Open questions in the theory of spaces of orderings

2002 ◽  
Vol 67 (1) ◽  
pp. 341-352 ◽  
Author(s):  
Murray A. Marshall

Spaces of orderings provide an abstract framework in which to study spaces of orderings of formally real fields. Spaces of orderings of finite chain length are well understood [9, 11]. The Isotropy Theorem [11] and the extension of the Isotropy Theorem given in [13] are the main tools for reducing questions to the finite case, and these are quite effective. At the same time, there are many questions which do not appear to reduce in this way. In this paper we consider four such questions, for a space of orderings (X, G).1. Is it true that every positive primitive formula P(a) with parameters a in G which holds in every finite subspace of (X, G) necessarily holds in (X, G)?2. If f: X → ℤ is continuous and Σx∈Vf(x) ≡ 0 mod ∣V∣ holds for all fans V in X with ∣V∣ ≤ 2n, does there exist a form ϕ with entries in G such that mod Cont(X, 2nℤ)?3. Is it true that Cont(X, 2nℤ) ∩ Witt(X, G) = In(X, G), where I(X, G) denotes the fundamental ideal?4. Is the separating depth of a constructible set C in X necessarily bounded by the stability index of (X, G)?The unexplained terminology and notation is explained later in the main body of the paper. In a certain sense Question 1 is the main question. At the same time, Questions 2, 3 and 4 are of considerable interest, both from the point of view of quadratic form theory and from the point of view of real algebraic geometry.

2007 ◽  
Vol 06 (02) ◽  
pp. 245-257 ◽  
Author(s):  
PAWEŁ GŁADKI ◽  
MURRAY MARSHALL

First counterexamples are given to a basic question raised in [10]. The paper considers the space of orderings (X,G) of the function field of a real irreducible conic [Formula: see text] over the field ℚ of rational numbers. It is shown that the pp conjecture fails to hold for such a space of orderings when [Formula: see text] has no rational points. In this case, it is shown that the pp conjecture "almost holds" in the sense that, if a pp formula holds on each finite subspace of (X,G), then it holds on each proper subspace of (X,G). For pp formulas which are product-free and 1-related, the pp conjecture is known to be true, at least if the stability index is finite [11]. The counterexamples constructed here are the simplest sort of pp formulas which are not product-free and 1-related.


ISRN Algebra ◽  
2011 ◽  
Vol 2011 ◽  
pp. 1-8 ◽  
Author(s):  
Karim Johannes Becher ◽  
David B. Leep

For a (formally) real field K, the vanishing of a certain power of the fundamental ideal in the Witt ring of K(-1) implies that the same power of the fundamental ideal in the Witt ring of K is torsion free. The proof of this statement involves a fact on the structure of the torsion part of powers of the fundamental ideal in the Witt ring of K. This fact is very difficult to prove in general, but has an elementary proof under an assumption on the stability index of K. We present an exposition of these results.


Author(s):  
Sandy Budi Wibowo ◽  
Franck Lavigne ◽  
Siddiq Luqman Rifai ◽  
Rani Rahim Suryandari ◽  
Idea Wening Nurani ◽  
...  

Strengthening geospatial technology is very important in order to support disaster mitigation strategy, to manage vulnerable communities and to protectcritical environments. The main challenge in identifying disaster characteristics such as mass movements is the lack of direct observation during the event because it is too dangerous for researchers. Geo-Information Technology as a product of Geographic Information Science can be used as a solution in order to model the characteristics of mass movements. The purpose of this study is focused on identifying landslide processes from point of view ofraster-based model. The method of thisresearch emphasizes dynamic landslide model derived from timeseries raster calculation using MassMov2D algorithm. The geographic database that was built for spatial modeling comes from pedogeomorphological and Remote Sensing survey outputs, especially topographic data, landforms and soil physical properties. The result shows that the relationship between pixels (neighborhood) is determined by the topology of the energy gradient line direction which allowsto transfer the value between each pixel.The movement of landslide material starts from the toe. This decreases the stability of the landslide material in the main body of the landslide and generate progressive erosion.The raster-based model can finally reconstruct and identify the stages of initiation, transport and deposition landslide material.


2020 ◽  
Author(s):  
Laura Chirila ◽  
Alina Popescu ◽  
Sabina Olaru ◽  
Angela Danila ◽  
Rodica Roxana Constantinescu ◽  
...  

