scholarly journals On the strong uniqueness of minimal projections in the space $l_\\infty^9$

Author(s):  
Олег Михайлович Мартынов

В работе рассматриваются минимальные проекции пространства $l_\\infty^9$ на некоторые подпространства коразмерности 3. Для них найдены относительные прекционные константы, а в случае минимальной проекции с единичной нормой найдено максимальной значение константы сильной единственности. Найденые проекционные константы могут найти применение в вычислительной математике, в частности, для оценки сходимости проекционных методов решения операторных уравнений и в оценках ошибки алгоритма Ремеза. In this paper we consider minimal projections of the space $l_\\infty^9$ on some subspaces of codimension 3. Relative projection constants are found for them, and in the case of a minimal projection with a unit norm, we find maximum value of the strong uniqueness constant.

1985 ◽  
Vol 97 (1) ◽  
pp. 127-136 ◽  
Author(s):  
E. J. Halton ◽  
W. A. Light

Let X be a normed linear space and let W be a proper subspace of X. A projection is a surjective linear map P: X → W such that P is idempotent. It is immediately clear that P has norm at least unity. Thus the problem of calculating the numberhas some interest. The number λ(W, X) is often called the relative projectiion constant of W in X. If the infimum is attained, any attaining projection is called a minimal projection. The problems of calculating λ(W, X) for a fixed X and W or finding a minimal projection turn out to be very dificult. For example, if X = C [0, 1] with the usual supremem norm and W is the subspace of polynominals of degree at most two then λ(W, X) remains unknown as does any example of a minimal projection. One of the few places where the problem shows much tractability is the case


Author(s):  
Michał Kozdęba

Abstract Let us consider the space M(n, m) of all real or complex matrices on n rows and m columns. In 2000 Lesław Skrzypek proved the uniqueness of minimal projection of this space onto its subspace $$M(n,1)+M(1,m)$$ M ( n , 1 ) + M ( 1 , m ) which consists of all sums of matrices with constant rows and matrices with constant columns. We generalize this result using some new methods proved by Lewicki and Skrzypek (J Approx Theory 148:71–91, 2007). Let S be a space of all functions from $$X\times Y \times Z$$ X × Y × Z into $${\mathbb {R}}$$ R or $${\mathbb {C}}$$ C , where X, Y, Z are finite sets. It could be interpreted as a space of three-dimensional matrices M(n, m, r). Let T be a subspace of S consisting of all sums of functions which depend on one variable. Let S be equipped with a smooth norm $$\Vert .\Vert $$ ‖ . ‖ . We show that there exists the unique minimal projection of S onto its subspace T.


1984 ◽  
Vol 52 (01) ◽  
pp. 015-018 ◽  
Author(s):  
A Girolami ◽  
A Sticchi ◽  
R Melizzi ◽  
L Saggin ◽  
G Ruzza

SummaryLaser nephelometry is a technique which allows the evaluation of the concentration of several serum proteins and clotting factors. By means of this technique it is also possible to study the kinetics of the reaction between antigen and antibody. We studied the kinetics of the reaction between prothrombin and an antiprothrombin antiserum using several prothrombins namely: Prothrombin Padua, prothrombin Molise, which are two congenital dysprothrombinemias, cirrhotic, coumarin or normal prothrombins. Different behaviors in the kinetics of the reactions were shown even when the concentration of prothrombins was about the same in all plasma tested. These differences were analyzed by means of a computer (Apple II 48 RAM) programmed to solve four unknown equations (Rodbard’s equation). From the data so obtained one can see that when voltages at the beginning and at the end of the reaction are in all cases about the same, a clear difference in the time required to reach half the maximum value of the voltage can still be demonstrated. This parameter, which is expressed in minutes, is longer in coumarin and prothrombin Molise than in controls. On the contrary it is shorter in prothrombin Padua and has about the same value of controls in the cirrhotic patient. Moreover the time at which the maximum rate is obtained is longer in coumarin and prothrombin Molise than in controls and shorter in liver cirrhosis and prothrombin Padua. In conclusion data obtained show that coumarin prothrombin behaves in a different way from cirrhotic prothrombin and also that there is a different behaviour between the two congenital dysprothrombinemias.


2017 ◽  
Vol 23 (2) ◽  
Author(s):  
AFSHAN ANJUM BABA ◽  
SYED NASEEM UL-ZAFAR GEELANI ◽  
ISHRAT SALEEM ◽  
MOHIT HUSAIN ◽  
PERVEZ AHMAD KHAN ◽  
...  

The plant biomass for protected areas was maximum in summer (1221.56 g/m2) and minimum in winter (290.62 g/m2) as against grazed areas having maximum value 590.81 g/m2 in autumn and minimum 183.75 g/m2 in winter. Study revealed that at Protected site (Kanidajan) the above ground biomass ranged was from a minimum (1.11 t ha-1) in the spring season to a maximum (4.58 t ha-1) in the summer season while at Grazed site (Yousmarag), the aboveground biomass varied from a minimum (0.54 t ha-1) in the spring season to a maximum of 1.48 t ha-1 in summer seasonandat Seed sown site (Badipora), the lowest value of aboveground biomass obtained was 4.46 t ha-1 in spring while as the highest (7.98 t ha-1) was obtained in summer.


