Isomorphic Systems Research Articles

Decidability of the isomorphism problem between multidimensional substitutive subshifts

Abstract An important question in dynamical systems is the classification problem, that is, the ability to distinguish between two isomorphic systems. In this work, we study the topological factors between a family of multidimensional substitutive subshifts generated by morphisms with uniform support. We prove that it is decidable to check whether two minimal aperiodic substitutive subshifts are isomorphic. The strategy followed in this work consists of giving a complete description of the factor maps between these subshifts. Then, we deduce some interesting consequences on coalescence, automorphism groups, and the number of aperiodic symbolic factors of substitutive subshifts. We also prove other combinatorial results on these substitutions, such as the decidability of defining a subshift, the computability of the constant of recognizability, and the conjugacy between substitutions with different supports.

Design and realization of an isomorphic master-slave robotic system for precise sub-micrometer manipulations in ophthalmic surgery

Design and realization of an isomorphic master-slave robotic system for precise sub-micrometer manipulations in ophthalmic surgery

State Observer Synchronization of Three-dimensional Chaotic Oscillatory Systems Based on DNA Strand Displacement.

Currently, DNA strand displacement (DSD) as the theoretical basis of DNA chemical reaction networks (CRNs) has promoted the development of chaotic synchronization technique. This paper introduces the synchronization technology of two isomorphic three-dimensional chaotic systems based on DNA strand displacement under state observer. By studying the theoretical knowledge of DNA molecules, multiple DSD reactions are used to construct three-dimensional chaotic system. Based on two isomorphic chaotic systems, the linear transformation system and the state observer system are designed according to the theory of state observer construction. In addition, in order to realize the synchronization of chaotic systems, a coupling controller is designed between the drive system and the linear transformation system, and a soft variable-structure controller is designed between the state observer system and the response system. Through multiple DSD reactions, the chemical reaction networks of four chaotic systems and two controllers are constructed, and they are cascaded to realize the synchronization of two isomorphic three-dimensional chaotic systems. Numerical simulations verify the effectiveness and robustness of the scheme. Our work will extend and provide a reference for new methods to achieve synchronization of chaotic systems using DSD.

An Introduction to Isomorphic Mathematical Analysis System

This paper is to build a primitive framework for a new possible extended system of real mathematical analysis - the Isomorphic Mathematical Analysis System (IMAS). It is based on some new concepts: e.g. isomorphic frame, dualvariable-isomorphic function, and isomorphic coordinate system. More concepts are introduced to constitute the whole IMAS framework. This IMAS attempts to provide current MA with new implements, which include isomorphic frame, thereby effectively putting the MA to work as well in some unevenly distributed coordinate spaces, realized by the isomorphic coordinate system. With these implements, many existing MA concepts are extended and incorporated into the new IMAS.

The Geometric Phase in Classical Systems and in the Equivalent Quantum Hermitian and Non-Hermitian PT-Symmetric Systems

The decomplexification procedure allows one to show mathematically (stricto sensu) the equivalence (isomorphism) between the quantum dynamics of a system with a finite number of basis states and a classical dynamics system. This unique way of connecting different dynamics was used in the past to analyze the relationship between the well-known geometric phase present in the quantum evolution discovered by Berry and its generalizations, with their analogs, the Hannay phases, in the classical domain. In here, this analysis is carried out for several quantum hermitian and non-hermitian PT-symmetric Hamiltonians and compared with the Hannay phase analysis in their classical isomorphic equivalent systems. As the equivalence ends in the classical domain with oscillator dynamics, we exploit the analogy to propose resonant electric circuits coupled with a gyrator, to reproduce the geometric phase coming from the theoretical solutions, in simulated laboratory experiments.

К 100-летию феноменолога А.-Т. Тименецки (1923-2014)

In connection with the forthcoming anniversary of the Polish-American phenomenologist the formation of her creative way which absorbed influence of aesthetics, philosophy of life, phenomenology, analytical philosophy is discussed. The paper compares the phenomenological concept of Tymieniecka to contemporary cinema as an isomorphic system reflecting reality.

