scholarly journals Polyprotic Acids and beyond—An Algebraic Approach

Chemistry ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 454-508
Author(s):  
Harald Kalka
Keyword(s):  
Algebraic Approach ◽  
Mass Action ◽  
Base System ◽  
Balance Laws ◽  
Acid Base ◽  
Acidity Constants ◽  
Isoelectric Points ◽  
Buffer Capacities ◽  
Special Case

For an N-protic acid–base system, the set of nonlinear equations (i.e., mass action and balance laws) provides a simple analytical solution/formula for any integer N ≥ 1. The approach is applicable for the general case of zwitterionic acids HNA+Z (e.g., amino acids, NTA, and EDTA), which includes (i) the “ordinary acids” as a special case (Z = 0) and (ii) surface complexation. Examples are presented for N = 1 to 6. The high-N perspective allows classification of equivalence points (including isoionic and isoelectric points). Principally, there are two main approaches to N-protic acids: one from hydrochemistry and one “outside inorganic hydrochemistry”. They differ in many ways: the choice of the reference state (either HNA or A−N), the reaction type (dissociation or association), the type/nature of the acidity constants, and the structure of the formulas. Once the (nonlinear) conversion between the two approaches is established, we obtain a systematics of acidity constants (macroscopic, microscopic, cumulative, and Simms). Finally, from the viewpoint of statistical mechanics (canonical isothermal–isobaric ensemble), buffer capacities, buffer intensities, and higher pH derivatives are actually fluctuations in the form of variance, skewness, and kurtosis.

scholarly journals Constructing Carrollian CFTs

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Nishant Gupta ◽  
Nemani V. Suryanarayana
Keyword(s):  
Scalar Fields ◽  
Higher Dimensions ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Relativistic Limit ◽  
Conformal Field ◽  
Local Symmetries ◽  
Derivatives Of ◽  
Special Case

Abstract We construct classical theories for scalar fields in arbitrary Carroll spacetimes that are invariant under Carrollian diffeomorphisms and Weyl transformations. When the local symmetries are gauge fixed these theories become Carrollian conformal field theories. We show that generically there are at least two types of such theories: one in which only time derivatives of the fields appear and the other in which both space and time derivatives appear. A classification of such scalar field theories in three (and higher) dimensions up to two derivative order is provided. We show that only a special case of our theories arises in the ultra-relativistic limit of a covariant parent theory.

scholarly journals Betti numbers and pseudoeffective cones in 2-Fano varieties

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Giosuè Emanuele Muratore
Keyword(s):  
Large Class ◽  
Betti Numbers ◽  
Fano Varieties ◽  
Higher Dimensional ◽  
Special Case ◽  
Answering Questions

Abstract The 2-Fano varieties, defined by De Jong and Starr, satisfy some higher-dimensional analogous properties of Fano varieties. We consider (weak) k-Fano varieties and conjecture the polyhedrality of the cone of pseudoeffective k-cycles for those varieties, in analogy with the case k = 1. Then we calculate some Betti numbers of a large class of k-Fano varieties to prove some special case of the conjecture. In particular, the conjecture is true for all 2-Fano varieties of index at least n − 2, and we complete the classification of weak 2-Fano varieties answering Questions 39 and 41 in [2].

scholarly journals Integrability of Riemann-Type Hydrodynamical Systems and Dubrovin’s Integrability Classification of Perturbed KdV-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1077
Author(s):  
Yarema A. Prykarpatskyy
Keyword(s):  
Conservation Laws ◽  
Hamiltonian Structure ◽  
Necessary Condition ◽  
Type Representation ◽  
Infinite Hierarchy ◽  
Polynomial Coefficients ◽  
Kdv Type Equations ◽  
Special Case

Dubrovin’s work on the classification of perturbed KdV-type equations is reanalyzed in detail via the gradient-holonomic integrability scheme, which was devised and developed jointly with Maxim Pavlov and collaborators some time ago. As a consequence of the reanalysis, one can show that Dubrovin’s criterion inherits important parts of the gradient-holonomic scheme properties, especially the necessary condition of suitably ordered reduction expansions with certain types of polynomial coefficients. In addition, we also analyze a special case of a new infinite hierarchy of Riemann-type hydrodynamical systems using a gradient-holonomic approach that was suggested jointly with M. Pavlov and collaborators. An infinite hierarchy of conservation laws, bi-Hamiltonian structure and the corresponding Lax-type representation are constructed for these systems.

