The aim of this work is to investigate sweeping surfaces and their local singularities due type-3 Bishop frames in Euclidean 3-space, E3. A surface a that designed from section curve positioned along path, which acts as the vertebral column or spine curve, it has symmetrical characteristics. In work, we have specified examined its geometry singularity. Thereafter, deduced circumstances required...

For the general class of pseudo-Finsler spaces with (α,β)-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means fundamental tensor has Lorentzian signature on conic subbundle tangent bundle thus existence cone future-pointing time-like vectors is ensured. The identified (α,β)-Finsler spacetimes are candidates for applications i...

We show that for any discrete finitely-generated group G and any self-adjoint n-tuple X1, . . . , Xn of generators of the group algebra CG, Voiculescu’s non-microstates free entropy dimension δ(X1, . . . , Xn) is exactly equal to β1(G) − β0(G) + 1, where βi are the L Betti numbers of G.

If X is the (unique) minimal set for a C1+α diffeomorphism of the circle without periodic orbits, 0 < α < 1, then the upper box dimension of X is at least α. The method of proof is to introduce the exponent α into the proof of Denjoy’s theorem.

In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To end, introduce new notion localised metric subdifferential compactly supported measures, and investigate intrinsic linearised Cauchy problems associated to non-local continuity equations. particular, show that when veloc...

We present a pivoting algorithm for solving linear programs with linear complementarity constraints. Our method generalizes the simplex method for linear programming to deal with complementarity conditions. We develop an anticycling scheme that can verify Bouligand stationarity. We also give an optimizationbased technique to find an initial feasible vertex. Starting with a feasible vertex, our ...

Suppose M is a von Neumann algebra with normal, tracial state ϕ and {a 1 ,. .. , a n } is a set of self-adjoint elements of M. We provide an alternative uniform packing description of δ 0

We find the microstates free entropy dimension of a large class of L∞[0, 1]–circular operators, in the presence of a generator of the diagonal subalgebra.