scholarly journals Vague Seperation and Connectedness

2019 ◽  
Vol 8 (6S4) ◽  
pp. 1414-1417
Keyword(s):  
Standard Space

In this paper we blessing dark standard space, questionable run of the mill space,vague entire common zone and besides deduce a couple of speculations on those. also mean cloud connectedness, dicey unequivocally connectedness, unsure insistently disconnectedness, questionable C5 detached, part and additionally choose a couple of theories

scholarly journals Thermal Effect on Elastic Waves of Anisotropic Saturated Porous Solid

2011 ◽  
Vol 2011 ◽  
pp. 1-5
Author(s):  
S. H. Guo
Keyword(s):  
Thermal Effect ◽  
Elastic Waves ◽  
Anisotropic Media ◽  
Mass Conservation ◽  
Porous Solid ◽  
Porous Solids ◽  
Elastic Model ◽  
Coupling Coefficients ◽  
Motion Equations ◽  
Standard Space

The motion equations of anisotropic media, coupled to the mass conservation and thermoequilibrium equations of fluid, are studied here based on the standard space of physical presentation for thermoelastic dynamics of anisotropic saturated porous solids. By introducing a new compressible thermo-elastic model, a set of uncoupled equations of elastic waves are deduced. The results show that the elastic waves and speeds of elastic waves are affected by both anisotropic subspaces of solids and thermal and compressive coupling coefficients between fluid and solid. Based on these laws, we discuss the propagation behaviour of elastic waves for various anisotropic solids.

scholarly journals On the Notion of Scalar Product for Finite-dimensional Diffeological Vector Spaces

2018 ◽  
Vol 34 ◽  
pp. 18-27 ◽  
Author(s):  
Ekaterina Pervova
Keyword(s):  
Vector Space ◽  
Bilinear Form ◽  
Scalar Product ◽  
Vector Spaces ◽  
Initial Space ◽  
Finite Dimensional ◽  
Standard Space

It is known that the only finite-dimensional diffeological vector space that admits a diffeologically smooth scalar product is the standard space of appropriate dimension. In this note, a way to dispense withthis issue is considered, by introducing a notion of pseudo-metric, which, said informally, is the least-degeneratesymmetric bilinear form on a given space. This notion is applied to make some observations on subspaces which split off as smooth direct summands (providing examples which illustrate that not all subspaces do), and then to show that the diffeological dual of a finite-dimensional diffeological vector space always has the standard diffeology and in particular, any pseudo-metric on the initial space induces, in theobvious way, a smooth scalar product on the dual.

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