Vector valued nonuniform nonstationary wavelets and associated MRA on local fields

In this paper we study nonstationary wavelets associated with vector valued nonuniform multiresolution analysis on local fields. By virtue of dimension function a complete characterization of vector valued nonuniform nonstationary wavelets is obtained.

Some Results on Fuzzy ω-Covering Dimension Function in Fuzzy Topological Space

The purpose of this paper is to study a new class of fuzzy covering dimension functions, called fuzzy

STRONG DENSITY OF DEFINABLE TYPES AND CLOSED ORDERED DIFFERENTIAL FIELDS

The following strong form of density of definable types is introduced for theories T admitting a fibered dimension function d: given a model M of T and a definable set X ⊆ Mn, there is a definable type p in X, definable over a code for X and of the same d-dimension as X. Both o-minimal theories and the theory of closed ordered differential fields (CODF) are shown to have this property. As an application, we derive a new proof of elimination of imaginaries for CODF.

Real Analyticity of Hausdorff Dimension Function of Disconnected Julia Sets of Parabolic Polynomials fa,b(z) = z(1 – az – bz2)

not available GANIT J. Bangladesh Math. Soc.Vol. 38 (2018) 119-125

Small sets containing any pattern

Given any dimension function h, we construct a perfect set E ⊆ ${\mathbb{R}}$ of zero h-Hausdorff measure, that contains any finite polynomial pattern.This is achieved as a special case of a more general construction in which we have a family of functions $\mathcal{F}$ that satisfy certain conditions and we construct a perfect set E in ${\mathbb{R}}^N$, of h-Hausdorff measure zero, such that for any finite set {f1,. . .,fn} ⊆ $\mathcal{F}$, E satisfies that $\bigcap_{i=1}^n f^{-1}_i(E)\neq\emptyset$.We also obtain an analogous result for the images of functions. Additionally we prove some related results for countable (not necessarily finite) intersections, obtaining, instead of a perfect set, an $\mathcal{F}_{\sigma}$ set without isolated points.

Non-invasive right ventricular load adaptability indices in patients with scleroderma-associated pulmonary arterial hypertension

Scleroderma-associated pulmonary arterial hypertension (SSc-PAH) is associated with worse outcome than idiopathic pulmonary arterial hypertension (IPAH), potentially due to worse right ventricular adaptation to load as suggested by pressure–volume loop analysis. The value of non-invasive load-adaptability metrics has not been fully explored in SSc-PAH. This study sought to assess whether patients with incident SSc-PAH have worse echocardiographic load-adaptability metrics than patients with IPAH. Twenty-two patients with incident SSc-PAH were matched 1:1 with IPAH based on pulmonary vascular resistance. Echocardiographic load-adaptability indices were divided into: surrogates of ventriculo-arterial coupling (e.g. right ventricular area change/end-systolic area), indices reflecting the proportionality of load adaptation (e.g. tricuspid regurgitation velocity-time integral normalized for average right ventricular radius), and simple ratios (e.g. tricuspid annular plane systolic excursion/right ventricular systolic pressure). The prognostic value of these indices for clinical worsening (i.e. death, transplant, or hospitalization for heart failure) at one year was explored. The two groups were comprised of patients of similar age, with similar cardiac index, pulmonary resistance, capacitance and NT-proBNP levels ( p > 0.10). There was no difference in baseline right ventricular dimension, function or load-adaptability indices. At one year, eight (36.4%) SSc-PAH patients had experienced clinical worsening (eight hospitalizations and two deaths) versus one hospitalization in the IPAH group. Load adaptation at one year in survivors was not worse in SSc-PAH ( p > 0.33). Patients with IPAH responded better to therapy than SSc-PAH in terms of reduction of right ventricular areas at one year ( p < 0.05). Right ventricular load-adaptability echocardiographic indices do not appear to capture the increased risk of negative outcomes at one year associated with SSc-PAH.

CRITICAL FACTORS OF THE APPLICATION OF NANOTECHNOLOGY IN CONSTRUCTION INDUSTRY BY USING ANP TECHNIQUE UNDER FUZZY INTUITIONISTIC ENVIRONMENT

Nanotechnology plays a significant role in construction industry. The construction industry has been employed nanomaterials to improve the performance of construction components and the safety of the structure and to reduce the energy consuming and the cost of maintenance. In other words, nanotechnology has a substantial impact on the construc­tion industry. Therefore, it is necessary to identify and evaluate the critical factors of the application of nanotechnology in construction in order to concentrate on the most critical factors. However, several techniques have been developed to prioritize the evaluation criteria. Analytical network process (ANP) technique, a branch of multi criteria decision mak­ing (MCDM) methods, is a powerful tool to rank a limited number of criteria. This technique takes into account both tangible and intangible criteria in the process of formulation of a decision making problem. This method is capable of handling all types of independence and dependence relationships. On the other hand, intuitionistic fuzzy set (IFS) is a well-known technique in considering the inherent uncertainty involved in the process of modelling a decision making problem. In this paper, a new model based on the IFS and ANP technique is proposed to evaluate the critical factors of the application of nanotechnology in the construction industry. The results demonstrate that the proposed model has a high potential for taking into account the uncertainty in the form of a three dimension function, including membership, non-membership, and non-determinacy.

Code Mixing & Code Switching—A Panorama (With Respect to Pondicherry UT & Cauvery Delta)

<p><em>The paper aims at presenting the rudiments involved of code mixing and switching along with the definition. It also seeks its uses, effects and affects with throwing a light on how it helps language growth and at the same time the possibility of marring the originality of the language. The paper would conclude with a clear tone, to the readers, of a general idea of code switching and mixing, and its different dimension, function and dimensional function with respect to India on the whole and Tamil Nadu on particular.</em></p>