О представлении решения задачи идентификации коэффициентов при дифференциальном операторе второго порядка в системе многомерных параболических уравнений

An identification problem of the coefficients at differential operator of second order and sum of lowest terms in system of multidimensional parabolic equations with Cauchy data was studied in this article. The theorems of existence and uniqueness of the solution for direct and inverse problems have been proved. The method of weak approximation is used to the proof existence of solutionsИсследована обратная задача с данными Коши для системы многомерных параболических урав- нений, содержащих неизвестные коэффициенты перед дифференциальным оператором второго порядка по выделенной переменной и суммой младших членов. Начальные данные имеют специ- альный вид и заданы в виде произведения двух функций, зависящих от разных переменных. Полу- чены достаточные условия существования и единственности решения вспомогательной прямой и исходной обратной задач. Для доказательства используется метод слабой аппроксимаци

ENGINEERING FOR RURAL DEVELOPMENT ESTIMATION OF OPTIMAL DEGREE OF STUDENT AUTONOMY IN LABORATORY AND CLASSROOM

Abstract. Creativity of students in the laboratory and classroom depends on the degree of his or her autonomy in the period of solving different educational problems. This degree is connected with the number of independent decisions which the student makes in the period of his or her training. It means the path of problem solving can be divided in several steps. The student has to choose the way of solving each step. This choice can be fully independent or can use any prompt. The fraction of solutions which are fully independent permits one to estimate the degree of student autonomy. This degree depends on the complexity of each choice and the sequence of independent decisions in their set, too. The total number of decisions is connected with the time given by the instructor for problem solving. It is not very high, really. To get success of his or her work the students' independent decisions must be correct no less than in 80 % cases. The total number of necessary decisions in the laboratory settings in several universities was investigated. The complexity of these decisions was also taken in account. It was found that the degree of student autonomy was practically the same in all studied institutions. That is why we can say that this degree may be determined as the optimal one

ENGINEERING FOR RURAL DEVELOPMENT WAY OF STUDYING GENERAL LAWS OF NATURE IN UNIVERSITIES

Abstract. The high mobility of modern specialists forced them to have universal background. Such background permits them to be adapted to the different social and professional environment. That is why it is necessary to introduce some basic laws of nature into the studied subjects. The optimal choice of these laws is a complex problem. The universities need to create new special education strategies and generate special concepts to transform the traditional curriculum to a new effective form. The main obstacle for new educational strategies is connected with the high abstraction of the general laws of nature which have to be included in the new scientific background. The most perspective way for solution of this problem is the high diversity of all practical classes and text-books which would be interesting for different students

О представлении решения задачи идентификации коэффициентов при дифференциальном операторе второго порядка в системе многомерных параболических уравнений

An identification problem of the coefficients at differential operator of second order and sum of lowest terms in system of multidimensional parabolic equations with Cauchy data was studied in this article. The theorems of existence and uniqueness of the solution for direct and inverse problems have been proved. The method of weak approximation is used to the proof existence of solutionsИсследована обратная задача с данными Коши для системы многомерных параболических урав- нений, содержащих неизвестные коэффициенты перед дифференциальным оператором второго порядка по выделенной переменной и суммой младших членов. Начальные данные имеют специ- альный вид и заданы в виде произведения двух функций, зависящих от разных переменных. Полу- чены достаточные условия существования и единственности решения вспомогательной прямой и исходной обратной задач. Для доказательства используется метод слабой аппроксимаци