In order to obtain biomaterials with potential use in the treatment of inflammatory skin conditions, this experimental study approached the immobilization on knitted fabric, made of 100% organic cotton, of oil-in-water emulsions type, based on xanthan-propolis-cinnamon essential oil, in certain formulations. For this purpose, seven experimental variants of emulsions were prepared and characterized, by specific methods, from physical-chemical and stability point of view. The functionalized textile materials were also characterized from morphological and antibacterial activity view point. The stability index, determined after 10 days, indicated that the emulsions are stable, without showing the presence of one of the flocculation, creaming / sedimentation, coalescence or Ostwald ripening phenomena. The lowest value of the turbidity was obtained for the experimental variant containing the lowest amount of essential oil and propolis. For the same variant, the highest value of viscosity was obtained, in which 0,363 mL water /mL emulsion and 0,5 mL xanthan/mL emulsion volume fraction was used. The textile materials treated with the synthesized emulsions based on xanthan-propolis-cinnamon essential oil shows antibacterial effect against S. aureus and E. coli test strains


Author(s):  
A. V. Anikeev

For an engineering geologist, covered karst areas are of special interest, not only because these are the most widespread on the Earth. More important, unlike the areas of bare karst, these areas are more favorable and suitable for economic development and human life as a whole. And the study shows that the greater is the thickness of the cover series, the more true is this statement. The local forecast of sinkholes appears to be the most important and difficult engineering geological problem in these areas. It is especially acute there, where collapses and subsidence are absent, not registered, or poorly expressed in the relief, that is, in the areas of unrealized (potential, expected) sinkhole hazard. One of the possible approaches to solving this problem is discussed in the paper. It is based on comparing the volume of incoherent and fractured rock removed from the cover deposits with the accumulation capacity of the karst massif, i.e., the volume of hollow space in the karstic massif capable of receiving and accumulating clastic material. The most common result of soils outflow in fissure-karst reservoirs is their loosening in the deformed-destructed area of the overburden. For the three canonical schemes of this area structure, the critical values of clastic matter volume were obtained from the equation for soil mass balance before and after loosening, the further removal of which will lead to the failure of the earth's surface. Some techniques and methods for assessing the accumulation capacity of soluble rocks are considered and serious differences in the use of the discussed approach in predicting the stability of karstified and undermined territories are revealed. In particular, it is shown that in karst areas, when performing calculations, one should be guided by the maximum values of the coefficient of primary loosening of soils. Otherwise, the predicted stability of the overburden will prove to be unjustifiably underestimated. The results obtained and the procedure for assessing the stability of covered karst terrains by the proposed method are exemplified by the construction site of the main buildings of the Nizhny Novgorod NPP (3.25 km2), where there are no collapse and subsidence sinkholes. However, the entire construction site (20 km2) is located in the area of active sulphate-carbonate karst. From the engineering-geological point of view, this is the main feature of the facility design.


Author(s):  
З.С. САНОВА

В статье представлены материалы о взаимосвязи продолжительности продуктивного использования коров с характеристикой устойчивости к деградации, с возрастом отела и удоем. В исследованной, разнородной по происхождению, группе животных для прогноза продуктивного периода коров, обусловленного устойчивостью к деградации и возрастом первого отела, пригодно уравнение регрессии, аргументами в котором являются индекс устойчивости, возраст первого отела в первой и второй степенях. Коэффициент корреляции межу предсказанными значениями продуктивного периода и его фактическими величинами в I группе составляет 0,502, во II - 0,604. При этом крайние варианты прогнозируются со статистическими ошибками 5 мес при оценке индекса устойчивости по 2 лактациям и 4,1 мес по 3, а средние варианты, соответственно, 1,6 и 1,51 мес. Индекс устойчивости к процессу старения является важной характеристикой биологических особенностей коров, определяющий их продуктивное долголетие. Его оценка по первым 2 и 3 лактациям имеет прямолинейную связь с продуктивным периодом (r=0,4109 и r=0,5270), соответственно. Зависимость продуктивного периода от возраста первого отела криволинейная — с увеличением возраста первого отела сокращается срок продуктивного использования, при возрасте первого отела более 1400 дней срок продуктивного использования колеблется от 1,33 до 1,41 лактации. Коэффициент корреляции между этими характеристиками коров составляет - 0,2164 в I и - 0,2620 во II группах. The article presents materials about the relationship of the duration of productive use of cows with the characteristic of resistance to degradation, with the age of calving and milk yield. In the studied group of animals, which is heterogeneous in origin, the regression equation is suitable for predicting the productive period of cows due to resistance to degradation and the age of the first calving, the arguments of which are the stability index, the age of the first calving in the first and second degrees. The correlation coefficient between the predicted values of the productive period and its actual values in group I is 0.502, in group II - 0.604. At the same time, the extreme variants are predicted with statistical errors of 5 months when evaluating the stability index for 2 lactations and 4.1 months for 3, and the average variants, respectively, are 1.6 and 1.51 months. The index of resistance to the aging process is an important characteristic of the biological characteristics of cows, which determines their productive longevity. Its estimate for the first 2 and 3 lactations has a direct relationship with the productive period (r=0.4109 and r=0.5270), respectively. The dependence of the productive period age at first calving curvilinear with increasing age at first calving reduces the time to productive use, while age at first calving of more than 1400 days, the period of productive use ranges from 1.33 to 1.41 lactation. The correlation coefficient between these characteristics of cows is-0.2164 in I and-0.2620 in II groups.


