Lattice Diagram Research Articles

Idempotent vector spaces and their linear transformations

Abstract This article extends topics about linear algebra and operator theoretic linear transformations on complex vector spaces to those on bicomplex spaces. For example, Definition 3 for the first time defines algebraically idempotent vector spaces, which generalizes the standard definition of a vector space and which includes bicomplex vector spaces as a special case, along with its dimension and its basis in terms of a corresponding vectorial idempotent representation. The article also shows how an n × n n\times n bicomplex matrix’s idempotent representation leads to a bicomplex Jordan form and a description of its bicomplex invariant subspace lattice diagram. Similarly, in a new way, the article rigorously defines “bicomplex Banach and Hilbert” spaces, and then it expands, for the first time, the theory of compact operators on complex Banach spaces to those on bicomplex Banach spaces. In these ways, the article indicates that the idempotent representation extends complex linear algebra and operator theory in a surprisingly generalized and straightforward way to vector space results with bicomplex and multicomplex scalars.

A simplified time domain approach to calculate lightning electric fields considering the grounded tower-line-tower (TLT) structure

This study describes a method for calculating electric fields radiated by lightning in the presence of a tower-line-tower (TLT) structure, extending a previous method developed by Rachidi et al. (2002). The method involves using a lattice diagram to analyze current distribution and deriving expressions related to the current distribution along the lightning channel and the TLT structure. Expressions associated with the current distribution along the lightning channel and the TLT structure are derived. The impedances of the towers, the connected overhead grounded wire, and lightning channel were treated as constant values. The subsequent return stroke was analyzed in the paper. The lightning radiated electric fields at an intermediate distance of 15 km considering lightning striking to ground, one single object, and the TLT structure were presented and compared. The directly strike of lightning on a tower plays an important role in the increase of the electric field magnitude, while the neighbored tower and the associated grounded wire contributes to periodical superimpositions on the middle-and-late response of the electric fields. Detail discussion on the influences of the different parameters of the proposed method on the electric fields at 15 km and comparison to the measured data were also presented.

A Novel Strategy for Preparing Nano‐Sized and High‐Performance LiMnxFe1−xPO4 Cathode Materials from Discarded LiMn2O4 and LiFePO4 Electrode

The research strategy of using discarded lithium manganate (LiMn2O4, LMO) and lithium iron phosphate (LiFePO4, LFP) electrode materials to obtain lithium manganese iron phosphate (LiMnxFe1−xPO4, LMFP) materials with high energy density and ionic conductivity is increasingly highlighted as powerful and effective. The study explores a new strategy to prepare high‐performance LMFP materials using high‐temperature sintering based on the successful recovery of LMO and LFP electrode wastes. X‐ray diffraction results show that the LMFP cathode materials are prepared successfully by using discarded LMO and LFP materials. LM0.4F0.6P and LM0.6F0.4P, whose manganese‐to‐iron molar ratio [MR(Mn/Fe)] 4:6 and 6:4, exhibit nano‐sized olivine spheres with lattice diagram corresponding to the (101) crystal planes. The constant current curves show that LM0.6F0.4P has a specific discharge capacity of 154.4 mAh g−1 at 0.2 C. The capacity retention rate is maintained at 96.2% after 100 cycles. The cyclic voltammetry curves show that two distinct pairs of redox potentials appeared for LM0.6F0.4P in the voltage interval located at (3.63 V/3.43 V) and (4.18 V/3.87 V). Thus, the proposed strategy predicts that the discarded LMO and LFP can be used as raw materials to prepare high‐performance LMFP cathode materials, significantly reducing energy consumption and environmental pollution.

On the frequency and damping of resonances in electrical networks: a discrete state-space approach using bounce Diagrams

The paper presents a novel method to compute resonances in a power system network using a discrete state-space approach based on bounce diagrams. The approach models the distributed parameter line as a lattice diagram, considering the refection/transmission of traveling waves. This model is then represented as a discrete-time linear time-invariant system, enabling the computation of resonances in the network. Two applications are demonstrated: fault location and load placement to improve damping in black start scenario. The method is particularly useful to understand and control resonances in electric grids. Theoretical analysis and numerical examples illustrate the behavior of resonances as resistive loads are connected along the transmission line, providing insights for fault location and load allocation strategies.

