Explicit Wiener–Hopf factorization and nonlinear Riemann–Hilbert problems

2002 ◽  
Vol 132 (1) ◽  
pp. 45-74 ◽  
Author(s):  
M. C. Câmara ◽  
A. F. dos Santos ◽  
M. P. Carpentier
Keyword(s):  
Linear Transformation ◽  
Relevant Information ◽  
The Other ◽  
Factorization Problem ◽  
Wide Range ◽  
Complete Determination ◽  
Definition Of ◽  
Class Of Functions

A method for explicit Wiener–Hopf factorization of 2 × 2 matrix-valued functions is presented together with an abstract definition of a class of functions, C(Q1, Q2), to which it applies. The method involves the reduction of the original factorization problem to certain nonlinear scalar Riemann–Hilbert problems, which are easier to solve. The class C(Q1, Q2) contains a wide range of classes dealt with in the literature, including the well-known Daniele–Khrapkov class. The structure of the factors in the factorization of any element of the class C(Q1, Q2) is studied and a relation between the two columns of the factors, which gives one of the columns in terms of the other through a linear transformation, is established. This greatly simplifies the complete determination of the factors and gives relevant information on the nature of the factorization. Two examples suggested by applications are completely worked out.

scholarly journals Dispersive evaluation and surface chemistry of advanced, multifunctional silica/lignin hybrid biomaterials

2013 ◽  
Vol 11 (11) ◽  
pp. 1860-1873 ◽  
Author(s):  
Magdalena Nowacka ◽  
Łukasz Klapiszewski ◽  
Małgorzata Norman ◽  
Teofil Jesionowski
Keyword(s):  
Zeta Potential ◽  
Surface Charge ◽  
Electrochemical Sensors ◽  
Relevant Information ◽  
Structural Features ◽  
Kraft Lignin ◽  
Morphological Properties ◽  
Wide Range ◽  
Hybrid Biomaterials

AbstractAdvanced silica/lignin hybrid biomaterials were obtained using hydrated or fumed silicas (Aerosil®200) and Kraft lignin as precursors, which is a cheap and biodegradable natural polymer. To extend the possible range of applications, the silicas were first modified with N-2-(aminoethyl)-3-aminopropyltrimethoxsysilane, and then with Kraft lignin, which had been oxidized with sodium periodate. The SiO2/lignin hybrids and precursors were characterised by means of determination of their physicochemical and dispersive-morphological properties. The effectiveness of silica binding to lignin was verified by FT-IR spectroscopy. The zeta potential value provides relevant information regarding interactions between colloid particles. Measurement of the zeta potential values enabled an indirect assessment of stability for the studied hybrid systems. Determination of zeta potential and density of surface charge also permitted the quantitative analysis of changes in surface charge, and indirectly confirmed the effectiveness of the proposed method for synthesis of SiO2/lignin hybrid materials. A particularly attractive feature for practical use is their stability, especially electrokinetic stability. It is expected that silica/lignin hybrids will find a wide range of applications (polymer fillers, biosorbents, electrochemical sensors), as they combine the unique properties of silica with the specific structural features of lignin. This makes these hybrids biomaterials advanced and multifunctional.

scholarly journals The error of determination of toxicity

1927 ◽  
Vol 101 (712) ◽  
pp. 483-514 ◽  
Keyword(s):  
Intravenous Injection ◽  
Lethal Dose ◽  
Unit Weight ◽  
Minimal Effective Dose ◽  
Quantitative Expression ◽  
Wide Range ◽  
Cocaine Hydrochloride ◽  
State Of Affairs ◽  
Definition Of

