Sentence examples for mixed surface area from inspiring English sources

with being mixed surface area element of ; see [38, 42, 46 48] for many interesting properties of mixed volumes.

If the mixed surface area measure S i ( K, ⋅ ) is absolutely continuous with respect to spherical Lebesgue measure S, we have f p, i ( K, u ) = f i ( K, u ) h ( K, u ) 1 − p. (1.13).

A convex body (Kinmathcal{K}^{n}) is said to have a continuous ith curvature function (f_{i}(K,cdot):mathbb{S}^{n-1}rightarrowmathbb {R}) if its mixed surface area measure (S_{i}(K,cdot)) is absolutely continuous with respect to the spherical Lebesgue measure S and has the Radon-Nikodym derivative (see [28]) begin{aligned} frac{dS_{i}(K,cdot)}{dS}=f_{i}(K,cdot), quadmbox{for } iin{0, 1,ldots,n-1}.

A convex body K ∈ K n is said to have a continuous i th curvature function f i ( K, ⋅ ) : S n − 1 → R if its mixed surface area measure S i ( K, ⋅ ) is absolutely continuous with respect to the spherical Lebesgue measure S and has the Radon-Nikodym derivative (see [29]) d S i ( K, ⋅ ) d S = f i ( K, ⋅ ) for  i ∈ { 0, 1, …, n − 1 }.

Lutwak (see [15]) defined the i th mixed affine surface area as follows: For K, L ∈ F n and i ∈ R, the i th mixed affine surface area, Ω i ( K, L ), of K and L is defined by Ω i ( K, L ) = ∫ S n − 1 f ( K, u ) n − i n + 1 f ( L, u ) i n + 1 d S ( u ).

Further, we establish some inequalities for the L p -dual mixed geominimal surface area.

In this paper, we first define the L p -dual mixed geominimal surface area for multiple star bodies with the same idea in mind as [12].

Interestingly, both lectins segregated into distinct domains within interfaces, while they remained homogenously mixed in the surface area outside of contact zones.

In this contribution, GO and MWCNT are hybridized to produce mixed substrates with improved surface area, and compatibility for the subsequent deposition of LDH platelets, compared to either phase alone.

Conversely considered, generalized classes of isoperimetric problems in higher-dimensional Minkowski spaces refer to all convex bodies of given mixed volume having minimum surface area.

A 24-year-old male had sustained 80% mixed depth, total body surface area (TBSA) flame burns following a road traffic accident.