Lightning transient response of bifurcation structure pylon and its empirical expression with high accuracy

This paper studies the transient responses to a lightning surge terminating on towers with a bifurcation structure and presents new empirical formulas for estimating the respective lightning performance. The multi-stage segmentation is adopted for down-lead modeling, and mutual coupling and parasitic capacitance are considered. By discussing the influence degree of these factors, we propose a simplified down-lead system for formula expression. These formulas are derived from the lattice diagram method, and the original lattice diagram method recommended by CIGRE is also compared. Taking the simulation results as standard, the results derived from the proposed method show a good match with the simulation values, due to the consideration of the down-lead bifurcation configuration. The critical current (Ic) at the full range of front time is obtained, and the errors for the Y-shaped pylon by the new method are much less than that of the CIGRE method when the lightning front time is in the 97.5 % confidence interval. Finally, the Monte Carlo method is employed to verify the superiority of the new empirical formulas.© 2017 Elsevier Inc. All rights reserved.

ANALISA TEGANGAN LEBIH AKIBAT SURJA PETIR DARI TRANSMISI YANG MASUK KE TRAFO DAYA I 20 MVA DI GARDU INDUK 150 KV BUMI SEMARANG BARU (BSB) DENGAN METODE DIAGRAM TANGGA

Lightning surges that come from transmission lines are very dangerous for equipment in substations, especially transformers. The transformer is a very important main component of the substation. As a result of damage to the transformer will result in the distribution of electrical energy to consumers can be disrupted. The solution to this problem is to install an arrester to overcome the lightning surge voltage in order to avoid damage to the transformer at the substation. To secure the transformer at the 150 kV Bukit Semarang Baru (BSB) substation from lightning surges, it can be analyzed using four conditions. The method used is the lattice diagram method. Based on the results of the tests carried out on the I 20 MVA power transformer, the results obtained that the transformer can be protected from lightning surges with only one arrester. If installed two arresters would be even better. However, if an arrester is not installed, this condition is very dangerous because it will cause the transformer to be damaged, because the voltage that appears on the transformer is 939.06 kV, exceeding the BIL value of the transformer, which is 650 kV.

Analysis of the pulse signal propagation in a turn of a meander line of two segments based on lattice diagrams

The analysis of the propagation of a pulse signal in a turn of a meander line of two segments is carried out. For this purpose, the plotting of lattice diagrams for the even and odd modes is carried out, as well as their subsequent comparison with the time responses to the pulse excitation in each node of the line. A complete coincidence of the amplitudes and arrival times of pulses obtained by different methods was obtained.

Novel Quantum Algorithms to Minimize Switching Functions Based on Graph Partitions

After Google reported its realization of quantum supremacy, Solving the classical problems with quantum computing is becoming a valuable research topic. Switching function minimization is an important problem in Electronic Design Automation (EDA) and logic synthesis, most of the solutions are based on heuristic algorithms with a classical computer, it is a good practice to solve this problem with a quantum processer. In this paper, we introduce a new hybrid classic quantum algorithm using Grover’s algorithm and symmetric functions to minimize small Disjoint Sum of Product (DSOP) and Sum of Product (SOP) for Boolean switching functions. Our method is based on graph partitions for arbitrary graphs to regular graphs, which can be solved by a Grover-based quantum searching algorithm we proposed. The Oracle for this quantum algorithm is built from Boolean symmetric functions and implemented with Lattice diagrams. It is shown analytically and verified by simulations on a quantum simulator that our methods can find all solutions to these problems.

