformation into ellipse based on logarithmic spiral properties