Isomorphous Structures Research Articles

Positive equilibria of power law kinetics on networks with independent linkage classes

Studies about the set of positive equilibria (\(E_+\)) of kinetic systems have been focused on mass action, and not that much on power law kinetic (PLK) systems, even for PL-RDK systems (PLK systems where two reactions with identical reactant complexes have the same kinetic order vectors). For mass action, reactions with different reactants have different kinetic order rows. A PL-RDK system satisfying this property is called factor span surjective (PL-FSK). In this work, we show that a cycle terminal PL-FSK system with \(E_+\ne \varnothing \) and has independent linkage classes (ILC) is a poly-PLP system, i.e., \(E_+\) is the disjoint union of log-parametrized sets. The key insight for the extension is that factor span surjectivity induces an isomorphic digraph structure on the kinetic complexes. The result also completes, for ILC networks, the structural analysis of the original complex balanced generalized mass action systems (GMAS) by Müller and Regensburger. We also identify a large set of PL-RDK systems where non-emptiness of \(E_+\) is a necessary and sufficient condition for non-emptiness of each set of positive equilibria for each linkage class. These results extend those of Boros on mass action systems with ILC. We conclude this paper with two applications of our results. Firstly, we consider absolute complex balancing (ACB), i.e., the property that each positive equilibrium is complex balanced, in poly-PLP systems. Finally, we use the new results to study absolute concentration robustness (ACR) in these systems. In particular, we obtain a species hyperplane containment criterion to determine ACR in the system species.

Congruence of rational matrices defined by an integer matrix

We study algorithms that construct an invertible matrix B∈Mn(Z) that defines congruence Btr·X·B=Y of given square rational matrices X,Y∈Mn(Q). We describe a general algorithm and discuss special cases of positive-definite and singular matrices. In the first case, the algorithm solves the decision problem and unequivocally determines if such an integer matrix exists.Since the problem of isomorphism of various finite structures can be viewed as a special case of matrix congruence problem, our results are applicable in this setting. We discuss this topic and show that the presented algorithms solve this problem in the case of partially ordered sets, vertex and edge labeled directed and undirected graphs. Moreover, they allow computing the automorphism group Aut(G) of a given (di)graph G.The results of this work are applicable in the general framework of Coxeter spectral analysis of signed graphs Δ introduced in (SIAM J. Discrete Math. 27:827–854, 2013) as they make it possible to calculate strong and weak Gram Z-congruences. Moreover, they can be used to compute isotropy groups and thus are useful in the study of matrix morsifications in the sense of (J. Pure Appl. Algebra 215:3–34, 2011).

Design and Validation of Isomorphic Crystal Library for Nonlinear Optics and THz Wave Generation

AbstractDevelopment of new organic crystals possessing large second‐order optical nonlinearity is very challenging because of strong tendency of centrosymmetric dipole–dipole molecular assembly in crystals. This tendency makes it difficult to develop various analogous crystals that allow fine tuning of optical and physical properties to enhance the device performance. A design approach of an isomorphic crystal library consisting of 11 highly efficient nonlinear optical salt crystals is reported. Analyzing the so‐called isomorphic tolerance space in previously reported mother crystals (PMnXQ chromophores, where PM denotes piperidin‐4‐ylmethanol electron donor, n corresponds to the substituted position of halogen (X) group on the quinolinium (Q) electron acceptor), various substituents are introduced into the PMnXQ crystals at different positions, considering their space‐filling characteristics and interionic interaction ability. All 11 PMnXQ crystals exhibit an isomorphic (or pseudo‐isomorphic) crystal structure, in which the cationic chromophores form a perfectly parallel assembly for maximizing the second‐order nonlinear optical susceptibility. The optical, physical, and crystal characteristics of newly designed, synthesized, and grown isomorphic PMnXQ crystals show both similarities and differences. Excellent THz wave‐generation performance is demonstrated in both kHz‐ and MHz‐repetition optical pump systems with new PMnXQ crystals. Therefore, the design approach using isomorphic tolerance space is very attractive for developing diverse isomorphic analogous organic crystals.

Synergy-Based Analytical Design of Wire-Driven Continuum Manipulators

This letter discusses the design for wire-driven continuum manipulators. To achieve multiple desired postures, a novel design method that analytically determines the mechanism and control parameters of the manipulator is proposed. First, by introducing a discrete model of the manipulator, the governing manner of the posture for tension and wiring is formulated. Based on the governing manner, the synergy relation of wire drive systems is derived. Next, by employing the principal component analysis, the synergy relation of multiple desired postures is derived. This synergy relation is customized suitably for designing the manipulator. Then, by focusing on the isomorphism of the mathematical operation structure in the two synergy relations, an analytical determination method for the mechanism and control parameters of the manipulator is developed. Finally, the proposed method is experimentally demonstrated. A continuum manipulator with two wire drive systems is developed for attaining five desired postures. The validity of the proposed method is confirmed through the design and fabrication of the manipulator and the attainment of desired postures.