Design without representation

Abstract Shapes are perceived unanalyzed, without rigid representation of their parts. They do not comply with standard symbolic knowledge representation criteria; they are treated and judged by appearance. Resolving the relationship of parts to parts and parts to wholes has a constructive role in perception and design. This paper presents a computational account of part–whole figuration in design. To this end, shape rules are used to show how a shape is seen, and shape decompositions having structures of topologies and Boolean algebras reveal alternative structures for parts. Four examples of shape computation are presented. Topologies demonstrate the relationships of wholes, parts, and subparts, in the computations enabling the comparison and relativization of structures, and lattice diagrams are used to present their order. Retrospectively, the topologies help to recall the generative history and establish computational continuity. When the parts are modified to recognize emergent squares locally, other emergent shapes are highlighted globally as the topology is re-adjusted. Two types of emergence are identified: local and global. Seeing the local parts modifies how we analyze the global whole, and thus, a local observation yields a global order.

Wat beteken B(b)oer in 2022?

What is the Meaning of B(b)oer in 2022? This article investigates the meaning of the words Boer and boer in Afrikaans. The study is the result of an incident in 2015 when the Afrikaans Language Commission considered the possibility of omitting the word Boer from the Afrikaanse woordelys en spelreëls. The rationale was that other race sensitive items, such as hotnot, kaffer and koelie, had been scrapped from the word list long ago. The proposal to omit Boer created havoc. In the following discussion, the encyclopaedic approach to meaning is used to determine what Boer and boer currently mean. An investigation into the lexical meaning of these two words is supplemented by highlighting one of the assumptions of the encyclopaedic approach to meaning, namely that encyclopaedic knowledge is dynamic in nature and furthermore that meaning is always constructed in the context of use. The current day use and meanings of Boer and boer are indicated via examples from newspaper articles, literary texts, lyrics, a brand name as well as the corpus of the Language Commission. A radiating lattice diagram for the words Boer and boer is provided to show how the various meanings of the words are related to one another and how they form a polysemous semantic network. Keywords: boer, encyclopaedic approach, polysemy, radiating lattice diagram, semantics

ANALISIS KEMAMPUAN BERPIKIR KREATIF MAHASISWA KELOMPOK ATAS DALAM MENYELESAIKAN SOAL STRUKTUR ALJABAR RING MATERI IDEAL PRIMA DAN IDEAL MAKSIMAL

This study aims to describe the creative thinking ability of upper group students in solving Ring Algebra Structure questions on the prime ideal and maximum ideal material. This research uses descriptive qualitative research. The research subjects are students of Mathematics Education-2 Semester VI who have taken the Ring Algebra Structure course. The research subjects are three (3) students of Mathematics Education-2 Semester VI who have high mathematical abilities based on test results in the form of assignments on Ideal material. The instruments used in the study include: 1) Test; 2) Interview guide; and 3) Documentation. Based on the results of research and discussion, the findings resulted that the thinking ability of upper-class students had fulfilled all aspects of creative thinking, namely fluency, flexibility, and originality. The subject has been able to explain all the indicators that have been set very well and precisely. Subjects have also been able to prove prime ideals or maximum ideals or not both and can identify examples and non-examples of prime ideals and maximum ideals through high-level elaboration and analysis carried out by the subject. Subjects are also very able to describe Lattice diagrams on each question and can determine the subring of a ring. It's just that there is a uniqueness of the worksheet between MS, ZB, and HF. But overall the subject has fulfilled the creative thinking aspect. Thus, it can be concluded that the upper group students can be categorized at level 4, which is very creative.

4-Connected triangulations on few lines

We show that 4-connected plane triangulations can be redrawn such that edges are represented by straight segments and the vertices are covered by a set of at most $\sqrt{2n}$ lines each of them horizontal or vertical. The same holds for all subgraphs of such triangulations. The proof is based on a corresponding result for diagrams of planar lattices which makes use of orthogonal chain and antichain families.

