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Travelling waves and conservation laws of a (2+1)-dimensional coupling system with Korteweg-de Vries equation

equations because of their many applications in scientific fields. See for example [ 5 , 6 , 7 , 8 , 9 ]. However, in this work we study the (2+1)-dimensional coupling system with the Korteweg-de Vries equation [ 2 ], namely c k d v 11 u t − 6 u u x − u x x x = 0 , $$\begin{array}{} \displaystyle {ckdv11} u_t-6uu_x-u_{xxx}= 0, \end{array}$$ (2a) c k d v 12 v t − 6 ( u v ) x − 6 u u y − 3 u x x y − v x x x = 0. $$\begin{array}{} \displaystyle {ckdv12} v_t-6(uv)_x-6u u_y-3u_{xxy}-v_{xxx} = 0. \end{array}$$ (2b) This system is a (2+1)-dimensional integrable

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AV nodal reentrant tachycardia with a 2:1 right bundle branch block missed as bidirectional ventricular tachycardia in the first superficial evaluation

Abstract

A 95-year old woman was admitted to our emergency unit because of acute abdominal pain. After urgent surgery according to the acute abdomen, she was referred to intensive care unit (ICU) of the emergency unit as she was intubated. It was developed a run of new arrhythmia which was diagnosed by cardiology resident as bidirectional ventricular tachycardia due to beat to beat changing the axis of the QRS. However, a second and more precise evaluation of the abnormal ECG suggested a narrow supraventricular tachycardia, most probably AV nodal reentrant tachycardia with a 2:1 right bundle branch block.

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Relationships Between Chemical Composition of Colostrum and Milk and Rearing Performance of Piglets During a 21-Day Lactation / Zależności Pomiędzy Składem Chemicznym Siary I Mleka A Wynikami Odchowu Prosiąt W Czasie 21-Dniowej Laktacji

Abstract

Normal development of piglets is determined principally by the milking ability of the sows. This study attempted to determine the relationships between sow’s milk quality and rearing performance of the piglets. The experiment was carried out under uniform conditions, with standard feeding of the sows and a similar number of piglets per litter. The study accounted for 109 lactations of second- and third-parity Polish Large White (PLW ) sows and 123 lactations of second- and third-parity Polish Landrace (PL) sows. Colostrum and milk were collected from the sows at 1, 7, 14 and 21 days of lactation and analysed for solids, crude protein, fat, lactose and somatic cell count (SCC). Rearing performance of second- and third-litter piglets was determined based on the number and weight of piglets at birth and at 7, 14 and 21 days of age. The coefficients of correlation, estimated between basic composition of milk and rearing performance of the piglets over subsequent weeks of lactation were low and exceeded r = 0.200 only for some traits. The experiment showed that a higher content of basic milk components, in particular protein, may be one of the factors contributing to an increase in weight gain of piglets during a 21-day lactation. Milk fat content may be of significance for rearing performance of piglets only during their first week of life. Rearing performance of the piglets is unrelated to udder health expressed as milk SCC.

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Perturbation analysis of a matrix differential equation = ABx

Abstract

Two complex matrix pairs (A, B) and (A′, B′) are contragrediently equivalent if there are nonsingular S and R such that (A′, B′) = (S −1 AR, R −1 BS). M.I. García-Planas and V.V. Sergeichuk (1999) constructed a miniversal deformation of a canonical pair (A, B) for contragredient equivalence; that is, a simple normal form to which all matrix pairs (A + , B + ) close to (A, B) can be reduced by contragredient equivalence transformations that smoothly depend on the entries of and . Each perturbation (, ) of (A, B) defines the first order induced perturbation AB͠ + A͠B of the matrix AB, which is the first order summand in the product (A + )(B + ) = AB + AB͠ + A͠B + A͠B͠. We find all canonical matrix pairs (A, B), for which the first order induced perturbations AB͠ + A͠B are nonzero for all nonzero perturbations in the normal form of García-Planas and Sergeichuk. This problem arises in the theory of matrix differential equations = Cx, whose product of two matrices: C = AB; using the substitution x = Sy, one can reduce C by similarity transformations S −1 CS and (A, B) by contragredient equivalence transformations (S −1 AR, R −1 BS).

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Regularizing algorithm for mixed matrix pencils

Abstract

P. Van Dooren (1979) constructed an algorithm for computing all singular summands of Kronecker’s canonical form of a matrix pencil. His algorithm uses only unitary transformations, which improves its numerical stability. We extend Van Dooren’s algorithm to square complex matrices with respect to consimilarity transformations ASAS¯1 and to pairs of m × n complex matrices with respect to transformations (A,B)(SAR,SAR¯), in which S and R are nonsingular matrices.

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A Note: To the Sierpiński First Class of Functions

Abstract

The purpose of this paper is to establish some theorems concerning approximation and representation of a function of the Sierpiński first class by Darboux function of the Sierpiński first class.

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Generalized Derivative and Generalized Continuity

Abstract

The main objective of this article is to show that generalized differentiation can be understood as a process of comparing functions and their generalized continuity properties. We show it by working with generalized notions of derivative and continuity. The article covers wide range of types of generalized continuity.

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On a Lindenbaum Composition Theorem

Abstract

We discuss several questions about Borel measurable functions on a topological space. We show that two Lindenbaum composition theorems [Lindenbaum, A. Sur les superpositions des fonctions représentables analytiquement, Fund. Math. 23 (1934), 15–37] proved for the real line hold in perfectly normal topological space as well. As an application, we extend a characterization of a certain class of topological spaces with hereditary Jayne-Rogers property for perfectly normal topological space. Finally, we pose an interesting question about lower and upper Δ0 2-measurable functions.

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Changes in Entrepreneurship Education in Secondary School under Curriculum Reform in Poland

Abstract

Objective: The article aimed at identifying the position of the entrepreneurship course in the Polish education system and analysing the changes in its curriculum in the condition of the education system reform since 2017. Besides, attempts have been made to determine changes in this regard in the light of the analysis of the “old” and “new” core curriculum of general education in secondary schools of various types.

Methodology: Research was conducted by analysing the teaching content and existing data (desk research), which are the provisions of the national core curriculum (NCC) for general education in various types of schools currently in force and implemented in the ongoing reform of the education system. This analysis has been carried out against the previous research results presented in the literature on the subject using previously used methods of teaching content analysis.

Findings: The conducted research has shown that more attention should be paid to developing business competencies as part of the reform of the education system. In the NCC, cross-subject correlations have been taken into account, so that the same content is not unnecessarily duplicated. Entrepreneurship education should become more practical and oriented towards preparation for running own business and using financial services.

Value Added: The findings show that the new entrepreneurship education program assumptions in Poland will influence the development of entrepreneurship to a greater extent than before.

Recommendation: The results indicate that in the process of implementing the NCC a key role is played by the teacher, therefore it is necessary to prepare them well for its realization. However, the effects of implementing the program reform may only be observed and investigated in the future, therefore further research after several years is needed.

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Cardiogenic shock after nifedipine administration in a pregnant patient: A case report and review of the literature

effects than betamimetics. [ 1 , 2 , 3 , 4 , 5 ] Maternal serious adverse events have been described in case reports. [ 6 , 7 , 8 , 9 , 10 , 11 ] We present the case of a 21-year-old woman who developed a severe cardiogenic choc after the administration of nifedipine. Case Report A 21-year-old Caucasian woman at 27 weeks of pregnancy was admitted to the obstetric department for pre-term labor. She received 10 mg of nifedipine 4 times in 1 h, according to the internal protocol. Shortly after, she brutally deteriorated with pulmonary edema and hypoxemia

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