PROPERTIES AND APPLICATIONS OF NEW POLYNOMIAL SPACES

2006 ◽  
Vol 04 (03) ◽  
pp. 489-507 ◽  
Author(s):  
PAOLO COSTANTINI
Keyword(s):  
Spline Functions ◽  
Variable Degree ◽  
Polynomial Space ◽  
Degree Polynomial ◽  
Tension Properties ◽  
Dimensional Variable

The aim of this paper is to describe a new five-dimensional, variable degree polynomial space. This space has the same properties of P4 and possesses generalized tension properties, in the sense that it is close to P2 for large values of the degrees. Its applications in the construction of spline functions will also be discussed.

Carotid endarterectomy in patients with foetal-type posterior circle of Willis: Is there an indication for local anaesthesia?

VASA ◽  
2011 ◽  
Vol 40 (5) ◽  
pp. 404-407
Author(s):  
Maras ◽  
Tzormpatzoglou ◽  
Papas ◽  
Papanas ◽  
Kotsikoris ◽  
...  
Keyword(s):  
Carotid Endarterectomy ◽  
Local Anaesthesia ◽  
Anatomical Variation ◽  
Anatomical Variations ◽  
Circle Of Willis ◽  
Variable Degree ◽  
Operative Complications ◽  
The Right ◽  
Ica Stenosis ◽  
Symptomatic Stenosis

Foetal-type posterior circle of Willis is a common anatomical variation with a variable degree of vessel asymmetry. In patients with this abnormality, carotid endarterectomy (CEA) may create cerebral hypo-perfusion intraoperatively, and this may be underestimated under general anaesthesia. There is currently no evidence that anatomical variations in the circle of Willis represent an independent risk factor for stroke. Moreover, there is a paucity of data on treating patients with such anatomical variations and co-existing ICA stenosis. We present a case of CEA under local anaesthesia (LA) in a 52-year-old female patient with symptomatic stenosis of the right ICA and coexistent foetal-type posterior circle of Willis. There were no post-operative complications and she was discharged free from symptoms. She was seen again 3 months later and was free from complications. This case higlights that LA should be strongly considered to enable better intra-operative neurological monitoring in the event of foetal-type posterior circle of Willis.

Abnormal Structure of von Willebrand Factor in Myeloproliferative Syndrome Is Associated to Either Thrombotic or Bleeding Diathesis

1987 ◽  
Vol 58 (02) ◽  
pp. 753-757 ◽  
Author(s):  
M F López-Fernández ◽  
C López-Berges ◽  
R Martín ◽  
A Pardo ◽  
F J Ramos ◽  
...  
Keyword(s):  
Von Willebrand Factor ◽  
Proteinase Inhibitors ◽  
Relative Proportion ◽  
Variable Degree ◽  
Bleeding Diathesis ◽  
Myeloproliferative Syndrome ◽  
Von Willebrand ◽  
Willebrand Factor

SummaryThe multimeric and subunit patterns of plasma von Willebrand factor (vWF) were analyzed in eight patients with myeloproliferative syndrome (MS) in order to investigate the possible existence of heterogeneity in the “in vivo” proteolytic cleavage of the protein, previously observed in this entity. Six patients lacked large vWF multimers, five of them having normal bleeding times (BT) and clinically documented episodes of thrombotic origin, whereas one patient had long BT and bleeding symptoms. Seven patients showed a relative increase in the 176 kDa subunit fragment while the 189 kDa polypeptide was increased in only one. In addition, another patient (and prior to any therapy) showed the presence of a new fragment of approximately 95 kDa which disappeared after Busulfan therapy. The collection of blood from these patients with proteinase inhibitors did not correct the abnormalities.The infusion of DDAVP to two patients with abnormal vWF was accompanied by: the appearance of larger vWF multimers which disappeared rapidly from plasma; an increase in the relative proportion of the satellite bands of each multimer and a further increase of the 176 kDa fragment. These data point to some heterogeneity in the vWF abnormality present in MS which may be related in part to a variable degree of proteolysis of vWF occurring “in vivo” rather than “in vitro”, and which may be associated to either a thrombotic or a bleeding diathesis. They also suggest that despite the presence of abnormal, already proteolyzed vWF, DDAVP-enhanced proteolysis occurs in MS to a similar extent to what is described in normal individuals.

