Eigenvalue Estimates via Pseudospectra

In this note, given a matrix A∈Cn×n (or a general matrix polynomial P(z), z∈C) and an arbitrary scalar λ0∈C, we show how to define a sequence μkk∈N which converges to some element of its spectrum. The scalar λ0 serves as initial term (μ0=λ0), while additional terms are constructed through a recursive procedure, exploiting the fact that each term μk of this sequence is in fact a point lying on the boundary curve of some pseudospectral set of A (or P(z)). Then, the next term in the sequence is detected in the direction which is normal to this curve at the point μk. Repeating the construction for additional initial points, it is possible to approximate peripheral eigenvalues, localize the spectrum and even obtain spectral enclosures. Hence, as a by-product of our method, a computationally cheap procedure for approximate pseudospectra computations emerges. An advantage of the proposed approach is that it does not make any assumptions on the location of the spectrum. The fact that all computations are performed on some dynamically chosen locations on the complex plane which converge to the eigenvalues, rather than on a large number of predefined points on a rigid grid, can be used to accelerate conventional grid algorithms. Parallel implementation of the method or use in conjunction with randomization techniques can lead to further computational savings when applied to large-scale matrices.

About the "supertask" ("sverhzadacha") of K. S. Stanislavsky... (about the history of the word supertask (sverhzadacha) in the Russian language)

The article is devoted to the history of the appearance and functioning of the word supertask (sverhzadacha) in the Russian language. Two lines of the lexeme functioning were distinguished: the first is associated with the etymology of the word, the second – with its use by K. S. Stanislavsky in the terminology system and the further entry of the unit into general use on the basis of determinologization. It is interesting that the second meaning has acquired the most widespread use. Only in the past two decades, the word has begun to lose its connection with the process of artistic creation. The purpose of the study was to briefly review the history of the word: from its first fixation in the Russian language and application by K. S. Stanislavsky (to designate one of the key concepts of Method Acting) up to modern contexts of use. The entry of the lexeme into the language was investigated using structural methods. The methods of contextual and distributive analysis were used to analyse both the contexts in which Stanislavsky used this word and the process of its fixation in the National Corpus of the Russian language. Statistical analysis was used to trace the dynamics of integration of the lexeme into the Russian language and its fixation in various spheres. The methods of component and comparative analysis were used to describe the formation mechanism of the initial term in the historical context. Borrowings of the term supertask (sverhzadacha) were found in other languages, indicating the spread of Stanislavsky’s system. The conclusion is drawn that the word supertask (sverhzadacha) functions in the Russian language mainly as a term from Stanislavsky’s system, gradually becoming determinologized and returning to the meaning conveying the logical sum of its constituent components.

Goal Directed Perfusion: Bibliographical Review

Objective: The aim of this study is to synthesize the existing evidence on Goal Directed Perfusion Methods: The search for the existing evidence was made in the MEDLINE databases, using the PubMed search engine. The initial search term was “goal directed perfusion.” In order to narrow the search, MeHS terms such as “cardiac surgery” and “cardiopulmonary bypass” were used together with the initial term and the Boolean operator AND. Results: At first, 238 references were obtained, combined whit “cardiac surgery” there were 49 references and finally whit “cardiopulmonary bypass” 21. We read 23 articles. Levels of oxygen delivery (DO2i) > 272 ml/min/m2, minimize hemodilution an maintain hematocrit values > 26% decrease acute kidney injury. A carbon dioxide production VCO2 i > of 60 ml/min/m2 and DO2i/VCO2i < 5 are predictors of hyperlactatemia. The mixed venous oxygen saturation (SvO2) and the oxygen extraction rate (ERO2) are better predictors of transfusion during extracorporeal circulation than hemoglobin value. The majority of the bibliography refers to adult surgery, but the application of GDP to the pediatric perfusion is beginning. Conclusion: The improvement of “optimal” perfusion, considered the gold standard, towards goal directed perfusion is already in use. Many hospitals are incorporating online monitoring of the new perfusion parameters in order to apply a specific perfusion to each patient as well as his metabolic needs during extracorporeal circulation.