2018 ◽  
Vol 6 (1) ◽  
pp. 5-21
Author(s):  
Ewa Skrabacz

AbstractConstituting the key element of a democratic system, political parties are among entities obliged by the Polish legislator to comply with the principle of disclosure by providing public information. The main objective of this paper is to determine the level of Polish political parties’ disclosure, understood here as their willingness to disclose information on their own structures. It seems that the practice of disclosing such basic organizational data may constitute a specific measure of Polish political parties’ respect for the idea of disclosure. The subject matter of the conducted research was particular parties’ sites in the Public Information Bulletin as well as their official websites. An attempt was made to acquire data concerning party structures by way of direct contact with particular parties’ organizational units – questionnaires were sent to both central and regional/district organizational units. In order to acquire a wider perspective, the research also included data provided by the Central Statistical Office concerning political parties’ organizational structures and election manifestos. The conducted analysis was summarized in the form of a ranking of the examined political parties based on a proposed political party disclosure index. This attempt to measure disclosure on the basis of data on internal structures provided by parties themselves is of a preliminary character which, nevertheless, makes it possible to capture the general properties of the phenomenon under analysis. Among the examined parties, it is PSL, SLD, and PO that, to an acceptable degree, follow the principle of disclosure in the analysed scope (indexes at the level of 60%-80% of the maximum value). Four other parties, i.e. N, Wolność, Razem, and Kukiz’15, are on the edge of the zone making it possible to regard their disclosure as sufficient (indexes at the level of around 50% of the maximum value). In the case of PiS, whose index does not reach 20% of the maximum value, it should be concluded that this party implements the principle of disclosure at a minimum level. The ranking did not show relationships between parties’ willingness towards providing information and their sizes or positions on the political scene (parliamentary parties vs. extra-parliamentary parties).


2020 ◽  
Vol 38 (1A) ◽  
pp. 25-32
Author(s):  
Waleed Kh. Jawad ◽  
Ali T. Ikal

The aim of this paper is to design and fabricate a star die and a cylindrical die to produce a star shape by redrawing the cylindrical shape and comparing it to the conventional method of producing a star cup drawn from the circular blank sheet using experimental (EXP) and finite element simulation (FES). The redrawing and drawing process was done to produce a star cup with the dimension of (41.5 × 34.69mm), and (30 mm). The finite element model is performed via mechanical APDL ANSYS18.0 to modulate the redrawing and drawing operation. The results of finite element analysis were compared with the experimental results and it is found that the maximum punch force (39.12KN) recorded with the production of a star shape drawn from the circular blank sheet when comparing the punch force (32.33 KN) recorded when redrawing the cylindrical shape into a star shape. This is due to the exposure of the cup produced drawn from the blank to the highest tensile stress. The highest value of the effective stress (709MPa) and effective strain (0.751) recorded with the star shape drawn from a circular blank sheet. The maximum value of lamination (8.707%) is recorded at the cup curling (the concave area) with the first method compared to the maximum value of lamination (5.822%) recorded at the cup curling (the concave area) with the second method because of this exposure to the highest concentration of stresses. The best distribution of thickness, strains, and stresses when producing a star shape by


2020 ◽  
Author(s):  
Wen-Xiang Chen

When \Delta x \Delta p < \hbar / 2 happens at the same time when the entropy reaches its maximum value, the boson will condense, and if there is a potential well but it does not explode, then the boson will gain high energy (more than normal).This article is to illustrate the possibility of a kind of Bose particle to obtain high energy.


2018 ◽  
Vol 3 (1) ◽  
pp. 22-27
Author(s):  
S. Supratman ◽  
Sri Wulandari Muhlis

The formulation of the problem in this research are: (1) How the result of learning mathematics of students after taught by SAVI learning model?, (2) How the result of learning mathematics of students after taught by NHT learning model?, (3) Is the result of learning mathematics of students who taught with SAVI learning model is higher than students taught by NHT learning model. The purpose of this study are: (1) To know how the results of learning mathematics students after teaching with SAVI learning model, (2) To find out how the results of learning mathematics students after being taught with NHT learning model, (3) To determine whether the results of learning mathematics students taught by SAVI learning models higher than students taught by NHT learning models. Type of research using experimental method. The population in this study is all students of class X spread in 11 parallel classes with the number of 310 people. Sampling was done by using cluster random sampling technique. In this research as a sample taken 2 classes from the entire population that is class X A3 as experiment class 1 using SAVI learning model and class X A1 as experiment class 2 using NHT learning model. From result of data analysis obtained that: (1) result of student learning taught by using SAVI learning model which consist of 25 students show minimum value 62, maximum value 96, mean (mean) 80,36, with standard deviation 9,10; (2) student learning outcomes taught using NHT learning model consisting of 25 students showing minimum score 62, maximum value 96, mean (mean) 79,62, with standard deviation 10,512; (3) result of t-test analysis using independent sample t-test obtained tcount = 0,302 at = 0,05 with degrees of freedom (dk) = 48 obtained t table = 2,011. Because t <t table then Ha is rejected and H0 is accepted. So it can be concluded that the mathematics learning outcomes of students who were taught with the SAVI model was not higher than the students taught by the NHT model.


2015 ◽  
Vol 9 (1) ◽  
pp. 135-140
Author(s):  
Dong Zhi-Ming ◽  
Guo Li-Xia ◽  
Chang Ji-Bin ◽  
Zhou Xue-Bin

Aiming to compare the cooling effect, two types of solar-powered semiconductor air-conditioning devices were designed in different structures. According to the cooling load in an experimental room, the solar panels and battery capacity were determined for the development of a test system. In the same working condition, a comparison test was carried out to examine the cooling performance. Experimental results showed that the design of dual water-cooled cooling unit presented a higher ratio of energy efficiency, with its maximum value of 1.08. By observing the experimental data of the prototype, its comparative economic evaluation results indicated that the annualized cost of solar semiconductor airconditioning was app. 2.7 times that of air-conditioning made from an ordinary compressor.


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