Some Views on Current Concerns About Pesticides

2020 ◽  
Vol 31 (5) ◽  
pp. 230-235
Author(s):  
Graham Matthews
Keyword(s):  
Green Revolution ◽  
Scientific Data ◽  
Second World War ◽  
Variable Degree ◽  
World War ◽  
Adverse Impacts ◽  
Current Concerns ◽  
Second World

There is little doubt that the introduction of modern pesticides since the end of the Second World War has enabled a significant increase in the production of many crops during the green revolution, but criticism of the use of pesticides has increased because more people are claiming that their use has resulted in unacceptable adverse impacts on the health of those applying the pesticides or who live near treated farms, as well as more general impacts on the environment. When these modern pesticides were first introduced, countries established registration requirements. These were based on scientific data at that time concerning their toxicity and persistence in the environment, and have been followed to a variable degree, depending on whether individual countries or regions had adequate facilities to assess the data presented by manufacturers.

On the approximation of $ \ exp (-x) $ on the half-axis by spline functions in three-point rational interpolants

2019 ◽  
pp. 32-37
Author(s):  
Abdul-Rashid Ramazanov ◽  
V.G. Magomedova
Keyword(s):  
Convergence Rate ◽  
Spline Functions ◽  
Rational Spline ◽  
Rational Interpolants ◽  
Half Axis

For the function $f(x)=\exp(-x)$, $x\in [0,+\infty)$ on grids of nodes $\Delta: 0=x_0<x_1<\dots $ with $x_n\to +\infty$ we construct rational spline-functions such that $R_k(x,f, \Delta)=R_i(x,f)A_{i,k}(x)\linebreak+R_{i-1}(x, f)B_{i,k}(x)$ for $x\in[x_{i-1}, x_i]$ $(i=1,2,\dots)$ and $k=1,2,\dots$ Here $A_{i,k}(x)=(x-x_{i-1})^k/((x-x_{i-1})^k+(x_i-x)^k)$, $B_{i,k}(x)=1-A_{i,k}(x)$, $R_j(x,f)=\alpha_j+\beta_j(x-x_j)+\gamma_j/(x+1)$ $(j=1,2,\dots)$, $R_j(x_m,f)=f(x_m)$ при $m=j-1,j,j+1$; we take $R_0(x,f)\equiv R_1(x,f)$. Bounds for the convergence rate of $R_k(x,f, \Delta)$ with $f(x)=\exp(-x)$, $x\in [0,+\infty)$, are found.

PREDICTING CHARACTERISTICS OF SELF SIMILAR TRAFFIC BY SPLINE-EXTRAPOLATION

2019 ◽  
Author(s):  
Irina Strelkovskay ◽  
Irina Solovskaya ◽  
Anastasija Makoganjuk ◽  
Nikolaj Severin
Keyword(s):  
Quality Characteristics ◽  
Traffic Prediction ◽  
Normative Values ◽  
Spline Functions ◽  
Network Nodes ◽  
Traffic Forecasting ◽  
Network Equipment ◽  
Self Similar ◽  
Accuracy Of Prediction

The problem of forecasting self-similar traffic, which is characterized by a considerable number of ripples and the property of long-term dependence, is considered. It is proposed to use the method of spline extrapolation using linear and cubic splines. The results of self-similar traffic prediction were obtained, which will allow to predict the necessary size of the buffer devices of the network nodes in order to avoid congestion in the network and exceed the normative values ​​of QoS quality characteristics. The solution of the problem of self-similar traffic forecasting obtained with the Simulink software package in Matlab environment is considered. A method of extrapolation based on spline functions is developed. The proposed method has several advantages over the known methods, first of all, it is sufficient ease of implementation, low resource intensity and accuracy of prediction, which can be enhanced by the use of quadratic or cubic interpolation spline functions. Using the method of spline extrapolation, the results of self-similar traffic prediction were obtained, which will allow to predict the required volume of buffer devices, thereby avoiding network congestion and exceeding the normative values ​​of QoS quality characteristics. Given that self-similar traffic is characterized by the presence of "bursts" and a long-term dependence between the moments of receipt of applications in this study, given predetermined data to improve the prediction accuracy, it is possible to use extrapolation based on wavelet functions, the so-called wavelet-extrapolation method. Based on the results of traffic forecasting, taking into account the maximum values ​​of network node traffic, you can give practical guidance on how traffic is redistributed across the network. This will balance the load of network objects and increase the efficiency of network equipment.

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