Arithmetic Triangle

The product of the first $n$ terms of an arithmetic progression may be developed in a polynomial of $n$ terms. Each one of them presents a coefficient $C_{nk}$ that is independent from the initial term and the common difference of the progression. The most interesting point is that one may construct an "Arithmetic Triangle'', displaying these coefficients, in a similar way one does with Pascal's Triangle. Moreover, some remarkable properties, mainly concerning factorials, characterize the Triangle. Other related `triangles' -- eventually treated as matrices -- also display curious facts, in their linear \emph{modus operandi}, such as successive "descendances''.

Algebraic data integration

In this paper, we develop an algebraic approach to data integration by combining techniques from functional programming, category theory, and database theory. In our formalism, database schemas and instances are algebraic (multi-sorted equational) theories of a certain form. Schemas denote categories, and instances denote their initial (term) algebras. The instances on a schema S form a category, S–Inst, and a morphism of schemas F : S → T induces three adjoint data migration functors: ΣF : S–Inst → T–Inst, defined by substitution along F, which has a right adjoint ΔF : T–Inst → S–Inst, which in turn has a right adjoint ΠF : S–Inst → T–Inst. We present a query language based on for/where/return syntax where each query denotes a sequence of data migration functors; a pushout-based design pattern for performing data integration using our formalism; and describe the implementation of our formalism in a tool we call AQL (Algebraic Query Language).

On the Constant in the Average Digit Sum for a Recurrence-Based Numeration

Given an integral, increasing, linear-recurrent sequence A with initial term 1, the greedy algorithm may be used on the terms of A to represent all positive integers. For large classes of recurrences, the average digit sum is known to equal cA log n+O(1), where cA is a positive constant that depends on A. This asymptotic result is re-proved with an elementary approach for a class of special recurrences larger than, or distinct from, that of former papers. The focus is on the constants cA for which, among other items, explicit formulas are provided and minimal values are found, or conjectured, for all special recurrences up to a certain order.

ON -ANTIMAGICNESS OF DISCONNECTED GRAPHS

A simple graph $G=(V,E)$ admits an $H$-covering if every edge in $E$ belongs to at least one subgraph of $G$ isomorphic to a given graph $H$. Then the graph $G$ is $(a,d)$-$H$-antimagic if there exists a bijection $f:V\cup E\rightarrow \{1,2,\ldots ,|V|+|E|\}$ such that, for all subgraphs $H^{\prime }$ of $G$ isomorphic to $H$, the $H^{\prime }$-weights, $wt_{f}(H^{\prime })=\sum _{v\in V(H^{\prime })}f(v)+\sum _{e\in E(H^{\prime })}f(e)$, form an arithmetic progression with the initial term $a$ and the common difference $d$. When $f(V)=\{1,2,\ldots ,|V|\}$, then $G$ is said to be super $(a,d)$-$H$-antimagic. In this paper, we study super $(a,d)$-$H$-antimagic labellings of a disjoint union of graphs for $d=|E(H)|-|V(H)|$.

Tree-Antimagicness of Disconnected Graphs

A simple graphGadmits anH-covering if every edge inE(G)belongs to a subgraph ofGisomorphic toH. The graphGis said to be (a,d)-H-antimagic if there exists a bijection from the vertex setV(G)and the edge setE(G)onto the set of integers1, 2, …,VG+E(G)such that, for all subgraphsH′ofGisomorphic toH, the sum of labels of all vertices and edges belonging toH′constitute the arithmetic progression with the initial termaand the common differenced.Gis said to be a super (a,d)-H-antimagic if the smallest possible labels appear on the vertices. In this paper, we study super tree-antimagic total labelings of disjoint union of graphs.

Time of guard of orthodontic records versus legal time for their prescription

INTRODUCTION: After promulgation and wider dissemination of the Code of Consumer Protection, there was an increase in the number of legal conflicts between patients and dentists, leading these health professionals to increasingly guard themselves from possible lawsuits. As such, it becomes critical the preparation of an adequate and complete clinical record, even though the keeping time remains uncertain. OBJECTIVE: To review the literature and discuss the keeping time of orthodontic records versus the legal time for their prescription, as well as to propose a model of a Term upon Completion of Dental Treatment. CONCLUSION: It is advised to return part of the clinical records to their rightful owners by means of an itemized receipt. The Term upon Completion reflects the patient's awareness and could be considered by the CCP as the initial term of the prescription time, because it implicates that the patient recognizes the quality of service provided and satisfactory results achieved.