Halogen Bonding Involving Gold Nucleophiles in Different Oxidation States.

A single-crystal X-ray diffraction (XRD) study of diaryliodonium tetrachloroaurates (or, in the recent terminology, tetrachloridoaurates), [(p-XC6H4)2I][AuCl4] (X = Cl, 1; Br, 2), was performed for 1 (the structure is denoted as 1a to show similarity with the isomorphic structure 2a) and two polymorphs─2a (obtained from MeOH) and 2b (from 1,2-C2H4Cl2). Examination of the XRD data for these three structures revealed 2-center C-X···AuIII (X = Cl and Br) and 3-center bifurcated C-Br···(Cl-Au) halogen bonding (abbreviated as XB) between the p-Cl or p-Br atoms of the diaryliodonium cations and the gold(III) atom of [AuCl4]-. The noncovalent nature of AuIII-involving interactions, the nucleophilicity of the gold(III) atoms, and the electrophilic role of p-X atoms of the diaryliodonium cations in the XBs were studied by a set of complementary computational methods. Combined experimental and theoretical studies allowed the recognition of the d-nucleophilicity of the [d8AuIII] atom which, regardless of its rather substantial formal 3+ charge, can function as a d-nucleophilic partner of XB. This conclusion was also supported by theoretical calculations performed for the structures' refcodes BINXOM and ICSD 62511; the obtained data verified the nucleophilicity of AuIII toward a K+ ions or a σ-(Cl)-hole, respectively. All our results, together with consideration of relevant literature, indicate that gold atoms in the three oxidation states (0, I, and even III) exhibit nucleophilicity in XBs.

虚实同形语言結構及其教学研究

The research object of this paper is the same-morphic language structure in Chinese, that is, the same language structure (word or structure) has two meanings of "real meaning" and "virtual meaning" at the same time. For example, "don't say" in Chinese can be used as a phrase with practical meaning to express the meaning of "don't say", and it can also be used as a discourse marker to lead out topics. This common language phenomenon in Chinese is one of the difficulties for foreign students to learn Chinese and understand Chinese. Therefore, looking for the reasons for this language phenomenon and trying to summarize some rules will help foreign students learn Chinese and understand Chinese. Specifically, it includes the description and analysis of the overall characteristics, types and causes of this language phenomenon. We need to determine a standard to judge this language phenomenon, analyze and explain different types of real-virtual isomorphic language structures and their causes, and then summarize the hidden laws, and apply the theoretical results to various aspects of teaching Chinese as a foreign language. Fields, such as: writing teaching materials, improving reference books, supplementing the teaching content of specific course types, etc.

ФОРМАЛНО ОПИСАНИЕ НА СЛОВООБРАЗУВАТЕЛНИТЕ СТРУКТУРИ В НОРМАТИВНАТА ГРАМАТИКА НА БЪЛГАРСКИЯ ЕЗИК / FORMAL DESCRIPTION OF WORD-FORMATION STRUCTURES IN BULGARIAN NORMATIVE GRAMMAR

This work proposes principles for the formal description of word-formation structures in a synchronic study within the framework of normative grammar. One of the basic postulates of normative grammar is the independence of the de-scription of form and meaning, which is motivated by relative, though sufficient, au-tonomy of the structure of meaning (semantic structure) and of the formal structure of complex language units. This study takes for granted the existence of structural isomorphism between clauses and derived lexemes. In the context of the description of word-formation phenomena, this means that – in parallel to what is found in clause syntax, which distinguishes between the conceptual structure of a clause and the clausal form – both semantic structure and formal structure are assigned to derived lexemes. The consistent implementation of this distinction leads to defining word-formation as morphemic syntax (similar to sentence syntax) and derived words as structures within which rules for formal and semantic combination of morphemes are applied. The attempt at developing a model for formal derivational structures presented in the paper is based on the formal features of derivational exponents. These features serve to derive the following dichotomic division criteria: 1) affixal – +/- attachment of a given type of affix to the stem; 2) confixal – +/- attachment of two affixes to the stem; 3) alternating – +/- qualitative stem alternation; 4) reductional – +/- stem reduction; 5) paradigmatic – +/- attachment to the stem of a grammatical morpheme other than the one in the derivational base. Keywords: formal description, formal word-formation structures, normative grammar