A Lightweight Exoskeleton Force Feedback Glove

The wearable force feedback glove provides a promising solution for enhancing immersion during teleoperation. In this study, a lightweight five-finger exoskeleton force feedback glove (EFFG) was designed, enabling driving force detection and flexible force feedback. This wireless prototype weighs only 278 g. The glove features a bionic structure and optimized linkage length to ensure operator safety while providing extensive coverage of the finger working space. Moreover, a detailed illustration of the kinematic and dynamic analyses, as well as the circuit structure, was presented. With this prototype as the basis, an isomorphic teleoperation system is designed to achieve force feedback during teleoperation. Concurrently, a driving force-based impedance controller was proposed to enable smooth and precise force feedback. Finally, the performance of the EFFG prototype was evaluated in both unconstrained and constrained environments, demonstrating that the proposed glove is lightweight, capable of detecting driving force, and provides flexible force feedback.

Compact ultrapseudometrics and inverse systems

A method of construction of an inverse system of finite compacta, indexed with positive reals, from a compact ultrapseudometric, is proposed. It is proved that homeomorphisms and natural preorder on the class of compact ultrapseudometrics correspond to strict isomorphisms and strict morphisms of the respective inverse systems. Properties of the poset obtained with "gluing together" of the isomorphic inverse systems, are discussed.

Collective Abstraction

This paper develops a novel theory of abstraction—what we call collective abstraction. The theory solves a notorious problem for noneliminative structuralism. The noneliminative structuralist holds that in addition to various isomorphic systems there is a pure structure that can be abstracted from each of these systems; but existing accounts of abstraction fail for nonrigid systems like the complex numbers. The problem with the existing accounts is that they attempt to define a unique abstraction operation. The theory of collective abstraction instead simultaneously defines a collection of distinct abstraction operations, each of which maps a system to its corresponding pure structure. The theory is precisely formulated in an essentialist language. This allows us to throw new light on the question to what extent structuralists are committed to symmetric dependence. Finally, we apply the theory of collective abstraction to solve a problem about converse relations.

Изучение понятия изоморфизма в университетском курсе алгебры как способ формирования математической грамотности будущих учителей математики

The aim of the research is to identify the particularities of formation of the isomorphism concept at mathematical faculties of universities when teaching undergraduate teacher training students. The paper provides examples of isomorphic systems studied in school and university mathematics courses, suggests a method for checking the associative property based on the Cayley’s theorem on isomorphism, presents situations where isomorphism of systems is used to solve computational problems. Scientific novelty of the research lies in the proposed method of checking the associative property of an operation in finite groupoids. As a result, using specific cases of isomorphism application, it has been shown that this phenomenon is an important component of mathematical literacy of future mathematics teachers.

Attack and protection schemes on fabric isomorphic crosschain systems

Crosschain solves the problem of value transfer and asset interaction between different blockchains with different consensus mechanisms, or different infrastructures. It not only realizes the mutual communication of multiple independent blockchains, but also ensures the data consistency. However, existing crosschain technologies like notary mechanism, hash locking, distributed private key control, and sidechain/relaychain have potential vulnerabilities, resulting in different kinds of attacks. For example, some vulnerabilities that only exist in a blockchain like DDOS, overflow, double-spending, and so on, may have an impact on another secure blockchain due to the openness of the crosschain system. Even if all blockchains are safe enough, the security of the crosschain system cannot be guaranteed, and there are still many loopholes in the process of crosschain, which affect all blockchains. The security of crosschain has emerged as an important issue. In this work, based on BitXHub, an open-source project of crosschain, we are motivated to study the security of Fabric isomorphic crosschain system. First, we analyze the vulnerabilities in different layers of Fabric isomorphic crosschain systems, and discuss the principles of different kinds of attacks. Based on the principles, we discover and define five new crosschain attacks, including crosschain integer overflow attack, crosschain transaction forgery attack, crosschain transaction replay attack, crosschain transaction sequence attack, and crosschain routing attack. Second, we implement all the five attacks, and indicate the applicable scenarios and the boundary conditions in which each attack may occur. Third, we propose five schemes to prevent the corresponding attacks and evaluate the effectiveness of the protection schemes. We comprehensively discuss and analyze the schemes of attacks and their corresponding prevention toward Fabric isomorphic crosschain systems.