The determination of toxicity is usually given quantitative expression by the statement of a minimal lethal dose. The common use of this expression in the literature of the subject would logically involve the assumptions that there is a dose, for any given poison, which is only just sufficient to kill all or most of the animals of a given species, and that doses very little smaller would not kill any animals of that species. Any worker, however, accustomed to estimations of toxicity, knows that these assumptions do not represent the truth. How widely different is the real state of affairs, however, is not, I think, sufficiently recognised. The fact that the “ minimal lethal dose,” whether calculated for unit weight, or for surface area, or on any other basis, varies widely for different species has, perhaps, led to the looseness of its definition for any one species. For the accurate standardisation, by biological methods, of drugs which are not available in chemically pure form, it is essential to establish a more accurate definition of such terms as “minimal lethal dose,” “minimal effective dose,” etc. Fig. 1 gives the results of the injection of four poisons into animals. The abscissæ are proportional to the doses injected, the scale obviously differing for the different drugs, and the ordinates give the percentage mortality for each dose injected. The number attached to each observed point represents the number of animals injected for its determination. The curves represent percentage mortalities produced by the subcutaneous injection of tincture of digitalis into frogs, by the intravenous injection of cocaine hydrochloride into mice (see also fig. 2 and Table I), by the intravenous injection of echitamine into mice, and by the injection of dysentery toxin into mice, the data for the last being taken from O’Brien, Sudmersen and Runge (1924). A similar curve is given later (fig. 7) for the percentage of convulsions produced in mice by increasing doses of insulin, the data being obtained by the use of large numbers of animals. Shackell (1925) has published a number of similar curves, relating percentage mortalities to varying doses of different poisons, in a wide range of species. It is suggested that the curve expressing the percentage of mortality, or of some other limiting biological effect, produced by varying doses of a drug on animals of a certain species, shall be called the “ characteristic” for that particular drug, effect and species. Thus, the curve relating the percentage of convulsions produced in mice to varying doses of insulin, would be termed the characteristic for the production of convulsions in mice by insulin.

scholarly journals BALANCE SHEET ANALYSIS OF CREDIT AND DEBT NETWORKS

2015 ◽  
Vol 18 (05n06) ◽  
pp. 1550025
Author(s):  
PAULO GARRIDO ◽  
PEDRO CAMPOS ◽  
ANDRÉ DIAS
Keyword(s):  
Balance Sheet ◽  
Relevant Information ◽  
Proof Of Concept ◽  
Network Sensitivity ◽  
The Matrix ◽  
Computing Procedure ◽  
Definition Of ◽  
Case Basis

In this paper, we present a computing procedure to analyze a network of credit and debt among agents (nodes) from a standpoint of balance sheet dependencies. The aim is to develop a method to assess thoroughly the sensitivity of the network to potential individual insolvencies. For this purpose, given a state of the network, the insolvency of an agent is assumed and the cascade of provoked insolvencies is simulated. Exploring the matrix definition of the network, this is made systematically for all agents. Therefore, in only one run of the procedure, all the possible trajectories of insolvencies, each beginning in a different agent, are calculated. This allows spotting at a glance which agents are “systemically riskier”. Determination of adequate capital levels can be made on a case basis by running the procedure repeatedly. This work contributes with two new aspects to the existing literature. First, given a known situation of a credit and debt network, a computing procedure is presented that allows to assess the network sensitivity to the exogenous insolvency of any of its nodes. Second, continued monitoring of a credit and debt network is computationally feasible. This “proof of concept” software can be extended into a tool useful for research and regulation, if the relevant information is made available.

Toward a comprehensive definition of oxidation state (IUPAC Technical Report)

2014 ◽  
Vol 86 (6) ◽  
pp. 1017-1081 ◽  
Author(s):  
Pavel Karen ◽  
Patrick McArdle ◽  
Josef Takats
Keyword(s):  
Oxidation State ◽  
Structural Formula ◽  
The Other ◽  
Bond Orders ◽  
Formal Charge ◽  
Technical Report ◽  
Electronegative Atom ◽  
Auxiliary Rules ◽  
Definition Of

