Ideal structure of rings of analytic functions with non-Archimedean metrics

The work of Helmer [Divisibility properties of integral functions, Duke Math. J. 6(2) (1940) 345–356] applied algebraic methods to the field of complex analysis when he proved the ring of entire functions on the complex plane is a Bezout domain (i.e. all finitely generated ideals are principal). This inspired the work of Henriksen [On the ideal structure of the ring of entire functions, Pacific J. Math. 2(2) (1952) 179–184. On the prime ideals of the ring of entire functions, Pacific J. Math. 3(4) (1953) 711–720] who proved a correspondence between the maximal ideals within the ring of entire functions and ultrafilters on sets of zeroes as well as a correspondence between the prime ideals and growth rates on the multiplicities of zeroes. We prove analogous results on rings of analytic functions in the non-Archimedean context: all finitely generated ideals in the ring of analytic functions on an annulus of a characteristic zero non-Archimedean field are two-generated but not guaranteed to be principal. We also prove the maximal and prime ideal structure in the non-Archimedean context is similar to that of the ordinary complex numbers; however, the methodology has to be significantly altered to account for the failure of Weierstrass factorization on balls of finite radius in fields which are not spherically complete, which was proven by Lazard [Les zeros d’une function analytique d’une variable sur un corps value complet, Publ. Math. l’IHES 14(1) (1942) 47–75].

Boundary quotients of the right Toeplitz algebra of the affine semigroup over the natural numbers

We study the Toeplitz $C^*$-algebra generated by the right-regular representation of the semigroup ${\mathbb N \rtimes \mathbb N^\times}$, which we call the right Toeplitz algebra. We analyse its structure by studying three distinguished quotients. We show that the multiplicative boundary quotient is isomorphic to a crossed product of the Toeplitz algebra of the additive rationals by an action of the multiplicative rationals, and study its ideal structure. The Crisp--Laca boundary quotient is isomorphic to the $C^*$-algebra of the group ${\mathbb Q_+^\times}\!\! \ltimes \mathbb Q$. There is a natural dynamics on the right Toeplitz algebra and all its KMS states factor through the additive boundary quotient. We describe the KMS simplex for inverse temperatures greater than one.

Sandwich semigroups in diagram categories

This paper concerns a number of diagram categories, namely the partition, planar partition, Brauer, partial Brauer, Motzkin and Temperley–Lieb categories. If [Formula: see text] denotes any of these categories, and if [Formula: see text] is a fixed morphism, then an associative operation [Formula: see text] may be defined on [Formula: see text] by [Formula: see text]. The resulting semigroup [Formula: see text] is called a sandwich semigroup. We conduct a thorough investigation of these sandwich semigroups, with an emphasis on structural and combinatorial properties such as Green’s relations and preorders, regularity, stability, mid-identities, ideal structure, (products of) idempotents, and minimal generation. It turns out that the Brauer category has many remarkable properties not shared by any of the other diagram categories we study. Because of these unique properties, we may completely classify isomorphism classes of sandwich semigroups in the Brauer category, calculate the rank (smallest size of a generating set) of an arbitrary sandwich semigroup, enumerate Green’s classes and idempotents, and calculate ranks (and idempotent ranks, where appropriate) of the regular subsemigroup and its ideals, as well as the idempotent-generated subsemigroup. Several illustrative examples are considered throughout, partly to demonstrate the sometimes-subtle differences between the various diagram categories.

What you need to know about falls

Falls are a common presenting complaint, particularly in older patients, and are associated with significant morbidity. Inpatient falls also have financial implications for healthcare systems, including litigation costs. This article provides an approach to assessing a patient presenting with a fall, encompassing the cause and consequence of the event. It also highlights the need to consider both the acute and chronic factors that predispose a particular patient to fall. Chronic factors such as frailty, sarcopenia, cognitive impairment, and continence issues are often under-recognised and, as a result, not managed optimally. A comprehensive geriatric assessment is an ideal structure to identify modifiable risks. Practical interventions that can be of benefit to minimise a patient's risk of falling include a medication review, assessment of their mobility and their environment. In addition, continence review and visual assessment may be appropriate.

Boundary Action On Simple Reduced Group C*-Algebras

A connection between boundary actions, ideal structure of reduced crossed products and C*-simple group is imminent.We investigate the stability properties for discrete group pioneered by powers and show that the non-abelian free group on two generators is C*-simple.Kalantar and Kennedy [32, Theorem 6.2] is now extended. Some examples are given using characterization of C*-simplicity obtained by Kalantar, Kennedy, Breuillard, and Ozawa [10, Theorem 3.1]

Welding procedure research of titanium heat exchangers

In order to manufacture Gr.1 titanium heat exchangers, the welding property and weld structure of titanium tube-to-tubesheet are analyzed. The procedure of Pulse GTAW is used and the visual inspection, dimensional inspection, chemical composition, mechanical properties and metallographic structures are tested and analyzed. The results show that the weld joint can get ideal structure and good chemical composition, mechanical properties and corrosion resistance. The successful welding qualification has accumulated valuable experience for manufacture of titanium heat exchangers.

DESTRUCTION MODEL OF IDEALIZED CONCRETE STRUCTURE BY SAWING

the requirements of modern construction are the strength of building structures, as well as low cost. It is these conditions that provide new technologies that are constantly being improved. The article is devoted to the consideration of cases of a probabilistic approach to solving the problem of theoretical energy consumption for the destruction of concrete of ideal structure. The processes of concrete deformation and its destruction are studied by building mechanics. Concrete is a multicomponent material, which presents a certain difficulty in the study of crack formation. In operating conditions, the concrete/reinforced concrete structure is affected by the properties of its constituent materials; therefore, one of the most important tasks is the selection of criteria that can comprehensively characterize the basic parameters of concrete. Obtaining the strength characteristics of concrete of operated structures remains an urgent task. The article proposes to consider the ideal structure of concrete. The features of this structure are the symmetry of fracture along two principal planes. The destruction of concrete was carried out by sawing individual strips of concrete. Moreover, to describe the sawing process, the authors proposed a model of a symmetric structure of concrete in which aggregate grains are idealized. They are presented in the form of balls in the body of concrete. The features of the sawing process are revealed. The analytical dependencies of fracture sawing the ideal structure of concrete are obtained. Conclusions are drawn about the possibility of using the ideal model for obtaining the strength characteristics of concrete. The analysis of symmetrical ideal concrete compositions with various variables is performed. The significance of the work done lies in the possibility of transferring the research results to real buildings and structures and solving the main tasks that are posed in the study

The Theory and Implementation of Bayesian Networks Structural Learning using Tabu Search Algorithm

This paper portrays the hypothesis and execution of Bayesian systems basic getting the hang of utilizing unthinkable pursuit calculation. Bayesian systems give an extremely broad but powerful graphical language for calculating joint likelihood disseminations. Finding the ideal structure of Bayesian systems from information has been demonstrated to be NP-hard. In this paper, unthinkable hunt has been created to give progressively proficient structure. We actualized auxiliary learning in Bayesian systems with regards to information characterization. With the end goal of correlation, we considered order task and applied general Bayesian systems alongside this classifier to certain databases. Our trial results show that the Tabu pursuit can locate the great structure with the less time multifaceted nature. The reenactment results affirmed that utilizing Tabu hunt so as to discover Bayesian systems structure improves the grouping exactness.