Information Retrieval from Software Bug Ontology Exploiting Formal Concept Analysis

Knowledge extraction and structuring is attaining importance in real world applications such as e-commerce, decision support, problem solving and semantic web. Extraction of knowledge from collection of text documents is based upon identification of semantic content. Ontology plays an important role in accessing and structuring information. Developing an ontology are at the core of new strategies which requires accurate domain knowledge. Identification of structural and logical concepts is a time-consuming process. This work presents an ontology-based retrieval approach, that visualizes and structure the data of software bug reports domain. It exploits formal concept analysis (FCA) to elicit conceptualizations from bug reports datasets and a hierarchical taxonomy is generated of extracted knowledge. A lattice diagram of concepts and relationships is constructed from concept-relationship matrix created by FCA. Ontology is constructed on fluent editor tool and knowledge is extracted with the help of small queries executed on a reasoner window. The proposed approach is evaluated on 21 bug reports of apache projects of jira repository. It can be concluded that information can be retrieved easily from ontology as compared to manual extraction of data.

Realization of Quantum Oracles using Symmetries of Boolean Functions

Designing a quantum oracle is an important step in practical realization of Grover algorithm, therefore it is useful to create methodologies to design oracles. Lattice diagrams are regular two-dimensional structures that can be directly mapped onto a quantum circuit. We present a quantum oracle design methodology based on lattices. The oracles are designed with a proposed method using generalized Boolean symmetric functions realized with lattice diagrams. We also present a decomposition-based algorithm that transforms non-symmetric functions into symmetric or partially symmetric functions. Our method, which combines logic minimization, logic decomposition, and mapping, has lower quantum cost with fewer ancilla qubits. Overall, we obtain encouraging synthesis results superior to previously published data.

A lattice method for jump-diffusion process applied to transmission expansion investments under demand and distributed generation uncertainties

Strategic decision making for rare events is considered to be an arduous course of actions as their impacts cannot accurately be modeled. Transmission of electrical power is a major challenge in this day and age due to the prevalent of rare events. Decision makers of generation units, distribution utilities, and transmission networks do not often cooperate, which creates severe uncertainties for all players. Growth of demand for electricity and installation or removal of distributed generation (DG), considered to be a rare event, are among uncertainties encountered by transmission network owners. Expansion decisions for transmission lines should be strategically executed because installations of DGs may create a stranded cost for transmission owners. In this study, we propose a real options framework that quantifies the values of transmission investments under demand and DG uncertainties to guide decision makers of transmission companies regarding how to adapt their expansions decisions. We model demand uncertainty as a geometric Brownian motion process and DG uncertainty as a Poisson arrival process. We devise a computationally-efficient lattice diagram to discretize both processes in a single grid, which can also be employed to model other types of rare events in various sectors. The proposed framework is demonstrated on a realistic transmission network. Numerical study shows that our proposed lattice model is computationally superior over existing diagrams. As for managerial insights, it shows that depending on the locations of DG installations, DG penetration may not reduce the value of a transmission network. If the center at which a DG is installed has a large-capacity local generator, the installation may not undervalue the transmission network.

Fault Model and Travelling Wave Matching Based Single Terminal Fault Location Algorithm for T-Connection Transmission Line: A Yunnan Power Grid Study

Due to the complex structure of the T-connection transmission lines, it is extremely difficult to identify the reflected travelling wave from the fault point and that from the connection point by the measurement from only one terminal. According to the characteristics of the structure of the T-connection transmission line, the reflection of the travelling wave within the line after the failure of different sections in T-connection transmission line are analyzed. Based on the lattice diagram of the travelling wave, the sequence of travelling waves detected at the measuring terminal varies with the fault distance and the faulty section. Moreover, the sequence of travelling waves detected in one terminal is unique at each faulty section. This article calculates the arrival time of travelling waves of fault points at different locations in different sections to form the collection of the travelling wave arrival time sequence. Then the sequence of travelling waves of the new added fault waveforms is extracted to compare with the sequences in the collection for the faulty section identification and fault location. This proposed method can accurately locate the fault with different fault types, fault resistances and system impedances by only single-terminal fault data. Both Power Systems Computer Aided Design/ Electromagnetic Transients including DC (PSCAD/EMTDC) and actual measurement data are implemented to verify the effectiveness of this method.