AbstractA generic definition of oxidation state (OS) is formulated: “The OS of a bonded atom equals its charge after ionic approximation”. In the ionic approximation, the atom that contributes more to the bonding molecular orbital (MO) becomes negative. This sign can also be estimated by comparing Allen electronegativities of the two bonded atoms, but this simplification carries an exception when the more electronegative atom is bonded as a Lewis acid. Two principal algorithms are outlined for OS determination of an atom in a compound; one based on composition, the other on topology. Both provide the same generic OS because both the ionic approximation and structural formula obey rules of stable electron configurations. A sufficiently simple empirical formula yields OS via the algorithm of direct ionic approximation (DIA) by these rules. The topological algorithm works on a Lewis formula (for a molecule) or a bond graph (for an extended solid) and has two variants. One assigns bonding electrons to more electronegative bond partners, the other sums an atom’s formal charge with bond orders (or bond valences) of sign defined by the ionic approximation of each particular bond at the atom. A glossary of terms and auxiliary rules needed for determination of OS are provided, illustrated with examples, and the origins of ambiguous OS values are pointed out. An electrochemical OS is suggested with a nominal value equal to the average OS for atoms of the same element in a moiety that is charged or otherwise electrochemically relevant.

For a Negative, Normative Model of Consent, With a Comment on Preference-Skepticism

Legal Theory ◽  
1996 ◽  
Vol 2 (2) ◽  
pp. 113-120 ◽  
Author(s):  
Donald Dripps
Keyword(s):  
External Force ◽  
Criminal Law ◽  
The Other ◽  
Normative Model ◽  
Bodily Movement ◽  
Other Hand ◽  
Wide Range ◽  
Nervous Disorder ◽  
Definition Of ◽  
Freedom And Responsibility

Let me begin by admitting that I am wary of any comprehensive definition of consent. This bias stems from my professional concentration on criminal law, in which nouons of freedom and responsibility play vital roles in a wide range of contexts. In each context, however, one discovers that freedom means something different. A voluntary act is any bodily movement not caused by external force or nervous disorder. On the other hand, a voluntary act, however horrific its results, ordinarily may be punished only if the actor was subjectively aware that the act was wrong. In any event, a voluntary act may be excused as the product of duress if another person procures the actor's cooperation in the crime by an illegal threat that would overcome the resistance of a person of ordinary firmness.

scholarly journals The Determination of Stacking Fault Energy by the Tetrahedron Method

1968 ◽  
Vol 21 (6) ◽  
pp. 941 ◽  
Author(s):  
P Humble ◽  
CT Forwood
Keyword(s):  
Electron Microscope ◽  
Stacking Fault ◽  
Stacking Fault Energy ◽  
The Other ◽  
Dislocation Loops ◽  
The Third ◽  
Wide Range ◽  
Length Measurements ◽  
Incomplete Theory

At present there are three methods for obtaining values of the stacking fault energy y of face-centred cubic (f.c.c.) materials by direct observation of dislocationstacking fault configurations in the electron microscope. These are based on measurements of extended three-fold dislocation nodes (e.g. Whelan 1958; Brown and ThOlen 1964), faulted dipole configurations (e.g. Haussermann and Wilkens 1966; Steeds 1967), and triangular Frank dislocation loops and stacking fault tetrahedral (e.g. Silcox and Hirsch 1959; Loretto, Clarebrough, and Segall 1965). The main advantages of the third method over the other two are that it is applicable to materials of a very wide range of stacking fault energy and involves only simple length measurements of defects that are easily recognized. However, it has suffered from the disadvantage that the values of y deduced from these measurements relied on an incomplete theory. The present authors have reconsidered this problem and, subject to the limitations of isotropic linear elasticity, have taken into account the major variables that may affect the values of y. It is the purpose of this note to present the results of this theory in a form in which values of y may easily be obtained from measurements of Frank dislocation loops and stacking fault tetrahedral without the resources of a large digital computer.

scholarly journals U.S. Supreme Court Brief of Professors of Conflict of Laws and Civil Procedure as Amici Curiae in Support of Petitioners, Animal Science Products, Inc. v. Hebei Welcome Pharmaceutical Co. Ltd.