Crystal structure prediction with machine learning-based element substitution

The prediction of energetically stable crystal structures formed by a given chemical composition is a central problem in solid-state physics. In principle, the crystalline state of assembled atoms can be determined by optimizing the energy surface, which in turn can be evaluated using first-principles calculations. However, performing the iterative gradient descent on the potential energy surface using first-principles calculations is prohibitively expensive for complex systems, such as those with many atoms per unit cell. Here, we present a unique methodology for crystal structure prediction (CSP) that relies on a machine learning algorithm called metric learning. It is shown that a binary classifier, trained on a large number of already identified crystal structures, can determine the isomorphism of crystal structures formed by two given chemical compositions with an accuracy of approximately 96.4%. For a given query composition with an unknown crystal structure, the model is used to automatically select from a crystal structure database a set of template crystals with nearly identical stable structures to which element substitution is to be applied. Apart from the local relaxation calculation of the identified templates, the proposed method does not use ab initio calculations. The potential of this substitution-based CSP is demonstrated for a wide variety of crystal systems.

Synthesis, chemical and physical properties of lanthanide(III) (Nd, Gd, Tb) complexes derived from (E)-ethyl 4-(2-hydroxybenzylideneamino)benzoate

The 1:2 reaction between Ln(NO3)3·6H2O (1) (Ln = Nd (a), Gd (b) or Tb (c)) and ((E)-ethyl 4-((2-hydroxybenzylidene)amino)benzoate) (LN,OH) in ethanol has provided access to the complexes [LnIII(LNH,O)2(NO3)3(H2O)] (2a–c) in good yield. The isomorphous structures of 2a–c have been determined by single-crystal X-ray crystallography. The LnIII ions in 2a–c are coordinated by 9 oxygen atoms: two from the phenolate oxygen atoms of the Schiff bases, six from three chelating nitrato groups and one aqua ligand. The ligands LN,OH behave as monodentate phenolate O–donors, whereby an additional hydrogen atom is bonded to the imino nitrogen atom, resulting in a formally neutral ligand that adopts an exceptionally unusual coordination mode engaging in the zwitterionic form. The nine donor atoms that define the coordination polyhedra surrounding the LnIII ion are best described as capped square antiprisms. The crystal structures are based on a variety of intermolecular interactions. Hirshfeld surface analysis was used to assess the degree of interactions between the molecules. Susceptibility measurements on 2a–2c confirm the occurrence of the free ion ground 2S+1LJ state at room temperature. However, the magnetization measurements at 2 K revealed a lack of saturation at the highest applied field of 70,000 Oe for both 2a and 2c, indicating the presence of substantial magnetic anisotropy in these compounds. On the other hand, 2b exhibits perfect paramagnetic behavior with magnetic saturation at high fields, indicating the absence of significant magnetic anisotropy in this compound. Solid-state IR and UV/VIS data are discussed in terms of the structural features. Solid 2a–c emit in the visible region upon UV-Excitation with the emission exhibiting dopant characteristics.

Two new isotypic Co(II)/Ni(II)-coordination polymers based on 5-(6-Carboxypyridin-2-yl)isophthalic acid: Synthesis, structure analysis and magnetism properties

Two new two-dimensional (2D) metal-organic frameworks (MOFs), named [Co3(L)2(H2O)4] (1) and [Ni3(L)2(H2O)4] (2) [H3L = 5-(6-Carboxypyridin-2-yl)isophthalic acid], have been solvothermally synthesized under different solvent systems, which have been well characterized by elemental analysis, FT-IR spectrum, powder X-ray diffraction (PXRD) and thermogravimetric analysis (TGA). Single-crystal X-ray diffraction shows that 1 and 2 are isomorphic structures, giving a 2D layer structure based on the trinuclear secondary building units (SBU). Topology analyses reveal that 1 and 2 can be simplified as a binodal (3, 6)-connected kgd topological net with the point symbol (43)(46·66·83). The magnetic properties for 1 and 2 have been systemically explored, which shows the antiferromagnetic interactions between metal ions in the solid state.

Analogue Models and Universal Machines. Paradigms of Epistemic Transparency in Artificial Intelligence

The problem of epistemic opacity in Artificial Intelligence (AI) is often characterised as a problem of intransparent algorithms that give rise to intransparent models. However, the degrees of transparency of an AI model should not be taken as an absolute measure of the properties of its algorithms but of the model’s degree of intelligibility to human users. Its epistemically relevant elements are to be specified on various levels above and beyond the computational one. In order to elucidate this claim, I first contrast computer models and their claims to algorithm-based universality with cybernetics-style analogue models and their claims to structural isomorphism between elements of model and target system (in: Black, Models and metaphors, 1962). While analogue models aim at perceptually or conceptually accessible model-target relations, computer models give rise to a specific kind of underdetermination in these relations that needs to be addressed in specific ways. I then undertake a comparison between two contemporary AI approaches that, although related, distinctly align with the above modelling paradigms and represent distinct strategies towards model intelligibility: Deep Neural Networks and Predictive Processing. I conclude that their respective degrees of epistemic transparency primarily depend on the underlying purposes of modelling, not on their computational properties.