Intersections of quotient rings and Prüfer v-multiplication domains

2016 ◽  
Vol 15 (08) ◽  
pp. 1650149 ◽  
Author(s):  
Said El Baghdadi ◽  
Marco Fontana ◽  
Muhammad Zafrullah
Keyword(s):  
Integral Domain ◽  
Algebraic Approach ◽  
Quotient Field ◽  
Topological Characterization ◽  
Locally Finite ◽  
Star Operation ◽  
Star Operations ◽  
Quotient Rings ◽  
Special Case

Let [Formula: see text] be an integral domain with quotient field [Formula: see text]. Call an overring [Formula: see text] of [Formula: see text] a subring of [Formula: see text] containing [Formula: see text] as a subring. A family [Formula: see text] of overrings of [Formula: see text] is called a defining family of [Formula: see text], if [Formula: see text]. Call an overring [Formula: see text] a sublocalization of [Formula: see text], if [Formula: see text] has a defining family consisting of rings of fractions of [Formula: see text]. Sublocalizations and their intersections exhibit interesting examples of semistar or star operations [D. D. Anderson, Star operations induced by overrings, Comm. Algebra 16 (1988) 2535–2553]. We show as a consequence of our work that domains that are locally finite intersections of Prüfer [Formula: see text]-multiplication (respectively, Mori) sublocalizations turn out to be Prüfer [Formula: see text]-multiplication domains (PvMDs) (respectively, Mori); in particular, for the Mori domain case, we reobtain a special case of Théorème 1 of [J. Querré, Intersections d’anneaux intègers, J. Algebra 43 (1976) 55–60] and Proposition 3.2 of [N. Dessagnes, Intersections d’anneaux de Mori — exemples, Port. Math. 44 (1987) 379–392]. We also show that, more than the finite character of the defining family, it is the finite character of the star operation induced by the defining family that causes the interesting results. As a particular case of this theory, we provide a purely algebraic approach for characterizing P vMDs as a subclass of the class of essential domains (see also Theorem 2.4 of [C. A. Finocchiaro and F. Tartarone, On a topological characterization of Prüfer [Formula: see text]-multiplication domains among essential domains, preprint (2014), arXiv:1410.4037]).

The influence of dissolved organic matter on the acid–base system of the Baltic Sea

2014 ◽  
Vol 132 ◽  
pp. 106-115 ◽  
Author(s):  
Karol Kuliński ◽  
Bernd Schneider ◽  
Karoline Hammer ◽  
Ulrike Machulik ◽  
Detlef Schulz-Bull
Keyword(s):  
Organic Matter ◽  
Dissolved Organic Matter ◽  
Baltic Sea ◽  
Base System ◽  
The Baltic Sea ◽  
Acid Base ◽  
The Baltic

scholarly journals SPECIFIC NATURE OF ACID-BASE INTERACTION OF OCTA(4-TERT-BUTYLPHENYL)TETRAPYRAZINOPORPHYRAZINE WITH ORGANIC PROTON-ACCEPTOR MOLECULES IN BENZENE

2021 ◽  
Vol 64 (3) ◽  
pp. 33-40
Author(s):  
Oleg A. Petrov ◽  
Aleksandr S. Semeykin ◽  
Mariya V. Shilovskaya ◽  
Tatiana V. Lyubimova
Keyword(s):  
Proton Transfer ◽  
Proton Acceptor ◽  
Base System ◽  
Excess Charge ◽  
Hydrogen Atoms ◽  
Acid Base ◽  
Base Interaction ◽  
Base Equilibrium ◽  
Acid Base Equilibrium ◽  
Acid Base Interaction

The reaction of acid-base interaction of octa(4-tert-butylphenyl)tetrapyrazinophosphyrazine with pyridine, 2-methylpyridine, morhpoline, pipyridine, n-butylamine, tert-butylamine, diethylamine, triethylamine and dimethylsulfoxide in benzene was investigated. It is shown that the researched porphyrazine forms kinetically stable proton transfer complexes with pyridine, 2-methylpyridine, morpholine and dimethylsulfoxide. In benzene-base system an acid-base equilibrium between the molecular form of octa(4-tert-butylphenyl)tetrapyrazinoporphyrazine and its proton transfer complex was established. The interaction of substituted tetrapyrazinoporphyrazine with morpholine in benzene was revealed to be a kinetically controllable process which occurs with low reaction rate and high values of activation energy. Such values are not inherent to most of relatively simple liquid-phase acid-base systems. The kinetic equation of the process was found, and, based on the spectral changes accompanying the reaction, a cheme of two-stage process of proton transfer of NH-groups of octa(4-tert-butylphenyl)tetrapyrazinoporphyrazine to morpholine in benzene was proposed. A possible structure of proton transfer complex of octa(4-tert-butylphenyl)tetrapyrazinoporphyrazine with organic bases is shown. In these complexes the inner hydrogen atoms of the cycle, bonded with base molecules, lie under and above the plane of the molecule, and the proton transfer from acid to base is limited either by the H-complex or the ion-ion associates constituting an H-bonded ion pair. Depending on the proton accepting tendency of the base, the acid-base equilibrium can shift towards or away from the more or less polarized structure. It was revealed that in benzene - n-butylamine (tri-butylamine, diethylamine, triethylamine, pipyridine) system the acid-base interaction involving octa(4- tert-butylphenyl)tetrapyrazinoporphyrazine occurs incredibly fast, with rates not measurable by standard spectrophotography methods. The forming proton transfer complexes are highly labile due to concurrent proton reaction occurring, leading to the formation of dianion form of octa(4- tert-butylphenyl)tetrapyrazinoporphyrazine. This form undergoes spontaneous dissolution into low-molecular colorless products due to the lack of compensation of excess charge in the macrocycle.