2018 ◽  
Author(s):  
Christopher A. Whytock ◽  
Zachary D. Clopton
Keyword(s):  
Relevant Information ◽  
Civil Procedure ◽  
Choice Of Law ◽  
Conflict Of Laws ◽  
Foreign Law ◽  
Wide Range ◽  
American Law ◽  
Foreign Governments ◽  
Court Proceedings

The Second Circuit held that “when a foreign government, acting through counsel or otherwise, directly participates in U.S. court proceedings by providing a sworn evidentiary proffer regarding the construction and effect of its laws and regulations, which is reasonable under the circumstances presented, a U.S. court is bound to defer to those statements.” In re Vitamin C Antitrust Litigation, 837 F.3d 175, 189 (2d Cir. 2016). This “bound-to-defer” rule is incorrect and unwise.First, the “bound-to-defer” rule is inconsistent with basic American conflict-of-laws principles governing the determination of foreign law. It is inconsistent with Federal Rule of Civil Procedure 44.1’s broad authorization for U.S. courts to “consider any relevant material or source” when determining foreign law. It is inconsistent with the principle that determinations of foreign law should be accurate. And it is inconsistent with the principle of judicial independence in the determination of foreign law.Second, the “bound-to-defer” rule is inconsistent with foreign and international practice. In most other countries, information about foreign law is not binding on courts. Moreover, the world’s two main treaties on the interpretation of foreign law expressly provide that information supplied by foreign governments in accordance with those treaties is not binding on courts. Simply put, foreign governments do not expect each other’s courts to be “bound to defer” to each other’s interpretations of foreign law, much less the interpretation of one executive agency of a foreign government.Third, there are important reasons why deference principles should be kept separate from the principles governing the determination of foreign law. The Second Circuit’s “bound-to-defer” rule would inappropriately delegate to foreign governments power to influence the application of domestic law — and hence the implementation of domestic policy — in a wide range of cases in which the proper application of U.S. law depends on the determination of foreign law. In addition, international comity does not require U.S. courts to defer to foreign governments in the determination of foreign law. International comity is a traditional rationale for choice-of-law rules that require the application of foreign law as a rule of decision under specified circumstances. But in this case, foreign law is at issue because the application of U.S. law depends on the interpretation of foreign law, not because choice-of-law rules require the application of foreign law. Therefore, this case does not implicate the comity rationale for choice-of-law rules. Moreover, the concerns that animate comity doctrines are not the same as those that animate the rules governing the determination of foreign law. The former are concerned with the respect owed between governments, whereas the latter are concerned with ensuring that U.S. courts independently and accurately determine the content of foreign law. In fact, the “bound-to-defer” rule raises issues that are likely to pose significant comity concerns that the ordinary Rule 44.1 approach avoids. U.S. courts can still address comity concerns — separately from their independent determination of foreign law.To be sure, U.S. courts should give respectful consideration to a foreign government’s statements about its law. But as a matter of law, a foreign government’s statements cannot be binding on U.S. courts. Instead, U.S. courts should accurately and independently determine the meaning of foreign law taking into account not only the foreign government’s own statements, but also other relevant information about that law. This independent approach is especially important when — as in this U.S. antitrust case and many other cases — the proper application of American law depends on a determination of foreign law.

scholarly journals Determination of sources of sulfur dioxide in confectionery

2019 ◽  
Vol 80 (4) ◽  
pp. 203-208
Author(s):  
N. B. Kondratyev ◽  
E. V. Kazantsev ◽  
M. V. Osipov ◽  
O. S. Rudenko ◽  
E. N. Krylova
Keyword(s):  
Sulfur Dioxide ◽  
Raw Materials ◽  
Customs Union ◽  
White Sand ◽  
Wide Range ◽  
Confectionery Products ◽  
Definition Of ◽  
The Impact ◽  
Technological Methods