THE MAXIMAL IDEAL IN THE SPACE OF OPERATORS ON

AbstractWe study the isomorphic structure of $(\sum {\ell }_{q})_{c_{0}}\ (1< q<\infty )$ and prove that these spaces are complementably homogeneous. We also show that for any operator T from $(\sum {\ell }_{q})_{c_{0}}$ into ${\ell }_{q}$ , there is a subspace X of $(\sum {\ell }_{q})_{c_{0}}$ that is isometric to $(\sum {\ell }_{q})_{c_{0}}$ and the restriction of T on X has small norm. If T is a bounded linear operator on $(\sum {\ell }_{q})_{c_{0}}$ which is $(\sum {\ell }_{q})_{c_{0}}$ -strictly singular, then for any $\epsilon>0$ , there is a subspace X of $(\sum {\ell }_{q})_{c_{0}}$ which is isometric to $(\sum {\ell }_{q})_{c_{0}}$ with $\|T|_{X}\|<\epsilon $ . As an application, we show that the set of all $(\sum {\ell }_{q})_{c_{0}}$ -strictly singular operators on $(\sum {\ell }_{q})_{c_{0}}$ forms the unique maximal ideal of $\mathcal {L}((\sum {\ell }_{q})_{c_{0}})$ .

КЫТАЙ ЖАНА КЫРГЫЗ ТИЛДЕРИНДЕГИ ТИЛДИК ПАРАЛЛЕЛДЕР

Language parallels selected for research are relevant for study in comparative linguistics, especially in noncognate languages. The ability to see the language material of the functional content helps the translator to construct isomorphic structures that ensure the transmission of information during translation. Despite this difference between languages, common points of contact are all the same, and they help in many ways to see the functional content, hidden behind the linguistic material. The main purpose of the articles is to determine the sound correspondences and changes in the language parallels in the Kyrgyz and Chinese languages. Within the framework of the idea of functional isomorphism, it is possible to recognize the existence of parallels between the Kyrgyz and Chinese languages.

Об адекватности психофизических измерений

The laws of Fechner and Stevens are the main psychophysical laws. The difficulty lies in the fact that the laws of Fechner and Stevens do not coincide. There are many ways to explain this contradiction. But the problem of the adequacy of psychophysical measurements has not been solved. The fact is that Fechner and Stevens define the method of measurement differently. But only the definition of Stevens is taken as a basis in the representative theory of measurements, which was developed initially as a theory of psychophysical measurements. There are a number of shortcomings in the representative theory. In particular, there is no built — in mechanism for verifying the adequacy of measurement results. Therefore, there are doubts about the quantitative nature of psychological attributes. And the question remains unresolved: what to do with Fechner’s law. In order to develop a quantitative measurement theory, a rating theory was proposed. From the standpoint of the rating theory, both psychophysical laws are equal and differ in the way of measurement. It is shown that the measurement results obtained by different methods are equivalent in a certain sense. The theoretical justification of equivalence is the isomorphism of algebraic structures. Such a solution to the Fechner-Stevens problem is constructive since it contains the possibility of experimental verification of the adequacy of the measurement results. An example of subjective measurement is considered in different ways. The example includes a procedure for checking adequacy.

Highly stable and isomorphic donor–acceptor stacking in a family of n-type organic semiconductors of BTBT–TCNQ derivatives

Unsymmetrically substituted donor–acceptor type compounds exhibit an isomorphous layered packing structure, which is discussed in terms of DFT-based quantum chemical calculations.

Structural Properties and Isomorphism Theorems for Cayley Digraphs of Full Transformation Semigroups with Respect to Green's Equivalence Classes

Structural Properties and Isomorphism Theorems for Cayley Digraphs of Full Transformation Semigroups with Respect to Green's Equivalence Classes

The Problem of Isomorphic Structures

Structuralism is one of the most popular contemporary accounts of mathematics. Despite its popularity, it has been challenged on the grounds of consistency. In this paper, I show that existing arguments purporting to establish an inconsistency miss the mark. I then proceed to develop a new argument against realist structuralism, to show that the commitment to mathematical pluralism and the structural identity criterion embraced by the realist structuralist jointly entail a contradiction.