Spatial composition distribution of a Ni-Cu binary alloy powder in a thermal plasma process

The composition of nanoparticles obtained by a thermal plasma process was quantitatively investigated using a Ni-Cu isomorphous alloy system. Specifically, a Ni-Cu alloy nanopowder with an average particle diameter of ~ 70 nm was prepared by the thermal plasma process and the particle composition was investigated. As the lattice constant follows the Vegard's law, a nanopowder with an average composition equivalent to the predefined composition was successfully obtained. According to the EDS analysis obtained from each particle, the standard deviation of composition distribution was 7.7 at% as a powder. The computational study indicated that each particle has a homogeneous composition because of the nanoparticle formation via nanodroplet and that a composition distribution of 1.05 at% is estimated in the powder. Further, the spatial composition distribution of the alloy powder in the reaction chamber was experimentally studied by trapping the powder at a certain location, and the results indicated that the composition distribution of the powder varied spatially.

Quasi-Synchronization Control of Multiple Electrohydraulic Actuators With Load Disturbance and Uncertain Parameters

This article discusses the quasi-synchronous tracking control of multiple electrohydraulic actuators (MEHAs) with load disturbances, and parametric uncertainties. Each electrohydraulic actuator (EHA) has a third-order nonlinear dynamics in the presence of unknown lumped uncertainties resulting from some uncertain hydraulic parameters, and external load. First, the isomorphic MEHA system is constructed, which extracts the nominal model from the lumped uncertainties. Then, an adaptive quasi-synchronization controller is designed such that each cylinder position of the MEHA system tracks the desired trajectory in a collaborative manner. To compensate the lumped uncertainties of the MEHA system, adaptive laws are constructed, and the resultant quasi-synchronization controller guarantees that all the closed-loop signals, and the estimate errors are uniformly ultimately bounded. Finally, the effectiveness of the proposed control method is verified by simulation, and experimental results.

Synthesis and characterization of carbon-coated Cu-Ni alloy nanoparticles and their application in conductive films

In this paper, an efficient fabrication route is presented for carbon-coated Cu-Ni alloy nanoparticles (Cu1-xNix@C NPs; x = 0–1.0) by means of electrical wire explosion under methane gas. The Cu-Ni binary system, which is considered to be an ideal isomorphous system, has carbon growth controllable by tuning the atomic fraction of Cu and Ni with largely different carbon solubility. As the Ni content increases, the average particle size and carbon layer thickness increase. It is notable that the carbon layer is very thin, <2 nm, regardless of the core size for pure Cu@C NPs. On the other hand, as the Ni content increases, the particle size dependence of the carbon-layer thickness becomes significant and the carbon layer is obviously tunable from amorphous to crystalline form. The high-temperature oxidation stability of Cu1-xNix@C NPs is enhanced with increasing Ni content due to the higher thermal stability of carbon layers with greater thickness and high crystallinity. The conductive films were prepared using screen-printing of paste containing Cu1-xNix@C NPs and the electrical resistivity was mapped according to the Ni content. The temperature stability of the sheet resistance and activation energy of oxidation for the conductive films increase with increasing Ni content.

Sintering mechanism of Ag-Pd nanoalloy film for power electronic packaging

Silver electrochemical migration causing short-circuit could be mitigated by Ag-Pd alloy. The conventional mechanical mixed Ag and Pd nanoparticles requires high alloying temperature as high as 850 °C. In this work, Ag20Pd nanoalloy film is prepared using pulsed laser deposition under room temperature as die attach material. After low temperature bonding at 300 °C, the bondline keeps in Ag20Pd alloyed state with a shear strength of 23.5 MPa (higher than MIL-STD-883 K, 7.8 MPa). The Ag20Pd nanoalloy exhibits superior resistance to Ag ionic migration with short-circuit time tripled than pure Ag sintered layer. A Ag-rich layer appears on the surface of Ag-Pd nanoalloy, although the Ag-Pd is the typical isomorphous alloy system. Molecular dynamics simulation reveals that Ag atoms (214.0 kJ/mol) diffuse easier than that of Pd atoms (234.6 kJ/mol) on the nanoalloy surface layer, while showing similar mobility for inner nanoalloy. The Ag-rich layer consisting of dynamic exchanging atoms has a prewetting effect and contributes to the neck formation among nanoparticles. This work sheds light on the sintering mechanism of Ag-Pd nanoalloy, and it is confirmed that Ag-Pd nanoalloy is promising for low temperature bonding in terms of the high reliability power electronic.