Application of digital phase shifting moiré method in interface and dislocation location recognition and real strain characterization from HRTEM images.

In high-resolution transmission electron microscopy (HRTEM) images of heterostructures, it is always difficult to accurately determine the interface position and identify dislocations in a large field of view at tens to hundreds of nanometers due to the small lattice differences. However, in the heterostructure, the determination of the interface position is the key to obtain the true mismatch stress/strain field of the interface. Due to the magnifying effect of the digital moiré method on small differences, digital moiré technology was applied to determine Ge/Si heterostructure interfaces and large-area identification interface dislocations in HRTEM lattice diagrams in this study. By optimizing the frequency and angle of the reference lattice, the interface and dislocation position are clearly and intuitively displayed. How to accurately determine the position of the heterostructure interface and the dislocation of the large-area recognition interface from HRTEM images are studied through simulation experiments. The results show that when the frequency of the reference lattice and the specimen lattice are close, and the angle between them is within 10°, the position of the heterostructure interface can be accurately and intuitively determined by the naked eye according to the distortion characteristics of the moiré fringe. When the frequency of the reference lattice is 0.7 to 0.9 times of the specimen lattice, and the rotation angle is within 8°, the visually clear crossover phenomenon of the moiré fringes is used for large-area identification of interface dislocations. Using the phase measurement interface position sensitivity can reach the Å level. Using the phase-shifting digital moiré method the strain field on the dislocation core at the Ge/Si heterostructure interface and the interface stress distribution were quantitatively analyzed. Compared with the Peierls-Nabarro dislocation model and the Foreman dislocation model, Foreman's variable factor α = 4 is more suitable for describing the strain field of misfit dislocations on the Ge/Si heterostructure interface.

Structure and enumeration results of matchable Lucas cubes

A lucasene is a hexagon chain that is similar to a fibonaccene, an L-fence is a poset the Hasse diagram of which is isomorphic to the directed inner dual graph of the corresponding lucasene. A new class of cubes, which named after matchable Lucas cubes according to the number of its vertices (or elements), are a series of directed or undirected Hasse diagrams of filter lattices of L-fences. The basic properties and several classes of polynomials, e.g. rank generating functions, cube polynomials and degree sequence polynomials, of matchable Lucas cubes are obtained. Some special conclusions on binomial coefficients and Lucas triangle are given.

Bewley’s Lattice Diagram Implementation by using ATP/EMTP

Transients caused by lightning that strikes to transmission lines, switching operations or faults, are fundamentals in selecting equipment insulation levels and protection devices. Thus, studies of electromagnetic transients on transmission lines have demonstrated that when a change on the normal operation of the system takes place, voltage and currents traveling waves appear and these are reflected and refracted in the transmission line. In this paper, an ATPDraw simulator is developed to observe the propagation of voltage and current traveling waves along the transmission lines. The Bewley's Lattice diagram is used into the simulator to show in a comprehensive manner the behavior of the traveling waves. The behavior of the traveling waves is strictly depending on the reflection and refraction coefficients in the sending and receiving nodes, in turn these coefficients are depending on the transmission network's parameters, such as the characteristic impedance and the impedance of the sending and receiving ends.

A hybrid SVM-TT transform-based method for fault location in hybrid transmission lines with underground cables

This paper proposes a hybrid fault location technique in an overhead line that contains an underground cable. Time-time (TT)- and S-transforms are used to extract information from the transient voltage signals measured at a single end. This information is used to train a support vector machine (SVM) which determines whether the fault occurs in the first or second half of the underground cable or overhead line. To enhance the classification accuracy, the SVM parameters are optimized using the particle swarm optimization (PSO). After the identification, the fault is located using Bewley’s lattice diagram and the transformed voltage signal. The performance of the proposed method is assessed under various parameters such as fault type, resistance, inception angle, and location. Simulation results validate the high accuracy of the proposed method in identifying the faulty section and locating the fault. Also, it is shown that the proposed technique outperforms other methods in the literature.