scholarly journals The Lattice of Definable Equivalence Relations in Homogeneous $n$-Dimensional Permutation Structures

10.37236/5980 ◽  
2016 ◽  
Vol 23 (4) ◽  
Author(s):  
Samuel Braunfeld
Keyword(s):  
Distributive Lattice ◽  
Equivalence Relations ◽  
Electronic Journal ◽  
Finite Distributive Lattice ◽  
Linear Orders ◽  
Finite Dimensional ◽  
Homogeneous Structures ◽  
Special Case

In Homogeneous permutations, Peter Cameron [Electronic Journal of Combinatorics 2002] classified the homogeneous permutations (homogeneous structures with 2 linear orders), and posed the problem of classifying the homogeneous $n$-dimensional permutation structures (homogeneous structures with $n$ linear orders) for all finite $n$. We prove here that the lattice of $\emptyset$-definable equivalence relations in such a structure can be any finite distributive lattice, providing many new imprimitive examples of homogeneous finite dimensional permutation structures. We conjecture that the distributivity of the lattice of $\emptyset$-definable equivalence relations is necessary, and prove this under the assumption that the reduct of the structure to the language of $\emptyset$-definable equivalence relations is homogeneous. Finally, we conjecture a classification of the primitive examples, and confirm this in the special case where all minimal forbidden structures have order 2. 

Surface Chemistry of Mesoporous Materials: Effect of Nanopore Confinement

2002 ◽  
Vol 751 ◽  
Author(s):  
Yifeng Wang ◽  
Charles Bryan ◽  
Huifang Xu ◽  
Huizhen Gao
Keyword(s):  
Surface Chemistry ◽  
Surface Acidity ◽  
Scale Space ◽  
Acid Base ◽  
Acidity Constants ◽  
Solution Interface ◽  
Ion Sorption ◽  
Alumina Particles ◽  
The Difference ◽  
Nanopore Confinement

AbstractAcid-base titration and metal sorption experiments were performed on both mesoporous alumina and alumina particles under various ionic strengths. It has been demonstrated that surface chemistry and ion sorption within nanopores can be significantly modified by a nano-scale space confinement. As the pore size is reduced to a few nanometers, the difference between surface acidity constants (ΔpK = pK2 – pK1) decreases, giving rise to a higher surface charge density on a nanopore surface than that on an unconfined solid-solution interface. The change in surface acidity constants results in a shift of ion sorption edges and enhances ion sorption on that nanopore surfaces.

Distributed Systems

2020 ◽  
pp. 143-198
Author(s):  
Andreas Bolfing
Keyword(s):  
Distributed Systems ◽  
Fault Tolerant ◽  
Deterministic Algorithm ◽  
Impossibility Result ◽  
Software Systems ◽  
Trade Off ◽  
Byzantine Failures ◽  
The Individual ◽  
Special Case

Chapter 5 considers distributed systems by their properties. The first section studies the classification of software systems, which is usually distinguished in centralized, decentralized and distributed systems. It studies the differences between these three major approaches, showing there is a rather multidimensional classification instead of a linear one. The most important case are distributed systems that enable spreading of computational tasks across several autonomous, independently acting computational entities. A very important result of this case is the CAP theorem that considers the trade-off between consistency, availability and partition tolerance. The last section deals with the possibility to reach consensus in distributed systems, discussing how fault tolerant consensus mechanisms enable mutual agreement among the individual entities in presence of failures. One very special case are so-called Byzantine failures that are discussed in great detail. The main result is the so-called FLP Impossibility Result which states that there is no deterministic algorithm that guarantees solution to the consensus problem in the asynchronous case. The chapter concludes by considering practical solutions that circumvent the impossibility result in order to reach consensus.

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