Polar and Helical Isomorphous Crystals of Proline Derivatives: Influence of a Fluorine Atom on the Electric Susceptibility

Two novel nonlinear optical isomorphous crystals of proline derivatives with alkyne functionality have been obtained (Boc-L-ProNH(CH2)2CCH and Boc-cis-4-fluoro-L-ProNH(CH2)2CCH). Both derivatives, which differ only by the substitution of a H atom to a F atom, adopt the same polar and columnar right-handed helix arrangement in the crystalline state. In addition, adjacent polar helical columns all point in the same direction, thus generating a macrodipole and a crystalline system conducive for second harmonic generation (SHG) properties. This isomorphous crystal system constitutes an interesting tool to study the effect of the fluorine atom on the dipole moment and on the first hyperpolarizability. Starting from the PBC optimized geometries of the crystals, the macroscopic second-order nonlinearity, χ(2), of the newly synthesized crystals has been estimated by quantum chemical calculations. These χ(2) responses are of the same order of magnitude as those of inorganic proline derivatives while smaller than those observed in crystals of push–pull π-conjugated molecules.Graphic

Isomorphic system modules for construction of scalable embedded computers

Isomorphic system modules for construction of scalable embedded computers

Effect of composition on the stacking fault energy of copper-nickel alloys using molecular dynamics simulations

Cu-Ni alloys, popularly known as Cupronickel, have gained a variety of interesting applications owing to their excellent corrosion resistance, excellent ductility when annealed and good tensile strength. The Cu-Ni system is a binary isomorphous system, a solid solution of FCC crystal structure exists at all compositions below the solidus. In FCC alloys, the type and amount of alloying has a profound effect on the stacking fault energy (SFE). In the present work, a molecular dynamics simulation technique has been used for creation of stacking fault and determination of SFE. A stacking fault is created in the simulation by the displacement of one atomic plane relative to the rest of the crystal, and the SFE is subsequently computed by the measuring the difference in energy of the system before and after the creation of the fault. The simulation is locally alloyed in the vicinity of the stacking fault and the SFE is plotted as a function of the Ni content. The stacking fault energy was found to increase with an increase the Ni content, conforming to experimental results, from 40 mJ/m 2 for pure copper to 70 mJ/m 2 for a Cu-Ni alloy with 40 atomic percent Ni.

Measurements of the melting points, liquidus, and solidus of the Mo, Ta, and Mo[sbnd]Ta binary alloys using a novel high-speed pyrometric technique

The measurement of high phase-transition temperature is equally challenging and useful for developing high-temperature materials for critical applications. Pyrometer is a suitable option to measure the phase-transition temperature above 2300 K. In this work, Mo, Ta, and their isomorphous binary alloys are selected as the target system for high-speed pyrometer temperature measurements in the arc-melting setup. The present phase transitions (melting point, solidus, and liquidus) measurements indicate that the MoTa is an isomorphous system with a narrow freezing range (i.e., an average value < 35 K). The results from this present work would change the existing MoTa phase diagram. The Gibbs energy modeling for liquid (L) and BCC_A2 (α) phases of the MoTa system are then performed, including the latest experimental results from this work. The applications of the current experimental methodology could be extended to measure the high phase-transition temperatures in superalloys with significant commercial values.

A Series of Organic-Inorganic Hybrid Compounds [(C2H5)4N]InCl4-xBrx (x = 0, 2, 4): Synthesis, Crystal Structure, and Nonlinear Optical Properties.

A series of noncentrosymmetric (NCS) tetraethylammonium tetrahalide indium hybrids, [(C2H5)4N]InCl4-xBrx (x = 0, 2, 4), was synthesized by a hydrothermal reaction. Their structures, thermal properties, and linear and nonlinear optical properties were identified. The crystals belong to an isomorphic hexagonal system and feature zero-dimensional structures containing isolated distorted InCl4-xBrx- tetrahedra with [N(C2H5)4]+ cations inserted as charge balance. On the basis of the powder second harmonic generation, the SHG levels of [(C2H5)4N]InCl4-xBrx (x = 0, 2, 4) were estimated to be approximately 0.5, 0.7, 0.8 × KDP, respectively. The relationship between halogen composition and band gap, optical anisotropy, and frequency doubling effects were evaluated by first-principles calculations, thus suggesting that halogen regulation favors the design of new organic-inorganic hybrid halides with excellent performances for many optoelectronic applications.