X-ray structure of a Ni(II)–tri-phenoxyl radical complex

International audienceThe diimino-diphenolato neutral square-planar Ni(II) complex, NiL 2 , is readily oxidised with 2 equiv. of Ag[SbF 6 ], to produce an unprecedented octahedral Ni(II) tris(phenoxyl) radical complex, [Ni(L •) 3 ]-[SbF 6 ] 2. This study reveals, for the first time, the X-ray structure of a metal–tri-phenoxyl radical complex. In the last two decades, inspired by the unique Cu(II)–tyrosyl radical moiety of the active site of galactose oxidase (GO) 1 [a fungal enzyme that catalyses the aerobic two-electron oxidation of a wide range of primary alcohols to their corresponding aldehydes], chemists have been successful in generating and characterising phenoxyl radical complexes of Cu(II) and other transition metals such as Fe(III), Zn(II), Co(II/III), and Ni(II). 2 However, isolated persistent phenoxyl radical complexes are still rare, 3 and only a few X-ray structures have been reported. 4–7 Thus, the isolation and exploration of transition metal compounds containing one (or more) phe-noxyl radical ligand(s) with the desired catalytic or magnetic properties still remain a significant challenge. In particular, compounds that possess two and/or three phenoxyl radical ligands are known to be highly unstable. 2f,8 In the continuous search for a suitable ligand framework capable of sustaining a phenoxyl radical state, we have recently designed 5,9 a versatile N,O-phenol-imidazole/pyrazole pro-ligand family that incorporates: (a) t-Bu protection of the phenol ortho-and para-positions, preventing radical coupling decomposition pathways, and (b) no other oxidisable position than the phenol(ate) moiety itself. These ligand frameworks have allowed tetracoordinated M(II)– (M = Cu, Zn, and Co) and octahedral Co(III)–mono-phenoxyl radical complexes to be isolated as air-stable crystalline powders. 5,9a,b Herein, we report, using the phenol-pyrazole pro-ligand LH 9c (Scheme 1), the synthesis, characterisation and X-ray structure of an unprecedented octahedral Ni(II) tri-(phenoxyl) radical complex, [Ni(L •) 3 ] 2+ (2 2+); produced by an unusual two-electron chemical oxidation of the parent Ni II L 2 phenolate complex (1) (Scheme 1). The reaction of LH with [Ni(H 2 O) 6 ][BF 4 ] 2 in methanol in a 2 : 1 ratio in the presence of triethylamine, affords a pale-green NiL 2 compound (1) (see the ESI †). The X-ray structure of 1 (Fig. 1, Tables 1 and SI1–3 †) is isostructural to that of neutral CuL 2 9c,d displaying a neutral centrosymmetric trans-N 2 O 2 square-planar geometry, resulting from the coordination of two N,O-ligands in their anionic forms. The Ni–O and Ni–N bond distances (1.869(2) Å and 1.850 (2) Å respectively) are as expected for Ni(II)-phenolato-imino complexes in an N 2 O 2 environment. 2 The planar structure of 1 is reinforced by two intramolecular N–H⋯O hydrogen bonds between the pyrazole N–H and the phenolate-O atoms (N⋯O distances of 2.717(2) Å, angle of 121°; Fig. 1). As expected for low-spin, d 8 , square planar Ni(II) ions, complex 1 is diamagnetic and exhibits a well resolved 1 H NMR spectrum in CDCl 3 , displaying one set of resonances for the two Scheme 1 † Electronic supplementary information (ESI) available. CCDC 1005503 and 1005504 of 1 and 2. For ESI and crystallographic data in CIF or other electronic format se

An Representation of the Solution of the Inverse Problem for a Multidimensional Parabolic Equation with Initial Data in the Form of a Product

В работе исследована задача идентификации коэффициента, стоящего перед дифференциальным оператором второго порядка, в многомерном параболическом уравнении с данными Коши. В пред- положении специальных условий на входные данные обратная задача приведена к прямой. Дока- заны теоремы существования и единственности решения прямой и обратной задач.An identification problem of the coefficient at differential operator of second order in multidimensional parabolic equation with Cauchy data was studied in this article. The theorems of existence and uniqueness of the solution for direct and inverse problems has been proved

О разрешимости системы двух многомерных нагруженных параболических уравнений с данными Коши

We study a multidimensional system of two loaded parabolic equations of a special kind with the Cauchy data. Sufficient conditions for the existence of a solution in the class of smooth bounded functions are obtained. The splitting method at differential level (the method of weak approximation) is used in the proofИсследована многомерная система двух параболических нагруженных уравнений специального вида в случае данных Коши. Получены достаточные условия существования решения в классе глад- ких ограниченных функций. Для доказательства используется метод расщепления на дифферен- циальном уровне (метод слабой аппроксимации