In Defence of Radically Enactive Imagination

Hutto and Myin defend, on the basis of their “radically enactive” approach to cognition, the contention that there are certain forms of imaginative activity that are entirely devoid of representational content. In a recent Thought article, Roelofs argues that Hutto and Myin’s arguments fail to recognise the role of representation in maintaining the structural isomorphisms between mental models and things in the world required for imagination be action-guiding. This reply to Roelofs argues that his objection fails because it fails to fully appreciate the resources radical enactivists have at their disposal in characterising basic imaginings.

Decomposition (Ferrogravitolysis) Water and Hydrocarbons by means of Technical Ferrogravitational Field

Experimental and theoretical studies of the author (period: 1968 - present) have shown that true sources of magnetic field are magnetic fundamental particles (magnetic charges), and not moving electrons. The main reason for the vicious ignorance of magnetic charges in physics is the super-hard conditions of confinement of these particles in atoms and substance which are cardinally different from the confinement of electrons. Magnetic charges together with electric charges form the shells of atoms which in reality are electromagnetic, and not electronic. The orbital electromagnetic currents in atomic shells are sources of the gravitational field which is the vortex electromagnetic field and is described by vortex vector rot[E–H]. Depending on the state polarization of vortex vectors rot[E–H] in compositions of the atomic gravitational fields its subdivided into paragravitational (PGF) and ferrogravitational fields (FGF). The main process defining formation of chemical compounds is the gravito-chemical binding or compression of atoms by the forces of the paragravitational "Dark Energy" which is realized between PGF atoms-sources. Between the atoms emitting PGF and FGF the effect of Gravitational levitation is realized the forces of which push the atoms away from each other. Therefore, the combination of carbon atoms (PGF sources) and hydrogen atoms (FGF–sources) with the formation of hydrocarbon molecules can be realized only if the hydrogen atoms are in molecular form (1H2). In the composition of water, within the framework of the chemical formula H2O, two stable isomorphic molecular structures are realized, the gravito-chemical bond in which is carried out, respectively of the hydrocarbon scenario described above, as well as under conditions of unidirectional ferropolarization of the gravitational fields of atoms in molecule and of the implementation of the so-called hydrogen bond. The external (technical) ferrogravitational field violates the initial (paragravitational) state of gravitational fields in interatomic regions what leads to the formation of positive (gravitational) “Dark energy” the forces of which break interatomic chemical bonds and leads to molecular decays. This process, by analogy with process of electrolysis, can be referred to as ferrogravitolysis. The Author's technology for the decomposition of water molecules by means of FGF is a technical analogue of the natural process of water decomposition which is realized in the cells of leaves of green plants and algae. The intensity of technical FGF, and, consequently, the efficiency of the process of decomposition water molecules can be thousands of times higher than the efficiency of its natural decomposition in plant cells, which makes it possible to obtain cheap green hydrogen for wide practical use. In addition, the effectiveness of the impact of (technical) FGF on the state of gravitational fields in the interatomic regions of molecules and the implementation of the process of their decomposition is many times greater than the capabilities of the currently used electric field.

Post-synthetic anchoring Fe(III) into a fcu-type Zr-MOF for the catalyzed hydrolysis of 5-hydroxylmethoxyfurfural

Metal-organic frameworks (MOFs) featuring a fcu-type net based on 12-connected [Zr6(μ3-O)4(μ3-OH)4] cluster have received considerable interest for the fundamental investigation of structure-property relationships in a wide range of catalytic reactions. In this work, the bipyridine (bpy) chelate group was introduced into the fcu-type framework of UiO-67, giving UiO-67bpy as the catalyst support. Then, FeCl3 was post-synthetically anchored to the bpy group, resulting into the isolation of FeCl3/UiO-67bpy. Catalyzed hydrolysis of 5-hydroxylmethoxyfurfural (HMF) into levulinic acid (LA) was then explored and revealed that it can efficiently and selectively catalytic convert HMF into LA, which is superior to that of FeCl3/UiO-67 where FeCl3 is encapsulated in the cage of UiO-67 and dispersed on the pore surface. The recyclability studies further confirmed the importance of anchored FeCl3 where there is no significant decrease in catalytic activity as compared with that of FeCl3/UiO-67. Taking the detailed textural porosity and catalytic results of isomorphous structures in consideration, our studies revealed that narrowing the pore size with anchored FeCl3 on the skeleton of the fcu-type Zr-MOF rather than encapsulating FeCl3 inside the cage is more favored for the rehydration reaction of HMF to LA.