Sulfur dioxide is used to ensure the safety of fruit raw materials and semi-finished products used for the production of confectionery. This preservative has allergenic properties. In accordance with the Technical Regulations of the Customs Union TR CU 022/2011 "Food products in terms of their labeling" the content of sulfur dioxide must be specified when labeling confectionery products, if its content exceeds 10 mg per kg. The definition of this preservative in raw materials, semi-finished products and confectionery in accordance with the current GOST 26811 “Confectionery. The iodometric method for determining the mass fraction of total sulfuric acid is often difficult because of the complexity of confectionery products, the formation of intensive staining of the solutions under study and the ability of sulfur dioxide to react with other components of the objects under study. Therefore, the task of developing methods with the optimization of the sample preparation stage of the samples under study, which allow one to fully determine sulfur dioxide in confectionery products, semi-finished products and raw materials, is relevant. The purpose of this work was to develop methods for determining sulfur dioxide in raw materials, semi-finished products and various names of confectionery products, as well as assessing the impact of these types of raw materials and semi-finished products on the content of sulfur dioxide in confectionery products. The results showed that sulfur dioxide is present in many raw materials. In mg per 1 kg of sugar in white sand from 1 to 9, molasses from 25 to 52, wheat flour from 9 to 15, starch from 3 to 17. In fruit raw materials from 5 to 545 mg per kg. In confectionery: marshmallow and marshmallow from 8 to 29, gingerbread from 6 to 25, biscuits from 0 to 16, chocolate from 8 to 13. Based on the data obtained, it can be concluded that the content of sulfur dioxide in raw materials and semi-finished confectionery products is a very wide range, which makes it necessary to control the quality of all raw materials entering the production. Sulfur dioxide, used as a preservative for fruit raw materials, can significantly increase the content of this allergen in confectionery made using such raw materials. Ensuring the level of sulfur dioxide less than 10 mg / kg is achieved using raw materials with low content of sulfur dioxide and technological methods.

Assessment of the Effect of Acidic Deposition on Canadian Lakes: Determination of Critical Loads for Sulphate Deposition

1993 ◽  
Vol 28 (3-5) ◽  
pp. 183-187 ◽  
Author(s):  
D. S. Jeffries ◽  
D. C. L. Lam
Keyword(s):  
Critical Load ◽  
Critical Loads ◽  
Acidic Deposition ◽  
Operational Definition ◽  
Eastern Canada ◽  
Wide Range ◽  
Sulphate Deposition ◽  
Definition Of ◽  
Terrain Characteristics

The operational definition of the “critical” load for wet SO4 deposition is that which does not increase the regional percent of lakes having pH≤6 for the portion of the population that historically had pH>6. Reviews of the effects of acidic deposition on aquatic biota show that the pH=6 threshold used to determine the critical load is sufficient to protect most organisms. It is inappropriate to specify a single critical load for the whole of eastern Canada due to variability in terrain sensitivity. The Atlantic provinces and easterr Quebec generally have very low critical loads (<8 kg. ha−1.yr−1). The terrain characteristics of this area dictate a critical load very close to background deposition. Lakes in southwestern Quebec and Ontario have critical loads of <8 to >20 kg.ha−1.yr−1 reflecting the wide range in terrain sensitivities that exist in each province.

Resilience and risk, metal health and well-being: How do these concepts relate?

2017 ◽  
Vol 41 (S1) ◽  
pp. S463-S463
Author(s):  
F. Schultze-Lutter ◽  
S. Ochsenbein ◽  
S.J. Schmidt
Keyword(s):  
Mental Health ◽  
Well Being ◽  
The Other ◽  
Cross Sectional ◽  
Wide Range ◽  
Proxy Measure ◽  
Competing Interest ◽  
Universal Definition ◽  
Definition Of ◽  
Relationship Of

IntroductionResilience and well-being have become commonplace and increasingly used terms in a wide range of scientific as well as mental health political contexts.ObjectivesThere is much confusion about the relationship of the two constructs: while some use well-being as a proxy measure of resilience, others treat one concept as a component of the other or see interchangeably one as the prerequisite of the other.AimsTo study the definition of these two concepts in relation to each other.MethodsLiterature review.ResultsBoth ‘resilience’ as well as ‘well-being’, have so far defied universal definition and common understanding of their respective measurement. Part of the confusion around these two concepts is the overlap in their components, in particular with regard to resilience and psychological well-being, and the lack of research on these concepts both by themselves, in relation to each other and in relation to other concepts like mental health, risk or protective (or promotive) factors.ConclusionOur critical and comparative inspection of both concepts highlights the need for more conceptual cross-sectional as well as longitudinal studies:– to uncover the composition of these constructs and to reach agreement on their definition and measurement;– to detect their potential neurobiological underpinnings;– to reveal how they relate to each other;– to determine the potential role of developmental and cultural peculiarities.Thus, the use of the terms resilience and well-being should always be accompanied by a brief explanation of their respective meanings and theoretical framework.Disclosure of interestThe authors have not supplied their declaration of competing interest.

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