Recently, S. Reich and S. Simons provided a novel proof of the Kirszbraun-Valentine extension theorem using Fenchel duality and Fitzpatrick functions. In the same spirit, we provide a new proof of an extension result for firmly nonexpansive mappings with an optimally localized range. Throughout this paper, we assume that X is a real Hilbert space, with inner product p = 〈· | ·〉 and induced norm...

The complete multipartite graph Kn(2t) having n partite sets of size 2t, with n ≥ 6 and t ≥ 1, is shown to have a decomposition into gregarious 6-cycles, that is, the cycles which have at most one vertex from any particular partite set. Complete sets of differences of numbers in Zn are used to produce starter cycles and obtain other cycles by rotating the cycles around the n-gon of the partite ...

We use the following two well known bounds in our proofs. Lemma 1 (Chernoff-Hoeffding bound). Let X1, · · · , Xn be random variables with common support [0, 1] and E[Xi] = μ. Let Sn = X1 + · · ·+Xn. Then for all t ≥ 0, Pr[Sn ≥ nμ+ t] ≤ e−2t /n and Pr[Sn ≤ nμ− t] ≤ e−2t /n Lemma 2 (Bernstein inequality). Let X1, . . . , Xn be independent zero-mean random variables. If for all 1 ≤ i ≤ n, |Xi| ≤ k...

The conformal symmetry SO(d, 2) of the massless particle in d dimensions, or superconformal symmetry OSp(N |4), SU(2, 2|N), OSp(8|N) of the superparticle in d = 3, 4, 6 dimensions respectively, had been previously understood as the global Lorentz symmetry and supersymmetries of 2T physics in d + 2 dimensions. By utilizing the gauge symmetries of 2T physics, it is shown that the dynamics can be ...

A DCC (disjoint consecutive cycles) linear congruential graph G(F,n) consists of n nodes and is generated by a set of linear functions F with special properties. It was proved that G(F,n) is a 2t-regular graph and has connectivity 2t, where t 1⁄4 jFj and 1 6 t 6 p 1 (n 1⁄4 2 for some integer p). For a multiprocessor system, its diagnosability is critical to measure the performance. In this pape...


 Data transfer between a processor and memory frequently represents bottleneck with respect to improving application-level performance. Computing-in-memory (CiM), where logic arithmetic operations are performed in memory, could significantly reduce both energy consumption computational overheads associated data transfer. This work presents revisited study of FeFET-CiM, CiM architecture ca...

The double Capelli polynomial of total degree 2t is

We study the vanishing of topological properties a quantum spin Hall insulator induced by deformation band structure that interpolates between Dirac and semi-Dirac limits tight-binding model on honeycomb lattice. The above scenario is mimicked in simple model, where there exists differential hopping along one three neighbors (say, ${t}_{1}$) compared with other two $t$). For ${t}_{1}=t$, phase ...