What are Reversed Spheres?

In our universe we have only two elements: mass which is a sphere and radiation which is a reversed sphere. A sphere has the maximum volume with minimum exterior surface and a reversed sphere has minimum volume while having maximum exterior surface. A sphere has a centre and a surface at a fix distance in all directions while a reversed sphere has the centre everywhere in all directions and the surface covering all radiuses heading towards its middle point. Interaction between mass creates events and exchange of energy, while interaction between radiations doesn’t. Interaction between mass and radiation is rare in universe. Any sphere of mass has around it a reversed sphere of radiation (gravity) which prevents it from exploding back. When mass and radiation interact, the reversed sphere surrounding mass disturbs the trajectory of pure radiation. The first one has a constant force due to surface of mass in the middle, while the second one has the tendency to expand as it has nothing in the middle. It is possible to transfer mass (spherical radiation) into radiation (linear radiation) and radiation into mass because of the formula E=mc2, but the conditions form initial big bang are needed in order to create/destroy gravity.

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The Arithmetic Tutte polynomial of two matrices associated to Trees

Special Matrices ◽

10.1515/spma-2018-0026 ◽

2018 ◽

Vol 6 (1) ◽

pp. 310-322

Author(s):

R. B. Bapat ◽

Sivaramakrishnan Sivasubramanian

Keyword(s):

Analogous Result ◽

Polynomial Matrix ◽

Tutte Polynomial ◽

Distance Matrix ◽

Minimum Volume ◽

Maximum Volume ◽

Recent Interest ◽

Minimum Volume Ellipsoid ◽

Tutte Polynomials ◽

Exponential Distance

Abstract Arithmetic matroids arising from a list A of integral vectors in Zn are of recent interest and the arithmetic Tutte polynomial MA(x, y) of A is a fundamental invariant with deep connections to several areas. In this work, we consider two lists of vectors coming from the rows of matrices associated to a tree T. Let T = (V, E) be a tree with |V| = n and let LT be the q-analogue of its Laplacian L in the variable q. Assign q = r for r ∈ ℤ with r/= 0, ±1 and treat the n rows of LT after this assignment as a list containing elements of ℤn. We give a formula for the arithmetic Tutte polynomial MLT (x, y) of this list and show that it depends only on n, r and is independent of the structure of T. An analogous result holds for another polynomial matrix associated to T: EDT, the n × n exponential distance matrix of T. More generally, we give formulae for the multivariate arithmetic Tutte polynomials associated to the list of row vectors of these two matriceswhich shows that even the multivariate arithmetic Tutte polynomial is independent of the tree T. As a corollary, we get the Ehrhart polynomials of the following zonotopes: - ZEDT obtained from the rows of EDT and - ZLT obtained from the rows of LT. Further, we explicitly find the maximum volume ellipsoid contained in the zonotopes ZEDT, ZLT and show that the volume of these ellipsoids are again tree independent for fixed n, q. A similar result holds for the minimum volume ellipsoid containing these zonotopes.

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Left atrial minimum volume is more strongly associated with N-terminal pro-B-type natriuretic peptide than the left atrial maximum volume in a community-based sample

The International Journal of Cardiovascular Imaging ◽

10.1007/s10554-015-0800-1 ◽

2015 ◽

Vol 32 (3) ◽

pp. 417-425 ◽

Cited By ~ 13

Author(s):

Pär Hedberg ◽

Jonas Selmeryd ◽

Jerzy Leppert ◽

Egil Henriksen

Keyword(s):

Natriuretic Peptide ◽

Left Atrial ◽

Minimum Volume ◽

Maximum Volume ◽

Community Based

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Feasibility and Reproducibility of Left Atrium Measurements Using Different Three-Dimensional Echocardiographic Modalities

Diagnostics ◽

10.3390/diagnostics10121043 ◽

2020 ◽

Vol 10 (12) ◽

pp. 1043

Author(s):

Andreea Motoc ◽

Bram Roosens ◽

Esther Scheirlynck ◽

Kaoru Tanaka ◽

Maria Luiza Luchian ◽

...

Keyword(s):

Cardiac Magnetic Resonance ◽

Left Atrium ◽

Three Dimensional ◽

Minimum Volume ◽

Heart Model ◽

Maximum Volume ◽

Interobserver Reproducibility ◽

Dimensional Echocardiography ◽

Three Dimensional Echocardiography

Left atrium (LA) volume is a biomarker of cardiovascular outcomes. Three-dimensional echocardiography (3DE) provides an accurate LA evaluation, but data regarding the optimal 3DE method is scarce. We assessed the feasibility and reproducibility of LA measurements using different 3DE methods. One hundred and ninety-four patients were prospectively analyzed. Conventional 3DE and two semi-automatic 3DE algorithms (Tomtec™ and Dynamic Heart Model (DHM)) were used in 110 patients. Intra- and interobserver reproducibility and intervendor comparison were performed in additional patients’ subsets. Forty patients underwent cardiac magnetic resonance (CMR). Feasibility was 100% for Tomtec, 98.2% for DHM, and 72.8% for conventional 3DE. Tomtec volumes were higher than 3DE and DHM (p < 0.001). Reproducibility was better for DHM (intraobserver LA maximum volume (LAmax) ICC 0.99 (95% CI 1.0–0.99), LA minimum volume (LAmin) 0.98 (95% CI 0.95–0.99), LApreA 0.96 (95% CI 0.91–0.98); interobserver LAmax ICC 0.98 (95% CI 0.96–0.99), LAmin 0.99 (95% CI 0.99–1.00), and LApreA 0.97 (95% CI 0.94–0.99)). Intervendor comparison showed differences between left ventricle (LV) software adapted for LA (p < 0.001). Tomtec underestimated the least LA volumes compared to CMR. These findings emphasize that dedicated software should be used for LA assessment, for consistent clinical longitudinal follow-up and research.

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