Author(s):  
Ramesh Raghavan

This chapter presents an overview of how D&I research can be evaluated from an economic point of view. Dissemination and implementation imposes costs upon knowledge purveyors, provider organizations, public health organizations, and payers (including governments). However, whether these added costs will result in improved service delivery and, perhaps more importantly, client outcomes and improvements in population health remain as open questions. If emerging studies reveal that defined implementation strategies are more cost effective than “usual” implementation, then policymakers and service providers will need to resource these added costs of implementation in order to assure the success and sustainability of high-quality health services over the long term.


Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1434 ◽  
Author(s):  
Wonhee Kim ◽  
Sangmin Suh

For several decades, disturbance observers (DOs) have been widely utilized to enhance tracking performance by reducing external disturbances in different industrial applications. However, although a DO is a verified control structure, a conventional DO does not guarantee stability. This paper proposes a stability-guaranteed design method, while maintaining the DO structure. The proposed design method uses a linear matrix inequality (LMI)-based H∞ control because the LMI-based control guarantees the stability of closed loop systems. However, applying the DO design to the LMI framework is not trivial because there are two control targets, whereas the standard LMI stabilizes a single control target. In this study, the problem is first resolved by building a single fictitious model because the two models are serial and can be considered as a single model from the Q-filter point of view. Using the proposed design framework, all-stabilizing Q filters are calculated. In addition, for the stability and robustness of the DO, two metrics are proposed to quantify the stability and robustness and combined into a single unified index to satisfy both metrics. Based on an application example, it is verified that the proposed method is effective, with a performance improvement of 10.8%.


Data ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 4
Author(s):  
Evgeny Mikhailov ◽  
Daniela Boneva ◽  
Maria Pashentseva

A wide range of astrophysical objects, such as the Sun, galaxies, stars, planets, accretion discs etc., have large-scale magnetic fields. Their generation is often based on the dynamo mechanism, which is connected with joint action of the alpha-effect and differential rotation. They compete with the turbulent diffusion. If the dynamo is intensive enough, the magnetic field grows, else it decays. The magnetic field evolution is described by Steenbeck—Krause—Raedler equations, which are quite difficult to be solved. So, for different objects, specific two-dimensional models are used. As for thin discs (this shape corresponds to galaxies and accretion discs), usually, no-z approximation is used. Some of the partial derivatives are changed by the algebraic expressions, and the solenoidality condition is taken into account as well. The field generation is restricted by the equipartition value and saturates if the field becomes comparable with it. From the point of view of mathematical physics, they can be characterized as stable points of the equations. The field can come to these values monotonously or have oscillations. It depends on the type of the stability of these points, whether it is a node or focus. Here, we study the stability of such points and give examples for astrophysical applications.


Inorganics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 20
Author(s):  
Antonio A. García-Valdivia ◽  
Estitxu Echenique-Errandonea ◽  
Gloria B. Ramírez-Rodríguez ◽  
José M. Delgado-López ◽  
Belén Fernández ◽  
...  

Two new coordination polymers (CPs) based on Zn(II) and Cd(II) and 1H-indazole-6-carboxylic acid (H2L) of general formulae [Zn(L)(H2O)]n (1) and [Cd2(HL)4]n (2) have been synthesized and fully characterized by elemental analyses, Fourier transformed infrared spectroscopy and single crystal X-ray diffraction. The results indicate that compound 1 possesses double chains in its structure whereas 2 exhibits a 3D network. The intermolecular interactions, including hydrogen bonds, C–H···π and π···π stacking interactions, stabilize both crystal structures. Photoluminescence (PL) properties have shown that compounds 1 and 2 present similar emission spectra compared to the free-ligand. The emission spectra are also studied from the theoretical point of view by means of time-dependent density-functional theory (TD-DFT) calculations to confirm that ligand-centred π-π* electronic transitions govern emission of compound 1 and 2. Finally, the PL properties are also studied in aqueous solution to explore the stability and emission capacity of the compounds.


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